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THIS volume is designed both for those who are com- mencing the study of Logic, and for those who have gone beyond the elements to the higher questions of the science. The portion of the volume which is printed in smaller type, as also the more strictly historical parts, may, as a rule, be omitted in the first reading by those who have not already mastered the main principles of General Logic. J. V. THE LOANING, PEEBLES, October 24, 1885. 11170Q5 CONTENTS. PART I. LOGICAL: PSYCHOLOGY. HISTORICAL NOTICES. THE LAWS OF THOUGHT. CHAP. PAGE I. INTRODUCTORY LOGIC : ITS NATURE ; RELATION TO PSY- CHOLOGY AND METAPHYSICS, .... 1 II. HISTORICAL NOTICES ARISTOTLE HIS VIEW OF LOGIC, . 9 III. HISTORICAL NOTICES LOGIC SINCE ARISTOTLE, . . 14 IV. TRUTH, AND THE RELATIONS THERETO OF LOGIC DEFINI- TION OF LOGIC, ...... 29 % V. OBJECTIONS TO LOGIC AS A FORMAL SCIENCE THE VIEWS OF KANT, HEGEL, AND UEBERWEG, . . .37 VI. LOGIC IS THE SCIENCE OF THOUGHT. SPEECH, THOUGHT, THINGS. THE CATEGORIES OF ARISTOTLE AND KANT, . 48 VII. LOGIC THE SCIENCE OF THOUGHT WHAT THOUGHT IS INTUITION AND THOUGHT, ..... 57 VIII. LOGIC THE SCIENCE OF THOUGHT, AS THOUGHT, OR OF THE FORMS OF THOUGHT WHAT ARE THE FORMS OF THOUGHT, 68 IX. THE CONCEPT HOW FORMED THE GENERAL AND THE ABSTRACT, . . . . . . .77 X. THE CONCEPT ITS CHARACTERISTICS SPECIALLY CON- SIDERED, . . . . . .88 Vlll CONTENTS. XI. THE CONCEPT ITS CHARACTERISTICS SPECIALLY CONSID- ERED COMPREHENSION AND EXTENSION RELATION TO LANGUAGE INTUITIVE AND SYMBOLICAL THINKING, . 100 XII. THE LAWS OF THOUGHT: IDENTITY NON-CONTRADICTION EXCLUDED MIDDLE DETERMINING REASON, . . 112 - XIII. THE LAWS OF THOUGHT HAMILTON AND MILL, . . 138 XIV. THE LAWS OF THOUGHT THE DOCTRINE OF HEGEL STATEMENT AND CRITICISM, . . . .148 PART II. CONCEPTS AND TERMS. XV. CONCEPTS AS NAMED TERMS THEIR PRINCIPAL DISTINC- TIONS, ....... 165 xvi. CONCEPTS: THEIR KINDS, ..... 182 XVII. CONCEPTS : THEIR EVOLUTION DEFINITION AND DIVISION, 207 PART III. JUDGMENT. XVIII. THE NATURE OF JUDGMENT COMPREHENSIVE AND EX- TENSIVE, ...... 220 XIX. JUDGMENTS SIMPLE OR CATEGORICAL AND COMPOSITE THE CATEGORICAL ITS ELEMENTS AND KINDS AFFIR- MATIVE AND NEGATIVE UNIVERSAL, PARTICULAR, SINGULAR, ...... 246 ~ XX. MODALITY IN PROPOSITIONS, .... 261 XXI. COMPOSITE JUDGMENTS HYPOTHETICAL OR CONDITIONAL, DISJUNCTIVE, DILEMMATIC, .... 270 xxn. HEGEL'S THEORY OF JUDGMENT, .... 275 XXIII. THE POSTULATE OF LOGIC THE QUANTIFICATION OF THE PREDICATE NEW PROPOSITIONAL FORMS, . . 288 XXIV. OBJECTIONS TO QUANTIFIED PEOPOSITIONAL FORMS GEN- ERAL CONSEQUENCES OF QUANTIFICATION OF PREDI- CATE, . . . . . . .311 -^,XXV. QUANTIFIED PREDICATE HISTORICAL NOTICES, . . 327 CONTENTS. ix PART IV. INFERENCE. XXVI. INFERENCE IMMEDIATE AND MEDIATE IMMEDIATE (1) TERMINAL EQUIPOLLENCE (2) PROPOSITIONAL EQCI- POLLENCE SUBALTERNATION CONVERSION, . . 337 XXVII. IMMEDIATE INFERENCE OPPOSITION CONTRARY AND CONTRADICTORY, ..... 347 XXVIII. IMMEDIATE INFERENCE OPPOSITION CONTRARY CON- TRADICTORY SUB-CONTRARIES INTEGRATION, . 362 XXIX. MEDIATE INFERENCE REASONING ITS NATURE AND LAWS THE SYLLOGISM ORDER OF ENUNCIATION, . 369 XXX. CATEGORICAL SYLLOGISMS ON ARISTOTELIC PRINCIPLES MOOD AND FIGURE, .... 387 XXXI. CATEGORICAL SYLLOGISMS ON HAMILTON'S PRINCIPLES FIGURED AND UNFIGURED SYLLOGISM ULTRA- TOTAL DISTRIBUTION, ..... 406 XXXII. CATEGORICAL SYLLOGISMS COMPREHENSIVE REASONING THE FIVE SYLLOGISTIC FORMS, . . . 428 XXXIII. COMPLEX AND INCOMPLETE REASONINGS DEDUCTIVE CHAIN-REASONING : EPICHEIREMA SORITES ORDI- NARY ENTHYMEME, . . . . .443 XXXIV. INDUCTION FORMAL AND MATERIAL ANALOGY, . 449 XXXV. THE METHODS OF INDUCTION, .... 469 XXXVI. QUA SI-SYLLOGISMS EXAMPLE ARISTOTELIC ENTHYMEME, 484 XXXVII. HYPOTHETICAL, DISJUNCTIVE, HYPOTHETICO-DISJUNCTIVE, FORMS OF REASONING, .... 492 XXXVIII. FALLACIES FORMAL AND MATERIAL. (1) FORMAL FAL- LACIES, . . . . . 512 XXXIX. FALLACIES (2) MATERIAL FALLACIES, . . . 534 INSTITUTES OF LOGIC. PAET I. LOGICAL PSYCHOLOGY, HISTORICAL NOTICES, THE LAWS OF THOUGHT. CHAPTER f. ' INTRODUCTORY LOGIC : ITS NATURE J RELATION TO PSYCHOLOGY AND METAPHYSICS. 1. THE central conception of Intellectual Philosophy is that implied in the term Truth. This, with the cognate term Certainty, indicates the aim of intellectual effort as animated by the natural desire of knowing. Knowing has various ends or degrees. We may seek simply to know ordinary matters of fact, to acquire science, to go back on the first principles and laws of knowledge itself. We may rest in the individual fact, we may generalise and classify, we may speculate on what is ultimate in knowledge. In each case, however, what we seek is Truth and Certainty. 2. Speaking generally, Truth is the harmony or conformity between fact or reality and our knowledge of it. Fact may mean either an individual thing, quality, object, or a class or law, generalised or necessary, of matter or mind. Con- formity always implies a certain plurality or dualism, for of 2 INSTITUTES OF LOGIC. the same to the same there is no conformity, only identity. Certainty is the consciousness of truth, conviction, as resting on evidence, immediate or mediate. 3. In ordinary knowledge, in history, in science, we aim at truths rather than Truth. Each fact, event, each law of nature, adequately known is in the mind a truth ; and a body of these laws, co-ordinated, classified, systematised, is a science in a more or less perfect form. We may ask the question, What are the truths of history or of science, and seek to find them. This would be historical or scientific knowledge. But we may also ask the question, What is Truth? truth itself- the essence or inner being of it, so to speak. What have truths in common that we call them truths ? Can we get the mark, criterion, test of truth itself, or of this or that truth ? How far can we go in assuring ourselves that what we believe to be true is true? And what is the meaning, or what are the meanings, of saying that there is truth, or that a given proposition is true? This is the question, or set of questions, with which Intellectual Philosophy is concerned. It occupies itself with the nature, conditions, criteria of truth. 4. If we take this question of what is truth, or true know- ledge, in its widest generality, it is obvious that we must raise the questions as to the ultimate ground and nature of knowledge and certainty. Supposing that we know at all, or believe that we know, as a matter of fact, this knowledge must have a ground or beginning, for us at least. " If it is not possible," says Aristotle, " to know first things, neither can we know, either absolutely or properly, things which result from these, but by hypothesis, if these exist. All science is not demonstrative, but the science of the immediate is inde- monstrable. . . . Some time or other we must stop at immedi- ate (propositions)." l And we thus are confronted with the question as to the first principle or principles of knowledge. And as true knowledge is real knowledge, or knowledge of what is, we are met by the con-elative question as to what we know of the real, what reality is, and what are its kinds. A science of knowledge, therefore, in its widest scope would be a science of first principles, and of being as it stands in know- ledge. This would lead to the discussion of the difference between phenomenal reality or knowledge, so called, and 1 Aristotle, An. Post., 1. i. c. 3, 4. PSYCHOLOGY AND LOGIC. 3 substantial reality, what is the nature and what the limits, if any, of our experience. - 5. These questions touching the nature of reality, the nature of the various objects of our knowledge, have been properly assigned to that branch of Philosophy known as Metaphysics or Ontology. We may confine our inquiries into the laws and conditions of our knowledge of the contents of experience, without, for example, considering whether these contents have a simply subjective reality, are mere conscious impressions, or, as known, are something more and other than this. We may further carry on this inquiry without considering the question as to the nature of ultimate or primary reality. It is sufficient for this end that we know, and know what we call objects, whatever these be in their essence or origin. That we are conscious, that we have experience at all, is a sufficient basis for certain questions regarding the conditions and possibility of this experience. 6. The discussion even of these ultimate questions may presuppose that there are certain laws or features of know- ledge, universal and essential in knowledge, and thus there may be a science which precedes even such discussion, as regulating human intelligence and thought itself, or the very conception of an object of knowledge itself. And if there be such a science, it will have a place of its own, and be so far independent of and above all other sciences. It would profess to lay down the conditions of the knowable, and especially of the thinkable, that is, to state certain laws or principles without which there is no object of knowledge or thought for us at all. As such, it will be found to embrace certain conditions of knowledge and thought, apart from the fulfilment of which the ideal existence of an object, or an object in knowledge, is not possible. This impossibility may arise from two sides : first, from the side of knowledge. Here there are certain conditions to be fulfilled ere an object can be an object of knowledge or thought at all. These are the conditions of Identity and Non-contradiction, and they are inseparable from the nature of the act of knowing. Certain conditions lie on the side of the object as existing, and these are given in the object or with the object. They form the essential elements or relations of the object. These are the relations of Subject and Object, Qualitative, as Substance 4 INSTITUTES OF LOGIC. and Quality ; Quantitative, as Time, Space, &c. These are properly metaphysical relations. They are part of the matter of knowledge, the given, yet essential, relations of things. 7. The questions regarding the metaphysical laws of knowledge are, first, as to their nature, number, genesis ; secondly, as to their objective validity, or agreement with the nature of things. The first question is obviously psycho- logical. It is a question of mental genesis. The second question may be regarded as coming under Logic, in as far as this science is led to deal with Evidence, immediate or mediate. This would form a special section of Logic rather than be the adequate object of the science itself. But the true relation of the metaphysical laws to Logic is simply that of being part of the matter of thought, in this case necessary matter to be legislated for in common with other matter. Logic can only, consistently with its specific scientific char- acter, treat such concepts as Cause, Substance, Unity, Iden- tity, as Concepts. 8. There may further be a question as to whether the logical laws are independent, or are deducible from certain corresponding metaphysical laws. But this is properly a psychological question, pertaining, it may be, to logical science. It concerns Logic only indirectly, especially if it be admitted that the logical laws are necessary and universal, for the results of those laws would be the same whether their necessity be primitive or derived from other necessary laws. Meanwhile, it is sufficient to say that it will be found that the logical laws are not derivable from any source higher than themselves, but are in fact presupposed in every known concept or law which can be in our consciousness Le,, in every process of analysis or reasoning, which might be ad- duced to show their derivation. 9. Logic Proper, Pure or Formal Logic, is the science of the conditions of the knowable and thinkable, in so far as these depend on the inherent constitution of the acts of knowing and thinking; and these acts are regulated by strict laws, called formal, inasmuch as their violation destroys the form or ideal being of the act and object of thought, as known or thought. Formal Logic is the science of the laws of possible, consistent, and necessarily connected thinking, or of harmony and of necessary implication in thinking. PSYCHOLOGY AND LOGIC. 5 10. But knowledge, true knowledge, of experience has what may be called a contingent side. Something is given, presented ; and this something is very various, and not origin- ally deducible or even predictable. There is the matter of experience, of knowledge and thought. That something be given to the knowing faculty, to sense, or intuition, is an absolute condition of knowledge. Thought without intuition is vain, empty. Here, too, we touch psychology, the analysis of the intuition and its matter. But all that we need mean- while to carry away is, that there is necessarily a given to help to constitute knowledge. And this is variable, passing, contingent. How much of it is subjective, how much ob- jective, is a separate question. Metaphysics considers this. As this given is essential to knowledge, it is essential to true knowledge. And we have to inquire as to how we are to secure the truth of our knowledge of the matter presented, or of the intuition or presentation. How is knowledge accu- rately to represent what is presented to us in the course of experience ? How are we to get not only at the individual or isolated fact, but at the law or laws which individual facts embody? How are we to reach the classes, laws, causes, which we suppose to be in experience ? How, in a word,, are we to acquire the truths of science ? There is a science which has for its aim to investigate the rules or laws of the processes by which we observe, generalise, and infer through induction and analogy, and not less through deduction. This is properly enough a part of Logic, in the wide sense of the term. It is known narrowly as Inductive Logic. It makes a part of what Hamilton calls Modified or Mixed Logic. By some it is called Applied Logic ; but this should not be understood as a special Logic, which is Logic in general applied in this or that determinate matter or science. For the rules of Applied Logic are generally, if not universally, applicable to the sciences, and this Logic involves also the universal use or application of the canons of Pure Logic. 11. This problem of the conditions of truth thus presents different aspects ; and, according as we regard one or other, we have a different speculative science, different, yet converg- ing in one great organic unity. Thus Psychology in dealing with the Intelligence looks at the act of knowing as it exists as a fact, or is spontaneously manifested in the consciousness, 6 INSTITUTES OF LOGIC. at its nature, kinds, degrees. It cannot be denied that we know, or believe we know. Even in such a denial there would be an assertion of knowledge. Knowing is a fact or phenomenon of experience. It is the inner fact of our being ; it is our being, so far. We are, as we know. Logic, too, looks at this act as fact. So far, it is identical with Psy- chology. But Logic looks at the fact of knowing with a view to ascertain its conditions, laws, if it have any, how it is car- ried on, and what it is when it is finished. And Logic pro- fesses to find that knowing is subject to certain conditions, and to show that these conditions are of two different kinds at least ; and, these being ascertained, to exhibit them in a sci- entific way, to formulate them, make a body of knowledge of them ; and, now indifferent to the actual fact whether know- ing is going on or not in this or that matter or science, to show ideally how it must go on, if it is to be successful in its aim, or even to be at all. While Psychology is thus the science of the facts of Intelligence, or of knowing, and also of its actual laws as matter of experience, a science of facts or phenomena of our conscious intelligence, as realities, Logic takes from it the laws which it reveals, the laws of the acquisition, the ordering, classification, and concatenation of knowledge, and represents these as ideal abstractions universally applicable in the processes of intelligence. Logic is thus wholly de- pendent on Psychology for its principles. It is Psychology carried up to its highest abstraction. And the moment it loses hold of Psychology, Logic becomes arbitrary and un- reliable, no longer applicable to the facts of experience. The nominal difference between the two sciences is simply that Psychology regards rather knowing in process, while Logic regards knowing as completed, as a product, and the laws which it has realised or fulfilled in becoming what it is, or in reaching what it attains. 12. Psychology thus, to a certain extent, and the method of Psychology, observation of the actual procedure of the understanding, are necessary to the knowledge of the nature and laws of the understanding. The understanding is simply the conscious mind acting and being conscious of its action in a definite manner, and about a definite object. In tlras acting it realises the law of its action ; it thinks i.e. } con- ceives, judges, or reasons coherently. Analysis and reflection PSYCHOLOGY AJTD LOGIC. 7 bring out with a fuller consciousness the law or laws which it naturally observes, and also reveal the necessity and uni- versality of the law. In no sense whatever does this analysis create the law ; in no sense whatever does it. impose the law on the understanding. The law is revealed in a definite instance, and it is shown by reflection to be supreme in all instances. (a) Kant objects to the introduction of psychological principles into Logic, or drawing the laws of thought from psychological observation. The reason he gives is, that thus we should get only contingent, not necessary laws ; and the question is not as to how we think, but as to how we ought to think. The necessary use of the understanding is discovered without any psychology. To this it is sufficient to say that observation, followed by generalisation, would give us only con- tingent principles ; but observation of the actual procedure of the understanding, followed by reflection, or an experimental testing of the procedure, may and does give us the necessary element in the pro- cess. We can learn how we ought to think only through an analysis of how we actually think, when we think consistently, i.e., think at all. Indeed, Kant himself subsequently admits all that need be con- tended for here, when he says "the necessary laws of thought can and ought to be conceived a priori, independently of the natural and con- crete exercise of the understanding and the reason, although they can at first be found only by observation of this exercise." On this point, as elsewhere, especially in the Critique, Kant shows that he had no clear idea of the scope of Psychology, of its method, and only slight acquaintance with the details of the science. He further excludes Psychology from Logic on the ground that Logic seeks to know not the contingent but the necessary, not how the understanding thinks, and has thought, but how it ought to think, the accord of the understanding with itself. This assumes that there can be no necessary exercise of the understanding in a given instance, for example, no absolutely necessary implication in a given reasoning performed by the understanding, and consciously known to be necessary ; whereas, this necessary relation is given and consciously realised in a single instance of valid reasoning. Kant thus confuses the particular or singular with the contingent. It assumes, further, that the understanding may think in experi- ence in a way different from that in which it must think, if it thinks at all. This is not so. There is only one way of thinking by the understanding, that is, the legitimate way. Any other is a mere illusion, not a reality of thought at all. And there is no reason why the understanding may not naturally perform its process of thinking rightly rather than wrongly. (6) One of the current Hegelian assertions, which is regarded as new and important, is that "the knowledge of what knows cannot precede the knowledge of reality." No one, -I should think, ever alleged, or at least required to allege, the converse of this. The 8 INSTITUTES OF LOGIC, knowledge of what knows is and can only be found in the knowledge of reality. We perceive, judge, and reason ; we get at, or think we get at, reality in our intuitions and judgments. But the philosopher says we get at more, we get at a knowledge of what knows, if only we will think of what a knowledge of reality is and means. For therein are manifested the character and law of the knower as well. And if we are ever to know the nature of the knower or knowing subject, we are to do it by a reflection on the spontaneous acts of knowledge, which are conversant directly with the reality, and reflexly show the reality in consciousness. But for this secondary or reflective knowledge, we should be wholly unable to estimate the value and reach of our know- ing, and only through this could we correct, if need be, our spontaneous or intuitive knowledge. CHAPTEK II. HISTORICAL NOTICES ARISTOTLE HIS VIEW OF LOGIC. 13. The ultimate aim of Aristotle in his logical treatises, especially those on the more advanced parts of the science, the Prior and Posterior Analytics, is to show the nature and laws of true Demonstration (obroSei^ts). In the opening of the Prior Analytics (1. i. c. 1) he tells us that the treatise con- cerns demonstration, and is undertaken for the sake of demon- strative science, and that consequently he has to define proposition, term, and syllogism. This affords a certain ground for a division of the parts of Logic, and the arrange- ment of the Aristotelic treatises. (1) The theory of the elements of the proposition, that is, the term, given in the Categories. (2) That of the proposition in the treatise On Interpretation. (3) That of the syllogism in the Prior Ana- lytics. (4) That of demonstration in the Posterior Analytics. These may be regarded as exhausting the essential parts of Logic, and as constituting Theoretical or Pure/ Logic. The Topics and the Sophistical Elenchi may be taken as in Applied Logic. In the Analytics and in the Topics, Aristotle treats of definition and demonstration. But in the former he seeks to give the theory of true definition, and how it is to be con- structed ; in the latter, what sort of definition can be im- pugned. In the Analytics, demonstration is the best, which is according to the true principles of its theory ; in the Topics, that demonstration is to be preferred which is the more difficult to assail. There is the difference in fact between the scientific theory of truth, and the dialectical interest of the appearance of truth and intellectual victory. 1 i Cf. Waitz, An. Post., ii. 297. 10 INSTITUTES OF LOGIC. 14. Aristotle tells us that he is to treat of syllogism pre- viously to demonstration, since syllogism is more universal, demonstration being a certain kind of syllogism. The differentia of demonstration is, that it is a syllogism from necessary matter. " If there be a demonstration that a thing cannot subsist otherwise, the (demonstrative) syllogism must be from necessary (propositions). For it is possible, without demonstration, to syllogise from what are true, but we cannot do so from things necessary except by demonstration, for this is now (the essence) of demonstration. . . . It is possible to syllogise the necessary from things not necessary, just as we may the true from things not true ; still when the medium is from necessity, the conclusion is also of necessity, as the true results from the true always." 1 In the Posterior Analytics he expressly expounds the theory of demonstration, with a view to show the use of syllogistic in the constitution of true and certain science, the science of necessary principles and its consequences, includ- ing the question of their guarantee. 'ETTIO-T^JU.^ aTroSaKTi*^ has thus been translated the theory of knowledge, and re- garded as part of Philosophy. On these grounds, it is held by St Hilaire and others that Aristotle viewed demonstration as the proper object of the books of the Organon, and of the science afterwards named Logic? 15. The principles of science (ap^aC), according to Aristotle, are KOIVO.I and tStai : under the former are, d^wo/Aara, the ori- ginal premises from which demonstration proceeds ; under the latter, assumptions, 0eVeis, that is, definitions, 6pr/Moi, and hypotheses (wro0rs), assumptions of the existence of the subjects. 3 16. The difference between a demonstrative and a dialec- tical proposition is, that the former is assumed by the demon- strator, the latter is accepted from another person. So far, however, as syllogising from either proposition is concerned, this difference, as Aristotle admits, is of no moment. All that the syllogism supposes is, that something is or is not present with something. We do not need to inquire why one thing is predicated of another ; all that we require is that it be predicated. A syllogistic proposition (irporao-is) is an 1 Post. An.,\. 6. 2 Cf. St Hilaire, Organon, art. Logique, Dictionnaire de S. P. 3 Cf. An. Post., i. 2; Mansel, Prol. Log., App. HISTORICAL NOTICES. 11 affirmation or negation ; it is demonstrative (aTroSeucTiK??) if it is true, and assumed on primitive data. By the phrase ai e apX^s V7ro0eo-is is meant axioms (d^tcu/x-ara) whose truth is in- demonstrable and self-evident. The demonstrative proposi- tion is thus of necessary matter. Thus X must be Y; but, so far as the syllogistic act is concerned, this is not affected by the necessity, Le, the modality, of the proposition. The consequence in syllogism is as necessary whether the major proposition be apodeictic, that is, of necessary matter or relation between the terms ; or merely assertory, that is, of a simple categorical relation, X is Y. The difference is purely extra-logical; the conclusion, as a proposition in the case of necessary matter, is a necessary proposition ; it must be true, or, as Aristotle puts it better, it must be thought in one form, and as excluding its opposite. But this is a pecu- liarity attaching to the matter of the proposition, not to the sequence of it from the premises, or its form. 17. It would be manifestly impossible to have a science of reasoning or inference, if we were to ask the title of every proposition to be regarded as necessary or as contingent, or as more than assertory. We should require in each case to go into Physical Science and Psychology to determine this point, and the inquiry would be endless. Besides, if the consequence of the inference depended on the modality of the proposition, there could be no one science of inference : con- clusions would be necessary or probable according to the matter. Probability would have its ever-varying degrees, and a science of pure inference would be impossible. The modality of necessity and contingency has no bearing on the nature of the sequence, or on the conclusion as a con- clusion. It is, therefore, wholly extra-logical. The quantity and the quality of a proposition affect, not the sequence, but the quantity and quality of the conclusion, as a conclusion from* given premises ; and hence they are to be regarded in the data as modifying the conclusion. Thus modality, as quantity and quality, if the term be stretched so far, may be regarded as of logical import ; but no other kind of modality is of any relevancy. 1 18. Further, if it be true, as is alleged, that the canon of demonstration is the principle that "two things compared and found equal to a third, are equal to one another," 2 i Cf. Mansel, Prol. Log., Appendix, Note H. * Post. An., i. 10. 12 INSTITUTES OF LOGIC. it is clear that demonstration has no law independent of ordinary syllogistic ; for this canon depends almost imme- diately on the law of non-contradiction. This, as stated by Aristotle, is " It is impossible that the same attribute should be and not be in the same subject, at the same instant and under the same relation." 1 19. In truth, demonstration, according to Aristotle, does not need to assume the common axiom in all its universality, but only in so far as is required by the genus about which the demonstration is concerned. The geometrician in demon- strating assumes, not that every whole is greater than the sum of its parts, but that every whole in the genus magni- tude is ; and the arithmetician does the same in respect of numbers. Demonstration is, in fact, not the whole of Logic, or the theory of Pure Logic, but an Applied Logic, logic applied to necessary matter. 20. It is held that while physical science is observational and inductive, and therefore of contingent value, demonstration may intervene and give absolute certainty. Thus a body is known to fall to the ground. This is a fact of observation and induction simply. But the fact may be connected with the laws of motion, and thus demonstrated. Or the planetary move- ments may be observed and described, and then led back to and predicted from the law of universal gravity. But in neither of those cases is there demonstration resulting in absolute certainty. There is simply the reference of a fact or law to a higher or wider law than itself. But this higher law is not a truth of absolute necessity, any more than the narrower law which is referred to it. It is a case simply of deduction ; and the certainty may be complete, given the higher law. But it is, after all, only a hypothetical necessity which subsists, be- cause the universal, though to thought contingent, law, exists. (a) Organon (Spyavov) generally, and with Aristotle, means simply instrument, or that which subserves the accomplishment of some end. The soul is compared to the hand, which is the ftpyavav opydvuv. (De Anima, ii. 8.) To discover the for and against of each question is a use- ful instrument for science and reflection. (Topica, viii. 14. Of. i. 13.) The term Organon, as subsequently applied to the six logical treatises of Aristotle, was wholly unrecognised by their author. As a general designation, it was equally unknown to the Greek interpreters, and, down to the time of Psellus and Blemmides, the name for the treatises 1 Met., iii. c. 3. HISTORICAL NOTICES. 13 of Aristotle afterwards comprised in the Organon was rj \oytid], or 77 \oyiK^i tirurT-hiJ.r], or irpa.yfna.Tfta. Diogenes Laertius had said that Aristotle made Logic Spyavov irpocrrjKptftufj.fi'oi'. It was, however, through the Greek interpreters that the term Organon came ultimately to be so generally applied. The doctrine of the Analytics, called by them TO, cbroSeiKTi/ca, was named by Alexander of Aphrodisias the Spyavov ; and the same designation was applied by Philoponus to demonstration itself. These were the instruments for reaching true and certain knowledge, necessary truth. The term thus at first applied to the Analytics came ultimately to designate the whole logical treatises of Aristotle. In the fifth century, Ammonius and Simplicius give, either originally or from tradition, going back to Andronicus of Rhodes, or Adrastus of Aphrodisias, the logical works, as a distinct class, as \oynta 1j opyaviKd. David the Armenian emphasised this view. With him the Aristotelic works are divided into theoretical and practical, with the supplementary branch of the organic. The syllogism is a fan for winnowing the true from the false, the good from the bad. From the commencement of the sixth century certainly logic in the Peripatetic school was called rb opyaviKbv (nfpos) of the Aristotelic philosophy. Further, a passage of Ammonius almost suggested the modern application to the logical treatises of the term organon. He says, speaking of the Introduction of Porphyry, that this work is comprised in the logical organon virb rb Xoyiitbv upyavov avdyfrai. It was not, however, until the fifteenth century that the term Organon came to be habitually used as the common name for the six logical treatises of Aristotle. This question of the name is connected with the controversy as to the sphere of logic, whether it is a part simply of philosophy, or the instrument. The Stoics held the first opinion; the Peripatetics the second; the dis- ciples of the Academy held logic to be at once science and instru- ment. It was no doubt with the Greek commentators that the exaggerated view of the Aristotelic logic as an instrument or method for securing real truth originated. But it was only towards the sixteenth century that some of the Peripatetics, in face of the energetic protest of Vives, maintained the extreme view of logic as the method of real truth, a view which was not only erroneous, but incapable of being put into practice. Hence arose the misconceptions of Bacon and Locke regarding the real Aristotle, which were excusable only on the part of the class of non-reading philosophers. No such view can fairly be attributed to Aristotle himself, notwithstanding what he says about demonstration. "It is not," says St Hilaire, "an organon which Aristotle professes to give to philosophy ; he has only intended to treat in his logical works, in the fdOotios rS>v \6yuv, of the instrument of all philosophy, of the vovs, which, as he himself says, is the organon of the soul, 'to the body the hand, to the soul the intellect; for the intellect is of those things naturally in us as the organon.' " (Proble- mata, 1. 30 e , quest, v.) Taken in this sense, the term organon is per- fectly correct. Logic is really occupied with the instrument of all knowledge, since it is occupied with the science of thought and the form under which thought is produced viz., reasoning. (St Hilaire, De la Logique d'Aristote, t. i. Part I. c. 2. Cf. Waitz, An. Post., i 1.) 14 CHAPTEE III. HISTORICAL NOTICES LOGIC SINCE ARISTOTLE. 21. Since Aristotle, logical investigation has been con- fined to two principal lines. The one proceeds on the con- ception and principles of the science as laid down by its founder, in what may be regarded as their formal aspect, and seeks to add to and modify certain of the doctrines, to in- troduce refinements and subtleties. The other has been the questioning of the exaggerated pretensions made by some regarding the science as a method of investigating and reaching real truth, truth of fact or science, and the legiti- mate attempt to found a method of truth and science which, rising beyond the merely formal relations of thought, strives to add to its content or matter, to acquire, build up, arrange, and classify science. The formal view of knowledge is so exact and complete in itself, that men are led to rest in its intellectual harmonies and adaptations, its refinements and subtleties. But the real needs of knowledge and of life have ever and again led to a protest against the mere intellectual sphere as narrow and insufficient, and compelled questions as to the best rules and methods for conducting thought through the broad field of experience, and guiding to a knowledge of fact or reality as we may find it. 22. This branch of Logic may be said to have two aims, the laws of Discovery and the conditions of Proof. In Bacon, Herschel, and Whewell, the former aim is the pre- dominant. In Mill, and in later writers on his lines, the second aim is the main one, his view of Logic being, that it is the science of the intellectual operations which serve for the estimate of evidence, at once of the general procedure HISTORICAL NOTICES. 15 which goes from the known to the unknown, and of the operations auxiliary to this fundamental operation. 1 23. This inquiry in either form is in no way against the doctrine and spirit of Aristotle. The method of real science is the complement, not the antagonist, of the Aristotelic logic. Aristotle has even recognised, and, in a way, analysed in- ductive method. Nor is he opposed to the method which would analyse the speculative side of knowledge. He runs Demonstration back to ultimate principles, first truths, them- selves indemonstrable, and thus connects logic with the First Philosophy, or theory of Ultimate Knowledge. " All demon- strative science is related to three things which are admitted without demonstration, and these are the genus, the essen- tial properties of which science considers ; and common things called axioms, from which as primaries one demon- strates ; and thirdly, the modifications of the genus, the signi- fication of each of which the demonstrator assumes." (Post. An., i. 10, et passim.} It is on this side that the Aristotelic logic touches the Method of Descartes, in not being satisfied until it can connect the theory of science with the first principles of knowledge. In fact, the need felt by Plato and reflected in his Dialectic is not without an inspiring power on the whole theory and development of human thinking, on the formal as well as the material side. (a) Aristotle distinguishes Induction from Syllogism. (Top. 12 ; An. Pr. , ii. 23. ) There is a great difference, he tells us, between knowing that a thing is, and why it is. We do not attain to the knowledge of the ichy when the syllogism is not formed of immediate terms, for then we have not remounted to the primary, which is cause. The middle term here is not the primary and immediate cause. So in the case of reciprocal terms that is, where the effect is of the same extent as the cause, and the one can be taken for the other, the term which is not the cause may be assumed as better known, and the why is not demonstrated. Thus it is demonstrated that the planets are near the earth, because they do not twinkle. Let C be the planets, B not twinkling, A being near. We may say B of C, for the planets do not twinkle. But we say also A of B, for when a body does not twinkle, it is near. We may suppose further, that this last proposition is fur- nished by induction or sensible experience (SI tira-yuyrjs 1j 5 alcrO-ncrftas) ; we conclude necessarily that A belongs to C, and in this way it has been demonstrated that the planets are near. But under this form the syllogism does not say why the thing is, it only says that it is ; for 1 Logic, Introd., 7. 16 INSTITUTES OF LOGIC. the planets are not near the earth because they do not twinkle, but, on the contrary, they do not twinkle because they are near. On the other hand, we may still demonstrate inversely the effect by the cause, and then the demonstration will give the why of the thing. Thus, whatever is near (B) does not twinkle (A) : the planets (C) are near (B), therefore the planets (C) do not twinkle (A). (An. Post., i. 13.) 24. The immediate successors of Aristotle seem to have restricted themselves wholly to the formal side of Logic, modifying details, and developing the theory of Hypothetical Eeasoning. This was done chiefly by Theophrastus (taught from 322 to 286 B.C.) and Eudemus. The Stoics cultivated logic, though the doctrines of the school are only preserved in fragments. Chrysippus (280-208 B.C.) followed in the line of Theophrastus and Eudemus ; but there was an attempt in the Stoical school to widen the scope of the science, so as to make it an instrument of real truth. Epicurus (d. 270 B.C.) regarded it as a canonic, and found the criterion of truth in sensation. With the quickening of speculation in Alexandria, attention was fixed on the logical writings of Aristotle. They gave the only form of methodical thinking known, and thus acquired great influence on the philosophical thought of the time. From the latter part of the second century to the beginning of the third, Alexander of Aphrodisias, so called from a city of Caria, his birthplace, was the greatest power in sustaining and spreading the influence of the logical treatises of Aristotle. His commentaries and expositions are admira- ble, still unsurpassed; and he was a man, besides, of orig- inal faculty, as shown especially in his treatises on the Soul and on the Fatalism of the Stoics. In the Schools he was the Commentator, as Aristotle was the Philosopher. Alexan- der seems to have taught both at Athens and Alexandria. Galen, in the second century (131-200 A.D.) was not less famous as an expositor of Aristotle than as a physician. His logical writings have, however, perished, with the slight exception of the -jrepl rwv Kara. rr]V Aeiv ro<^to-/x,aTO)V. The Introduction to Dialectic, discovered at Mount Athos, and published in Greek, 1844, is probably spurious. Plotinus (205-270 A.D.) assailed the Categories ; and Porphyry (233- 304 A.D.), his disciple, expounded them in his Introduction, so valuable as to have since been uniformly prefixed to the Organon. Themistius, who taught at Constantinople in HISTORICAL NOTICES. 17 355, paraphrased the logical treatises. Ammonius Hermeias (after 485 A.D.), Simplicius, who was banished from the School by the decree of Justinian (529), have left valuable expositions of Aristotle. David the Armenian and John Philoponus (about 533) in Egypt, are to be added to the list of commentators. 25. The contributions of the Latins to Logic are not of much value. After the taking of Athens by Sylla (84 B.C.), the writings of Aristotle were carried to Home. There they were arranged and edited by Andronicus of Khodes. We have notices of the doctrines in Cicero, and subsequently a series of abbreviators, Appuleius (160 A.D.), the Pseudo- Augustine, and Marcianus Capella (c. 474 A.D.) Victorinus (c. 350) translated the Eio-aywyr? of Porphyry. Boethius (470-524) was the only Koman logician of consequence. He translated a great part of the Organon, and contributed commentaries and discussions of his own. The chief import- ance of his writings arises from the circumstance that they were for long, in the absence of a knowledge of Greek, the means of making Aristotle known in the West. 26. Even in the ages following the end of the Western Empire (476 A.D.) and during the irruption of the barbarians into Europe, the logical writings of Aristotle were never wholly without study. We have Isidore of Seville (d. 636 A.D.), Bede (673-735), John of Damascus (d. 754), Alcum (736-804). The last named introduced the study of Logic into the Court of Charlemagne, and this and his other teaching determined the line of thinking in Europe down to the time of Abelard (1079-1142). In that period we have among the Greeks the name of Michael Psellus (1020-1100 or later) ; and following him Italus, Ephesius, Eustratius, and Leo Magentinus. 27. With Abelard, the logic of Aristotle acquired a new and powerful place in philosophy and theology. Though but imperfectly acquainted even with the logical treatises of Aris- totle, and ignorant of Greek, such was the force of his charac- ter, that he sought on the one hand to widen logic so as to be a method of real truth, and on the other to apply it to theology as the regulator and even judge of its coherence and content. His teaching at Paris was the most powerful factor in the European thought of the age. It marked the commencement of the spirit of modern inquiry, the piercing through the 18 INSTITUTES OF LOGIC. forms of words and facing the reality of things. The ques- tions of Nominalism and Kealism are in another form chiefly the modern metaphysical questions. John of Salisbury (d. 1180), the disciple of Abelard, defended logic in his Meta- logicos, and showed a knowledge of the whole of the logical treatises of Aristotle. Up to this period only certain of those treatises were known in Western Europe. Hence we have the designations of the Old and the New Logics. The result of the most recent investigations on this point seems to be, that, until nearly the middle of the twelfth century, the only logical writings of the ancients known in the middle ages were the Categories and Interpretation of Aristotle, as translated by Boethius ; Porphyry's Isagoge, in the translation and com- mentary of Victorinus and Boethius, the works of Marcianus Capella, the Principia Dialectics of Augustine, the Pseudo- Augustine on the Ten Categories, and Cassiodorus, and cer- tain of the writings of Boethius (cf. Ueberweg, Logic, 21 Hist, of Phil.} The Categories && Interpretation, witli the Isagoge of 1'orphyry, iunm-d the Log tea Vctus. The Analytics, Topics, and Sophistical Elenchi were as yet unknown, and when intro- duced about the middle of the twelfth century, constituted the Logica Nova. 1 These were known only in translations. It was not until after the taking of Constantinople by the Cru- * saders, in 1204, that the Greek texts were obtained. The Logica Nova must not, however, be confounded with the Logica ^ Moderna or Tractatus Modernorum. This arose from the Sum- mulce Logicales of Petrus Hispanus, who died as Pope John XXI. jn 1277. The Summulce consist of seven Tractatus. Tlie seventh is entitled De Terminorum Proprietatibus, called also Parva Logicalia, and is mainly grammatical, developing, among other things, the doctrine of Suppositio. This was the specific doctrine of the Moderns and of Modern Logic. In this work of Hispanus appear for the first time the well-known mnemonic lines Barbara, Celarent, &c. That they are original to Hispanus, or at least were first given in the Summulce, there can be now no doubt. For it is now certain that the Synopsis Organi attributed by Ehinger to Michael Psellus (the younger) was not by him at all, but was simply a translation into Greek of the work of Hispanus (see Hamilton, Discussions, i See Questiones Magistri Johannis Versoris in Totam Novain Logicam. Cologne, 1497. HISTORICAL NOTICES. 19 p. 128 and 671 ; cf. Ueberweg, Logic, 22; Hist, of Philosophy, i. p. 404 ; Saint Hilaire, De La Logique d'Aristote, ii. p. 160, on the other side). The rough version of the mnemonic lines, given on the margin of the Epitome Logicce of Blemmides, is obviously a copy of the Latin of Hispanus. 28. It was not until towards the end of the twelfth century that the other works of Aristotle were introduced into Western Europe. This was due to intercourse with the Arabians, mainly through the Crusades. The Arabians had been for centuries diligent students of Aristotle. Alkendi (fl. 800), Alfarabi (d. 954), Avicenna (980-1036), Alghazel (1072-1109), Averroes (d. 1206 or 1217), were all distin- guished names in this line. Averroes translated and com- mented on the whole logic of Aristotle, and divided with Alexander Aphrodisiensis the title of the Commentator. In the reign and by order of the Caliph Abdallah alMamon, about 819 A.D., the works of Aristotle were for the first time translated into Syriac by Joannah Mesnach, Christian of the sect of the Nestorians. They were translated a second time into the same language by Hona'in and his son Isaac, who also professed the doctrines of the Nestorians, and lived at Bagdad in the beginning of the tenth century. After them came the Arabian translators and commentators, a school of Dialectic, frequently mentioned by Moses Maimonides and the other Spanish rabbis under the name of Medabrim, speakers, dialec- ticians. The matter of their teaching was the Organon, with the Introduction of Porphyry. The Jews translated into Hebrew the lessons of their Arabian masters. Maimonides wrote an abridgment of the Organon in Hebrew, very precise and clear, under the title of Vocabulary of Logic. This was translated in 1527 into Latin by Sebastian Munster. Another Hebrew translation of the Organon is Hebraica editio universal rei logiccR Aristotelis ex compendiis Averrois, Rivce de Trento, anno MDLX. (Cf. Franck, Logique, p. 248, and Jourdain, Sur Aristote, c. iii.) The Arabians brought their learning, with the Aristotelic works and commentaries, into Spain ; and their doctrine nourished in the Universities of Cordova, Seville, and Grenada. Amid the differences of religious belief, there was thus formed between Mohammedan and Christian the bond of a common philosophic culture and faith. 20 INSTITUTES OF LOGIC. 29. It was from this importation into Western Europe of the Aristotelic books that Scholasticism took its rise and im- pulse ; and henceforward, with the temporary check of the burning of the non-logical works of Aristotle in Paris in 1210, in accordance with the demand of the Papal Envoy, Aristotle reigned supreme in Europe, as logician and philosopher, the Master of Human Thought, his works " The Evangel of In- telligence," until the gradual decay of his empire through the Renaissance, the foundation of Modern Method by Bacon and Descartes, and the Reformation. Albertus Magnus (1193 or 1205-1280), in full possession of the Aristotelic works, and with a thorough mastery of them, as shown in his commentaries, was the man who, by his writings and teachings in the University of Paris, then the centre of intellectual influence in Europe, laid the foundations of the Aristotelic,.,empire ; which, lasting for four centuries, moulded the European mind and languages, united the nations of Europe in commoi^inteneOTOalconceptions, formed, in fact, modern intelligence on its side of clearness, distinct- ness, and connectedness. For true it is that the moulds even of that science and of that thought which repudiate Aristotle are his creation. " The dialectic," says St Hilaire, " which presided over the infancy of the European sciences, has permeated our entire civilisation. The logic of Aristotle, though dead in the schools, lives in the general thought which it has so greatly contributed to form and to instruct." 30. The scholastic study of logic, and, in most cases, the application of logic to theology, were carried on through Thomas Aquinas (1224-1274), Nicephorus Blemmides (fl. 1254), Duns Scotus (1275-1308), Walter Burleigh (1275- 1337), Petrus Hispanus (Pope John XXL, d. 1277), Georgius Pachymeres (d. about 1310), William of Occam (d. 1343 or 1347), John Buridanus (alive in 1358), Cardinal Bessarion (1395-1472), George of Trebisonde (1395-1486), Laurentius Valla (1408-1457), Rodolf Agricola (1443-1485). In the critical period of the Renaissance we have Ludovicus Vives (1492-1540), Peter Ramus (1515-1572), James Zabarella (1532-1589). 31. The criticism of the Renaissance was the prelude to a period of violent, and not particularly discriminate, attack on Aristotle. The new philosophic spirit, and the HISTORICAL NOTICES. 21 Eeformation movement, were hostile to his authority ; the mystics of the time were likewise opposed to his definite- ness of form ; he was attacked by Vives, Kamus, Gassendi, Gerson, Nizzoli, Patrizzi, and Luther ; then by Bacon, and virtually by Descartes. But in the end, and very shortly, it was found that the method and discipline of the logical treatises Qjild not be digpensed_with by any school or sect, philosophical or theological ; and all the essentials of the logical theory were readopted by the followers of those who had assailed it. 32. There were two things which led to the passionate revolt against the Aristotelic logic in the sixteenth and seven- teenth centuries. The one was the misapplication of its laws, to some extent at least, as if aiming at positive truth or science ; the other was the speculative misapprehension of its nature on the part of several reformers, not excluding even Bacon and Locke, as a method of real truth, whereas it but showed the forms. The methods of Bacon and Descartes had totally different aims from those of the Aristotelic logic ; yet these are complementary, not opposed. The necessity of recurring to the school logic was shown very shortly after the first im- pulse of Bacon and Descartes had spent itself. Hobbes gave us a logic ; the school of Descartes did the same in the Port Eoyal Logic of Arnauld ; the Eeformation gave us the logics of Melanchthon, Derodon, and Goveanus, all essentially Aristotelian. Kant himself only touched logic to recognise that Aristotle had created a science which, in his view, had neither advanced nor receded for twenty-two centuries. All this clearly shows what is apparent, from the nature of the case itself, that a logic of form and formal method is an in- dispensable need of intelligence, and that the attempted sub- stitution by Bacon of Induction for Syllogism proceeded on a misconception of the province of the latter and its place in the sphere of human knowledge. It might further be very readily shown that Aristotle had a sufficiently accurate con- ception of Induction as a real method. The exception of the logical treatises of Aristotle from the flames in Paris in 1210 is, as has been remarked, charac- teristic of the history of those books themselves. While his other writings have been repudiated or partly superseded, the logical treatises cannot reasonably be either cast aside 22 INSTITUTES OF LOGIC. or neglected. They are of universal truth and application. They are indispensable to different nationalities and to varying faiths. The Induction of Bacon and the Analytic Eeflection of Descartes alike need them. Modern science, in the person of certain of its followers, is supercilious enough about them. This only shows that these people do not know their own origin, or appreciate their own needs. They act as scientifi- cally in this as if they were to contemn the study of gram- mar, because certain people have accidentally learned to speak grammatically without it. Empirical accomplishment is not a thing which modern science can consistently, with its character or pretensions, afford to applaud or exalt above methodical culture. 33. In the seventeenth century, the logic of Burgersdyk (Institutionum Logicarum Libri Duo, 1626), especially with Heereboord's annotations (d. 1659), is very valuable (Er- meneia Logica, 1666). The influence of Descartes is recog- nised in the logics of Clauberg (1625-1665), the Port Eoyal (of Antony Arnauld, d. 1694). We find Leibnitz (1646-1716) returning to precise views of the nature and laws of formal Logic, and these were systematically developed by Christian Wolf (b. 1679). The logicians of the eighteenth century on the Continent worthy of note are Leclerc (d. 1735), after Locke ; Crousaz (d. 1748), after Leclerc ; Ploucquet (d. 1790) ; Wyttenbach (d. 1820). The short treatise of Kant on Logik first laid down pre- cisely the lines of the science, as a body of formal doctrine, in the terms since accepted in modern philosophy. 34. The logicians of the Kantian school, more imme- diately related to Kant himself, are Jacob, Kiesewetter, Hoff- bauer, Maass, Krug, E. Eeinhold, Twesten, Bachmann, F. Fischer. Fries and Herbart follow the same line, with im- portant independent investigations and contributions to the science ; and connected with Herbart are Drobisch, Harten- stein, Waitz, Allihn. (See Ueberweg, 29, p. 60.) 35. Since the time of Kant, in Germany, Fichte and Schelling have done nothing in formal logic. Hegel recog- nised the value of the Aristotelic treatises, and gave a certain impulse to the study of them. But, as has been said of his own Logic, it has nothing in common with Aristotle but HISTOEICAL NOTICES. 23 the name. It is an ontology, to be criticised on its own assumptions and method. Hegel has discussed Logic in the Wissenschaft der Logik, 1812-16, 2d ed. 1833-34, and in the Encyclopddie der philosophischen Wissenschaften im Grundrisse, 1817, Part I., 19-244. There are three main points in Hegel's view, as Ueberweg has thus succinctly put them : " 1. He identifies the form and the most general content of thought i.e., what is regarded as logical with what is held to be metaphysical. But even supposing these to be essen- tially connected, they cannot be identified ; and, besides, their proper scientific treatment demands two distinct sciences or departments of philosophy. The discussions on Being and Essence have no proper place in Logic. " 2. Hegel identifies the forms of thought with the forms of existence, and regards the Notion, Judgment, and Inference as of metaphysical or objective significance. ' The notion is immanent in things, things judge and infer, the planetary system, the state, everything in accordance with reason is an inference.' There is in this simply an absence alike of scientific and philosophical precision. The mind conceives, judges, infers. Things do not, they only show analogies and correlations with these processes. They are like but not the same." To be trained to think in a rut of this sort is, as Fechner justly puts it, " to unlearn thinking." " 3. The dialectic method sets before it a false problem, and solves it only apparently, (a) Pure thinking, thinking that does not depend on and relate to experience, to the matter of outer and inner perception, thinking in itself, cannot pro- duce human knowledge. This arises from the action of thinking on the material of outer and inner perception. It is this knowledge which Logic considers, not the (so-called) working of thought in vacuo. (b) Further, the more ab- stract and extensive notion cannot produce in the thinking subject the more concrete and comprehensive. 'The pro- duct,' says Beneke, ' cannot contain more than what the fac- tors have given.' (c) The logical categories, as transferred to reality, are hypostatised and treated as independent essences, which are capable of a peculiar development, and of passing over the one into the other. The outgoing in the objective reality from Being to Nothing, and then to Becoming, and so on to the Absolute Idea, is given as a timeless prim in the 24 INSTITUTES OF LOGIC. development of nature and spirit. But such an outgoing is utterly unthinkable." (Ueberweg, 31, p. 68.) The chief logicians of the Hegelian school are Erdmann, Eosenkrantz, Kuno Fischer. The chief critics of the Hegelian logic are I. H. Fichte, Schelling, Trendelenburg, Kym, Lotze, Chalybaus, George, Ulrici, Von Hartmann, Herbart and his school. (Of. Ueberweg, 31, 32.) 36. Schleiermacher (Dialektik, 1839) adopts the concep- tion which makes the forms of thinking and knowing parallel, while not identical, with the forms of real existence. The notion and judgment correspond respectively to substantial forms and to actions. He denies Hegel's doctrine that " pure thinking " has a character or beginning distinct from all other thinking, ordinary or reflective, and can arise specially for itself. He properly makes human thought dependent on per- ception. There can be no act of knowledge apart from two functions, the " intellectual " and the " organic." H. Eitter, Vorlander, Beneke, Dressier, Trendelenburg, Hoffmann, Lotze, Braniss, are all more or less related to Schleiermacher. (Cf. Ueberweg, 33.) Occupying a position intermediate between the Kantian and Hegelian views of Logic are I. H. Fichte, Balzano, Chalybaus, H. Ulrici, Katzenberger, Sengler, Friedrich, Von Kirchmann, Seydel, and others. In the Aristotelian line, yet with modern reference, are Hagemann, Eabus, Hoppe (Ueberweg, 34, p. 72 el seq.) 37. In France, during the eighteenth century, formal logic was neglected, even despised. In the present century, Cousin drew attention to it and its place in philosophy ; and to his influence we may attribute the valuable and learned works of B. St Hilaire on the Organon of Aristotle, De la Logique cCAristote, 2 tomes (1838), and his Logique (TAris- tote traduite en Franqais (1844), 4 tomes, and also Franck's Esquisse dune Histoire de la Logique (1838). Vacherot, Tissot, Duhamel, Waddington, Duval-Jouve, Pellissier, Delbceuf, are the chief recent French logicians. 1 38. From the middle of last century down to a date well past the first quarter of the present, the important branches of Logic, Deductive and Inductive, especially the former, 1 See especially Reiffenberg, Principes de Logique (Brtixelles, 1833), p. 289, for a Precis de I'Histoire de la Logique, and p. 350, for Bibliotheque Logique. HISTORICAL NOTICES. 25 were imperfectly treated in the Scottish Universities, and hence in Scotland itself. The Experimental Method of in- quiry, as it was called, which, through the precept of Bacon and the practice of Newton, had become dominant in Britain, powerfully affected the habits of thought in last century in Scotland. Its results were so great and brilliant, and its promise so high, that there was an unreasoning reaction against Deductive Logic, whereas all that really deserved censure was its wearisome and fruitless application in books to abstract terms and definitions. From 1453 up to the end of the seventeenth century there had been a tolerably con- tinuous course of instruction in the Aristotelic logic in the University of Glasgow. What John Major had taught, even Andrew Melville resumed and continued. The lingering influence of this is seen in the teaching, but especially in the text-books on Logic, of Gershom Carmichael (1672-1729), and Francis Hutcheson (1694-1746). Carmichael's treatise is entitled Breviuscula Introductio ad Logicam (1722); that of his successor Hutcheson, Logicce Compendium. Praefixa est Dissertatio de Philosophies Origine, ejusque inventoribus aut excultoribus pr&cipuis (ed. 1759-1764). Both treatises show an acquaintance with the Aristotelic writings, accuracy and precision in the definition of terms, and both bear traces of the advance of new doctrines on the older stereotyped formulae, probably mainly suggested by the Port Royalists. We have in them distinctions set forth which were subsequently lost sight of, and only revived and scientifically applied in our own time, such as the discrimi- nation of Extension and Comprehension in notions, of Imme- diate and Mediate Judgment involving Eeasoning, and of Immediate Judgments as abstract and concrete. Hutcheson distinguishes with precision Sensation, Imagination, and Pure Intellection (Pars I. c. 1.) Both treatises contain valuable rules of Deductive Logic. The Elements of Logic of William Duncan of Aberdeen are of but slight relevancy and value. Even Dr Thomas Reid could speak of the syllogistic art " as a mechanical mode of reasoning, by which in all cases truth and falsehood might be accurately distinguished," l though he has left us a very intelligent abridgment of the Organon ; 2 1 Statistical Account of the University of Glasgow, Works, p. 735. a Works, p. 763. 26 INSTITUTES OF LOGIC. and there is now evidence that in his teaching at Aberdeen he gave considerable importance to Logic. (a) In a MS. volume in my possession there is a short compend of 101 pages, entitled 'A System of Logic taught at Aberdeen, 1763, by Dr Thomas Reid, now Professor of Moral Philosophy at Glasgow.' This is obviously made up of notes of lectures given by Reid. It is full and clear, and gives a very good view of Reid's opinions on Logic. Reid refers under Simple Apprehension to the Predicaments and Predi- cables, criticises Locke and Hume, deals with Judgment, Belief, Evidence, Induction, and Method. (The part on Reasoning is not given by the transcriber, on the ground that it contained nothing new.) These lectures, in fact, contain the germ of the most important of the new views of Reid, afterwards more fully developed in the Essays on the Intellectual Powers. 39. Dugald Stewart echoes the crudities of Locke on the subject of Deductive Logic, and seldom loses an opportunity of speaking disparagingly of "the logic of the Schools." Owing to a current of opinion of this sort, Logic as a science and organic branch of Mental Philosophy ceased to be studied in the Universities of Scotland. It was treated in a cursory manner as an intellectual curiosity which had enjoyed the attention of men in " the dark ages," but which must give way to new and fresh studies conducted by the advanced intellects of the time. 1 The increase of the material of know- ledge was regarded as all-important. It was forgot that the science of method and form, of the processes of the acqui- sition and concatenation of knowledge, cannot be set aside without a disregard of the completeness and symmetry of knowledge itself; that the assumptions of the scientific pro- cesses need vindication ; that the processes and their results need rules of purification, testing, and verification ; and that Logic which deals with those points is not rendered super- fluous, but only widened by the opening up of new spheres of inquiry and science. 40. It was not until Hamilton fully and lucidly set forth the true character and place of Formal Logic as a depart- ment of Mental Philosophy, in a contribution to the Edin- burgh Review of 1833, that the study recovered its true posi- tion in Scotland and in the Scottish Universities. Of the influence of this remarkable essay, we could not have a better 1 There is a very meagre compend by Professor Jarcline, Qtucdam ex Logica Compendiis Selectee. HISTORICAL NOTICES. 27 illustration and evidence than in the Elements of Logic of the late Professor Spalding of St Andrews (1857), one of the ablest of our modern logics, and one which shows the high tone of teaching in that ancient though small University from 1845 to 1860, the recovery in fact of its mediaeval prestige. From 1836 to 1856, the period during which Hamilton occupied the chair of Logic in the University of Edinburgh, he developed in his lectures the science of formal logic with a fulness, precision, and learning wholly new to Scotland, even to Britain. These lectures, published, after his death, in 1860, represent the Aristotelic doctrines, the Kantian point of view and some of its subsequent modifica- tions, and, in part, the author's own new logical development. 41. One of the earliest treatises which aimed at extend- ing a knowledge of Hamilton's logical system beyond the class-room, was an Essay on the new Analytic of Logical Forms, by Thomas Spencer Baynes (1850), now Professor of Logic in St Andrews. Mr Baynes is also the author of an excellent Translation of the Logic of Port Royal (1850). 42. The same influence which acted in Scotland ex- tended to Oxford, and freshened the faded dialectic of that University, as represented by the meagre and inaccurate com- pend of Aldrich ; for the Outline of the Necessary Laws of Thought, by William Thomson of Queen's (1842), now Arch- bishop of York, and the able, learned, and valuable logical writings of the late Dean Mansel are, with much that is distinctively original, especially in the latter, the almost direct inspiration of Hamilton. We have to thank Oxford for Whately's Elements of Logic (1826), as one of the most useful and practical books on the subject which we yet have ; but Oxford has had to look to Scotland, rather than to its own Oriel, for a systematic development of the science, and for the learning needed to correct errors in its nomenclature and history. The most recent additions to the literature of Logic in Scotland are by Professor Bain of Aberdeen, who has given us two important treatises on Inductive and on Deductive Logic. His Deductive Logic is marked by Mr Mill's peculiar view of the syllogism, which need not at present be dis- cussed. It is curious and interesting to find that one who may be regarded as the most eminent of the school of Locke 28 INSTITUTES OF LOGIC. in Scotland in our time, has written valuable works on that department of philosophy which Locke himself so greatly misunderstood and contemned. Since the date of Hamilton's essay in 1833, and with it the rise of an accurate view of the province of formal logic, the revival in Britain of logical studies, deductive as well as inductive, has been very remarkable. In Deductive Logic, we have had the treatises of De Morgan, Boole, and Jevons. Other writers in the department are Maccosh, Kidd, Morell, Karslake, Milnes, Swinbourne, Abbott, Monck, W. G. Davies, Alfred Sidgwick, Fowler, Stebbing, Hughlings, Poste, Venn, Lindsay, and Bradley. The abridgment of Hamilton by Bowen of Harvard is well worthy of notice and study. One important function of this branch of literature is that it serves to preserve the balance and the symmetry of human knowledge, aids reflective thought, gives us a width of vision over the realm of science, otherwise unattainable, and thus helps to save us in a measure from the besetting sin of modern intellectual habit, blinding specialism. 29 CHAPTEE IV. TRUTH, AND THE RELATIONS THERETO OF LOGIC DEFINITION OF LOGIC. 43. While Truth in general may be regarded as a har- mony or conformity between thought and reality, or more precisely, between thought as representative and fact as given in intuition or presented, it is to be observed that the consciousness of truth as a mental act implies a synthesis, or composition of notions or terms as one, or better as in one. 1 So long as notions or terms are in the mind apart from this synthesis, we have not properly either truth or error. And this applies equally to nouns and verbs, for the verb, apart from its relation to time or assertion, is essen- tially an attribute or noun. Notions out of combination, and combination as one, are merely representations devoid of truth or error. The notion, for example, of goat-stag (rpay- e'Xa^os) may be in the mind, but it is neither true nor the reverse, until it is added that it is, or is not, either absolutely or in some determinate time. 2 A sentence even may be significant without being prop- erly either true or false, as in the case of the expression of a prayer or wish. The sentence which admits of truth or error must be enunciative (a7roy Epicurus, and adopted by Kant. 36 INSTITUTES OF LOGIC. analysed, the exercise of the understanding at all, it is a legislative science in the highest sense. Any so-called thought, be it a concept, a judgment, or a reasoning, which violates the form of the Understanding, ceases to be, becomes, in a word, nonsensical and merely verbal. This is shown in detail, with the strictness of demonstration, by the application of the rules of logical science to the various products of the understanding Notion, Judgment, Reasoning. These special rules strictly form the fundamental laws of thinking, and partake of a demonstrative character. The special rules of Reasoning, for example, are but tests of validity which, resting ultimately on the character and num- ber of the primary laws of thinking, are deducible from them. (a) On this head, Kant says that, as canon of the understanding, Logic can borrow nothing from another science, or from experience. It must contain only the pure a priori laws, which are necessary, and which are the heritage of the understanding in general. This language is misleading and exaggerated. Along with other expressions of the same sort, it has led to the delusion that there is " a rational science, " or science of abstractions ; and this has been employed to supersede even abolish the reality from which the abstraction was taken, and which alone gave it meaning. Logic is, in a sense, an abstraction from experience, and can be nothing else. It is the science of what is neces- sary in experience, and, therefore, universal. Our means of knowing and testing the necessity of its laws are found in experimenting on particular instances. The strength of the particular thought which embodies truly a law is as great as the strength of the abstract law itself ; it is only not so extensive as the law. (ft) " Ratio de suo actu rationari potest . . . et luec est ars logica, id est rationalis scientia, quse non solum rationalis est ex hoc quod est secundum rationem, quod est omnibus artibus commune, sed etiam in hoc quod est circa ipsam artem rationis sicut circa propriam materiam." (St Thomas, quoted by St Hilaire, i. p. 24.) " Logica enim est omnium artium aptissimum instrumentum, sine qua nulla scientia perfecte haberi potest ; quze non more materialium instrumentorum usu crebro consumitur, sed per cujuslibet alterius artis vel scientise studiosum exercitium continuum recipit incrementum. " (Occam, Prooem. Sum t. Log.) 37 CHAPTER V. OBJECTIONS TO LOGIC AS A FORMAL SCIENCE THE VIEWS OF KANT, HEGEL, AND UEBERWEG. 50. If Logic be, as Kant puts it, the rational science of the necessary laws of thought, and as these have to do not with particular objects, but with all objects generally, this science cannot be said to be subjectively formal, or to be divorced from any relation to objects, even real objects. On the contrary, it embraces the most general aspects of objects as these are actually and possibly cognised and cog- nisable by us. These aspects, no doubt, are named forms of thought, our notions, judgments, and reasonings. But they are also, in relation to intuition or perception, forms of the realities, the objects therein given. They are the ways in which we may, nay, must, mediately represent to ourselves what is given in the course of experience, through intuition. If the forms apply to all objects generally, and to every object indifferently, they ought not to be represented as having no application to any object. 51. Further, as it is very distinctly the doctrine of Kant and of others on whom this exaggerated formal view is charged, that the contradictory is necessarily non-existent, unreal as it is nonsensical, it can hardly be fairly maintained that the logic they teach is abstracted from any relation to objective existence. Kant's vital mistake lay in regarding the laws of thought as of a wholly subjective character, and in restricting in the Logic as elsewhere what is necessary in thought to a purely subjective function, a function of constitution, whereas they represent but one side of a coincidence between human thought and divine thought as embodied in things. 38 INSTITUTES OF LOGIC. The true conciliation of the Kantian and the realistic view is to be found in the principle that the understanding is appre- hensive as the intuition, apprehensive, to wit, of relations, as the latter is of the terms of the relations. 52. We may go quite beyond saying that we have only to do with the consistency of our thoughts. We may quite well hold that this consistency is essential, negatively, to truth of fact, and we may even vindicate the many connections of Identity and Non - Contradiction as correspondences to the actual connections of things. For these may be denied, and spoken of as " not absolute," that is, the actual oppositions of experience may be denied to be such, because it is assumed that behind this experience there is some one thing, or force, or entity which, being one, manifests itself in all. This, even if it could be proved, could not be shown to abolish the differ- ences in time or as we actually perceive things. 53. There is the view of Hegel, which, assuming the identity of thought and existence, identifies the laws of thought with the laws of being, or the forms of thought, as he interprets them, with the forms of being ; then describes a certain pro- cess of so-called self-development of pure thought as also the process of the self-production of existence ; identifies (or con- fuses) the form and the matter of thought, professing to evolve the latter out of the former as a pure evolution, apart from intuition or experience. This may be called the meta- physico-logical theory. But, in point of fact, there is nothing in its method in the least analogous to any recognised logical law ; in fact, there is, from first to last, an absolute, even proclaimed, reversal of logical law, and thus of definite intel- ligibility, even rationality. 1 54. This is not the place to enter into a full discussion of the Logic of Hegel, what may be called Speculative Logic. This would involve a discussion of the whole principles of his philosophy. But I may indicate generally the nature of his logical theory, and its relation to the Aristotelian. In Aris- totle throughout truth is regarded as a relation, a harmony between thought or judgment, our judgment and reality. The spirit of realism or dualism permeates the whole think- ing of Aristotle, and no where is it more felt and seen than in the Organon. The logical conceptions, forms, terms, 1 On this see Descartes, Introd. , xi. xii. VIEW OF HEGEL. 39 laws, are taken directly from experience, and they are tested by reference to experience. Aristotle is the most concrete of logicians, in some respects the healthiest. His practical sense is as outstanding as his unmatched subtlety. His con- ception of truth as a relation or harmony between thought and reality, it is the principal end of Hegel to break down. With him there is no such distinction. There is no dualism, either of man and nature, of subject and object, of spirit and matter, of finite and infinite, of the real and the ideal, of man and God. So that logic in his conception need not seek to lay down criteria or rules for testing the true or real har- mony of thought and things. There is no difference or dis- tinction. And how does he proceed to show this ? Of course, his process is that of Reason, the pure reason, pure thought. The idea in its total development. And what is this ? In plain words, throw away man, nature, God, go back to the stage of thought in itself pure thought, objectless, indeterminate ; or as it is identical with being, go back to qualityless being, without mark, feature, or discrimen of any sort, and you will get what will develop necessarily into all truth or reality, for these are but names for the same thing. This is thought in itself; the bare form of thought without object is your starting-point, Reason in its first expression, Being in its primary reality. The develop- ment of this prius of all is the dialectic process, the march of the speculative reason, the ongoing of the speculative logic. It makes, it is, in its course, man, nature, God, all being ; it is in its course all truth. " What is rational is real ; what is real is rational." And this is the rational ; this is the real. In the march the wonderful march of the Idea from in selfness, which is not yet even conscious, and is objectless, from Being, which has not quality to distin- guish it from nothingness, the Aristotelic Logic is com- prised. It is a stage, an early stage of the course, which is trampled out and yet absorbed. Aristotle represents the ab- stract point of view, the point of view of the understanding, which still holds by difference and distinction and the laws of Identity and Non-contradiction. Speculative truth, how- ever, lies in the fusion of contradictories and the march of universal identity. Yes is only yes as it is also no, and no is only no as it is also yes ; and the truth lies in the yes which 40 INSTITUTES OF LOGIC. is no, and the no which is yes. And we must not speak of contradiction as " absolute"; it is only temporary; in the real nature or truth of things opposites are one, and are only as they are one. What, in this case, we may ask, comes of moral distinctions ? What, for example, of veracity and unveracity? Are these simply temporal distinctions, to be fused in a higher medium, since contradiction is not absolute but perishable ? And what of man the worshipper, and God the object of worship? When man worships does he wor- ship only himself in another form? And is this God? Are there two orders of truth? One in which there is difference and distinction, another in which all this is abolished ? Then, which is the true ? and who is to decide this question ? It will be meanwhile more reasonable for us intellectually, and better for us morally, to keep by the knowledge we have than trust in the " Speculative Logic." 55. The Idea is developed, or rather develops itself, from stage to stage in virtue of its inherent power, its being all potentially, though it is at the same time a perfectly quali- tyless conception, in three great lines, Being, Essence, No- tion, which of course come in the end to be the same. The treatment of these makes up the Philosophy or Logic of Hegel. And under the first two heads Hegel borrows the Aristotelic and Kantian categories, and seeks to show how they arise, move, and are transmuted. Under the third, Notion, we have the Aristotelic forms, Notion, Judgment, and Reasoning, taken up and dealt with according to Hegel's conceptions. These forms are not in his view to be taken as modes of our knowing merely or as representing reality. They are " the living spirit itself of the reality, and nothing in the reality is true except what is by those forms and in those forms " (En., p. 161, 162). The notion is an abstraction, but in its true concrete totality it is all that is. Judgment is the identity of the general and the particular. Attribute is only the general. The subject is the particular. The cop- ula is their identity, and so on. The outcome of the whole matter is that there is but one reality, and that is the Idea or Eeason ever developing itself, absorbing its developments, and so becoming enriched, and rising, we cannot say finally, for there is no limit anywhere, but somehow and somewhere, - to the consciousness of itself, as God who manifests all and VIEW OF TJEBERWEG. 41 is all. This system here concerns us principally under the third head of Notion, and the theory of contradiction, to which reference will be made below. Meanwhile it is enough to say that a system which alleges the law of non-contradic- tion in reference to a definite concept or judgment not to be absolute, i.e., that the statement is simply other than it is, even not what it is, must imply that this very statement is impossible ; for it cannot be made except in terms of a definite proposition, and therefore, as at once alleging and denying the very same point, cannot be made at all. 56* Another view which professes to follow Aristotle in substance is that of Ueberweg, who makes Logic " the science of the regulative laws of human knowledge." He explains his position thus. It is opposed to that of Kant " in the thoroughgoing proof of the way by which scientific insight is obtained, which is not brought about by a priori forms of purely subjective origin, finding application only to phe- nomenal objects present in the consciousness of the subject, but is reached by the combination of the facts of experience according to the logical rules which are conditioned by the objective order of things and whose observance secures an objective validity for our knowledge." 1 Ueberweg in this view follows in the line at least of Schleiermacher (Dialektik 1839), Ritter, Vorlander, George, Trendelenburg, Lotze, Beneke. Ueberweg's view may be summarily stated thus : That Logic is the science of the forms of knowledge in general, of perception as well as of thought proper mediate or repre- sentative knowledge ; that the logical forms, or the forms of knowledge Intuition, Notion, Judgment, Inference, System correspond to, and are derived from the forms of real existence, the metaphysical laws ; and that through the harmony of the forms of knowledge with those of reality, we obtain truth, material truth, or the correspondence of knowledge with what actually exists, at least as a presen- tation. This view approaches that of Aristotle. Aristotle " finds the standard of truth in the agreement of thought with what actually exists, which is the limit of science. The notion rightly formed, corresponds, according to Aris- totle, to the essence of the thing (ovo-i'o, or TO ri rjv etvat) ; the 1 Logic, Preface. 42 INSTITUTES OF LOGIC. judgment is an assertion about an existence or a non-exist- ence ; affirmation and negation correspond to union and separation in things ; the different forms which the notions take in the judgment (or the kinds of denotation of existences, aX^p-o-Ta TT}S KaT^yopi'as TWV OVTWV) determine themselves accord- ing to the forms of existence ; the middle term in a syllogism, correctly constructed, corresponds to the cause in the con- nected series of real events ; the principles of scientific know- ledge correspond to what is actually first in the nature of things." (Of. Met., iv. 7 ; ix. 10 ; x. 6. ; Categ., 12, 14 B, 21.) Ueberweg develops his view more completely in 36 et seq. Those who, like Ueberweg, hold that there is a correspond- ence between the logical laws and forms and the order of things, do not dispute the psychological fact of the necessary character in consciousness of these laws and forms. When it is said that there is this correspondence between the law in the consciousness of the subject, and the fact in the con- stitution of the object, a reference is made to the origin of the law as conditioned by the objective reality, and also as expressing and representing that reality. These are no doubt very important points ; but they are rather of meta- physical import and significance than of logical. It is pos- sible at least fully and scientifically to consider the nature and number of the logical laws as in consciousness, the forms of thought which flow from them, and their mutual relations, without considering especially the origin of the laws, or their representative character in relation to reality. Logic would thus be a complete though an abstract science ; but not more abstract, or less capable of concrete application than arith- metic, which deals with numbers, their laws and relations, apart altogether in the first instance from any conception of their application, and apart also from the question as to the origin of number, in, for example, the successive units of time. We may thus deal abstractly with the laws of Logic and their evolutions, without at all, as Kant is supposed to have done, committing ourselves to the view of their purely subjective character, or a purely subjectivo-formal logic. 57. Besides, the question of the origin of the laws and their precise metaphysical import may give rise to much doubtful disputation, and must necessarily involve both psychological and metaphysical theories, which, if kept up, as they need to VIEW OF UEBERWEG. 43 be, through a whole treatise of logic, may hamper greatly the systematic development of the science. To confine Logic as a science to what is common and universal in all human thinking, whatever be the particular psychological, meta- physical, or moral opinion we hold, is to give it a good, useful, and legitimate sphere. And so to treat it, does not imply or demand a greater abstraction than is common in kindred sciences. Besides, nothing could be of greater im- portance than that varying thinkers should agree as to a general science or canonic of thought for all actual and possible matter of thought. 