ftsi.A, f ■■' ■A. Mmh H Mji 1-i % CORNELL UNIVERSITY LIBRARY FROM Cornell University Library The original of tliis book is in the Cornell University Library. There are no known copyright restrictions in the United States on the use of the text. http://www.archive.org/details/cu31924028996572 THE LOGIC OF SCIENCE A TRANSLATION POSTERIOR ANALYTICS OF ARISTOTLE,' WITH NOTES AND AN INTRODUCTION. BY EDWARD POSTE, M.A. FELLOTV OF OBIEL COLLEGE. OXFORD: FRANCIS MACPHBRSON. MDCCCL. 1 UNSVERSITV I \LIBRARY.^ -' PREFACE. There is a pretty general agreement among those who have devoted any attention to Logic, that the Logical works of Aristotle would repay the labour of a perusal. In spite, how- ever, of this opinion, it does not appear that the pages of the Organon are often turned over by very diligent hands. Nor is this very difficult to be accounted for, if we consider their obscurity — a quality, indeed, which they share with most of Aristotle's productions. It was to facilitate the study of the original that this translation of a portion of it was undertaken : and the Posterior Analytics was the portion selected, both because it is intrinsically the most valuable, as affording the greatest insight into Aristotle's views, and bringing him on to the same ground with modem writers on the Philosophy of Science ; and because the remaining parts are already tolerably weU known through the works of the Scholastic logicians, while this, though far more interesting to a student of the Baconian Logic, has been comparatively neglected. In the Introduction a sketch has been given of the whole of the Organon. ERRATA. Page 18, Note ' for ^ /liaovg twoq, read ^ fispovQ nvog. 47, Note " for System of Logic, BOOK II. read System of Logic, BOOK III. . 113, Note • for The conclusion deducted, read The conclusion de- duced. 114, for CHAPTER XII. read CHAPTER XI. 117, for CHAPTER XIII. read CHAPTER XII. 121, for CHAPTER XIV. read CHAPTER XIII. 126, for CHAPTER XVI. read CHAPTER XV. ADDENDUM. Page 4, to Note ', add traaa yap in-iarriiiri xai ivvajtii rov PeXriarov SoKfT ttvai. Topics, \i. 5. CONTENTS INTRODUCTION. Page § 1. 2. Idea of Logic gathered from modern writers.. . 1 3. Sketch of the Organon. General Logic 8 4. Logic of Deduction 10 5. Logic of Opinion 16 6. Logic of Induction 31 POSTERIOR ANALYTICS. BOOK I. Chap. I. Infekence 39 § 1 . All Inference implies Antecedent knowledge. 2. Reducible to three classes. 3. "When a conclusion is particular, the minor pre- miss is rather Simultaneous, than Antecedent. 4. The Antecedent knowledge of a conclusion is only Implicit. Chap. II. Scientific Peincipies 41 §1. Definition of Science. 2. 3. Scientific principles are indemonstrable, 4. Causal, and absolutely Antecedent, 5. and Appropriate. 6. Are divisible into Axioms and Theses : the latter are Definitions or Hypotheses. 7. Possess higher evidence than the Conclusions. Chap. III. Some tetjths ake Indemonsteabie. . . 43 § 1 . Two opinions on Demonstration — that it is Impos- sible ; and that it is Circular. 2. Arguments against the latter opinion. Chap. IV. Univebsal, Essential, Commensueate. . . 44 § 1. The premisses of Science are necessary. 2. Definition of Universal. vi CONTENTS. Paciii § 3. Two kinds of Essential : the latter kind is neces- sary by the Axiom. 4. Definition of Commensurate. Chap. V. Commensukate Peopositions 46 § 1. A Commensurate proposition is Essential, and dis- tributes the predicate. 2. A Commensurate subject is the lowest ineliminable genus. Chap. VI. Scientipic Peinciples ake Essential. . . 48 § 1. Because they are Necessary. 2. Arguments to show that Scientific principles are Necessarj'. 3. A conclusion from Contingent premisses is only Hypothetically Necessary. 4. Scientific principles are Essential because they are Causal. Chap. VII. Scientific Peinciples aee Appeopeiate AND Intkansfeeable 50 § 1. Only the Axioms are common to heterogeneous sciences ; for the other principles are Essential. 2. Sciences only examine their Appropriate problems. Chap. VIII. Scientieic Peinciples aee Eteenal. . . 51 Chap. IX. Theee is no Uniyeesal Science 52 § 1. Scientific principles are Peculiar to the subject- matter, because the conclusions are Essential. 2. They are common to Generic and Specific sciences only. 3. No Universal science can demonstrate the Appro^ priate or Specific principles of the particular sciences. Chap. X. Hypotheses 54 § 1. An Hypothesis agserts the Existence of an elemen- tary substance or power. 2. Axioms need not be expressed in their most universal form. CONTENT^. Page § 3. The Predicate is only assumed in Definition : the Subject both in Definition and Hypothesis. 4. Three elements, though not always expressed, are essential to all sciences. 5. Hypothesis difiers from Axiom. 6. Postulate and Relative Hypothesis. 7. Hypothesis difiers from Definition, and from the suppositions of the geometer with respect to bis Diagrams. Chap. XI. Axioms 56 § 1. Universals are indispensable to science ; but not the Platonic Ideas. 2. The Axioms are not expressed, but implied. The principle of Direct proof, that both of two Con- tradictories cannot be true. The terms of syllogism are not necessarily Com- mensurate. 3. The principle of Indirect proof, that one of two Contradictories must be true. 4. The Axioms are common to all the sciences, to Dialectics, and to Metaphysics. Chap. XII. PECULiAEiTiEs of Science 57 § 1. The Geometrician is not bound to argue with one who disputes his principles, nor to discuss extrageometrical questions. 2. Two senses of ungeometrical. 3. Geometry not liable to Dialectical fallacies. Instance of fallacy of Consequens. 4. Why Analytical reasoning is possible in Mathe- matics. 5. Exainple.^ofJhe Synthetical process. Chap. XIII. Fact and Reasoned Fact, or Induction AND Deduction 60 § 1. Two kinds of Fact-conclusion. 2. Examples of Fact-conclusion which involve a Rea- soned conclusion. 3. Examples of Fact-conclusion which involve no Reasoned'conclusion. viii CONTENTS. PAGE § 4. The Fact and Reason may belong to different Sciences. Chap. XIV. The fikst Figuee is the most Scientific. 63 Chap. XV. Indemonstrable Negatives 64 § 1. A negative is indemonstrable if both its terms are summa genera. Chap. XVI. Eekok in Peinciple 65 § 1 . May be founded on supposed proof. 2. If the conclusion is a universal afBrmative, either both premisses, or the minor singly, may be false. 3. If the conclusion is a universal negative, in the first figure, both premisses, or either singly, may be false. 4. In the second figure, both premisses cannot be contraries of the truth. 5. But both may be contradictories of the truth. 6. And either singly may be contrary. Chap. XVII. Eekok in Conclusion 68 § 