58. It seems to me that the whole of Ueberweg's reason- ing on this point is really guided by extra-logical considera- tions. He holds a certain metaphysical doctrine of the truth or agreement of intuition, inner and outer, with reality. He holds distinctly that our internal intuition, or apprehension of the states of consciousness and of Self, is identical with the reality, that there is nothing in itself, self in itself or phenomenon in itself, above and beyond the actual self and phenomenon of conscious intuition, to which the latter have to conform, in order to be real or true. He discards all this superfine transcendentalism or verbalism. And very properly so. He further maintains the reality of space and time, as objects perceived, and not merely imposed on the matter of perception, as actual precepts as well as the matter, or ele- ments in the matter, and as objective, conditioning our particular perceptions. He further maintains, on the ground of analogy, the reality of minds similar to our own in this world of experience, and on the same ground of analogy he holds that individual intuitions in general arise out of the original blur of perception, when man first begins to recognise himself as an individual essence in opposition to the outward world. 59. The logical correctness of the application of this form of knowledge is to be tested by the same criteria as the truth of all those elements of knowledge which originate in our internal, and go to complete our sense perception. 1 The whole of this doctrine really is based on an unverifiable trust in our faculties of intuition, a certain psychological analysis of their declarations, and a certain metaphysical i Logic, 46. 44 INSTITUTES OF LOGIC. theory founded partly on this analysis and partly on analo- gical inference from it. But there is nothing here specially logical, except the principle of analogy, the laws of which it is the function of logic to investigate. There is also, of course, the special application of the principles of reasoning in general to certain psychological data. But to suppose that this par- ticular realistic theory of inner and outer Intuition is the essential basis of Logic, is to peril the whole character of the science as a body of assured universal principles. We have a much wider, and, I think, a truer conception of Logic as a science when we leave those problems to psychology and metaphysics, and restrict, really widen, Logic by regarding it as the science of those principles which regulate our con- ceptions of any sort, negatively by the law of non-contradic- tion, and positively by the laws of necessary inference, and which, while not assuming any special psychological or meta- physical theory to be the true one, can yet, to a certain extent, regulate all. Even Material or Inductive Logic, on which the doctrine has the closest bearing, is independent of metaphys- ical theories regarding the nature of reality, and the corre- spondence therewith of human thought. All that it does or needs to do is to seek causes and laws or uniformities. The principles which regulate these, the tests of them, are very much independent of our views as to the exact contents of the notions and their relation to reality. It is clear at least that on such a view of the sphere of Logic, " the regulative laws " of which it is called upon to treat must be of the most varied sorts. It must deal with matter of fact in intuition, and its general laws of cognition, with the necessary conditions, space and time ; it must deal not only with the nature of conception, but with its relations to actual existence, not only with the nature of judgment as a process or product of cognition, but with the question of its relation to things. These are the questions of Psychology and Metaphysics. The theories, for example, of Descartes, Locke, Berkeley, Hume, Condillac, Kant, regarding the ob- ject of perception, and the process of perception, would all, on such a hypothesis, fall to be reviewed and the true theory given. The question of the origin of knowledge, the validity of our primal beliefs, the nature of causality and substance as forms of existence to which our knowledge ought to conform, VIEW OF UEBEKWEG. 45 these would be treated, as well as the laws of Inductive and Deductive Inference. This is true even though we dis- tinguish the several contents of thinking from the contents of thought in general. This method can only lead to delay in the decision of the logical questions, to the confusion of what may be truly dealt with on any theory of the universe, real or ideal, with what is now, and may ultimately remain doubtful and unsolved. Surely we may treat of what is common in Concept, Judgment, and Inference, as we find these in actual and necessary exercise, without waiting for or even seeking for a settlement of all the possible ques- tions, which may be raised regarding their origin, nature, and relations to their materials or contents, considered as objects of actual reality. 60. The value of Ueberweg's doctrine lies in drawing attention to the genesis or grounds of logical forms and processes viz., Conception, Judgment, Reasoning. Why, it may be asked, does thought take the forms of conception, judgment, and reasoning? This is no doubt a question preliminary to a study of the essential features and neces- sary laws of those processes. To answer this question of ground and origin, we need to go back to psychology and even to metaphysics ; for we first spontaneously conceive, judge, and reason about the matter of intuition or experience. In other words, we exercise definite acts of consciousness, in the face of objects and upon objects. We affirm existence, we distinguish the permanent from the passing ; we divide or conjoin existences, and We connect these causally or uni- formly with the other. Still these acts have what may be called a logical side ; they have a community of character subject to certain essential and necessary laws ; and these we may study without specially considering whether the ob- ject apprehended, conceived, and judged is real or ideal, and what are the differences in the metaphysical characters of the objects which form the matter of our knowledge. This is truly all the formality which Logic need claim. 61. But it may be asked, What precisely is the meaning of the reference or relation in these cases ? How are they related the logical and metaphysical judgments for ex- ample ? Animal has organisation. This is Substance and Inherence. This corresponds closely to the Comprehensive 46 INSTITUTES OF LOGIC. Judgment. It is the logical relation of subject and attri- bute. Again, fire burns. This is the relation of causality. But the advantage of the logical expression is that it is more general than either, and embraces both, and can be legislated for as such. In fact, the logical relation means that there are laws, possible laws, for predication whatever be the ground of predication, or whatever be its specific relation to the forms of reality. 62. Further, this relation of Substance and Inherence, or Substance and Attribute, is not the only possible form of enunciation. We refer the subject to a class. We have judgments in extension. This represents quite a different relation in reason, or logically. The real relation here symbolised is that of Kind and Species, or Species and Individual in nature. Any given judgment is to be tested as true or false by reference to the actual matter which it embodies, the subject and class as these really are. But logic, as the universal science of thinking, finds points in common which can be legislated for in all class references, just as it does in all references of inherence. And these are dependent on the essential in the act of judging, and, there- fore, indifferent to the matter judged. And what is more, logic finds, in its higher universality, points in common between the judgment of inherence and the judgment of classification, and these, too, dependent on the nature of the judging act, and is thus able to reach scientific precision, necessity, and universality, and to lay down the laws or conditions so far ; of a valid act of judging. Logic has in its proper or scientific character only remotely to do with even the abstract metaphysical forms, the Predicaments of Aristotle, or the Categories of Kant. 63. With regard to the Conditional Judgment if A is, B is this may refer to the relation of Cause and Effect. But in that case it would not be a strictly necessary inference, not properly logical. For we can only know the terms of any causal relation by experience. It is, then, for us wholly contingent. The relation itself of causality, if an event be, it has a cause, is strictly necessary, but it can never warrant us in determining a similar necessity regarding any special instance of cause and effect, regarding, in a word, actual effects and causes. VIEW OF UEBERWEG. 47 64. When formal truth is represented as simply the absence of contradiction i.e., the agreement of thought with thought as consequent with antecedent, a question may be raised as to whether we have in this agreement any ground for holding it to represent material or real truth. We think the consequent as dependent on the antecedent e.g., the motion of the tide on the position of the moon ; or the responsibility of man on his possessing free- intelligence, or the predicate of every one, as likewise the predicate of this or that one of the class. The general answer to this is, that where the antecedent is already found to be real i.e., real as a matter of fact, the consequent as necessarily involved in it is real also as a matter of fact. This holds in inference from whole to part. If the whole, of which something is predi- cated is, the part as involved in the existence of the whole is justly credited as really possessing a similar predicate. Valid or correct thought guarantees the connection between the antecedent and the consequent ; and if the antecedent is, the consequent justly drawn from it is also. 48 CHAPTEE VI. LOGIC IS THE SCIENCE OP THOUGHT. SPEECH, THOUGHT, THINGS. THE CATEGORIES OF ARISTOTLE AND KANT. 65. Logic is the science of thought, not of speech. Logic is from Aoyos, and this means thought and word equally, ratio et oratio. The thought indicated may be taken as mean- ing intelligence or reason generally, or this or that intel- lectual act, be it concept, judgment, or reasoning, as con- trasted with its expression in words. Etymologically, Logic may mean the science of the mental or inward thought, or of the outward expression ; it may thus be the science of thought, or of language, Grammar. Omitting meanwhile special consideration of the relations of thought and language, Logic is not the science of language. It only indirectly affords the main principles of Universal Grammar. (a) Plato defined thought as the internal word, the communion or dialogue of the soul with itself, evrbs rrjs fyvxris irpbs eavrfyi' 5td\oyos A6yos, or discourse, with Aristotle is made up of the noun and verb, and has its meaning through convention ; but each part has sig- nificance, at least has simple expression. (De Int. c. 4.) A.6yos and other similar expressions in Aristotle appear with a clear grounded reference to the mental acts, the iraOrmaTa, ultimately, in fact, to the essence (rb ri ?>v eTwi). (Cf. Met., ii. 4, 1029, b. 19.) (b) The Stoics distinguished the \6yos evSiaOeros, and the \6yos irpoQo- pii(6s. In later logicians this appears as the inward and outward word, as Discursus M entails and Discursus Vocalis. (Wallis, Logica, P. I. c. i.) "Ita quamvis \6yos sua significatione tarn sermonem quam rationem complectatur, tamen non a sermone sermocinalem, ut nonnulli autum- nant, sed a ratione rationalem et Logicam appellandam existimo." (Brevia et dtiucida qucedam Prceludia de Divisione, Dejlnitione, et Argu- mentatione. Auctore Joanne HamUtonio Scoto-Parisiis. 1580.) Logic was not applied by Aristotle as a name for the science which LOGIC AND GRAMMAR. 49 he founded and nearly perfected. He had, indeed, no one name for it. Analytic, as applied to the principal parts of it, is the widest term to be found in Aristotle himself. Cicero (De Fin., i. 7, 22) uses the term loijica for the science. It is in common use in this application with Alexander of Aphrodisias, and even with Galen. It was probably due to the earliest Aristotelic com- mentators, who employed it in opposition to the Dialectic of the Stoics. (See Boethius ad Cic., Top., p. 766. Cf. Prantl, G. d. Loyik, i. 9, p. 535.) A late commentator on Hermogenes divided Logic into Dialectic and Rhetoric. (Cf. Prantl, ibid.) (c) Aristotle speaks of those who contemplate logically (\oyixias ptv Ofwpovaiv, An. Post., c. 21, 88 b. 35). On this Wait/, following Philo- ponus, remarks that rb ai>a\vTiKws is opposed rf \OJLKWS. The former is an accurate demonstration, which depends on the true principles of the thing itself, as opposed to that which is contained in a certain probable ratiocination. Biese translates \oyiKws "out of general grounds," avaA-vTucws "out of the essential determinations of proof." The logical is thus almost the same as the dialectical, or that which does not belong to the truth itself, but to the art of discussion, by which we defend an opinion either as true or false. Hence is clear the sense in which the logical syllogism (\oyticbs x' oTrXws a\X' liro/teW). (Cf. Met.\i. 4, 1030, a. 22.) Occam's view regarding the classification of the categories is that of things taken simply, or without connotation, there are only three supreme genera viz., Substance, Quality, Relation. No quantity, he holds, is in Aristotle's view, really distinct from substance and quality. (Logica, i. 44. Cf. Prantl, iii. 372.) If genus be taken for every- thing predicable for itself and in abstraction from another, then there are ten genera generalissima. It may be said that, properly speaking, ova-la is a subject, not a predicate. But the truth on this point is, that ovV tlSuv TOVTCOV yfflj). The first substances are the ground and principle of all the others, for they serve as subject to all, either of attribution or inherence. Without them nothing would be (fdi ovcriOav ofo r They do not exist, and cannot be conceived out of relation, relation of contrast and opposition. But Hegel confounds the merely relative both with Contraries and Contradictories. 195. But all this criticism on the part of Hegel is mere 1 See above, p. 125. 2 Categories, c. x., and below, p. 179. SPHERE OF LAW OF NON-CONTRADICTION. 159 trifling with the subject. The broad question is : Are there mutually exclusive conceptions in human knowledge ? That there are such it is only trifling with meaning and intel- ligibility to deny. We have examples in a thing being and not being, in consciousness and unconsciousness, in life and death, in yes and no. Unless there be this reciprocal exclusion of predicates, yes and no, truth and error, right and wrong, are mere illusions of the understanding, to be finally absorbed in some generic identity of the speculative reason ! 196. There can be no doubt that contradiction is accepted as absurdity by the common consent of mankind, and as de- structive of the very essence of human reason or knowledge. The understanding is satisfied that a notion or a proposition which involves contradiction, properly so called, is a nullity. Such a proposition can hardly even be called false. It is rather non-existent ; it is a form of words into which we can put no meaning. Here one statement destroys the other. If, for example, a historian says : This man A. B. lived in the fifteenth century ; another historian says, no, he did not live in the fifteenth century or in any other. We know very well that these statements are exclusive of each other, and we should certainly be greatly astounded if the specula- tive philosopher were to appear on the scene and tell us that both statements are true ; for everything is also the con- trary of that which it is. We should very properly, I think, dismiss both him and his philosophy, and hold by the much- abused common-sense of mankind. If two systems give to me no guarantee but self-assertion or an appeal to conscioiisness, I confess that I feel constrained to accept that one which does not reverse either the facts of experience or history. 197. Suppose we apply the principle for a moment to morals. We have what is known as the moral law. It is supposed to prescribe certain actions, even certain motives, and to forbid others. It is further absolute, imperative. We may be doubtful in some cases about what is right or wrong ; but we know all the same there is a right and wrong. And we know also definitely enough that particular actions and particular motives are to be regarded as such. Veracity, justice, purity, these are absolute things for us. Self-sacrifice is a law of moral life. Will it be maintained, for a moment, that the principle that everything is also the 160 INSTITUTES OF LOGIC. contrary of what it is holds here ? Is veracity, is justice, IB purity, is self-sacrifice not separated each by an absolute yes and no from its opposite ? Are the just and the unjust com- patible things? When I resolve to do a certain thing, is irresolution not absolutely exclusive of the opposite resolu- tion or action ? What meaning can there be here in saying that every one of those notions is identical with its contra- dictory, or is a union of contradictories, which is the same thing? I confess I cannot see that on such a system there can be either truth or falsehood, right or wrong, at all. There is an everlasting play of yes and no, successively subverting each other. Each stage or movement is a third only of the truth, and as the yes and no of stages one and two gather themselves up into a third, called yes, the truth develops. But then this new yes or notion begins immediately the same process, and the result of the whole is the absolute identity of things fully developed. At no stage in history or in individual life, do we know the whole truth. Every yes that is evolved is a partial falsehood, until we get to absolute identity in the end ; and this only shows us how completely we were deceived in supposing that the difference of truth and falsehood, of right and wrong, were anything beyond mere temporary appearances or passing illusions. " If the end of man," says a writer, " be action, be the accomplishment of duty, and if this be as it is the very negation of contradic- tion, is it likely that human reason is to find its essence in contradiction ? The moral law and the Hegelian method are in insoluble contradiction. You can choose which should go to the wall." 198. Hegel, indeed, says in regard to some propositions, that these are not identical in the sense that being and non-being are e.g., / am and J am not. This house is there or it is not. But this does not mend matters. As has been well said, " the sense in which being and non-being are identical may be different from that which differences these propositions. But if everything contain contradiction, and if there be no affirmation which is not the negation of itself, these propo- sitions must be identical in his view, in virtue of the principle of contradiction itself. Every affirmation, the simplest as well as the most abstract, is equivalent to its negation, and thus it matters not whether we take the one form or the other." It HEGEL'S FORMULA OF CONTRADICTION. 161 is here that practical absurdity shows the theoretical absurdity inherent in the system, and it is here that Hegel is found to recoil from the legitimate consequences of his own principles. 199. Let the system be judged from the point of view of ordinary reasoning. Let it be tested by the possibility of reasoning itself. Does Hegel not seek to prove that which is to be proved, and not the contrary of it ? He does not mean surely to say no, when he says yes. He proceeds as other people do, and as every one must, by the ordinary acknow- ledged canons of reasoning. Then has he established his peculiar system by this method? In that case, we must regard the foundation as utterly rotten. If he accepts the ordinary canons to any extent whatever, how is his system, which is wholly subversive of them, to be reconciled with them ? On the other hand, if his system is based on the sub- version of those canons, has he not at the outset assumed what he ought to have proved in the end ? Is not thus the whole method a gigantic petitio prindpii ? 200. For the ordinary statement viz., That a thing which is cannot be the contrary of that which it is, Hegel would substitute this : That everything ichich is is also the contrary of that which it is. As grounds of a progressive development, neither formula is of use. If we take the former principle, it is obvious that we can- not proceed by negation to a new idea in other words, we cannot construct knowledge a priori. It is what is called an analytic principle i.e., we can deduce from the notion of the subject any attribute involved in it ; but we cannot in this way add to the notion of the subject, particularly, we can- not add incompatible attributes. From the notion, for example, of organisation we can draw out, as it were, the attributes of growth, and end or purpose, and living form conformed to this end, because we have already fixed these attributes as con- tained in the notion of organisation. The principle would keep us to these attributes and only to these i.e., it would keep us consistent in our thinking about the object of thought. But if you say that the object spoken of is also the oppo- site, or contrary, or contradictory of that which it is, you cannot add an attribute in this way. What would come of identifying, for example, organisation and its opposite? Or 162 INSTITUTES OF LOGIC. of negating organisation ? Yet it is supposed that simply by denying the notion you begin with, you can add a new idea to the notion, and finally unite this idea and the original notion in a third term, which again is a new idea. No progress in knowledge can really be made in this way. It is, in fact, simply a suicidal process. And if this be so, the whole system of Hegel is sapped from the foundation. 201. The illustration which is usually given of this process is that of the growth of a plant or tree. We are supposed to begin with the germ or seed. This develops into stem, branch, leaf, &c. And finally there is the union of all these in the plant or individual thing. The germ or seed is spoken of as the uni- versal or possibility of the plant ; the stem, branches, leaves, &c., as the particulars or differences or negations of the germ. The union of all these is regarded as the individual thing or plant itself. These three points, universality, particularity, individuality, are called moments, and it is said that in this way human knowledge is developed, developed from the bare abstraction of pure being or pure nothing. The whole process, including the universal, particular, and individual, is called the concept or Begriff. This is the type of human thought, and of all thought human and divine. But the whole illustration is fallacious. In the first place, it confounds the order of observation, or, if you choose, thought, with the order of production. My mere seeing or thinking this order of development does not make the development itself. If I say so, I have assumed here that the order of my thought is the same with the order of being or reality, that, in fact, my thought is not only observational but creative, -that thought of this order is the divine creative power working in me. Now I do not admit this general assumption, and I hold further that merely to state the observed order of the develop- ment of the plant, and to ticket it with certain big words, is to leave out of account altogether the essential element in the process, the causal or productive power at work, the life within the germ, which, working long silent and unseen amid the chaos and the decay of matter, gathers, assimilates, and at length evolves the form of beauty, grace, and symmetry, that form which rooted in a darkness as of the tomb, yet spreads itself out in cheerful greeting to the light of heaven. CONTRADICTION NOT DEVELOPMENT. 163 202. But, further, this is no illustration or even analogy of the true concept of human thought, nor does it properly illustrate the so-called Begriffot Hegel. The seed or germ is said to pass into the root, stem, branches, leaves, and fruit. But how is this known ? I cannot predict this from the knowledge merely of the germ or seed. I am not now deal- ing with a comprehensive or individual whole, but with a mere class or genus, which I have filled up by generalisation, and which I can unfold at pleasure. I never could tell how or in what way this germ would develop by any a priori process. No negation certainly of the germ would help me to this. This development is known through intuition or observation and generalisation. It is seen and followed by me, not made merely by my seeing it, far less by my thinking it out from the germ. If I associate the particulars, as they are called, of stem, branch, leaf, &c., with the germ, I do so not from an analysis of the notion of the germ, but from direct experience of what follows in certain circumstances. It is the germ in the soil and under atmospheric conditions whose development I follow, not the germ as germ or seed in pure thought. The germ is here improperly described as a uni- versal at all. It is not a genus or class embracing certain particulars, as organised embraces animal and plant. Or- ganised can be predicated or affirmed of animal and plant. These are the species which it contains, and to which it is applicable. But stem, branch, leaf, &c., cannot be said to be kinds or species of germ or seed. You may say a plant is organised, or has organisation, but you cannot say that a leaf is a germ or seed. That would really be too absurd. And much less could you go the length of saying that the nega- tion of the seed led you to the idea of the stem or branch, or gave you that idea in any way. The seed is not a universal, properly speaking ; the stem, branch, leaf, &c., are not par- ticulars, properly speaking. They do not stand to each other in the relation of genus and species. And as for the indi- vidual plant being the union of the genus and species, the thing is simply ridiculous. Genus and species are united in the individual. Animal and man are united in this man ; but this man is not constituted by the union of these simply. Individuality is something higher than mere membership of a logical class. In this case, the colour red would be an indi- 164 INSTITUTES OF LOGIC. vidual, because it happened to unite the genus colour and the species red. But red, though numerically one colour, is not exactly the kind of indivisible unity which constitutes each of mankind, or even the unconscious plant or tree which lives and possesses its own individual being. 203. It is said in regard to limit in thought that the consciousness of limit transcends limit, that there is only limit in natural or unconscious things, that the moment we reach consciousness of limit, limit itself is destroyed. My answer to this is that so far from consciousness of limit destroying limit, this consciousness of limit is essential to consciousness itself. I never could be conscious unless in so far as I set up limit, either a not-self against myself, or a negative against my affirmation. If in the act of conscious- ness, I transcend limit, I necessarily transcend consciousness itself, and if I do so I pass into the sphere of the meaning- less. You can no more abolish the eternal yes and no in truth, than you can abolish by a mere consciousness of limit right and wrong, virtue and vice, beauty and deformity, in the ethical and resthetical spheres. ''Nay, the very assertion is suicidal. How can I know that consciousness transcends limit, and unconsciousness does not, unless I affirm that consciousness is one thing, and unconsciousness another i.e., unless I proceed on a principle of strict and definite limitation ? I distinguish, define, and limit, in order to show that all limit is really impossible. I seek to show, in fact, that no gun- powder will explode, by using a train of gunpowder which explodes the whole magazine. The truth is, that consciousness or knowledge, as we have it, is possible only under conscious limitation. Our thought is constituted by limitation ; we may substitute one kind of limit for another; but we have no power of transcending limit absolutely, any more than the bird can outsoar the atmosphere. PART II. CONCEPTS AND TEEMS, CHAPTER XV. CONCEPTS AS NAMED TEEMS THEIR PRINCIPAL DISTINCTIONS. 204. Term in the widest sense may indicate either the knowledge of an object (quality) apprehended by Outer or Inner Intuition, an object represented as in Memory or Simple Representation, or it may mark the concept of the Under- standing, whether of an abstract quality, or of a subject (synthesis in one object) of a series of qualities. Term in the stricter sense of the word indicates the logical concept ; and it is extended to individual qualities, or objects, only in so far as these typify a concept whether generalised or uni- versal a priori ; for it is essential to a term that what it signi- fies should be discriminated from what is signified by other terms, that is, it is only applicable where there is discrim- ination and distinction, therefore unity amid diversity, and this is a function of logical thinking. 205. Simple Apprehension is wider than Conception, and has for its object individual quality, image, or concept, merely as a fact of consciousness. In every case, it involves a psychological or existential judgment ; it affirms the reality of its object as a thing apprehended, as subjectively at least real. When Simple Apprehension realises the meaning of a 166 INSTITUTES OF LOGIC. concept, it passes into Conception ; because in that case the concept is thought as representative of an object whether real or ideal, it matters not. The further question as to whether we apprehend, intuitively perceive the quality of an external thing or object, or only an image of it, is a psychological point of importance. But the decision of it one way or another need not affect the character of the act of Conception qua act of Conception. The laws of the act are the same in either case. Simple Apprehension is usually limited to our grasp of the meaning of the concept, as house, man, organised. But there is no reason in the nature of the case why its object should not be the relation involved in a proposition, even that in- volved in a reasoning simply as apprehended, without actual affirmation or negation on our part. In fact, this was the ancient and proper extent of the sphere of Apprehension ; for with the schoolmen term in its widest sense meant what terminates any act of apprehension ; and this may be either incomplex, as individual quality, or simple concept, or complex, as the proposition. While the term subjectively indicates the completion of the intellectual act, objectively as applied to the concept, it in- dicates limitation. A concept implies the limitation of its object through certain attributes, hence the term in language which indicates it has for its essential feature the marking this limitation, this determination, implying distinction from other concepts. Every term thus implies distinction in thought of one concept from another. (a) Occam distinguishes the indicative from the apprehensive act. The object of the latter is a simple or incomplex knowledge of terms, propositions, or reasonings. By the former the intellect not only appre- hends the object, but assents to it, or dissents from it ; and this act regards the complex only, for in assenting we esteem as true, in dis- senting we repute as false. (Sent. Prolog., qu. 10. Prantl, iii.xix. 753.) 206. Words have been divided into Categorematic and Syncategorematic. The former are held to be significant by themselves, the latter 'only consignificant. The former fully signify the thing or concept, the latter do not so much signify as consignify. The noun is categorematic ; the conjunction, preposition, adverb, and several pronouns only syncategore- matic. This is properly a grammatical distinction. In the CATEGOREMATIC AND SYNCATEGOREMATIC. 167 synthesis of words, called Speech, there are words indicating subject and predicate and relations of these. The subject and predicate are, or may be, significant out of relation to each other, as indicating each a quality, qualities, or a class. The words of relation, such as conjunction, preposition, are properly significant in the synthesis or combination called the sentence. The logical copula is, is properly syncategore- matic; it is only consignificant, that is, it expresses a relation between concepts supplied. The relation of course indicated by each of the consignificant words may be made an object of abstract contemplation, but still it subsists only as a relation in some sentence or other, not by itself as an independent or non-sentential object of thought. (a) A categorematic word or term has a definite and certain significa- tion. Thus man signifies all men, u-hiteness all whitenesses. It has a definite suppositio, or representative function. A syncategorematic word has no definite and certain signification, and does not signify any- thing distinct from what is signified by the predicate. As in arithmetic the cipher standing by itself signifies nothing, but added to another figure makes it significant, so the syncategorematic word, properly speaking, is not significant, but consignificant as added to another term. It may even give the predicate determinateness, and enable it to stand definitely for another or others. Such words are alt, none, some, whole, except, only, &c. All, per se, has no fixed signification, but as joined to man makes the term stand for all men. So also are conjunctions and prepositions. Significant is here employed, according to the usage of Boethius, as meaning not merely something determinate, for all, none, &c., are so, taken per se, but as making significant or able to stand in the place of something in a certain manner i.e., giving a term suppo- sitio, or the function of representation. (Sum. t. Log., i. c. 4, p. 8.) Significant and consignificant here are very much equivalent to ab- stract and applied. The syncategorematic word has a meaning of its own, as expressing only an abstract relation, conjunctive or preposi- tional, or adverbial or quantitative ; but as not applied or realised in a definite subject or predicate, it has not yet a representative force. 207. Term has two meanings (1) as distinguished from speech (oratio), it denotes everything incomplex. (2) Strictly it denotes that which, taken significatively, can be the subject or predicate of a proposition. In this sense no prepo- sition, conjunction, adverb, or interjection is a term. These are syncategorematic. These words taken simply or materially can of course be placed as subject or predicate of a proposition. We may say "he reads 11 is a verb, or "all" is an adjective, 11 if" is a conjunction, "from " is a preposition. But thus taken 168 INSTITUTES OF LOGIC. they are not significant, in the sense of standing for or defi- nitely representing anything in a fixed mode. (Cf. Occam, Log., i. 1, f. 2, 2 B.) (a) "Opos est nota, qua unum quid et simplex mente reprsesentatur. (Goclenius, sub voce.) (b) I call that a term into which a proposition is resolved, as the predicate and that of which it is predicated, whether to be or not to be is added or separated. (An. Prior., I. i. ) (c) Occam makes the term " the proximate part of the proposition " (pars propinqua propositionis). (Sum. t. Log., i. c. i.) (d) Speech, according to Boethius, is threefold viz. , written, spoken, conceived, the latter having being in the intellect alone. So term is written, spoken, conceived (conceptus). The concept or mental term is the intention or affection (passio) of the mind, naturally signifying or consignifying something, produced to be part of a mental proposition. Concepts and propositions composed of them are those mental words (mentalia verba) which remain alone in the mind, and which, as Augus- tine says, are of no language, and cannot be externally set forth, al- though articulate sounds (voces) as signs subordinate to them may be outwardly pronounced. Articulate sounds, however, are not properly significant of concepts themselves primarily and properly, but only secondarily of the same things, which are signified by the concepts of the mind. As the concept or affection of the mind naturally, from the nature of the thing, signifies what it does, and as the term spoken or written is according to voluntary institution, the term may change its significate at pleasure, but the concept cannot. In other words, the concept would cease to be the concept it is, or to be significant of that of which it was formerly the concept. 208. The term may be a single word, or a plurality of words. The essential point is the preservation of the unity of the concept, as distinct from the unity of any other concept. That word, or series of words, is properly a term which is significant of the total concept of which the predicate is said, or which is predicated of the subject. Thus we may equally well designate the concept of triangle by the single term triangle, or by a figure bounded by three straight lines. We may equally indicate the same concept by Centaur, or by an animal with the upper parts human, the lower equine. The metropolis of Britain and London, the first man and Adam, signify respectively one and the same object. The con- cept number is that of continuous addition of unity to unity. The concept binary is that of unity coalescing with another unity in one and the same number. 1 These expressions are 1 Wolf, Logica, 34. CLASSES OF TERMS. 169 all equally limitative and distinctive. The single word has the advantages of brevity, convenience, and force. 209. Terms have been divided into various classes, chiefly the following : (1.) Univocal, Equivocal, Analogous. (2.) Singular or Individual, and General or Universal ; corresponding in a measure to Proper and Common Nouns. (3.) Of the First and Second Imposition and First and Second Intention. (4.) Concrete and Abstract. (5.) Connotative and Non-Connotative or Absolute. (6.) Distributive or Sejunctive and Collective. (7.) Definite and Indefinite, or Infinite, Privative and Negative. (8.) Categorical and Transcendental. (9.) Relative and Correlative. (10.) Contrary and Contradictory. (11.) Of Possession and Privation. 210. This division is founded on no clear principle, pro- ceeds, indeed, on the confusion of several points of view. Some terms, such as the Abstract and Concrete, are so from the nature of the concept signified by them. The considera- tion of the distinction thus belongs to the nature of the concept. Other of the distinctions, such as the Univocal and Equivocal, may depend on the accident of the naming of concepts, and are mainly of grammatical import. At the same time, as the term is so often used as equivalent to the con- cept, and its distinctions treated as conceptual distinctions, it is necessary briefly to indicate the meanings of some of the names applied historically in the Classification of Terms. 211. The distinction of terms as Univocal or Equivocal is obviously a grammatical one. A word or term may be equivocal, as Occam has remarked, but not a concept. 1 The univocal term or sign is that which is applied and sub- ordinated to one concept. It may thus be predicated in one and the same sense of the many objects under the concept. The equivocal is that which, signifying many, or having more than one definite meaning, is applied but not subordi- nated or restricted to one concept. In this case there is not one common predicate, but as many predicates as there are 1 Cf. Occam, Sum. t. Log., i. 14, and Wallis, Logica, i. 3. 170 INSTITUTES OF LOGIC. various meanings. Terms may be equivocal, through acci- dent, or by design. 1 As examples we have light; crab (crab- fish, crab-apple, crab-tree, constellation). An Analogous term indicates an identity of relation as opposed generally to an identity of feature or attribute e.g., the foot of a table and the foot of a mountain, the foot of a tree, the foot of a man. The objects in themselves are not resem- bling, but they fulfil similar relations. These terms are only indirectly uni vocal. Besides Analogy strictly taken, Likeness in the things gives rise to similarity in terms. We speak of a blade of grass and the blade of a sword, though these have different functions. We say of a portrait, This is the Queen, though portrait and Queen are only resemblances. Terms of Simile and Metaphor come under Analogy and Likeness. 212. The Singular or Individual term is opposed to the general or universal. The singular is logically that which, indicating an attribute or attributes, is not predicable of more than one object- as Julius Catsar, Edinburgh, Glas- gow. It may be taken as indicating the individual conceived as distinct from others, or from what is thought to coexist in a given moment of time or in another portion of space. The universal term is that which is predicable of many, as man, city, mountain. The Singular or Individual should not be confounded with the Particular, as is generally done. The particular refers to quantity, and is some of all. But it is not identical with the one or individual in fact, is opposed to it as signifying an indefinite plurality. Some men and Julius Ccesar are by no means convertible. As already explained, the universality of the concept, and therefore of the term, is a potential universality. This lies in its being predicable of several or many. Concept and term alike, as each act and name, one in number, and not many, are singular. (a) Logically the terms individuum, supposition, singulare, are con- vertible ; though theologically suppositum means substantia and accidens contains individuum and sinyulare. Individual (individuum) has three meanings : (1.) That which is one in number, and not many. In this sense every universal is individual. (2.) That which exists without the mind, which is one and not many, and is not the sign of anything, as Socrates, Plato. (3.) The sign proper to one, called discrete term. As Porphyry says, 1 Cf . Occam, Sum. t. Log. , i. 14, and Wallis, Logica, i. 3. FIEST AND SECOND INTENTION. 171 the individual is that which is predicated of one only. In other -words, it is not predicated of anything which can stand for many in the same proposition. A sign of this sort is (a) Proper Name, as Virgil, London, (b) De- monstrative Pronoun this is the man, meaning Socrates, (c) Demon- strative Pronoun taken along with a common term, as this animal, that stone. The supposita per se of any common term are demonstrative pronouns taken along with the same term. (Occam, Sum. t. Log., i. 19.) To these may be added designation by Emphasis, through custom or restricting circumstances, as when an Englishman or Scotsman speaks of the Queen, he means one person, the reigning monarch, Vic- toria. The use of the City by a Londoner, of bird, fish, &c., by sports- men, implies either an individual or specific reference. (Cf. Wallis, Logica, L 2.) (6) Occam gives us the true theory of the singular and universal. The singular is that which is one and not many. In this sense, every universal as a quality of mind predicable of many is truly and really singular, just as a word, though common by institution, is really singular and one in number. But if singular mean that which is one and not many, and is the sign of any singular, no universal is singular, for it is the sign of many. There is no universal which is not one in number, and is only uni- versal by signification, as Avicenna teaches. One form in the intellect is related to a multitude and in this respect is universal, for it is itself the intention of the mind, whose operation is not varied wherever you look. In respect of individuals this form is universal ; in respect of the mind, one of whose forms it is, it is singular. A universal, there- fore, is one singular intention of the mind itself naturally fitted to be predicated of many not for itself, but for the things themselves. In this respect, as predicable of many, it is universal ; as a form really existing in the mind it is singular. ' (Occam, Sum. t. Log. , i. 14.) (c) The doctrine of Scotus was that the universal is in some mode without the mind, and in individuals, not indeed really distinct from them, but only formally. Human nature is in Socrates, which is con- tracted to Socrates, by one individual difference, which is, not really but formally, distinct from that nature. Hence there are not two things ; the one, however, is formally not the other. This opinion Occam rejects. (d) The universal of Occam is in the mind, has no existence out of the mind, and is a natural sign of things. The term again is a conven- tional or voluntary imposition of a sign on the universal ; and has no import apart from this. To call such a doctrine Nominalism is a mis- nomer. It is a conceptualism, pure and simple, and it shows how closely the two theories approximated. 213. The distinction of terms of the First and Second Intention has been already explained in connection with the definition of Logic. 1 A word further is required to show their relation to terms of the First and Second Imposition. 1 See above, pp. 34, 69. 172 INSTITUTES OF LOGIC. Impositio and Intentio, as applied to terms, indicate an im- portant scholastic distinction. It is found in Burleigh and Armandus (see Prantl, iii. 584, 629) ; but the distinction of names of the First and Second Intention can be traced at least to Avicenna. Occam has put the distinction precisely. Some names signify things beyond the mind ; others the concepts of the mind ; others significant words themselves ; and there is the ancient distinction of names of the First and Second Im- position. Names of the second imposition are those imposed to signify names themselves, such as noun, verb, pronoun, con- junction, &c. ; in fact, the different parts of speech, as in grammar, though syncategorematic words are sometimes excluded. Names of the first imposition are divided into names of the first, and names of the second, intention. Those of the first intention signify real things ; those of the second concepts of the mind, as genus, species, universal, predicable. These indicate intentions of the mind, which are natural signs, or signs voluntarily instituted to indicate these. Second intentions thus mark what is predicable of the names of things regarded simply, or apart from their application to the things signified, in a word, the classes of predicables, and the abstract relations among the predicable classes or concepts. 1 (a) This distinction may, indeed, at least in matter, be fairly enough carried back to Aristotle, in his discrimination of First and Second Substances. First substance is that which is not said of a subject, and is not found in a subject, as a Man, a Horse. Second substance is the species or genus of first substances. A man is in the species man; man is in the genus animal. Hence man and animal are second sub- stances. (Gat. v., 1, 2.) This corresponds pretty closely to First and Second Intention, and certainly may have suggested it. 214. The proper distinction of Concrete and Abstract is that the latter may be taken as standing for any quality, accident or form, inherent in the subject, as whiteness, &c. ; while the former indicates the subject or object of inherence as well as the quality, as white. At the same time, logically it seems impossible to conceive the quality as a pure abstract ; it must be realised and thought in an individual subject. The difference is mainly a grammatical one. Another application of these terms, already noticed, is that 1 Occam, Sum. Logicce, i. 12. ABSOLUTE AND CONNOTATIVE. 173 the abstract is regarded as that which is higher or superior in the order of generalisation, as animal in regard to man, or living in regard to animal ; whereas the concrete represents the lower concept. The abstract is thus ultimately the highest in the scale of general ideas, the concrete the lowest, the species or even the individual. (a) The scholastic usage in regard to concrete and abstract was much wider than the modern. Three points at least may be noted : (1.) The abstract term was used to stand for any accident or form whatever really inherent in the subject; the concrete for the subject of the same accident or form as lohitoiess, v:hite conversely, fire, on fire. (2. ) The concrete was used to stand for a part, and the abstract for the whole; or conversely as life, living, man is living; he is not life. (3.) Concrete and abstract sometimes stand for distinct objects, of which neither is the subject nor the part of the other, as sign and signi- faate. (Occam, Log., i. 5.) (b) Abstract and Concrete in Hegel have reference to what is called the development of the concept. The concept (Begriff) is a completed idea, which in its unity contains difference. The concept is a sub- stance which contains all its being or properties in itself, and develops this fully. It has thus a number of moments ; these grasped fully constitute truth. Each moment by itself is false. When the concept has arrived at the full development of its moments, it is concrete. Each moment of the unity taken by itself is abstract. It may be re- marked on this, that as at any moment of the development, the concept is not completed, there can be no truth except in the Absolute Idea, and as then all differences are abolished or identified even the finite Ego itself, there is no truth in time at all. 215. An Absolute Term is one which is significant of some one concept or object without anything conjoined to it ; or it is that which does not signify something primarily and also something secondarily, but whatever is signified by it is signified, as -AnznzaT^signifies Horse, Ass, A Connotative Term is that which signifies something primarily and something secondarily. That which it pri- marily signifies is- usually an attribute, and secondarily the subject in which the attribute inheres. 1 (a) In the definition of a connotative name, there is something straight and something oblique. Thus, white means something possessing white- 1 Cf. Occam, Log., i. 10 ; and Goclenius, sub voce. 174 INSTITUTES OF LOGIC. ness. All concrete names of the first order are connotative, as just, white, animated. So are all relative names, as similar, which is denned as that having a quality such as another has, those belonging to the genus quantity, as figure, curvity, &c. Intellect is connotative, inasmuch as it means power and act, so one, good, true, potency, act, &c. (Sum. t. Log., i. x. p. 21.) (b) The concrete term is divided into absolute and connotative, or, which is almost the same thing, into substantive and adjective. Sub- stantive indicates that which subsists by itself, as man, stone, colour, beauty. Adjective is that which signifies a thing as being the accessory of an other, as human, coloured, beautiful. All abstract terms are sub- stantives; although they sometimes signify things which can exist only in a subject, theyyet express them as self -subsisting, as prudence, science, i love. These can be only in a subject, yet in view of the mind they are self-subsisting. They are substantive bjrthe mode of signification. * " (Aquinas, Logica Minor, Pars I. q. I.) (c) This original distinction of Absolute and Connotative Terms is of considerable importance ; and it is unfortunate that in some modern works on Logic the proper use of Connotation has been perverted to designate the comprehension or attributes of a concept. For this we jfc- had already a perfectly unexceptional term, and connotation as thus applied is really misleading. 216. The scholastic distinction of Concrete and Abstract terms does not seem well marked off from absolute and con- notative. It is clear enough that the concrete represents i something different from, or more than the abstract. Thus just and justice are not convertible. jVhilfl \y..can say the just is virtuous, we cannot put justice as the subject of the same proposition. 1 Yet just as' a concept, in its "comprehen- sion, contains no more attributes than, justice. It differs from the latter in its connotation as signifying or consignifying a subject of inherence, or possessor of the quality justice. It is, in fact, the quality of justice conceived as inherent or possessed, that is, as realised in extension. Thus Occam was right in saying that in one respect concrete and abstract names are synonymous. Nothing is signified by man more or other than is signified by humanity, or by Deity than by the term God. 2 217. A Distributive or Sejunctive Term is a term indi- cating attributes common to many individuals, and belonging to each of the class, as life, sensation, motion, to horse, cow, mule, species of animal. A Collective Term indicates the repetition of the same or similar quality in a sum of individ- 1 Cf. Occam, Log., i. 5. 2 Occam, Log,, i. c. 7. CATEGOKICAL TERM. 175 uals, as senate, regiment, army, that is, the quality which makes each a member of the body. These are made up of units repeated, and gathered into one whole. The collective term applies only to the individuals in their totality ; the distributive is applicable to each individual under it. In the latter case we naturally say, Each is or Every one is, All are, in the former, The whole is. We predicate only of the totality, as a singular, or of all considered as one. We can say of a senate or army what we cannot say of each man in it. Man is affirmatively predicable of Socrates, but not mankind. 218. Logically a noun is called dopio-rov, or infinite, better indeterminate or indefinite, by which all things can be named except those named by the finite that is, determinate or defi- nite noun, to which it is relative, as Homo, Non-homo ; l Albus, Non-albus. This distinction is due to Aristotle, but he de- clines to call the indefinite a noun " Not-man\R not a noun, for there is no name which we can apply to iT; it is neitner an affirmation nor a negation ; it is that which I would call an |nde^erminate noun, because it agrees equally to all, to being and to non-being." 2 Not-man, in other words, has no real determination ; it designates all which is not the thing or concept spoken of, but it determines nothing. 3 __ i Boethius translated dopicrrov by injint^uM-^ -not a suitable word. Hamilton gives in^ffifffnf 1 ^ The true place of the indeterminate term in Logic will be considered in the sequel. 219. A Categorical Term is any term comprised in Ten Categories of Aristotle. A Transcendent or Transcen- dental Term is one that designates a notion above or beyond the Categories. The Pseudo-Thomas gives six transcendentia viz., Ens, Res, Aliquid, Unum, Bonum, Verum. Res and Aliquid are new. The others are given by Aquinas. 4 ^gidius Romanus holds these six to be in the knowledge common to all things, and as belonging to the first conceptions of the intellect. 5 With the schoolmen the transcendental term was held not only to transcend, but to include the categorical- term or terms. 6 1 Cf. Goclenius, sub voce, 2 De Int. , ii. 4. Waitz omits the last two clauses. 3 Cf. St Hilaire, in loco. 4 Opuscula, 42 f, iv. B. : see Prantl, iii. xix. 274. 5 See in Prantl, iii. xix. 355, p. 257. 6 See Aquinas, Logica Minor, pars i. q. 1. 176 INSTITUTES OF LOGIC. Kant borrowed the terms, and gave each a different and both a new signification, though there is a hint of his meaning of transcendental in JEgidius Romanus, quoted above. Trans- cendent with Kant means what is entirely beyond experience, as given neither in a posteriori datum nor a priori form, and thus beyond the categories of thought, beyond knowledge in fact. Transcendental means with him the a priori or neces- sary conditions of knowledge, which as such transcend the contingent or adventitious data of experience, yet constitute the knowledge we have. 1 220. A Kelative Term is said to be what it is by reference to something else, or some other term. Thus, double is double of half. 12 Father and child, debtor and creditor, are ordinary relatives, and make up a complete thought. The term from which we start in apprehending a relation may be called the Eelative, and that to which it is related the Correlative or Correlate. Subject is the relative ; object the correlate. But . each term may in turn be relative or correlate thus, Father and Son, relative and correlate ; or Son and Father, relative and correlate. The true conception of Eelation implies (1) Two terms, and (2) these apprehended in the way of constituting ^a whole, of which they are the parls, and which cannot be con- ceived as a whole without each of the terms. Relatives are the terms of a sundered totality, which is unthinkable apart from the union of the terms. Thus King and Subject, Half and Double, Height and Depth. These terms integrate or make up a complete thought. 221. But relatives are not properly mutually convertible. For the relation regarded from the one side is not identical with, nay, is the converse of the relation viewed from the other. The relation, for example, of Creditor to Debtor is precisely the reverse of the relation of Debtor to Creditor. You owe me, I owe you. Owing to me is not possible with- out obligation by you. The two terms are necessary, but the relation, respectively viewed, is by no means the same. The debtor side may here be regarded as the correlation. For the positive ground of it is, say, money lent, first of all, as a matter of fact. Thus the relative is constituted as against 1 Kritik, passim. Cf. Hamilton, Reid's Works, p. 762. 2 Cf. Aristotle, Cat. x. RELATIVE TERMS. 177 the correlative, in this case the respondent or defendant. So the relation of Father to Son, is not convertible with the relation of Son to Father; the one is the converse of the other. So with Ruler and Ruled, Master and Vassal. The relation of the ruler is that of authority, the correlation of the subject is that of subjection to authority. The master orders, the vassal or servant obeys. 222. In simple relation the essential thing is a term, rather concept, positive and determinate, to begin with. Yet when explicated, or in determining it, this is found to imply another term, or concept, ere we can put meaning into it. Thus Uncle is meaningless, unless as we know he is uncle of Nephew or Niece ; and so Nephew or Niece is meaningless, unless as we know Uncle. But Uncle is first of all a deter- minate concept implying all the attributes of man, and only on the ground of these is the relation, wholly accidental, of man as uncle to nephew or niece realised. The relation is possible, through a previous concept or reality ; the relation in no way constitutes this, is, in fact, dependent on it, and this underlying positive or object would remain, whether the accidental relation were constituted or not. So that relation between terms or concepts never constitutes the reality of the term or concept ; but is possible only through a definitely apprehended or comprehended object. As has been said, "relation is the accident of a thing, not considered abso- lutely, but as compared with some other thing. Its essence depends on comparison." l In fact, relation, ultimately ana- lysed, means one of the accidents or properties of an object or concept. And the whole idea of reducing reality to relation is as suicidal in expression as it is untrue in point of fact. "There is a great difference," says Aristotle, "between a thing being relative, and a thing being that which it is, only because it is said of another thing." Head is head of gome one, but its being does not consist only in this relation^" asJjflSj^MJgjjjgf jp frying fat ( TiBr fa son? Even In regard to^, simple relatives, we. cannot know anything to be relative, until we know that to which it is relative, and in what respect it is so relative. If we know a thing, as Aristotle remarks, to be a double, we must know that of which it is the double. If we know ten to be the half of another number, we must i Wallis, Log. i. 10. * Cat. vii., 26. M 178 INSTITUTES OF LOGIC. know that it is twenty of which it is the half, and so on. If we know a thing as greater we must know that which is the less of the two. But this applies in a very limited way to the objects of knowledge. We may know an object, whose reality^aa an object does not in the least consist in the circumstance 01 its being a mere relation toTanotaer "bBject, or depend on a relation of reciprocity in reality or cogni- tion. In fact, mere being in the relation is not possible in existence, it is possible only as it is grounded by a definite or positive something which founds the relation. And the true place of relation alike in knowledge and being is the secondary one of property or attribute or reference to some other thing. All or even the ultimate relations of a thing we do not and can never know, its relations to all actual, far less possible, objects of experience. We may have a perfectly definite knowledge of an object without any pretension of this sort. The primary metaphysical relations are the necessary modes in which objects exist for us and are known by us. But these even do not constitute the objects ; rather the objec- tive, whatever that may be, constitutes them, is their real ground, and manifests itself through them. To say gener- ally, as is done, that every object of experience is a relation, or constituted by a relation, is to assume the possibility of a relation, while there are not two terms or objects to be related. A relation in an object is either between the parts of the object itself, or between it and another object. In either case, . the relation is grounded in something beyond itself, whether this be a point or object directly cognisable by us, or whether we have to pierce backwards to something which is only known to us in the manifestation of the terms of the relation. Mere relation, as an object of experience or knowledge of ex- perience, is a pure and simple contradiction. Kelationis only possible through things related ; and its reality is founded on them. (a) Founding on Aristotle, relatives are said to be twofold, some are secundum did, others secundum esse. The essence of the former does not lie in mere relation ; the essence of the latter does so lie that is, there is nothing in them besides reference to another in some mode. E.g., scientia et scibile, cognition and object, are relations secundum did, for cognition is a real quality or act ; so perception and percept, so quantity and quality. But other relations such as master and servant, father and son, husband and wife, are secundum CONTEAEY AND CONTEADICTOBY TEEMS. 179 esse ; for the essence of each relation is in the mere relation of master to servant, &c. , and is nothing apart from this. Again, there are four things to be distingiiished in Relatives viz. , Subject, Ground, Term, Relation. Subject is always different from Term in real relatives e.g., Virgil is the author of the ^Eneid. Here we have (a) subject in Virgil, ground in production, term in JSneid, relation in authorship. (Cf. Duncan, Inst. Log. L. i. c. viii.) In the distinction of relatives secundum did and secundum esse, there seems to be a confusion between the fact of the existing relation, and the possibility of the subject of it entering into other similar relations with different terms. Every relation qua relation is that which the subject has or shows -in a definite aspect. The relation of knowledge and the relation of service, even of double or half, are equally the definite or specific relations of two things, and subsist only through these ; though the subjects of them are not necessarily either identical with the relation or exhausted by it. Mere or pure relation as identical only with itself is an abstraction. (b) In the case where an antecedent is supposed, and where what follows is limited or depends upon it for its place and import, we have more properly relation than correlation. This is chiefly the case in what are known as grammatical relatives e.g., The house which stands there. Here house is antecedent, which is its relative. But which has no force apart from the antecedent. These are not properly cor- relatives ; for -they are of unequal import and not convertible, so as still to preserve the knowledge of the relation. The latter supposes the former, but they cannot change places as in proper correlation. (Cf. Note by Latham on Correlation, Johnson's Diet.) 223. Contrary Terms indicate concepts or qualities that are most oppoeed in the same class, or general conception as good ana evil, jiist and unjust) wise and foolish. 1 But these are not connected or opposed as relatives propei\_ j _JxP' vj * a uble ofhalf^ And con- fV|fl 0aMLfl^adLM!auAfc i* the dou trades do not make up the total thought as simple relatives do. We can think what is good, a good, say, truthful- ness or justice, without thinking untruthfulness or injustice as a part of it, as a necessary constituent of our complete thought of it, while we cannot think a double without tbink- ing it the double of the half. When we think justice we do think injustice, but not as a part of justice. When we think the double, we do think the half as an essential part of the^ double. This is the only analogue of the Hegelian other; every- thing is also the other of itself. But it applies only to a few limited relations, chiefly verbal, and in regard to these it is but a poor and inaccurate expression of the fact. In regard 1 See Aristotle, Cat. vi.; Met. \. 10. 180 INSTITUTES OF LOGIC. to the whole wide sphere of thought and experience, espe- cially contrary opposition, it has no application, and is the merest illusion of verbalism. 224. Contradictories as terma relate only to concepts, and they are usually marked in language by not, or its equivalent. The essential feature of contradictory terms is that they can- not be combined in the same indivisible act of thought, they are mutually exclusive, and if the one is thought, the other is sublated. Thus man and not-man, mortal and im- mortal, being and non^ing, are contradictory terujs. These cannot be joined in one thought -of an- object. In contra- dictories a first or positive concept or cognition is always presupposed ; and the contradictory may be of two kinds. (1.) It may be the mere indeterminate concept of negation, indicated by not or its equivalent, which only precisely sig- nifies the negation of the positive and nothing more, yield- ing no determinate or significative concept, as one and none, being and not-being. (2.) The contradiction may be a positive, like that which it contradicts. Mortal may be contradicted by immortal, life by death existence at a given time by existence at another time the equality of the three angles of a triangle to two right angles, by their (alleged) inequality less or more. (a) In the former kind there is nothing positive. When we say non-ens est ens, this is true only as far as non-ens represents the term of a proposition, but not as taken significatively. One opposite even may be predicated of another simply or materially, but not significa- tively i.e., as standing for a definite object Non-dictio est dictio, Non-pars est pars, Non-vox est vox. (Cf. Occam, Log., i. 36.) (6) With Aristotle the term TO, avriKei^tva. does not necessarily imply contradiction. It designates the two corresponding terms of a definite relation. It may be translated by Correlatives. Of these Aristotle makes four classes : (1.) Those of Simple Relation (rh irp6s TJ), as double and half. These have only a reciprocal reality. Each is dependent on the other in thought and in fact. This is not the case in any of the three classes following (2.) Contraries (T& ivarrtd), as good and evil. These cannot be in the same subject together in the same respect, but may be in the same subject in succession. (3.) Possession and Privation (efts /cai avat, quinque voces. What we say of a subject is supposed to be found under one or other of those heads. What each has in common is that it is predicable of many. This classification is due to Porphyry, as given in the Eisagoge to the Categories of Aristotle. 2 1 Eisagoge, v. 3. 2 See Eisagoge, i. 1 et seq. 202 INSTITUTES OF LOGIC. (a) In the view of Aristotle there are four Predicable classes, or the Four Differences (airer-rapes Statpopa.}) viz., Definition, Genus, Property, Accident. Definition (opos, 6pnrfj.6s) expresses the essence or essential qualities of the thing (rb ri ?>v eli/at). Hence, in the proposition, the subject may be put for the predicate or the predicate for the subject. A square is that which has all its sides equal, and all its angles right angles. This as a definition is convertible. Genus (ytvos) is that which is attributed essentially to several objects which differ in species. An essential attribute is that which answers to the question What is the object? Thus, What is man? The answer is conveyed by the genus animal. Here the subject and predicate are not reciprocally convertible. Animal is a part of man, but it is wider than man. Property (rb fSiov) does not express the essence of the thing ; but it belongs to the thing alone, and can be taken reciprocally for it. Thus the property of man is to be able to learn grammar : if he is man he can learn grammar, and if he can learn grammar he is man. We should not call that property which might belong to another thing ; we should not say that to sleep is the property of man. Here there can be no reciprocal attribution or substitution. Accident ((rv;uj8ej8jK<$s) is that which may or may not be in one and the same thing. Thus, to be seated, may or not be present in one and the same person, and so whiteness. Aristotle did not regard Difference as a kind by itself. Difference, in so far as belonging to the Genus, should be classed with it. It is the limit which separates one genus from another, and can be predi- cated of several species. (Topica, i. c. 3, 4, 5, 6.) Ether may be regarded as an imponderable fluid with an undulatory motion. If undu- latory motion be taken as the difference of ether from say mechanical motion, it may yet be regarded as the concept of a species of mo- tion, which is capable of being predicated of other objects besides ether. It is obvious that the distinctions of difference and property are relative, and are not always capable of accurate grounding. Of accidents belonging to a class, the inseparable are those which are found in all the members simply as a matter of experience, the separ- able only in some. An inseparable accident of an individual, such as native of London, is predicable of the subject always. What attributes are essential, what are properties, and so on, can at the best be deter- mined only on extra-logical grounds. '254. Notions in Comprehension may be further viewed as in the relations of Involution and Co-ordination. Involu- tion corresponds to Subordination in Extension : " One notion is involved in another, when it forms a part of the sum total of characters, which together constitute the comprehension of that other ; and two notions are in this quantity (comprehension) co-ordinated, when, whilst neither DISPAEATE AND DISCRETE NOTIONS. 203 comprehends the other, both are immediately comprehended in the same lower concept." x The example given is the notion of the individual Socrates. This contains, among others, son of Sophroniscus, Athenian, Greek, European, man, animal, organised being, &c. Of these, some are given through the others. Socrates is Athenian only through son of Sophroniscus, only Greek as Athenian, only European as Greek, only man as European, only animal as man, only organised being as animal. These characters, as given in and through others, stand to those others as parts to wholes ; and it is only on the principle that part of the part is part of the whole, that the remoter parts are parts of the primary whole. 2 But how, it may be asked, is this relation known ? There is no a priori connection between son of Sophroniscus and Athenian. Being son of Sophroniscus does not tell me that Sophroniscus was an Athenian, or being an Athenian does not tell me on any logical principle of whole and part that Athenian was Greek, and so with the others. There is no connection of whole and part here at all, but of one attribute involving another through a mere contingent happening or experience. There is no reasoning here possible on the principle of the dictum of Aristotle, that is, from whole to part. This point will be more fully discussed when we come to treat of Seasoning in Comprehension. 255. " Notions co-ordinated in the whole of Comprehen- sion are, in respect of the discriminating characters, different without any similarity. They are thus, pro tanto, absolutely different ; and, accordingly, in propriety are called Disparate Notions. On the other hand, notions co-ordinated in the quantity or whole of Extension are, in reference to the objects by them discriminated, different (or diverse) ; but, as we have seen, they have always a common attribute or attributes in which they are like. Thus they are only relatively different (or diverse) ; and, in logical language, are properly called Disjunct or Discrete Notions." 3 As an illustration of Disparate Notions, we may take oviparous and warm-blooded as co-ordinate parts of the com- 1 Hamilton, Logic, L. xii., par. 44. 2 Ibid., par. 44 et seq. 3 Ibid., par. 45. 204 INSTITUTES OF LOGIC. prehension of bird. These are relative and correlative, but not involved in each other. Oviparous is not always warm- blooded; and warm-blooded is not always oviparous. 1 (a) This view of Disparates does not coincide with that of the earlier logicians. Disparates are in extension as well. Thus Disparates are those concepts which are only diverse from each other, and not opposed as contraries, as earth, vestment, fire. (Boethius, De Syll. Hyp., p. 608.) (b) The difference between Disparate and Opposite Concepts lies in this, that the former are only mutually repugnant, as when one is opposed equally or in the same mode to many, as man to ox, horse, dog, lion, and other species of animal. Opposition arises when one is opposed only to one. (Cf. Wallis, Logica, i. 16; Duncan, Inst. Log., Lect. i. , xiv. 2 ; Dounam in Kami Dial. i. , xiv. ) Avarice, as opposed equally to liberality and prodigality, would be taken as representing Disparates ; parent and child, good and bad, see- ing and non-seeing, Contraries, (the latter rather contradictories.) But this principle obviously does not hold universally in simple contraries. Of colours, red is equally opposed to green and yellow; of figures, triangle to square and circle. In contradictories alone does the principle hold completely, and in relatives and privatives as these approximate to contradictories. 256. Concepts are, in respect of their Quality, regarded as Clear and Obscure, Distinct and Indistinct. A concept is clear when in our consciousness of it we are able to distin- guish it as a whole of attributes, from another or other concepts. It is obscure when we cannot do this. A con- cept is distinct when we can distinguish from each other the various attributes or marks which make it up. It is indis- tinct when we cannot do this. Obscurity and indistinctness may arise from defect on the part of the individual think- er. In some cases it arises from the nature of the object thought about. In the case of some mathematical figures, we have both a clear and a distinct knowledge. We can dis- tinguish triangle as a whole from square, and both from circle; and we can further specify the marks by which we are able to do so, and make them distinct to others. We can distinguish buildings of Norman and of Early English architecture from each other, and specify the discriminating marks of each. But it is quite possible for us to have a clear concept of an object, which is yet indistinct. We can quite well discriminate red, white, and green from each other; but it would puzzle us to tell the marks or express them to others. 1 Hamilton, Logic, L. xii. CLEAR AND DISTINCT NOTIONS. 205 Shades of the same colour can also be discriminated, but not by specific marks : so with sounds, tones of the voice, and different odours. The mind of average capacity and activity is satisfied with being able to distinguish things as wholes or in a general way ; it is only the active, scientific, or philo- sophical mind which seeks distinct knowledge. Descartes laid down Clearness and Distinctness as the criterion of true knowledge. " I call that clear which is pres- ent and manifest to the mind giving attention to it, just as we are said clearly to see objects when, being present to the eye looking on, they stimulate it with sufficient force, and it is disposed to regard them ; but the distinct is that which is so precise and different from all other objects as to compre- hend in itself only what is clear." l This criterion is, however, ambiguous in its applications. When it is said that whatever we clearly and distinctly con- ceive is true, we may mean that it is possible, that is, an ideal possibility; or we may mean that it is real, that is, a matter of fact or existence. Leibnitz much more fully and precisely indicates the various degrees of our conceptual knowledge. 2 According to him, cognition is obscure, when the object is not dis- tinguished from other objects or the objects around it. Here the object is a mere something, not nothing ; but what it precisely is, either in its own class of things, or as contrasted with other things, we do not apprehend. Cognition again is clear when we are able definitely to comprehend the object as in contradistinction from others. Clear Cognition is further divided into Confused and Distinct. Tt is confused when we are unable to enumerate the marks or characters by which the object is discriminated from other objects, while it yet possesses such marks. Thus we can distinguish colours, odours, taste, from each other, yet we cannot specify the marks by which we do so. At the same time such marks must exist, seeing the objects are resolvable into their respec- tive causes. Our knowledge again is distinct when we can specify the discriminating marks, as the assayers in dealing with gold ; and as we can do in the case of number, magni- tude, figure. But distinct knowledge may still further be 1 Principles, part I, 45, p. 212. 2 De Cognitione Veritate et Ideis, Erdmann, p. 19. 206 INSTITUTES OF LOGIC. Inadequate or Adequate. It is inadequate when the dis- criminating marks are not analysed or resolved into more elementary notions, being sometimes clearly, and sometimes confusedly, thought, as, for example, the weight and colour of gold. Knowledge, again, is adequate when the marks in our distinct cognition are themselves distinctly thought, that is, carried back by our analysis to an end or termination. Whether any perfect example of this exists is, in the view of Leibnitz, doubtful. Number is the nearest approach to it. Then there is the distinction of the Blind or Symbolical and the Intuitive in cognition, the former being the potentiality of conception which lies in terms ; the latter being the clear and distinct or individual picture of each mark so lying undeveloped. When cognition is at once Adequate and Intuitive, it is Perfect. But Leibnitz hesitates to say whether such can be actually realised by us. Adequate knowledge involves cognition through means of a priori possibility. But " whether such a perfect analysis of notions can ever be accomplished by man whether he can lead back his thought to first possibles (prima possibilia) and irresolvable notions, or, what comes to the same thing, to the absolute attributes of God themselves viz., the first causes, I do not now dare to determine." l 1 De Coy., se__attributes ;we specify, we rnay explain, even n1aggifv I jf ntf. -fJannfl. by negation. 1 Thus we can give knowledge and classify scientifically organised and non- organised, vertebrate and in- vertebrate, phanerogamic and cryptogamic, that is, flowering and flowerless plants, rectilinear and not-rectilinear. So in regard to the terms finite and infinite, or non-finite ; here knowing /O what the finite is, or at least knowing certain positive attri- butes of it, we can in a way, or negatively, know what that is which is conceived as devoid of those attributes. So with personal and impersonal, relative and absolute. 269. (3.) There should be no circle in the proposed Defini- tion, or what is contained in the clause defined should not be repeated in the clause defining. As the one clause is thus defined through the other, we have what is called Diallelon (8C oAA^Awv), or " circulus in definiendo." Thus to say that law is a lawful command, or that plant is an organised being possessing vegetable life, or life is a vitalising power, is to define in a circle. There is here no explication of the subject de- fined. " Concealed circular definitions are of very frequent occurrence when they are at the same time mediate or remote ; for we are very apt to allow ourselves to be deceived by the difference of expression, and fancy that we have declared a notion when we have only changed the language." 2 270. Other rules that the definition should be precise in terms, perspicuous and direct, that is, not ambiguous, figura- tive, or metaphorical, are cautions mainly regarding the use of words, in so far' as this may aid or hinder us in attaining clearness. The readiness with which people are impressed by figurative and metaphorical words, when the object re- quires direct and unambiguous thinking, is a proof of how far the average culture of intelligence is, in our so-called civilisa- tion, below the normal standard. 271. Description is usually made up of what are known as Common Accidents, that is, attributes which distinguish the object or species from others that come under the same general class. K^is in fact a characterisation of the object, through comprehension, or specifying its marks. Description refers chiefly to the characteristics of individuals, as each the sum of its own marks. The laws of 'Description fall to be l Cf. Hamilton, Logic, L. xxiv. --^ 2 Ibid. ** f l X LIMIT OF DEFINITION. 215 treated of under the Science of Literary Criticism, or Rhetoric. It will be found, however, as a general rule, that the best masters of description in verse or prose, follow consciously or unconsciously certain very definite rules, which are quite capable of being specified. First among these is the principle of general picturing or outline, and then the gradual filling in of characteristic features with a view to the unity of real pres- ence. Even the most picturesque description never loses sight of, far less violates, those definite laws of imaginative construction. Take Scott's ballad of Rosabelle, follow it, note the commencement, and watch the gradual evolution of the picture, and this will be found to be true : " O'er Roslin all that dreary night, A wondrous blaze was seen to gleam ; 'Twas broader than the watch-fire's light, And redder than the bright moonbeam. It glared on Roslin's castled rock, It ruddied all the copse- wood glen ; Twas seen from Dryden's groves of oak, And seen from caverned Hawthornden. Seemed all on fire that chapel proud, Where Roslin's chiefs uncoffined lie, Each Baron, for a sable shroud, Sheathed in his iron panoply. Seemed all on fire within, around, Deep sacristy and altar's pale ; Shone every pillar, foliage-bound, , ^ And glimmered all the dead men's mail." > 272. The limit of Definition is met with at the simple idea, that is, a concept which does not contain a plurality of attributes, as time, extension, being. Here there is no higher genus. At the same time we must not suppose that such notions are not distinguishable from other notions. But in order to this they must be given in intuition. This readily founds a judgment of Difference, though the grounds of it are not always expressible in terms. Logic carries us to the thresh- old of the real, but is there arrested. - No form of words in which oral Definition or even Descrip- tion can be couched is adequate to all the objects of the senses. The intuition or presentation of the quality is here 216 INSTITUTES OF LOGIC. indispensable, and it is the mode of conveying the clearest and most distinct knowledge ; omnis inluitiva notitia est de- finitio. We are thus enabled actually to experience the per- ception or sensation. This holds of colours, as red, blue, yellow; of light, brightness, and darkness; of tastes, odours, sounds, &c. indeed of nearly every sensation and percept. 273. All Division supposes a whole of some sort, and we must distinguish simple Partition (aTraptfyiT/o-is), real or ideal, from Division Proper (Statpeo-ts). In the former case we sunder the whole, generally individual, into its con- stituent parts, as when we divide a tree into root, trunk, branch, leaf, or such elements as make up the whole. We may do this really or ideally only. Logical Division, on the other hand, deals only with a uni- versal, that is, where there is a plurality of objects or classes contained under the concept. And it draws out or specifies the classes thus contained. The tree, logically divided, would give, say, deciduous and non-deciduous, and these again oak and pine. In the case of simple partition, the name of the whole is not predicable of each of the parts. Tree is not predicable of root, or trunk, &c. In the case of logical division, it is so predicable. Tree is predicable of deciduous and non- deciduous, otpine and oak. 274. As Definition refers to the comprehension of a notion, and serves to make the meaning clear, so Division refers to the extension of a notion, and serves to make our meaning distinct. A notion is clear when I can distinguish it as a whole from other notions ; a notion is distinct when I can enumerate or specify the sub-notions or classes contained under it. Division draws out these. 275. In Division you will find that we come to a point or object which cannot be further divided. This is the individual (aro/xos, individuum) i.e., literally what is indivisible, or that notion or name which can be predicated only of one subject, not of a plurality. The individual cannot be logically divided, because it contains no species under it. Glasgow cannot be logically divided, for it contains no lesser Glasgows, no classes under it. This or that house cannot be divided, for it is one, logically one. It is only the universal which you can divide. You may enumerate the parts physical or other of which this city is composed, the parts of which this tree DIVISION. 217 is composed ; you may describe each, but you cannot logi- cally divide either. 276. Logical division cannot proceed until a principle of division is selected from the whole. This may be either one of the constitutive features of the concept, or it may be the relation of the concept to some end or aim which we select or have in view. The law of Logical Division is strictly that of Non-contradiction. Starting from a given attribute, we divide into the classes under it, through its opposite or con- tradictory. Thus, taking animate, we fix on sentiency, and divide into the sentient and the non-sentient. What are the non-sentient under the genus, or whether they actually are at all, is to be determined, not by the logical law, but by experience. Still, the ground of exclusion lies there in the element of opposition or contradiction ; and but for this no progress were possible. " Contradictio est mensura omnis oppositionis." l We may divide plants into flowering (Phanerogamic] and non-flowering (Cryptogamic). The latter we may again sub- divide, according to subordinate differences, into ferns, mosses, lichens, fungi, algce, &c. But what these are, or how many, is not determinable by any law of pure thinking. Take what is known as Porphyry's tree : Substance. Corp (Be Ani (Ani Sen (Am Rati (M oreal dy) Incorporeal Spirit (Angels, Souls, &c.) mate mate) Inanimate (Water, Stones, Minerals, &c.) 1 ient mal) 1 Insentient (Plant) 1 onal an) Irrational (Brute). Plato, Socrates, Paul, Peter, '- John, Richard, &c. 1 Duncan, Inst. Log., L. i., xiiL 4. 2 Eiwgoge, ii. 23. 218 INSTITUTES OF LOGIC. Again, heather is of the genus flowering plant, and under Octandria i.e., it is a plant bearing flowers with eight stamens, and, under this class, with one pistil. Under this genus (Mono- gynia), it is but a co-ordinate species. As a genus, Erica, it has certain marks, calyx inferior, four-parted, persistent, corolla monopetalous, &c. Under this we have various differ- ences, which mark out the species, as anthers with two simple bristles at the base, &c. This gives the cross - leaved heath (Erica tetralix). Anthers with two serrated appendages at base, &c., gives the fine-leaved heath (Erica cinerea) ; and finally, through difference of leaf and capsule, we have the common heather (Erica vulgaris, Galluna vulgaris). 277. In a concept, this or that feature may be fixed on for the principle of Division. Taking the corolla of a plant, and looking to the tube, it may be long or short, as in prim- rose, bell-flower. The throat may be open or closed, as in digitalis, snap-dragon. The limb may be erect or spreading, as in hounds-tongue, primrose.^ Book I may divide according to its subject, its size, its antiquity. All are equally valid divi- sions, provided I preserve the feature or principle from which I start. Of course no principle of Division is of any real use which is not a constitutive attribute of the whole. 278. The rules of Division are specially as follow : (1.) There ought to be a regulative principle in the Divi- sion. (Divisio ne car eat fundamento.) (2.) There should be but one principle in one Division. (3.) The principle should be an actual and constitutive attribute of the whole to be divided. (4.) No predicate in the division must, per se, exhaust the subject. (5.) The dividing members must together exhaust, and only exhaust, the subject. (6.) The divisive members must be mutually exclusive, that is, there must be no cross-division. (7.) There should be no leap in the division, but a descent from immediately higher to immediately lower classes. 2 Thus, for example, to illustrate the main rules, take the notion figure. I wish to enumerate its species. To do 1 Cf. Hoblyn, Botany, p. 2 Cf. Hamilton, Logic, L. 43. ILLUSTRATIONS OF DIVISION. 219 this, I must find a principle of Division. Here the natural principle is straight or curved line. Taking this, I first divide figure into rectilinear and curvilinear, i.e., straight - lined figure and curved-line figure. But I have not yet made my notion distinct enough. What are the sub-classes under rectilinear figure ? According to the number of sides triangle and square. Under curvilinear figure, I draw out circle and ellipse. My division of figure is now distinct. I know what object or classes of objects it denotes or contains in its extension. And observe that this division proceeds in a regular order from the widest notion to the narrower ones, from the Genus Summum or highest class to the Species. Figure is widest or highest notion ; rectilinear and curvilinear is the next, narrower ; triangle or square still narrower than rectilinear ; circle or ellipse narrower than curvilinear. This is an important principle in Division, viz., that of preserv- ing due subordination, making no leaps in the Division over intermediate classes. If I had divided figure into triangle and circle, I should have made a bad division, for I should have omitted the intermediate classes. 279. One most important thing in Logical Division is to have a principle of Division, and to keep by it. Otherwise the whole division will get into confusion. Suppose, for example, I were to divide the notion man or mankind into Englishmen, Frenchmen, Scotsmen, Episcopalians, Roman Cath- olics, Presbyterians. This would be a bad division ; for the members of the division are not exclusive of each other. An Englishman may be an Episcopalian, a Frenchman may be a Roman Catholic, and a Scotsman may be a Presbyterian. To avoid this, we must keep by one principle of Division ; state it distinctly. We may divide book according to its sub- ject, historical, philosophical, scientific, according to its lan- guage, French, English, Latin, Greek, and so on. But we must not mix up those principles of Division ; for the parts of the division as inclusive, would be inconsistent with the nature and process of division itself. This fault is what in Logic is called a Cross Division. PART III. OF JUDGMENT. CHAPTER XVIII. THE NATURE OP JUDGMENT COMPREHENSIVE AND EXTENSIVE. 280. Every act of consciousness is a judgment, or judg- ment is involved in every mental act. As I am conscious, I am conscious of some thing or object some definite thing, and this I distinguish from another act of conscious- ness which had for object something different from the present. There is here affirmation, and there is negation. Consciousness is thus primarily a judgment or affirmation of existence, that some thing is. This form of judgment, the existential, is prior to the judgment which is a form of comparison. Through the latter process, based on the former, we grasp resemblances in several things, and group them into classes. We may then compare the classes, or the concepts of the classes, i.e., the attribute or sum of attributes which make up each concept, and judge them to agree or not, to be technically congruent or conflictive. We may compare the individual as a presentation with the concept, and include or exclude it as a member or not of the class. This would be logical judgment. Here we look, in the first place, merely to the congruence of attributes ; or we look, in the second place, to the relative coincidences of objects as members of EXISTENTIAL JUDGMENT. 221 the class. We may say This thing I see is now and here. I /eel cold. These are existential judgments, and have a reference to a definite time and definite reality. I might say, the river runs, man is organised, and the three angles of a triangle are equal to two right angles. These are logical judg- ments. I do not require the actual existence of the objects, or imply them. I merely state a congruence or coincidence between two concepts, or a concept and its property. (a) This distinction was foreshadowed in the enunciatio apprehensiva et judicativa of Scotus and Occam. The former referred to the appre- hension of the relations, say of likeness or equality among sensible or immediately perceived objects ; the latter, to notions compared by the intellect. The existential judgment is clearly recognised by Biel, Sup. Sent. q. 1. Prol. (b) Mill is pleased to say that to hold both those forms of judgment the existential and the logical is " the very crown of the self-contradic- tions which we have found to be sown so thickly in Sir W. Hamilton's speculations." The crown here of the sown contradictions is evidently a vegetable product. But how the self-destroying contradictions have had vitality to grow even a crown, we are not told. The existential judg- ment is, it appears, not a comparison of concepts or of an individual and a concept. The self-contradiction only emerges as a spectral illusion, because Mill will insist that Hamilton, in his Logic, is not speaking of the character of logical judgment, of which he is there bound to speak. Besides, Hamilton would probably have told Mill that, in the existential judgment this is here, that is there, I am conscious of heat or cold we do compare and contrast an individual and a concept, though we at the same time in such an act go beyond this, and relate them to a given time and space. He would probably have added that, while we do not get the judgment / am conscious, from a comparison of concepts, self and being, the consciousness of these is there all the same ; and that the logical judgment is reflectively reached in the moment in which the real judgment is given. They are in fact implicative ; and were there any logical confliction in the concepts, self and being, there could be no real judgment or union of them. So far, then, from its being a crowning contradiction to hold the two together, it would be a crowning absurdity not to hold them together. Logical judgment is secondary and reflective ; it presupposes the consciousness in the exis- tential judgment of the special forms of existence, afterwards to be reflectively realised as categories, and even of features to be generalised into classes of objects. 281. It is clear from this that judgment, that is, logical judgment, in no way implies belief in the reality or existence of the subject and predicate as facts of experience, or in the truth of the relation of congruence or confliction expressed in the judgment. We are here dealing with judgment simply 222 INSTITUTES OF LOGIC. as judgment, or with what is essential to it as an abstract act, or in its abstract possibility. Its conditions are congru- ence or confliction of subject and predicate, viewed in com- prehension. Judgment thus considered obviously does not involve belief at all in the reality corresponding to the judg- ment. We cannot disbelieve, unless we have a judgment before us ; but we may have a judgment before us, and neither believe nor disbelieve in the truth of it as a statement of experience. That the notion of man agrees with the notion of organised, or that man is organised, I can quite well assert, without believing or disbelieving that there are men in the world at all. That equilateral is equiangular, I can quite well assert, though I know no objects of experience corre- sponding to the one or the other. So I can say that lying is dishonourable, though I may know no one who is telling a lie in the world at the present moment. That the Dodo is so and so characterised, I can assert, though I suspend my belief as to whether the species is extinct or not. As Occam said : I may know that a stone is not an ass, though I do not know that there is either stone or ass at this moment in the world. (a) Mill challenges Hamilton's definition of judgment, on the ground that Belief, meaning belief in the objective reality of the judgment or thing judged of, is essential to a judgment. " The recognition of it [the judgment] as true is not only an essential part, but the essential element of it as a judgment ; leave that out, and there remains a mere play of thought in which no judgment is passed. Every judgment consists in judging something to be true. The very meaning of a judgment is something which is capable of being believed or disbelieved ; which can be true or false ; to which it is possible to say yes or no." (Exami- nation, p. 348.) What has been already said disposes of any point in this criticism ; but it may be added that truth is here ambiguously, or rather abusively, used for truth of fact. But there is truth of con- sistency as well, and this is, in the first place, simply in our concepts and judgments ; and unless this be as a condition, all our judgments about matters of fact are futile, not judgments at all. Further, "the recognition of the judgment as true " can hardly be essential to it, if there be false judgments, as there happen to be ; and if also, as Mill tells us, a judgment is that which is capable of being true or false. If a judgment is capable of this, it must be capable of being regarded as a judgment, ere we either believe or disbelieve it. It is nothing to Mill that in this criticism of Hamilton he flatly contradicts his own theory of belief as given in his Logic. (See i. p. 96, 8th edition.) Belief in the reality of the things judged is not essential to judgment, if it be simply possible as it is to form an ideal combination of terms. The centaur is an animal with the body of a horse and the head of a man. NATURE OF JUDGMENT. 223 Does any one imagine that if we do not believe in centaurs, that this statement is therefore not a judgment ? (b) Mill objects and asks : " Do we never judge or assert anything but our mere notions of things ? Do we not make judgments and assert propositions respecting actual things?" (Examination, p. 346.) In turn, I ask do we judge or assert anything about things, which we do not know, or of which we have no notions ? What are actual things for us but the things as known and conceived by us ? How can we assert anything about an actual thing, unless we have a notion of the thing and of that which we assert of it ? And does not this judging through our conception of things yield the variety in our judgment of things? Would it not be a wonderful faculty of judging which could determine about actual things, not known or conceived by us ? This would be getting at things in themselves with a wonderful leap ; only what we overleap is our knowledge of them. But if we cannot compare the naked actual things, what about them can we compare except our notions, or symbols of the things ? Does Mill contend that we compare words minus notions or meaning, or what ? 282. In a Judgment there is obviously a plurality of thoughts and terms. But as Aristotle long ago pointed out, there is not necessarily any judgment in such a bare plurality. We may think of whiteness and wall in succession ; of a, b, and c ; but unless we join them through a definite relation of is or is not, we have no judgment. Nay, Aristotle goes further. We may even have sentences, in which words are joined together, which are yet not properly judgments. " I deprecate," " I wish," " I pray ; " in each case I express myself in a sentence, but I do not properly judge. I do not definitely assert or deny one thing or another. As Albertus Magnus puts it : " Nee deprecativa nee optativa, nee infinitiva cum vero vel falso significant, sed quando est indicativa. . . Oratio per- fecta dividitur. Non enim omnis oratio enuntiatio est, sed ilia sola in qua indicative est significatum." l Wish and prayer, threat and command, may indicate convictions on the part of the person using them ; but these are implicit. There is as yet no form of judgment as to the matter of them. All the judgment that even approaches explicitness is the assertion of the act or state of consciousness in which they are realised. (a) The first enunciation, in as far as it makes one expression, is, ac- cording to Aristotle, affirmation, then negation. Affirmation (KaTacu'ffts and irp6Tairi$ are, according to the usage of Aristotle, to be distinguished. The former is the general word ; when used as the premiss of a syllogism, it is called irp6To.ais, proposition. To propose, irpo-re'ivfiv, is to lay down the propositions of a syllogism. (d) Verbs by themselves are simply nouns. They do not signify whether a thing is or is not. Neither "to be" nor "not to be" is a sign of a thing; nor is "being," for that is nothing. They signify a certain composition, which is unintelligible apart from the constituent members. Hegel's dictum "Being is nothing," is thus anticipated by Aristotle, but in a very different sense. . Being (rb flvai) is nothing according to Aristotle, unless as a connective of one thing with another. (Waitz, in De Int., c. iii. 1.) 283. In a judgment there is, first of all, to be considered the precise nature of the copula, is or is not. This may mean (1.) that the subject contains in it an attribute, as the sun shines, man is responsible, birds fly. (2.) That the subject belongs to a class of which it forms a part, as some men are European, plant is organised, a good orator is impressive, the cow is ruminant. In the former case the judgment is in Comprehension. The subject contains in it the attribute specified at least. In the latter case, the judgment is in Extension. The subject is contained under the predicate as a part at least ; other things may be also contained. This class or object is at least a portion of a possibly wider class of objects. This relation of subject and predicate is sometimes expressed as that the subject is the containing whole (in comprehension), and that the predicate is the containing whole (in extension), under which the subject is a part. 1 (3.) The copula may indicate an exact equivalence between subject and predicate, as Homer was the author of the Iliad. 1 Cf. Hamilton, Logic, L. xiii. COMPREHENSIVE JUDGMENT. 225 Newton was the author of the Principia. All equilateral is all equiangular. All the planets are some stars. Some stars are all the planets. In this case we have Equivalent or Sub- stitutive propositions. 284. Hamilton holds that the comprehensive proposition is the first or primary form, and that this proposition always implies a corresponding proposition in extension. He does not maintain that these two kinds of propositions can be separated, and set apart absolutely, whether in thought or in fact But he holds that they are two modes of looking at the same matter, that every proposition may be expressed in the one way and in the other, and that we do actually judge sometimes in the one way and sometimes the other. When, for example, we say, man is two-legged, we may mean that the notion man contains as one of its characters the attribute two-legged. This is a judgment in comprehension. Obviously, the comprehensive proposition implies an exten- sive proposition ; for if the subject-notion be an individual and have an attribute, this attribute is the property of at least one individual, and ideally of a whole possible class, and if the subject-notion be a class (or plurality of objects), extension is equally implied. Conversely, the extensive pro- position implies a comprehensive, for we cannot have a class or plurality of objects grouped together unless on the ground of a common attribute. Otherwise we should fall into the arbitrary and meaningless. 285. In the ordinary Logic, the predicate had hitherto been regarded as exclusively the whole, and the subject as a part of this whole or predicate. The river runs had been understood in the sense that the river is one or a part of the class or whole running things. There are other running things. Man runs and the horse runs. The river is only one of them. But Hamilton would urge that the subject is a whole as much as the predicate, and it too may contain the predicate as a part. Thus in the river runs, the river or subject may be regarded as containing as a part of its con- cept the single attribute running ; but this is only one of its many attributes, and running is but a part of its whole concept. Here the subject is the whole, and contains in it the attribute as a part. This, too, is a logical whole ; it is the relation of whole and part in thought, as much as the 226 INSTITUTES OF LOGIC. relation in extension of the subject to the predicate as the whole. Why, then, should Logic neglect this? Every proposition and every reasoning is, in Hamilton's view, affected by this distinction, for we may read each proposition, each reasoning in turn, in the whole of Comprehension and in the whole of Extension. Nay, the reading in Comprehension of the subject as whole is the primary and natural reading of a proposition ; the reading in Extension is only secondary and derivative, being founded on the Comprehension. The statement made by Mill that Hamilton separated these forms, or held the extensive reading to be possible by itself, or real apart from the implied comprehensive reading, is merely one of his innumerable misrepresentations of plain and explicit statement. Comprehension is essential to extension ; exten- sion is inseparable from comprehension ; where the one exists the other exists ; yet they express different aspects of the same matter, different relations in the mind, and so yield different kinds of reasoning. Hamilton expresses the distinc- tion in the propositions of extension and comprehension, by saying that the copula is means in the former is contained under, whereas in the latter it means comprehends or contains in it. Thus God is merciful, means in extension is contained under the notion (or class) merciful; in Comprehension it means, God comprehends in it the attribute (notion] merciful. (a) Mill objects to this doctrine that " these two supposed meanings of the proposition are not two matters of fact or thought reciprocally inferrible from one another, but one and the same fact written in dif- ferent ways ; that the supposed meaning in Extension is not a meaning at all, until interpreted by the meaning in Comprehension ; that all concepts and general names which enter into propositions require to be construed in Comprehension, and that their comprehension is the whole of their meaning." (Examination, p. 362.) "'All men' and 'the class man ' are expressions which point to nothing but attributes ; they cannot be interpreted except in comprehension." There is little in this that has any relevancy as a counter-statement to Hamilton's doctrine. To suppose so is a mere mistake. The only thing about it that calls for notice is the extravagance of the assertions that extension is not inferrible from comprehension, and that there is "meaning" in comprehension alone. If by "meaning" Mill means the attributes of the notion, it is self-evident that meaning belongs to comprehension alone. But does "the class man" mean "no- thing but attributes " ? Does it not indicate or imply individuals with attributes ? Does not any attribute imply some subject of inher- ence ? And if so, is there not both room and need for the extensive MILL'S CRITICISM. 227 proposition ? And is not this further or other meaning or implicate of the attribute necessarily involved in its very predication ? And if so involved, is it not a new form of judgment inferrible from the other? Hamilton says a judgment can be read both in Comprehension and in Extension God is merciful means either God is contained under mer- ciful, that is, under the notion merciful, or class of merciful beings ; or God comprehends merciful, that is, the notion God contains in it the attribute merciful. Mill says no. When we say God is merciful, we speak not of the notion God, but the Being God. In Comprehension it means, "this being has the attribute signified by the word merciful. " In Extension it means, "The Being, God, is either the only being, or one of the Beings forming the class merciful. The difference is that the second construction introduces the idea of other possible merciful beings, an idea not suggested by the first construction. This suggestion gives rise to the idea of a class merciful, and of God as a member of that class ; notions which are not present to the mind at all when it simply assents to the proposition that God is merciful. " (Examination, p. 432. ) Has Mill in these statements really said anything that in the least degree controverts Hamilton's interpretation of propositions in Com- prehension and Extension ? Nay, has he not fully admitted, even in words, that very construction which Hamilton puts upon them? In Mill's view we can have the comprehensive meaning of the proposition in the mind without having the extensive. We can think God is merciful, has the attribute, and not think at the same time that God is one of the class merciful. Does he not see that the moment God is thought to possess the attribute, other beings too, at least ideal, may ; and that thus there is necessarily implied and constituted a class through the possible application of the attribute? Worse than all, however, is the supposition, at once groundless and irrelevant, that we are not speaking of the notion of God, but of the Being God. Pray, how can we speak of the Being except through the notion of the Being God ? How can we with a meaning speak of anything except through its notion, or as we have the notion of it in our mind ? Is it words we are speaking of merely? mere blank unintelligibility ? or are we speaking of things in themselves which are quite superior to our notions? But his whole criticism of this point is a mass of contradiction. (1.) On the previous page (p. 432) the objection is taken that the judg- ments in Comprehension and in Extension are totally distinct ; that the latter introduces what was not at all in the mind while making the former. (2.) On page 433, these are affirmed to be " one and the same assertion in slightly different words." Here he contradicts No. 1. (3.) The judgment in Comprehension warrants by immediate infer- ence a judgment respecting Extension, but this judgment respecting Extension is in Comprehension. In other words, there are two differ- ent judgments in the case, and yet only one in kind. (4.) But how does he show both in Comprehension? "A is part of class B." "The concept A comprehends the attribute of being in- 228 INSTITUTES OF LOGIC. eluded in the class B" or "Man is mortal." "Man comprehends the attribute of being included in the class mortal," or rather as with no class predicate, "Man comprehends the attribute of being included in the attribute mortal," which is neither sense nor truth ; for man is not included in the attribute, mortal. The attribute may exist with- out including man, though he includes the attribute, and is included under the class, which is a very different point. But apart from its falsity, what a luminous and scientific statement have we here ! ' ' Gold is in the class mineral." "Gold includes the attribute of being included in the class mineral. " Pray, what is the attribute in addition to the attributes of the class mineral which gold includes or comprehends ? It includes the attribute of being included ? Is this in addition to being one of the class mineral, or what ? (b) Mill admits that the relation of whole and part applies to judgments in Extension (in affirmative propositions). " The object or class of ob- jects denoted by the subject is a part (when it is not the whole) of the class of objects denoted by the predicate." This holds, too, he admits, in analytical judgments in comprehension. But in synthetical judg- ments in comprehension, "the relation between the two sets of attri- butes is not a relation of Whole and Part, but a relation of Coexist- ence." Hoofed animals are ruminant. Supposing this synthetic ru- minant coexists with hoofed animals, does not the judgment in the synthetic act join ruminant to the subject hoofed-animal, and make it a part of my concept of hoofed-animal ? What is the sense of talking of coexistence except for the purpose of a semblance of difference ? Did ruminant coexist in my mind with hoofed-animal, before I knew that hoofed-animal was ruminant ? If so, did this coexistence constitute a judgment? Surely not. At length I knew that ruminant was an attribute of hoofed-animal, or I felt myself justified in so alleging. Then I judged or joined them, and I expressed this in a proposition. But is this any longer mere coexistence ? Is not ruminant now a part of the whole subject hoofed-animal ? Is this not as much a relation of whole and part as any case of Extension ? The very act of synthesis abolishes mere coexistence, makes a union, constitutes whole and part. (c) "All judgments are really judgments in comprehension, except where both the terms are proper names. We never really predicate anything but attributes, though, in the usage of language, we commonly predicate them by means of words, which are names of concrete ob- jects." "When I say the sky is blue, my meaning and my whole meaning is that the sky has that particular colour. I am not thinking of the class of blue as regards extension at all. I am not caring nor necessarily knowing what blue things there are, or if there is any blue thing except the sky. I am thinking only of the sensation of blue, and am judging that the sky produces this sensation in my sensitive faculty, or (to express the meaning in technical language) that the quality answering to the sensation of blue or the power of exciting the sensation of blue, is an attribute of the sky." " So in all oxen ruminate. I have nothing to do with the predicate considered in extension. I may know or be ignorant that there are other rumin- ating animals besides oxen. The comprehension of the predicate, the MILL'S CRITICISM. 229 attribute or set of attributes signified by it, are all that I have in my mind." (Examination, pp. 423, 424.) The subject, too, is an attribute or sum of attributes only. All oxen ruminate. There is no image of all oxen. I do not know all of them, and I am not thinking even of all those I do know. All oxen means "not particular animals, but the objects, whatever they may be, that have the attributes by which oxen are recognised, and which compose the notion of an ox. " ' ' Wherever these attributes shall be found, there, as I judge, the attribute of ruminating will be found also." "This meaning supposes subjects, but merely as all attributes suppose them." Or if, as Mill admits later, "attributes, even, if they come to be conceived, cannot be conceived in a detached state, but are always (as may be said by an adaptation of the Hamiltonian phrase- ology) thought through objects of some sort." (Examination, p. 426.) First, these statements are absolutely contradictory. It cannot be true that the subject of a proposition is an attribute alone, or sum of attributes alone, if every attribute implies a subject. That of which I speak is a subject with attributes. Secondly, it is not true that the predicate is only and always an attribute or sum of attributes. This is the first form of predication, but it is not the only one. It is not true that when I say the sky is blue, I express only an individual fact. This might have been the case at the point of the earliest abstraction. But now blue is already a general concept or term, ^applicable, or possibly applicable, to many objects. My first conscious impression of the sky as blue could not have been put in words. I could not have said blue, unless I already had assigned a meaning to it in thought, as a term indicating an attribute generalised and thus formerly frequently experienced. Blue means previous knowledge ; it means not red, white, black, or green. And all this implies generalisation and discrimination. And when I now speak of the sky as blue, I discriminate it from other colours, and thus mean more than merely saying it is blue. In this sense there is already an implicit attribution of quantity to the predicate. Thirdly, it is contradictory to say all oxen ruminate, and to say that I do not know whether all do or whether even some do. It is not neces- sary that I should know every ox in the sense of having seen every ox past, present, and to come, much less that I should have in my mind " the images of all oxen." What an image ! But when I speak of all oxen, it is necessary that I should have in my mind the equivalent or representative of all oxen as objects. If all our ordinary, usually all, judgments are in Comprehension only, Extension not being thought of, perhaps Mill might have told us how in that case we can speak with discrimination of all or some ? When I say oxen ruminate, I express only certain attributes of oxen, but what of the all ? Has this no meaning ? If it has a meaning, is this meaning in Extension or not ? When I say, some men are vicious, are burglars, what does the some mean ? Does it mean attribute, or quantity in Extension? Surely if I can speak with knowledge of all or some of the subject, I have more in my mind than the mere attributes of the subject. Mill's theory is utterly inconsistent 230 INSTITUTES OF LOGIC. with the possibility even of a definite proposition, or even ordinary statement. He further confounds together as equally "collective, though in definite aggregates," all oxen and some ruminant. He thus abolishes the very possibility of a discrimination of universality and particularity in propositions, by identifying the universal and particular as indiffer- ently expressions of the same. Further, though propositions with him are only in Comprehension, yet logicians were right in admitting only into their logical system reasoning in Extension. " They did not concern themselves with pro- positions or reasonings as they exist in thought, but only as they are expressed in language. " (Examination, p. 429. ) A very philosophical procedure this. They did not concern themselves with what is ad- mitted to be the true reality of the proposition or reasoning, what it is in thought, but with what it is in language, which is not as it is in thought, not necessarily in thought at all. Whatever absurdity or inconsistency is to be perpetrated, let it be done if a position of Hamilton can be contradicted. " The propositions in Ex- tension being, in this sense, exactly equivalent to the judgments in Comprehension, served quite as well to ground forms of ratiocination upon." "They are practically equivalent that is, so long as the propositions in words are always true or false, according as the judg- ments in thought are so. " (Examination, p. 429. ) Will any one explain how it is possible that a judgment in thought can be equivalent to a proposition in language which has no counterpart in thought ? Or if the comprehensive judgment is the same with the extensive, while "the mode of contemplating the fact is different," the act of thought being not only a distinct act, but an act of a different kind," will it not be necessary philosophically to vindicate this ere we can accept the form of reasoning in Extension for form in Comprehension ? Nay, these things being so, is not Hamilton right in saying that the ordinary logicians have erred in neglecting reasoning in comprehension, the primary essential form of reasoning, the reasoning of the very inner thought, and instead dealt with reasoning as vulgarly expressed in ordinary language, without telling us what it really represents ? 286. Determination, that is, fixing or settling, is essential to judgment, whether it be in Comprehension or Extension. In the former, where predicate is an attribute, we determine the subject by the attribute, as plant has organisation, man dies, beauty fades. Thus we limit or determine the sub- ject by the predicate, and exclude it from the opposite or in- definite class. In Extension, determination means the setting of a sub- ject under one definite class, to the exclusion of other classes, as man is mortal, critics are fallible, insects are short-lived, dogs are sagacious. Logical determination is impossible apart from a previous LOGICAL DETERMINATION. 231 knowledge of the characters of the subject and predicate. And any determination in regard to actual experience is either by means of what we already know, and, therefore, secondary, or in virtue of the first spontaneous acts of intelligence con- ditioned by what is actually presented to us, and what, therefore, determines us, rather than we it. There is no determination by us even possible, apart from the secondary logical process, or the spontaneous cognition through intuition of objects and relations, given us to know. We can put nothing into objects which are either wholly indefinite, or which are not cognised by us as already furnished with definite relations. (a) Mill utterly mistakes the meaning of Determination, and this has helped to lead him astray on this point. He asserts that it means only " our conceiving one of two notions as adding on additional attributes to the other." Hamilton of course uses no such redundant phrase in connection with the verb " to determine," or with determina- tion. And Mill's representation of Hamilton's meaning has really nothing whatever to do with determination itself. It is a clumsy and inaccurate way of stating what Hamilton had explained, when Deter- mination was used "in a particular relation," &c. viz., the process of Specification, "when descending from the highest notion, we, step by step, add on the several characters from which we had abstracted in our ascent . . . and thus limit or determine more and more the abstract vagueness or extension of the notion. " (Logic, xi. , iii. p. 94. ) We determine a notion, whether the predicate be an addition to thf subject or not, whenever we make an affirmation. When we say that the number four, or our notion of it is made up of the units 1, 1, 1, 1 ki succession, we have determined our notion, though we have added no new attribute. And when we say that the conscious act is or exists, we have determined our subject-notion, though we have added nothing to it. When we say this" colour I perceive is red, we have deter- mined, because we have restricted the subject we speak of to a definite class of things : the determination lies in the act of judging, and, as Hamilton points out, only in that ; for until we have judged congruence (or confliction), there are only floating, unconnected concepts. 287. Concepts and Judgments, as Hamilton expressly holds, and constantly repeats, are the results of the same process, Comparison. Every concept is, in fact, a judgment fixed and ratified in a sign. In consequence of this acquired permanence, concepts afford the principal means of all subse- quent comparisons and judgments. A concept may be viewed as an implicit or undeveloped judgment ; a judgment as an explicit or developed concept. He, accordingly, defines judg- ment, logical judgment, thus : "To judge is to recognise 232 INSTITUTES OF LOGIC. the relation of congruence or of confliction, in which two concepts, two individual things, or a concept and an indi- vidual compared together, stand to each other." l Congruent concepts are such as are mutually compatible and representable in the same indivisible act of thought. They may differ in themselves from each other as learning and virtue, beauty and riches, magnanimity and stature; but as each of these pairs may be easily combined in the notion we form of one thing or subject, they are congruent. Conflic- tive notions, again, are those only whose difference is so great that each involves the negation of the other, as virtue and vice, beauty and deformity, wealth and poverty? Congruence and confliction, it should be carefully noted, express a re- lation of concepts under comprehension, and viewed as attribute or sum of attributes. 3 As attributes, congruent concepts are said by Hamilton to coincide or coexist to- gether, in thought, though they are not in themselves identical, because they form elements of one mental image or representation. As attributes, connective concepts can- not be united in one representation, either because one im- mediately negates another contradictory opposition that is, the one abolishes directly what the other establishes ; or because one mediately negates another contrary opposition that is, when one concept abolishes what the other estab- lishes through the affirmation of something else. It should be observed that concepts are not in themselves affirmative or negative. In so far, however, as two concepts afford the elements, and, if brought into relation, necessitate the for- mation of an affirmative and negative proposition, they may be considered affirmative and negative. 4 To give, thus, the distinction between two concepts simply as congruent, or two concepts simply as conflictive, and judgment proper, we have to accentuate the recognition and expression of this congruence or confliction. We advance, in fact, from the simple representation or mere conception to the stage of the is and the is not, as expressing the relation conceived be- tween the concepts as elements or terms of the judgment. Thus, for example, we may have the three concepts or thoughts, water, iron, rusting. These as mere concepts are i Logic, L. xiii., pp. 225, 226. 2 Logic, L. xii., p. 214. 3 Logic, L. xii., p. 213. * Logic, L. xii., pp. 215, 216. WHAT JUDGMENT SUPPOSES. 233 congruent ; they are capable of being represented in imagi- nation in one notion, or as the elements of a single notion, that is, a complex notion. If, however, we proceed beyond this, and, so to speak, articulate the relation subsisting among them, we form a judgment, an affirmative judgment, and we say water rusts iron. In this, of course, we meanwhile pro- nounce no judgment on the matter of fact, whether this is truly and really a fact of experience or not. All that we are supposed to have before us is the material or constituted concepts in which we find or are supposed to find no incom- patibility. And the act of judgment is the recognition and expression of this compatibility. (6) Mill actually criticises this illustration as if Hamilton had con- tended that we know or discover the truth or fact that water rusts iron, from comparing merely the concepts or thoughts water, iron, rusting. The proposition, he holds, expresses a sequence or connection between the facts, not between our concepts. " If we lived till doomsday, we should never find the proposition that water rusts iron in our concepts, if we had not first found it in the outward phenomena." Did Mill for a moment seriously imagine that Hamilton, or any sane person, ever held the converse of what he here states ? or that when Hamilton speaks of the congruence, he meant to imply that ? But did Mill suppose that when he substituted the word facts for thoughts, he could possibly deal with the phenomena water, iron, rusting, per se, or apart from our con- cepts or thoughts of them ? Yet this must be so, if Hamilton is to be corrected. What is the fact of water, iron, rusting, apart from our knowledge or thought of the fact ? When we compare these, present or absent in sense, what are we comparing but our thoughts or con- cepts of them ? Even in a real judgment, or judgment about a matter of fact, it is, after all, our thought, knowledge, or concept of the fact with which we are dealing, and which we compare in the subject and predicate of a judgment. Does Mill suppose that we can deal with facts which are not thought and known facts ? When he further talks of such a judgment as resulting from " direct remembrance of the facts," his position is quite as suicidal, unless he can show that remem- brance of the facts is a thing apart from conception of the facts. 288. Judgment, that is, logical judgment, supposes the concepts given. It thus supposes them to be in themselves conceivable, that is, actually concepts, each conceivable by itself, therefore, not in themselves self-contradictory, not vio- lating any logical law of conception, and not violating any mate- rial law of conception. Logically, then, judgment is restricted to recognising congruence or confliction under the condition of non-contradiction. What is non-contradictory is logically 234 INSTITUTES OF LOGIC. congruent; and hence "all positive and affirmative notions are congruent, that is, they can, as far as their form is con- cerned, be thought together ; but whether in reality they can coexist, that cannot be decided by logical rules." l Hence, even contrary opposition is not decided on logical grounds, but on material, on the incompatibilities of intuition, or of the matter of the concepts. A, B, C, sitting, standing, tying, black, red, blue are groups of contraries, because we can- not unite the attributes they represent in one image. But this we learn from experience. While A and not A sitting and not sitting, we can at once, a priori or logically, pro- nounce to be conflictive, the moment the terms are enounced. Mediate or contrary opposition (confliction) comes under logical rule only indirectly. Sitting is incompatible with standing, blue with white, because perception does not give us and we cannot represent each pair together, but only in separate intuitions. But logical law can deal with contrary opposites the moment they are known to be such, and constituted into the members of a sphere of opposition. Logical law can regulate the passage from the one to the other, by affirmation or by negation. 289. It would seem from this that what attributes are op- posed mediately or in contrary opposition, must be learned from experience ; while contradictory opposition may be deter- mined by simple logical law. I must learn, for example, that sitting, standing, tying, walking, are conflictive concepts from experience wholly ; while sitting and not-sitting, standing and not-standing, are known a priori, or from the concept itself, to be conflictive. The congruence or compatibility of attributes must thus in the main be learned from intuition, the observation of the realities which are combined in the outward or inward world of our experience. In our concept of tree, we combine form, colour, growth, organisation. Our only means of knowing these to be compatible is through a reference to intuition and representation working on the data of sense. The confliction of attributes must be learned in the same way, all except those that are immediately con- tradictory. We cannot combine in one and the same surface black and white, or red or green, because intuition never gives us such a combination, but the opposite. There is a material 1 Hamilton, Logic, L, xii., p. 216. CONGRUENCE IN JUDGMENT. 235 barrier in this case to unifying, or to congruence. But in whatever way congruence between attributes may arise, whatever its ground or conditions, its test logically is the power of representing the two attributes as in the one sub- ject, or the one attribute as a mark or attribute of the other. When we can do this, and when we recognise and enounce the congruence, we have an act of judgment, properly logical judgment. (a) It has been remarked on this point of the congruence of notions, that it may be of two different kinds. The concepts or attributes may be such as we must necessarily unite in thought, or such as we may or may not unite, according to circumstances. Man and animal are con- cepts of the former kind ; man and the concept ten feet high are of the latter. (Monck's Hamilton, p. 132.) Hamilton has himself touched on this distinction, when he distinguishes notions in Comprehension as Intrinsic and Extrinsic. The former are made up of those attributes which are essential, and, consequently, necessary to the object of the notion. The latter consist of those attributes which belong to the object of the notion only in a contingent manner or by possibility. (Logic, L. xii., iii. p. 216.) But this is wholly extra-logical. The knowledge of what is essential to the object of a notion is obvi- ously a process subsequent to the formation of the notion itself. The object of a notion is simply that of which the attributes of the notion can be predicated ; and when the attributes of the notion can be predi- cated, there is the object of the notion. Animal or organised is necessary and essential to the notion man, because we have already determined the notion as that which possesses this particular attribute. This is a wholly hypothetical necessity ; it is an analytical exposition of the con- tents of a given notion. Ten feet high, again, is a possibility and a contingency of the notion ; it is compatible with it, but not essential to it, or an element of the definition of that which would constitute a man. But the congruence needed for the judgment is the same in both cases, and it is fulfilled in both cases. If we say man is animal, or man is organised, we judge, we enounce congruence, and congruence between man and one of its essential, because already determined, characters. If we say man is ten feet high, we judge equally, we enounce congruence between man and a character not essential to the notion or a part of it. We have fulfilled all the conditions of (formal) judgment in this latter case ; but we have erred if we imply that the attribute ten feet high is an essential, that is, already defined, charac- ter of man, the concept. This distinction, accordingly, of the essential and the non-essential characters of the concept is extra-logical, and in no way affects the nature of logical judgment as in itself simply the enouncement of congruence or confliction. 290. This leads to the further question Is Judgment, as thus denned, limited to Analytical Judgments alone ? Or 236 INSTITUTES OF LOGIC. does it also include Synthetical ? In the analytical predicate we enounce an attribute already contained in the subject, as body is extended. In the synthetical judgment we add or enounce a new predicate not already contained, or rather not known to be already contained in it. The law of Iden- tity warrants the former enunciation ; it cannot of itself warrant the latter, or lead us to it. I do not see that this should give rise to any difficulty. In the first place, the distinction between synthetical and analytical judgments is in a great measure relative. What is synthetical at one stage becomes analytical at another, when the concept is more fully determined. This is the case with most scientific concepts. In the second place, even though the attribute confronted with the existing concept be new, its congru- ence with it alone satisfies the affirmative judgment. . Ex- perience may evolve a new attribute, congruence is still the logical test of its (possible) combination. That it is actu- ally combined is grounded on conditions not involved in the mere congruence. This is to confuse congruence with belief in the reality of the congruent. In case of synthetical judg- ments a priori, as cause added to the concept of an event apparently beginning, the ground of the assertion is extra- logical, not found in the. law of Identity ; but the recognition of congruence between the concept of an event apparently commencing and a cause is still there, and there as a condition of its assertion as a law of reality. The distinction of syn- thetical and analytical judgments, whether well founded or not, in no way affects the doctrine that congruence of repre- sentation is the condition of the logical judgment, and that this judgment consists in apprehending and enouncing the congruence. 291. In synthetical judgments a priori, there is of course no preliminary comparison of two concepts. The subject concept is supposed to be given, and to this we add the new predicate concept. We have, for example, an apparent com- mencement of an event in time ; we add on the concept of cause and form a synthetical judgment. The relation between the two concepts is said to be necessary. Thinking the one, I must think the other. But in this case, are we correct in holding that the subject concept is conceived first and inde- pendently, and then the predicate concept is added to it ? If JUDGMENT ANALYTIC. 237 the concept event and the concept cause be correlatives, and necessary correlatives, can the one be conceived apart from the other ? Is not the true state of the case this, that there is the coequal revelation of one double-sided concept ; and the so-called synthesis or adding on of the predicate is a mere making explicit of what we think implicitly and vaguely ? If this be so, the so-called synthetical a priori judgment is simply the full consciousness of a necessary relation, and different altogether from judgments of experience, in which we add on not by way of necessity, new attributes or concepts to the subject. The nearest approach to the synthetical a priori apprehension is in those cases where an attribute is ultimately seen to be necessarily implied in a given attribute, as divisi- bility in extension, although this judgment is synthetical only relatively to the development of our knowledge, and not in relation to the nature of the original notion. 292. Logically all judgments are analytic, for judgment is an assertion by the person judging of what he knows of the subject spoken of. To the person addressed, real or imaginary, the judgment may contain a predicate new a new knowledge. But the person making the judgment speaks analytically, and analytically only ; for he sets forth a part of what he knows belongs to the subject spoken of. In fact, it is impossible any one can judge otherwise. We must judge by our real and supposed knowledge of the thing already in the mind. Even when we add a wholly new predicate to the sub- ject, as in scientific discovery, we, in the judging, state only analytically what we already know. Even when we form a syn- thetic judgment a priori, we analyse a complex notion ; for as the so-called new predicate is a necessary one, a necessary correlative, we never really had the subject in the mind per se, but always with the predicate implicitly. 293. What, then, it may be asked further, is the import or nature of this act of judgment ? What is the condition, so to speak, implied in it ? The answer, in the first place, is, that this recognition, when affirmative, or of the congruent, is a determination, a limitation. It is also, in a sense, a deter- mination, when negative, or of the conflictive. How in one complex notion, first, can we conceive two notions as in one, or as united in an affirmative judgment ? Clearly the notions cannot be regarded as both subjects in a judgment, that is, 238 INSTITUTES OF LOGIC. as both equally determined or limited, for there is nothing here in the one to limit the other. They are still represented or conceived apart. But an affirmative judgment requires and expresses union, the union of two. Hence the one notion must stand to the other in the relation of subject to predi- cate, that is, something must be attributed to the subject, or the subject must be included under some class-notion. For the same reason, the two notions, if attributes, cannot be regarded as one, or as united in a judgment, if neither deter- mines or qualifies the other. There must thus in a judgment be a relation of the thing or concept determined (the subject), that by which it is determined (the predicate), the relation or determination between the two (the copula). These three elements constitute one indivisible act of thought. Thus a judgment is a determination, a limitation. For example, we say iron is a mineral. The subject iron is limited to or by the notion mineral. If mineral be regarded as a class, iron is a part of it, or included under it, that is, limited to it, as distinguished from the sphere outside of it. If mineral be regarded as an attribute, it is a part, mark, or character of the notion iron, that is, it is limited to it or distinguished from what does not possess it. The electrical is polar. Electrical, if taken as attribute, has polar as an attribute or mark of it. It is subject, or determined ; polar is predicate or determining. In each case, however, whether the predicate be class or attribute, the subject is thereby marked off, limited, distin- guished from what it is not, from other things not possessing the distinctive mark or belonging to the definite class. Ham- ilton, accordingly, finally defines logical judgment " to be the product of that act in which we pronounce that of two notions thought as subject and predicate, the one does or does not constitute a part of the other, either in the quantity of Exten- sion or in the quantity of Comprehension." x The phrase, " a part of the other," will mean, in the case of Extension, that is, where we compare a subject with a class-notion, as man with organised, a portion of the class, an object or individual under the extension of the class, and thus one with it when actually thought in connection with it. In the case of Comprehension, " a part of the other " will mean that the predicate is thought as a mark, character, or 1 Logic, L. xiii., p. 229. CONGKUENCE IN JUDGMENT. 239 attribute of the subject, and thus conceived as one with it, as it may be either inseparably connected with it, or as, for the time at least, actually connected with it in the unity of a single complex notion. Congruence, as thus finally ex- plained or elucidated by Hamilton, does not imply in the case of the comprehensive predicate that it is identified with the subject. He does not say that the electrical is polarity, or that electricity is polarity, that free-intelligent is responsibility, or that free-intelligence is responsibility. He says the electrical contains polarity as a mark or attribute, or that polarity is a mark of electricity, or that free-intelligent contains in it responsibility. There is a congruence, a unity between the notions, when, compared as subject and predicate, the one forms part of the other. (a) Mill puzzles himself sadly over these two statements or defini- tions of Judgment, and regards them, as usual, as inconsistent. He cannot reconcile the "congruence" of the first with "a part of the other " of the second statement. So far from being inconsistent, the latter phrase simply renders the former more explicit. " Congruence " does not mean, as Mill conceives, that "the attributes comprehended in both of them [the concepts] can be simultaneously possessed by the same object." Hamilton says no such thing. All the congruence he needs or asks for is that they can be simultaneously thought or con- ceived as possessed by the same object, or better, united in the same subject of thought, that they be not in thought repugnant. Nor does the phrase " a part of the other " mean, as he imagines, that " the one concept is actually a part of the other." It means simply that the one concept is conceived and pronounced to be in thought an object under a given class, or a subject possessing a definite attribute. There is no distinction here corresponding to " a part of " and " along with." Learning and virtue are congruent, since I can conceive them together in the same object of thought, and in the same indivisible act of representation. They are thus conceived along with each other in one act, while virtue and vice cannot be so represented. But I do not say, or need to say, that learning is virtue, or virtue is learning. So when I say that learning and virtue are parts of the comprehension of the notion of Socrates, or of the notion of an ideally perfect man, I no more say, or need to say, that learning is virtue, or virtue learning. But, as parts of the same complex notion, they are congruent. The latter statement about judgment simply explains the two forms of Congruence, that which lies in a subject possessing, or conceived as possessing, parts or attributes ; and that which lies in a subject con- ceived as being a portion of a (wider) class than itself. There is not the slightest contradiction in Hamilton's doctrine here. Two attributes, or groups of attributes, are congruent when we can think them as one, or in one notion as coincident, as the one qualify- 240 INSTITUTES OF LOGIC. ing the other, and not unless this be so. We cannot think ivisdom and circle as one or congruent, or the one as qualifying the other, but we can think circle as ivhite or black, as thus qualified and deter- mined. And in this case the blackness or the whiteness is part of the concept we form of the circle, not along with it merely, but one of its qualities in the group of qualities which we name this circle. Hamilton illustrates this by the notions electrical and polar. He says "we cannot think the two attributes electrical and polar as a single notion, unless we convert the one of these attributes into a subject to be determined or qualified by the other." (Logic, iii. p. 227.) Mill asks, "Do we ever think the two attributes electrical and polar as a single notion ? We think them as distinct parts of the same notion, that is, as attributes which are constantly conjoined." (Examination, p. 344. ) Does Mill not know what a single notion in Logic means ? Does he suppose that a single notion means only one or a single attri- bute, or two attributes identified ? Does he not know that a single notion is not necessarily a simple notion, but may be a complex notion, provided only the attributes which make it up can be thought in one representation, and not merely successively, or as repugnant ? Hamilton has not two meanings of the word " congruent," as ap- plied to the concepts of attributes. He does not mean by it " along with " at one time, and at another " actually a part of." His sole test of congruence is compatibility of representation of the two attributes in the same subject ; but he does not make the one attribute a part of the other. He does not say that beauty is a part of riches ; but he says we may represent and affirm these attributes to belong to one and the same subject, or that the beautiful one is rich. And then rich or riches is a part of the subject-notion, a part of that subject which is beautiful. We might no doubt form a judgment in which we should make one attribute a part of another attribute, as when we say extension is (contains in it) divisibility. We know that divisibility is a necessary implicate of extension. But we do not identify the two ; we say only divisibility is a mark of extension, or the subject-notion extension has as part of it divisibility. It would certainly be ridiculous in this case to say that the judgment states that divisibility is conceived merely " along with " extension ; that thus the two can be conceived apart ; and that all we assert in the judgment is a separable conjunction. (b) Mill conjures up another inconsistency, in what he calls Hamil- ton's first theory of judgment. Judgment is regarded as the recognition of congruence or confliction not only between concepts, but between "two individual things." But as in the so-called second theory, Hamilton declares it to be "the product of that act in which we pro- nounce that of two notions, thought as subject and as predicate, the one does or does not constitute a part of the other, either in Extension or in Comprehension," he is to be held as denying that one individual thing is predicable of another ; ' ' one at least of the terms of compari- son must be a concept." It would be enough to say, in regard to this, that Hamilton recognises a " notion " of the individual, where the image of the individual and concept proper coincide. But Mill further contends that " if the predicate in a judgment be held to be part of the CONGRUENCE IN JUDGMENT. 241 subject, then the individual cannot be predicable of an individual ; for one notion of an individual object cannot be a part of another notion of an individual object. One object may be an integrant part of another, but it cannot be a part in Comprehension or in Extension. St Paul's is an integrant part of London, but neither an attribute of it, nor an object of which it is predicable." 1 Here we may well ask, Did Mill know what is meant by predicable ? Evidently he supposes that predicable means only affirmatively predicable, and, in fact, identifi- cation. We cannot say London is St Paul's, but we can say what is correct, that London is not St Paul's ; and thus St Paul's, the indi- vidual thing or notion, is the predicate of London, the individual thing or notion. We cannot say, The donkey is its leg, but we can say, it is not. And here we as truly predicate, as if we had identified the donkey and its leg. But is it so certain that one individual cannot stand as a logical part, say attribute or determination in relation to another individual object? Can the individual as predicate not be logically a part of the subject? The truth is, that one individual notion can be part of another, can be affirmatively predicated of another. We affirm this every day. We do it when we speak of Sir Isaac Newton as the author of the Principia, or of Victoria as the Queen of England. In these subject and predicate are strictly indi- vidual notions, and the predicate is part, and in a good sense a part only, of the subject. A little further on, Mill, in pursuance of his chimerical contradictions, represents Hamilton as holding that, in order to form concepts, we first of all compare and judge between individual objects ; and he maintains this doctrine to be true. If we so judge apart from concepts, do we not predicate, both affirm and deny, one individual thing of another ; and in so predicating, do we not pronounce the one thing to be or not to be a part of the other ? Hamilton is perfectly consistent ; Mill is neither accurate nor consistent, (c) It may be objected that congruence between two concepts is sometimes partial, and thus that the same two concepts may be described as both congruent and conflictive, as the ground thus equally of affirmative and negative judgments. Thus, tall and man are congruent, some men are tall. Again, they are conflictive, some men are not tall they are dwarfs. But this has nothing to do with congruence in comprehension, or attribute : and Hamilton is dealing with congruence as a relation under comprehension. Man and tall are congruent as attributes ; and we may unite them formally, that is, unite them in one subject in a judgment. We may also unite them really, or as in presentation. This implies also that so far their extensions coincide. Comprehension implies always some (imaginary or real) extension. But it does not imply absolute coincidence or co- equality of extension. That the extension of a congruent concept, say tall, is wider than the extension of that with which it is congruent, say man, is no proof that the two concepts are not congruent in com- prehension or as attributes, or, in other words, that as attributes they are to be regarded as both congruent and conflictive. Further, when tall is predicated of some men, and not-tall of others, there is no conflic- 1 Examination, p. 422. Q 242 INSTITUTES OF LOGIC. tion, for we are speaking of different subjects or portions of the same class. (d) This mode of speaking of Judgment as the comparison of one notion with another, and the recognition of the one as a part, comprehensively or extensively of the other, or as not a part, requires some slight modi- fication to suit Hamilton's later doctrine that a proposition is, in exten- sion, an equation or non-equation of subject and predicate. It needs no change to suit it to his later statements of the comprehensive pro- position, for from this he properly excludes the notion of quantity (see Logic, Appendix iv. 271 and 276) in the sense in which it is applicable to the proposition in extension. But even with regard to the judgment in extension there is no conflict between the earlier and the later doc- trines. In the four affirmative propositional forms, the earlier language applies strictly, to (Afl) all is some; (IfA) some is all; (Ifl) some is some. With regard to Af A, or all is all, we compare two wholes, and regard them as convertible. But logically the predicate whole is declared to be the constituent of the subject whole. All equilateral is all equiangular. Equiangular is "a part" of equilateral in the logical sense of the coincidence of one notion with another. That they wholly coincide, or are coextensive, does not destroy the concept of them as reciprocally parts of the whole notion of equiangular-equilateral. 294. The element of determination of the judgment in comprehension may, in a sense, be said to depend on the amount or degree of the specification of action and object. (1.) This may be said to be incomplete, as Bruce gained a victory, or the man was killed. (2.) Or complete, as Bruce gained a victory at Bannockburn over Edward II. ; the man was killed by being run over by the express, fyc. Complete- ness and incompleteness of determination are relative to the purpose or end of the judgment. It depends, indeed, on what we mean precisely to assert, or need precisely to deny. The distinction made by some between objective completion and objective determination is wholly groundless, from a logical point of view. Every determination by any attribute whatever, or by any class whatever, is a completion of the judgment; because this is a case of determination against indetermination, of a definite affirmative against a negative. Of course, looking to the actual fact or possibility of obser- vation and generalisation, any determination, through a predicate, is incomplete. But this has no logical signifi- cance. The logical essence of the judgment is as clear and marked in the first predicate as in the most advanced, or in the most complex series. When I say this is, my judgment is perfectly complete or determinate, as contrasted JUDGMENT IN EELATION TO EXISTENCE. 243 with its negation, this is not. And when I say this is a metal, the judgment is really not more determinate as a judgment, though the predicate contains more attributes, for the deter- mination is always in relation not merely to the possible predicates of the subject, but to what I know definitely of the subject. As against the knowledge asserted there is always the negation of the opposite determination. 295. Judgment in its objective relation may be supposed to represent all the actual and possible forms or relations of existence. The first relation of existence is a thing and its quality, a substantive or permanent, and its action or pro- perty. This is equivalent to the relation of inherence or of subject and phenomenon. The subject of the judgment may be taken as representing the thing or permanent subject, the predicate as representing the action, quality, or property. In language these are expressed by the noun and the verb. This form of judgment is in logical language the comprehen- sive, the predicate is regarded as quality or attribute. Under this head of comprehension is included every judg- ment which expresses the relation of causality between thing or cause and its effect, as the sun is the cause of heat, opium causes sleep. The action or the passion in a given case may be related to the subject as a singular effect, or it may be regarded as the fixed and constant effect of the thing. This would yield one feature of the distinction between accident and property. Sequence, concomitance, and coexistence may fairly be regarded as coming under Comprehension. The sun is fol- lowed or accompanied by day. A is constantly followed or accompanied by J3, or A and B always coexist. Things re- lated alike in time and space, through uniformity or con- stancy of conjunction, come under the head of subject and property. There may be simple simultaneity, and simple co-adjacency, as in the case of my writing while the clock strikes twelve, or the co-adjacency of the planets in space. This and that may be together in time or in time and space, apart from the relation of cause and effect, or of substance and accident; but a judgment regarding these would come under the head either of simple individuals or of classifica- tion by resemblance in time or in time and space. And this suggests the second great relation of things indicated 244 INSTITUTES OF LOGIC. by judgment, that is, similarity or resemblance among the objects or qualities of objects. This does not take into account either substance or causality, or even properly time or space. It only considers whether two given qualities are like or unlike, compatible or incompatible, unifiable or not in thought, and this gives rise to the notion of the class, to the judgment in Extension or Classification. Here we may be said to state the relation between two ideas, and to refer to, include in or exclude from, a class. These two forms of judgment, the Comprehensive and Extensive, are, logically considered, wholly independent of their actual or metaphysical relations ; at the same time, they represent in a general and scientific form those various metaphysical rela- tions, are, in fact, fitted for thinking those relations, stated in their highest abstraction. It indicates simply a narrow, in- adequate, and one-sided view, to represent logical judgment as founded on or expressing coexistence, or concomitance of attributes, or immediate succession, and to deny reference to a class, as is done by Mill. Logical judgment is, on its real side or application to reality, as wide as the relations of things themselves, and that mainly because, while indifferent to special relations, it formulises all. It is a remarkable theory of judgment which, while limiting judgment to coexistence, and excluding inherence, would tell us that three-sided figure only coexists with triangle, or extension with body. And not less so would be the theory which implies that while consuming paper succeeds flame, the power of consuming is not a property inherent in flame. (a) " In the judgment A is a coward, the combination of the notion of A with his deeds is the basis of the judgment ; its subsumption under the notion of cowardice is the judgment proper. The logical element is the analytic subsumption of the less general subject-notion (or subject- conception) under the more general predicate notion." (Beneke, in Ueberweg, Logic, p. 193.) The combination of A with his deeds is simply, to begin with, a judgment. Mere coexistence of A with his deeds, as in Mill's view, is no judgment. There might quite well co- exist in my mind the conceptions of competent learning in metaphysical philosophy and Mr A B ; but I need not, therefore, think of combin- ing them. Their coexistence and the attribution of the former to the latter might be to me wide as the poles asunder. When I combine A with certain deeds, and say that A is the author of them, I judge as much as when, having referred those deeds to the class cowardly, I predicate cowardice of A, and refer him to the class of cowards. JUDGMENT WITH HEGEL. 245 (6) Judgment with Hegel is equivalent to "the determination given to the notion by itself, or the notion making itself particular, or the original self-division of the notion into its moments with distinguishing reference of the individual to the universal, and the subsumptioii of the former under the latter, not as a mere operation of subjective thought, but as a universal form of all things." (Ueberweg, Logic, p. 192.) Ueberweg's only objection to this is the confounding of reference to reality with reality. But the fundamental objections to such a state- ment are ( 1 ) the absurdity of hypostatising the notion, as yet a pure abstract without individual instance, and regarding this as capable of passing into the individual, confounded usually with the particular. (This, that, with some of all.) (2) The attribution to the notion per se, or notion in any way, the power of consciously passing into the indi- vidual, or the power of conscious process at all, which is competent only to a conscious subject cognisant of itself and difference. The notion, in fact, as a pure abstraction, is credited with all the attributes of a conscious subject or thinker. In other words, simply and ulti- mately because there is a (supposed) necessity of connection between notion and individual, this connection is hypostatised as a thing per se, and regarded as the universal in things ; whereas it is and can only be, and be intelligible, in this or that individual consciousness, and thus subject to all its conditions. (For a fuller statement and examination of Hegel's theory of Judgment, see below, chapter xxiL) 246 CHAPTER XIX. JUDGMENTS SIMPLE OR CATEGORICAL AND COMPOSITE THE CATEGORICAL ITS ELEMENTS AND KINDS AFFIRMATIVE AND NEGATIVE UNIVERSAL, PARTICULAR, SINGULAR. 296. Judgments considered as to the most general relation of subject and predicate are divided into Categorical or Simple, and Composite, called also Conditional. When the predi- cate is referred to the subject simply or absolutely, that is, without contingency, we have the Categorical Judgment or Proposition, as A is B; A is not B. When the judgment is contingent, and the statement is made under a condition or with an alternative, we have the Composite Judgment or Proposition, If A is, B is. A is either C or D. 297. Looking specially meanwhile to the Categorical, it is essential to a judgment, as already defined, that there should be subject, copula, and predicate, whether implicitly involved, or explicitly stated. In order to judge we must have that of which we predicate the subject ; we must have that which is predicated the predicate ; and we must have that by means of which we predicate, that is, affirm or deny, the copula. Thus, the sunset is lurid; the moon is bright; the temperature is 32. The Subject of a judgment was called vTroKft/tevov, subjectum ; the Predicate Ka.-njyopovp.fvov, prcedica- tum. A concept as predicable of a subject is, with Aris- totle, Ka.-rrjy6prip.a ; as actually predicated, Ka.rrjyopoviJi.evov. The subject and predicate are naturally called the terms or limits of the Judgment (opoi, axpa, Trepara, termini}, 1 because it is within these that the predication, affirmation or denial, is made. Thus, we may say, plant is organised. Plant is sub- 1 Hamilton, Logic, L. xiii. SUBJECT AND PEEDICATE. 247 ject ; organised, predicate ; is, copula. Some marble is white. A judgment expressed in words is a Proposition (enunciatio, (a) There is sometimes the assertion of mere action, without definite reference to a subject which acts. It rains, it snows, it thunders. There, is rain, snow, thunder. This is the first stage. Then there comes the definite subject; then the definite subject with reference to the specifica- tion and object. This is substantially the view of Schleiermacher and others. (Cf. Ueberweg, Logic, p. 200.) It may be said there is no assertion of action without reference to a subject which acts, though there may be reference to a subject which we do not wholly know. When we say it rains or snows, we simply express a reference to the ultimate power beyond the sensible phenomena ; but in so far as we regard this as the subject or cause of rain or snow, we regard it as a perfectly definite subject or cause. There is no such thing in human thought or experience as the apprehension or conception of an action or property without reference to a subject or substance, whether this be wholly known or not. 298. The Subject of a proposition has sometimes been called the Minor Term ; the Predicate the Major. This arises from considering one special kind of proposition, in which the subject is either species or individual. When I say man is organised, or triangle is figure, the subject term is less, under- stood as less, than the predicate. It is part at least of its sphere or ambitus. But there may be more, or the sphere of the predicate may be larger than that of which it is predicated. Organised is or may be wider than man ; figure is or may be wider than triangle. Or if we say Bucephalus is horse, we have a predicate of which only a part is taken. But there are cases in which this distinction does not exist. Whenever the subject and predicate are substitutive, or convertible, there can in the proposition be no distinction of major or minor term. This at least is clear, that the extension of the predicate can never, in a true or competent predication, be less than that of the subject. In fact, this distinction of less and greater, of species and genus, is that expressed in the relation of subject and predicate in Universal Affirmative Propositions. The universal affirmative was usually regarded as propositio potissima. The relations of Minor and Major are most pro- perly applicable when terms are compared in the syllogism. 299. It ought to be noticed that a subject may be either incomplex or complex. The subject of which we speak may be man, plant, mineral. Or it may be grammatically a com- 248 INSTITUTES OF LOGIC. plex expression, as, to obey the law of truth is incumbent on every man; or to shun vice is a virtue. Here the infinitive phrase is as much a term or subject as if it had been put in a single word. Logically these phrases, whether single terms or a plurality of words, indicate one concept, regarded as subject or predicate, as that whole of which something is said, or as that whole which is said of something. 300. Terms and the parts of propositions are not given explicitly in ordinary language. The complex or irreflective expression is matter of analysis. If I say, / walk, or leap, or run, I express what I say in an implicit propositional form, and the science of logic has to ask me to make my meaning or mental act explicit in words. I must, therefore, resolve each expression into subject, copula, and predicate. (a) Each proposition recognised by Aristotle represents a universal and invariable form of words, and a universal and invariable act of thinking, the former apart from the particular words, the latter apart from the particular matter. Thus, the affirmative proposition is a synthesis by which we unite one representation to another. The words and the form of thought in one proposition may be used in all. The Categories of Kant represent the universal forms of thought. These functions of the understanding are united in a supreme act, the pri- mordial fact of pure apperception. But while Aristotle considers the judgment to have a reference to existence and non-existence, Kant's expression, objectivity, has not a similar reference. This means merely the (fixed or universal) relations of knowledge, as the material is acted on by the Ego, and subsumed under the Categories. It is bringing, for one thing, the special under the universal ; but the universal itself, with its relations and connections, is the product of the Ego, the out- come of its activity. Aristotle's objective reference, if we may use the expression, was wholly different from this, which is simply subjective, though necessary. (b) "fwoKftfj.fvov with Aristotle has two grand meanings, it indicates the subject of a judgment, and also the substance or substrate to actions in the nature of things. This was indifferently translated subjectum by the Latins, as by Boethius. 'A.vTiK(i/j.vov or object was translated by Boethius oppositum. Hence subject in the middle ages is equivalent to substrate, and so it is with Descartes and Spinosa. Esse subjectivum means with Occam that the thing in nature is placed beyond the mental species, and is not framed by thought alone. On the other hand, esse objectivum is that whose reality is known as a mental product or crea- tion. Objective reality with Descartes is thus in modern language sub- jective or a representational notion. Kant and Fichte reverse this usage. The subject is he who knows ; the object is the thing, as far in- deed as it is subjected to the knower, and yet preserves its own nature free from the opinion of the knower. Hence it happens that that is JUDGMENTS OF QUALITY. 249 called subjective which lies in the varying condition of the knower, and that objective which lies in the constant nature of the thing itself. Wherefore if truth be denned the harmony of the subjective with the objective, nothing more is postulated than that the thing is simply thought as it is, and the cognition is adequate to the thing known. (Trendelenburg, Elementa Logices Aristotelece, pp. 52, 53, ed. 1845. Compare Descartes, English Translation, Appendix, Notes iii. and vii.) (c) Ka.TTiyopf'iv is sometimes simply to say, at other times to prove by certain arguments, as with Plato in the Thecetetus. In logic, Kar-rj- yopovpevov is the predicate, or principal predicate ; irpoffKa.Triyopov/j.evoi', or appredicate, is that which is placed to the predicate, or rather placed before it, that it may be enunciated of the subject viz., is, since it has the force of a tie, and is not itself predicated. 2v7/carij- yopovfj.fva are those words which belong to the principal predicate e.g., Alexander is the son of Philip of Macedon. Here son is the prin- cipal predicate ; the other words are syncategorematic ; is is not pre- dicated, but it is the instrument and medium through whose interven- tion the predicate is attributed to the subject. (Goclenius, sitb voce.) (d) The infinitive is very commonly the subject of a proposition. It is a virtue to shun vice. Here to shun vice is subject. The infinitive is, of course, simply a form of the noun, as containing merely the attribute indicated by the verb. In the resolution of a proposition, grammatically considered, we may have various subjects and predicates, according to the emphasis or intention of the person employing the set of words. / ought to love my neighbour. This may be resolved : (a) 7 (subject) am one who ought to love my neighbour, (b) To love my neighbour (subject) is my duty, (c) My duty (subject) is to love my neighbour, &C. 1 In the case of a proposition referring to past time, as Homer was a poet, we may consider the element of time part of the predicate, or resolving the was into is, we can say Homer is a poet, or to be reckoned as a poet, and conversely some poet is Homer. 2 301. It is usual in logical treatises to consider judgments in respect of their Quantity, before treating of them in re- spect of their Quality. This seems to me to be an ill- grounded arrangement. The form of a judgment, what is essential to it, lies in the copula, and in the copula as marking inclusion or exclusion, attribution or non-attribution. Affirmation and negation, dependent on quality, as it is technically understood, are thus the essential characters of the judgment. We can have either the one or the other, while the subject is an indivisible unity, and does not admit of more or less in quantity. And it is not essential to affirma- tion or negation whether we take the subject, being a com- mon term or concept, as in all its extent or in some. All i Wallis, Logica, ii. 2. a Ibid. 250 INSTITUTES OF LOGIC. and some are indeed, in a sense, syncategorematic. Hence the relations of Quality ought to be considered before those of Quantity, in judgments. Predication, in truth, and the forms of it, lie at the very heart of judgment. And as ex- pressed in language a proposition is always essentially a sentence indicative, not expressive merely of apprehension, or wish, or threat. 302. Further, predication, as involving affirmation or negation, is a point antecedent wholly to the quality of truth or falsity in a judgment. It lies nearer to its nature or essence, in fact makes it. A judgment can only be true or false, as it in the first instance affirms or denies. This is the strict logical presupposition of truth and falsity alike ; and these are only possible as the judgment is a predication, an inclusion or exclusion of a given subject and class, or an attribution or definite non-attribution of a quality to a subject. Hence it is a mistake to place, as Mill does, the truth or falsity of a proposition in the foreground. This is necessarily a property or result, because it is only possible through a full-formed judgment. 1 And we must know about the nature of the subject and predicate from intuition and actual conception, before we can pronounce on the truth or falsity of their synthesis or disjunction. In a word, the form of the proposition precedes, is independent of the matter; and can be legislated for apart from consideration of this altogether, though originally, no doubt, we were led to join or disjoin subject and predicate through the force of intuition and the conditions of actual conception, as we actually numbered or measured, before we thought of the pure rela- tions of number or extension. (a) Ueberweg makes judgment essentially consist in "a conscious refer- ence to what actually exists, or, at least, to the objective phenomena. This gives the judgment its character of a logical function." (Logic, p. 188.) What has been already said shows that this is a secondary ref- erence in strict logical judgment, and is possible only in and through the constitution of the judgment, for which logic legislates. 303. A judgment (or proposition) is properly negative only when the negation affects the copula. The negation may be joined to the subject or to the predicate, while the pro- position remains affirmative. An animal which is not rational 1 Cf. Wallis, Logica, ii. 1. DEGREES OF NEGATION. 251 is a brute; what is not an animal is not a man or not-animal is not man. These are affirmative propositions, because the negation in no way affects the copula. We may say not- animal is not man. In this case the proposition is negative. 1 (a) In Latin the negative particle (non) is usually put before the sub- stantive verb (est) ; in English it is put after it Non est, is not. (Wallis, Logica, ii. 3.) (b) Every man is not wise. If this is taken distributively, then no man is ivise. But if we say, not every man is wise, we leave it_tp_be infgrml that some are. QT .may oe. Wo do not absolutely negate. (NVallis, Log., iii. 2.) "Not every one~~that saith unto me, Lord, Lord, shall enter into the kingdom of heaven." (Matt. vii. 21.) This does not mean none who say so shall enter ; but only some who so speak shall not. 304. We ought to distinguish two degrees, or rather effects, of negation. In the first place, we may deny an attribute of a subject, as the pine is not deciduous. Here the subject still remains, although the attribute has been negated. And the subject may be either what we find actually to be, or what we suppose ideally may be, for the whole class pine is to us an object of thought, an ideal class. In the second place, our negation may be such that the subject itself does not survive the negation. If I say a square circle does not exist, or is an impossibility in thought and fact, or there never was such a person as Presbyter John, I abolish not merely all attributes, but I wholly sweep away the subject of the pro- position. In the former case, the subject is but a form of words, with no unity of meaning or representation to begin with ; and I assert this of the proposition. In the latter, the subject has a definite meaning ; I do attach some conception to Presbyter John, but I sweep away the subject as a real existence. 305. "Non-homo is not a noun, for none is constituted which can be applied to it. It is neither enunciation nor negation. Let it be an indefinite noun (oVo//.a a'opwrrov), because it can be equally predicated of every, whether what is or what is not." (De Int., c. ii.) The OVO/AO. ao/Horov has only the form of affirmation. It really posits nothing ; hence it has been translated by Boethius nomen infinitum. The elephant is not man, is a finite or definite negative. The elephant is not-man means 1 Wallis, Log., iii. 2. 252 INSTITUTES OF LOGIC. that the elephant is something which is not man ; hence infinite, or better indefinite. To attach the negative particle to the predicate is an artificial form of expression. 1 In a proper negation, the negative belongs to the copula, or act of judg- ment. (a) Non-homo is not said in reference to man only, but in reference to horse and dog, and goat, stag, and hippocentaur, and all things absolutely existing and non-existing. (Ammonius Hermise, quoted by Trendelenburg, in loco.) The elephant is something not man, or something which is not in- cluded under man as a class, or as a sum of attributes. If I know men, and the attributes of man, I know what does not belong to the elephant, or objects among which the elephant is not to be classed. But this does not tell me what attribute or attributes elephant possesses, or what objects it is like. So far as this affirmation is con- cerned, elephant might not possess life, sensation, locomotion, organ- isation, &c. all these being in man. It tells me nothing, there- fore, of elephant more than that as subject of a proposition it means something, something conceived only, it may be, but I do not know what or more. If elephant as a simple concept be held as a subject defined, its attributes would be less than those of man, though in some respects congruent. To say it is not-man would be only to say that it is a concept having definite attributes, but less than those in the concept man. But obviously such a judgment would add nothing to our know- ledge of elephant ; it would only negatively say what already we posi- tively know of the subject. It would not even articulately develop what we knew. It would not amount even to an analytical judgment. The logical developments, or more properly manifestations of this form of the indefinite concept are founded on an essential misconception of the nature of negation, and a wholly artificial form of expression. Without a verb, says Aristotle, there is neither affirmation nor negation. (b) The judgment a6piiros faov). The article has the power of universal determination (prsefmition), (TOU na0u\ov Trpoa-Siopifffjiov^. But the article agrees to the unifying of the universal subject ; wherefore it is conjoined to each of singulars (pov- atiiKtav) and of individuals (ar6/Mtv), for we say 6 ?i\ios (the sun) and 6 ZScoKpaTTjs (Socrates), and sometimes we apply to what is excellent amid the like, as when we say, 6 TTOJIJT^S (the poet), 6 p-firup (the orator). (Ammonius Hermeise, M. De Int. f. 67 b ; Latine, p. 108 cf. pp. 118, 188, 299, 300. Ed. Venetiis : 1549.) The force of the Greek article, therefore, is twofold : (1.) To render the noun universal, to gather up the individuals of the class into a whole that is, to render the concept universal, and therefore definitely general ; (2.) To mark in singulars and individuals their definitude as such, and thus to individ- ualise, or render the noun definitely individual. This testimony of expression goes to confirm the logical accuracy of the classifying of the universal and the singular under the common head of the Definite. We have other examples of the power of the article to render definite, or to mark precise determination in the case of abstract nouns in which the unity or completeness of the attribute is indicated by the prefixing of the article, as fj aperr), ^ Sidvoia. So 6 crb? vlbs means thy son that is, one definite one ; while vl6s crov means any one of thy sons ; TO TroA.m/coj' means the citizens as a body ; rb Papfiapmbi', the barbarians taken collectively ; of OvrjTol means the class ; OvriTol, mortals, some at least, though it may mean the whole class ; ol-ros fsrl 6 Mtviinros means this is the distinguished Menippus ; i\ovs iroieurOcu, means to make the friends spoken of. So in German, when we speak of the class (definitely), the article is prefixed, as das Metall ist niltzlich metal (that is, the class) is useful. Die Stadt, the town, indicates definitely the single or individual town. Das Brod, bread, the class ; ein Brod, a loaf. In English the usage is rather the other way. The man would mean the individual ; whereas der Mensch means the class man. But if we say the dog, the cat, &c., we generally mean the class. In French the articles show whether a subject is taken universally (definitely) or particularly. When we say I'homme est capable de Utn et de mal, we mean tons les hommes, or the whole or class. As in Greek, the article is prefixed to abstract nouns, as la beaute, le courage, &c. This has the effect of individualising, and yet indicates the uni- versal quality in all of the class. So long as there is no express restric- tion, the term is understood universally. (Cf. Delariviere, Nouvelk Logique Clawique, 580-1.) ARISTOTLE S VIEW OF JUDGMENTS. 259 312. Judgments considered according to Quantity and Quality are usually divided into four kinds : A. Universal affirmative All A is B. E. Universal negative .ZVb A is B. I. Particular affirmative Some A is B. 0. Particular negative Some A is not B. Asserit A, negat E, sunt universaliter arnbee ; Asserit I, negat 0, sunt particulariter ambae. In those forms, the subject in universals, whether affirma- tive or negative, is taken in its whole extent, or distribu- tively ; in particulars, in part of its extent. The predicate in affirmatives, whether universal or particular, is held to be taken in part of its extent, only, or at least ; in negatives, whether universal or particular, the predicate is held to be taken in the whole of its extent. This classification of judg- ments, accordingly, must be regarded as referring to their extension only, and we shall consider below what modifica- tions and additions require to be made to it. (a) Aristotle's test of the universal (rb Se n.a66\ov) is that it may be predicated of many (De hit., c. vii.) ; of the singular (/ca0' tKaiTTov) that it cannot be so predicated. In Met., iii. 4, he says the individual is that which is one in number. Man is a universal ; Callias is a singular. As a proposition is an enunciation affirmative or negative, it is either universal, particular (tv p-fpti), or indefinite (a.8i6pt(TTos). I call the universal, says Aristotle, the being present (virdpxfiy) with all or with none ; the particular, the being present with some, or not with some, or not with all ; indefinite, the being or not being present, the mark of the whole, or the part being omitted, as the knowledge of opposites is one, or pleasure is not a good. (An. Pr., i. 2.) (b) 'r-n-dpxfti', with Aristotle, means that what is in the nature of the thing may be predicated in enunciation of the thing as subject. Pred- ication would thus be opposed to arbitrary mental creation, and would be an expression of reality. (Cf. Trendelenburg, El., 6.) 'firdpxftv is held to have two meanings (1.) One in which the predicate is said to be in the subject, as all B is A, 'A is predicated of every B. (2.) One in which the subject is said to be in the predicate, as att A is B, A is in the whole B. This is said to be the reverse of the former. Every B is A, means every one, hence all, omnitude. A is predi- .cated of every one of the subject, taken distributively. A is in the whole (of) B, means in the totality represented by B as subject. Hamil- ton's view, however, of the statement (in An. Pr., i. 1) is that it is 260 INSTITUTES OF LOGIC. " the preliminary explanation of the two ordinary modes of stating a proposition, subsequently used by Aristotle. In both convertibles he descends from extension to comprehension, from the predicate to the subject." (Log., iv. 302.) (c) Universal and particular are taken relatively. The universal may be predicated of many, and yet be itself a part of a wider notion. The genus which comprehends individuals may be a species of a higher genus, as man, Ccdlias, animated. The universal is more excellent than the particular. Thus of two propositions, he who holds the prior (the universal), also, in a certain manner, knows the posterior ; as if any one knows that every triangle has angles equal to two right, in a certain manner also he potentially knows this of an isosceles triangle, even although he does not know that the isosceles is a triangle. But he who knows the other proposi- tion [the particular] in no way holds the universal, either in faculty or in act. Further, the universal proposition is apprehended by the intellect alone ; the particular falls under the sense. (An. Post., i. 24.) There are three classes of objects of thought, according to Aristotle. (1.) Some things are such that they cannot be universally predicated of any other thing, as Clean, Callias, the singular thing, and the object of sense alone, the percept. These are properly only subjects. (2.) But of such subjects there are things which may be universally predicated, as man, animated. These express the genus or general nature of the subject. (3.) There are notions which may be predicated of others, but of them nothing prior or higher can be predicated. These are summa genera, to which nothing is prior and more universal, so that there is nothing which can be predicated of them. If being or unity be attrib- uted to these, this, according to Aristotle, is not true predication. Being and unity are only true predicates when they define the singular, by itself indefinite. (An. Pr.,i.27, and Trendelenburg, in loco.) In the Cater/ones, c. 2, Aristotle says that " individuals, and all that is numerically one, cannot be said (predicated) of any subject. But nothing prevents these being sometimes in a subject ; for example, grammar is one of the things which are in a subject, and yet it is not predicated of any subject." But, as Hamilton remarks, this is refuted by the admitted reciprocation of the singular. (An. Pr., ii. 23, 4.) " Let A be long-lived, B that which has no gall, and C all long-lived animals, as man, horse, mide, &c. Then A is in all C, for all C is long- lived ; but B also, that which has no bile, is in all C ; if, then, C is reciprocal to B, and does not extend beyond the middle, A must be in B." ( Cf. Logic, iv. p. 301.) (4.) Aristotle hesitates as to whether what were afterwards known as transcendent notions are to be regarded as universals. (Met., iii. cc. 3, 4; Eth., i. c. 6; Met., iv. c. 2.) Being, thing, something, are tran- scendent; animal, virtue, colour, figure, &c., are determinate and circum- scribed by certain limits of predication. The former are universal in the sense of being applicable to a plurality of objects ; but they are not so universal or applicable in so precise a signification as the deter- minate concepts. (Cf. Mark Duncan, Inst. Log., i. 2 ; Salmurii, 1612.) 261 CHAPTER XX. OF MODALITY IN PROPOSITIONS. 313. When the predicate is said of the subject barely or merely, as by is or is not, we have a pure, simple, absolute, or categorical proposition, that is, one merely assertory. When the proposition is wholly resolvable into its three logical elements, subject, copula, predicate, we have this kind of proposition, as A is B, A is not 13, the sun shines, bodies gravi- tate. When, however, the proposition contains a modification or qualification, which affects the copula, we have what is called a Modal Proposition. It is certain that A is B. It is believed that A is not B. It is perhaps true that C killed D. It is impossible that he can run over the ground in that time. Some modes of propositions appear to strengthen the statement ; others to lessen its effect, or the effect of a simple assertion. It is certain, absolutely certain, above doubt, &c., may be taken as intensifying the assertion. Perhaps, it seems, it may be, &c., may be regarded as diminishing the force of the simple statement. At the same time, the simple unqualified statement conveyed by is or is not, really often conveys a higher sense of assurance on the part of the speaker, than the use of epithets implying absolute certainty, or the absence of doubt. These epithets rather suggest an attempt to suppress doubt in the mind of the writer or speaker. 1 In the language of the older and more exact logicians, Modal Enunciation consists of the Dictum and Mode. The Dictum corresponds to the subject, the Mode to the Predicate of a Pure Enunciation. The Dictum is an expression consisting of the case of the noun and the verb of 1 Cf. Wallis, Logica, ii. 8. 262 INSTITUTES OF LOGIC. the infinitive mood, as Hominem esse animal necesse est. Here the Dictum is hominem esse animal; the Mode, necesse est. The Mode, it is added, is not the attribute in the Modal Enun- ciation, and the Dictum is not the subject, but correspond proportionally to the attribute and subject in the pure propo- sition. 1 314 The so-called modality of a proposition in many cases depends on the use of the adverb, and its natural expression of an attribute, and an attribute usually of the verb, or it may be adjective. We may happen to express in language an attribute which is one only of the complex attributes expressed by the predicate ; but thus to regard our proposition as essentially different from the simple or assertory, would be the merest bowing down before the husk, the accident of expression, and worthy only of the weakest nominalism. Whenever the mode is in the form of the adverb, it is resolv- able into an attribute of the predicate. This man was justly convicted, is readily resolved into a case of just conviction, and so with all ordinary adverbial phrases or clauses. Proper logical modality affects the cohesion of subject and predicate alone. (a) Every proposition expresses either that the subject is in the predi- cate, or is in it necessarily, or may be in it. (An. Pr., i. 2.) The first is the absolute proposition, the propositia pura of the schoolmen. It is called categorical by Kant and others ; but categorical with Aristotle means the universal affirmative proposition or simply the affirmative proposition. Under the necessary, Aristotle comprehends the impossi- ble, under the contingent the possible. (St Hilaire, in loco.) The terms modal and modality are due to the commentators, not to Aristotle; and they are akin to the grammatical moods of the verb. With Aristotle, mood (rpSiros], primarily and properly, means any ad- verbial qualification, as sunftly, beautifully, always, &c., and hence mood came to mean the most general classes of those qualifications, especially necessity, possibility, contingency, impossibility. Boethius translated rp6iros by modus, borrowing it probably from the gram- marians. The corresponding modern names are Assertory, Apodictic, Proble- matic. The rb fvSfx^^fvov of Aristotle was translated by Boethius contingens, i.e., in which the issue is such that whether it may or may not take place, is left undecided. The other meaning of contingent is that which is, but is opposed to what is necessary. (Cf. Trendelen- burg, in loco. ) Properly the possible is that which is not, and might be ; the contingent is that which is, and might not be. Aristotle has 1 Cf. Duncan, Inst. Log., L. ii. c. ii. 4 ; and Wallis, Log., L. ii. 8. NECESSITY OF THOUGHT. 263 distinctly noted these two meanings, but apparently uses them without always discriminating them. (Cf. Zabarella, In De Int., c. 12.) It is clear that the modality of a proposition, as such, depends wholly on the form of the copula. As Vives has well said, those propositions to which the mode is added have not a dialectical but a grammatical significance. (Cf. Mark Duncan, Inst. Log., L. ii. c. 2, 4.) 315. Logicians who have admitted modality into the science have usually contented themselves, though illegiti- mately, with recognising four kinds viz., Necessity, Con- tingency, Possibility, Impossibility. By Necessity is meant that the thing or subject spoken of cannot be otherwise ; by Contingency it is, but it might have been otherwise ; by Possibility it is not, but may be ; by Impossibility it cannot be, it is against the nature of the thing. Of Necessity, such an example as this may be given ; animal [is sentient, that is, sentiency is of the essence of animal. It belongs to animal, and this cannot be otherwise. Of Impossibility, the example may be given, man is not a stone. Man being sensitive, he cannot be stone. Of Possibility, Aristotle might have been a king, though he was not. Of Contingency, Alexander was a king, and Aristotle was a philosopher. Such things were so, but they might have been otherwise. (a) Kant joins together Possibility and Impossibility, Existence and non-Existence, Necessity and Accidentality or Contingency. But the impossible has no proper relation to the problematic. What is impos- sible is what cannot be; and the statement is given in a negative judg- ment, necessarily negative or apodictic. A cannot be B. Of necessity, no A is any B. Again, the accidental or contingent, what is, but may not be, or might not be, is assertory, and ought not to be coupled with what is necessary, or what must be, that is, with what is apodictic. (Cf. Ueberweg, Logic, p. 208.) 316. Obviously there is no necessity in sentiency as an attribute of animal. There is the simple fact that such a feature is a part of the concept animal, and that this is war- ranted by experience ; and further, that it is in all animals, or a property of the class. But a necessity of thought there is not in this case, nor in any case of generalisation from experience. We find certain objects distinguished by this feature, and we, therefore, classify them as one, or of the 264 INSTITUTES OF LOGIC. same kind. But we do so simply on the ground of a constant or never-failing experience ; and the feature becomes essen- tial to any individual object to which we give the class name, because we have already fixed on it as part of the con- cept, for reasons sufficient or insufficient. But necessity of thought there is none, only constancy or uniformity of experi- ence. So with consuming paper as a feature of fire, so with a stone falling to the ground when thrown into the air. All is matter simply of experience, and our concepts are, as to their constitution, relative to given experience. The essence, or essential features of a concept, are first of all determined, and then, of course, it is necessary that the object classifiable under it should possess the corresponding essence or sum of features. But this is a purely hypothetical necessity ; and in no way makes the concept itself a necessity of thought, however well founded as a generalisation from experience. Impossibility has as little reference to the facts of experi- ence. It is, in truth, merely the converse or negative of necessity. It is necessity that a thing should not be in such and such a manner. But so far as our ordinary and scientific knowledge go, we have no such necessity. To logical law, numbers, relations of space, even to meta- physical law, impossibility of conception distinctly applies ; but it stops there. There is no impossibility in conceiving the reverse of any purely physical law or relation of things. As applied to ordinary thought, it is a mere confusion of uni- versal negation with proper impossibility. 317. Necessity as applied to propositions of experience, ordinary or scientific, means only universal affirmation ; and this, run back to its elements, is grounded mainly on sci- entific induction. It is equivalent, in fact, to the universal affirmative of the logical treatises. Impossibility, in the same relations, may be fairly translated into Universal Negation. Thus A is necessarily B i.e., all A is B. It is impossible that A can be B i.e., no A is B. Contingency has the same references as possibility. Plato was a philosopher, but might have been something else. Some of the As are Bs, but they might have been otherwise. Some men are prudent, all the men in the ship were drowned. The cases of Possibility are obviously instances of hypotheses, or propositions to be tested by material evidence, and thus do not MODALITY. 265 fall within Pure Logic. Contingency is wholly extra-logical, and depends on our view of the nature of reality and its rela- tions. Possibility and Contingency may apply to the indi- vidual subject, to the particular, or even universal. Possibility This city may possibly be ruined by an earth- quake. The Pretender might possibly have been a King. Some of the sailors may have been drowned. All of the As may be Bs. 318. The true view of the modal proposition is that which makes what is called the dictum, or subordinate pro- position, the subject of the whole proposition, and the mode, whether necessary, possible, or contingent, the predicate of the dictum. In this way every modal proposition really becomes a singular, either affirmative or negative. Thus, it is possible that all metals are electrical, in other words, this definite proposition, all metals are electrical, is one of our possible conceptions or propositions. There is here, properly speaking, no question of whether the proposition (subject) is true or false. The reference is wholly to its possible verification. So in the case of a particular affirmative dictum, as it may be that some men are rogues or red-coloured. The some men are rogues or some men are red-coloured is the subject, and the predicate of contingency is affirmed of it. Here the subject is one definite individual statement. It is not possible, it is not contingent, it is not necessary, these would indicate singular negative propositions. 1 It is of no consequence to the defin- iteness or individuality of the proposition, taken as subject, whether it be of universal or particular quantity. It is re- garded simply as a complete or integral statement or proposi- tion. The subject and predicate are to be regarded merely as simple terms, seeing that they indicate one simple definite conception. Modality is wholly indefinite, in fact, infinite. And there is no reason whatever why, if any modality is admitted in Logic, all may not. Thus we might take anything in the form of a proposition as the dictum anything, in fact, which the in- definitude of expression might afford or the licence of fancy suppose. Then the modes might be as varied, and we should have every indirect form of speech, evasive or suggestive phraseology, possible in rhetoric or language, to consider, and all this, forsooth, that Logic may be expanded to the neces- i Cf. Wallis, Loffica, il 8. 266 INSTITUTES OF LOGIC. sities of what is called human thought or experience, an expression which is made to stand for accurate thinking and discrimination of points that differ. All modal expressions are, in fact, syncategorematic, and wholly external to the true nature of the proposition, of which even they form part. 319. But what is necessity ? On what ground is a proposi- tion necessary ? Is there more than one kind of necessity ? These questions require to be answered in regard to the first form of modality. What branch of philosophy is to give the answers ? Clearly that which deals with the nature, origin, guarantee of human knowledge. But this is obviously, at least, a very different science, or series of sciences, from that which deals with the nature and relations of concepts in every matter, judgments of every kind, and propositions in every form of reasoning. As to the possible, that which may or may not issue, what is to be our test of this? Clearly something in the character of the matter or cause, something, therefore, to be determined by observation and induction. The possible may depend on a law or rule of doubtful application, on a converging series of causes, whose total result we cannot beforehand predict with certainty. Is it seriously maintained that an inquiry into principles which would help us to reg- ulate knowledge or anticipation of this sort, is to be classed with the laws which regulate actual and possible conception, judgment, and reasoning ? We should thus require to have recourse not only to the whole rules of Induction, but to those of the estimate of Proof. And if the conclusiveness of our inference from the proposition were to depend on its character as contingent, this would be paralysed in a thousand cases, and never be absolutely strict in any. At any rate, we should be driven to a set of inquiries wholly foreign to the precise and useful rules of consistent and connected thinking, with the prospect only of indefinite delay. To reproach the Science of Formal or Deductive Logic for not taking into account the modality of propositions, is utterly beside the point and futile, just as much so as to say that Geometry does not tell you of the particular spaces it can measure, or Arithmetic the properties of the things, pears, apples, or cherries, which it can help you to number. (a) Aristotle said, iracro trpiraffis UEBERWEG'S VIEW or MODALITY. 267 t) rov tvSexfffBai iJirapx 61 "- (An. Pr., i. 2.) From this hint logicians have worked out modal judgments ; and though it may be said that Aristotle's statement refers to the relations of existence or actuality, this may readily further be taken as the ground of the various degrees of certainty regarded as represented by modal judg- ments. According to Ueberweg, the notion of affirmation is "the conscious- ness of the agreement of the combination of conceptions with actual existence; the notion of negation, "the consciousness of the want of agreement of the combination of conceptions with actual existence." According to modality, "the judgment is problematic, assertory, or apodictic. Its problematic character lies in the uncertainty of coming to a decision upon the agreement of the combination of conceptions with actual existence. Its assertory character lies in the immediate certainty (based on one's own or another's perception) ; and its apo- dictic character in the mediately acquired (based on demonstration, clir($8et|is) certainty of coming to such decision." (Logic, p. 206.) From what I have already said, it is, I think, clear that no one science, call it Logic or anything else, could possibly deal with all the grounds on which such judgments ought to be made, even as with a view simply to specify the conditions, laws, and methods of determining matter of fact, what only may be, what cannot be, what must be. This would be the most heterogeneous science conceivable, or a series of logics of the most varying order. One's own perception is the basis in some cases ; " authentic witness " in others ; inference, necessary inference, from another judgment. How can these be dis- cussed from a single point of view ? Or how can they be discussed at all, apart from the whole range of Mental Philosophy ? Avvaadai (to be capable), in the Aristotelic use, may be taken as meaning possibility in the sense of the existence of the cause, and thus of its possible operation, as a matter of fact. The seed is capable of developing into the plant ; the plant is capable of flowering ; eV5<= x* ffOai may be taken as meaning the absence of hindering or hostile circum- stances, in other words, causes that might frustrate the possible (natural) effect, aa frost in respect to the seed in the earth. Hindering circum- stances may further be represented by the absence of concauses, as apart from moisture, air, suitable soil, &c., the seed will not develop into what is potentially in it. These concauses, sometimes called con- ditions, are truly parts or elements of the cause, which is generally the sum of concauses. (On this point cf. Waitz, Org., i. 376, and Ueberweg, Logic, p. 208 et seq.) Supposing the sum of concauses or the cause to be present, and there being no counteracting cause, the effect will follow with necessity, that is, hypothetical necessity, or uni- formly without exception. There is, however, even here no true logical or even metaphysical necessity. In an Assertory Judgment, the certainty is said to depend on the cor- respondence between the judgment and our observation or generalisa- tion of facts, as bodies gravitate. All the planets move with the sun in space. Some, A is B. This refers to what is known as a matter of fact. But there is really no true distinction in respect of generalisations from 268 INSTITUTES OF LOGIC. experience between assertory and problematic judgments. The assert- ory judgment all bodies gravitate is not a matter of past experience, it is not even a matter of fact. It is a matter partly of fact and partly of objec- tive possibility, or probability, and therefore of belief. Some bodies have been found to gravitate; all bodies will or may gravitate. This lat- ter proposition is not strictly assertory ; it is a problematic proposi- tion, with the highest degree of subjective certainty. It is a descrip- tion of the state of my knowledge or assurance regarding fact, rather than of fact itself. It is my belief that all bodies will or can gravitate, is the true form of the universal assertory judgment, and it is simply a modification of the problematic. Then the Problematic Judgment has no proper place by itself. It, too, describes a state of my knowledge or a limited degree of assurance regarding fact. It is the case or I know that this event can happen, either because I know the sum of its concauses exist, or more slightly still, because I do not know anything that can prevent it hap- pening. This seed can or may grow into a tree, this person may com- mit suicide ; either because there is nothing to hinder the one, or it is in the power of the person to do what I suppose possible. But this indicates merely a state of limited certainty or expectancy on my part. The subject of the judgment, if it can be so called, is not pri- marily, as in the assertory judgment, the seed or the person spoken of, but the state of my mind is such that I believe that the seed can grow, or the person destroy himself. The problematic judg- ment is simply the statement of a hypothesis which is not itself a judgment but a conception. As far as the problematic judgment is one, it is simply assertory. The problem is merely a stage on the way to judgment proper, in which quite different terms will appear, for we shall then be able to say, the seed has become a tree, not, it is my belief that it may. The Apodictic Judgment has no better title to be considered as a separate form. It, too, refers to the degree of certainty or assur- ance, and is properly expressed in the assertory form it is the case, or I knoiu or believe that A must follow B. In the first place, must here is ambiguous. It may refer to a mere physical sequence, in which must simply represents unexceptional uniformity, as, all bodies must gravitate; or to a sequence, metaphysical or other, in which must is strictly taken as representing a relation the reverse of which is inconceivable, as, this change has a cause ; 5 + 5 = 10; all the angles of a triangle are equal to two right angles; nothing is less than something; one is not none. In the former case there is no necessity, that is, absolute necessity, in the sequence. There is simply the high, very high, certainty which attends a sound generalisation from experience ; and this in its univer- sality is always only problematical, only relative to grounds of belief, the actual facts not having, from the nature of the case, happened. In the latter case, the judgment is simply assertory of a state of my knowledge or belief, or of a condition of my knowledge. A change has a cause, and I know it must have a cause, for the reason that I can- not think it otherwise ; 2 + 2 = 4, for the reason I cannot conceive the sum any more or less. The objective necessity lies properly in the UEBEKWEG'S VIEW OF MODALITY. 269 matter of the judgment, or in that about which I think. I express the state of mind produced by this necessity by must, as I might express a generalisation from experience by will, or an objective possibility by may or can; but all these are properly distinctions arising from the matter or application of the complex subject or predicate, which is really change having a cause, all bodies gravitating, this seed growing. These refer to degrees of my knowledge, founded no doubt on objective fact, but none the less capable of being stated in a plainly assertory form. That the simple assertion is the essential and only necessary thing, ia proved by the fact that it alone is sufficient to guarantee a necessity of inference. All A is B, all C is A, all C is B, is as valid as all A must be B, all C must be A, therefore all C must be B. Whatever be the relation of the terms, as to material connection, this does in no way affect the necessity of the inference. (6) "There is no modal enunciation," says Valla; "there is neces- sity and possibility in the conclusion, as there is truth in all parts of the argumentation. For all must be true whether you say it is neces- sary, or possible, or easy, or honourable, or anything else. In this respect the true is the same as the certain, for nothing is true that is not certain and confessed. But the truth of the two prior parts of the syllogism and argumentation is placed as certain and confessed ; in the last, however that is, in the conclusion it is extorted, and therefore there is in it necessity or quasi necessity." (Dialectica, L. ii. c. 39, f. 50 a , ed. 1530.) 270 CHAPTER XXT. COMPOSITE JUDGMENTS - HYPOTHETICAL OR CONDITIONAL, DISJUNCTIVE, DILEMMATIC. 320. Looking to the special relation of the subject to the predicate of a judgment, as direct (or unconditional), or in- direct (or conditional), we have, as has been already said, the various forms of judgment, known as Categorical, and Com- posite or Conditional. For we may assert directly, absolutely, or simply one thing of another that an attribute belongs to the subject or that something will be or happen, or needs to be thought, if only something else in the first place hap- pens or is thought. We may say A is B, or if A is, then B is. If the sun is up, then it is day. A is either B or not-B. A is either B or C or D. The world is either eternal or not-eternal. The world is either the work of chance, or the work of intelligence. This intelligence is either a single act in a remote past, or it is a continuous act. We have thus the Hypothetical Judgment (called also Conjunct and Conjunctive) if is, there is ; or the Disjunctive Judgment this is either, or. To these should be added the Hypothetico-Disjunctive, also called Dilem- matic, being a combination of the two first-mentioned, as if A is B, it is either C or D. (a) With Aristotle categorical (/car^opi/c^s) means affirmative. In later usage, it is applied to a judgment of simple or absolute assertion or denial, as opposed to the hypothetical or disjunctive judgment. (Cf. Hamilton, Logic, L. xiii.) Aristotle cannot be said to have recognised the dis- tinction of categorical and conditional (conjunctive and disjunctive) judgments, at least as grounds of reasoning, so as to form hypothetical and disjunctive syllogisms. This distinction or addition to the Aris- totelian view seems to be due to Theophrastus and Eudemus. It was among the Latins elaborated by Boethius. (De Syllogisimo Hypothetico.) HYPOTHETICAL JUDGMENT. 271 (6) With regard to the use of Hypothetical and Conditional, it ought to be noted that the former is sometimes employed to mark the genus of Conditional and Disjunctive judgments, as by Aldrich and Whately. This usage ought not to be followed. Conditional is better suited to mark the genus of which hypothetical and disjunctive are species, though even this term is not unambiguous. (Cf. Hamilton, Logic, L. xiii.) 321. The Hypothetical or Conditional judgment is a statement of relation between an antecedent and a conse- quent, or reason and result. The form lies in the connection or consequence. If A is, B is ; or B is on the supposition or condition that A is. Should a stormy wind blow, that wall will fall. In this form of judgment, the condition or hypo- thesis is attached to the antecedent or subject. 322. The hypothetical judgment thus differs from the categorical, inasmuch as the latter affirms an attribute existing in a subject, or a subject as belonging to a certain class ; whereas the affirmation, mental or real, of the consequent in a hypothetical judgment, depends on the previous or con- temporaneous affirmation of the subject. It is one thing to say Lying is dishonourable; it is quite another to say If this man lies, he dishonours himself. In the former case we affirm an attribute of a subject ; in the latter we do not pro- perly affirm, but state a supposition or sequence following the realisation of a definite hypothesis. This is simply a preparation for absolute affirmation. It is not wholly deter- minate. 323. In the hypothetical judgment there are three ele- ments the Antecedent, the Consequent, the Connection or Sequence as, If A is B, C is D. A being B is the antecedent, C is D is the consequent. If is, or if then, is the copula, and indicates the sequence. The effect of the copula is to bind up antecedent and consequent into one act of judgment. It is, in fact, a statement simply of connection. As Ammonius Hermieae puts it : " Hypothetic enouncements are made up of categoric. For they express the consequence or opposi- tion of one categoric proposition and another, uniting them with each other, by either the conjunctive "or disjunctive particles, in order to show that they constitute together a single enouncement." l 1 On De Interpretatione, f. 3, 1546. Quoted by Hamilton, Logic ii , Ap- pendix B, p. 389. 272 INSTITUTES OF LOGIC. 324. The sequence, moreover, is a necessary one ; for we are supposed to have in the antecedent a reason, full and adequate, otherwise there would be no reason at all for the consequent. This may be founded on material considerations of causality in the antecedent ; but this is merely the ground, more or less valid, of the reason, or cause as a reason, in a word, of the necessary form into which we suppose ourselves entitled to put the particular sequence. If the one thing is, the other thing is. This formula, however grounded in any partic- ular sequence, is yet independent of the given sequence, and raises the connection to the form of a necessary one, neces- sary in our thinking. Even if the reason or antecedent given were found to be insufficient to warrant the consequent, this would not affect the validity of the principle of connection, but only its material truth. At the same time, the principal value in practice of hypothetical judgment and reasoning is the material truth or actual sufficiency of connection between antecedent and consequent in any given case. 325. The Hypothetical judgment may be regarded as in Extension, and as in Comprehension. In the former case, the formula will be, If A is, B is ; if man is, animal is. If all A is B,'then C (a part of A] is D (a part of B}. Or, If all man is animal, European (a part of man) is mortal (a part of ani- mal). Here the supreme law or canon regulating the infer- ence will be simply that of Identity. In this case Eeason and Consequent will be completely identified with the formal law of the relation of whole and part. In the latter case in Comprehension the formula will be (a) If A is, B is ; if the sun is up, it is day. (b) If A have for its mark B, then C (a mark of B} is a mark of A. If the moon presents always the same face to the earth, then, having no diurnal revolution on her axis (a mark of always presenting the same face to the earth] is a mark of the moon. The law which immediately governs this proposition, or rather the inference from it, is A mark of the mark is a mark of the thing itself, or Pradicatum prcedicati est prcedicatum subjecti. Nota notce est nota rei ipsius. - The subject in this case is taken comprehensively, as that which has immediate and mediate marks or attributes. The strength or validity of the assertion lies in the connection, however materially grounded, between the immediate and the DISJUNCTIVE JUDGMENT. 273 mediate attributes. This may depend on inherence or caus- ality, on coexistence or succession, and affects the actual truth of the judgment ; but the form or supposition being given, we are able logically, independently of this, to educe the formal consequence. 326. In the Disjunctive judgment, the essence or form lies in the opposition or contrast of the several members of the predicate, as A is either B or not-B ; A is either B or C or D. The opposition among the disjunct members means that one is to be affirmed, and one only. There is just this much truth or assumption, that the subject is to be found in one or other of the members, and, if found in one, is not to be found in the other or others. In the former case, or strictest kind of disjunction, the logical form alone necessitates the exclusion ; in the latter case, the whole of disjunction has been constituted through intuition ; the members are given as exclusive on this ground ; and hence the inclusion in one (or affirmation) implies the exclusion from the others. The world is either eternal or non-eternal, is an instance of the former contradictory disjunction. A was born either in 1801, or 1802, or 1803 ; the burglar made his escape either by leaping from the window, or from the roof, or by sliding down the rone, are instances of the latter contrary disjunction. Contrary alternatives are properly, in the end, forms of contradictory. A is either B or C or D, means really, A or not- A, B or not-B, O or not-C. The world is either eternal, or it is the work of chance or of intelligence. This, strictly taken, means the world is either eternal or non-eternal (that is, it had a beginning in time) ; it is either the work of chance or not, i.e., it is the work of intelligence. As the work of intelligence, it may be of a single act or not ; that is, it is plural or continuous. The disjunctive statement is thus also a preparation for determinate affirma- tion or negation, rather than affirmation itself. 327. In the case of the disjunctive judgment, the copula is eithei or ; this brings together the alternatives in one act of conception. And this synthesis is the preliminary to the analysis or ultimate exclusion of the one from the other. All disjunction is affirmation and negation through affirmation, or it is affirmation through negation. For when we say A is J9, then it is neither C nor D. It is neither spring nor summer ; therefore is is either autumn or winter. s 274 INSTITUTES OF LOGIC. (a) It should be noted that disjunction has nothing whatever to do with Community or Reciprocity, as Kant would have it. Disjunc- tion may refer to exclusive alternatives in time, or place, or quality, or quantity, which admit of not the slightest possibility of community or reciprocity, in any scientific sense of the terms, or in any logical or metaphysical sense. This time, that time, this place, that place, this quality, that quality, &c., have, as to real reference, or logical reference, not the semblance of reciprocity. All actual fact, indeed, is fact, whether there is reciprocity or not ; for all fact of intuition every per- cept is exactly as it is perceived, as every concept is exactly as it is apprehended, whatever may be its possible or discoverable relations. 328. There is a distinction between the hypothetical and disjunctive, which has not received sufficient attention. In the case of the hypothetical, as usually put, the consequent, while dependent on the antecedent, may not be dependent on it alone. When we say, if it rains, the earth will be wet, we connect reason and consequent, but we do not (materially) con- nect the consequent exclusively with the antecedent, for dew or pouring water on the ground may make it wet. Or when we say, if this man is sick, he is not Jit to travel, the consequent may depend or be realised through other causes or reasons than the one specified. But in the case of disjunction, there is a wholly different conception. Our predicate in disjunc- tion implies, from its very form, a whole, the distribution, in fact, of a genus into its parts or species, and these taken exhaustively or exclusively. This is either A or not-A. This is either A, or B, or C, or D. The season is either spring or summer, or autumn or winter. This planet is one or other of the eight. In all these cases we have determined a whole within which the subject of which we speak must be found or thought. There is no room for an indefinite number or plurality of dis- junct members, as there is for a plurality of antecedents, as -in the case of the hypothetical judgment. The disjunctive judgment, therefore, approaches much more closely strict logical form of whole and part than the hypothetical, at least as commonly understood and interpreted. 275 CHAPTEK XXII. HEGEL'S THEORY OF JUDGMENT. 329. In the following paragraphs my aim is to notice the principal points in Hegel's doctrine of Judgment. I do this chiefly because I find that they have been adopted without any definite acknowledgment by writers who have referred to certain logical points, or have expressly treated of them. I notice them, also, because they are brought forward as speci- mens of " advanced thought." In themselves they are of the very slightest value indeed, none. But as they are fitted to impose on people, simply from their novelty a great charm in these times the truth of a thing, if old, being rather against it they require notice. 330. According to the principle of the immanent dialectic, which has been laid down as absolute, and foreclosing a system of the universe, an idea posited opposes itself to its negation. This, in its turn, produces a new idea, neces- sarily better defined or more true than the first. In this second part, however, of the Science of Logic, called the Sub- jective Logic, it seems that development that is, from notion to judgment and judgment to reasoning does not take place according to the principle of negation, but quite another, viz., that of evolution or development, akin to the progress of organism in nature. The grain becomes the plant ; it be- comes in an explicit form what it was virtually before. Thus the notion passes into the judgment. The notion is the ab- stract form, the judgment the dialectical, and the reasoning the speculative form. Notions exist in things things are only living notions, also things are judgments realised ; and reasoning is the reality in its true or speculative form. 1 1 Compare for this chapter Die Subjective Logik, being the second part of 276 INSTITUTES OF LOGIC. 331. But supposing the notion to be the grain from which the judgment is evolved or which evolves the judgment, what of the origin of the notion itself? It will surely be admitted that the concepts of experience, and of science, are generalisations, that they depend upon, are due to some pro- cess of elaboration or constitution by the mind. We need not at present refer to the universal concepts of intelligence, such as cause, substance, quantity, quality, &c. which may be sup- posed to have another origin and character. The generalised concept is at least a cognition or relation among individual objects of time and space, a cognition, in fact, of similarity amid objects or impressions at different times. Can this be cognised without a judgment? without judgments of various orders? We judge surely when we apprehend a reality or impression in time. We judge or subsume under certain universal concepts of being, unity, difference, &c. We remember, compare, generalise. Not one of these acts is possible apart from judgment, apart even from what is essential to logical judgment ; and yet, according to Hegel, we have to wait for judgment until the notion develops itself into it, the notion or so-called grain of the judgment being, in the first instance, the product of it. By judgment we form notions ; notions, again, evolve into judgment ; and thus judg- ment is explained ! Such is the theory of advance in Psychol- ogy and Logic. 332. The notion or idea of a thing is precisely the gener- ality which exists in its individual. It is neither abstract nor distinct from things, nor posterior to them, but, on the contrary, pre-exists in them. Our religious understanding proves it in saying that God made the world out of nothing, or that the world is the work of thought, or of the ideas of God. This clearly proves that The Idea has by itself a crea- tive power which has no need, in order to manifest itself, that things are already produced, but which, on the contrary, precedes their birth ! 333. The idea is at first general ; but its proper dialectic force obliging it to determine itself, it becomes particular in derfying itself; and this particularising, which is the negation Wissenschaft der Logik, ed. Berlin 1841. Of this there is an excellent abridg- ment in La Logiqiie Subjective de Hegel, by Sloman and Wallon (Paris, 1854), which I have found of much use. HEGEL'S THEOBY OF JUDGMENT. 277 of the general, is manifested or comes to existence under the form of the individual. The particular and the individual are not, therefore, separate or distinct from the general ; this takes these forms without changing its nature ; it particu- larises and individualises itself, but always remains what it was at first. 334. From the decrease in comprehension and the increase of extension in the ascending scale of generalisation, Hegel argues that God or the Supreme Being, as the last or highest notion, is necessarily to be regarded as the poorest of all in attributes, instead of, as He ought to be, the richest. In this it is assumed that God or the Supreme Being is identical with the abstraction Being, which is the suminum genus in generalisation. Of this there is no proof; in fact, it is a perversion of accurate logical phraseology, and it is disproved by the fact, that while Being as a general notion can be predi- cated of all lower in the scale, God or the Supreme Being cannot properly be predicated of any. 335. The general and the particular always subsist in the- individual ; hence there are no individual notions . . . Every individual thing is at the same time general and par- ticular ; and this union of the general and the particular in its bosom is precisely that which constitutes its proper notion or its individuality, which is thus only the product or image. 1 It follows from this that in the case of a generalised con- cept, as book, house, this book, this house, is, as individual only, an image or instance, represented in the imagination of the general (concept) and the (individual) picture, and that this in no way differs from the book or the house, which I perceive or reach by intuition, that is, it is untrue to our experience. All individuals, accordingly, in time or in history, are simply instances of general concepts embodied. Their whole in- dividuality lies there. Proper names ought, therefore, to be discarded from language as a superfluity. Only the particular (some or one of all) is vindicable. 336. In Hegel's view, the body and the soul of a judg- ment are its individuality and generality, that is, the subject and predicate. The answer to a question gives necessarily a subject, which is only a simple word without meaning, on 1 Cf. Die Subjective Logik, L c. 1. 278 INSTITUTES OF LOGIC. which I arrest my attention to find the predicate of it. This is a thing without attributes or qualities, which is about to receive its determination, but which is yet absolutely noth- ing. It is only a name or sound. 337. Modern logicians say or assume, that in the judg- ment the subject and predicate are two things or substances equally real, having the same value, existing on the same title and the same line, to be met with here or there in the world, and that the human intelligence unites or relates them in the judgment. But this hypothesis contradicts com- mon sense and language, according to which the copula is, which joins the subject to the predicate, says that the first is the second ; that which proves that the act of our mind called judgment, does not unite two things which without it would be separated, but, on the contrary, that it separates or divides into two parts, named subject and predicate, things or notions, which by themselves are at the same time that which marks the subject and the predicate. Judgment is, therefore, an act of the mind by which we divide into subject and predicate an idea or a thing which had not yet been divided, before this act, into its two constitutive parts. Thus the copula is marks not a conjunction but a disjunction, not only an identity but a difference between the subject and predicate, which by it are at once united and separated. There is a thing total or one, cut, so to speak, into two by judgment, which enables us to see it under the form of sub- ject and predicate. In the eyes of the grammarian, the sub- ject and predicate have an independent and distinct existence ; but in logic, as in reality, there is absolutely none. The pre- dicate is the subject, or rather the thing is actually the subject and the predicate together. 1 338. (1.) There is no meaning in a subject taken by itself. If this means merely that a notion or concept can- not be realised in the mind without thinking its attribute or attributes, or the marks which make it up, it is an idle truism. If it means to call this process attaching a predicate to the subject by a definite assertion implied in the copula is, that is, a definite judgment, it is psychologically false. The marks contained in a concept as subject, can be realised in the imagination as a picture without any such explicit 1 Die Subjective Logik, i. c. 2., especially pp. 66, 67. HEGEL'S THEOEY OF JUDGMENT. 279 or express assertion. This representation is, moreover, the ground or condition of any such judgment. If there be no meaning in a subject that is, a notion or individual taken by itself, on what ground do I add a predi- cate to it ? If it is on the ground of identity, or as an analysis of the subject, how can I predicate at all if the sub- ject is purely a void notion ? If it is that I add on a new predicate, how is it that I can attach in any way a predicate, new or old, to a void subject? When I say something of a thing, surely I know the thing to some extent ere I say something of it. 339. (2.) Logicians, in saying or assuming that the sub- ject and predicate in a judgment, or in some judgments, are actually separate, either in the world or in thought, until they are conjoined by the intelligence in an act of judgment, are quite right. For they are speaking not immediately of things, but of concepts simply, or of the individual and the concept. When I say that water rusts iron, or that fire con- sumes paper, I join together two concepts representative of things or facts in my sense-experience. And until I have done so, or have knowledge enough to do so, the facts lie out of my experience. Nor in this case do I need to say that the subject is the predicate, or that the subject is identical with the predicate ; which would simply be false. Water is not rusting iron, fire is not consuming paper but they form two elements in one synthesis, and the latter is an attribute of the former. I may represent water rusting iron, or fire consuming paper, as a whole or one thing one complete fact which by the act of judgment I divide or separate into two parts sub- ject and predicate at once separating or conjoining and dis- joining in the same mental act ; but all the same, I have not identi6ed the two concepts, I have not even found the two things, water and rusting iron, together only at one time, for these are generalised concepts. I have, in order to make this one representation in the mind of water rusting iron, or water wearing the rock, been obliged to collect together facts from various points of time and space ; and this gathered experience is the ground at once of my total representation of the thing and the judgment which follows. If the thing be " a judgment realised," there is simply a judgment before my judgment, which I come to learn, and to gather, through 280 INSTITUTES OF LOGIC. generalisation, extending over time, and varied particulars, not necessarily set together, and not yet gathered into one total representation. 340. (3.) One would be curious, too, to learn how such a theory of judgment, even when applied to experience, would suit those cases in which we add a new predicate to the sub- ject, as when Newton said, the planetary motions are due to gravity. Was it that this hitherto unknown fact was reached by him by dividing in the first instance a totality in his mind gravitating-motion, or by coming to unite, through experience and inference, gravity to motion, which, though joined in point of fact, had been hitherto separated in all human in- telligences? Is not the representation as one or a whole of gravitating-motion, of motion due to gravity, or light flowing from ethereal undulation, the result of a synthetic judgment, rather than the ground of it ? And is it not an abuse of words to call the complex fact in nature a judgment, unless as the supposed act or result of an intelligence conscious of realising the synthesis ? And are we to talk of this with an assurance as complete as we can of our own act of judgment ? 341. (4.) Further, if the judgment be the breaking up of a known whole, containing what we then call subject and predi- cate, and we do not know which is which until the judgment shows it, how can we by judging show it, and how. can the subject judging know the difference? Is this not simply to suppose that we have a judgment before we have a judgment? 342. The essential character of every judgment, whatever its form, is to express that an individual thing posited as sub- ject, is a general notion given as predicate, in other words, that the generality marked by the predicate is (or exists) in the individual thing expressed by the subject. . . . The subject or individual thing is raised to the sphere of its predi- cate, and the predicate or the general, in its turn, is placed in existence or realised by the subject. 1 Hence, an enuncia- tion which expresses an individual thing by its characters is not a judgment, as, Aristotle died in the fourth year of the one hundred and fifteenth Olympiad, aged seventy-three; or, Caesar was born in Rome ; he made war on the Gauls for ten years, and passed the Rubicon. Such statements are propositions, but not judgments. 2 1 Die Subjective Logik, pp. 69, 70. 2 2bid., pp. 67, 68. HEGEL'S THEORY OF JUDGMENT. 281 343. There is a judgment, only when an individual thing is determined by a general notion. Therefore, one subject cannot be a concept, it cannot be an abstract gen- eral concept, we cannot state the relation between con- cept and concept ; we cannot speak of an abstract term ; we can only predicate in a judgment of the individual. Nor if the predicate be singular have we a judgment. I venture to say that such a criterion of proposition and judgment was never before proposed, and none more groundless or futile could be given. We cannot say, this is not the man you mean, or took him for. The predicate is singular, therefore there is no judgment. Is there any further reductio ad absurdum needed of reckless speculation or assertion? 344. Hegel seems to find this doctrine rather too much even for him. He therefore hastens to add that individual enouncements are judgments, if they be stated in answer to a doubt. If the time of the death or the age of the philoso- pher were put in doubt, or if it were asked whether an indi- vidual was really dead, or only seemingly so, the answer to such a question would be a judgment, because generality is involved Has the train really passed the station or not ? It has passed the station. This is now a judgment ; but if we had not been in doubt about it, and asked the question, it would not have been one ! It comes to this, that no histori- cal proposition is a judgment. 345. To show that the predicate fills the subject, regarded as essentially void, with content, Hegel gives us the example God is all-powerful. Without this predicate, God would be an empty frame. This, as the proof of a universal feature of judgment, is simply worthless. Even as filling the subject with content, it is not true ; it is simply adding a predicate to what we know and may know of God otherwise. Because we happen to add a predicate to a subject, it does not follow that the subject was originally void. Had the predicate embodied an adequate definition of God, it might have been plausibly said to have filled the subject with content ; but the predicate in this case is not such. All-powerful is not convertible with God ; and were the statement even true of defining propositions, this would not make it true of all. Nay, the predicate here is even analytic, for we use it because we already know that, if this attribute were lacking, the sub- 282 INSTITUTES OF LOGIC. ject spoken of would not merit the name God. And what, on such a doctrine, becomes of synthetic propositions, in which we are supposed to add a new predicate to that which we already know of the subject? 346. The qualitative judgment represents the agreement or disagreement of two notions. This, according to Hegel, neglects what merits more attention the coupling of the individual to a general notion. Starting from the position that judgments are enunciations expressive of individual things by means of general notions, Hegel divides judgments into four kinds, viz. : (1.) Qualitative, or of Simple Apperception. (2.) Keflective. (3.) Necessary. (4.) Ideal. 347. The Qualitative Judgment or Judgment of Apper- ception affirms or denies a quality. But under this qualita- tive form, judgment is not yet developed : for the subject, which is nothing in itself, is here supposed essential ; the predicate, on the other hand, being nothing in itself, and only united to it in an accidental manner. By this form of judgment is obviously meant the comprehensive or attributive judgment of modern logicians. 348. One of the greatest errors of logicians, according to Hegel, is to hold that such a proposition as this violet is blue or not blue, necessarily embraces in one or other of its alterna- tives the truth. This may be true or false without reaching the reality of things. That which is just is not always true. We reply to this that the proposition is both just and true, so far as it aims or need aim at truth. Whether violet be blue or not, is not here the question ; nor is such a point decided. All that is said is, these are exclusive alternatives ; they cannot coexist in the subject ; if one is there, the other is not. Our intuitional perception prevents us making the union. A subject say violet, which would unite both, would be meaning- less, void in the true sense of the word ; as void and mean- ingless as to say this is a case of murder or it is not ; and yet it may be both murder and suicide, or both murder and accident. Hegel's argument in support of his paradox is as weak as the absurdity of the paradox is strong. What is just is not always true, is proved, according to him, by such examples as HEGEL'S THEORY OF JUDGMENT. 283 a man is sick ; some one has committed a robbery. These judg- ments may be just or accurate, but they are not true ; for a sick organism is not a true organism, and theft does not enter into the true notion of humanity ! 349. There is nothing peculiar to this first form of judg- ment, which does not belong to the third and fourth forms. It merely says, the individual (I) is a generality (Gr), that is, I G. The violet is blue, or the individual violet is the generality colour blue. That the individual is a generality is expressed in the same judgment under another form ; for this proposition, the violet is blue, expresses, rather implies, two things at once, that the violet is a whole endowed with several qualities, and that it has that of blue. But it does not expressly say the former, as it does not expressly say that the colour blue may belong to other individual objects besides the violet. This first form of judgment is imperfect, and therefore untrue. 350. It is a wonderful test of the truth of a judgment, even of its imperfection, to find it stated that as the form of it does not express all that is possible about the matter, or all that is implied in the matter, though what it expresses may be both consistent and accurate, it is yet to be set down as imperfect and untrue. Pray, what single judgment would stand this test, except, perhaps, strict logical definition ? Are the exigencies of thought as a process of abstraction and con- centration to have no fitting form of expression or judgment ? 351. About equally instructive and convincing is the proof that every negative judgment is necessarily affirmative. This violet is not red, implies that it has a colour ! This ob- viously is not implied in the form of the proposition, it is inferred from the matter ; because we are already supposed to know, regarding violet, that it belongs to the class of coloured things. But this is a wholly secondary form of judgment, an accident, indeed, of the matter about which we judge. The negation of the predicate as the form of judgment does not put a positive in the place of the negation, even in the case of the qualitative or comprehensive proposition. For we may say, The man of whom you speak did not inherit the property. This, certainly, does not imply that he inherited anything else, or that there was anything else to inherit. 352. The insufficiency, according to Hegel, betrayed in 284 INSTITUTES OF LOGIC. those two sorts of judgments, the qualitative affirmative and negative, is corrected by making the two terms of the proposi- tion identical Thus, this Hue violet is a blue violet. But this is not a judgment, it is simply a tautology. So with all nega- tive judgments called impossible or infinite, as this table is not an animal; the rose is not a plant. In the case of tautology, the predicate is absolutely identical with the subject ; in the other case, absolutely different. There is no putting an individual subject (I) in relation with a general predicate. All qualitative judgments issue either in tautology or in a futile infinity. And yet, as if to show the very licence of the possibility of differing, Hegel holds that negative infinite judgments exist. A crime is a negative infinite judgment, for the criminal not only denies the right of the individual, but the right of the State. Death, too, is a negative infinite judgment, for soul and body are separated so as to have no further relation. 353. One fails rather to see the point of the imperfection of the form of the qualitative judgment ; and certainly, if there be imperfection, we shall not find the correction in the formula given by Hegel, which is a simple travesty of fact and form. This violet is blue, means, it seems, this blue violet is a blue violet. It means necessarily nothing of the sort, and it can only be travestied into this on the basis of another previous judgment and meaning. This violet is blue means (1) that I select or attend to the colour or blueness of the violet I see, and not to its shape or form, or other qualities, to which I might have attended ; (2) that it has the mark blue, and not that of any other colour which it might have had. All this implies judgment, and judgment of an important and essential kind. It is the foundation, and affords the formula, of all observation, all concentration, and therefore of accu- rate thinking and science. Nothing of this is formulated in saying this blue violet is a blue violet, for this is a secondary or derivative statement, founded on the primary observation and judgment that of fact regarding the object I see, and only possible after I have apprehended the predicate blue as its mark. I am not first speaking of what I know to be a blue violet, for violet and blue violet are not identical ; and this statement, this blue violet is a blue violet, is only possible through an addition to my experience, that is, the HEGEL'S THEORY OF JUDGMENT. 285 other natural judgment by which I superadd a new predicate to the subject. 354. As to negative infinite judgments, as Hegel calls them, it is clear that he does not know precisely what an infinite or rather indefinite term, ovo/aa ddpio-rov, is. 1 The so-called predicate in such a judgment is not in the least degree more in analogy with the predicate of a qualitative judgment than with that of any other. 355. But as there is thus tautology in identifying the two terms, there is no correction of the imperfect form of the qualitative judgment. Also, when the two terms are abso- lutely unlike, there is as little correction of the imperfect form. Hence the dialectic force drives us to the following form Reflective Judgment. 356. The Eeflective judgment explicitly translates the truth of the qualitative viz., that the subject does not exist alone, but that there is a predicate, that is, a relation to a thing which exists out of it. When we say this violet or this flower is blue, we may con- sider the subject or individual (I) as existing of itself; in this reflective judgment, on the other hand, as this plant is salutary, besides the thing in itself, we always think of some other thing, as the malady which the plant can cure. In the Qualitative judgment, the individual was the prin- cipal thing, in which only the predicate appeared to inhere. In the Eeflective, it is the predicate or general which becomes the important element. Thus Man is mortal ; all matter is heavy ; all things are perishable ; certain forms of matter are elastic. 357. There is no such difference in those two kinds of judgments as is here supposed. The qualitative judgment about the individual passes readily into the reflective, really extensive judgment. The predicate in the former case may be at first individual, but as such it is the ground of a class actual or ideal. And this class it grounds or forms is just as much a generality as that given in salutary, useful, &c., or any other common term. The whole of this is a mere wandering from what is essential and relevant, and shows a constant confusion of matter and form. 358. What can be more arbitrary or more misnamed as 1 See above, p. 175. 286 INSTITUTES OF LOGIC. necessary evolution or dialectic than this progress from the reflective judgment to the necessary? Certain forms of body are elastic, means, it seems, that elas- ticity belongs to all bodies, but more particularly to some ! Hence the subject loses its character of individuality, becomes general, and thus the subject and the predicate may be substi- tuted for each other ! But when the generality enters ex- pressly into the subject, as all bodies are elastic, it is no longer a fact which we express, but a necessity. Hence the tran- sition from reflective to necessary judgments. A doctrine which is based on the identification of some and all, which confounds universality with necessity, and is supposed to be bolstered up by a hypothetical dictum, what can be said of all the individuals belongs necessarily to the species, may be fairly left without comment. 359. In necessary judgments, the subject and predicate are so related that the one is the true essence or substance of the other, and reciprocally. Further, they are subordinated as individual to the species of which it forms part. Thus, the violet is a flower, this ring is of gold, gold is a metal. The copula is here marks not simple existence, or relation, but absolute necessity. To say that gold is dear, and gjold is a metal, is to state two totally different judgments.,. 'Bear . is an accident, and metal marks the essence. 'jifjr- * The form of proposition, gold is a meteft, says implicitly that the quality of metal belongs not only to gold, but to silver, copper, iron, &c. Whence it follows that judgment does not carry in itself the proof or reason of its truth or necessity. This reason is expressed in the second form of necessary judgment, the Hypothetical or Conditional as, if this thing is, this other thing must be also, or if A is, B is. Judgments of this class almost deny the existence of the two terms A and B, by showing that neither A nor B can exist alone by themselves, because A is not only A but B. Without losing the one, we recover the other in the Dis- junctive form that is, the third and last form of the neces- sary judgments. Thus A (genus) is either B, or C, or D (species). These are the only species and all the species. But we need science to show us that the species actually enumerated complete the genus. We need, therefore, another form of judgment to show this. HEGEL'S THEORY OF JUDGMENT. 287 360. This leads to the highest of all, the Ideal Judg- ments. These are conformed to the idea by which we judge that which is according to that which ought to be. Here the copula is has acquired all the energy which it ought to have. The first form of the Ideal Judgment is purely Assertory, as, this action is good, this house is beautiful. But as doubt is not resolved, this judgment is really problematic. The second form, the Problematic Judgment, is more advanced, since it is more explicit. It says, In this or that point of view this house is beautiful. But in this form there is still a doubt. Hence the need of another form the Judg- ment Apodictic. This tends by itself to reject all uncertainty, repel all objection. This (which shows the individual thing] house (which marks the general] built in such and such a way (which indicates that which it has of the particular} is bad or beautiful (which formulates the apodictic judgment]. Hence this (individual] is finally a genus, rendered manifest in particu- larising itself. The dialectical force disengages itself from the apodictic judgment, and passes into reasoning. 1 These latter dogmata may very fairly be left without comment. 1 Die Subjective Logik, p. 89 et seqq. Cf. the summary given in La Logique Subjective, p. 40 et seqq. 288 CHAPTEE XXIII. THE POSTULATE OF LOGIC THE QUANTIFICATION OF THE PREDICATE NEW PROPOSITIONAL FORMS. 361. Logic, as the science of the form of thought, neces- sarily demands that in the case of every given thought, be it Concept, Judgment, or Seasoning, the thought should be strictly analysed and determined, so that all that is in the thought, and nothing but what is in the thought as a mental fact, should be expressly set forth in language or symbols. In this Logic asks nothing more than is required by every science which seeks its own perfection. Every science, in dealing with a matter or datum, seeks to know precisely and determinately what that datum is ; and Logic as the science of the form of thought, requires to know exactly the thought, and its precise limitations, as in the mind. Hamilton has expressed this in what he calls the Postu- late of Logic. " The only postulate of Logic which requires an articulate enouncement is the demand that, before dealing with a judgment or reasoning expressed in language, the import of its terms should be fully understood. In other words, Logic postulates to be allowed to state explicitly in language what is implicitly contained in the thought." 1 This is essential to a scientific Logic. As a science of law and of the laws of thought, it must know precisely what it has got to regulate. The ambiguities and ellipses of language are thus, first, to be cleared up. Neither purely empty terms, nor ambiguous terms, nor so-called indefinite judgments, nor enthy- mematic reasonings can be accepted by Logic as they occur. Logic demands that these be rigorously cleared. And, in this 1 Logic, ii. sect. 6, and ii., Appendix, p. 252 et seq. POSTULATE OF LOGIC. 289 precision, there is revealed the true state or process of the thought. Whatever amount of elliptical expression may be permissible in ordinary or in rhetorical speech, Logic allows none. It is not necessary as a speaker or writer that one should use the explicit form of thought which logical analysis demands, but it is necessary that the logician should make articulate the state of any concept, judgment, or reasoning, or that it should be given to him in an articulate form. Logic will thus teach us how we really think, when we seem to think otherwise than we do. Contradiction, vagueness, want of consecution, in our thinking, can thus, and thus only, be scientifically exposed. Such a postulate is a simple necessity for logical purposes. Thus only can we extricate the meaning clothed or hid in words. A proposition, as ex- pressed in language, may have various meanings, according to intention and emphasis. It may be involved, defective, redundant, obscure, and until it is stated directly, categori- cally, in the case of a purely affirmative or negative judgment, it is unfit to be dealt with logically. This postulate not only may, but must be made by logic ; and it underlies the practice of every logical analyst. " It is the function of the logician, from the various formulas of speech (however involved), and from the scope of the oration or speaker, like a skilled anatomist to resolve or to dissect, member by member, what is said, that he may dis- tinctly perceive (at least in his own mind) what is said of what, and how far, whether of the whole or of the part." 1 As has been said, whatever helps to exclude error, and to simplify logic, is a real addition to the science. 362. It is from an application of this postulate that Hamilton reaches his doctrine of a Quantified Predicate ; and on it as a general principle this doctrine rests for its vindi- cation. It is clear that the postulate must be admitted, in other words, ordinary language must be translated into exact terms ; ellipses must be supplied. We rtmst state in language what is efficient in thought ; and before proceeding to deal logically with any proposition or reasoning, we must be allowed to determine and express what it means. 2 The pos- tulate is demanded by the ordinary logic not less than by that 1 Wallis, Logica, ii. 11. 2 Logic, ii., Appendix, p; 270. 290 INSTITUTES OF LOGIC. of Hamilton. And if Hamilton's application of it in the analysis of judgment and reasoning show elements essential to those processes in our ordinary or actual thinking, it only carries out the Aristotelic analysis to a fuller and more sci- entific issue ; and its pretensions to this must be tested by the accuracy of the analysis, and the necessity of the new forms in thought. 363. The first application of the Postulate may be fairly taken in reference to the subject of Propositions. Here as everywhere we need explicitness in the data. Hamilton's classification of Propositions (Judgments) according to Quantity is new and important. The judgment is the pro- position as thought ; the proposition is the judgment as expressed in language. The judgment is (a) either of de- terminate (definite) quantity, according as we know and cir- cumscribe the objects of which we speak ; or (b) it is of indeterminate (indefinite) quantity, according as the sphere is not known and not circumscribed. Determinate or Definite Judgments relate either (a) to an undivided whole, and thus form a General and Universal Proposition, or (ft) to a unity indivisible, and thus form an Individual or Singular Pro- position. An Indeterminate (indefinite) judgment refers to some indefinite number less than the whole of a class, and thus forms a Particular Proposition. Thus, every X is Y ; every mineral acid is a poison is a Universal Proposition. Here we speak of the whole number of objects in the class. Catiline is ambitious is an Individual Proposition. Here we speak of the whole, but it is a single object. Some men are virtuous is a Particular Proposition. Here we speak of some indefinite number less than the whole. The quantity of a judgment is thus always either indefinite or definite. In judging, we must judge either of some, or of the whole, taken universally or individually. These are the only quantities of which we ought to hear in Logic ; and the expression, the prepositional form of the inner thought, must, for purposes of exact logical analysis, adequately and thoroughly indicate the extent of the judgment. Hence what are called Indefinite Propositions that is, propositions which do not indicate by their language the extent in which the sub- ject is taken, whether indefinite or definite, cannot as such be dealt with logically. They should be called Preindesignate QUANTIFICATION OF PREDICATE. 291 Propositions that is, propositions to which in language no mark or designation of their quantity, as in thought, is attached. When this is done, when a verbal sign, some or all, marks the extent in which they are actually thought, we have Predesignate Propositions. 364. The new prepositional forms arising from the Quan- tification of the Predicate are vindicated as legitimate, as proper material of the science of logic, the moment they are shown to be possible forms of judgment or thought, and they can be shown to be more than that, even necessary forms. Logic, as a science, must be " an unexclusive reflex of thought, and not merely an arbitrary selection out of the forms of think- ing." What may be the frequency or infrequency of the use of the form, its importance or comparative insignifi- cance, has really little to do with the question of the legiti- macy and necessity of it in the pure science of logic. All that is required to be shown is that the form in question is at work in our actual thinking, it may- be to us wholly unconsciously at work, but if it be so, it is the function of Logic as a science to detect and unfold it, to bring it clearly out in the light of consciousness and explicit knowledge. And Logic is not complete as a science, until it has done this with every form of thought, be it judgment or reason- ing, actually in operation in the mental processes. And this can be shown by even the weakest of the prepositional forms parti-partial negation. In other words, Logic, as at least the science of inference, must know as a requisite to inference the precise meaning of the concept, or proposition, from which the inference is supposed to be possible. And if there be even the shadow of a lurking " meaning " in the proposition, that must be explicitly stated, otherwise Logic cannot begin even to exercise its function. And this com- pletely vindicates Hamilton's Quantified Predicate ; for the express quantification is, as he says, to be produced "on demand," and that is all which his doctrine requires. (a) Mill actually regards the logical postulate as a particular case of the Principle of Identity " in, as he says, its most generalised shape. It is a case of postulating to be allowed to express a given meaning in another form of words. "{Examination, p. 483.) It is a case of nothing of the kind. There is no "given meaning "to commence with. It is a case of asking that the person speaking should expressly say what he means to say, and all that he means to say. His meaning is only given when 292 INSTITUTES OF LOGIC. it is fully expressed. If, for example, he is speaking of all of a thing, he should say so ; or of some, that he should say so. Or, if he is reason- ing with a suppressed premiss or reason in his mind, that he should state it in order that it may be scientifically that is, logically, dealt with. 365. " In fact, says Hamilton, ordinary language quanti- fies the predicate, so often as this determination becomes of the smallest import." x This is done, for example, when we speak of any definite number, as all of a class. The three boys here are all that were in the field. Eight stars are all the planets. These were certainly some of the rioters. 366. We further expressly quantify the predicate every time we frame a definition, for in a definition proper, sub- ject and predicate are not only convertible, but alone con- vertible as man is rational animal. The test of this is that all rational animal is man. A good government is that which has the happiness of the governed for its object ; hence every government which, has the happiness of the governed for its object is a good one. Common salt is chloride of sodium, and conversely. Unless the universal quantification of the predi- cate be here admitted, and that in an affirmative proposition, it will follow that a definition cannot be stated in a single proposition. In fact, every simply convertible universal affirmative, implies that the predicate is taken in its fullest quantity, as all, either every one or the whole. This occurs every time we identify one class with another one total or whole with another. (a) The quantification of the predicate is further justified by gram- matical usage that is, by the form which expresses the ordinary requirements of speech. In Greek the definite article, as we have seen, has a power of specification, in other words, of rendering definite, either in the form of universality or singularity. (See above, p. 258. ) And the rule as laid down by Ueberweg is as follows: "Whenever the predicate in Greek has the article, the spheres of the subject and predicate notions coincide ; when the spheres of the subject and predi- cate notions do not coincide, the predicate in Greek has never the article." (Logic, p. 315.) When we say flpiivn ffrl To.ya.6Av, peace is the good, or highest good, we quantify the predicate by the article, both in Greek and English. Quantification of the predicate by the superlative degree is of course of the commonest occurrence, as Kivyais yap alirrj neylffTT] S^ TOIS "E\\i), sinning, rb tlvat, rb $iAeos 6 irais nai^i (predicative) ; 3 fidvos TTCUS walfa, the only child plays (unions). (See Clyde's Greek Syntax, pp. 18, 19.) In the connection of iras with numerals, we have an example of the quantified predicate of absolute totality, as ra iravra 8^/ca, ten in all. Take away the article, and say travra. 8/ca, and then it means ten oj each that is, there is the difference between totality and distribution. 367. There are certain propositions regarded as com- pound, which proceed on a total quantification of the predi- cate, even in affirmatives, and which are most readily and properly resolved into the logical formula of .A is all B, or all A is all B. These are chiefly Exclusive and Exceptive Propositions. Exclusive and Exceptive Propositions are known in the Parva Logicalia, and in subsequent logical treatises as Pro- positiones Exponibiles. They formed the stock-in-trade of the Terminalists from Hispanus downwards. Scheibler, among others of the moderns, has given an exposition of them. One general rule is that every exclusive proposition is resolvable into an affirmative and a negative, man alone is rational is equivalent to man is rational, and what is not man is not rational ; the first is the propositio exponibilis, the other two the propositiones exponentes. 1 In Exclusive Propositions, or rather " inclusive limited by an exclusion," 2 there is a tacit quantification of the predi- cate, thus, God alone is worthy of being loved for His own sake is called an exclusive. It is held to contain two judgments, (a) that Grod is to be loved for His own sake, and (b} that other things are not to be loved for their own sake, or ought to be loved for God's sake. According to the principle of the quantified predicate, this would make one proposition viz., God is all that is worthy of being loved for its own sake. 1 See Scheibler, Op. Log. iii. 7. Hamilton, Logic, iv. , Appendix v. (c). 2 Hamilton, Logic, iv., Appendix v. (c). 294 INSTITUTES OF LOGIC. And this is convertible. Others may be similarly resolved, as Quas dederis soles semper habebis opes. Nobilitas sola est atque unica veritus. Hoc unum scio quod nihil scio. Una solus victis nullam sperare salutem. Unus Dominus, una fides, unum baptismum. These and other apposite examples of Exclusives x may be readily reduced to one proposition, on the principle of the Quantified Predicate. At the same time, every such propo- sition may be contradicted or negated in three ways, for (a) we may deny, for example, that virtue is nobility, or agrees with the subject at all ; (b) we may maintain that birth confers nobility as well that is, agrees with something else ; and (c) that birth confers nobility and not virtue that is, we may maintain both. 2 It is certain that there is nothing certain or, uncertainty is all (the only) certainty. This may be denied (a) by saying, with the dogmatists, there are things of which we are certain, and there is certainty ; or (6) with the Pyrrhonists, everything is so uncertain, that it is doubtful whether there is nothing certain. 3 368. It is clear, I think, in such cases, that the proper opposite of such propositions is that which denies the exclu- sion. We deny, for example, that virtue is the only nobility, or is all nobility. Other propositions may follow from this as immediate inferences, as, for example, that other things make nobility, or that there are some things which are noble, though not virtues. To maintain that virtue is not nobility at all, is to go beyond the limit of the negation which we need to assert as the opposite of the proposition. 369. In Exceptive Propositions, we affirm something of the whole subject, with the exception of certain subordinate objects or clauses under it. This is indicated by an excep- tive particle. Thus, none of the philosophers, except the Pla- tonists, recognised the spirituality of God. Except the wise man (of the Stoics) all men are truly fools. Avarus nisi cum moritur, nihil rectefacit. Nemo Iceditur nisi a seipso.* These are obviously resolvable into, those who recognised the spirituality of God were all Platonists ; or better, Platonists were all ivho recognised the spirituality of God. The wise man of the Stoics is all the class wise, or the wise man of the Stoics is 1 See Port Royal Logic, Part II. c. 10. 2 Ibid. 3 Ibid. * Ibid. QUANTIFICATION OF PREDICATE. 295 the wise man. The proper opposites here are, other besides Platonists recognised the spirituality of God, or Platonlsts were not all who recognised the spirituality of God. So other men were wise besides the wise man of the Stoics, or he does not exhaust the class wise. This is all we need to assert for purposes of denial. We need simply to deny the convertibility of the proposition. We do not require to say, the ivise man of the Stoics was a fool, or he was a fool and other men were not, as has been suggested ; * though no doubt such propositions would have the effect of denial. It may thus be admitted that Exclusive and Exceptive Propositions may be regarded as compound, but it is obvious that they do involve the quantification of the predicate, and the simple and scientific way of treating them is to resolve them into this logical form. Thus only can we set against them their proper and relevant contradictory, or bring them to the test of the mutual convertibility of subject and predicate. When it is said that pain is the greatest of all evils, we need only to deny its maximum degree, not the fact of its being an evil, or to assert that it is no evil, as has been suggested. 2 370. But in truth the express quantification of the predi- cate follows as a necessity from the very nature of predication in extension. The predicate in extension indicates a class. Affirmative predication is the reference of the subject to the class. It must have some place in the class some at least. This is the first requisite of the act. Plant is organised that is, some at least. This I must know before I say it, before I express predication at all. Why, then, not designate the extent in which I mean the predicate term to be taken? Again, I may know and mean that the place of the subject in the class is that it occupies the whole of it. I say, all tri- lateral is triangular, meaning all triangular. Why not, even, to avoid ambiguity, express this? I may, of course, only need, for the purposes of my argument, to say that it is some at least. Then let me say so. But if I mean all, I am equally bound to express it in logical argument. So with not any, and with not some, as a mark of particularity in negatives. If what I have in my mind is not any of the class in a negative, I am bound to express it designately. If only not some, I am under a similar obligation, for these are very different state- i See Port Royal Logic, Part II. c. 10. 2 Ibid. 296 INSTITUTES OF LOGIC. ments. I am not bound, of course, to express in language more of the predicate than I mean, or use, or need, in the argument. I am thus not bound always to say, though I know it to be the case, that all of the subject is all of the predicate, if some of it will suit the needs of my argument. But I am bound in logical strictness to state whether I use all or some. This is really all which the quantification of the predicate implies. And as such, it is a simple necessity of logical exactness, and therefore of logical science. 371. While the predicate of any one of the four ordinary logical forms remains without express quantification, the pro- position is left ambiguous. If I say, for example, All A is B, I may mean some of the Bs, or all of the Bs. I may mean all A is some B, or all A is all B. If I say no A is B, I may mean no A is any B, or no A is some B. No plant is any animal ; no planet is some star. The ordinary Logic assumes that men usually, or rather universally intend to assert in a universal affirmative (.4) that all A is (some] B, and in a universal negative (E] that all A is not any B, or in a particular (0} that some A is not any B. But even adding to these the particular affirmative (7), do these exhaust the possible or scientifically valid forms of statement or proposition ? Do they exhaust even the necessary and useful forms ? Hamilton answers no ; and he claims the right (1) to give express, not merely understood, quantifica- tion to the predicate alike in affirmative and negative pro- positions recognised on the ordinary system, and (2) in virtue of the same principle to give an express quantification to the predicate in other prepositional forms. He further challenges the validity of the two received logical canons () that in all affirmatives the predicate is particular, and (5) in all negatives this predicate is universal. Hamilton's procedure is in no way a departure from logical method or principle. It is simply a demand that what is understood in thought, as the nature of certain propositions, should not remain implicit or understood, but should be expressly set forth, and that this demand, realised in some propositions, should be applied to all. 372. The vindication of the quantifying of the predicate depends mainly on this, as to whether it subserves the end of testing inference, the main aim of Logic. That it does so, as regards immediate and mediate inference alike, is indisputable. QUANTIFICATION OF PREDICATE. 297 When I apply the predicate to a subject, do I mean to say that it applies to the subject only, or to the subject at least V Plant is organised do I mean by organised some at least or do I mean that organised applies to nothing more than plant ? These are two very different statements indeed ; and they afford very different kinds of inference. Organised as a predicate, and therefore as a middle term in a reasoning, is wholly ambiguous, until the specific limit of it is precisely cleared in expression. Logic to be scientific, to exhibit pro- perly inferences, must demand the explicit quantification as a preliminary. Common thought and speech may be satisfied with the minimum of quantification the some at least. Logic must know whether or not the maximum is intended and meant. (a) " The syllogistic theory is not an analysis of the reasoning process, but "only furnishes a test of the validity of reasonings, by supplying forms of expression into which all reasoning may be translated if valid, and which, if they are invalid, will detect the hidden flaw. " (Examina- tion, p. 513.) That is, we can have a test of valid and invalid reasoning, which is not founded on an analysis of the reasoning process. A form of expression which does not express any analysis whatever of the reason- ing process, might be nay, is alleged to be, the test of the validity and invalidity of all reasoning. Words are higher than thought the test of its validity words that do not in any way necessarily express the inner process of thinking ! On this supposition, Mill for a moment admits that " a form which always exhibited the quantity of the predi- cate might be an improvement on the common form." (Ibid.) He is even " not disposed to deny that for occasional use, and for purposes of illustration, it is so." (b) " There is not a single instance, nor is it possible in the nature of things that there should be an instance, in which a conclusion that is provable from quantified premisses, could not be proved from the same premisses unquantified, if we set forth all those which are really involved. If there could be such an instance, the quantified syllogism would be a real addition to the theory of Logic ; if not, not. " (Ibid, p. 518.) In other words, there is not a single instance in which a conclusion that is provable from quantified premisses could not be proved from the same premisses unquantified, if we quantify these. What is the setting forth all those which are " really involved," but the express statement of the degree of distribution or quantification of the terms ? And this is the summary of Mill's criticism of a new logical theory, which, whether competent logicians accept all its details or not, has certainly modified all logical doctrine since its promulgation. (c) The climax of objections to the quantified predicate is reached in the grand, undefined, verbalism "a psychological irrelevance." Yet Mill tells us this process, in general forms of proposition, is familiar to the ordinary logic which represents accurately processes of thought. That which is essentially sound in several cases, and, 298 INSTITUTES OF LOGIC. therefore, in its principle, becomes "a psychological irrelevance, " when extended to other cases. 373. Hamilton says every predicate is quantified in thought at least in extension. But what is meant by quantified ? In the first place, when we say that the predi- cate applies to the subject, be it attribute or class, we must mean and say that it is coextensive with the subject at least. The predicate is thus necessarily quantified in thought, whether taken comprehensively or extensively. In comprehension the attribute does not vary ; in exten- sion the class does vary. In extension the predicate may not be quantified at more than the necessary minimum ; but it is quantified. In the second place, if the predicate apply to more than the subject, as it may, and if we know this, as we may, the predicate is quantified in thought by some only. The river runs, it is one only of the running things. Other things run also. In the third place, if the predicate apply to the subject only, as equiangular to equi- lateral, and we know this, then it is quantified in thought. It is a very odd ground of objection to the doctrine that the predicate is always quantified in thought that there is al- ways a minimum amount of quantification in thought that there may be a higher known to us that is, in thought. Why not, therefore, to remove ambiguity, on demand, state expressly in language what we think and mean ? How else can we logically deal with the thought? Hamilton's state- ment is thus thoroughly vindicated, that in every case there is a quantity in thought, and this ought to be set forth in expression. The habit of looking explicitly at the quantity of the predicate considering in all cases exactly what we mean, is of the greatest utility in simplifying our logical statement, in restricting it, guarding it against ambiguity and the possi- bility of invalid conclusions. (a) Mill has no correct conception of what quantification of the predicate means. He has no conception that when the subject is regarded as coextensive with the part at least of a class, this is quantify ing the predicate i.e., particularly. His confusion is that he imagines that to quantify the predicate means always thinking of it as embracing other things (or subjects) besides the present subject or subject spoken of. This, no doubt, is quantifying the predicate, but it is only one case of it. The river runs is one only of the running things, this is quantification ; but there is no less quantification when OBJECTIONS TO QUANTIFICATION. 299 I say the river rims at least, or simply the river runs, because I have made the quantity of the predicate coextensive at least with the sub- ject river ; it is one at least of the running things. This comes out quite clearly in the statement that the predicate has usually no quantity in thought, because it is simply thought as coextensive with the sub- ject ; and in the statement that in a universal proposition we think of the subject "as its several parts." (Ex., p. 512 and note.) (6) Mill imagines that he disproves the existence of a quantitative judgment in thought, because we can judge qualitatively or in com prehension without reference to quantity. He appeals triumphantly to "every reader's consciousness" that we can judge that all oxen ruminate, without knowing or considering whether anything else does. He might have learned from Hamilton himself that in the comprehen- sive judgment the predicate as attribute appears without quantifica- tion. But this in no wise settles the question as to whether, judging in quantity with the predicate as a class, we can judge without a specific meaning as to quantity. In this case we must mean that oxen are some at least of the ruminant, or all of the ruminant, or some only of the ruminant. It is true, as Hamilton lays down, that " in reality and in thought every quantity is necessarily either all, or some, or none." It is as ridiculous to say that no predicate is universally quantified in thought as to say that every predicate is. If we understand our meaning, if we have a definite meaning, which we ought to have, we either think of the predicate as some, or all. 374. It is not true that " the logic of the quantified pred- icate takes the comprehension out of propositions, and leaves them a caput mortuum" l A proposition in Extension derives its meaning from the corresponding proposition in Compre- hension, on the general principle of the correlation of the two quantities. This is Hamilton's doctrine from beginning to end of the whole matter. (a) Mill admits everything for which Hamilton contends as to the fact of our judging and reasoning in Comprehension as well as in Extension. He admits that the former is prior and more natural ; that the latter flows from the former is, in a sense, identical with it, true if it is true ; that the ordinary logics proceed exclusively on Extension in judgments and reasonings ; that this is hurtful in practice. I appeal to the pages of his Examination, in chapter xxii., p. 497 el seqq., for the truth of these statements. Yet he makes these admis- sions as a preliminary to an attack on Hamilton for holding them for introducing Comprehension into Logic ! On this and other points in Mill's criticism, see the admirable exposure given in Hamilton versus Mill [by Mr Simon]. It is greatly to be regretted, in the interest alike of fair criticism and the science of Logic, that the author has not yet given Part III. to the public. (6) But the critic waxes still bolder. We do not, according to Mill, 1 Examination, p. 517. 300 INSTITUTES OF LOGIC. usually quantify even the subject in thought, in the sense which Sir W. Hamilton's theory requires. "In an universal proposition we do not think the subject as an aggregate whole, but as its several parts. We do not judge that all A is 13, but that all As are. Bs. Att A is a very different notion from each A. What is true of A only as a whole forms no element of a judgment concerning its parts." . . . " If all A is all B is true at all, it is true only of A considered as a whole, and expresses a relation between the two classes as totals, not between either of them and its parts." (Examination, pp. 512, 513.) Hamilton's theory requires only what in fact and reason must be admitted the two meanings of all, as every and the whole. In a proposition with a universal subject, do we not speak of all the parts that is, of every one gathered into a whole? All plants are organised, means that organised applies to the whole sum of objects classed as plants ; or that we shall find the totality called plant under the class organised. This supposes, of course, that organised is pred- icable of every plant, and that we have summed up the every into a whole or all. But do we now continue to think or to speak merely of " the several parts " ? Nay, do we not think and speak of plant, the class, rather than of this or that plant ? It is not merely of ' ' the several parts " we speak, but of every one, and, if of every one, then of the whole class. We never can, according to this view, predicate of a sum or class of objects regarded as a whole ; we must always predicate of each part forsooth ! If we speak but of the parts sev- erally or separately, how is it possible thus to say that the whole class is included under organised ? Each plant is in its turn a part of organised, no doubt ; but this is a very different judgment from the whole are, or the whole class plant is so included. Again, Mill reads all A is all B as all A only is all B, or, A regarded as a whole is all B. A taken as a class only. This is not the necessary meaning of all A. It is only the meaning in the case of a Collective notion proper, made up of units different from the sum as an army, a regiment, a ministry, a presbytery, &c. Here what is true of the whole is not necessarily true of each unit ; but this is a special kind of whole not the ordinary logical whole in which the class-name is always predicable of each of the parts. Army, regiment, is not predi- cable of soldier he is not the regiment ; nor presbytery of presbyter he is not the presbytery. But in the case of the ordinary logical whole, the class-name is predicable of each member of the class. Animal is predicable of man, bird, and beast. And if we speak of all the class, or all A, in this sense, we can say that it is all B. We can say, for example, that all equilateral is all equiangular, or that the whole class equilateral is identical with the whole class equiangular. And this expresses not only a relation, as Mill alleges, between the two classes as totals, but between them as parts (ibid., p. 513) for it implies that every A (equilateral) is to be found in every B (equi- angular). Otherwise we should have the absurdity, the contradiction, that the whole objects included in the class A are convertible with the whole objects included in the class B, and yet there is an A which is not a B ! OBJECTIONS TO QUANTIFICATION. 301 (c) Again, it is said, all A is B is not spontaneously quantified in thought as all A is some B. When the speaker or learner is told this, it is a new idea to him. (Ibid., p. 512.) Suppose it were, what then? Has he not now been told what his statement must at least mean ? Is it not necesary to the coherency, to say nothing of the truth, of the state- ment, that A is some at least of the 13s ? And whether the individual thinker had this or more in his mind, does not the thought he ex- presses demand him to mean this, or something more than this ? And if he be confused or ambiguous, does not this very confusion justify the logical postulate that the thought must be explicitly stated in lan- guage ? And of what highest use or precision is such a judgment, if the speaker does not know whether he means some, or all ? As it has been well put, when I say all A is B, or all asses bray, it is not maintained by Hamilton that we must know whether brayiny actually extends beyond asses, or not ; but he maintains that we must know it extends to all asses. And it is not true that, in order to form a proposition in Extension, we must know this greater extension. All we need to form such a proposition is that the braying extends to the asses at least. This is to quantify the predicate (particularly). (Hamilton versus Mill, Pt. ii. p. 216.) 375. Hamilton has indeed already answered these and other objections made to the quantification of the predicate. (1.) In the case of Universal Affirmatives, the universal quantification of the predicate is " always untrue," all man is animal, but all animal is man, the supposed converse is not true. This is of course materially untrue ; but what then ? It so happens to be so in this particular case ; but is it untrue, much less formally illegal in all ? What, then, of the propositions, all rational is all risible, all trilateral is all triangular, all triangle is all figure with its angles equal to three right angles? Aristotle, who makes this objection in practice, proceeds, as he must proceed, on the quantification of the predicate, as in Induction and Demonstration. (2.) In the case of Reciprocating Propositions as all man is all risible it is alleged that if the predicate were quanti- fied, the all as applied to the subject being distributively taken, this would imply that every individual man, Socrates, Plato, is all (that is, the whole class) risible. There is nothing in this. All may be used either distributively or collectively ; but if it be used in the one sense in the subject, it ought to be used in the same sense in the predicate. " In the same logical unity (proposition or syllogism), the same term or quantification should not be changed in import." Thus we should have, collectively, all (the whole class) man is 302 [INSTITUTES OF LOGIC. all (the whole class) risible ; distributively, all (every several) man is all (every several) risible. (3.) With regard to the objection that the quantification of the predicate is useless, Hamilton points to its consequences as shown in the changes thereby introduced into the science of Logic. There is in the main the restoration of the science of logic to simplicity and truth ; and especially (1) the sim- plified and scientific treatment of Exponibles Exclusive and Exceptive Propositions ; (2) simplification of Conver- sion ; (3) of Mood and Figure, and their rules ; (4) restora- tion of forms of Reasoning illegitimately and inconsistently excluded ; (5) theory of Proposition and Reasoning as Equa- tion. 1 All these points will be illustrated in the sequel. 376. The term quantity has been indiscriminately applied to a concept viewed in Extension and in Comprehension. In this, as it seems to me, there is both confusion and inaccu- racy. A concept viewed extensively has obviously a quan- tity it is a whole which contains objects, and it may be greater or less ; it may be taken in the whole of its extent, or only in part of its extent. Animal is a whole ; it contains species and individuals under it, and we may speak of the whole of the class all, or of a part of the class some. The conception of quantity is not, however, as appears to me, so strictly, if at all, applicable to the concept in Compre- hension. No doubt, if a notion contain in it a plurality of attributes, it may be said to possess quantity ; for it contains a variety of constituent elements. At the same time, it is obvious that a notion as a sum of attributes cannot be subject to degrees of greater or less ; for if we take from any notion even one of the attributes which it contains, it ceases to be the notion which it was before. If, for example, we take from animal the attribute sensation, leaving only being with life, &c., what remains is not the notion of animal. So that a notion, viewed as a sum of attributes, is absolutely indivisible, and cannot in strict propriety be said to possess quantity. This is even more apparent respecting a notion which has only one attribute as mortal (subject to death), extension, succes- sion, unity. An attribute is absolutely indivisible, and as such has properly no logical quantity. When we think or speak of the attribute mortal or sentient, it is of the attribute 1 Logic, ii., Appendix, p. 295 et seq. COMPREHENSION IN PROPOSITIONS. 303 as absolutely entire or indivisible. When we use the terra mortal as the name of a class, we think and speak of all or some of the beings of the class ; but when we use mortal as the name of an attribute, we must think and speak of the attribute in its indivisible integrity. Sentient or mortal as the name of a class is repeated in each of its portions or sub- classes ; mortal as an attribute, if divided, is destroyed. 377. It does not affect this doctrine that the indivisible mark or attribute may be also in other objects besides the subject or predicate of the given proposition. It may quite well inhere in other subjects or objects. Wood is combustible, so is coal. Iron is a mineral, gold is a mineral. All the same, the attribute as attribute is entire in each it is capable of distribution over many subjects ; but it is complete, indi- visible in each ; and is thus wholly different from the predi- cate as a class-notion. 378. This distinction does not appear sufficiently marked in the doctrine of Propositions in the ordinary logic, or in that of Hamilton. In the Lectures on Logic, the term quantity is applied indiscriminately to concepts in Extension and in Comprehension. In the later forms of his theory, Hamilton recognises the distinction in words ; but he makes no thorough- going application of it to the theory of Propositions. He says : " A judgment or proposition is only a comparison resulting in a congruence, an equation, or non-equation, of two notions in the quantity of extension ; and that these compared notions may stand to each other, as the one subject and the other predicate, as both the subject, or as both the predicate of the judgment." l " I say in respect to their Extension for it is this quantity alone which admits of ampliation or restriction the comprehension of a notion remaining always the same, being always taken at its full amount." 2 379. But the view has a very important bearing on Pro- positions, especially on the doctrine of a Quantified Predicate. Whether the attribute stand as subject or as predicate, it is to be taken as a unit as indivisible. We speak of the whole of it or not at all. As a predicate, therefore, it does not admit of greater or less, unless intensively, which does not affect its character or mark ; it has no extensive quantity, or it is 1 Logic, App., iv., 276. 2 Ibid., p, 271. 304 INSTITUTES OF LOGIC. always quantified to the full, if we may apply quantity at all. In an affirmative judgment, therefore, the attribute is predi- cated as a unit or whole. Man is mortal, animal is sentient that is, everything in the mark mortality is in man, and every- thing in sentiency is in animal. In a negative judgment, the attribute or mark is denied of the subject, wholly or com- pletely. Sugar is not chloride of sodium ; ether is not ponder- able ; matter is not a thinking substance ; some sins are not crimes. Here the attribute as predicate is wholly or absolutely denied of the subject ; and we could not do less without destroying the judgment itself. It may be maintained, as with the Port Eoyalists, that " the negative proposition does not separate from the subject all the parts contained in the comprehension of the attribute, but separates only the total and complete idea composed of all these attributes." This can only even seem to apply to a case where the predicate is complex, or the sum of a plurality of attributes, as in thinking substance. Matter is not a thinking substance, but it is not said that it is not a substance. The total or complete concept alone is denied. Animal is not a rational and responsible being it may still be a being of another sort. This does not affect the main position ; the comprehensive concept as a predicate is a unity, and as such it is absolutely or wholly denied of the subject. Whether another notion, containing a part of the one element of the complex concept may be affirmed or not, in no way appears from the proposition itself, or what are the other marks of the subject. A does not contain in him magnanimity. Other virtues he may have, and virtue is an element in magnanimity ; but the exclusion is complete, for we deny the virtue represented by or in magnanimity, the substance represented by or in think" ing, the being represented by or in rational and responsible. (a) The author of the Logic of Port Royal the acute Antony Arnauld has the merit of at least partially recognising this principle of the indivisibility of the attribute predicate. " An idea is always affirmed according to its Comprehension, because in taking away one of its essential attributes we utterly destroy and annihilate it, so that it is no longer the same idea ; and, consequently, when it is affirmed, it is always affirmed in relation to everything which it comprehends within itself. Thus, when I say that a rectangle is a parallelogram, I affirm of rectangle everything contained in the idea of parallelogram. For if there were any part of this idea that did not belong PROPOSITIONAL FORMS. 305 to a rectangle, it would follow that the whole idea did not belong to it, but only a part of that idea ; and thus the word parallelogram, which signifies the whole idea, ought to be denied and not affirmed of the rectangle." (Part II. c. 17.) With regard to affirmatives, the rules are : (a) The attribute of an affirmative proposition is affirmed according to its whole comprehension ; and (6) affirmed not according to its whole extension, if it is in itself greater than that of the subject ; (c) the extension of the attribute is restricted by that of the subject, so that it denotes no more than that part of its extension which agrees with its subject. In men are animals, animals means not all, but simply those animals which are men. (L., Part. II. c. xvii.) With regard to negatives, it is held (a) that the proposition does not separate all the parts of the comprehension of the attribute from the subject, but only its totality ; whereas (b) the proposition separates from the subject the idea of the attribute according to the whole of its extension. (Part II. c. 19.) The distinction of comprehension and extension in the rules is not clearly marked ; nor is the conception of the true nature of the comprehensive predicate steadily applied to negatives. 380. The theoretically valid forms of proposition, on the principle of the quantified predicate, are, when fully stated, as follow : (1.) All X is all YAfA. (A) (ii.) All X is some TAfl. (3.) Some X is all YIfA. (I) (iv.) Some X is some Y If I. (E) (v.) Any X is not any Y AnA. (6.) Any X is not some Y AnI. (0) (vii.) Some X is not any Y InA. (8.) Some X is not some Y Inl. 381. Thomson's classification is as follows : 1. A. All plants grow Universal Affirmative Attributive. 2. E. No right action is inexpedient Universal Negative. 3. I. Some muscles act without our volition Particular Affirmative Attributive. 4. 0. Some plants do not grow in the tropics Particular Negative. 5. U. Common salt is chloride of sodium Universal Affir- mative Substitutive. 6. Y. Some stars are all the planets Particular Affirmative Substitutive. u 306 INSTITUTES OF LOGIC. 382. In what may be regarded as his final logical doctrine, Hamilton explains, first of all, the nature of Affirmation and Negation. Affirmation means inclusion, and absolute affirma- tion absolute inclusion. The subject in this case is definite. It is this or all, the individual or the class of individuals. We say, this man is tall ; all planets are stars. Negation, on the other hand, is exclusion ; and absolute negation is absolute exclusion. We say, this man is not a European ; all plant is not any animal ; no plant is an animal. Looking merely to the class-notion, affirmation proceeds downwards or inwards from the greatest to the least, from the whole to the parts. Negation proceeds upwards or out- wards from the least to the greatest, from the parts to the whole. Thus we say all A is B, or A contains the part B. On the other hand, we say any A is not any JB, or taking any one A the least it is not any one B, even though you go through the whole class B, or accumulate all the Bs to confront it. Any man any one is not any horse, even suppose all the class horse is examined or brought to con- front the one man, or any one man. At the maximum of Breadth, affirmation predicates the least of the most, the fewest attributes of the greatest number of things ; as, Man is or exists animal is organised. Negation, again, here says the most of the least. It with- draws the greatest number of attributes from the fewest things. At the maximum of Depth, affirmation says the most of the least, it predicates the greatest number of attributes of the individual. Man is living, sentient, rational, organised. Negation here says the least of the most, it withdraws the fewest attributes from the greatest number of things. 1 383. In ordinary language, Negation is a privative or correlative act that is, it supposes an affirmation or inclusion which it reverses. We deny what has been affirmed. But here we must distinguish between all, and not any. The former, all, we use in universal affirmatives, and we say all is, all are. This may mean the whole, collectively; or every, each, each several, distributively. When we deny a universal affirmative, so expressed, as all As are Bs, we assert that some are not ; when we deny that all the men in the ship were drowned, we assert that some were not. In the same way, when we deny 1 Discussions, p. 680. DEFINITUDE AND INDEFIN1TUDE. 307 that all the men in the ship were not drowned, we affirm that some were. To avoid this ambiguity, the proper logical predesignation in universal negation is not any (none], is. All are thus excluded, through the non-inclusion of any. Any stone is not any plant ; any A is not any B ; any one of the persons accused of this theft is not any one of those guilty ; or none not one of them is guilty. 384. It should be noted that any is not properly adapted to affirmation, but only to negation. It is the same with ullus, and means primarily (even) one, (even] the least or fewest. It ranges from least to greatest from the non-inclusion of the least to the exclusion of the whole. Any one is not, thus all are not. We can say, the whole (or class] triangle is the whole (or class] trilateral; or, every (or each several] triangle is every (or each several] trilateral. If we were to say, any triangle is any trilateral, we should speak nonsense, confounding every triangle with every other. Or if we were to say some one X is any one Y that is, some one figure is any one triangle, some one animal is any one man we should say what is absurd in terms, and we should not express what the proposition is intended to mean. Any is contained under some, as the genus. Any, any one, must always be some ; some is not always any. 1 385. Hamilton has analysed anew the doctrine of par- ticular quantity, and formally introduced into Logic a new meaning of the designation some. In the ordinary or Aris- totelic logic, some means, in affirmatives, some at least some, perhaps all. Some itself here is indefinite, but it does not definitely exclude all. In negatives, not some means not some at least, not some perhaps none. Not some is itself thus indefinite, but it does not definitely exclude not any, or none. This sense of some, some at least Hamilton names Indefinite Definitude. But there is another meaning of some. It may mean, in affirmatives, some at most, some not all some only. Some itself is here indefinite, but it is definitely exclusive of all. In negatives, not some means not some at most not some and yet not none not some only. The not some is itself in- definite, but it is definitely exclusive of not any or none. This meaning of some some at most Hamilton names Definite Indefinitude. 1 Digcustions, p. 683. 308 INSTITUTES OF LOGIC. 386. Hamilton holds that the latter meaning of some some at most, or some only is the more prominent in ordinary thought and language ; while the former some at least is a mere accident, depending on our ignorance in special cases. Every quantity is necessarily either all, or none, or some. The third is formally exclusive of the other two. Some only excludes equally all and none. Aristotle confounded what was indefinitely thought, with what was thought as indefinite, and thus hindered the scientific development of the logical theory of propositions. Hamilton would thus introduce some only into the theory of propositions, without, however, dis- carding the meaning of some at least. On this principle he has constructed a table of the mutual relations of the Eight Prepositional forms on either system of particularity. This shows what propositions are incompossible (inconsistent, contrary, contradictory), and what yield immediate infer- ences (integration, restriction). 1 It is thus not correct to say, as has been said, that Hamilton discarded the ordinary logical meaning of some. He simply supplemented it by introducing into the propositional forms that of some only. 387. But there may be a question as to whether some only is equally fundamental with some at least. I rather think it is not. It is quite clear that I can speak of some at least, with- out advancing to the more definite stage of some only. I may know that all the metals are at least conductors that is, some conductors without knowing that they are some only, if this should chance to be true. Some at least does not imply some only; but some only implies some at least, and more. It implies some at least are, and some at most are. No doubt there is an inference from some only to some other. Some only is, therefore, some other is not. Only some of the As are Bs ; therefore some other of the As are not Bs ; or there are other As which are not Bs. But before I can speak of some only, must I not have formed two judgments, the one that some are, the other that others of the same class are not ? Only some presupposes this, or these judgments. The in- tegration, then, is rather a re-integration, it is a filling up of what I have already thought or determined, of what I have already presented only in part. The some only would thus appear as the composite of two propositions already 1 Discussions, p. 692. DEFINITUDE AND INDEFINITUDE. 309 formed first, that some are; secondly, that some (others of the class) are not. It seems to me that we must, first of all, work out logical principles on the indefinite meaning of some at least. This is the primary requisite and meaning of affirma- tion the least possible in dealing with a class. Some only, as appears to me, is a secondary and derivative judgment. Still this need not interfere with the recognition of the mean- ing in propositions. Nor does it make it less a single judg- ment, after the process of formation has been completed. It is then no more a double judgment than all are; and, like it, may appear as a single premiss in a reasoning. 388. There can be no doubt of the common use of this definite meaning of some in ordinary thought and speech. When I say, some of the men in the ship were drowned, I natur- ally mean only some ; I oppose this definite particularity to all, all the men in the ship were drowned. I should not, in this connection, naturally say, some of the men in the ship were not drowned. The positive element in the occurrence is that to which I should naturally refer, and in wishing to express that all were not, I should say some were, that is, only some were. (a) " I saw some of your children to-day." These words, according to Mill, do not mean that I saw some only. But we are led to infer that they do, because it is most likely, if I had seen them all, that I should have said so ; " and it is further presupposed that I must have known whether the children I saw were all or not. " Any tyro in Logic would say in reply to this, that if I say I saw some, I must mean not all, but only some, in whatever way I may have come to know this. Logic begins with the assertion made, and demands its explicit meaning. Is it conceivable that even Mill could have imagined that some, said of what had been seen, might mean more than the some seen ? or that the some expressed did not exclude cM ? (b) In Greek we have a means of distinguishing the some and some. In the case of an individual object, say in space, we have one part of the object distinguished from the other by a definite form of expression. Thus, if we only mean to speak of the middle market-place, we should say TI fj.(0"n dyopa. ; but if of the middle of the market-place, we should say, ^ ayopa /t' verpa. jaaAax^ tffnv evravOa, is predicative ; the soft stoiie is here, TI /j.a\aKT) vfrpa. eTa.v9a., is attributive marking a difference in the kind of stone. / see the mountains white (predicative) ; / see the ivhite mountains (attributive)." (Clyde's Greek Syntax, p. 19.) (c) Laurentius Valla, long ago, vindicated the practical use of the bi-particular pi-oposition (propositio biparticularis) some is not some. "Non totus orbis," he said, "paruit Alexandro," i.e., "pars orbis parttit, pars non paruit." So "tota Grsecia non paruit Alexandro," i.e., "non tota Grtecia." This was a distinct and formal anticipation, as well as vindication, of the necessity for thought and expression of the some and the some not in reference to the same class. (See Dialec- tica, c. xxvi.) CHAPTER XXIV. OBJECTIONS TO QUANTIFIED PROPOSITIONAL FORMS GENERAL CONSEQUENCES OF QUANTIFICATION OF PREDICATE. 389. It has been urged, that if we expressly quantify the predicate, we shall have a form or formula of judgment which is a simple repetition or tautology. This criticism must be held to be taken to the form of the proposition in Exten- sion. Indeed, those who urge it seem utterly ignorant of any other form of proposition. In Comprehension, as we have seen, the predicate as attribute is, in affirmatives, necessarily taken in its totality, as an indivisible unity. No attribute is properly divisible, and is thus necessarily taken in its in- tegrity. When we say A is B, or the river runs, the attribute is taken wholly or completely, but it could not be represented in the formula A is A B, the river is the river running. This is a different statement from the river runs, or has this par- ticular mark. Gold is soluble in aquafortis does not mean that gold is gold soluble in aquafortis; for we are speaking of gold itself, and we have added a mark, and until the mark has been added it is not, to begin with, gold soluble in aqua- fortis. The Black Watch were the first in the breach, does not mean that the Black Watch were the Black Watch first in the breach; for this is precisely what we have to add to what the Black Watch already is or is known to be. 390. In any affirmative judgment, we necessarily, in thought, quantify the predicate to the full extent of the sub- ject. A is B, means A is some B at least ; or B is in A, all or some A ; man is organised that is, some part of the class at least, or organised is in A, all or some. If, therefore, the criti- cism have any force at all, it must imply that in every such 312 INSTITUTES OF LOGIC. judgment, whether the predicate be expressly quantified or not, the meaning is A is A B ; and it is thus not an objec- tion, even if it be an objection at all, to the express quantifi- cation of the predicate but to the judgment as thought that is, to the judgment as a judgment. 391. But suppose the predicate expressly quantified, as A is (some] B water is a (some) useful tiling, does this mean only or at all that A is A B, or water is water useful f In no way whatever. It means simply, that taking the two con- cepts or classes of things represented by A and B, water and useful, the subject is a part at least, some at least, of the predicate class, but whether all, or how far short of all, we cannot tell. Water and water useful are quite distinct con- cepts ; we are speaking of the former, not of the latter. Use- ful water is not the subject of which I speak, but water; and these are two very different things. The extent of useful, of which I speak, is limited to the extent of the subject water ; but I am still speaking of water, not merely of useful water, and I am not repeating what I said in the subject, but adding to it specifying and relating it to a class which may or may not be coextensive with it. The oak is a deciduous tree that is, some part of the deciduous. The oak is the oak decidu- ous, are wholly different propositions not the least of the same import. All equilateral is (all] equiangular, the totality in the one case is convertible with that in the other ; but all equilateral is equilateral -equiangular, does not assure me of the convertibility of the subject and predicate. 392. It is further contended, that in the case of the ex- press quantification of the predicate, the subject should be qualified (!) by the predicate. Why we are not told, nor what qualified judgment means in such a case. But it seems that if we say all man is some mortal, we ought to say all man is man mortal, and then man mortal is man mortal ; or A is B, then A B is A B. I submit there is no equivalence in those statements or propositions, no necessary connection between them. When I say all man is some mortal, I am speaking of the class man and the whole class man. But when I say man mortal, or mortal man are so and so, I speak of a part of the class man viz., the mortal part, and I imply that there is or may be another part of which I am not speaking at all viz., the non- mortal or immortal part. The one is a universal proposition PREDICATES EXTENSIVE AND COMPREHENSIVE. 313 in which I speak of the whole subject ; the other is a par- ticular proposition, in which I speak only of some of the class, a supposed part of the subject. To say that the violet is blue, is not the same as to say that the blue violet is the blue violet. In the former case I am supposed to speak of all the class violet, and to say it is blue ; in the latter case I am supposed to take a part of the class by restriction viz., the blue violet, and to say simply that it is identical with itself. This arises from the elementary principle that any adjective applied to a subject is limitative. Mortal man is necessarily less than all man, and blue violet is necessarily less than all violet or all of the class. Hence to say that all of one class is equivalent to some of another or possibly wider class, is one thing ; but when I say man mortal is man mortal, this does not tell me that I am speaking of the whole of the subject, and the pro- position is not the convertible equivalent of all man is some mortal. It is simply a narrower proposition, and at the ut- most a puerile verbal inference from it, which depends on the wider proposition. But if the some in the predicate means some only, which it might do, the attempted equation of the two propositions is even ludicrous. All men are (only some) mortal, cannot be translated into all men are men mortal, for this does not in the least tell me what I said originally that all men do not exhaust the class mortal, but are only a part of it. And to put men mortal for the predicate all men, is merely to repeat the blunder already exposed. The formula becomes even more inappropriate when the subject and predicate are each universally quantified. We may say, all the men at the bar are all the rioters. This, ac- cording to the formula, should be, all the men at the bar are the men at the bar-rioters. And this paltry tautology is actually to be regarded as representing the statement made in the original proposition ! Again, let us take such a proposition as some stars are all the planets. Here, according to the formula, we ought to mean some stars are star-planets which is pretty well non- sensical, and certainly not in the least the equivalent of the original proposition. 393. The criticism, indeed, proceeds on the confusion of the Comprehensive and Extensive Predicates. 314 INSTITUTES OF LOGIC. (1.) In regard to concepts, when we translate man is some mortal, into man is man mortal, we pass from the pred- icate in extension to that in comprehension from what has quantity to what has none, but is indivisible. The some mortal of the first proposition indicates the limited place of the subject in the class ; the man mortal of the other clumsily indicates mortality as an attribute of man. Instead of saying this simply, we say man is man (the) mortal, or man is the (or a) subject which possesses the mark mortal. To pass from the comprehensive predicate to the extensive is natural and legit- imate ; to repass from the extensive to the comprehensive is arbitrary and wholly unnecessary, and it does not proceed on any equivalence of quantity ; for we really pass from what has quantity to what has none from extension to comprehension. To take an individual subject : Simon is a tanner that is, one of the tanners or class. If, however, we thus quantify the predicate, we ought, on the principle stated above, to have this form Simon is Simon tanner, as man is man mortal. Now this is not the equivalent of the original proposition at all. This means that of those named Simon, the one of whom I now speak is tanner, or the tanner, as opposed to Simon the miller or butcher, or some one else of the same name. He is marked, in fact, by an attribute as one of the Simons ; whereas, when I say Simon is a tanner, or one of the class, I am not considering whether there are other Simons, but only that he is one or a part of a definite class. He is in the class, but does not necessarily exhaust the whole extension. The proposition, Simon is Simon (the) tanner, is in Comprehension as giving the mark of the individual ; the proposition, Simon is a tanner, is in Extension, and gives the place of the subject in the class. 394. Objections have been made to the scientific validity of certain of the Propositional Forms : (1.) Toto-total affirmation. All is all. All X is all Y. It is objected by De Morgan (1) This is complex. (2) It cannot be denied by a simple proposition. (1.) It is complex ; and all Xs are Ys is compounded of all Xs are some Ys, and some Xs are all Ys. (a) All Xs are all Ys is not more complex than its alleged constituents all Xs are some Ys, or some Xs are all Ys. One OBJECTIONS TO QUANTIFIED FORMS. 315 quantity cannot be more complex than another. All is not compound, while some is simple. The truth is that some is made up of several, as this, that, &c., just as all is made up of every one. It is the business of Logic to consider a judgment as a completed or finished product. The psycho- logical complexity of the judgment is a wholly different point. Moreover, to admit that some is all some figure is all triangle is simple, renders it impossible to conceive that all is all, or all triangle is all trilateral, is compound. All and some are both made up of a plurality. The attempt has been made to show the composition in question, on the ground that the propositions which make up all X is all Y viz., all X is Y, and all Y is X, are independent of each other ; while the propositions which make up all X is some Y viz., all X is Y, and some Y is X, are not, the one being inferrible from the other by conversion. But when we find that this proceeds on the assumption (1) that the predi- cate as predicate has no quantity, and (2) nevertheless, that in conversion the quantity acquired is particular when the convertend is affirmative, and universal when it is nega- tive, we need not argue the point. If the predicate in the convertend had no quantity, and yet acquired it in the conversion, the acquisition was at once arbitrary and illogical. 395. (b) All Xs are all Ys is said to be compounded of two propositions viz., all Xs are some Ys, and some Xs are all Ys. In concrete language, all triangle is all trilateral, is said to be made up of all triangle is some trilateral some triangle is all trilateral. But these are incompatible propositions. If either of them is true, the other is false. Nay, if either of these alleged generating propositions be true, the so-called product, all triangle is all trilateral, is false. Here some is used in the sense of some only. All triangle is (only some) trilateral is con- tradictory of (only some] triangle is all trilateral; and either of these is contradictory of all triangle is all trilateral. Nor can it be shown that this form AfA is made up of these two forms, even if we take some in the ordinary Aristotelic sense of some at least. Thus (a) all triangle is some at least trilateral; and (b) some at least of triangle is all trilateral. For the quantity of the predicate in (a) is wholly indefinite, and the quantity of the subject in (b) is wholly indefinite, and the two 316 INSTITUTES OF LOGIC. indefinites put together cannot logically yield the definitude or totality of the same subject and the same predicate in a conclusion. Thus : (a) All triangle is (some) trilateral. (b) (Some) triangle is all trilateral. (c) All triangle is all trilateral. All triangle is some trilateral at least, perhaps all, how much I know not ; some triangle at least, how much I know not, is all trilateral. These propositions are vague, even if they were consistent, and cannot form the elements of the com- pound, all triangle is all trilateral. 1 (2) The objection that all X is all Y, all man is all mortal, cannot be denied by a simple proposition, is groundless. We can say readily the whole class man is not identical with the whole class mortal. That is all we need to say in order to deny, and it is conveyed in one proposition. The denial here is perfectly definite. We deny the equiv- alence of the terms as wholes. It is said by De Morgan that such a proposition all X is all Y, can be denied only by the disjunctive assertion, " Either no Xs are some Ys, or some Xs are no Ys." Though one of these were true, the power of denying all is all in an elementary form is refused me. Hamilton, in dealing with this objection, shows that De Morgan does not distinguish contrary from contradictory de- nial. In contrary opposition the original statement may be denied by a plurality of propositions. A denial need not rest on a single alternative case on a contradictory proposition but on one or other of two incompossible contraries, and it will be valid if one or other of the contraries be true. "All (class, whole, every, $c.) triangle is all (class, whole, every, fyc.] trilateral, is contradictorily denied by the proposi- tion. All (class, $c.) triangle is not all (class, $c.) trilateral, in the sense ' This proposition, All triangle is all trilateral, is untrue.' The denial here is necessarily vague, for there are five several cases, any of which it may mean, and of these any will validly support the negation of the affirmative proposition. These are : 1, Not-all triangle is all trilateral, i.e., Some triangle is all trilateral. 2, All triangle is not- all trilateral, i.e., All triangle is some trilateral. These are inconsistents. The following are contraries viz., 3, No 1 Cf , Hamilton, Discussions, p. 688. OBJECTIONS TO QUANTIFIED FORMS. 317 triangle is any trilateral. 4, Some triangle is no trilateral. 5, No triangle is some trilateral. 1 " 1 l All that needs to be done in the case seems to rne to make such a denial as will affect the equality of the two classes, that is, the point asserted. An antagonist does not require to do more in the first instance. The special proof or oppo- site case on which he relies is a secondary point. If it be said, all the men at the bar were all the men in the field, I "can deny this by saying this was not so. I may yet hold my proof in reserve. I may be able to show that one man in the field leaped the wall and escaped, or that one of the men at the bar was not in the field at all, or that none of the men at the bar was in the field, and so on. Either of these alternative cases would disprove the assertion, that is, the equivalence of subject and predicate alleged. I can legitimately make a contradictory negation in the first place, though this in the end may depend on the truth of one or other of several alternatives. 396. The use of the form, all is all, is common and necessary. Every adequate Definition supposes it. If I say proportion is the similitude of ratios, then, the defini- tion being accepted, the predicate can be put in the place of the subject, and nothing else. This is simply AfA. And surely, if I can think the subject and predicate of a definition nay, must think them as precisely convert- ible, it is ridiculous to suppose that I cannot express this in a single propositional form, that I am to be called upon to define, and then in another proposition to say this is a good definition, or its terms are convertible. The form is further obviously necessary and useful in expressing equivalence between two undivided wholes, as copper is sulphate of iron that is, all of the one is all of the other. Common salt is chloride of sodium, and so on. In ordinary language we do, wher- ever it is necessary, attach a sign of universality to the predicate by limitative and exceptive particles. . We say, God alone is good ; Virtue is the only nobility ; Of animals man alone is rational. We use besides one, only, precisely, just, sole, &c. 397. In Induction and in practical reasoning, the need of the form is obvious. As Professor Bowen well illustrates this 1 Discussions, p. 689 et seq. 318 INSTITUTES OF LOGIC. point : " If I am playing chess, and my king is in fatal check, I must reason thus I can neither move my king, nor inter- pose a man, nor capture the attacking piece. But these are all the modes of obviating check. Then I am checkmated." 1 (a) "All A is all B is inadmissible, because it is not the equivalent of any single proposition capable of being asserted in an unquantified form." (Examination, p. 514.) It is the equivalent of two separate judgments, All As are Bs, and all Bs are As. All man is all rational. This means, every man has the attribute reason, and nothing which is not man has that attribute. It is not possible to make only one judg- ment out of an assertion divisible into two parts, one of which may be known and the other unknown." (Ibid., p. 515.) ' ' Unless Sir W. Hamilton was prepared to maintain that, whenever the universal converse of an universal affirmative proposition would be true, we cannot know the one without knowing the other, it is in vain for him to contend that a form which asserts both of them at once is only one proposition. ... If ' all equilateral triangles are all equi- angular,' is only one judgment, what is the proposition that all equi- lateral triangles are equiangular ? Is it half a judgment ? " (Ibid.) In the first place, all A is all B, or all man is all rational, does not mean what Mill says it means. It is a judgment of quantity equivalence in quantity, and not directly in quality at all. It is a judgment of two convertible totalities, not merely of equivalence in attributes. In the second place, the argument amounts to this, that att A is" all B is a compound proposition, and therefore is not ad- missible as one propositional form. Without referring expressly to the test of the proposition as compound given by Mill, his argument is futile ; for if it held good, no proposition would be admissible as one propositional form except a Singular Judgment. This is the only pro- position which is strictly indivisible its subject being an indivisible unit, one, this, that. Every other proposition, whether the subject be quantified as some or all, would in this case be compound and inad- missible as a single propositional form. Some is compound of several units, all is made up of every unit of the class. Some men are just, att metals are conductors, are in this case compound propositions. And it matters nothing, so far as this point is concerned, whether we also speak of all in the predicate. We may say, Some stars are all the planets, or all equilateral is all equiangular. These propositions are not, in principle, more compound than all the planets are stars, or all equilateral is equiangular. Mill, in fact, confuses the process of the psychological formation of judgments with its logical results. The logical unit, whether concept or judgment, is necessarily compound, but it still remains and can be dealt with as a logical unit. And the propositions which Mill regards as compound, because they are " divisible into two parts, one of which may be known and the other unknown," are not more compound than those which he regards as single. We may know that some metals are electrical without knowing that all are, though we cannot make this assertion without knowing 1 Logic, p. 134. PARTI-PARTIAL NEGATION. 319 the former ; just as we may know that all equilateral is (some) equi- angular, without knowing that they are all equiangular, though we cannot know this without knowing the former. No doubt, whatever proposition is capable of division into two separate assertions, one of which may be true or assumed without involving the other, is psycho- logically a compound proposition ; but this applies to every proposition except the Singular, whose subject is logically an indivisible unit. (b) " Some A is some B, i.e., only some B, is a double proposition, com- pounded of some A is some B and some (other) A is not any B. The one statement affirms, the other denies, a different predicate of a differ- ent subject, and these are, therefore, two distinct judgments." (Exam- ination, p. 517.) Do they really? (Some) man is (only some) of the six-feet things (some) (other) man is not any of the six-feet things. Does the subject man differ because we speak of some and some other of the class ? Does the predicate, six-feet things, differ because we speak of some and any of the class ? Are we not still dealing with the same genus in each case, and simply subdividing it? And even if this were true, would this prove the judgment with some only in it to be any more compound than that all A is some B implies the fore- gone judgment that some (at least) are ? (c) " All Xs are all Ys," says De Morgan, is compounded of " all Xs are some Ys," and " some Xs are all Ys." No, replies Hamilton these are incompatible, mutually exclusive. They cannot unite to form one proposition. X cannot be thought both as only some Y, and as all or every Y. Mill rejoins : yes ; for if all Xs are some Ys identifies X with only some Y, some Xs are all Ys " superadds the remainder"! (Examination, p. 516.) In other words, we first say X is only some Y, and then, we say no, it is the whole of Y. We thus make one proposition every X is every Y. Some only may mean more than some only ! 398. But Hamilton answered this and other objections by anticipation. To the objection that in Eeciprocating pro- positions the predicate is taken in its full extent, vi materice, Hamilton replies, "that as form is merely the necessity of thought, it is as easy to think two notions as toto-totally coinciding (say, triangle and trilateral) as two notions toto- partially, and parti-totally coinciding, say, triangle and fgure. Accordingly we can equally abstractly represent their rela- tions both by geometric quantities (lines or figures) and by purely logical symbols. Taking lines : the former [_ I ; the latter |~ ~~. Taking the symbols : the former C : : F ; the latter A, : B- But if the recipro- cation were determined by the mere matter, by the object con- tingently thought about, all abstract representation would be impossible." l 1 Logic, ii. Appendix, p. 297. 320 INSTITUTES OF LOGIC. 399. The objection made by Thomson to the forms AnI and Inl, is that they have the semblance but not the power of a denial, is unfounded. To take AnI. If we say, any bird is not some animal, we can still say, any bird is some animal. This is no proper objection to the original form, for the some animal spoken of in the two propo- sitions is different. In fact, we are dividing a class or genus into its parts and species. We suppose animal the genus, and divide it into some and some. These are exclusive, and yet possess a common quality. All roses are some flowering shrubs, and all roses are not some flowering shrubs that is, flowering shrubs contain roses and some other shrubs. As Professor Bowen has well remarked : " Any limitation of the predicated class by a limiting adjective is equivalent to quantifying that predicate particularly. Pines are not deciduous trees that is, pines are not some trees." * 400. The same principle justifies parti-partial negation Inl Some is not some. The peculiar use of this form is to express the divisibility of any whole. When we say, some A is not some A, we assert parts, and that these can be divided, or that there are parts and parts. If we deny this statement, we assert that the thing spoken of is indivisible or a unity. .This form is implicitly at work in every science in every case, in fact, in which we divide a genus into its species, or a species into sub-species, or these, again, into individuals. When we speak of some and other men, for example, we have presupposed this form that some is not some that the class man is capable of division, capable of being sundered and separated, and yet remaining the supreme whole which contains the some and the other say, the European and the Asiatic. We may say there are men and men. We say, as we do every day, there are poli- ticians and politicians, there are ecclesiastics and ecclesias- tics, there are sermons and sermons. These are but covert forms of the some is not some, and unless this is formally vindicable, the greater part of our ordinary language is wholly baseless in reason. 2 401. Is some is not some not an available proposition? May I not say do I not need to say planting is not some planting ? Planting monotonous larches all over a hillside is 1 Logic, p. 139. 2 Cf. Discussions, p. 695 et seq. CONSEQUENCES OF QUANTIFIED PREDICATE. 321 not planting the same with graceful birches. Planting in oue sort of way is not planting in another sort of way. And yet both are planting. Only the one is good, the other bad. And if I can state this propositionally, why may it not appear in a reasoning ? Again, some vivisection is not vivisection. This is nonsense ; but some vivisection is not some vivisection, is true and important ; for the one may be with an anaesthetic, the other without it. 402. There are objections against their scientific and prac- tical necessity. (1.) Some X is all Y If A. This is merely a new mode of expressing Afi A, all X is some Y ; for we can convert Afi into IfA and say all X is some Y, and some Y is all X. So with AnI and InA any X is not some Y some Y is not any X. These are thus virtually identical forms, and the new ones, IfA and InA, are, though valid, not scientifi- cally or practically necessary. That some stars are all the planets, and all the planets are some stars, are no doubt deducible directly the one from the other. But that does not bear on the point, that the logical doctrine of the universal particularity of the predicate in an affirmative proposition, is by the admitted legitimacy of IfA at once dis- proved, as that of the invariable universality of the predicate in a negative proposition is equally disproved by the admitted legitimacy of AnI. And if these forms be legitimate, their scientific value in reasoning is at once vindicated, and we can now employ these propositions as premisses, and draw conclu- sions directly from them. This we could not do before on the ordinary logical principles, being driven to the circuitous process of reduction in order to reach what is now a direct conclusion. And being thus both legitimate and valuable in a scientific aspect, it may happen practically that we approach the knowledge of the proposition through the new form Some stars are all the planets, or all A is not some Y rather than in the old. This being so, there is no reason why we should be debarred from their direct use, and be made to state each in the form of an equivalent. 1 403. Among the consequences of the doctrine of the quan- tified predicate, we note (1) propositions become equations or non-equations of subject and predicate. They are equations or non- equations in quantity proper that of Extension ; 1 For further vindication, see Discussion*, p. 662 et seq. X 322 INSTITUTES OF LOGIC. for, as I have said, quantification of the predicate does not and cannot apply to comprehension. All the same this relation of equation need not abolish the relation of whole and part. (a) It has been supposed that when Hamilton said ' ' every proposi- tion expresses an equation between its subject and its predicate," he meant to speak of the terms taken absolutely, or each regarded for itself. (Cf. St Hilaire, art. Proposition Diet, de S.P.) Hamilton has no such meaning. He refers merely to the proposition in question, to the proposition as determinate, as far as it expresses the quantity of the terms. This is shown by the very nature of explicit quantification ; for example, all man is some mortal. By this he does not mean an equation absolutely between the terms man and mortal, but only between as much of them as is taken or considered in the one case all, and in the other some. It is not that all terms are equivalent or identical, but that the proposition expresses how far they are so. It is actiially objected by the same writer that the idea of equa- tion is inapplicable to negative propositions, as if Hamilton had not repeatedly and expressly said that the relation is one either of equa- tion or non-equation. (6) Hamilton nowhere says that "every proposition which I affirm respecting a subject must include all I know about it," and there- fore, that if I know all trilateral figures to be triangular, I must say not "all triangles are trilateral" but " all triangles are all tri- lateral." (Examination, p. 516.) What Hamilton says is, that what I know, judge, and mean to say in a prepositional form in language I should say expressly, that it may be clear to myself and others, and that logical science may unambiguously deal with it. If, for example, I mean merely to state that the predicate extends to all of the subject, I should say all trilateral is triangular; and if I mean to say that it is coextensive with it, and not more, I should say all trilateral is all triangular. (2.) Propositions (in extension) are seen to be immediately convertible. The predicate can be immediately put in the place of the subject, and a proposition of precisely the same force or import emerges. The various methods of Conversion devised by logicians are thus abolished, and all conversion becomes absolutely simple, and by a single method mere transposition of the terms, as every A is (some) B ; some B is every A ; any A is not (some} B ; some B is not any A. . 404. The scientific value of the quantification of the pred- icate is, in Hamilton's view, shown expressly in regard to Syllogism. Its necessity and logical importance are vindi- cated by the fact that it is really assumed in the ordinary syllogistic view, though not acknowledged in fact, repudiated. CONSEQUENCES OF QUANTIFIED PREDICATE. 323 In the First Figure, there is the acknowledged peculiarity of indirect moods such as Bamalip, Celanes, Dabitis, Fapesmo, Frisesmo. These moods, as well as all the moods of the Fourth Figure, are simply sub-conclusions from the direct conclusions of the premisses employed. There is the secret conversion of the undeclared direct conclusion. But there is the further peculiarity, not acknowledged, that these indirect conclusions are immediate inferences from a proposition which, on the ordinary logical doctrine, is illegitimate viz., a negative pro- position with a particular predicate (AnI, In A.) To take Fesapo, for instance : No planet is (any) comet ; (AnA). All comets are some (stars) revolving round the sun ; (Afl). (.*. No planet is some star revolving round the sun) ; AnI. .'. Some stars revolving round the sun are no planets; (InA). The proposition within brackets, AnI, is the immediate, though undeclared, conclusion from the premisses. The last proposition, InA, is merely an inference from this immediate conclusion. The logicians are thus here obliged to acknow- ledge as efficient in thought a judgment which they regard as illogical viz., the negative with a particular predicate (AnI). For the converse of this proposition cannot be true or legiti- mate, unless it is so itself. The contracted views of logicians as to the indefinite quantification of the negative predicate are thus refuted by their own practice. The general result of this analysis is that all the indirect moods of the first figure, and all the moods of the fourth, are only mediate conclusions from moods (or conjugations) of the first figure. Consequently there is no ground for maintaining a fourth figure at all. The conclusion of each of the indirect moods of the first figure is simply a process of conversion from one quantity into an- other ; the moods of the fourth figure are merely the indirect moods of the first figure, the premisses being held to be transposed a circumstance which can cause no syllogistic difference. 1 405. While, since the time of the Port-Koyalists, the doc- trine of Comprehension has been recognised and received into logical systems, it seems to me that the salient and essential feature of the doctrine in its relation to judgments has either been generally overlooked, or when noticed at all most im- 1 Discussions, p. 663. 324 INSTITUTES OF LOGIC. perfectly appreciated. This is the individuality or totality of the attribute as predicate, which gives an entirely new and yet natural form of proposition and series of prepositional forms. In regard to these, quantity is of no consequence ; it falls out of consideration. 406. This new classification of propositions is formally legitimate, and is at the same time suitable to the actual facts of our experience and the needs of our thought. Taking Comprehension first as the basis of the whole, we have : A. All man is mortal (indivisible attribute or mark) ; .. Mortal is a mark of all man. E. No man is quadruped ; .'. Quadruped is not a mark of any man. I. Some man is learned ; .'. Learning is a mark of some man. 0. Some man is not learned ; .'. Learning is not a mark of some man. U 1 . This man is artist ; .'. Artist is a mark of this man. U 2 . This man is not an assassin ; .'. Assassin is not a mark of this man. In each predicate there is quality, not quantity. The judg- ment is simple, natural, and easy ; it is suitable to experience ; it is simply convertible, and may be expressed in either form as convertend or converse. To distinguish such preposi- tional forms, we might call them A Comp., E Comp., I Comp., Comp., U Comp. 1 , U Comp. 2 It is to be observed that the predicate (attribute) is taken in its whole comprehension, whether the judgment be affirmative or negative. When we say this man is not an assassin, we speak of the whole comprehension of the concept, as marked off from every other, either fuller or less in compre- hension. We do not deny anything of him, except the com- plete whole essentially involved in the concept assassin. He may be homicide, or he may not; but this is neither (im- plicitly) affirmed nor denied in our judgment. 407. In Extension, the following will be the scheme of forms : PROPOSITION AL FORMS. 325 A 1 . All man is (some) mortal. A 2 . All man is (all] risible. E 1 . Any man is not (any] stone. E 2 . Any man is not (some) biped. I. Some man is (some) biped. 1 . Some man is not (any] happy. 2 . Some man is not (some] biped. U 1 . This man is not a thief (any]. U 2 . This man is not biped (some). These may be marked : A Ex. 1 , A Ex. 2 ; E Ex. 1 , E Ex. 2 ; I Ex. ; Ex. 1 , Ex. 2 ; U Ex. 1 , U Ex. 2 . (a) The Port Royal Logicians were really the first to give effective prominence to the distinction between Extension and Comprehension in Notions and Propositions. But there are references to the distinction by other writers, before and after the date of the Port Royal Logic (1662). To say nothing meanwhile of the obvious references to the dis- tinction in Aristotle himself, we have its apprehension and statement by Cardinal Cajetan in 1496. (See Port Royal Logic, Introd. p. 33.) Collection of many is twofold ; intensively, and thus the species is more collective, because it rather unites the adunata ; extensively, and thus the genus is more collective, because many more fall under its unification (adunatione) than under the compass (ambitu) of the species. The species and genus are like generals the one of which has a small army, but wholly unanimous ; the other great, but of diverse factions. For that collects more intensively, this more extensively. Porphyry speaks of the extensive collection, and therefore says the genus is more collective. (Cajetanus in Porph. De Genere et Specie.) The species is in itself more one than the genus, since the species ex- presses a nature absolutely indivisible formally, whence it is called atoma; but the genus imports a nature divisible. (Cajetanus in Porph. De Genere et Specie, quoted by Stahl, Heyulce Philosophies, Tit. xii. Reg. v., p. 381 : London, 1672; first ed. 1635.) (6) Avicenna had said Predication is of two sorts, either univocal or denominative. Socrates is a man, is univocal. Here there is true and univocal predication. Man is white, or man has whiteness, this is denominative. Man is not said to be whiteness ; as Socrates is said to be man. (Log., p. 3 v. B. ; Prantl, ii. p. 325.) (c) The universal which Logic examines contains three things : the name, which expresses several things ; the idea, which represents general things ; and the nature, which is in several things. (La Dialectique du Sieur de Launay, Dissert, iii. p. 72 : Paris, 1673.) (d) Universale inest singulis inferiorum, et de illis potest pnedicari, non secundum extensionem, seu universalitatem, sed secundum naturam tantum et comprehenxionem. Ut tota essentia naturae sensitive, secundum omnia attributa sua, est in singulis animalibus ; non atitem in tota extensione, qua' una cum convenientia eorum in quibus cxtendi- 326 INSTITUTES OF LOGIC. tur, est forma universalis. (Goveanus, Logica Ehnctica, Disp. x. p. 128 : Dublinii, 1683.) There are explicit and intelligent notices of the distinction in Hutche- son, Lo(j. Comp, pp. 24, 25 (ed. 1754) ; in William Duncan's Elements of Logick, I. iv. 2 ; Kirwan, Logick, i. p. 41 (1807). With all this, the doctrine has remained comparatively unfruitful until our own day. 408. The table of prepositional forms given by Hamilton is defective, in so far as it does not specially provide a form for Singulars. The form which is the nearest approach to this is AfA, but this is not adequate, and does not mark out the Singular either properly or without ambiguity. The following scheme may be given as a complete and specific statement of Categorical Prepositional forms : Affirmative I. X is Y. Singular Definite, Comprehensive only, in two forms. (a) Newton is the author of the Principia. Concrete. (b) Veracity is the harmony between expression and conviction. Abstract. II. All X is all Y. Definite Omnitude Double, cor- responding in Extension to Definite Singularity in Comprehension. III. All X is (so)jie) Y. Definite Omnitude Single. IV. Some X is (all) Y. V. Some X is (some) Y. Negative X is not Y. I. Newton is not the author of the Principia. II. Any X is not (any) Y. III. Any X is not (some) Y. IV. Some X is not (any) Y. V. Some X is not (some) Y. No. I. is in Comprehension alone ; No. II. is in Extension alone. All the others may be read both in Extension and in Comprehension. In the latter, the predicate is taken as in- divisible and unqualified. If the predicate Y be taken as a class, we have an Extensive Proposition ; if it be taken as a mark or indivisible attribute, we have a Comprehensive Pro- position, and that in both cases, whether Affirmative or Negative. CHAPTER XXV. QUANTIFIED PREDICATE HISTORICAL NOTICES. 409. The history of opinions regarding the legitimacy or the opposite of quantifying the predicate is one in itself of much interest, and it has acquired importance from its bearing on the logical theories of Hamilton, Thomson, and De Morgan, and other recent developments in formal logic. So far as Aristotle is concerned, the principle of quantifying the predi- cate was rejected by him, when he had the doctrine expressly before him. 1 On other occasions, Aristotle may be regarded as having proceeded on the legitimacy of the doctrine, and thus accepted it in practice. This is seen especially in his treatment of the formal Inductive Syllogism. 2 The great body of logicians, since the time of Aristotle, have been content to acquiesce in Aristotle's rejection of a quantified predicate, and generally for the reasons he has given, which are by no means cogent or satisfactory. 3 The notices hitherto given of writers favour- able to the doctrine of a Quantified Predicate, either in theory or in assumption in practice, are to be found mainly in Hamil- ton's Logic, and in Mr Bayhes' New Analytic of Logical Forms.* Neither Prantl nor Ueberweg has given adequate attention to this point in their historical references. Mr Baynes, in the New Analytic, published in 1850, refers to certain names as recognising the doctrine in theory or in 1 See Categories, ii. 1, v. 7. De Int., c. vii. 2-4 c. x. An. Prior., i. c. xxvii. 9. An. Post., i. c. xii. 10. 2 See below, p. 449 et seq. 3 For a statement and criticism of Aristotle's views, see Hamilton, Loyic, iv. Appendix g, p. 298 et seq. 4 New Analytic, App. i. p. 81, 328 INSTITUTES OF LOGIC. practice. The first is Laurentius Valla (1408-1457), in his De Dialectica, libri. iii. The references are to the edition at Paris of 1530, though the work was probably first published much earlier. 1 Following Valla, is Ambrosius Nolanus in his Gasti- gationes adversus Averroem: Venetiis, 1517. Then, Jodocus Isenacensis, or Jodoc Trutfeder of Eisenach, who was the instructor in philosophy of Luther, by no means a sympa- thetic pupil, and who died in 1519. His work is Summulce Totius Logicce, 1501. In England we have Joshua Oldfield, in his Essay towards the Improvement of Reason, 1707 ; and there is a reference to Godfrey Ploucquet, Fundamenta Philosophice Speculative, 1759. Thynne, in his notes to Walker's Com- pendium of Logic, the Trinity College, Dublin, text-book of the time, makes applications of the doctrine. Hamilton refers to authorities for and against the prin- ciple, among the former Titius, Ars Cogitandi (1721), and Ploucquet. His reference to Titius is, however, very incom- plete. 2 410. Valla recognises the principle alike theoretically and practically, though he cannot be said to have carried it out with anything like scientific development or precision. He adduces a number of instances of express quantification in ordinary language, for his criticisms of the approved logical doctrines of his day were made chiefly from a grammatical standpoint. There is universality in the predicate in such expressions as these Nego aliquem esse beatum. Aliquem is here equivalent to ullum. Veto ullum intrare ; prohibeo quem- quam loqui. 3 Then he recognises the equivalence of subject and predicate in such expressions as the lion roars (rugit), the horse neighs (hinnit), man laughs (ridet). The predicate here is coextensive with the subject, and precisely convertible. 4 Valla's doctrine acquires its importance from his application of it to the Conversion of Propositions. His doctrine on this point proceeds on the postulate of an express quantification of the predicate, and is perhaps the earliest application of it to this subject, affording at the same time a legitimate and useful simplification of the ordinary logical rules. 1 There is a later edition Laurentii Vallce Romani dialecticarum dispu- tationum libri tre-s eruditiss. Opera Joannis Noviomagi casligati diligenter Colonicc, 1541. 2 See Logic, iv. Appendix g., and below, p. 334. 3 De Dial., ii. c. xxix. See above, pp. 257, 310. 4 De Dial., ii. xxii. COEONEL. 329 (a) "Although the signification of the predicate may be wider than that of the subject, yet it is not taken [in the proposition] as wider ; and therefore subject and predicate are convertible as every man in animal. This is not taken as the whole genus animal, but as some part of this genus ; therefore some, part of animal is in every man. In the same way, some man is animal means some part of animal ; therefore some part of animal is some man. ... In negation the principle is different, as no man is a satyr tli&t is, no man is any satyr, therefore, no satyr '.< any man. Collectively, satyr is not a species of man, that is, any species of man, therefore any species of man is not a satyr. . . . In negatives, that or this fish is not fcntus-brinyiny forth, but ova-laying ; to wit, of those which bring forth foetus, but do not lay eyys, is not that or this fish. " Thales is one of the seven wise men that is, some one (aliquis) of the seven therefore some one of the seven is Thales. Pythagoras was not of the seven wise men that is, any of the seven ; therefore any of the seven loos not Pythagoras." In arguing against the opinion that two sub- contraries are sometimes false together, when their predicates have a universal sign, as Plato is every animal, Plato is not any animal, Valla says: "These are not true sub-contraries, of which the second does not negate what the prior affirms. Plato is every animal has for its negative Plato is not every animal ; and this negative has for affirmative, Plato is some animal, because we are not now able to say any." 1 411. But the treatise which first most fully anticipated the main results of the doctrine of a Quantified Predicate, in re- spect not only to Conversion but the Moods and Figures of Syl- logism, is one entirely unnoticed in the history of logical doc- trine. It bears the following main title : Habes studiose lector Magistri Lodovici Coronelli in sacra pagina doctoris exiimi amplissimum non solum syllogismorum trium figurarum de media communi tractatum ; sed et syllogismorum expositoriorum in tcr- minis divinis artem syllogisandi. Necnon conversiones simplicem et per accidens continentem. Omnemque ferme difficultatem dia- lectices enodantem Magistri Joannis Guidonis magna diligentia recognitum et emendatum. Veneunt Parrhissiis in via Jacobea in edibus honesti viri Bernardi Aubry. (1518). The sub-title is : Syllogismoram tractatus a Magistro Ludo- vico Coronel Hispano artium professore editus auspicato incipit. (a) Guido is the editor of the work or treatise, and he calls himself " Billarensis " in the preface to his pupils. He speaks of Coronel in the highest terms both as to character and learning. Neither Ludovicus Coronel nor Guido is noticed by Prantl, while there is mention by him of Antonius Coronel, a prolific logical writer, who i Dialectica, L. ii.c. 24. 330 INSTITUTES OF LOGIC. taught in Paris in the early part of the sixteenth century, and who, like Ludovicus, was a native of Segovia. They were probably brothers. An- tony dedicates his commentary on the Later Analytic* to a brother, Fran- ciscus Fernandus Coronel, a distinguished soldier, 1510. The treatise of Ludovicus Coronel, which is exceedingly rare, is in the spirit of Petrus Hispanus and the Terminalists. He and Antony had evidently come under the influence, at that time very powerful in Paris, of the Scot John Major (1478-1540) now almost only a name, but in his day and for more than a generation afterwards, one of the most influential of thinkers, and especially successful in creating a line of followers, the last representatives of a retreating and modified scholasticism. Among these we can reckon Robert Caubraith, Scot ; David Cranston, from Glasgow ; William Manderston, Scot ; George Lockhart, Scot ; Caspar Lax and Johannes Dolz, both of Arragon, Johann Mayr or Eck, Antonius and Ludovicus Coronel, Joannes Dullaert of Ghent, and several others. The line of Major and his school was nominalistic, terminalistic in fact, which meant an attempt to render the scholastic logical abstractions more concrete by bringing them face to face with the forms of lan- guage, and thus nearer to actual human thinking. The line of Major, the relations ultimately of Logic and Grammar, requires still to be worked out. 412. Ludovicus Coronel does not lay down explicitly or as a principle the doctrine of a quantified predicate, but he criticises the ordinary theory of Conversion, the general and special rules of Syllogism, even the distinctions of Mood and Figure, on a tacit assumption and application of this doctrine. And he proceeds, as will appear, on the principle which grounds the whole doctrine of express quantification, that we ought to distribute according to meaning, or enounce as we think. He is very cautious in dealing with the received rules, and the authority of Aristotle, which he tries con- stantly to claim ; but he seeks, if not to substitute new rules for the old, at least to supplement them by others which he holds to be equally valid, and to yield " good and formal consequences." In regard to Conversion, the author comes in the end to the view that all conversion is simple. Only let the same quantity remain in the process of conver- sion, and let us suppose the terms of the conversa and con- vertens in the same species of representation (in eadem specie suppositionis), and conversion is effected simply. Thus, by simple conversion, we can say, All man is animal, therefore, animal is all man. Man is Socrates, therefore, Socrates is man (fol. xxxb). This mode of it is to be applied to the imperfect moods. Conversion, moreover, is an inference, CORONEL. 331 implying antecedent, consequent, and illation. To say all man is animal, therefore all animal is man, is not conversion ; because this is made from a suppositio conjusa, in modern language, from a lack of explicit quantification of the predicate. But we can convert simply all propositions by distributing according to the kinds of each (distribuendo pro generibus singulorum), as the sense may be. Thus even the universal affirmative proposition is converted simply, as all man is all animal is convertible into all animal is all man. About the Universal Negative there is no doubt. The Particular Negative thus admits of simple conversion, as, man is not animal, therefore animal is not man (fol. xxxvib). Then he says, that every proposition is converted per accidens, by dis- tributing according to the kinds of each, as Universal Nega- tive and Universal Affirmative, and so may the Particular Negative, as, Socrates is not an ass, therefore no ctss is Socrates ; and some man is not an ass, therefore every (any) ass is not some man. The Particular Affirmative may also be thus converted, Some man is all animal, therefore all animal is man (fol. xxxvib). We have here an express recognition of several of the new prepositional forms in Hamilton's table, viz., AfA, IfA, Afl, AnI, InA and their simple con- vertibility. If it be said, it is added, that these views are opposed to the common mode of speech, that two kinds of propositions are converted simply, and two per accidens, the reply is, that the common method refers to propositions taken in the accustomed manner. Let the same quantity remain and let the logical proprieties be accepted in all respects in the same manner, which is nothing else than that the terms in the conversa and convertens should stand in the same relation (kind) of representation (suppositionis), then all conversion IB simple (fol. xxxvi b ). 413. In accordance with these views, a particular pro- position is defined as that in which no term is distributed ; a universal as that in which either term, subject or predicate, is distributed. He holds also that the rule regarding the invalidity of a conclusion from pure particulars does not apply to pure singulars, or the expository syllogism, which is "argumentum efficacissimum." The rule against pure par- ticulars refers to common terms. Further, if the antecedent 332 INSTITUTES OF LOGIC. * be formally impossible, or the consequent formally necessary, the consequence is good from pure particulars, or from pure negatives, as (1) Man is not man; (2) Man is or is not animal; Socrates is or is not running (fol. v b ). It is also held that there is consequence, which is non- syllogistic, and therefore not disposed in mood and figure. This does not depend on the premisses and the union of the extremes with the middle, but on the inference from the disjunctive part to the disjunctive whole (fol. ii b ). (a) Coronel criticises the special rules of Syllogism, on the same principle. The Second Rule, the major in the first figure, being particular, nothing follows ; for as the middle term is the highest it is not dis- tributed, and being the predicate in the minor (affirmative) it is not distributed. Against this you may argue, and well, these senses of the two rules of the First Figure are superfluous. Other rules of the First Figure commonly assigned are : The middle ought to be the total predicate of the minor. But, on the other hand, it follows validly Every man (quilibet homo) is running, Some ass is the ass of a man, therefore, Some ass is the ass of one running. Nor in a like form is an objection (instantia) capable of being given, yet the middle, which is the term man, is not total predicate of the minor, as is clear ; therefore, it is said that that rule is not always to be observed. Secondly, the middle in the minor ought not to be ac- cepted for others, nor for more than in the major. On the other hand it validly follows, all man runs, all white was all man, all white runs, or thus, all white was running, yet the middle in the minor is taken for more (as well present and past) than in the major, in which it was precisely taken for the present. Therefore it is said that that rule is not absolutely to be observed. The Third Rule majore de inesse et minore de prceterito velfuturo aut possibili consequentia non valet. On the contrary it validly follows, all man is running, all white was all man, therefore all white was running. Hence it is said that rule does not hold, and ought to be limited. In the criticism of the moods of the different Figures, there is some well-founded argument, but also a good deal of verbal and irrelevant remark after the fashion of the subtleties of terminalism, and often grounded on a change of the terms themselves. In the First Figure, the following is held valid : All man is risible. Some rational is all man (or ass.) Therefore, some rational is risible (or ass.) This may be taken as equivalent to the mood Afl, If A, If I. The rule is, that from a negative minor in the First Figure nothing follows, (1) because this would be arguing from the non-distributed to the distributed ; (2) be- cause the conclusion is unusual. Thus, CARAMUEL. 333 All man in running, No ass is man, Therefore, no ass is runnimj. But put it thus : All man is all running (AfA). No ass is a man (AnA). Therefore, no ass is runnimj, (AiiA). "This is a good and formal consequence, but" (it is added, by way of salvo, to the received views) "it does not proceed against those instituting that rule, who were not using an affirmative proposition, whose predicate might be distributed. Also in thus inferring ; therefore, any (quilibet) ass is not running, although the predicate of the major be not distributed, it validly fol- lows. Nor does this even proceed against them, because that mood is not used among them. But for all instances which can even be ad- duced, it is said that the sense of this rule, the minor being negative in the first figure, nothing follows, is that it is not inferred from the non-distributed to the distributed in respect of the major term ; with this it stands th&tFapesmo andFrisesmorum are good inferences, although the minor is negative." Again, with regard to the distribution of the middle term, there is, it is held, a good syllogism in Barbara, apart from perfect distribu- tion of the middle, which is contrary to the common opinion. Let the minor term in the minor be completely distributed, and thus let the sense of the minor be all ivhicfi is man is animal ; if, therefore, the distribution of the middle, according to the kinds of each, be sufficient to Barbara, it would be legitimate from those premisses to infer all man is running, the subject being completely distributed (fol. viii"). The major here supposed is evidently animal is running. Again : Omnis homo est currens, Hisibile quilibet homo est, Ergo, risibile est current. This may be said not to be in Darii, for it does not consist of a universal affirmative major, and a particular affirmative minor, for both premisses are universal. Of the first there can be no doubt. Aa to the second, one of the terms is distributed, and this is enough. 414. Joannes Caramuel reduces all Conversion to Simple by explicit quantification of subject and predicate, and ex- pressly recognises all the new prepositional forms. He indi- cates the universality, particularity, singularity, and indefmi- tude of subject and predicate in a proposition by U, P, S, I. Thus, All man is animal, is U I. All man is some animal, is U P. Some animal is all man, is P U. Some man is not some stone, is P P. Some man is not this stone, is P S. Some animal is this man, is P S. The defect of his doctrine is that he does not perfectly distinguish between material and formal truth and falsity. 1 i See Logica Vocalis, Opera, p. 220 : Francofurti, 1654. 334 INSTITUTES OF LOGIC. 415. Titius, in his Ars Cogitandi, first published in 1701, very fully and explicitly anticipated the doctrine of the quantification of the Predicate ; he recognises it not only in Propositions, but applies it to Conversion and Syllogism. Titius holds that in universal affirmative propositions the predicate, for the most part particular, is sometimes attributed to the subject, according to its whole comprehension, but not according to its whole extension; while in negative propo- sitions, although particular, the predicate for the most part being universal, is removed from the subject according both to its whole comprehension and its whole extension. 1 (a) Titius recognises universal affirmatives with universal predicate as Evert/ man is (every} risible, and a negative with particular predi- cate as no Turk is (some) man viz., Christian or, some doctor is not some man. (Ars Cogitandi, c. vi. 44, 45.) The error of the common doctrine of Conversion lies in the supposi- tion that the predicate should assume the sign and quantity of the subject. (Ars Cogitandi, c. vii. 3 et seq. 1721.) Titius holds conversion to be a simple transposition of subject and predicate, with the quantities of the convertend unchanged. Hence all conversion is simple and uniform. For example, (1) No man is a stone ; no stone is a man. (2) Some man is not medical (any) ; any medical is not some man. (3) This Peter is not learned (any); any learned is not this Peter. (4) Every man is animal (some); some animal is man. (5) Some man runs (any) ; some runner is man. (6) This Paul is learned (some) ; some learned is this Paul. (Ars Cogitandi, c. vii. 3 et seq.) 2 416. In 1827 appeared the work of George Bentham, Outline of a New System of Logic. In this we have a very close approach to the new Prepositional Forms. Speaking of Propositions, he says : (a) " In the case where both terms of a proposition are collective entities, identity and diversity may have place : 1. Between any individual referred to by one term, and any individual referred to by the other. Ex. The identity between equiangular and equilateral triangles. 2. Between any individual referred to by one term and any one of a part only of the individuals . referred to by the other term. Ex. The identity between quadrupeds and swimming animals. Whenever a term is intended to be applied to any individual referred to by a common name, that term is called universal. Wherever it is intended to be applied to any one of a part only of such individuals, the term is called partial. 1 Ars Cogitandi, c. vi. sections 37 et seq. 2 See the editorial references in Hamilton, Logic, iv., Appendices V. (a), p. 298, VIII. A. p. 375, X. p. 442. BENTHAM. 335 In affirmative propositions, universality is ascribed to the first term by prefixing to the common name the words every or any, to the second term by the word any ; but, in the latter case, it seems necessary to express identity more distinctly than by the simple copula is ; by some such expression as is the same as. In the same propositions, partiality is ascribed to the first term by the words some or some one (in Latin aliquis) ; to the last term by the same words when the first term is partial ; by the word a when the first is universal. Ex. : Every horse is a quadruped (partial). Some quadrupeds (partial) are some flying animals (partial). Every equiangular triangle (universal) is the same as any equilateral triangle (universal). In negative propositions, universality is ascribed in the same manner, as also partiality to the first term ; but in the case of the first term being universal, the negative sign (in the English language) must be combined with the sign of extent of the second, in order to avoid ambiguity. Ex. gr. : Every horse (universal) is no cow (partial or universal). Some quadrupeds (partial) are not flying animals (partial). Every equiangular triangle (universal) is the same as no isosceles triangle (universal or partial). Simple propositions, considered in regard to the above relations, may therefore be either affirmative or negative ; and each term may be either universal or partial. These propositions are, therefore, reducible to the eight following forms, in which, in order to abstract every idea not connected with the substance of each species, I have expressed the two terms by the letters X and Y, their identity by the mathematical sign = , diversity by the sign 1 1, universality by the words in Mo, and partiality by the words ex parte. These forms are : 1. X in toto = Y ex parte. 2. X in toto || Y ex parte. 3. X in toto = Y in toto. 4. X in toto || Y in toto. 5. X ex parte = Y ex parte. 6. X ex parte || Y ex parte. 7. X ex parte = Y in toto. 8. X ex parte || Y in toto." Bentham rejects Some X is all Y, some X is not all Y, as identical with all X is some Y, and all X is not some Y. He retains : ( 1 ) A II is all ; (2) all is some ; (3) all is not all or some ; (4) some is some ; (5) some is not some. But beyond thus stating these prepositional forms, he attempts no application of them in the science of Logic, except to say that the ordinary rules regarding distribution are not correct, and that for conversion, which he regards as a " conversive syllogism," the extent of the terms should always be distinctly expressed. (Outline of Logic, chap. viii. p. 130 et seq.) 417. As early as 1833, Hamilton had recognised the necessity for quantifying the predicate in affirmative propo- 336 INSTITUTES OF LOGIC. sitions. This appears from the exposition of the Inductive Syllogism given by him in the contribution to the Edinburgh Review in April of that year. Therein is the principle assumed and applied. Before 1840, he had become con- vinced of the necessity of applying it to negative Proposi- tions. 1 (a) Ueberweg remarks that the quantification of the predicate ' ' has been carried out by Hamilton on the basis of assertions of Aristotle, and according to partial precedents in the Logique ou Part de Penser, and in Beneke." (Logic, p. 219.) The first portion of this statement is not exact ; the whole only shows the small degree of attention which Ueber- weg has given to the subject of the quantification of the predicate and its history. 1 Discussions, Appendix II. A. PART IV. OF INFERENCE. CHAPTER XXVI. INFERENCE IMMEDIATE AND MEDIATE IMMEDIATE (1) TERMINAL EQU1POLLENCE (2) PROPOSITIONAL EQUIPOLLENCE SUBAL- TE RN ATION CONVERSION. 418. The third product of the Faculty of the Understand- ing is Inference. This is of two kinds Immediate and Mediate Inference, or Reasoning. The nature of each of those kinds of inference lies in what I would call necessary implication. As our basis we have a judgment, or judg- ments. As, in order to form the judgment, we advance from concepts or terms to their junction or disjunction ; so, in in- ference, we advance from a judgment or series of judgments to another founded on that or those. If we have but one judgment as a basis or ground, and if this yields another necessarily, as every judgment must, we have immediate inference. If we have two judgments so related that they necessitate a third, we have Mediate Inference, or what is known as Reasoning. As an ex- ample of the former, we may take what is popularly known as the Conversion of Propositions. Conversion arises when, retaining the same subject and predicate, we inferentially put the predicate in the place of the subject, and the 338 INSTITUTES OF LOGIC. subject in the place of the predicate. Thus, if I say no planet is inhabited, I am entitled forthwith to say anything inhabited is not a planet. Or if I say every X is Y, I am entitled forthwith to say some Y is every X ; or if every X be included under (some) Y, then some Y includes every X. Now these are cases of immediate inference, because I do not require to go beyond the terms or data of the proposition given to be able, or even necessitated, to affirm the other or consequent proposition. 419. Hamilton states the distinction between those two kinds of inference thus : " Reasoning [better Inference] is the showing out explicitly that a proposition not granted or supposed is implicitly contained in something granted or supposed. What is granted or supposed is either a single proposition or more than a single proposition." Immediate Inference arises when a second proposition is necessitated directly and without a medium by the first. In this species of inference there are only two notions and two propositions. In Mediate Inference, on the other hand, or Reasoning proper, there is the mediate eduction of one proposition out of the correlation of two others, and there are thus three collated notions. 1 420. While it may be admitted that there is a difference between Immediate and Mediate Inference, it seems to me that it would be a mistake to suppose that those processes are regulated by different laws. They are simply forms, less or more complex, of the same process, and they are regulated by the same laws. The Law of Identity, for example, applies as readily nay, more proximately to immediate inference as to mediate, and is truly the ground of both. If I say every A is B, or every covetous man is needy, I can say with formal necessity some A is B ; some, or this covetous man, is needy. Here I am really saying that if the whole is or is affirmed, the part is, or may be stated as being also. There is a direct application of the principle of containing and contained. There is no need of any third and mediating term or proposi- tion in order to necessitate the conclusion, and this is truly all the difference between immediate and mediate inference. The law of inference or validity is the same in both cases. If I say A is B that is, a part of B, but is a part of A, 1 Disclaims, p. 651. TERMINAL INFERENCE. 339 therefore, C is a part of 7?, I apply precisely the same law as in the former case ; only here I directly apply it to a part of the whole (A), in order to make it clear that this part (C) is also a part of B. The explicit application of the law to a part of the inferior whole A, and through that to another part of the superior whole B, is merely an additional step in a process substantially identical with that of direct inference from whole to part. 421. The cases of immediate inference are varied ; and to this head may be reduced many logical processes which have not been considered as inferences at all, but which are truly such. It is necessary to show that these are re- ducible to a single head or principle, in the interest of a scientific logic. The practical use of their consideration is to bring out clearly what lurks in everyday statements, often without consciousness of it on the part of those making them. 422. Immediate Inference may be divided into Terminal and Propositional. The main form of Immediate Terminal Inference is Equipollence. Equipollence is the complete agree- ment in meaning of two propositions which are enounced in different forms of expression, so that, given the one form of ex- pression, we may translate this strictly into the other. This is obviously not so much a case of immediate inference that is,' inference grounded on the thought as a case of recog- nised equivalence between two different forms of expression for the same concept, degree of quantity, or proposition. It may thus be described as immediate terminal inference or equivalence, and properly belongs to the domain of Grammar. Here the postulate of logic imperatively applies : State in a definite form of language what you definitely think as to meaning, quantity, and quality. The consideration of the Equipollentia of propositions has occupied a large space in Logic, especially since the time of William of Shyrewood and the date of the Summulce of Petrus Hispanus. But the whole discussion, while of grammatical and general import, is strictly extra - logical, and only requires a passing reference. (a) "Equipollence is that by which two or more enunciations, a negation mediating, are reduced to the same value of quantity and quality." (Stier, Prcecepta Doctrince, Tract, ii. p. 17. 1659.) 423. Equipollence in propositions arose very much from 340 INSTITUTES OF LOGIC. the use of the negative particle in Latin, before signs of universality, and also before signs of negation. Thus, when we say non omnis (not every one), we mean some are not. Omnis non, every one not, means nullus, not any one. Non nullus, not none, means quidam, some. Nullus non, none not, means every one; and so on. Thus, non omne peccatum est crimen, not every sin is a crime that is, some is not. If we had said omne peccatum non est crimen, we should mean no sin is a crime, which is a very different proposition. Hamilton recognises Equipollence as a form of Immediate Inference ; but he restricts it considerably, and identifies it mainly with Double Negation. Thus, A is not not-A. This is merely translating an affirmation into a double negation, and is, as he remarks, of merely grammatical import. 1 (a) The forms of Equipollence have been expressed by the Latin logicians in mnemonic lines. Shyrewood, probably the oldest (died after 1249), gives : " ^Equivalent omnis, nullus non, non aliquis non; Nullus, non aliquis, omnis non, sequiparantur ; Quidam, non nullus, non omnis non, sociantur ; Quidam non, non nullus non, non omnis, adhserent. Or all together : Prse Contradic, Post Contrar, Prse Postque Subalter." (See also Lambert of Auxerre, quoted in Prantl, iii. 28.) Non omnis, quidam non. Omnis non quasi nullus. Non nullus, quidam ; sed nullus non valet omnis. Non alter, neuter. Neuter non prsestat uterque. (6) (1.) Sign of negation prefixed to a universal or particular sign im- plies the contradictory. (2.) Sign of negation placed after a universal sign implies the contrary. (3.) Sign of negation placed before and after a universal or particular- sign implies the subaltern. Hence, (4.) when two universal negative signs are placed in the same expression, one in the subject and another in the predicate, then the first is equipollent to its contrary by the second rule, and the second to its contradictory by the first rule. (Hispanus, Summul., i. 3, 2, f. 36 A. Prantl, iv. 44.) The forms of expression and rules have been repeated by logicians with very slight variations since the time of Hispanus. On the author- ship of these and other mnemonic lines, see below, p. 399. 424. (1.) The first and simplest form of Immediate Proposi- tional Inference is that of Subalter nation or ^Restriction, usu- ally placed under Conversion. This arises when we infer some from all, or restrict the quantity either of the subject or 1 Logic, iv. p. 269. CONVERSION. 341 predicate, or both. Thus all X is Y, therefore some X is Y. Some X is all Y, therefore some X is some Y. All X is all Y, therefore some X is some Y. Here some means some at least. 1 This obviously proceeds on the Law of Identity of whole and part. Subalternation is commonly regarded as a form of opposition. It is really not so. There is no opposition be- tween all or the whole of a class, and some of the same, pro- vided some be taken as meaning some at least. If some be taken as meaning some only, there is not only opposition, but contradiction. All men are civilised, and some only are civilised, are opposed as negatives and contradictories. 425. (2.) Conversion is commonly spoken of as a transposi- tion of terms that is, of subject and predicate. It is this ; but it is so only through the necessity of inference or con- sequence. It is because from the original form of the propo- sition or convertend we can infer the same proposition or an equivalent in a new form, that conversion is possible. No conversion is true or real which is not strictly inferential, or dependent on a necessity of consequence. There is and can be no change, as is supposed, in the quantity of the terms, no change from universal to particular in legitimate conversion. The warrant of the inference is in the original proposition, and in that alone ; hence conversion is inference, and properly immediate inference. 426. Conversion arises only when the convertens, better conversa, follows necessarily from the given proposition or convertend. It is, in fact, a process from equal to equal. But this necessity can never be accurately ascertained until the terms of the proposition are definitely that is, in the case of Extension, quantitatively given. All conversion in extension supposes explicit quantification alike of subject and predi- cate ; it is only thus that conversion is logically or scien- tifically possible, and that we can avoid the mistake of sup- posing a change or accommodation of terms different from the original, and in the interest of artificial processes and rules. 427. The canon of Conversive Inference may be thus stated : The predicate of a proposition, in so far as it is affirmed or denied of the subject, may become subject to the original or given subject, now predicate. Thus All X is some Y; hence some Yis all X. No Xis any Y; therefore no Yis any X. i Cf. Hamilton, Logic, App. p. 269. 342 INSTITUTES OF LOGIC. (a) Conversion proceeds on the necessity of the consequence, through this, that the predicate is said of the subject. In this Conversion dif- fers from Syllogism and Enthymeme. Because it is necessary, it differs from the conversion of a particular negative, for although that may be transposition of subject and predicate, it is not conversion, because it is not a formal consequence. Whence it follows that conversion is a hypothetical, conditional, or rational proposition, whose antecedent is called the Converse (conversa), the consequent the Converting (con- vertens) ; and therefore the proposition given to be converted (conver- tenda) is the converse, and the other through which it is converted the converting (convertens). (Duns Scotus, In Universam Aristotelis Logicam Exactissimce Qcestiones. In An. Pr., i. qucest. xii.) 428. According to the ordinary logical doctrine, we have three kinds of Conversion. (1.) Simple Conversion is that in which are preserved, in the converse, the quality and quantity of the original proposition. Universal negatives and particular affirmatives are thus convertible. Thus, no (not any] X is Y; therefore, no (not any] T is X. No horse is a biped; hence, no biped is a horse. Some men are tall ; therefore, some tall things are men. Some animals are short- lived ; therefore, some short-lived are animals. Some X is Y; therefore, some Y is X. 429. (2.) Conversio per accidens, or Kara fiepos, is that in which the quality is preserved, but the quantity is diminished. The universal, in a word, is converted into the particular of the same quality. All universal affirmatives are thus con- vertible as, every man is animal; therefore, some animal is man. Every A is B ; therefore, some B is A. It is further held generally that where a universal affirmative is con- vertible into a universal affirmative, or rather an affirmative proposition with a universal subject, this takes place, not by reason of the form, but of the matter as, every man is capable of philosophy ; hence, every one capable of philosophy is a man ; otherwise, we might infer from every man is an animal, that every animal is a man. 1 This represents the common view of logicians on the point. 430. (3.) Conversion per contrapositionem is simply through contradiction and then transposition of subject and predicate. In place of the subject of the proposition, we have the con- tradictory of the predicate laid down; and in place of the predicate, the contradictory of the subject. Thus, every man 1 Cf. Mark Duncan, Inst. Log., ii. 4. CONVERSION. 343 is capable of being a grammarian ; hence, he who is not capable of being a grammarian is not a man. Every A is B ; therefore, everything that is not B is not A. Aristotle recognised this form of conversion, and called it indirect consecution in con- tradictories. 1 This is a form of Equipollence. (a) FEcI simpliciter convertitur, EvA per accid, AstO per contra, sic fit conversio tota. (Petrus Hispanus, Summ., i. 24, p. 30 B. Prantl, iv. 43.) 431. The rules for these processes in the ordinary logical system are cumbrous, and, in several respects, inadequate. They do not always accomplish what they profess, and they often assume other hidden processes which are necessary to their working. 432. Conversion per accidens is applied to A and E. But in neither case is the process a scientific one. To take A, as has been pointed out, conversion per accidens is not a conversion of A, but of the particular included in A. Thus : all X is Y, is converted into some Y is X. But some Y is X is the direct converse of some X is Y, and only indirectly of all X is Y, because all X includes some X. This is not pro- perly conversion, but Immediate Inference of Subalternation, because all is, some is. The conversion of 0, some X is not Y, is done by Contra- position attaching the not to the predicate. This is rather evading conversion than accomplishing it. There is a change of terms. Neither Conversion by Limitation nor by Contra- position is a self-sufficient process. There is always in each another process implied, but not unfolded. 2 433. According to Hamilton, the first great source of error in the ordinary doctrine of Conversion is that the quantities are not converted with the quantified terms. Logicians have looked at the naked terms of the proposition ; whereas the terms with which they ought to have dealt, are the terms as quantified in the original proposition. When we say all plant is organised, we ought not to consider merely plant and organised in the conversion, but the quantity of each term as well. The moment we do this, the so-called limitation of all to some disappears ; for it was all and some to begin with, and we can say by Simple Conversion some organ- ised is all plant. The quantity of the proposition in Conver- i Top., ii. 8. a logic, App. v. (c) p. 275, 344 INSTITUTES OF LOGIC. sion is thus shown to remain always the same. That of the Converse is exactly equal to that of the convertend or original proposition. Logicians, looking only to the quantity of the subject, and not considering that the predicate has always a quantity in thought as well, called the one proposition uni- versal, and the other particular, whereas in quantity they were precisely equivalent All X is (some) Y is precisely equivalent to Some Y is all X. It is not maintained that this express quantification of the predicate is always necessary in ordinary thought and language. It is sufficient if the predi- cate be as extensive as the subject, which every affirmative judgment must assume. Whether it be in itself more exten- sive is generally of little moment. But as soon as we have to find its immediate implicate by Conversion, we must ask the quantity of the predicate which subsists in thought to be explicitly stated. This being done, all Conversion of Propo- sitions becomes one simple, natural, and thorough-going. There can be no doubt that Hamilton has for the first time clearly shown the true character of Conversion, its requisite, and its rule. Wherever thought needs to seek the converse of a proposition, its best, easiest, and most scientific way is to conform to the simple principle which Hamilton has given. 434. The table of Hamilton, with the Eight Propositional Forms, shows at a glance the convertibility of each : AfA, All X is all Y = AfA. (A) Afl, All X is some Y = IfA. IfA, Some X is all Y = AfI. (I) Iff, Some X is some Y = IfI. (E) An A, Any X is not any Y = AnA. AnI, Any X is not some Y = InA. (0) InA, Some X is not any Y = A n I. Inl, Some X is not some Y = Inl. (a) The attempts at modifying the current doctrine of conversion by the older logicians are curious and suggestive. Universal Negative is twofold, (1) in which the predicate is distrib- uted, as no man is an ass; (2) in which the predicate is not distributed, as when the predicate precedes the negation, as omnis homo animal non est (every man is not animal.) In the first case, the conversion is simple, as every suppositum in the subject is removed from it in the predicate, so every suppositum in the predicate is removed from it in the subject. ERRONEOUS IMMEDIATE INFERENCES. 345 In the second case, there cannot be simple conversion, as every phnenix is not animal (omnis phnnix animal non est), therefore, some animal is not phoenix. This per atcidens. (Duns Scotus, In An. Pr., L. i. c. xii.) The particular affirmative proposition is of two sorts, (1) with the predicate discrete, as some man is Socrates. This cannot be converted simply, but only per accidem into one singular, Socrates is a man. But, with addition, this can be converted simply, as aliquid quod est Socratex est homo. Such a particular implies a universal from the terms trans- posed, as some man is Socrates, therefore, all ivhich is Socrates is man. This does not hold in divine things, as, this essence is the father, therefore, everything ichich is this divine essence is the father. The son is this divine essence, and he is not the father. This consequence is, therefore, not formal. (Duns Scotus, In An. Pr., L. i. c. xiii.) Scotus recognises a particular affirmative proposition with a distrib- uted predicate, as some moon is every moon (qucedam luna est omnis lund). This can be simply converted, every moon is (the) moon. Here the predicate stands for every one of its supposita; the subject for one suppositum, and these are equivalent. (Ibid.) (6) ^Equalis vero est subjectus terminus praedicato, ut si quis dicat "homo risibilis est"; ut vero id quod subjectum est majus possit esse prsedicato, nulla prorsus enuntiatione contingit, ipsa enim prsedicata natura minora esse non patitur. (Boethius, Introd. ad Syll. Cat., p. 562. Prantl, i. p. 696.) (c) Mark Duncan argues against simple conversion of Particular Nega- tive thus : Some man is not stone ; e converse, some stone is not man. This is not formally good. For, by parity of conversion, if some animal is not man, some man is not animal ; therefore some stone is not man, not because some man is not stone, but because no man is stone. (Inst. Log. , L. ii. c. v. 5.) (d) The particular affirmative is not converted per contrapositionem Something intelligent is man; something not man is not intelligent. (Shyrewood. Prantl, iii. 15.) On Conversion, see especially Marsilius von Inghen. (Prantl, iv. 97.) 435. Some logicians, among others Thomson, regard the following as cases of Immediate Negative Conceptions. A statement made in a positive predicate regarding a subject inference, implies a statement regarding its opposite, or con- tradictory. The bodily organism is material ; this implies that it is not immaterial. All human virtues are not without alloy or imperfection. This implies that all human virtues are short of their type, and that a perfect act of virtue is not within the power of man. These are virtually the same statements, but they are made from different points of view, and they may be supposed to bring out what is implied in the original state- ments. It is clear, however, that, unless in the case of the simple contradictory, there is here no purely formal inference. 346 INSTITUTES OF LOGIC. It is either a case of the same predicate in other words ; or of a predicate implied through a medium or process of reasoning. All actual human virtues may be imperfect, without the con- sequence that all possible virtues of man are so. There is no immediate connection between those two statements. This so-called form of immediate inference, in so far as it is non- contradictory, comes properly under the head of Equipollence, being purely terminal. 436. Immediate Inference through Determination. De- termination means adding a predicate or term to a notion, so as to make it more specific or determinate. We determine every time we proceed from higher genera to lower species. Thus, an animal is like ourselves a sentient creature ; therefore, an animal struck or wounded is a creature in suffering like our- selves. There is here no purely formal immediate inference ; the connection between a sentient creature, struck or wounded and suffering, is known through induction, and is here inferred through a major. Sentiency, wounded, suffering, are after observation associated or connected, but the con- cept of the one does not necessarily lead in any way to that of the other. 437. Immediate Inference by Complex Conceptions. This arises when the subject and predicate, that is, the entire pro- position, is added comprehensively to the original conception. Thus, the molecule of sand consists of silicon and oxygen ; there- fore, the analysis of the molecule of sand into those elements would be an analysis of a molecule. Not, certainly, of a molecule, meaning any molecule, but simply of the molecule of sand. But to call this an inference, immediate or other, is a simple misnomer. It is a mere tautology. The doctrine of Ex- ponibles, with the old logicians, and the propositional impli- cates unfolded according to their rules, were much better grounded than this. 347 CHAPTER XXVII. IMMEDIATE INFERENCE OPPOSITION CONTRARY AND CONTRADICTORY. 438. " Since it may happen that what is may be enun- ciated as if it were not, and what is not as if it were, and what is as if it were, and what is not as if it were not ; further, as this applies equally to the present and to other times, therefore it is lawful to deny all those things which any one has affirmed, as well as to affirm those things which any one has denied. Whence it appears that to every affirma- tion is opposed a negation, to every negation an affirmation ; let this be contradiction (cUri'^acris), the affirmation and nega- tion of the opposite. But I call opposed that which is of the same concerning the same, not the species alone of one expression." l 439. Aristotle here raises a very important and fundamental question. We seek frequently to deny or contradict, to state the opposite of a given proposition. The question arises, How can we best do so? In other words, how are we to make a statement which shall deny a given statement or proposition without doing more than exactly denying it^- that is, without doing more than is logically required of us ? Out of this need or question arises what is called the doctrine of the Opposition of Propositions. And this is one of the most important and also one of the nicest points in Logic. It depends essentially on the negation or negative proposition which is strictly implied in any advanced or given proposi- tion. The proposition we advance may be an affirmative. In this case, what we have to took for is the negative which 348 INSTITUTES OF LOGIC. will precisely deny it, and do nothing more. The proposition advanced may be a negative. In this case, what we have to look for is the affirmative which will directly confront and conflict with it, and which, if established, will render it un- tenable. These propositions will be regarded as opposites of various kinds, and the test of them in each case will be the strictness of the Immediate Inference with which, as negatives or affirmatives, they are implied in and follow from the original proposition. He who makes a statement is bound to accept all that which it logically implies, and only that which it logically implies, in affirmation, therefore, to ex- clude the immediately involved negation ; in negation to exclude the immediately conflictive affirmation. 440. In dealing with this point, it may be well to sketch generally, before proceeding to detail, the main forms and features of the Opposition of propositions. This will be found to admit of degrees. Let us take, first, universal affirmative and universal negative propositions. If it is said that every X is Y, I can deny this by saying that no X is Y. Or, to take a concrete example, if it is said that every planet is inhabited, this may be denied by saying that no planet is inhabited. Now, look at these two propositions. The one, every planet is inhabited, is a^universal affirmative t the other. no planet is inhabited, is ;i universal negative. They agree in quantity, but they differ in quality. They are both universals : they speak of the whole of the subject ; but the one is affirma- tive, and the other negative. The opposition, therefore, here is tolerably complete ; for the one affirms universally of the subject, or affirms of the whole subject ; the other denies universally of the subject, or of the whole subject. Yet this is not the highest or the extreme form of opposition. For while the assertion or the truth of the one proposition implies the denial or the falsity of the other, the denial or the falsity of the one does not, frpply fflp afflnnation or the truth of the other. Thus it cannot possibly be asserted or be true that every planet is inhabited, and that no planet is inhabited; that every X is Y, and that no X is Y. If the former of these statements be true, the latter is false. But the denial of the former statement does not imply the truth of the latter. It may be false that every planet is inhabited, yet it does not follow that all planets are not inhabited ; for if even one planet, CONTRADICTORY OPPOSITION. 349 or some planets were not inhabited, it would be false that every one is. All, therefore, which I have to prove or assert in order to deny that every X is Y, is not that every X is not Y, t but only that some X is not Y. And if I did not see this in an argument, and did not keep by it, I should simply be giv- ing up my fair logical position and advantage. This kind of opposition between Propositions is what is called Contrary Opposition, or the Opposition of Contraries. It holds only between A and E. 441. But there is still another and a stronger degree of opposition between projjositions than this. This degree con- sists in such a contrast or opposition, that if the one propo- sition be true, the other is necessarily false ; or if the one proposition be false, the other is necessarily true. Or, to put it in logical language, if the one proposition be affirmed, its opposite must be denied ; or if the one proposition be denied, the other must necessarily be affirmed. This mutual relation holds only when the opposing propositions differ alike in quantity and in quality. Thus, we may say, (A) every planet is inhabited, and in opposition we may say, (0) some planets are not inhabited. If it be true that every planet is inhabited, it is false that some are not. If it be false that every planet is inhabited, then it is at least true that some are not. In other words, the truth of the one proposition implies the falsity of the other ; and the falsity of the one implies the truth of the other. So it is also with E and I universal neg- ative and particular affirmative. This form of opposition is called^ Contradictory Opposition : it is the strongest or the extreme form known to human thought. It is absolutely insuperable. No compromise, no conciliation is possible between those two forms of statement, of affirmation and negation, of yes and no. Between Contrary Propositions jja a possible n^ftdintn nr mjditiTpfMiitinTi we do not paaq ftpm the one to the other, from all to Tvre myv reafr in some. But irT the case of contradictory opposition, there is no such medium or resting-place possible. Between saying that every one is, and that some are not, we cannot find a compromise or resting-place for thought. These statements are absolutely exclusive of each other. Hence it is laid down as an imperative logical rule that is, a supreme law of human thinking that there is no medium or middle 350 INSTITUTES OF LOGIC. between contradictory propositions. This is called the law of Excluded Middle between Contradictories. Contradictory opposition holds^between A and 0, and E and I. 442. It is right to say that these two kinds of opposition Contrary and Contradictory hold in relation not only to Propositions but to Terms or Notions. Thus, e.g., black and 'white are contrary terms, for an object cannot be both at once ; and there may be objects that are neither the one nor the other. A stone cannot be both ; but a feeling, or a desire, or a volition cannot be either the one or the other. Again, organised and non-organised cannot be applied to the same thing in one act of conception or judgment ; and there is nothing, in extreme logical exactness, of which we can think, which does not fall under the one head or the other. So that these notions exhaust the whole sphere of the thinkable. Being and non-being, for example, are absolute contradic- tories, to those who understand the meaning of the terms. There is no possibility of conciliating these by a medium or middle notion. Nothing can at once be and not-be ; to say that these are the same because the term being occurs in the second half of the thought, is arbitrarily to leave out the difference expressed by not, and thus say that there is a unity when you have merely abolished the real difference i.e., changed the terms. This application, however, of negation to concepts seems to me to be a secondary one, grounded on the negation properly expressecTnTthe judgment, and transferred for the sake of brevity and grammatical purposes to language. (a) That the same, in the same reference, at the same time, should belong and not belong to the same thing is impossible. This is the most certain of all principles ; for it is impossible that any one can con- ceive as the same being and not-being. Wherefore, all recall demon- stration to this ultimate belief. (Met., iv. 3.) Aristotle says rb avro cijua Kal Kara rb O.VTO, because affirmation and negation of the same thing or the one after the other, or the one in respect of the other, there may be. If the same, at the same time, and in the same thing, could both be and not be, and in reason be affirmed and denied, all things would be mixed, and nothing stable. There would be no species which you could define as universal ; there would be no necessity, nothing of which the nature is not to be both one way and another. To pursue truth would be to follow the flying (TO. ireT^uei/a Stdicfiv) but it is the nature of intelligence to intelligise unity. The sublation of this principle, that is, non-contradiction, is the abolition of cognition and of reality. (Of. Met. iv. 3-7, xi. 5, and Trendelenburg, EL Log. 9.) CONTRADICTORY AND CONTRARY OPPOSITION. 351 443. There is a good deal of misconception prevalent re- garding the true character and import of Contradictory and Contrary Opposition, whether as regards propositions or con- cepts. People talk in a vague and inaccurate manner about these two kinds of opposition, and continually confound them. But the truth is that Contradictory Opposition means an absolute or irreconcilable opposition, while Contrary Opposition does not. If a beggar asks me for a halfpenny, and I say no, or I shall give you none, I should be properly understood to say absolutely none, not even one halfpenny. If I gave him a halfpenny, he would have something what is positive ; if I gave him no halfpenny, he would have nothing what is negative. This seems tolerably clear, but we are told that Contradictory Opposites are equally positive, or real ; that halfpenny and no-halfpenny, or penny and no-penny, are equally positive in thought and in reality. I am perfectly certain that the beggar does not think so. The assumption underlying this view must be, that we cannot negate except by putting something positive on the other side. We cannot say no halfpenny without im- plying a farthing, or a penny, or a sixpence, or something of that sort. Now I venture to think this a total miscon- ception of the nature of negation. We may deny, and deny abeoltitelY^ witlumt. Rnpposiny or implvinp- a positive ,at all. We do so in every case of Contradictory Negation. Tne apparent exceptions are really cases of an inferior kind of opposition Contrary Opposition. E.g., to take number. We say one and two are opposites. When we deny or negate one, when we say there is not one, we may of course be supposed to mean there is more than one there are two. We here, however, first of all suppose that the tiling we speak of is and may of course be numbered. We regard it as coming under a class, and as belonging to some portion of that class viz., number either one, two, three, or four, &c. But two or three is not the true contradictory of one. This is none not even one not any ; and in the denial here we lay down nothing, we simply sweep abso- lutely away. That is true contradictory denial ; and here there is no possible alternative, and no positive notion laid down in opposition. The importance of this distinction is seen the moment you come to deal with a philosophy which 352 INSTITUTES OF LOGIC. professes to construct all thought and reality by the law of contradiction, which alleges that the contradictory actually passes into its opposite, and so passing forms knowledge and reality. Nothing can be more futile,*Wid even meaningless, than such a pretension. When we abolish or supersede the law of contradiction, we abolish all knowledge, we reduce everything to chaos. 444. True logical opposition, whether contrary or contra- dictory, is an opposition of quality in concepts, and as such it is independent of time. But when we apply opposition to xperience, the element of time necessarily comes into con- sideration. A subject of a judgment may be quite capable of contraries in successive times as a body at rest and in motion. And so of contradictories even, for what lives may pass into what does not live ; what feels into what does not feel. This, however, in no way affects the laws regulating what is ideally contrary or contradictory. It only modifies their application. It makes not the slightest difference in the concepts of the qualities as different, or even in the fact of their difference as a matter of experience. 445. Opposition in propositions, as founded on opposi- tion in qualities of things, and in their concepts, is of those qualities or concepts which differ the most in the same genus. In colour we have the various forms of colour, such as black and white ; in the sensible sphere we have pleasure and pain, heat and cold, light and darkness, motion and rest, &c.; in the moral sphere, good and evil, avarice, prodigality ; in the intellectual sphere, belief, doubt, unbelief. In other words, Contraries are positive concepts which exclude each other from a subject capable of them. 1 446. The older logicians recognised different grounds in the opposition of judgments. Some they regarded as opposed materially, others formally. In this, indeed, they followed Aristotle. 2 The chief principle of difference is, that material Qpposites admit of a medium, while formal opposites do not. The application of this principle is not always quite clear; but probably concepts under a genus, as red, green, yellow, rich and poor, &c., might be regarded as materially opposed, seeing that any one of these affirmed and denied as a predi- 1 Cf. Cat. vi., Met. vi. 10. 2 See De Int., vi., De Soph. Elench., v., An. Pr., ii. 35. CONTEADICTORY AND CONTRARY OPPOSITION. 353 cate would admit of a medium. The object might be neither one nor other of two, yet something else under the genus. In formal opposition, affirmation and mere negation is, or is-not there is no medium, as rich and not rich. The same is affirmed and denied of the same in name and thing. In modern language we should say that the former kind of opposition depends on difference qf^intuition, this being ultimately referable to the constitution of the outer and inner faculties of observation and reflection ; while the latter depends on the simple application of the formula of non-contradiction. But the truth is, that all opposition depends for its force ultimately on Contradiction. The first in every genus, as Aristotle remarks, is the measure of the rest. Contradiction is the first, simplest, and truest form of opposition. Con- tradiction is, therefore, the measure of all opposition. White is opposed to black through intuition, but the intuition is founded op t.h implied ^jfforenoe or contradiction of white and _ > not-white. The world is either eternal, or the work of chance, or l/ie work of intelligence. This division is primarily through the contradictory The world is either eternal or non-eternal that is, it had a beginning in chance or in intelligence* 447. Now the question arises as to the possibility of a middle or uniting term. In the case of Contraries, as they belong to the same genus, they may be conceived as each a species of the genus e.g., white and black is each a species of colour, as pleasure and pain is each a species of sensation. In the case of Contradictories, affirmation and negation of one and the same attribute noay be regarded as included under Consciousness. But tins is tho genus of the acts of mind ; it is not the genus^>roperly~speaking, _of the attribute affirmed and denied, as sensation is the genus of pleasure and pain. The attribute and its contradictory negation donot come under the same genus. The attribute and its contrary nega- tion do so. This genus may be said to unite in a sense the two contraries ; bxit the position and the negation of the same attribute cannot be so united. 448. It follows from this that, while in Contrary opposi- tion the mutual exclusion of the attributes is through two positive attributes, the mutual exclusion of the attributes in i Cf. Aristotle, Met., x., and Duncan, Jnst. Log., i. 13. z 354 INSTITUTES OF LOGIC. Contradictory opposition is not necessarily through two posi- tive attributes, but through a positive attribute and its bare negation the mere absence of it. Hence, when I negate contradictorily, I do not necessarily posit another attribute in the place of the negated attribute ; I only absolutely take it away. I negate, e.g., contradictorily sensation. I say this subject is insentient, or it is incapable of vision. Here I put nothing in the place of the sensation or the vision negated ; I J merely leave the subject of which I speak to be referred to I any one in the sphere of possible predicates the only limit ] to this being that the predicatejs compatible with the nature of the subject, whatever that may be. The negation affirms nothing beyond the indefinite possibility of some other com- petent predicate. In the case of Contraries, affirmation and negation differ. Here I am dealing with a class of things already constituted. I am dealing with opposites or the greatest opposites in that class. I affirm one of them ; I necessarily deny the other. I say this figure is a square, it is not a circle ; this sensation is pleasurable, it is not painful. Here I select, as it were, among the members of a constituted genus. But what of negation ? Suppose I say of the sensation, it is not painful, or of an object of vision, it is not green. Do these necessarily put anything in the place of the attribute negated ? I have made the object I speak of more determinate, in the sense of having excluded it from a particular predicate in the class to which it belongs. But that is all. The sensation may be either pleasurable or indifferent. The object seen is some other colour. But I do not by this act say definitely what other colour it is. It is not green ; it may be red, or Hue, or white since it must be one or other. That I know independently. But {^ thj^t_my negation of the particular attribute implies is that ^qme>q)redicate of..cQlou^m"ax/be attributed to it ; beyond this indefinite possibility nothing is implied. 449. Accordingly, while it is true that every determina- tion is a negation, the contrary is not true that every negation is a determination. A negation is a determination only in the sense of excluding from a particular attribute, and leaving the subject to be referred to some other class, or to be clothed in some other attribute not specified. The negation itself does not fix anything, does not really determine, IMMEDIATE AND MEDIATE OPPOSITION. 355 restricted the sphere of predication to .two. ) possibilities, which supposes the principle of Non - Contra- diction. Tf the possible predicates bo more, we know only that the subject is in one or other a case, in fact, of contrary disjunction. And contrariety itself, as restricted to the species under a class, supposes also the principle of Non-Contradic- tion ; for this class must first of all by it be discriminated from other classes. 450. As to a medium between two Contradictories, the very conception of its possibility is precluded. Affirmation and negation of the same attribute in respect of the same subject are not only impossible ; they are irreconcilable by any third notion, for the reason either that the subject of the predication itself has been sublated, as A is, A is not, or that the attribute and its contradictory opposite abolish the attri- bute itself, as organised and non-organised. 11 In all attributions," says Aristotle, " where there is no con- tradiction, although even the definitions are substituted for names, and where the attributes are in the subject by them- selves and not by accident, we can always, without deceiving ourselves, apply absolutely the isolated attributes to the thing. Nevertheless, non-being, simply because it is rational, cannot with truth be expressed as being; for the thought which we form of it is not that it is, but on the contrary, that it is not." l 451. Opposites are thus, according to Aristotle, of two kinds, Immediate and Mediate. The Tmmp.f1ia.fft ffopt.rftfi'flg ({.e.^ Cnntrfl.fHotm-ip.a'l are Such that one of them must necessarily be in InCSe things in which it can naturally be, or of which it is predicated. These have nothing intermediate. Thus, number must be odd or even. Here there is nothing intermediate no middle. S 452. Mediate Contraries, on the other hand, have some- i .1.. . thingMntermediate, in which one of them need not be inherent. Thus, blagfc and white are both predicable of body, yet it need not be either. R) of another, or that a thing is attributed to all of another (xara TravTos), these expressions are the same in sense. To say that a thing is attributed to all of another (or to another in its entireness), is to say that we suppose there is no part of the subject of which the other thing cannot be said ; and, in the same way, the not being attributed to any. (An. Pr., i. 1.) We have here apparently a formula of the Syllogistic Canon, which is much wider than most subsequent logicians have supposed, or at least accepted and applied. The Canon takes in reasoning alike in Extension and in Comprehension. " To be comprised in the totality," " to be attributed to DEFINITION OF SYLLOGISM. 379 all," are different expressions, with the same logical effect, referring to different aspects or forms of reasoning. The former refers to the subject as forming part of the extension of the predicate as, all gold is (some] metal. The latter refers to the predicate as forming a part of the total comprehension of the subject as, every mineral acid is a poison, or has the mark poison. The former proposition states the relation of the part to the whole (species to genus) ; the latter states the relation of the whole to the part as min- eral acid to its part or one of its marks, poison. The one is the relation of the particular or species to the universal or genus ; the other is the relation of the universal to the particular, or at least the complex to the particular or indi- vidual mark. 1 (a) Trendelenburg, however, remarks that the expression tv S\ j. V- FOURTH FIGURE. 395 (a) All Y is X \ All Y i s Z V = Darapti. .'. Some Z is X ) (b) No Y is X \ All Y is Z V =Fdapton. .'. Some Z is not X ) When one term, says Aristotle, is in all, but another term in none, of the same term, or when both terms are or are not universally in this same term, I call this the Third Figure ; the middle in this I call that notion to which both are re- ferred as predicates, and the extremes the predicates ; the major extreme is that furthest removed from the middle, the minor that which is nearest it ; but the middle is thus placed beyond the extremes, that it may occupy the last place. The conclusion is valid, whether the terms are universally or not referred to the middle notion. When P and R are in all S (as subject), then necessarily P is in some R (as part). Thus All S is P) AH S is R V = Darapti. .'. Some R is P) By conversion, since all S is R, some R is S. Then all S is P, some R is S (as predicate), therefore some R is P. This is Darii of the First Figure. There is no universal conclusion in this figure, either affirmative or negative. 1 504. Aristotle did not recognise the Fourth or (so-called) Galenic Figure as distinct ; but he has indicated some moods which were afterwards referred to it. 2 Theophrastus and Eudemus, according to the testimony of Alexander of Aphro- disias and Boethius, added five new moods that is, what are known as indirect moods of the First Figure. These are Bamalip, Calemes, Dimatis, Fesapo, Fresison. These at first given as indirect or imperfect moods of the First Figure, got through conversion, were constituted into moods of a new or Fourth Figure. 3 The attribution of the Fourth Figure to Galen as his creation has not been proved. It i An. Pr., L 6. * Ibid. i. c. vii. * Cf. Ueberweg, Logic, p. 868. 396 INSTITUTES OF LOGIC. rests mainly on a statement of Averroes ; and what of Galen's writings remain show no proof of his authorship. But the truth is, that the moods of the Fourth Figure were recognised long before his time, and all that he could have done was to call them moods of a new or Fourth Figure. The moods Fa- pesmo and Frisesmo are also regarded as indirect moods of the First Figure. (a) The form of syllogism with Aristotle depends, according to Trendelenburg, on the different relations of the terms, grounded on the principle of the wider containing the narrower. Hence there are but three positions : (1.) When the middle term is in the middle position, as in the first figure ; (2.) when it is highest, as in the second figure that is, predicate in both premisses; (3.) when it is lowest, as in the third figure that is, subject in both premisses. With three terms in the syllogism, and the relations of the middle, these are properly all the figures. The so-called Fourth Figure does not depend on any new necessary relation of the terms, but on the fortuitous position of these in the premisses. This is quite a different principle of division, and really arbitrary. Further, there is nothing in the arrangement of the Fourth Figure which can yield a conclusion different from what can be reached in the others. It is, therefore, unnecessary and useless. It is simply not a new figure but a variation of arrangement, founded on the pos- sible place of the middle term in the premisses. (Trendelenburg, EL Log. Arist., 28.) On Trendelenburg's view in relation to Aristotle, see Ueberweg, Logic, p. 358. On the difference between Hegel's view of the figures and that of Aristotle, see Trendelenburg, Logische Un- tersuchungen, iv. p. 251. (b) Against Kant's conclusion in The False Subtkty of the Four Syllo- gistic Figures (1762), Ueberweg urges that the conclusion in the other figures besides the first may be directly found without reduction to the first. They are simple, as much as the first. (Logic, p. 373.) (c) Hegel places the third figure before the second, or rather names the third second, and the second third. The change, if it be not a historical blunder, has no ground in reason. (d) Herbart and Drobisch reject the moods of the Fourth Figure. Trendelenburg rejects those of the third, on the ground of ambiguity and tendency to error. But this is excluded by a strict determination of the nature of particular judgment. (Ueberweg, Logic, p. 375.) (e) Hamilton's view of the Fourth Figure is, that it is a hybrid reasoning. Its two premisses run in one quantity Comprehension ; its conclusion is in another Extension. Further, the conclusion is in- direct or mediate, being the converse of what is natural. The Fourth Figure is really the First, with premisses transposed, and the indirect conclusion of the First given as a direct conclusion. (See Logic, iv., App. D. (a), p. 449.) Thus Bamalip is only Barbara, with transposed premisses and con- verted conclusion : MOODS. 397 (2.) All irons are some metals, (1.) All metals are some minerals, All irons are some minerals. (By conversion) .'. Some minerals are all irons. And so of the others. (/) Ueberweg seems to suppose that the spherical representation may equally symbolise Extension and Comprehension. (Logic, p. 379.) In this he is wrong. Of course whether Extension and Comprehension can be united in the same reasoning, as Trendelenburg supposes, is a different question. If Ueberweg further supposes, as he seems to do, that the representation by spheres of propositions and syllogistic moods really proves anything regarding their congruence or confliction, he is equally mistaken. Diagrams only show only can show what is valid on a law of thought. Picturing to the eye by diagram is nothing more than individualising, and this is only the shadow of proof. The truth is, seeing that the concept is essentially unpicturable, spherical diagrams are inadequate as representations, and only rude aids to thinking. 505. In consequence of the application of the rules already specified : In the First Figure the moods are AAA, EAE, All, EIO. In the Second EAE, AEE, EIO, AGO. In the Third AAI, IAI, All, EAO, OAO, EIO. In the Fourth, or Indirect Moods of the First AAI, AEE, IAI, EAO, EIO. 506. These are summed up in the mnemonic lines : (1.) bArbArA, cElArEnt, dArll, fErlOque prioris. (2.) cEsArE, cAmEstrEs, fEstlnO, bArOkO, secundae. (3.) Tertia, dArAptl, dlsAmls, dAtlsI, fElAptOn, bOk- ArdO, fErlso, habet : quarta insuper addit (4) brAmAntlp, cAmEnEs, dlmArls, 1 fEsApO, frEsIsOn. 507. The first mood of the First Figure, Barbara, is in letters : All Yis X. AllZ is Y. All Z is X. i Otherwise, bAmAlIp, cAlEmEs, dlmAtls. 398 INSTITUTES OF LOGIC. Symbolically (in extension) : All animal is sentient, All man is animal, Therefore all man is sentient. 508. In the Second Figure we have the mood Cesare. This is in letters : No X is Y. All Z is Y. :. No Z is X. Symbolically (in extension) : Anything lasting is not violent. Every unjust law is violent, Therefore any unjust law is not lasting. 509. In the Third Figure the mood Darapti is in letters : All Yis X. All Y is Z. .'. Some Z is X. Symbolically (in extension) : MNEMONIC LINES. 399 All temperance is a virtue, All temperance is praiseworthy, Therefore some virtue is praiseworthy. (a) There is a sharp controversy in regard to the original authorship of these and other of the logical mnemonic lines. Prantl and others at- tribute them to Michael Psellus (the second) ; while Hamilton, Thurot, and Val Rose, hold that the author of the Synopsis, which has passed under the name of Psellus since 1597, was the borrower. Psellus was born in 1018 or 1020, and he died after 1077. He was the author of a paraphrase of the De Interpretatione, published at Venice in 1503, and of a 'Svvofyts rcav irfvrt tpovcav Kal T>V S^KO. Kartjyoptiav, pub- lished at Venice, 1532. In 1597, Ehinger edited a MS. entitled 2t/V<4s e irpa>r6^ tanv. a? re yap fj.a6i}- ariKal TUV eVjcmjjtaJi/ Sta. rovrov tytpovtrt ras a7ro8ei|fi$ u'tov dpid/j.r]TiK^i Kal oirTinr]. (An. Post., i. 14.) 516. Eeduction in the Aristotelic sense, means the bring- ing back of a mood of the Second and Third Figures, and latterly of the Fourth, to one of the First Figure as perfect. The means of doing this are two : (1.) Conversion of the premisses or conclusion ; (2.) Trausposition of the pre- misses. To this may be added Contraposition. We thus can get from the given premisses either the original conclusion, all in the First Figure, or a conclusion from which the original conclusion follows by conversion. In the mnemonic lines those means of reduction are marked by the letters s, m, p. These, in their order, mark simple conversion, trans- position of the premisses, conversion per accidens. The initial consonant of the mood of the figures after the first indicates the mood of the first to which the mood in question is to be reduced. Thus Cesare of the Second Figure is to be reduced, as indicated, to Celarent of the First. Cesare : No X is Y, All Z is Y, .-. No Z is X. 1 Ueberweg, Logic, p. 437. REDUCTION. 403 No plant feels, Every animal feels, So Therefore no animal is a plant. Celarent : No Yis X, All Z is Y, .-. NoZ is X. Nothing that feels is a plant, Every animal feels, Therefore no animal is a plant. In the Second Figure Camestres : Every animal lives, No stone lives, Therefore no stone is an animal. This is converted into Celarent thus : Nothing living is a stone, Every animal lives, Therefore no animal is a stone, Therefore no stone is an animal. So Darapti: All Yis X, All YisZ, .'. Some Z is X. This is reduced to Darii : All YisX, Some Z is Y, .'. Some Z is X. And so with the others, according to indication affording a good enough exercise for beginners in logic. Here we have employed Conversion and transposition of the premisses. This is known as Ostensive Reduction. 517. Reductio or Deductio ad Impossibile is that in which from the contradictory of the conclusion to be proved, and another proposition manifestly true, or at least conceded by an opponent, we infer the absurd or impossible. If in a mood of the Second and Third Figures the premisses are con- ceded, but the conclusion denied, as not necessarily following from the premisses, the contention may be reduced to absurdity by the syllogism being reconstituted in the First Figure, one of the premisses being preserved and the con- 404 INSTITUTES OF LOGIC. tradictory of the conclusion put in the place of the other. In the Second Figure, the major is preserved, and the con- tradictory of the conclusion put in place of the minor ; in the Third Figure, the minor is preserved, and the contradictory of the conclusion is put in place of the major : Servat majorem, variatque secunda minorem ; Tertia majorem variat, servatque minorem. 1 Thus, Baroko : All X is Y; Some Z is not Y; Some Z is not X. Every animal feels ; Some living thing does not feel ; Therefore, some living thing is not animal. Eeduced to Barbara : All X is Y (conceded) ; All Z is X; .: AUZ is Y; Every animal feels ; Every living is animal ; Therefore, every living feels. As this conclusion is the contradictory of the original (given) Minor Premiss, it must be false ; one of the premisses must, therefore, be false. But the original major as given is (supposed) true. The falsity is thus in the minor. This is the contradictory of the original conclusion ; therefore, the original conclusion is true. 2 The K in Baroko and Bokardo means that the premiss indicated by the vowel before it is to have the contradictory of the conclusion put in its place. In the one case, this is the major premiss ; in the other, the minor. But the whole of reduction is simply unnecessary ; the moods of the Second and Third Figures are on any system equally and as directly valid as those of the First. The superiority of the First Figure over the others lies not in a higher cogency or necessity of sequence, but in greater per- spicuity in respect of the principle of inference. 1 Of. Duncan, List. Log., L. iv. c. iii. 2 Cf. Whately, Logic, B. ii. c. iii. 6. CONTKAPOSITION. 405 Keduction by Contraposition has also, though not gener- ally, been employed. Thus Camestres : Every animal feels ; No plant feels ; Therefore, no plant is animal. Convert the major by Contraposition What does not feel is not animal, preserve the minor, and we have the same conclusion in Celarent : What does not feel is not animal ; No plant feels ; Therefore, no plant is animal. So Baroko to Ferio. This was not generally received, be- cause the converse of the minor is less clear as in effect affirm- ative than the simple affirmation which has been transposed into it. 1 1 Cf. Duncan, Inst. Log., L. iv. c. iii. 406 CHAPTEE XXXI. CATEGORICAL SYLLOGISMS ON HAMILTON'S PRINCIPLES FIGURED AND UNFIGURED SYLLOGISM ULTRA-TOTAL DISTRIBUTION. 518. Hamilton has singular merit in his analysis of Figure, Major and Minor Terms, and Propositions. The whole tendency of his inquiries on this point is to simplifica- tion, scientific completeness and unity, leading ultimately, in fact, to the position that Figure, with all its complexities, is unessential to reasoning. The ordinary view rather led to the notion that reasoning depended on the order of expres- sion, certainly that the difference of Major and Minor in terms and propositions did. Hamilton has shown that reason- ing depends on the internal thought, on the essential mental relations of Containing and Contained, of Inclusion and Exclusion in thought. His view on this point was developed prior to that of the quantification of the predicate. But this doctrine completed the theory. 519. Mediate or Syllogistic Reasoning (Categorical) is, according to Hamilton, divided into two kinds the Unfigured and the Figured. In the former, which results directly from the quantification of the predicate, and from regarding the proposition as an equation, the terms compared do not stand to each other in the reciprocal relation of subject and predi- cate, being in the same proposition, either both subjects or (possibly) both predicates. The canon for this form of reason- ing is : " In as far as two notions (notions proper or indi- viduals) either both agree, or one agreeing, the other does not, with a common third -notion ; in so far these notions do or do not agree with each other." 520. In the Figured Syllogism Proper, again, the terms ARISTOTLE'S DOCTRINE OF FIGURE. 407 compared are severally subject and predicate, and thus con- taining and contained. Its general canon is : " What worse relation of subject and predicate subsists between either of two terms and a common third term, with which one at least is positively related ; that relation subsists between the two terms themselves." l The Figured Syllogism runs in the counter wholes of Intension and Extension. 521. According to Aristotle's mode of statement, the middle term was intermediate in nature and in position in the two premisses. Thus : P is in M ; M is in S ; .: P is in S. This shows the middle term, M, as lying in the middle and between the two extremes, P and S. But later logicians did not so enounce such a reasoning. They said : Mis P; S is M; .-. S is P. Here the middle term does not lie between the extremep ; and in the Second and Third Figures it no more does so, being in the one twice predicate, in the other twice subject. The Aristotelic form indeed is suitable at once to reasoning in comprehension and in extension. 522. To preserve the Aristotelic position of the middle term in extension, the subject being usually first, it was necessary to state the minor premiss first, even in the First Figure. This was done by a majority of the older logicians. But subsequently this order was departed from, and the major premiss was stated first, thus displacing the middle term from its intermediate position in the syllogism. Now the question arises Is there any natural rule or law regulat- ing the order of enouncement? In Figured Syllogism, the true principle is the relation of the middle term, as including or included under the subject of the conclusion. It matters nothing as to which premiss is placed first or last in the expression. But to avoid ambiguity that premiss which expresses the relation of the greatest to the less, that which expresses the relation of the less to the least, should 1 Discussions, p. 654. 408 INSTITUTES OF LOGIC. be placed first and second. The conclusion would, of course, state the relation of the least to the greatest. Thus, in Ex- tension in the First Figure, we should have : M is contained under P S is contained under M ; .'. S is contained under P. Here P is major, predicate of major premiss ; S is minor, subject of minor premiss 5 S is subject of conclusion, P pre- dicate. P= the greatest whole ; M = the less ; $=the least. This being so, S the least must be contained in P the greater. 523. In Comprehension, the same principle would lead to the reversal of the order of the premisses. Thus : S is M; Mis P; .-. Sis P. This means S } the greatest whole, contains in it one mark M; M, the less, contains in it one mark, the least, P ; .: S, the greatest whole, contains in it one mark P, the least. Animal contains in it sentient ; Sentient contains in it life; .'. Animal contains in it life. It is clear from this that as the premisses in this First Figure determine the relation of the subject of the conclusion to the predicate, as either a part contained under the predicate, or as a whole containing the predicate in it, there can be but one immediate or direct conclusion in each of the moods, and in Extension and Comprehension. The First Figure thus still retains and admits of the distinction of major and minor terms, major and minor propositions, and the conclusion is single or direct, in each of the quantities of Extension and Compre- hension. It admits, however, of two conclusions, a direct and an immediately inferred conclusion. 1 We can say : - 1 Discussions, p. 658. ARISTOTLE'S DOCTRINE OF FIGURE. 109 All M is (some) C ; All F is (some) M ; .-. All F is (some] C. Or, some C is all F. 524. But let us look at the Second and Third Figures, and we shall find that we no longer have the same kind of rela- tions between the terms, and consequently, no longer the distinction of major and minor in terms and premisses. We shall thus have two conclusions equally direct, either extreme being taken as subject or as predicate of the conclusion. In the Second Figure, the middle term is the predicate of both premisses, not as in the first the subject of one extreme and the predicate of the other. C is M. F is M. This form thus merely tells us that each extreme is contained under the middle, but it says nothing of the relation of the one extreme to the other. There is no subordination of greater or least. We may thus reason : (Some) C is (some) M ; (Some) F is (alt) M; ,'. (Some) C is (some) F. Or, (Some) F is (some) C. Here each extreme is major or minor, or neither. And there are two direct conclusions, differing only according to the manner of reading. In the Third Figure the same holds. Here the middle term is subject in both premisses, it is contained under each extreme. Thus : (Some) M is (some) C; (Alt) M is (some) T ; .'. (Some) C is (some) F. Or, (Some) F is (some) C. Here there is as little subordination of extreme to extreme of C to F and consequently the relation majority and minority in extremes is abolished. And we have two equally direct conclusions. 410 INSTITUTES OF LOGIC. 525. Now it is obvious that we are very near the aboli- tion of Figure altogether. We may now reason that as C is M, and T is M, C is T or T is C. Indeed, if we quantify the predicate, and thus reduce the proposition to a simple equa- tion, the identity of a reasoning in all the three Figures becomes clear. The Second Figure is only the First, with the major premiss converted and transposed ; the Third Figure is only the First, with its minor premiss converted and transposed. Figure is thus unessential to the validity of a reasoning. Mood alone is the essential thing. In prac- tice, the Figures have at the same time special uses and functions. The First Figure affords a form for reasoning in Extension and in Comprehension alike. The Second Figure naturally fits Extension ; for the middle term is predicate in both premisses, each extreme is contained under it as a common whole. The Third Figure equally suits Comprehen- sion ; for the middle term, as subject of both premisses, nat- urally contains in it each of the extremes, as the parts of a common whole. It will thus be found, further, that the Second and Third Figures are specially suited the one to Deductive Reasoning in Extension ; the other to Inductive Reasoning in Comprehension. The general distinction be- tween Deductive and Inductive reasoning, regarded here as processes of formal inference, is that in the former we reason downwards from the greatest whole or law to the particular instance or fact contained under it ; in the latter we reason upwards from the particular instances or facts to the whole or general law. In the former case we proceed on the principle that " what belongs to the containing whole belongs also to the contained parts ; " in the latter case on the principle that " what belongs to the constituent parts belongs also to the constituted whole." Now, Deductive Reasoning naturally takes the form of Extensive Reasoning; Inductive that of Comprehensive Reasoning. For in Extension we begin with the widest notion ; in Comprehension with the particular or individual fact. Thus, in the Second Figure, we should naturally have a Deductive Reasoning in Extension : X Y Z are (contained under") all M ; a b c are (contained under] all M; .*. a b c are X Y Z. DISTINCTION OF SUBJECT AND PREDICATE. 411 Responsible persons are all man ; Slack, white, copper-coloured are all man ; .'. Black, white, copper-coloured are responsible persons. This inference is to the similarity or identity of the parts, through the common whole M, which contains them. The Third Figure would suit an Inductive Reasoning in Comprehension. XT Z are all P ; XYZareAs; .'. Some As are all P. Peter, John, $c. (12), are all the apostles ; Peter, John, c. (12), are zealous persons ; .: Some zealous are all the apostles. This inference is to the common whole through the similarity or identity of the parts which constitute it. 1 526. The distinction of Subject and Predicate, as usually taken in Extension, by the Aristotelic logicians, arises mainly from the circumstance that the predicate is supposed to be a wider notion than the subject. The subject is contained under the predicate as a part of it at least. The genus thus was pre- dicated of the species, as the oak is a tree, the species was predicated of the individual, this tree is a birch. The subject notion, therefore, was regarded as of less extent than the pre- dicate. In comprehension, however, the subject might be regarded as the greater, seeing that the predicate usually expresses only one of its attributes, as fire burns water runs : burning and running, being only each a small part of the notions ofjire or water. The subject thus comprehends the attribute, and more or others. The quantification of the predicate in extension abolishes the essential distinction of subject and predicate. We may say as we please : all plant is some or- ganised, or some organised is all plant. The only difference of subject and predicate here would be in the accidental interest we have in the one or other, as first in thought. (a) Robert Kilwardby, Archbishop of Canterbury (1276) (died 1279), who does not use the Byzantine art words or memorial verses, speaking of the Second Figure, says : The middle is that by which one extreme is distant from another, but, as predicated of both extremes, there is no difference in the distance, and therefore no medium. The middle 1 Cf. Discustioju, App. II. 412 INSTITUTES OF LOGIC. is equally distant from both extremes (terms) ; therefore the terms are equidistant from the middle. (Kilwardby in Prantl, iii. p. 186.) 527. And carrying out this principle to its ultimate issue, we may have the simplest form of reasoning in the Unfigured Syllogism. This is the simplest form, for here we have no longer the distinction of Extension and Intension, and the order of the premisses is thus wholly arbitrary. The terms do not stand to each other in the relation of subject and predicate, being in the same proposition either both subjects or (possibly) both predicates. The formula for this is : Subjects : All and some B are (some) convertible ; All B and all A are (some) convertible ; .'. All C and some A are (some) convertible. Predicates : (Some) convertibles are all C and some B ; (Some) convertibles are all B and all A ; .'. (Some) convertibles are all C and some A. 528. The canon for this reasoning is : u In as far as two notions (notions proper or individuals) either both agree, or one agreeing, the other does not, with a common third notion ; in so far, these notions do or do not agree with each other." This canon excludes (1.) an undis- tributed middle term, as then no common notion ; (2.) two negative premisses, as then no agreement of either of the other notions therewith. In ordinary discourse we regularly use the unfigured form of reasoning when we apply the prin- ciple that, as A is equal to B, and B to C, A is equal to C. This form regulates our dealings with quantities, and our processes in Geometry. 529. The Unfigured Syllogism of Hamilton is closely akin to what is known as the Expository Syllogism (Syllogismus Expositiorius, Sensilis) of the Peripatetics and other subse- quent logicians. Its principle was given as : Those things which agree with the same singular third agree with each other. (Quce congruunt eidem tertio singulari ea congruunt inter se.) This syllogism was usually run through the three Figures, but it was held to be less natural in the First and Second than in the Third, where the middle was subject, EXPOSITORY SYLLOGISM. 413 it being held that a singular is less properly a predicate than a subject. Thus we may have in the First Figure : Aristotle was a Greek ; The author of the Analytics was Aristotle ; Therefore the author of the Analytics was a Greek. In the Second Figure : Aristotle was the tutor of Alexander The author of the Iliad was not the tutor of Alexander ; Therefore he was not Aristotle. In the Third Figure : Epicurus was bold; Epicurus was a philosopher Therefore some (a) philosopher was bold. This form, which is not recognised by Aristotle as a syllo- gism, because there is nothing in it universal, was called by him ec0e Affirmative. 3. Parti-total some is all. 4. Parti-partial some is some. 5. Parti-partial some is not some. 6. Parti-total some is not any. _, . , > Negative. 7. Toto-partial any is not some. Toto-total any is not any. 533. To the universality of the canon there is an appar- ent, but only an apparent exception. That is, in those moods in which the particular quantity of the affirmative conclusions disappears in the negative moods giving place to a univer- sal quantity in the negative. This occurs in the (negative) moods IX a ., X b ., XP., and XIIV In these Take the following (IX.) Affirmatively we read : All M is all 0; All F is some M; .'. All F is some C ; Or, Some G is all T. Negatively this becomes (IX a .) Any M is not any C ; All F is some M ; .'. Any F is not any C. Or, any C is not any F. Take the following (X.) Affirmatively we read : Some M is all C ; All F is all M ; .'. Some F is all C. Negatively (X b .) Some M is all C ; Any F is not any M ; .'. Any F is not any C. 1 From the table of moods, Logic, iv., App. v. (e) Syllogisms, p. 285. HAMILTON'S SYLLOGISTIC MOODS. 417 Affirmatively Some animal is all man ; All sentient is all animal ; .'. Some sentient is all man. Deny the minor Some animal is all man ; Any sentient is not any animal ; .'. Any sentient is not any man. Or, Some animal is all man Any mineral is not any animal .'. Any mineral is not any man. 534. Here the change is from a particular affirmative conclusion to a universal negative. But this is a passage simply from the worst in affirmation to the worst in negation. Had the change been from a particular affirmation to a uni- versal affirmation, it would have been from the worse to the better, or best. But seeing that it is a change from particular in affirmation to universal in negation, it is a passage only from the worst in the one quality to the worst in the other. The validity and applicability of the canon are thus not shaken but confirmed. (So in XI a . and XII b .) As Hamilton has remarked : " The worst relation between either extreme and middle is here preserved in the conclusion. As affir- mation comes in from the greatest whole, while negation goes out from the least part, so, in point of fact, the some of the one may become the not any of the other." * 535. With the Eight Prepositional Forms as a basis, there is a corresponding increase of the syllogistic moods. A simple arithmetical calculation of the combinations (syzygies) gives 512 conceivable moods. But applying the canon, these are reduced to 36 valid moods, 12 affirmative and 24 negative. These are essentially the same through the Three Figures, the Fourth Figure being excluded by Hamilton as illegitimate. If we pass the moods through each of the Three Figures, we get the 36 moods three times repeated, making 108 moods in all. But these are really only got through a change in expression, the mood is always essentially the same figure making no valid diffor- 1 Loffic, App. iv. p. 286. 2 D 418 INSTITUTES OF LOGIC. ence. No mood can be valid in one figure which is not valid in every one. Indeed, looking at the mere formal equivalence of the moods, we may reduce the number of affirmative moods to 7, and of negative to 14, 21 in all. This arises from the circumstance of the possible interconversion of certain of the moods. In some the middle term is balanced, that is, it is universal in both premisses. The extremes are balanced when both are taken universally ; unbalanced when the one is so taken, and the other not. If we take the unbalanced moods iv., vi., viii., x., xii., as simply the converse of the one preceding it, which they are, only seven valid affirmative moods are left. With these five affirmatives, ten corresponding negative moods would be struck out, or reduced to the corresponding negatives of the affirmative mood which afforded the (abolished) converse. This would leave fourteen negative moods, or twenty-one affirmative and negative. The cumbrous rules of reduction are thus abolished, simple conversion (with transposition) will enable us to turn any mood into any figure. And taking the quantification of the predicate into account, we abolish as not only useless, but false, the special rules of each figure. By admitting the universality of the predicate in affirmative judgments, the particularity of the predicate in negative judgments, right in the face of the Aristotelic prescriptions, we show that the usual rules of the First, Second, and Third Figures are false, and the syllogistic process stands out vin- dicated as one, evident, and simple, conformable to a Single Universal Canon. 536. Hamilton's Table of the Moods of Figured Syllo- gisms is printed at the end of the Lectures on Logic the moods being also given or symbolised in the forms of his notation. The diagram representing Figured and Unfigured Syllogism alike, and in Extension and Comprehension, is to be found in the Discussions, p. 658. Eeference may be made to these for details. The following are the twelve moods in Extension of the First Figure : (1.) All M is all G; All T is all M; :. All T is all C. HAMILTON S SYLLOGISTIC MOODS. 419 (2.) All M is some C ; Some r is all M ; .'. Some r is some C. (3.) All M is some C; All r is some M ; .'. All r is some C. (4.) Some M is all C; Some r is all M ; .'. Some r is some C. (5.) All M is some C ; Some r is some M ; .'. Some F is some C. (6.) Some M is some C ; Some F is all M; .*. Some F is some C. (7.) All M is all C; Some F is all M ; .'. Some F is all C. (8.) All M is some C; All T is all M; .*. All T is some C. (9.) All Mis all C; All F is some M ; .*. All F is some C. (10.) Some M is all C; All T is all M; .'. Some T is all C. (11.) All Mis some C; Some F is some M ; .*. Some F / some C. (12.) ome Af is some C ; All T is all M; .'. Some T is some C. The first mood of the First Figure is thus symbolised : 420 INSTITUTES OF LOGIC. Kead in Extension it runs : All M is (included under] all G ; AllT is (included under) all M ; .'. All r is (included under) all C. Or, as an indirect conclusion, All C is (included under) all F. Read in Comprehension, it runs thus : All M is (includes in it] all F ; All C is (includes in it) all M; .'. All G is (includes in it) all F. Or All C is (includes in it) all T ; All M is (includes in it) all T : .'. All C is (includes in it) all I\ 537. Twelve pairs of premisses, with the same quantities as in the First Figure, may be run through the Second and Third Figures, and each mood may be read in Extension and in Comprehension. Thus, to take No. 2 in the Second Figure, we have : In Extension, this reads : Some C is all M; Some F is all M ; .'. Some F is some C. Or Some C is some T. In Comprehension, it reads : All M is some C ; All M is some F ; .'. Some C is some T. Or Some T is some C. HAMILTON'S NOTATION. 421 538. There are thus 12 affirmative moods in each of the Three Figures in all 36 affirmative moods. As each of these affirmatives yields by negation in turn of major and of minor premiss, two negative moods, there will be 24 negative moods in each figure, in all 72 negatives some of which are, how- ever, of little or no actual value. Thus, to take No. 2 of the First Figure, we have (a) .ZVb M is any C ; Some F is all M ; .'. Some r is not some C. C, -:M: All M is some C ; Some r is not any M ; .'. Some r is not some C. 539. The symbolical notation here employed, though simple, requires a word of explanation. It is that devised by Hamilton. He has the merit of having added to Logic a system of notation which is at once simple, perspicuous, and adequate. First of all, a proposition is represented by a horizontal line. If either of the terms can stand as subject or as predicate if, in a word, there be no distinction of Sub- ject and Predicate, as in the Unfigured Syllogism the line is drawn as of equal thickness throughout. Thus C HEU^HBW F C is r, or r is C, or C and F are equal. But if the one term be regarded as Subject and the other as Predicate, the line is represented thus c r And this proposition may be read in either of two ways, as in Breadth or in Depth. The thick end of the line represents the subject of the proposition in Breadth, and is read C is F, or C is contained or included tender T. 422 INSTITUTES OF LOGIC. The tlrin end of the line represents the subject in Depth, and is read r is G, or F includes or contains in it C. This applies to affirmative propositions. Negation is de- noted by a perpendicular line drawn through the horizontal. Thus C | F, is read, C is not F. The quantity or distribution of the terms, is indicated by points. Thus a comma (,) placed after a term indicates that it is to be taken particularly or indefinitely; a colon (:) that it is to be taken universally or definitely. As the middle term appears twice in the syllogism, it will have two separate marks of quantity. That on the right colon or comma indicates how it is to be taken, universally or particularly, with the term on the right ; that on the left colon or comma with the term on the left. Further, in a syllogism the conclusion is indicated, in Breadth and Depth, by a line sim- ilar to the lines of the premisses, extending from the one extreme to the other. The following will readily illustrate the notation. In the First Figure we may take the following : This is read in (a) Breadth. (b) Depth. All M is some C ; Some M is all F ; All F is some M ; Some C is all M ; .'. All F is some G. .: Some G is all F. Negation is thus indicated (a) Breadth. (b) Depth. Any M is not any G ; Some M is all F ; All F is some M ; Any G is not any M ; .'. Any F is not any C. .'. Any G is not any F. In the Second Figure we may take the following : HAMILTON'S NOTATION. 423 C, (a) Breadth. Some C is all M ; All Y is some M ; .'. All F is some C. (Or, Some C is all T.) In the Third Figure : M, :T (b) Depth. Some M is all T ; All M is some C ; .-.Some C is all T. (Or, All T w some C.) (a) Breadth. -4JZ M is some C ; Some M is all T ; /. All F is some C. b} Depth. All F zs some J/; e (7 zs all M ; .'. Some C is all T. (Or, All T is some C.) In the Second and Third Figures there are two horizontal lines above and below the extremes, indicating that two equally direct and immediate conclusions may be drawn in these figures. In these figures there is properly no distinc- tion of major and minor terms, and consequently no distinction of major and minor propositions. This is true equally of the Unfigured Syllogism. It is only in the First Figure that the distinction of Breadth and Depth is preserved, and conse- quently that of major and minor in terms and propositions. 540. The Canon of Syllogism laid down by Hamilton, 520 et seq., as proceeding on the mere formal possibility of reasoning, necessarily comprehends all the legitimate forms of quantification. " This Canon supposes that the two extremes are compared together through the same common middle, and this cannot but be if the middle, whether subject or predi- cate, in both its quantifications together, exceed its totality, though not taken in that totality in either premiss. 1 Ac- cordingly, " the rule of the logicians, that the middle term should be once at least distributed [or indistributable], (i.e., taken universally or singularly = definitely), is untrue. For 1 Logic, iv. p. 355. 424 INSTITUTES OF LOGIC. it is sufficient if, in both the premisses together, its quantifica- tion be more than its quantity as a whole (Ultratotal). Therefore, a major part (a more or most), in one premiss, and a half in the other, are sufficient to make it effective. It is enough for a valid syllogism, that the two extreme notions should (or should not), of necessity, partially coincide in the third or middle notion ; and this is necessarily shown to be the case, if the one extreme coincide with the middle, to the extent of a half (Dimidiate Quantification) ; and the other, to the extent of aught more than a half (Ultradimidiate Quantification.) " l Thus we may reason : One-half of A is B ; Two-thirds of A is C ; .'. Some C is B. Or Three-fourths of A is B ; Two-thirds of A is G ; .'. Some C is B. Or Most of the As are Bs ; Most of the As are Cs ; .'. Some Cs are JBs. In concrete examples : Three-fourths of the army were French ; Three-fourths of the army were killed ; Therefore some French were killed. Three-fourths of the twelve pears were ripe ; Three-fourths of the twelve pears were stolen ; Therefore some that were ripe were stolen. This form of quantification and reasoning was first sug- gested by Lambert (Neues Organon, Dianoiologie, 193 et seq.} It has since been adopted by De Morgan. . Hamilton's view of it is, so far, a sound one : " These two quantifications should be taken into account by Logic as authentic forms, but then relegated as of little use in practice, and cumber- ing the science with a superfluous mass of moods." 2 Again, 1 Logic, iv. p. 355. 2 Ibid. ULTRA-TOTAL DISTRIBUTION. 425 he lays down the principles which ought to limit a genuine science of Logic in the following words : " Such quantifica- tions are of no value or application in the one whole (the uni- versal, potential, logical), or, as I would amplify it, in the two correlative and counter wholes (the logical and the formal, actual, metaphysical), with which Logic is conversant. For all that is out of classification, all that has no reference to genus and species, is out of Logic, indeed out of Philosophy ; for Philosophy tends always to the universal and necessary. Thus, the highest canons of Deductive Reasoning the Dicta de Omni et de Nullo were founded on, and for, the procedure from the universal whole to the subject parts ; whilst, con- versely, the principle of inductive reasoning was established on, and for, the (real or presumed) collection of all the subject parts as constituting the universal whole. 2, The integrate or mathematical whole, on the contrary (whether continuous or discrete), the philosophers contemned. For whilst, as Aris- totle observes, in mathematics genus and species are of no account, it is, almost exclusively, in the mathematical whole that quantities are compared together, through a middle term, in neither premiss equal to the whole. But this rea- soning, in which the middle term is never universal, and the conclusion always particular, is as vague, partial, and con- tingent of little or no value in Philosophy. It was accord- ingly ignored in Logic ; and the predesignations more, most, &c., as I have said, referred to universal, or (as was most common) to particular, or to neither, quantity." 1 This is a true insight into the real essence and needs of logical reason- ing, as a universal means of thinking, and consequently of logical science. These words hold in themselves the con- demnation, scientifically and practically, of the " advances " in Formal Logic, made on geometrical and algebraical lines, of De Morgan and Boole, and even of the more enlightened Jevons. 541. A reasoning in which the middle term is never de- finitely known, and in which accordingly we have always a vacillating and particular conclusion, is of no use practically, or in the wide sphere of probable thought. Scientifically, it is a mere tentative, ending in some is some, a mere ap- i Logic, iv. pp. 353, 354. 426 INSTITUTES OF LOGIC. proach to satisfactory certainty. And even when the prem- isses are made numerically definite, as with De Morgan, the reasoning is of not the slightest use unless in reference to numbers and a numerical or mathematical whole. It is really of not the smallest consequence, as a rule, that we should know the exact numerical proportion of the middle term to the extremes. We seldom do know it, as a matter of fact, and when we do, we may remit the calculation to arithmetic. 542. It ought further, I think, to be noted in connection with this form of reasoning, that it readily lends itself to ma- terial fallacy, or a conclusion materially untrue. No doubt, in the abstract, if \ of Y are X, and f of T are Z, some of the Zs are Xs. So if X contains (the part} Y, and Y contains (the part) Z, X contains Z. But this latter formula embodies the law of inference from genus to species, or from whole to part. The other formula does not. It does not tell us in what relation X stands to Y, or Z to Y, whether that of part and whole, or of subject and attribute. Nor do we know, taking X and Z as attributes, whether they are compatible with each other or not. The practical application of the bare fornmla is therefore of but little use, and readily leads to material error. Thus, if we say : f of the potatoes were diseased ; was eaten by the crows ; Therefore the crows must have eaten some of the diseased ; this is correct, because there was not a half left not diseased. If, however, we substitute for diseased, hard as a stone, we should on the same formula have the conclusion that the crows ate some potatoes hard as a stone. There is nothing in the formula itself to prevent us substituting for X and Z incompatible attributes. Thus the following is quite com- patible with the formula: Three-fourths of men are saints ; Three-fourths of men are sinners ; Therefore some who are saints are sinners. Such a formula can thus give a valid and true conclusion only in certain matter, where the distribution refers to a whole of which the predicates are parts, or in which they ULTRA-TOTAL DISTRIBUTION. 427 are compatible attributes. In fact, the necessary premisses are : Three-fourths of the Ys are Xs ; Three-fourths of the Ys are [also'] Zs ; Therefore some of the Zs are Xs. Or, if three-fourths of Y are X, And if three-fourths of Y are Z, And if X and Z represent things u-Jt/ch coexist in the same (or are compatible), Then some Z is X, or some Z may be thought to be X. 428 CHAPTER XXXII. CATEGORICAL SYLLOGISMS COMPREHENSIVE REASONING THE FIVE SYLLOGISTIC FORMS. 543. The Aristotelic Categorical Syllogism proceeds mainly, if not exclusively, in the quantity of Extension. But according to later views, as we have seen, we have reasoning in Comprehension as well. 544. In the view of Hamilton, every notion has not only an Extensive but an Intensive quantity breadth and depth and these quantities always stand in an inverse ratio to each other. It would thus seem likely that if notions bear a cer- tain relation to each other in Extension, they must bear a counter -relation to each other in Comprehension. Hence there will be reasoning in Comprehension, as there is reason- ing in Extension. In Extension the reasoning runs : All responsible agents are free-agents (i.e., are contained under the class) ; Man is a responsible agent (i.e., contained under the class) ; Therefore man is a free-agent (i..e., contained under the class). In comprehension we necessarily invert the process of this reasoning. The notion free-agent, which in the extensive reasoning is the greatest whole or major term, becomes in comprehension the smallest part or minor term, and the notion man, which is in extension the smallest part or minor term, now becomes the greatest whole or major term. The notion responsible agent remains the middle term in both reasonings ; but what was formerly its part is now its whole, and what was formerly its whole is now its part. In Com- prehension we reason thus : REASONING IN COMPREHENSION AND EXTENSION. 429 The notion man comprehends in it the notion responsible agent; The notion responsible agent comprehends in it the notion free- agent ; Therefore the notion man comprehends in it the notion free- agent. In Extension. In Intension. Bis A; CisB; CisB; Bis A; .'. CisA. .-. CisA. Thus, by reversing the order of the premisses and the mean- ing of the copula, we can always change a categorical syllogism of Extension into one of Intension, and vice versa. The reasoning in Comprehension has been generally overlooked by logicians ; but it is genuine, and it is prior to extensive reasoning in the order both of nature and knowledge. Aris- totle gives a definition of the middle term, which applies to the comprehensive reasoning. 1 545. Hamilton holds broadly that whatever mood and figure is valid in the one quantity is valid in the other, and every anomaly is equally an anomaly in both. The rules of Extensive reasoning are equally applicable to the Compre- hensive reasoning, with the single proviso that all that is said of the sumption (major premiss) in extension is to be under- stood of the subsumption (minor premiss) in comprehension, and vice versa. 546. Of course the mere transposition of the premisses does not constitute the difference between reasoning in Comprehen- sion and in Extension ; that depends on the inner relation of the subject and predicate of the propositions as whole and part, or as part and whole. The transposition of the premisses in Extension or in Comprehension might, as Hamilton elsewhere remarks, be made without changing the essential character of the reasoning. It would not be natural, bat it would not affect the reasoning as a mental process. But the position of the premisses as indicated is the natural way of showing when we reason in Comprehension or in Extension. Of course, it is hardly necessary to say in passing that Hamilton does not, as Mill states, make the distinction of Comprehen- sion and Extension depend merely on the transposition of the premisses. 2 i Logic, L. xvi. p. 299, and above, p. 407. 2 Examination, p. 605. 430 INSTITUTES OF LOGIC. 547. The quantities of Breadth and Depth are explicitly held by Hamilton to be merely views of the same relation from opposite points, not things in themselves different. 1 He combats the view that the reading a proposition in depth in contrast to its reading in breadth is " not another reading of the same proposition, but another proposition derived in- ferentially, though not syllogistically." He holds very distinctly that Breadth and Depth, though named quantities, are really one and the same quantity, viewed in counter-relations and from opposite ends. Nothing is the one which is not, pro tanto, the other. Though different in the order of thought (ratione], the two quantities are identical in the nature of things (re). In effect it is precisely the same reasoning, whether we argue in Depth or in Breadth. Thus, in Depth, we may argue the individual Z is (or contains in it attribute) some Y ; all Y is some U ; all U is some ; all is some I ; all I is some E ; all E is some A ; therefore Z is some A. (Take Socrates, Athenian, Greek, European, Man, Mammal, Animal.) In Breadth, the argument would be the same : Some A (i.e., as class contains under it the subject part) is all E ; some E is all I; some I is all 0; some is all U; some U is all Y; some Y is Z ; therefore some A is Z. (Eeverse the concrete concepts already given.) Hamilton adds that as the propo- sition in either quantity is only an equation, only an affir- mation of identity or its negation, the substantive verb is or is not expresses the relation more accurately, than containing and contained, whether in or under. We are told, also, that in syllogisms the contrast of the two quantities is abolished, and the differences of figure, major and minor, premiss and term, likewise disappear. 548. It has been objected to this that "the two modes of reading propositions in Depth and Breadth are not convert- ible ; the extensive mode gives the intensive, but not vice versd in all cases." " In the affirmative, any portion of the intension of the predicate may be affirmed of the subject ; in the negative, it is not true that any portion of the intension of the predicate may be denied of the subject. Thus, 'No 1 See Discussions, p. 697. Hamilton gives the fullest and most explicit account of his views on Breadth and Depth in Reasoning in connection with the Table figured in Discussions, p. 699. REASONING IN COMPREHENSION. 431 planet moves in a circle/ gives us a right to deny any consti- tutive attribute of circular motion to that of a planet, but not any attribute ; not, for example, the progression through every longitude." l Against this Hamilton strongly maintains that the correla- tion of Breadth and Depth in Propositions and Syllogisms is thoroughgoing, universal, applying equally to affirmative and negative. The rule is : " The predicate of the predicate is, with the predicate, affirmed or denied of the subject." " All that enters into the predicate notion is denied of the subject, if the predicate itself be denied." There is no difference whatever between " constitutive " and " attributive " in the case. We have nothing to do with what has been previously known or discovered. We have only to do with what we formally think. In saying, " No planet moves in a circle," we do not uni- versally deny of a planet any progression through every longitude, but we deny of it a circular progression that is, a particular kind. And so it is also when we say Newton is not Leibnitz. Here every attribute of Leibnitz is denied of Newton contradictorily denied. But we say again, Leibnitz is a mathematician, or mathematician is an attribute of Leibnitz. Do we infer that Newton is not a mathematician ? That the attribute mathematician does not belong to Newton ? We do, and we do not. We deny that Newton is a certain mathema- tician this mathematician who is Leibnitz. But we deny in- ferentially nothing more. We do not exclude Newton from the whole of the class mathematician. We only exclude him from that unit of it which is identical with Leibnitz. Wo infer that Newton is not the mathematician Leibnitz, we spoke of nothing more than this in connection with Leibnitz ; but it would be going beyond our premisses to deny abso- lutely that Newton is a mathematician. So far as De Morgan's criticism is concerned, the answer is complete ; but there are some points about the nature of comprehensive reason- ing which require attention and examination. 549. It seems to me that in Hamilton's vindication of the Comprehensive Reasoning there is a tacit change in the minor premiss from Comprehension to Extension. To put it formally : i Discussions, p. 697. De Morgan, as there quoted. 432 INSTITUTES OF LOGIC. ( The concept) Newton does not contain in it (the concept} Leibnitz ; i.e., the one sum of attributes in Newton does not contain in it any of the other sum in Leibnitz. But (the concept) Leibnitz contains the concept (attribute) mathematician ; Therefore (the concept) Newton does not contain the concept (or attribute) mathematician. Here it seems to me that the proper and logical conclusion is that Newton does not contain the attribute mathematician. We avoid this only by reading the minor premiss in Exten- sion, not in Comprehension ; and think of a mathematician or one of the class mathematicians, and thus only are we able to allow in the conclusion that Newton is not a mathematician, or this one of the class. But this seems to me to be a reason- ing which does not proceed wholly in Comprehension, but really both in Comprehension and in Extension. To put it in letters : X (the individual Newton) does not contain in it Y (the indivi- dual Leibnitz) ; Y (Leibnitz) contains in it the mark Z (mathematician) ; Therefore X (Newton) does not contain in it the mark Z (mathematician) . No, only the mark Z in so far as it is in Y ; but this amounts to making the predicate " the mark Z (mathema- tician)" equivalent to one or some mathematician only, for we have not said that Y alone contains the mark Z, in which case X could not contain the mark Z. We have thus intro- duced into the minor premiss the conception of distributed quantity that is, extension. 550. If we mean by the sum of attributes certain specific attributes, a, b, c, &c. man, mathematician, &c. the concept Newton, or other attributes regarded as in it, are not those which are actually or numerically in Leibnitz. But then the denial here is not in respect of the attributes properly re- garded, but of the distribution of them, and would mean that while the same attributes logically considered may be or are in both individuals, they are yet numerically different ; or there are several of the same kind only the one individual REASONING IN COMPREHENSION. 433 has them as well as the other. In this case, our denial merely amounts to saying that the individuality of Newton is not the individuality of Leibnitz, or there are two units, possessing, it may be, logically identical attributes. But this cannot be regarded as a conclusion wholly in comprehension. 551. It seems to me that in all this the nature of reason- ing in Depth or Comprehension is virtually identified with that in Extension or Breadth. If the proposition in each be an equation, we have in each extensive quantity. It matters little or nothing to the nature of a reasoning whether we begin with the individual or the genus, if in each process we require to introduce all and some, or extensive quantity into the premisses. We are no longer reasoning from one indi- visible attribute, or indivisible sum of attributes, to another ; but from one quantity of these to another, and that is pre- cisely reasoning in Breadth. If Hamilton had persistently kept in view the principle of the indivisibility of the attribute which he laid down some time before these views were given in the Discussions, 1 he might have developed a doctrine of strictly Comprehensive Reasoning ; but as it is, he does not seem to me to have done so. 552. The defects of the theory of reasoning in Compre- hension come out most markedly in relation to negative con- clusions. Here, in fact, it seems to me to break down, when left wholly to itself. The law for affirmatives as given by Hamilton is : " The predicate of the predicate is, with the predicate, affirmed of the subject." Thus : Man includes in it sentient ; Sentient includes in it capable of suffering ; Therefore man includes in it capable of suffering. Or Socrates is son of Sophroniscus ; Sophroniscus is Athenian; Therefore Socrates is Athenian. This is quite valid, and, is strictly a reasoning in Com- prehension. But take the other half of the rule that for negatives " The predicate of the predicate is, with the predicate, denied of the subject." Thus : i See Logic, iv. Appendix v. (c), p. 271. 2 E 434 INSTITUTES OF LOGIC. Man does not include in it mineral ; Mineral includes in it weight; Therefore man does not include in it weight. This is wholly invalid as a reasoning in Comprehension. All that is denied is some weight, the weight that is in mineral. But this is in Extension, and the conclusion is so cloaked as to be deceptive. Again, suppose we reason thus : Socrates is not the son of Eutryphon ; Eutryphon is Athenian ; Therefore, Socrates is not Athenian. This is invalid. Here we are not entitled to infer that Socrates is not Athenian. The mark of the mark is the mark of the subject itself, but what is not the mark of the mark is not necessarily not the mark of the subject itself. The prem- isses do not exclude Socrates from being the son of a man who was Athenian. This holds true, so long as we keep to the limits strictly of the Comprehensive reasoning. The conclusion no more follows than if we were to argue that what is not a part of this part is not a part of the whole. Thus : Mortal contains man; Man does not contain horse; Therefore mortal does not contain horse. Or Man has for its part European ; European has not for its part African; Therefore man has not for its part African. This, of course, explicitly quantified would be quite valid. Thus : Man has for its part European ; European has not for its part African ; Man has not for (this one) of its parts African. 553. Hamilton, in dealing with the Intensive Syllogism in the Lectures - 1 lays down the rule that " the sumption must in quality be affirmative, and the subsumption in quantity definite (that is, universal or singular)." This is the converse of the rule for the Extensive Syllogism, which is, " that the 1 Logic, L. xvii. REASONING IN COMPREHENSION. 435 sumption must in quantity be definite ; the subsumption must in quality be affirmative." To illustrate the former rule he gives comprehends M ; M does not comprehend P ; Therefore S does not comprehend P. Or Prudence comprehends virtue ; But virtue does not comprehend blameworthy ; Therefore prudence does not comprehend blameworthy. If we were to say that prudence does not comprehend learn- ing ; but learning comprehends praiseworthy, we could draw no conclusion, either that prudence does or does not comprehend praiseworthy. Then the subsumption must be universal or singular i.e., definite. Prudence is a virtue ; i.e., prudence comprehends virtue; (Some] virtue is praiseworthy i.e., some virtue comprehends praiseworthy. Here there is no conclusion, "for the indefinite some virtue does not connect the major term prudence and the minor term praiseworthy into the necessary relation of whole and part." l 554. In the first place, it seems to me that there is no valid conclusion in the illustration given. Virtue is a mark of prudence, i.e., the attribute virtue is an attribute of prudence; the attribute blameworthy is not an attribute of virtue; it does not follow from this that the attribute blameworthy is not an attribute of prudence. We might just as well argue that be- cause animal life is an attribute of man, and weight is not an attribute of animal life, that weight is not an attribute of man. What is not simply a mark of the mark is not necessarily not a mark of the thing itself. It may yet be so, either directly or indirectly. And to introduce universal quantity or defini- tude into the subsumption or minor proposition, is to depart from the form of reasoning in comprehension altogether, to introduce, in fact, an extensive premiss. And it is, besides, futile. If I say : Prudence comprehends virtue ; (All) virtue does not comprehend blameworthy ; Or, Blameworthy is not in any part of virtue ; 1 Logic, L. vi'u., iii. p. 317. 436 INSTITUTES OF LOGIC. I cannot infer that blameworthy is not in prudence; but only not in that part of prudence which is convertible with virtue. If I say : Man comprehends animal life ; No animal life has weight ; I cannot, therefore, say that no man has weight, but only that weight is not in that part of man which is convertible with animal life. But weight may be an attribute of man, after all. Praiseworthy ($) is a mark of learning (M) ; Learning (M) is not a mark of prudence (P) ; Therefore praiseworthy () is not a mark of prudence (P). Taking S, M, and P to represent attributes throughout, and each attribute in its indivisibility, this is a bad reasoning. We have, in fact, in the premisses compared attributes as indivisible wholes with each other, and in the conclusion drawn an inference limiting their distribution or distributive application. 555. As thus put, reasoning in Comprehension with a negative conclusion is illogical. There are two special condi- tions which must be fulfilled, ere it is at all valid. These are (1.) Where the attribute of the subject is assumed to be alone or single. In this case, we could argue from the attribute wanting another specific attribute, that this is also absent from the subject E.g., S has the (single) mark M ; M wants the mark P ; .'. S has not the mark P. In the case of a Defining Proposition, in which the subject and predicate are necessarily convertible, we may have a negative reasoning in Comprehension. Thus we may reason : Oratory is the art of persuasive speaking; Sculpture is not a mark or part of persuasive speaking; .'. Sculpture is not a part or mark of oratory. In this case, however, the predicate or mark of the subject must be convertible with it that is, it must be its single mark. (2.) Where the mark of the mark is in contradictory rela- tion, or absolute repugnance. As : SEASONING IN COMPEEHENSION. 437 S (Animal) comprehends M (Organisation) ; M (Organisation) does not comprehend P = not- M (Non-or- ganisation) ; .'. S does not comprehend P. But this is hardly worthy of the name of reasoning. We have immediately implied the absence of P (not-M) in the assertion of M. (3) There is a third case where the mark implies the neces- sary exclusion of another mark as contrary, incompatible, or repugnant. The soul is an indivisible unity; An indivisible unity has not extension (is contradictory of exten- sion, or extension is contradictory of indivisible unity] ; Therefore the soul has not extension. Mis an invariable mark of S ; P never is a mark of M; .'. P never is a mark of S. If M be supposed in every S, and P never in any M ; yet P may be a mark of S, for it may have other marks than M. But if it be alleged that P cannot coexist with M, or is re- pugnant to M being at all, then we may infer, on the sup- position that M is an invariable mark of S, that P never is a mark of S. But this is to state much more in the premisses than the simple fact of the one being or not being a mark of the other. Thus : Electricity (s) has the mark (m) of travelling along a tied nerve ; The nervous fluid (p) has not the mark (m) of travelling along a tied nerve ; . : Electricity (s) is not the nervous fluid (p). Here the marks are absolutely repugnant contradictory tra- velling and not-travelling along a tied nerve. Hence the reason- ing is sound. (a) Professor Bowen in his able and clear exposition of the logical doctrines of Hamilton, offers a solution of the difficulty here stated, which I cannot regard as satisfactory. He says " In intension the parts are not species, but attributes or marks, and these do not exclude each other. Each part or attribute here interpenetrates, so to speak, and informs the whole. Black is a part of negro in the sense of being only one of his attributes, since he has many others, such as being long- heeled, prognathous, &c. ; but it is a part which colours the whole, for the 438 INSTITUTES OF LOGIC. negro is black all over. . . . The maxim for the reasoning in com- prehension is that a mark of the mark is also a mark of the thing itself, of the whole thing. Free agency, which is a mark of responsibility, is also a mark of man, because responsibility is a mark of the whole man." Thus read, the above syllogism would be valid. "S has M for one of its marks or attributes. M, though only one of the attributes of S, affects or colours the whole of S ; therefore P, which is not an attribute of M, is not an attribute of S. Thus A negro has a black skin ; But a black skin is not an invariable sign of a brute intellect ; Therefore, a negro is not necessarily brutish in intellect." It seems to me that this does not meet the difficulty. We have here a totally different conclusion from that alleged in the formula. 8 comprehends M ; M does not comprehend P ; .'. 8 does not comprehend P. The parallel reasoning should have been : A negro has a black skin ; The notion of a black skin has not the mark or notion of a brute intellect ; Therefore the notion negro has not the mark or notion of a brute intellect. This absolutely stated is illogical. And when we argue that because being brutish in intellect is not the mark of a black skin, the negro is not brutish in intellect, we state a very different conclusion from that which follows when we argue that because a black skin is not invari- ably or necessarily a sign of a brutish intellect, a brutish intellect is not invariably or necessarily a sign of the negro. This means merely that so far as these signs go, it is not proved that the negro is brutish in intellect. But it is not proved that he is not brutish in intellect, which is the conclusion required. The two cautions already laid down are necessary. Either the mark of the subject is single, exclusive of others, or convertible with the subject ; or the mark of the mark is essentially repugnant to contradictory of the mark of the subject. 556. The Canon of Comprehension should, therefore (for negatives), run thus : A mark repugnant to a mark of the subject is repugnant to the subject itself. Or, A mark contradictory of a mark of the subject is contra- dictory of the subject itself. For affirmatives : A mark essential to a mark of the subject is essential to the subject. This is necessary : S contains M ; M contains P ; S contains P. KINDS OF CATEGORICAL REASONING. 439 It is only as M contains P always, or essentially as part of it, or identical with it, that we can be sure that S always or essentially contains P. If M contains P only sometimes, or now has it, and then not, we cannot have the conclusion that S contains P. Thus, if we reason : Poison is a mark of every mineral acid ; No mineral acid has for its mark digitalis ; Therefore poison is not a mark of digitalis. This is clearly incorrect. It is equivalent to : If this be a mineral acid, it is a poison ; but it is not a mineral acid ; therefore, it is not a poison. Here is the usual hypothetical or equivalent categorical fallacy. But we may reason validly thus : Man has the mark morally responsible ; Necessitated volition is repugnant to (incompatible with) moral responsibility Therefore man does not possess the mark necessitated volition. In Extension this would run : A Man is morally responsible ; E A being with necessitated volition is not morally responsible; E Therefore a being with necessitated volition is not man. = Camestres. The result is that mere exclusion is not sufficient for a comprehensive negative conclusion. As we are not dealing with classes, but with attributes, and as these are indivisible, the attributes must not only lie out of each other simply, but must be mutually incompatible. This, I apprehend, was what was dimly and imperfectly recognised in the phraseology of the negative rule Re- pugnans notoz est repugnans rei ipsi. 557. From what has been said under the head of the Categorical Syllogism, it may be inferred that there are at least three kinds of Categorical Reasoning, To these I pro- pose to add other two viz., those marked (3.) and (5.) (1.) There is the Extensive Reasoning. In this the predi- cate in both premisses is taken as the genus of the subject. Thus : 440 INSTITUTES OF LOGIC. Animal is organised; Man is'animal; Therefore man is organised. The characteristic of this reasoning is, that as it passes from genus to species and individual, what is predicated in the genus of the subject is predicated of the species or indi- viduals of the subject, but not conversely. For what may be said of the species need not be said of the genus, and so of the individual and species. Animal is, therefore man is, does not follow. Animal is, therefore risible is, does not follow. 558. (2.) There is the Comprehensive Seasoning, strictly so called, in which the predicate is taken as attribute of the subject, be it mark, property, action. Thus : Plant has organisation ; Organisation has reciprocity of vital action Therefore plant has reciprocity of vital action. 559. (3.) There is the Combined Extensive and Comprehen- sive Reasoning. Here the predicate will be taken in one premiss as genus, in the other as attribute. Thus : All Xs have the mark Y (Comprehension) ; All Zs belong to the class of Xs (Extension) ; Therefore all Zs have the mark Y (Comprehension). All gold is a metal ; All metal has the mark lustrous ; Therefore all gold has the mark lustrous. This form of reasoning, though not usiially recognised in Logic, is in common, even necessary, use ; and, in fact, is the formula according to which we most usually subsume the individual under the general. How am I to know, I may ask myself, whether this substance I have found is a metal or not? Only by gome mark say lustrous. Thus through the mark I refer it to its class. Will the oats be a good or bad crop this season ? I might determine this through cer- tain marks as the yellow look of the braird, the shortness of the straw, the poverty of the ear, &c., and so on. This is really a mixed reasoning, partly in Comprehension and partly in Extension. It occurs constantly in pure Geometry. KINDS OF CATEGOEICAL REASONING. 441 560. (4.) There is the Syllogism of Equivalence, the rea- soning from equal to equal. This is the Unfigured Syllogism of Hamilton the Expository Syllogism of others. The former is wider than the latter, which referred only to Singu- lars ; but Hamilton, by making equivalents in quantity, widened its scope. There is not only reasoning from this to that, or individual A to individual B, but from the equivalence of all of one class to some of another. The formula of the Syllogism of Equivalence is, however, in all cases the same. What are equivalent, or non-equivalent, to a common third term, are equivalent or non-equivalent to each other. If X be equivalent to Y, and Y to X, X is equivalent to Y. If all X be equivalent to some Y, and all Z be equivalent to all X, all Z is equivalent to some Y. 561. (5.) To these I am disposed to add a fifth form what I would call the Syllogism of Collection. Here we literally gather into one in the conclusion what we stated separately, yet as implicated, in the premisses. Thus : The crops this season are good in quality; The crops this season are good in quantity; Therefore the crops this season are good both in quality and in quantity. So negatively : The crops this season are not good in quality; They are not good in quantity; Therefore they are not good either in quality or quantity. This is a perfectly simple form of reasoning, in common use, though not fitting into any of the received formulae, nay, in the negative form, even apparently violating the rule against two negative premisses. The law may be generalised thus : Where the same middle term admits of predicates of opposite kinds or genera, these, when both positively related, may be affirmed, or, when both negatively related, may be denied, of the middle term as subject of the conclusion. This reasoning differs from the ordinary forms by admitting middle as subject of the conclusion, and in the negative 442 INSTITUTES OF LOGIC. form the rule against double negatives does not apply, for the comparison has been instituted not through comparing major and minor through the middle, but collating major and minor in succession with the middle. The middle again appearing as subject of conclusion, with the gathered predi- cates, constitutes the conclusion naturally and simply a col- lectio collection. 443 CHAPTER XXXIII. OP COMPLEX AND INCOMPLETE REASONINGS DEDUCTIVE CHAIN - REASONING : EPICHEIREMA SORITES ORDINARY ENTHYMEME. 562. According mainly to the manner of enouncement or expression, a reasoning may be Simple or Complex, Complete or Incomplete. A reasoning is simple in nature when it con- tains three and only three related propositions, constituting a single reasoning. It is simple in expression when these propositions are explicitly stated in the order either of Ex- tension, Comprehension, or Equivalence. This is properly a Monosyllogism that is, a single independent reasoning. 563. But Syllogisms may be connected in a succession or series, and thus stand to each other in the relation of antece- dent and consequent. This is regarded as a composite or complex reasoning, and is called a Poly syllogism, also a Chain- syllogism or Chain of Reasoning. 564. In a Chain of Reasoning the order may be either that of thing proved and reason, or of reason and thing proved. In other words, " each successive syllogism is the reason of that which precedes it, or the preceding syllogism is the reason of that which follows it." The former order is called the Analytic or Regressive ; the latter is the Synthetic or Progressive. The reason-containing Syllogism is called the Prosyllogism ; the consequent-containing Syllogism is called the Episyllogism. 1 If the Chain of Reasoning be com- posed of more than two links, the same syllogism may be, in different relations, prosyllogism and episyllogism. 565. A polysyllogism, not explicitly enounced, is made 1 Cf. Krug, Logik, iii. ; and Hamilton, Logic, iii. 364. 444 INSTITUTES OF LOGIC. up either of partially complete and partially abbreviated syllogisms, or of syllogisms all equally abbreviated. In the former case we have what logicians call the Epicheirema (eTTi^etp^a) ; in the latter the Sorites. 1 Of the Epicheirema or Keason-rendering Syllogism, the following is an example : X is Y; But Z is X, for it is D ; Therefore Z is also Y. It is permissible to take the life of a man who lays an ambush with the purpose of taking yours ; Milo, therefore, was justified in killing Clodius, for Clodius had laid an ambush against Milo's life. 2 566. The Chain-syllogism proper or Sorites coacervatio, congeries, gradatio, climax, de primo ad ultimum) arises when we carry on the principle of Inference beyond the part of the highest part, and take in the part of that part, and so on through a series of successive parts. 3 Thus a simple syllogism would run : (All) B is a part of A ; (All) C is a part of B ; .'. (Alt) G is apart of A. But we may proceed thus : B is A i.e., A contains B ; G is B i.e., B contains G ; D is G i.e., G contains D ; E is D i.e., D contains E ; Therefore E is A i.e., A contains E. In this case we have the Chain-syllogism or Sorites, and this example in Extension. The predicate is the containing whole. But the ordinary logical Sorites sometimes called the Aristotelian really proceeds in Comprehension, and this is the more natural form. Thus : 1 Esser, Logik, 104 ; Hamilton, Logic, iii. 364. 2 Cicero, pro Milone. See Port Royal Logic, p. 231. 3 See especially Hamilton, Logic, iii. L. xix. , who gives the best analysis of this form of reasoning, and who for the first time accurately stated its history. SORITES. 445 E is D i.e., has the mark D ; D is C i.e., has the mark C ; C is B i.e., has the mark B ; B is A i.e., has the mark A ; Therefore E is A i.e., has the mark A. Here the subject is the containing whole, and the predicate the contained part. Both of these forms are Progressive, in the sense of proceeding from whole to part in the respective quantities. 1 A concrete example in Comprehension is found in the following : Every body is in space; What is in space is in one part of space; What is in one part of space may be in another; What may be in another part of space may change its space; What may change its space is movable; Therefore every body is movable. 2 (a) Sorites, a heaper, is from pbs, a heap, and originally desig- nated the sophism named by Cicero acervalis. The Sorites, as the name for a form of reasoning, is not to be found in Aristotle. Nor was the form of reasoning afterwards designated Sorites developed by him, though it is improperly named the Aristotelian form. (See the reference in An. Pr., i. 25.) The name was probably first applied to the reasoning by Valla in his Dialectics Disputations, published after the midddle of the fifteenth century. (See Hamilton, Logic, iii. p. 377.) Mark Duncan thinks this form is called the heaper, because as grain is superadded to grain in a heap, so proposition is superim- posed on proposition in the reasoning. His definition of it is "an argumentation in which the attribute of every prior proposition is the subject of the posterior until, through several middles, we reach the term to be connected with the subject of the first proposition. It con- tains as many syllogisms as there are propositions between the first and the last." (Inst. Log., L. iv. c. vii. 6.) 567. It is easy enough to state each of these in a Regressive form. Hamilton lays down the rules : " In the Progressive Sorites of Comprehension and in the Regressive Sorites of Extension, the middle terms are the predicates of the prior premisses and the subjects of the posterior ; the middle term is here in position intermediate between the extremes. On the con- trary, in the Progressive Sorites of Extension and in the i Hamilton, Logic, iii. p. 366. 2 Hamilton, Logic, iii. p. 381. 446 INSTITUTES OF LOGIC. Eegressive Sorites of Comprehension, the middle terms are the subjects of the prior premisses and the predicates of the posterior ; the middle term is here in position not intermediate between the extremes." l 568. The Sorites known as the Goclenian being that first formulated by Rudolph Goclenius of Marburg 2 is the Regressive Sorites in Comprehension. The difference may be shown thus : (1.) Progressive Comprehensive, (2.) Regressive Compre- hensive/ (1.) EisD; (2.) Bis A; Dis G ; G is B ; Gis B ; DisC; B is A ; E is D; .'. E is A. .'. E is A. (1.) Bucephalus is a horse ; A horse is a quadruped ; A quadruped is an animal ; An animal is a substance ; Therefore Bucephalus is a substance. (2.) An animal is a substance ; A quadruped is an animal ; A horse is a quadruped ; Bucephalus is a horse ; Therefore Bucephalus is a substance. It is to be noted that these reasonings are both progressive, in the sense that prosyllogism precedes episyllogism in each. 569. The rules of the common Sorites are as follow : " 1, The number of the premisses is unlimited. 2, All the premisses, with the exception of the last, must be affirmative, and, with the exception of the first, definite. 3, The first pre- miss may be either definite or indefinite (Universal or Singular, or Particular ). 4, The last may be either negative or affir- mative." 3 The reasoning would thus be vitiated in two ways (1.) by a particular premiss in the series after the first ; (2.) by a negative premiss between the first and the last. 1 Logic, iii. pp. 379, 380. 2 Goclenii Isagoge in Organum Aristotelis. Francof., 1598 : p. 255. 3 Hamilton, Logic, iii. pp. 371, 372. ENTHYMEME. 447 To these it should be added that in the case of a negative conclusion in Comprehension, the mere denial of the predicate is not enough. This denial must, in accordance with the principles already laid down, be a statement of incompati- bility or contradiction between subject and predicate. 570. If it be thought necessary to resolve the Sorites into Simple Syllogisms, the rule is that there are as many simple syllogisms as there are middle terms between the subject and predicate of the conclusion, or propositions between the first and the last. Biit the truth is, that the Sorites is simply the natural form of a sequence in reasoning ; without the use- less repetition of conclusions, which everybody of ordinary intelligence is able to supply. 571. The Enthymeme is usually regarded as an incom- plete or defective reasoning, one of the premisses, major or minor, being suppressed, or retained in the mind. Thus : (a) The air has weight, for it is body. The major is here suppressed, (b) Every murderer deserves death; there- fore this man deserves death. The minor is here suppressed. As Hamilton has pointed out, even the conclusion may be understood or suggested merely. Thus : " Sunt monachi nequam ; nequam non unus et alter : Prseter Petrum omnes : est sed et hie monachus. " l 572. The Enthymeme is wrongly regarded as a special form of reasoning co-ordinate with syllogism. It arises sim- ply from the need of expressing thought in a terse and abbre- viated form. As Mark Duncan has well put it : " Dicitur syllogismus imperfectus lion respectu mentis, sed prola- tionis : nam in mente proponentis integer esse potest et solidus syllogismus, etsi proferatur truncatus." 2 Duncan and the older logicians, who really knew something of the literature of the subject, were well aware that Aristotle gave no countenance to the view of the Enthymeme as a specific form of reasoning. They were also well aware of the fact that, with Aristotle, Enthymeme does not signify a syllo- gism or abbreviated expression at all, but a reasoning from signs and likelihoods, a reasoning, in fact, of probability. 3 i Logic, iii. p. 393. 2 Inst. Log,, L. iv. p. 252. s See Duncan. Inst. Log., L. iv. p. 251. On the nature and literature of the Enthvnieme, see especially Hamilton, Lectures on Logic, L. xx., and DMCIU gions,p. 154. He there clears up the whole matter, leaving almost nothing more to be done. 448 INSTITUTES OF LOGIC. 573. Enthymematic expression is not simply an accident, but a necessity of language in a rhetorical interest. What is evident is passed over. What is prolix is avoided. What is brief is sought after ; and what can be left through suggestion to the imagination or reason of a hearer or reader, is allowed to make for itself its special effect. Some of the finest effects alike in oratory and in poetry are made through enthymematic expression. Thus : 'A.6dvarov opyrjv pr) vXa.TTe, 6vr]Tos wv. (Mortal, cherish not immortal hate.) " When, fast as shaft can fly, Blood-shot his eyes, his nostrils spread, The loose rein dangling from his head, Housing and saddle bloody red, Lord Marmion's steed rushed by." SCOTT. 449 CHAPTEE XXXIV. INDUCTION FORMAL AND MATERIAL ANALOGY. 574. According to the view of Categorical Reasoning which makes it dependent on the Law of Identity, or whole and part, it is obvious that we may reason not only from the whole or genus to the parts, but conversely from the parts to the whole. In the former case we have Deductive Categorical Reasoning, in the latter Inductive Categorical Reasoning. In the latter case we argue from " the notion of all the con- stituent parts discretively, to the notion of the constituted whole collectively. Its general laws are identical with those of the Deductive Categorical Syllogism, and it may be ex- pressed, in like manner, either in the form of an Intensive or of an Extensive Syllogism." l 575. Strictly formal induction has been named Perfect Induction or Perfect Enumeration, as compared with Imper- fect Induction or Enumeration. In the former case, there is an enumeration of all the singulars under the species, or of all the species under the genus i.e., under the universal in question. The latter founds merely on some of the singulars under the species, or some of the species under the genus i.e., under the universal in question. Aristotle recognised the distinction of reasoning either from singulars or from parts to the whole. He regards Induction as cVaywyr) rj avo rS>v KO.O' e/caorov CTTI TO. Ka66\ov i Or Every X Y Z is A ; X YZisall B; Therefore all B is A. This is a reason apparently in the Third Figure ; but in it, according to the ordinary rule, it is illegitimate, because the conclusion is universal. But the conclusion is legitimated on the principle that when two terms are attributed wholly to a third, and when this third is reciprocal to the second of the two terms, the first of these terms is also attributable to the second. On this ground Aristotle may be supposed to rest the inductive syllogism as a valid independent form. No doubt he seems to suggest in ( 4) the conversion of the minor premiss into All devoid of bile is man, horse, mule. We should thus have the inference in Barbara of the First Figure. Thus : Every man, horse, mule is long-lived ; All devoid of bile is man, horse, mule ; Therefore all devoid of bile is long-lived. But this is by no means conclusive, though through the emphasis given to the moods of the First Figure by subse- quent logicians, the validity of the inductive form has been made unwarrantably to depend on its capability of reduction to this Figure. The validity of the inductive form obviously depends on the principle, which Aristotle himself elsewhere expressly disavows, of the universality of the predicate in an affirmative proposition in fact, on the recently much-ques- tioned form all is all. But this may be taken as an instance at once of its validity and utility. (a) Aristotle evidently recognises Material Induction when he tells us that " induction is a progress from singulars to the universal, as if the skilled pilot is the best, and the skilled charioteer, the skilled in every genus is the best ; " and especially when he adds that " induction is more fitted for persuasion, and more certain as well as more evident to the sense and common to the many ; but syllogism presses with a greater necessity and repels opponents with greater force." (Top., i. 12.) Formal induction is, of course, as cogent as (Deductive) syllogism. We have also the recognition of Imperfect Induction as the basis of the reasoning from Example (see below, p. 484 et seq.) In the following passage, however, he refers obviously to that form 452 INSTITUTES OF LOGIC. of Induction in which the Universal is constituted through a complete enumeration of the parts. "There is, therefore, induction, and inference from induction, when we conclude one of the extremes of the middle by the other extreme. Thus, for example, if B is middle of A T, to demonstrate by r, that A is B ; for this is how we make the induction. Let A be long-lived, B that which has not bile, and C all long-lived animals, as man, horse, mule, &c. Then A is in C all entire ; for all C is long-lived ; but B also, that is, that which has no bile, is in all C ; if, then, C is reciprocal to B, and does not exceed the middle, it is therefore necessary that A is in B ; for it has been demonstrated that any two things being the attri- butes of the same subject, if the extreme is reciprocal to one of them, it is necessary that the other attribute should also be in the reciprocal attribute. Further, it ought to be supposed that C is composed of all the particular cases ; for induction comprehends all. Such is the syl- logism of the primitive and immediate proposition." (An. Pr., ii. 23.) There are other passages in which Aristotle referred to what we call material induction, as, for example, An. Post., i. 18 ; ii. 19. He tells us expressly that imperfect induction is only allowable, where there is no contrary instance (tva-rao-is) . (Top., vii. 8.) And he certainly prac- tised it not without success in his History of Animals. In this use of the inductive method he but followed Hippocrates in medicine. But the truth is, there has been no time in the history of observational science in which Material Induction has not been followed more or less faithfully. Even Bacon, who signalised and emphasised the method mistaking, at the same time, the place and scope of the Formal Induc- tion and Deduction of Aristotle had before him, as exemplifying the method, Copernicus, Kepler, and Galileo. Newton but took up the thread of the predecessors of Bacon, with the advantage of the illumina- tion which Bacon had thrown on the method. Even Newton's deduc- tion could be verified only by Bacon's observation and induction, as to coincidence with actual fact. 578. Hamilton regards Induction as proceeding equally in Comprehension and Extension, and gives the following formulas for Induction : A. In Comprehension (1.) (The parts holding the place of the major term S.) X Y Z constitute M ; M comprehends P ; Therefore X Y Z comprehend P. (2.) (The parts holding the place of the middle term) S comprehends X Y Z ; X Y Z constitute P ; Therefore S comprehends P. PERFECT INDUCTION. 453 B. In Extension (1.) (The parts holding the place of the major term P) X Y Z constitute M ; & is contained under M ; Therefore S is contained under X Y Z. (2.) (The parts holding the place of the middle term) X Y Z are contained under P ; X Y Z constitute S; Therefore S is contained under P. 579. Perfect Induction may very properly be extended to cases in which there has been the observation or analysis of the individual constituent elements of a concrete, say physical whole. Thus we may reason : Quartz, felspar, and mica are all the constituents of ordinary granite ; Ordinary granite is an igneous rock ; Therefore quartz, felspar, and mica are all the constituents oj an (some) igneous rock. Or Cognition, feeling, desire, will, are all the phcenomenal mani- festations of mind in man ; Mind in man is the only mind we directly know ; Therefore cognition, feeling, desire, will, are all the phcenomenal constituents of mind directly known to us. This principle applies very strictly to the constitution of geometrical figures, to all chemical analysis of bodies ; and it serves to explain how, from a single analysis of a body or description of a figure, we are able to extend our analysis or description to all similars. Thus geometrical demonstration may be taken as a form of Perfect Induction, although in it we specify only a single figure. Exhibiting only a single diagram, we are able in a valid demonstration to draw a conclusion which is not only true, but necessarily true. As the latter it is universal, that is, applies to every figure of the same character. Thus, given a parallelogram, or a four-sided figure of which the opposite sides are parallel, it can be proved that the opposite sides 454 INSTITUTES OF LOGIC. and angles of this figure are equal to one other ; and that the diameter bisects the parallelogram, that is, divides it into two equal parts. 1 This, as a consequence, necessary and neces- sarily true, applies to all parallelograms whatever, and we need but the one figure through which we demonstrate the con- clusion. The confidence with which we extend our conclusion to all figures of the same class, whether these actually exist or are only ideally conceived, whether they agree or not in size, material, &c., with the one figure we know, is based on the conception and conviction of the essential similarity of all the other figures to the one before us. This may pos- sibly in the end be found to depend on the nature of the matter space or extension about which we reason, and its adaptability to explicit or essential definition. In the same way, we may demonstrate the most abstract relations of numbers in Algebra, through formulae which, while in- dependent of any given number, are yet applicable to all which fall under the specified conditions. In Arithmetic there is an approach to this universality, for we know, for example, that 10 + 10 = 20 in all instances and in every kind of matter, whether we speak of pence, pounds, or shillings of pears, apples, or men. In the case of Chemical Analysis, the resolution of a single body, that is, specimen of a class, may enable us to ascertain the exact constituents of each substance of the class as in the case of water. Here electricity enables us to decompose water " into two perfectly different substances, oxygen and hydrogen gases, and into nothing else," and to show " that water when thus decomposed yields twice as large a volume of hydrogen as it does of ogygen." 2 We are confident after this analysis that any example of water afterwards taken will yield those elements. This is founded, however, partly on the direct evidence afforded by the analysis of the single sample, and on an inductive law already established, that chemical combination is constant in its nature, that it takes place according to uniform law ; one feature of this law being that it does so most readily between those bodies which least resemble each other. 580. The practical value of Perfect Induction lies in its enabling us to summarise particulars or details in one total 1 Euclid, Prop. 34. 2 Koscoe. MATERIAL INDUCTION. 455 concept or expression. Under its guidance we may unite in one expression particulars which otherwise we should be obliged specially and tediously to enumerate. It has thus an important synthetic value, as enabling us to predicate of the whole of a series of particulars or individuals known to lie within certain limits. We can predicate definitely of all the apostles, all the months of the year, all the people in this room, all the objects at a given time, or in a given space, &c., only through the form of Perfect Induction. 1 581. Material Induction and Analogy are both founded on the principle known as the presumption of the Uniformity of Nature. Without, meanwhile, entering into a consideration of the ground and genesis of this principle, it is enough for the present purpose to refer to the two applications of it in Induction and Analogy. In Material Induction we proceed from the parts that is, some of the parts to predicate of the whole or class of things to which these belong. The part may be an individual thing, or a species ; but ultimately what we found on is the individual of observation or experience. Thus This, that, and the other metal has a peculiar lustre ; But this, that, and the other metal represent all metals ; Therefore all metals have a peculiar lustre. Or A B C D have each the attribute Y ; A B C D belong to the same class X ; Therefore the whole, class X has the attribute Y. Such an inference supposes at least two things (1.) That no negative or contradictory instance be given or known ; and (2.) That the attribute is not a merely temporary, passing, or accidental state of the individual, but permanent and essen- tial. This, of course, raises the question as to what an essential attribute is. To this point I have already referred, 2 It means in this connection, as we shall see, causal relation or sequence. (a) " Material or Philosophical Induction," says Hamilton, " is not BO simple as commonly stated ; but consists of two syllogisms and two deductive syllogisms, and one of them an Epicheirema. Thus : i Cf. Jevons, Logic, p. 214. * See above, p. 102 t ttq. 456 INSTITUTES OF LOGIC. "I. What is found true of some constituents of a natural class, is to be presumed true of the whole class (for nature is always uni- form) ; a a' a" are some constituents of the class A ; therefore what is true of a a! a" is to be presumed true of A . 11 II. What is true of a a' a" is to be presumed true of A ; but Z is true of a a' a"; therefore Z is true of A. 1 ' It will be observed that all that is here inferred is only a presump- tion founded, 1, on the supposed uniformity of nature ; 2, That A is a natural class ; 3, On the truth of the observation that a a' a" are really constituents of that class A ; and 4, That Z is an essential qual- ity, and not an accidental." (Hamilton, Logic, iv. p. 368.) 582. In regard to the statement that Induction supposes a natural class, it ought to be noted that it is often required to establish a natural class. Induction is indeed necessary in order to establish the concepts of species and genera, in all cases in which these do not depend on mere observation and description of coexisting features, as in Descriptive Botany, Zoology, &c. A species or genus which is consti- tuted through a knowledge of the essential attributes of a thing, through its properties, is the concept of the causal or constant relation of that thing to its properties. In many cases we have the concept of the causal sequence when we do not know more than the immediate terms, and are unable to run back the relation to anything higher, as in gravity, chemical affinity, electrical attraction of two metals in juxtaposition. 583. The difference between Formal and Material Induc- tion appears to lie in this, that in the former case there is an actual enumeration of all the individuals in the class ; in the latter there is no such enumeration, but only a statement of some. In the former case, we infer of all in the conclusion because we have supposed or are certain that all the in- dividuals constituting the class have been enumerated ; in the latter we infer of all in the conclusion because the some one or several are taken on extra-logical grounds known to us to be capable, in a given respect or attribute, to repre- sent all of the class. In both cases the whole is supposed to be constituted, but in different ways ; and in both cases the mere formal inference may be regarded as hypothetically neces- sary, the one on the assumption of the actual enumeration of all, the other on the assumption of the guaranteed equivalence of some in a given respect to the all in that respect. So far MATERIAL INDUCTION. 457 as the formal inference is concerned, there is no difference ; for before we infer, logic receives or accepts the totality. 58-1. In elevating the some observed into the all unob- served in the minor premiss of the Material Inductive Syllog- ism, there is always a weakness in the assumption made that the observed cases actually represent the whole of the un- observed or possibly observable cases. And a single instance to the contrary an instant ia is sufficient to destroy the universality. " Una instantia, cadit inductio." Thus, let us reason : This, that, and the other metal are between seven and eight times heavier than an equal bulk of water; This, that, and the other metal represent all metals ; Therefore all metals are between seven and eight times heavier than an equal bidk of water. This is formally good ; but we have been given erroneous data, for the metal lithium, to say nothing of potassium and sodium, is lighter than an equal bulk of water. The validity of the formal inference in such a case is really of subordinate importance. The point to be attended to is the ground of the equivalence stated in the minor premiss. 585. It must at the same time be admitted that there are very few cases in actual practice in which we can have ab- solute assurance of a perfect enumeration. We may have it in the case of numerical definitude, as the number of the apostles, or the number of the primary planets though in the case of the planetoids it would have been rash and wrong, as a matter of fact, to stop at any ascertained number during the last forty years, as it would be rash to do so now. In Geometry, our enumeration of the species of triangle, &c., may be quite definite and complete. But usually, even in what is known as perfect enumeration, there is a certain amount of assumption ; and one contrary instance would de- stroy the universality, just as one contrary instance in the minor premiss in material induction would destroy the uni- versality. Considered as formal inference, both as seems to me are only hypothetically necessary, and in this respect the one is as strict as the other. (a) As Bacon remarks, perfect induction is especially liable to be con- tradicted by a simple opposite instance turning up, or may depend 458 INSTITUTES OF LOGIC. on imperfect knowledge of the existing cases. The true or material induction is through an analysis of experience, by means of proper re- jections and exclusions, and after or through negations to conclude the affirmation. (Nov. Org., i. 105.) 586. Whately, without properly distinguishing Formal and Material Induction, makes the Inductive Syllogism deductive with the expressed major, which is usually understood. " What belongs (or does not belong) to the individuals we have examined, belongs (or does not belong) to the whole class under which they are contained." But in truth there is neither really nor formally any such principle as thus ex- pressed, and such a proposition could form no valid major premiss for a reasoning no law that could necessitate an inference. This is really an inadequate expression of the minor premiss in the Material Inductive Syllogism. The ob- server working on experience thinks himself justified, by wholly extra-formal considerations, in saying that the in- stances which he has examined warrant him in making them stand for or represent all the possible instances of the kind or class. It is true that they are only some, but on their nature or character he judges them to be equivalent to all. This handed over to the formal logicians is translated into the pro- position that these some represent all, or are conceived to represent all, and the proper conclusion is, that the property which they manifest is thus conceived as applicable to the whole class. If we take the common illustration, this, that, and the other magnet represent all magnets, or are all mag- nets, the conclusion is necessary that all magnets attract iron; but the conclusion is only necessary on the formal law of whole and part, and it is only necessary hypothetically that is, given these as being all, the conclusion follows. 1 (a) Induction, in the view of Trendelenburg, " only sums up the fact of the universal from the individuals, while Analysis seeks the universal cause from the given phenomenon." But Ueberweg objects " that the so-called analytical procedure must take the inductive form, and scientific induction the ' analytical ' element, which refers to the causal nexus. Hence every such distinction only corresponds to that of the ' formal ' and ' real ' sides of Induction." (Loyic, p. 487.) 587. Syllogistically in Imperfect Induction a particular conclusion alone is possible. If this, that, and the other magnet 1 Cf. Hamilton, Discussions, p. 167 et seq. MATERIAL INDUCTION. 459 attracts iron, then it follows that some magnet attracts iron. This can hardly be called a syllogistic inference : it is merely a summation, or at best an immediate inference, for there is as yet no third term. But what we have to establish further is, that attracting iron is a property not only of the individual magnets we have observed, but of every one or all. How is this to be done ? How is it possible ? It is possible, in the first instance, on the supposition or assumption or ascertained principle that the two things, magnet and attracting iron, may Btand in the general relation of cause and effect ; and, in the second instance, on the ascertainment, through certain tests or rules, that they do as a matter of fact so stand. If it can be found that magnet in this case is a cause, and that its pro- perty is attracting iron, then we have found what in point of fact is an invariable or universal relation between the subject and the predicate. And on this ground we extend the limited or observed relation all that actual experience can give us to the unlimited and unobserved, and constitute our partial observation but essential knowledge into the type of the class, or the condition of future possibility. This leads us back to the notion and principle of Causality, and to the principle of uniformity or invariableness in the manifestations of Causality in other words, to the law that similar antecedents are fol- lowed by similar consequents. This is not itself the law of Causality : it is a most inadequate expression for the law ; but it is a manifested property of the law, and it is that through which we are able actually to determine what things are causes and what effects amid the numerous relations of mere sequence or succession. (a) Does the predicate, asks Ueberweg, belong to the subject because of its generic nature or its individual nature ? or because of accidental circumstances ? that is the problem of Induction. (Ueberweg, Loyic, p. 485.) If the first question can be answered in the affirmative by the experience of a single instance, as is quite possible, we need no more cases : we have got the causal relation, and this is universal. 588. The reference of Induction, says George, to the objective causal nexus is a circle, since the knowledge of the real nexus is always based upon incomplete inductions. To this Ueberweg replies : The causal nexus as existing precedes our inductions ; but our knowledge of it in a universal form 460 INSTITUTES OF LOGIC. results after a multiplicity of special inductions. 1 But the question really is : How are we to know that the predicate say, attracting iron is an effect of each magnet observed ? This can only be by observing that one after another of magnets attracts iron that this actually happens. How many of these observations entitle us to say that magnet is cause in this case ? that it is of the nature of the magnet to attract iron ? The force of the inductive illation lies there, that is, in our knowing from observation that a causal relation really is, for the causal relation is, as a matter of general- isation, only another expression for universal and invariable relation. What, in other words, enables us to pass from the mere sequence, from which we could never infer uni- versality, to the causal sequence from which we can? Only the number and kind of the instances. But our test of this cannot be the causal nexus itself in the things, for as yet we do not know it we are seeking to find whether it exists or not in the instances in question. A sequence that has occurred in a given number of instances in cer- tain circumstances may be supposed or presumed by us to happen again in similar circumstances, from the number of times or the frequency with which it has already occurred. That this sequence is the result of a cause, and a permanent cause, if known to us, would no doubt explain the expecta- tion of the recurrence ; but as we cannot know it to be due to a permanent cause until we have generalised the succes- sive instances of the sequence, we cannot possibly say that the knowledge of a causal nexus in things is the only ground of our expectancy for the future. We have in this three dis- tinct stages (1.) The experience, more or less frequent, of the sequence. (2.) The reference of the sequence to a cause and a permanent cause in nature definitely known. (3.) The expectation based on this of the invariable recurrence of the sequence in the future, provided the antecedent be the same or similar. This would be the strongest form of Inductive Expectation, or the widest universality. But it is conceivable nay, a fact that we have experience of uniformities of sequence, whose cause we cannot discover, or which are not known to be connected causally, as day and night, light and darkness ; i Logic, p. 490. MATERIAL INDUCTION. 461 and yet we expect the recurrence of these with as much con- fidence as if we knew them to be causally related. It is thus, as seems to me, to be a narrowing of the grounds of the In- ductive Inference to limit it to a knowledge of causal relations among things. Mere constancy in experience is as frequently the ground of our inference. This is essential to our know- ledge of the causal relation itself in any given instance, and we should properly cherish a probable expectancy even where we could not discover causality at all, or at least were not aware of its actual existence. Mankind confidently expected the recurrence of night after day, and day after night, long before any one was aware of the daily revolution of the earth round its axis. And even now we should confidently expect rain rapidly to dissolve limestone rock, although we might not be aware that the main causal efficiency lies in the car- bonic acid taken up by the rain. 589. For the inductive illation proper, from the some to the all, no one formula no a priori formula can be stated, nor can we prescribe by formula beforehand the number of cases which warrant a universal inference. For syllogism we can lay down one universal rule, founded on the very condi- tions the very possibility of human thinking ; for Induction we can do no such thing. Violate the syllogistic law and thinking no longer exists ; it is only in appearance. Violate any of the laws of Induction, and you do not abolish the process ; you only conduct it wrongly. There is thus the absolute distinction between what is fundamental in human thought the very condition of it and what is needed in the application of thinking. An incoherent syllogism is not a syllogism ; is not even thinking. An imperfect, hasty, or un- warranted induction is still an induction, only a bad one. 590. "Almost all induction," says Hamilton, " is necessarily imperfect ; and Logic can inculcate nothing more important on the investigators of nature than that sobriety of mind which regards all its past observations only as hypothetically true, only as relatively complete, and which, consequently, holds the mind open to every new observation, which may correct and limit its former judgments." 1 Mr Jevons has amply endorsed this opinion. 2 "No imperfect induction," he says, " can give a certain conclusion. It may be highly 1 Logic, iv. p. 170. 2 EL Logic, p. 213, cf. p. 223. 462 INSTITUTES OF LOGIC. probable or nearly certain, that the cases unexamined will resemble those which have been examined, but it can never be certain. It is quite possible, for instance, that a new planet might go round the sun in an opposite direction to the other planets. . . . Mistakes have constantly occurred in science from expecting that all new cases would exactly resemble old ones. Imperfect induction thus gives only a certain degree of probability, or likelihood that all instances will agree with those examined." 591. This is not the place to enter on a discussion of the ground of the principle of the Uniformity of Nature, as it is called, or of the belief in Cosmical Order. I can afford space only for a remark, in passing, on Hume's well-known view on the subject, and for a few paragraphs in which what seems to me the true theory may be indicated. It may fairly be said that the ground Hume alleges viz., custom or customary experience is obviously insufficient as a ground, on his own theory of knowledge, or on any theory of knowledge. Custom is but repetition, or the constant recur- rence of impressions in a certain uniform order. Whence, we ask, is this recurrence, this uniform recurrence, this order in the subjective impressions? From the Ego, is it? Does it depend on a permanent self in consciousness amid the im- pressions ? No ; for, according to Hume, there is no such thing, no self or subject of impressions. But whence, then, does the order come, the custom of the uniformity in the impressions ? Not surely from the custom itself ; for while this may be put forward to explain the expectancy of the recurrence in the future, it cannot reasonably be taken as ex- plaining itself. Whence still, one asks, a customary uniform order of impressions, if there be nothing behind it, or along- side of it, acting in a customary and uniform manner ? Would this not be not only the most mysterious but the most irra- tional of all conceptions of the fact, to say nothing of the origin, of experience ? And, further, how possibly can there be a known series or order of impressions, many, varied, successive, if there be no permanent knower in or amid the series subsisting through time, looking behind and before, and through a continuous knowledge grasping the isolated impressions, as they fly, into one comprehended whole of succession ? GKOUND OF INDUCTION". 463 592. The principle known as that of the Uniformity of Nature, which is at the root of inductive illation, may, as I think, be regarded as founded on causality, and as simply its manifest application. We have, in inductive illation, the fol- lowing stages (1.) The ascertainment by observation, analy- sis, experiment of the number of cases, which varies in dif- ferent matter, necessary for the inference that they depend on a definite cause. The problem here is truly to distinguish casual sequence from causal sequence. For this no one gen- eral rule can be given, either a priori or founded on experi- ence, such as we have in Deductive Inference. (2.) Once the step is taken from merely casual to causal sequence, we then attach the uniformly observed to a cause, and to this or that cause. The cause is known as existing, and as manifesting certain definite relations or properties. It has now two features, (a) that of permanency or stability, and (6) that of uniformity implying generality. For if a cause acts, and always in a similar way, the law of its action is general. If the mode of action is changed, the cause itself is changed. 593. (3.) Induction is not confined to cases in which the causes are merely similar ; it operates where the cause is it- self single, but subsists during a continuance of time. When precisely the same cause numerically one is found after a lapse of time, by inductive inference we predict that its mani- festations will be as they were originally inductively estab- lished. The same hammer which split the stone yesterday, is expected, when applied in the same circumstances, to split another stone to-day. Let the wind withdraw the cloud from the sun, and it will be expected to shine now as it did an hour ago. 594. (4.) The inductive illation of cause from observed uniformity of sequence extends beyond the same permanent cause to similar causes that is, to causes sensibly similar for thus only by sense-appearance can we judge of similarity in causes. Hence we get the general principle at the root of all induction which takes in similars viz., that of general effects of the same genus the causes are the same, or similar causes produce similar effects, or similar antecedents are followed by similar consequents. 595. (5.) The principle, accordingly, of the uniformity of 464 INSTITUTES OF LOGIC. nature, or of the expectation of similar consequents from similar antecedents, is resolved into two elements : ^ (a) The conception of a cause as manifesting certain prop- erties or effects. (b) The presumed stability of the cause, on the ground mainly that we do not know, or have not observed, that its causal efficiency has been impaired or destroyed. This could only be done by the supposition of another cause acting in the interval, and impairing, destroying the efficiency of the cause whose operations were inductively known. On the absence of any knowledge to this effect, we continue to expect that the cause we have known as operating will subsist and operate as before. This applies especially and in the first instance to a cause which is the same in time, or numerically one. It applies, in the second place, and not less, to a cause similar to the cause which we have known as operating. For here we connect the sensible appearance of the cause with its causal efficiency, as we did in the first instance observed. We suppose that under a similar appearance we shall find a similar causal efficiency, and this because we have not observed or do not know that another cause has been in operation to deprive it of this supposed efficiency. This seems to me to be the genesis of the principle known as the uniformity of nature. It is the only theory of it which fully accounts for its place and character in our knowledge, for the principle, while it is almost universally operative in ordinary experience, in the conduct of affairs, in the guidance of life, in professional work, and in the highest science, is never necessary, never gives results of absolute irreversible import, yet leads with probability, and even cogently con- strains. And this feature of it its most characteristic feature is at once explained by the fact that our expectation of recurrence in the future is determined by the condition that we do not know that any negative or destructive caxise has been at work. This theory of the Inductive Principle is at once positive and negative, or rather is positive and non- negative. It supposes a cause, and a cause to subsist, until the proof of its negation or destruction has been given. It is thus in its essence a principle simply of Probability. 596. (6.) This principle of uniform expectation being once in operation, it receives confirmation from the fulfilment of ANALOGY. 465 the expectation in given cases. Every time we expect a similar consequent from a similar antecedent, and find it follows, our belief in the principle of uniformity is strengthened. This confirmatory experience reacts on the original pre- sumption of uniformity, until it gradually becomes one of our most familiar, most firmly established, and most trusted principles. 597. While Syllogism is an inference from whole to part, and Induction an inference from the parts to the whole, Analogy may be regarded as inference from individual to individual, or from part to part. 1 Generally speaking, the inference of Analogy is founded on similarity, and it proceeds from partial to total similarity in objects, from likeness in some points to likeness in all The formula of it is : Many in one, therefore all in one. In Induction we proceed from the fact that a property or mark belongs to many objects of a class, and infer that it belongs to all of the class. The formula -is : One in many, therefore one in all. 2 598. Analogy must not be confounded with Proportion, or a resemblance of ratios. Thus we have proportion when two numbers agree in being half of another yet different number, as 2 is to 4, as 5 is to 10. These are definite or known ratios in each case. In Analogy proper there is a similarity of objects in certain known properties, and an inference to similarity in certain other unknown or unobserved properties. 599. The Inference of Analogy has two main forms, (1.) It may proceed from some individuals of a class to another or other individuals of the class ; (2.) From several known attributes in an object to other attributes in that object not known or observed. In both cases, however, it proceeds from the known to the unknown from the individual to the individual, or from the mark to the mark. These are not essentially different forms of Analogy. 600. Of the First Form of Analogy the rule may be thus generalised : (1.) A property which is known to belong to several members of a class, probably belongs to another member of that class, in which it is not observed or not capable from circumstances of being observed, provided * Cf. Aristotle, An. Pr., ii. 24. 2 Cf. Kant, LogiL; 84. Krug, Logik, 168. Hamilton, Logic, iv. p. 173. 2 G 466 INSTITUTES OF LOGIC. always the known property belongs to the several members of the class in their generic capacity. Thus, in letters : A, B, C, D (individuals of a class X}, have the property Y; F also belongs to the class X Therefore probably F has the property Y. Ceres, Pallas, Juno (all of them planetoids), have the property of greater eccentricity of orbit ; Vesta is also a planetoid ; Therefore probably Vesta has the property of greater eccen- tricity of orbit. 601. Of the Second Form of Analogical Inference the rule may be generalised as follows : (2.) If one object agrees with another in certain known properties, it is probable that it will also agree with it in all its other properties, in so far as these are generic and not individual merely. Thus, in letters : If we find in X the marks a, b, c, d, and if we find in Y a, b, the probability is, that Y also contains the marks c and d. Or This disease has the marks a and b ; a and b are usually accompanied with c and d in jaundice This disease will probably develop the marks c and d ; In other words, The disease will probably be jaundice. The Earth, a planet, revolving on its axis, having an atmos- phere, water, change of seasons, $c., supports organic life ; Mars is a planet, revolving on its axis, having an atmosphere, water, change of seasons, $c. ; Therefore Mars probably supports organic life. 602. In both those forms the force of the argument will increase in proportion to the number of the resembling fea- tures, their nature as not temporary and individual, but as permanent and generic. We shall fall into error, as we found on attributes known to be common to the two objects, while the unobserved attribute inferred is connected not with these but with points of difference between the objects. Thus X may resemble Y in the points a, b, and it may also possess the ANALOGY. 467 points c, d, because it is one individual and Y is another, in this case we should have no inference. If X be a statesman, able, eloquent, modest, and truthful ; and Y is a statesman, able and eloquent; it does not follow that Y is modest and truthful. For modest and truthful are by no means generic properties of a statesman. 603. Another element which adds to the force of Analogical Inference especially in the Second Form is that of time or circumstance in which a particular set of marks may be ob- served. If, for example, in the course of a disease, not exactly known as to its nature, the physician were to note the develop- ment in succession, or in anticipated circumstances grounded on previous observation, of certain symptoms, he would, with the probability of being right in the end, infer that the other symptoms which usually follow these would in due course be developed, and thus be able to forecast the real nature of the malady. He would, in a word, infer the unknown from the known the undeveloped from the developed on the principle of Analogy ; and the force of the inference would depend not only on the nature of the symptoms, but on the fact of their specification or precise limitation in time. 604. One special form of analogy the Third may bo called that of Analogy of Function. Thus the geologist who finds a fossil skeleton similar to the structure of an animal of the present day fitted to browse on herbage, will readily infer that this also was a function of the creature whose fossil remains are found. This can hardly be said to be similarity in another or new property, but the completion or integra- tion of the idea involved in structure. Yet it is properly an Analogical Inference. 605. Both Astronomy and Geology are now prosecuted in the large spirit of analogy. Laws of motion, similar to those on this planet are supposed to hold in regard to the planetary bodies. And the causes and laws of change operative on the globe at the present time, are accepted as the grounds of ex- plaining the geological phenomena of the past. 606. In Induction, and also in Analogy, the essential point is the determination of the value of the individuals or of the attributes as capable in the one case of standing for the whole members of the class ; in the other, of guaranteeing the community of the further attribute or attributes inferred. 468 INSTITUTES OF LOGIC. And the inference in each case points to a common cause or principle upon which the individuals and the attributes, ob- served and unobserved, but inferred, are to be taken as dependent. 607. Induction and Analogy are to a large extent the grounds of syllogistic inference, inasmuch as it is from them that we obtain our major proposition ; but they are not the regulative principles of the pure illation. Nor is it correct to say, as Hegel apparently does, 1 that these are the only grounds or bases of universality in the inference. Geometry, not less than Metaphysics, repudiates this. 469 CHAPTER XXXV. THE METHODS OF INDUCTION. 608. It has been said (1.) " That in the complexity of things or sequences, observation and experiment are needed to analyse the accidental from the essential or permanent, and to determine regarding a given phenomenon that upon which its real existence depends that is, its cause or condition for all the finite is conditioned. (2.) "That we must seek not only the conditions which determine the existence of a phenomenon, but the properties which exclude it or which are indifferent to it." l We thus need certain rules and methods of Observation and Induction, in virtue of which we may find what is in- variably connected in experience ; mainly, in a word, distin- guish the casual from the causal, what is connected simply by arbitrary or contingent association from what is linked together objectively, or in the order of nature. 609. The aim of Inductive Method with Bacon is the search after " Form." Concrete substances are made up of " simple natures " or qualities they are " forme copulates " ; if we can reach the form of the simple nature, we can see how it is pro- duced, and thus proceed to the composition of substances. The forms of substances are, at least, ultimately discoverable. A substance with him means a congeries of qualities. Qualities are " simple natures " ; but form is ambiguous. It is taken to mean essence, definition, &c., of a thing, and the cause, hence law, of a thing. Form thus applies to the essential 1 Franck, Diet. Phil. Ind. 470 INSTITUTES OF LOGIC. qualities of a class, to the attributes of a concrete substance, or to a quality itself. 1 610. As in an object the essential qualities are those upon which certain other or derivative qualities depend may depend even as their cause ; and as the form of a quality is really the cause of that quality, the two meanings of form come to coincide. The essential qualities, for example, of a trian- gle or square are given in the definition, and on these all the demonstrated properties depend. The form or cause of heat, to use Bacon's illustration, is motion a kind of motion. Thus the search after form resolves itself practically into the search after causes. If by cause we understand, as we ought to do, not only what as a determination precedes the effect or consequent in time, but that also which is concomi- tant with the effect in time, the expression " form " may well take in the whole scope of causal relation as sought for by induction. 611. The essential point of Bacon's inductive Method lies in Exclusion (Exclusiva) : " Inductio mala est quse per enu- merationem simplicem principia concludit scientiarum, non adhibitis exclusionibus et solutionibus, sive separationibus naturas debitis." 2 Again : " Naturam separare debet, per re- jectiones et exclusiones debitas ; ac deinde, post negativas tot quot sufficiunt, super affirmativas concludere." 3 Again, more particularly, he says : " Est itaque Inductionis verge opus primum (quatenus ad inveniendas formas) rejectio sive exclusiva naturarum singularum, quse non inveniuntur in aliqua instantia, ubi natura data adest ; aut inveniuntur in aliqua instantia, ubi natura data abest ; aut inveniuntur in aliqua instantia crescere, cum natura data decrescat ; aut decrescere, cum natura data crescat. Turn vero post rejec- tionem et exclusivam debitis modis factam, secundo loco (tanquam in fundo) manebit (abeuntibus in fumum opinion- ibus volatilibus), forma affirmativa, solida, et vera, et bene terminata." 4 612. As aids to the Method of Exclusion, Bacon gives the three tables viz. : (1.) The table of Presence or the appearance (comparentia) to the intellect of all known instances, which agree in the i Of. Fowler, Nov. Org., Int. 2 Nov. Org., i. 69. 3 Ibid., i. 105 ; cf. ii. 15, 16, 19. 4 Nov. Org., ii. 16 ; cf. ii. 19. BACON'S RULES. 471 same nature, although the matter or circumstances are most unlike. (2.) The table of Absence, or the appearance to the intel- lect of instances which want the given nature ; because the form, as has been said, ought to be not less absent when the given nature is absent, than to be present when it is present. (3.) The table of Comparison, or the appearance to the intellect of instances in which the nature, regarding which there is inquiry, is present according to greater and less ; whether the appearance made be of increment or decrement in the same subject or by turns in diverse subjects. . . . Any nature may not be received for the time as form, unless it uniformly decrease when the nature itself decreases ; and, in like manner, is constantly increased when the nature itself is increased. 1 613. After the tables, Bacon proceeds to state certain re- maining auxiliaries of the intellect in seeking a true and per- fect interpretation of nature and induction. Under this head he gives the first place to " the Prerogatives of Instances " (Prcerogativis Instant iarum). These are " characteristic phe- nomena selected from the great miscellaneous mass of facts which occur in nature, and which, by their number, indis- tinctness, and complication, tend rather to confuse than to direct the mind in its search for causes and general heads of induction." 2 614. First among the Prerogative Instances, Bacon places the Solitary Instances (Instantias Solitarias). Those are solitary instances, he says, which exhibit the nature concerning which there is inquiry in such subjects as have nothing in common with other subjects, except that nature itself ; or again, which do not exhibit the nature regarding which there is inquiry in such subjects as are similar through all with other subjects, except in that very nature itself. It is manifest that instances of this sort remove doubts, and accelerate and strengthen the exclusion ; so that a few of these are equivalent to many. This and other examples which follow in illustration, leave but little to make explicit Mill's 1 Nov. Org., ii. 11, 12, 13. 2 Herschel, Discourse on Study of Natural Philosophy, % 190. Cf. Fowler, Nov. Org., ii. 21. 472 INSTITUTES OF LOGIC. methods of agreement and difference. 1 Bacon even speaks of the instances solitary, " quatenus ad similitudinem " ; and those solitary, " quatenus ad discrepantiam." 2 The Instantice Migrantes, under the Prerogative, readily suggest the method of Concomitant Variations. 3 615. Among the Prerogative Instances, Bacon has the Crucial Instance (Instantia Cruets). This means an observation or experiment which by its nature definitely settles one or other of two or more hypotheses, or possible antecedents, as the true one. We suppose nothing changed, except a partic- ular antecedent as present or absent ; and with this we find the effect in question, present or absent. This readily sug- gests the method of Difference. 4 616. The Tables given by Bacon, and other statements, seem to indicate that he supposed science was to be built up, first, by observation of facts arranged as the same or different ; secondly, by induction therefrom, giving us laws of more or less generality, the axiomata media ; and thirdly, from these intermediate laws rising to the highest generalisa- tions. This cannot be taken as the sole mode in which science has progressed since his time ; for the element of Deduction, making use of the imperfect or limited general- isation in new spheres, and where the antecedent or cause was not observable, has done most to build up our know- ledge of the physical universe. But the method of Bacon did forecast the mode of certain discoveries, and in its re- verse form it is that in which the ascertained laws of science are best stated. And its influence as a protest against arbitrary anticipation of the order of nature cannot be over- estimated. 617. As has been pointed out by Herschel, Mill, and frequently illustrated by Professor Fowler, Bacon's Method of Exclusions " proceeds on the assumption that every phaeno- menon has only one cause, that is to say, is due to only one set of conditions. Of the ' simple natures ' there is some one, and one only, which, if it could be found, is the ' form ' of the natura data. But the same event may be due to one set of conditions at one time, and to a different set at another. 1 Novum Organum, ii. 22. 2 Cf. Professor Fowler's admirable edition of the Novum Organum, p. 409. 8 Nov. Org., ii. 23. * Nov. Org., ii. 36. METHODS OF INDUCTION. 473 Hence, though it is invariably true that the same cause is always followed by the same effect, the converse proposition that the same effect is always due to the same cause would frequently be misleading." l 618. Mill has well analysed the methods of Induction, and gives certain Rules or Canons, which, though open to criticism in expression and details, are in substance those generally received. Mill, in fact, has made explicit what Bacon foreshadowed, and what Herschel had already in the main put more clearly. The First Method called the Method of Agreement is thus stated : " If two or more instances of the phenomenon under investigation have only one circumstance in common, the circumstance in which alone all the instances agree, is the cause (or effect) of the given phenomenon ; " or, as it has been put, " the sole invariable antecedent of a phenomenon is probably its cause." 2 619. In order to make this canon available, the first re- quisite is ample observation of the circumstances or actual antecedents of the phenomenon in question. When we find among those antecedent circumstances that there are some whose presence or absence does not affect the actiial occur- ence of the phenomenon or event, we infer that these are not essential to it ; in a word, that they are casual not causal. If, however, we be able to find an antecedent, either one cir- cumstance or sum of circumstances, which alone invariably precedes or accompanies the phenomenon, we are entitled to infer with probability that that is the cause, or that the phenomenon depends on it as effect. But we ought to ob- serve in regard to this method, that all which it tells us is simply that the antecedent is the cause in the given circum- stances ; in other words, it is a cause of the effect, but not necessarily the only cause, or the cause at all times and in all circumstances. 620. As has been pointed out by numerous logicians, and in these days emphasised by Mill and others, the same (similar) phenomenon, or event, or effect, may follow from several different causes. This was the very commonplace of logic and of usual prac- tice ere modern ignorance invested it with the dignity of a 1 Fowler, Nov. Org., Int., p. 62. 2 Jevons, Logic, 241. 474 INSTITUTES OF LOGIC. discovery. Even Roger Bacon taught it, as common-sense had forestalled him. Electricity, for example, may be excited by friction, cleav- age, pressure, change of temperature, motion of the magnet, &c. Supposing, therefore, that electricity as an effect is pres- ent in different times and circumstances, it does not follow that this particular antecedent, which is a known cause of it, is the actual cause in each of the instances. One of the other causes may be in operation. But if we find one ante- cedent constantly present when the phenomenon occurs, and constantly absent when the phenomenon does not occur, there being no other change in the circumstances, we may infer that that antecedent is the cause of the phenomenon in question. 1 Hence the need of the second Rule or Canon the Method of Difference. It is thus stated : " If an instance in which the phenomenon under investigation occurs, and an instance in which it does not occur, have every circumstance in common save one, that one occurring only in the former, the circum- stance in which alone the two instances differ, is the effect or the cause, or an indispensable part of the cause, of the phenomenon." " We learn," says Jevons, " that sodium or any of its com- pounds produces a spectrum having a bright yellow double line, by noticing that there is no such line in the spectrum of light when sodium is not present, but that if the smallest quantity of sodium be thrown into the flame or other source of light, the bright yellow line instantly appears." 2 A dead body is found floating in the river. We might infer at once that drowning, or suffocation through drowning, was the cause of death. This would be simply on the Method of Agreement. This would be a sufficient cause, and it is (possibly) present. But suppose we find a sword-wound in the body, obviously dealt while living, sufficient to cause death, we should at once attribute the death or event to another cause or antecedent. Here the circumstance in which the two cases differ is the cause. We find, for example, that electricity can be produced by friction ; and seeing that the body thus electrified loses its electricity after a time, when the friction has ceased, we 1 Cf. Jevons, Logic, p. 242. 2 Logic, p. 243. METHODS OF INDUCTION. 475 prove that this was the cause, as by renewing the friction we again electrify the body. Here we have, first, the presence of the antecedent, then its absence and the absence of the consequent ; we have the renewed presence of the antecedent and the renewed appearance of the consequent. This is the great Canon of Experiment, and of what may be called Concentrated or Exclusive Observation. We ask what, among other concomitant circumstances, is the cause, or at least indispensable condition of life in the animal ? We isolate one known circumstance, we with- draw from the breathable atmosphere one of its elements oxygen and the animal speedily dies. Oxygen is thus proved indispensable to life. In order to test the effect or consequents of a particular cause, the essential preliminary is its isolation as far as pos- sible from the concomitant circumstances, or placing it in a position where its specific action can be definitely ascer- tained. It is thus only we can truly study its proper or specific effects. Of this Pascal's well-known experiment on the column of mercury in the Torricellian tube may be given as a good illustration. It was surmised that the column of mercury in the tube was sustained or counterpoised by the weight of the air. Is this so ? was the question. Pascal argued if it be so, when the weight of the air is diminished, the mercury ought to stand lower. On carrying the mercury in the tube up the mountain the Puy de Dome, " the weight of the incum- bent air was diminished, because a shorter column of air was to be sustained ; the mercury in the barometer ought to sink, and it was found to do so accordingly." l This experiment proceeded on a certain isolation of the main circumstance, and it may be taken also as illustrating the Method of Con- comitant Variations. Bacon would probably have called it an Instantia Migrans. 621. Mill's third canon is the Joint Method of Agreement and Difference. It is thus expressed : " If two or more instances in which the phenomenon occurs have only one circumstance in common, while two or more circumstances in which it does not occur have nothing in common save the absence of that circumstance, the circumstance in which alone i See Playfair, Prel. Diss. En. Brit. 476 INSTITUTES OF LOGIC. the two sets of instances (always or invariably) differ is the effect or the cause, or an indispensable part of the cause, of the phenomenon." This is the rule, as amended by Jevons. 1 There is a reference in this canon to those cases in which the effect is present, and also to those cases in which the effect is absent. This is virtually a union of Bacon's two tables Presentice and Absentice. 622. By a cause we ought not to understand merely a single antecedent. As a rule the cause of a phenomenon is itself a sum of phenomena or antecedents. The cause, in fact, is made up of con-causes or conditions, all acting together, and producing a definite effect. Now there are cases in which the resultant effect is wholly different in kind from that which would follow from each of the con-causes, supposing them to act separately. Thus oxygen and hy- drogen together produce water, but neither of them would produce it by itself. And so generally of chemical com- binations. The man, the gun, the shot, the powder, the percussion-cap together, produce a result which neither of them has separately. But it may happen that the total effect is of the same kind as that which would be produced by each of the antecedents taken singly, though probably less in degree or quantity. The result, as it has been phrased, is homogeneous. Thus, to borrow an illustration, friction, com- bustion, compression, &c., all in operation at one time will produce the same common effect heat. The cuirassier and his armour will both result in weight for the horse. The question thus arises how, in such instances, we are to deter- mine what or how much of the joint common effect is due to each con-cause ? How are we to find the proportionate result? In order to this, we must know or ascertain the amount due to one or more of the con-causes. Mill gives the following direction or rule called that of the Method of Residues. " Subduct from any phenomenon such part as is known by previous inductions to be the effect of certain antecedents, and the residue of the phenomenon is the effect of the remaining antecedents." Thus it would be easy in the instance given to tell the weight which the rider con- tributed to the sum total, if, knowing that sum, we knew also the weight of the armour. i Logic, pp. 245, 246. METHODS OF INDUCTION. 477 In Dynamics, where we are dealing with the sum of a series of forces, we can ascertain the relative degrees only by separating the effect of each concomitant force. In Chemistry this method is constantly employed " to determine the proportional weights of substances which com- bine together." Thus after an ingenious process, known to chemical analysis, it is found that " 88 '89 parts by weight of oxygen unite with 11*11 parts of hydrogen to form 100 parts of water." l In Astronomy its use is constant. The residual irregular- ity of Uranus, after deduction had been made of the effects of all known attractions on it, led Adams and Leverrier to the inference of the existence of a planet beyond, and thus to the discovery of Neptune. It is easier, perhaps, to lay down this rule of induction, like some of the others, than to put it in practice. We may take the effect known in these days as the depression of trade. To this no doubt several causes concur. We have, probably, over-production, excessive competition at home, foreign com- petition, the appreciation or comparatively higher value of gold, exclusion from foreign markets, the result of sending shoddy exports abroad, &c. ; but it would puzzle most people to tell how much depression is due to each cause. And it does not help us much to ask us to determine, in the first place, through previous induction, how much is due to this or that of the complex causes or con-causes actually in operation. In the case of a complexity of motives, terminating in a single action, the application of this rule would be exceedingly difficult, if not impossible. The motives or con-causes of the action might be self-interest, fear of consequences, shame of exposure, sense of duty. It is conceivable that any one of these, taken singly, would not have been powerful enough to lead to the action in question ; but all combined might result in the particular action or course of conduct. But how would it be possible in such circumstances to estimate the force of each ? The canon is obviously of use only where the causes are quantitative and capable of separate measurement, or where . each cause is known to be related to a definite part of the total effect. 623. But a phenomenon or effect not only depends on a 1 Cf. Jevons, Logic, p. 254 ; Roscoe, El. Chem,, p. 38. 478 INSTITUTES OF LOGIC. certain antecedent or cause, it may depend for its quantity or degree on the quantity or degree of the cause. For precise scientific statement, it is not enough merely to ascertain the uniform antecedent, we must further seek in most cases to ascertain the relation between the degree of the antecedent and that of the effect. This seems to be what Bacon points to in the tables of Comparison or Proportion. In the case of an effect which admits of more or less of quantity, it is clear that the cause, as more or less, will produce an effect differing in quantity or degree. Effect is always proportioned to cause, and a less degree or quantity is as much effect of its cause, as if that cause were exercised to the full. The degree of temperature which makes water simply warmer, is as much a cause as that which makes it boil. The difference is not in the causal relation, but simply in the degree of it, or in the correlation of the cause and effect. There may be, as Sir John Herschel has put it, " increase or diminution of the effect, with the increased or diminished intensity of the cause, in cases which admit of increase and diminution." " It is necessary to inquire," says Franck, " whether prop- erties which we have recognised in an individual, in a species, or in a genus, are not produced in different proportions according to different circumstances, and whether these pro- portions themselves can be led back to a uniform rule. It is thus only that induction can attain the knowledge of laws, and that these laws, in certain cases, can receive the sanction of reasoning and the calculus." Hence the further canon, as stated by Mill, that of the Method of Concomitant Variations: " Whatever phenomenon varies in any manner wherever another phseomenon varies in some particular manner, is either a cause or an effect of that phenomenon, or is connected with it through some fact of causation." The canon as thus put, points to the proof of the cause which variation gives us ; but its true value rather lies in the precision of proportion to which the canon con- tributes. We have familiar examples of this rule in our ordinary ex- perience. Every time we exert force or pressure, we know that the effect say the degree of motion of the body on which we act is determined by the degree of force or pressure METHODS OF INDUCTION. 479 which we put forth. In the case of heat, we find that a body expands, generally speaking, according to the degree of tem- perature. We find that water grows warm, and finally boils, according to the continuance and increase of the temperature applied to it. The " waxing " and " waning " of the moon may be taken as a good illustration of the method of Concomitant Varia- tions. Both in the " waxing " and in the " waning," the varying amount of illuminated surface displayed by the moon to a spectator on this globe, depends on and corresponds with the varieties in her motions and positions as receding from or approaching the sun. We have with increase of distance, increase of light, and with decrease of distance, decrease of light. After what is known as " new moon," the moon, from a thin crescent, with the horns turned to the east, grows, as she increases her angular distance from the sun, to a semi- circle of light. When the moon, after passing through the " gibbous " stage, reaches the position of 180 in advance of the sun, she appears as full moon, and the whole illuminated disc is visible. From this point, beginning to draw nearer to the sun, she gradually wanes, passing again through the " gibbous " phase to the stage of the last quarter or semicircle of light. Nearing the sun still more, she reassumes the crescent form, with the horns turned to the west, and grad- ually passes into the darkness of the position of the " new moon." Here you have a series of concomitant variations be- tween the elements of motion, distance, position, on the one hand, and degrees and forms of illumination on the other. Jevons gives a very good illustration of variations " in the connection which has of late years been shown to exist be- tween the aurora borealis, magnetic storms, and the spots on the sun. It has only in the last thirty or forty years become known that the magnetic compass needle is subject at inter- vals to very slight but curious movements, and that at the same time there are usually natural currents of electricity produced in telegraph wires, so as to interfere with the trans- mission of messages. These disturbances are known as mag- netic storms, and are often observed to occur when a fine display of the northern or southern lights is taking place in some parts of the earth. Observations during many years have shown that these storms come to their worst at the end 480 INSTITUTES OF LOGIC. of every eleven years, the maximum taking place about the present year, 1870, and then diminish in intensity until the next period of eleven years has passed. Close observations of the sun during thirty or forty years have shown that the size and number of the dark spots, which are gigantic storms going on upon the sun's surface, increase and decrease exactly at the same periods of time as the magnetic storms upon the earth's surface. No one can doubt, then, that these strange phaenomena are connected together, though the mode of the connection is quite unknown. It is now believed that the planets Jupiter, Saturn, Venus, and Mars are the real causes of the disturbances ; for it has been shown that an exact correspondence exists between the motions of these planets and the periods of the sun-spots. This is a most remark- able and extensive case of concomitant variations." 1 At the same time, it must be observed that this is a wholly em- pirical concomitance. We know only that great variations mutually correspond, but we do not see or know the link of connection. 624. Where the relation of Cause and Effect enters into the strictly inductive illation, that is, truly the valid con- stitution of the minor premiss, that some stands for, or is equal to all Ueberweg has well summed up the rules in operation : (1.) " Inductive inference has strict universality when S (the subject) contains the sufficient reason of P (the predicate) ; and when P is related to S as its only possible cause or con- ditio sine qua non ; and, lastly, when S and P are both neces- sary consequences of a common cause, sufficient for P and the only possible cause of S." (2.) " Induction leads only to comparative universality, or to rules which may be limited by exceptions, when S is only a single co-operative cause or condition of P : or when, on the other hand, P is not the possible cause of S, or when S and P are consequences of a common cause, but may also result singly under different conditions." 2 625. The place of Hypothesis in science and of a limited induction, which comes to be much the same thing, is that of inciting to testing and verification. The question really is, Does the hypothesis in question does the limited law I 1 Logic, p. 251. - Logic, p. 486. HYPOTHESIS. 481 have already got by induction explain the facts, more of the facts, all of the facts ? Does it extend to cases where I can- not observe the cause already in operation, but the results of which seem to be in conformity with this as the cause ? What is its probability, its generality ? This is frequently to be tested by deduction Material Deduction. This means taking the conception formulated in the hypothesis, or taking the limited uniformity, and calculating with this as a basis what should happen in certain circumstances, or in a sphere wider than that already embraced by us. This is experimen- tal rather than observational. Newton might apply the con- ception of gravity to the motion of the moon to discover whether attraction subsisted between it and the earth. Ob- servation of the facts corresponded with the results of the deduction that is, what ought to be the hypothesis or limited law extended to this new sphere. And so with the moon and the sun. Doubtless this is the way in which science progresses, and this was not a form of method, at least explicitly contemplated by the modern founder of In- ductive Method Lord Bacon. At the same time it is not just to say that Bacon limited scientific method simply to observation and induction from facts and laws of increasing generality. His Prerogative Instances, especially the Mi- grantes and Crucial, show how he could look at characteristic facts, and specially select them. Modern Deductive Method is in no way incompatible with Baconianism. Bacon's de- nunciation of "the anticipation of nature," as opposed to " the interpretation of nature," was eminently sound. In warn- ing men against projecting their mere "conceits" into the course of nature, and thinking they find them there, Bacon did an incalculable service to science. Facts are the first thing conceptions, hypotheses, modes of explanation may follow. He fully admits the value of hypotheses that is, of questions to put to nature. The most and best questioning man will be the discoverer in the end, provided he has caution, zeal, ap- plication, as Newton had. But testing, verification, deduc- tion are in the end to appear before the bar of Observa- tion ; and it is because of the harmony which subsists between the most laborious, the most ingenious deductive results and the facts as tested by observation, that Deduc- tion as a method has its value in relation, at least, to the 2 H 482 INSTITUTES OF LOGIC. physical universe. We use deduction when we cannot ob- serve the cause, but only suppose it. All the same, the result of the deduction, in order to have any validity, must harmon- ise with the facts, or supposed effects as observed by us. If Newton showed that there was attraction between the earth and the moon, by reasoning deductively, the criterion of this reasoning was the harmony between the actual motions and positions and the result of the deduction. And so it is in all cases where a conclusion arrived at deductively reaches full verification or certainty ; otherwise, the supposition in- volved is only a probable hypothesis. Of this we have an illustration in the supposition that the brighter parts of the moon consist of mountains. These, in themselves, are be- yond direct observation : yet this hypothesis explains certain appearances which those parts present. They are found (1.) to cast shadows when the sun's rays fall upon them obliquely ; (2.) in the interior illuminated border of the moon there are points illuminated before the others, thus showing them to be higher. The hypothesis, thus, of a mountainous surface is rendered highly probable. The facts we observe, are as if there were mountains of a great ele- vation. 626. The rules of Induction are, as it seems to me, not really by themselves rules of discovery; they are rather rules of guidance and verification or testing in the process of dis- covery. The discoverer must start with an hypothesis a question to put to nature or the facts. This is the guiding spirit of investigation : if, with this in his mind, he tests its applicability according to the canons of induction, he will do well either in finding in it a probable solution, or in casting it aside as useless. And, certainly, before he can vindicate his theory to the world, he must show that his hypothesis has fulfilled those conditions. As to the value of the rules of Induction in the matter of culture, they are wholly secondary as compared with the high abstract training, the precision of logical thinking, the orderliness of thought, the power of consecution, which are developed by the study of Formal or General Logic. Compared to this, their influence is weak and unsteady as is the swaying chaos of fact in the world compared with the grasp of the universal laws which regulate concepts, proposi- VALUE OF RULES OF INDUCTION. 483 tions, and reasonings. And while in the world of physical phenomena definite, visible, tangible, or to be reached by microscope or telescope they are valuable and important, they cannot for a moment be placed on the same high level as those laws which regulate all human thinking in its very essence, its very possibility form, in fact, the conditions of any concept, any judgment, any reasoning whatever. These are the first things to be studied, and the man who knows not these in their grounds and basis, is, whatever he may know of rules applied to so-called phenomena, a mere empiric. 484 CHAPTEE XXXVI. QUASI-SYLLOGISMS EXAMPLE ARISTOTELIC ENTHYMEME. 627. What is known as Reasoning from Example has an apparent likeness to Analogy. In Example the process is from one particular to another particular, similar to the former. Thus we may say : Socrates (a philosopher) was modest; therefore Diogenes (a philosopher) was modest. In this there is really no valid in- ference the one particular does not necessarily imply the other. If, further, we explicate what is apparently involved in the one premiss, we should have Socrates is modest ; therefore all philosophers are modest, which is a paralogism. We need somehow to connect modest and philosopher into a universal proposition, All philosophers are modest, and this is not provided for by the terms of the propositions or data given us. 1 Yet this is typical of the reasoning from Example set forth by Aristotle. His reasoning from Example (TrapaSeiy/xa) is really a com- plex process, consisting (1.) of an inference so-called, from one single case to every case of the same kind ; (2.) of a syllogism properly constituted, in which the supposed uni- versal conclusion of the first reasoning becomes the major proposition of the second. Aristotle defines Example as that in which, among three notions, the extreme is affirmed of the middle through a term similar to the third. But we must know, he adds, that the middle is with the third term, and that the first is with the similar term. 1 Cf. Duncan, Inst. Log., L. iv. c. vii. 2. EXAMPLE. 485 Thus, to take his own illustration, which may be put thus : (a) The war by the Thebans (neighbours) against the Phocians was destructive ; Therefore the war by the Athenians (neighbours) against the Thebans will be destructive. This implies the reasoning (6) The war waged by the Thebans against the Phocians was destructive (A is A) ; That was a war against neighbours (A is B) ; Therefore every war against neighbours is destructive (B is A). Then we have the following : (c) B is A ; T isB; .'. F is A ; Or Every war against neighbours is destructive ; The war of the Athenians against the Thebans would be a war against neighbours ; Therefore this war would be destructive. 628. The latter reasoning is perfect ; but the major, every war against neighbours is destructive, depends on the preceding reasoning, if it can be called such, which it is not in any proper sense. It may be brought under the head of Imperfect Induction ; but it is a thoroughly weak case. The point to be established, which is not, but is simply assumed or left to be inferred from the nature of the case as known to us, is the connection between the destructiveness of the war and its being between neighbours. As Aristotle himself points out, the reasoning in the former case is really only of rhetorical import or influence fitted to persuade, but not cogent enough for conviction. Or, to take another illustration : (a) A (a statesman) is patriotic ; Therefore B (a statesman) is patriotic. This implies the reasoning 486 INSTITUTES OF LOGIC. (b) A is patriotic ; A is a statesman ; Therefore all statesmen are patriotic. Hence we reason (c) All statesmen are patriotic ; B is a statesman; Therefore B is patriotic. The reasoning (&) is obviously a paralogism, while the reasoning (c) is formally valid; but, as borrowing its major from an unsound reasoning, is materially wrong. (a) It is evident that Example is not a relation of the whole to the part, nor of the part to the whole ; it is the relation of a part to a part, since the two terms are the subjects of one and the same, and that only the one is more known than the other. Example differs from Induction in this, that the one demonstrates, through all the particular cases, that the extreme is in the middle, and does not bind the syllogism (conclusion) to the other extreme, while example does so, and does not demonstrate through all the particular cases. (An, Pr., ii. 24.) (6) Pacius gives this illustration of the difference of Syllogism from Induction and Example : (1.) Syllogism All war against neighbours is fatal ; The war of the Athenians against the Thebans is a war against neighbours ; Therefore the war of the Athenians against the Thebans will be fatal. (2.) Induction The war of the Thebans against the Phocians, the war of the Athenians against the Thebans, and all similar wars, are fatal ; hence all war against neighbours is fatal. (3.) Example The war of the Thebans against the Phocians has been fatal ; hence the war of the Athenians against the Thebans will be fatal. (c) Example is an argument in which some Singular is inferred through one or other similar. Formally, it has no force of proba- tion, because there is no process from one singular to another unless through the universal, which cannot be concluded from the one or the other singular. (Duncan, Inst. Log., L. iv., c. vii. p. 249.) 629. The inference from one case to another similar is not a necessity but a simple presumption or probability. In a given instance, A 1 has been followed by B 1 ; in another in- stance A 2 occurring will not necessarily be followed by B 2 . EXAMPLE. 487 The presumption is that it may ; or, owing to the specific character of the instances, we may be certain that A 2 will bo followed by B 2 , as in the case of the elements of a chemical analysis. But there is here no real syllogistic inference as from whole to part, or all parts to whole. Example is but a stage in induction, and is often a good practical rule to act on in the interest of caution and the avoidance of danger. But that is all. It is no doubt the form of reasoning, if it may be called reasoning, which appeals most strongly to the average irreflective intellect. The average intelligence seldom rises above process from similar to similar, or from particular to particular. The moment the question is raised, similar in what, and why is this particular result likely to follow? we get into the sphere of Induction and the search after causes. At the same time, the presumption on which example is founded often strikes home. When, after the slaughter of King Ahaziah, Jezebel, looking from the window, called out to Jehu " Had Zimri peace, who slew his master ? " the question passed with winged force to the heart of the red-handed Jehu. 1 630. Example may be of use in illustration, though it is not a reasoning. It has, however, semblance enough to infer- ence to pass as such in popular oratory, and even in other departments of literature, as a valid argument. The majority of men are much more ready to catch at and fix on an example as at least convincing or persuasive, than to follow the links of sound argumentation, however clearly stated. The proper use of Example is to lead us to inquire whether the attribute alleged to be predicable of the second subject is really con- nected with the quality common to both. In some cases there may be a strong presumption that the attribute is con- nected with the common quality. Thus A (a Christian) was put to death under Nero, therefore B (a Christian] was put to death under Nero. If we find that B died in Nero's reign at Borne, and while other Christians were being put to death, the likelihood of his also having been a sufferer is increased. And thus example may be a help to discovery, or, at least, to some form of probability in a doubtful matter. (a) To allow, as Duncan does, that Example may be valid per i 2 King* ix. 31. 488 INSTITUTES OF LOGIC. accidens or by help of the matter is simply to give up the form, as a proper mode of reasoning. Thus, Plato is by nature risible, therefore so is Socrates, since the nature of all men is the same. The by nature introduces a universal. It is equivalent to man naturally or all man is risible. (Ibid.) 631. The Enthymeme is a reasoning from likelihood or signs, or from both in the single reasoning. It is unessential to the Enthymeme of Aristotle whether a premiss be sup- pressed or not, as is the case in the ordinary enthymeme; the reasoning would still be an enthymeme that is, " of a pecu- liar matter from signs and likelihoods." 632. Likelihood and Sign (ei/cos Se KCU o-^/xetov), says Aris- totle, are not the same. The likely is a proposition based on opinion. What people know for the most part as happening or not happening, or being or not being, this is the likely. For example, the envious hate, lovers love. The Sign, on the other hand, tends to be a proposition capable of demon- strating, either necessary or proved by the opinion of men. That which existing implies the existence of another thing, or which haVing been produced, another thing is implied as produced, before or after, this is the Sign, indicating that the thing is produced or exists. The Enthymeme, accor- dingly, is a syllogism from the likely or from signs. 1 (a) The term incomplete (art \fys ' fln&rt/3oXia (am- biguity") ; (3.) s r/ yu/r) ch-Aws (a dicto simpliciter ad dictum secundum quid) ; (3.) -f] rov eAey^ov ayvoia (ignoratio elenchi) ; (4.) Trapa TO eTro/xei/ov (fallacia ratiocinationis ex comequente ad antecedens) ; (5.) TO / dpxf? \a/j./3dvew alrfio-Oai (petitio principii) ; (6.) TO /AT) amov u>s amov TitfeVai (fallacia de non causa lit causa) ; (7.) TO TO. TrAet'w epcoT^/xaTa ev Troteiv (fallacia plurium interrogationum). 1 667. Aristotle has thus really anticipated all the forms of fallacy which have been dealt with by subsequent logicians. But the division into in Dictione et extra Dictionem is not satisfactory or well founded. The class, in Dictione, may pro- perly be referred to fallacies in the inference, to cases, in fact, in which the conclusion does not follow from the pre- misses, that is, Formal Fallacies. 668. Those under the second head, extra Dictionem, may as a rule be referred either to the class of formal fallacies, or to that of Material Fallacies, in which the conclusion, while following from the premisses, is based on false or irrelevant premisses. This will appear as we proceed. 669. There is, properly speaking, no specific class of the fallacies of language (in Dictione). Language may doubtless give rise to incorrect or invalid inference, but it does so because it leads to a violation of formal or logical law, chiefly, in fact, to the making use of four instead of three terms in a reasoning. This is known as quaternio terminorum, or the logical quadruped. This is most commonly manifested in what is known as Ambiguous Middle; in other words, in the use of a term which indicates more than one notion, and which is taken in a double sense in the reasoning. For the ambiguity of a word does not necessarily lead to invalidity of inference, unless in so far as the ambiguity is made use of in the reasoning process. 670. The only sound division of Fallacies accordingly is into (1.) those in which the fault is in the reasoning process itself, in other words, those in which the conclusion 1 Top. viii. 11 ; De Soph. JSlench., i.. c. iv. v. 2 K 514 INSTITUTES OF LOGIC. does not follow from the premisses ; and (2.) those in which, while the conclusion is justly drawn, one or more of the prem- isses is incorrect, in point of fact, unduly assumed, or such as, while professedly meeting the point at issue, really do not, and only yield a conclusion irrelevant to the question pro- posed. Thus there emerge only two grand kinds of Fallacies those in the Form and those in the Matter of the reasoning. 671. It should be noted generally regarding fallacies, that several of them have a tendency to run into each other, and that a so-called reasoning may be fallacious in more than one way. It is enough, however, if a bad reasoning can be fairly referred to one class or species of fallacy. All that can be aimed at in the classification of fallacies is to make the classes as exact as possible, to specify their discriminating feature, and to show generally how the particular fallacy is to be avoided. And this classification at present must be based on the logical point of view. The sources of fallacy and of sophism, lying in natural tendencies and in surrounding circumstances in the intelligence, and in the moral and imaginative nature of man, in impulses and preconceptions form quite an independent sphere of inquiry. This was sketched in general, and, at the same time, grand outline by Bacon in his well-known Idola: 1 "A complete history of sophism," says a French writer, " would be the political history of mankind." 672. Under the first head the class of Formal Fallacy we have the following : (1.) Those which violate the essential principle of the con- stitution of syllogism, as involving more than three terms. (2.) Those which proceed on the non-distribution of the middle term that is, on its particular distribution in each premiss. (3.) Those that proceed on the universal distribution or quantification of major or minor term in the conclusion, while it was not taken universally in the premisses. (4.) Those which proceed to an affirmative conclusion, while one premiss is negative. (5.) Those which proceed on a so-called reasoning, in which neither premiss is affirmative. (6.) (In Hypothetical Eeasonings.) Those which proceed 1 See Novum- Organum, Book I. aph. xxxviii. et seq. FORMAL FALLACIES. 515 from the denial of the antecedent to the denial of the con- sequent. (7.) Those which proceed from the affirmation of the con- sequent to the affirmation of the antecedent. These exhaust the possibilities of formal error in Mediate Inference. There are other possibilities of error in Immediate Inference, as in Conversion, Opposition, Integration, Restric- tion ; but these have already been provided for in the rules laid down regarding them. 1 673. (1.) To the first of those heads the quaternio ter- minorum may be referred all the cases of what is known as Ambiguous Middle. Here we have really two middle terms whose difference is cloaked under some accident of expres- sion ; and thus, as we have a different concept in each of the premisses, the extremes of the conclusion have not been com- pared with the same third. Whately regards Ambiguous Middle as a semilogical fallacy that is, partly in the matter (or expression), and partly in the form. It is essentially the latter a formal fallacy, for it misleads only through its in- formality. 674. Fallacies whose invalidity arises from ambiguity in terms, and the formal vice of which is a quaternio termino- rum, may be classed as follows : (1.) Homonymia, or Equivocation. (2.) Prosodia, or Accent. (3.) Amphiboly. (4.) Figura Dictionis, including Paronymous Words, Etymol- ogy, Figurative and Direct Sense. (5) Composition and Division, including the fallacy of In- terrogation. (6.) Fallacia a dicto secundum quid ad dictum simpliciter ; and the converse, A dicto simpliciter ad dictum secundum quid. 675. Those kinds of fallacies may be found in any term of a reasoning ; but as a rule they are cases of what is known as Ambiguous Middle, the middle term being that upon which the conclusion essentially depends. In the case where a premiss is not false, or unduly assumed, and where the con- clusion is not invalidly drawn from the premisses, the fault will usually be found in the double sense of the Middle Term. There we ought to look for it. 1 See above, chapters xxviL and xxviii. 516 INSTITUTES OF LOGIC. 676. It is obvious that if the middle term in a reasoning be ambiguous, or equivocal i.e., capable of being taken in either of two senses our reasoning is likely to be utterly- futile. And no form of fallacy is more common and more difficult to detect than this, especially when the two prem- isses containing the middle term stand far apart from each other. Thus, for example, the word expedient may be used as meaning conducive to the greatest good, or conducive to temporary prosperity. I may argue that a particular course of conduct is expedient, by showing simply that I should by it secure a temporary object which I have in view. There would be no harm in my thus arguing, and thus acting even. But if I attempted further to vindicate my conduct by saying that it was expedient in the other or higher sense of being conduc- ive to the greatest good in fact, being absolutely useful and right I should be guilty of identifying the two senses of the word, and substituting for the lower sense of the term the higher one, which I had not vindicated, or shown to be the sense in which my action was originally understood. This would be a case of Ambiguous Middle, in which I took a term in one sense in the one premiss, and in a different, even it might be conflicting, sense in the other. As a simple instance of Ambiguous Middle, take the fol- lowing : Cicero's style entitled him to rank in the highest class ; So did the style of Beau Brummell ; Therefore Cicero and Beau Brummell loth rank in the highest class. The Middle Term here is, of course, style ; but the style of the one referred to the turn of his sentences, that of the other to the fashion of his garments. On a par with this is such a so-called reasoning as the following : This side of the river is different from the other side ; But the other side is a this side as well (say to the man opposite to me) ; Therefore this side and the other side (that is, the different sides) are the same. 677. The most common type of ambiguity in the Middle FOBMAL FALLACIES. 517 Term is when it appears to be one, but in point of fact is not. In the major premiss, it may be coupled with a condition ; in the minor, it may be taken singly. Of this sort is the old fallacy called the Horned (Cornutus, KcpaTuv)). As He who has not lost a thing, has it; You have not lost horns ; Therefore you have them. Here the major refers only to what was actually in pos- session. This is the key to the solution of many sophisms, as Aris- totle shows in the De Sophisticis Elenchis. 1 678. The first form of ambiguity in terms is known as Homonymia (oyLion/v/Aia), or Equivocation, This arises when a term, taken by itself, has more than one signification, that is, denotes more than one concept, and is thus capable of being taken in two different senses in the reasoning. Common examples are light, meaning not heavy, and not dark ; and box, meaning a tree, a chest, a blow. As an example of fallacy arising from this source, we may take this : The end of a thing is its perfection ; Death is not the perfection of life ; Therefore death is not the end of life. End is here ambiguous ; it means final cause, or that for the sake of which a thing is ; and it means termination. Hence the seeming paradox in the conclusion. Again, the various meanings of the term substance give rise to fallacies of the same sort. Thus : Substance is not quantity; Body is substance; Therefore body is not quantity. Some of the examples given by the older logicians are simply a play on words, or species of verbal pleasantry. Thus : Every dog can bark; Some star is a dog ; Therefore some star can bark. i Cf. Trendelenburg, El. Log., 27. 518 INSTITUTES OF LOGIC. 679. The term truth, from its various applications or denotations, lends itself readily to the fallacy of Ambiguous Middle. It may mean truth of fact, truth of consistency, truth of possibility, as opposed to actuality, &c. Some demonstrative systems of philosophy confuse the two first mentioned meanings, and thus make consistency in think- ing equivalent to harmony of thinking with experience. Des- cartes, apparently, in his Criterion of Truth, clearness and distinction, confounds the conditions of possible thinking with the conditions of thinking a thing, as it really is. 680. Sensation, Impression, Reason, Idea, Individual, and Individualistic, Subjective, Objective, and many of the terms in Psychology, are peculiarly liable to ambiguous meaning and application. Sensation is constantly confounded with Perception, with- out remark or explanation on the part of those using it. And thus the whole controversy between Eealism and Ideal- ism in Perception is obscured, and the point in many cases begged from the beginning. 681. Hume's use of the term impression is of the most varied and misleading sort. It starts with an unproved assumption, and it ends in confounding together mere sensa- tion, apprehension, emotion, desire, and volition. Impression, as he employs it, is of no valid use whatever as a middle term in a reasoning. 682. Reason is nearly equally misleading. It is used for Understanding, Reasoning, Reason as source of principles, what is called Pure Reason, and in a host of other ways. Idea means almost anything, and therefore practically nothing, in connection with knowledge. And the Idea, the Universal, &c., as used for the bare form of knowledge, has the worst possible suggestion of the separability of matter and form, and the hypostatising of the latter as, first, a dis- tinct entity, and then as all in all in the end. Individualistic, as applied in these days to systems of phil- osophy of the most opposite sort, has the vaguest and most shifting of meanings. Individual, individualism, or individualistic, may be em- ployed in at least the following applications, which are varied, and some of which are conflicting. (1.) Individual may be used for singular and particular. AMBIGUITY IN TEEMS. 519 In the former case, it means this, that, one ; in the latter case, it means some (at least]. In the first meaning it is opposed to the plurality of units in time ; in the second, to the univer- sality of the concept. It is one of many, and some of all. This is the logical ambiguity of the term. (2.) Individualism in philosophy may mean that knowledge is the impression or state of the consciousness of each indi- vidual in the world; that, however different, these impressions are equally true or the truth, simply because they are the im- pressions of the individual. The truth, thus, for the individ- ual in his youth may be wholly different from the truth for the same individual in his prime ; and what is true for one, may be false for another. This is in substance the Protagor- ean Homo mensura. (3.) Individualism may mean a series of sense impressions, regarded simply as conscious states, and as forming the sense experience of each individual, and even being all that is of world reality. (4.) Individualism may mean that, in the last resort in hu- man thinking, the test of a principle or universal condition of knowledge is the self-evidence and necessity which constrain each individual to accept it as a principle or condition of our knowledge. This constraint, as not peculiar to one individual more than to another, would be a common or universal pro- perty of all human thinkers ; such a theory would be quite opposed to the Protagorean Homo mensura. (5.) Again, it may be held that as man thinks only as sharing or being a part of the consciousness of God, a philo- sophy which repels this view is individualistic. A classifi- cation of philosophies under this negative head would lead to the most indiscriminate grouping which it is possible to conceive. (6.) Individualism may further mean the negation of Pan- theism, or the assertion of finite reality in a sense which is incompatible with Pantheism, understood as the doctrine of a single consciousness pervading the world. 683. Subjective and Objective admit of various meanings. In contrast, the one marks the knower, the other the known. The known may be regarded as (1.) that which is in relation to the knower ; (2.) that which is independent, and subsists per se ; (3.) that which transcends the known and definitely 520 INSTITUTES OF LOGIC. knowable. Objective is, however, sometimes used for that which is necessarily or universally connected in knowledge. This may, after all, be but a series of sensations, and there- fore wholly subjective as to matter, and even form. To these may be added such phrases as the government, the church, experience, wealth, &c. Definition, consistently held by, is the only remedy for ambiguous terms. 684. The second form is Fallacy of Prosody, or Accent This arises when the same word, having different significa- tions, receives its meaning from the mode of pronunciation. Words vary in meaning according to accent proper, quantity of syllable, spiritus lenis et asper, &c. Accentuation may either remove or cause ambiguity. The same word or phrase may be so pronounced, accent- uated, or emphasised as to convey one of two wholly distinct meanings. And if the term or phrase be a quotation, it may, by the accent or mode of pronunciation which accompanies it, be made to convey a meaning wholly different from that originally intended. What was ironically said, or said in joke, may thus be made to appear as if it were seriously spoken, and conversely. In quotation, by the introduction of italics, as has been remarked, we may wholly change the scope of a statement. 685. The third form of ambiguity is Amphiboly. This is a double meaning in or through the structure of the sen- tence, or somehow from the context, while the words them- selves may have but one definite signification. It depends, in fact, frequently, on that fault in syntactical construction through which a word or expression may be connected either with what goes before or with what follows it. . Thus : Qui scit literas hodie didicit. This may mean either qui scit literas hodie, didicit, or qui scit literas, hodie eas didicit. 1 I have made thee free a slave. Then there is the well-known line, which has come down in nearly all logical compends : Aio te, JEacida, Romanos vincere posse. (Pyrrhus the Romans shall I say subdue.] 1 Given by Duncan as an example of the Fallacy of Division, but better as Amphiboly. FIGUKA DICTIONIS. 521 And we may add : TTCVT^KOVT' avSpwv IKCLTOV XtVe Stos 'A^tXXcw's. But as Achilles could not out of fifty men leave a hundred, we must suppose that out of a hundred he left fifty. 686. The fourth form is Figura Dictionis (cr^/xa TT}S Ae'^ews). Aristotle describes this as taking place when that which is not the same thing is expressed in the same way, as masculine taken for feminine, or feminine for masculine, or neuter for either, or action for suffering. Thus, because to burn and to cut are actions, we may suppose that to rest, to be loell, &c., are also actions. More important forms of this fallacy arise when, under the same word, different categories, or kinds of categories, are con- founded. Thus : What is snow, that is not milk; But snow is white; Therefore milk is not white. Here the reference in the what (quod] is to snow as a sub- stance or distinct object, while the conclusion refers to quality. So : Qui heri eras idem hodie es; At qui heri eras sanus ; Ergo hodie sanus es. 1 687. To this may fairly be referred the commonplace fallacy usually classed under the head of Fallacia ex Acci- dente : What is bought in the market is eaten Raw meat is bought in the market ; Therefore raw meat is eaten. Raw meat is not properly an answer to what, but to what sort of meat. 688. Under this head may, also, be included the fallacy known as that of Paronymous or Conjugate Terms. Paronymous terms are terms derived from the same root. They may be substantive, adjective, or verb. Thus we have presume and presumption, project and projector, assume and as- sumption, expedient (noun), expedient (adjective), expediency 1 Top., i. iv. ; Duncan, Inst. Log., L. v. c. vii. 522 INSTITUTES OF LOGIC. (noun). Each of these sets of words is from the same root. But they have not necessarily the same or a synonymous meaning. If we employ them in a reasoning as if they had, we shall probably draw a false conclusion. To take a common example : Projectors are not to be trusted ; This man has formed a project ; . ' . He is not to be trusted. In this case the ambiguity lies in the middle term, and it leads us wholly wrong. So with assume, assumption, and assumptive. We may innocently assume a thing to be true ; we may be guilty of assumption in our conduct. These are paronymous terms, but they are not synonymous. 689. To the Figura Dictionis may be referred the Fallacy of Etymology. This arises when it is supposed that, because of the original meaning of a word being such an one, it must necessarily retain that meaning through all subsequent usage, or that this meaning is to override or supersede an acquired, and, it may be, extended or purified signification. Most of the words in the science of mind had originally a material reference. And in this instance the fallacy would consist in assuming or maintaining that such words have thus neces- sarily no wider or higher reference. We have illustrations of the fallacy of Etymology in such cases as right, truth, &c. As right is from rectus, and this from rego to rule, it has been inferred that all right is a creation of the law. There is here as gross a hiatus in the proof as can well be conceived. So with truth. As this comes from trow, to believe, it has been inferred that truth can only mean what each believes, or individual opinion, the Protagorean Homo Mensura. Spiritus, animus, anima, avc/^o?, signifying originally breath and air, are not to be held as only signifying these. Comprehension, Conception, meaning originally a grasping or holding several sensible things, as one or in one, are not on that account to be limited merely to sensible objects or singulars. In all these cases there is a hiatus which virtually begs the question regarding the present meaning of the word. 690. To the Figura Dictionis may be referred the fallacy ai-ising from a change of the Figurative to the Direct Sense thus : COMPOSITION AND DIVISION. 523 The mind sees ; Seeing is an organic act ; Therefore the mind in seeing puts forth an organic act. 1 691. The fifth form includes the fallacies from Composition and Division. Fallacia a sensu diviso ad sensum composition, and A sensu composite ad sensum divisum. (1.) The fallacy of Composition (rarie3, and of the War of the Succession. Third Edition, 2 vols. 8vo. Portraits and Maps, 308. 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Embracing Scientific and other Terms, numerous Familiar Terms, and a Copious Selection of Old English Words. To which are appended Lists of Scripture and other Proper Names, Abbreviations, and Foreign Words and Phrases. BY THE REV. JAMES STORMONTH. The PRONUNCIATION carefully revised by the Rev. P. H. PHELP, M.A. CANTAB. Royal 8vo, handsomely bouivl in half-morocco, 31. 6rf. Opinions of the British and American Press. {TitTie0 "This may serve in great measure the purposes of an English cyclo- pedia. It gives lucid and succinct definitions of the technical terms in science and art, in law and medicine. We have the explanation of words and phrases that puzzle most people, showing wonderfully comprehensive and out-of-the-way research. . . . We need only add, that the dictionary appears in all its departments to have been brought down to meet the latest demands of the day, and that it is admirably printed." pall dRall (5a3CttC. " The pronunciation of every word is given, the sym- bols employed for marking the sounds being commeudably clear. . . . After the pronunciation comes the etymology. It has, we think, been well managed here. And the matter is, oil the whole, as judiciously chosen as it is skilfully compressed and arranged." . " There can be no question that the work when completed will form one of the best and most serviceable works of reference of its class. . . . It is admirably adapted to meet the requirements of every ordinary reader, and there are few occasions of special reference to which it will not be found adequate. The definitions are necessarily brief, but they are almost always clear and pointed. ... A word of praise is due to the beauty and clearness of the printing." STOKMONTH'S DICTIONARY Continued. Opinions of the British and American Press Continued. Ci\>il SCtViCC (5a3CttC. " We have had occasion to notice the peculiar features and merits of ' Stormonth's Dictionary,' and we need not repeat our commendations both of the judicious plan and the admirable execu- tion. . . . This is a pre-eminently good, comprehensive, and authentic English lexicon, embracing not only all the words to be found in previous dictionaries, but all the modern words scientific, new coined, and adopted from foreign languages, and now naturalised and legitimised." "fflOtCS ailJ) Q.Uerie0. " The whole constitutes a work of high utility." 2)UbHn 3-tisb Crimes." The book has the singular merit of being a diction- ary of the highest order in every department and in every arrangement, without being cumbersome ; whilst for ease of reference there is no dic- tionary we know of that equals it. ... For the library table it is also, we must repeat, precisely the sort of volume required, and indispensable to every large reader or literary worker." . "Every page bears the evidence of extensive scholar- ship and laborious research, nothing necessary to the elucidation of pres- ent-day language being omitted. ... As a book of reference for terms in every department of English speech, this work must be accorded a high place in fact, it is quite a library in itself. . . . It is a marvel of accuracy." tribune, " The work exhibits all the freshness and best results of modem lexicographic scholarship, and is arranged with great care, so as to facilitate reference. " Jt)0rfc f^^{\ an & Bjpresa. " Is the nearest approach to the ideal popular dictionary that has yet appeared in our language. " l?0r.& Sun. "A well-planned and carefully-executed work, which has decided merits of its own, and for which there is a place not filled by any of its rivals. " Journal. "A critical and accurate dictionary, the embodiment of good scholarship, and the result of modern researches. ... It holds an unrivalled place in bringing forth the result of modern philological criticism." ," There can be but little doubt that, when completed, the work will be one of the most serviceable and most accurate that English lexicography has yet produced for general use." (BlObe, "In every respect this is one of the best works of the kind in the language." WILLIAM BLACKWOOD & SONS, EDINBURGH AND LONDON.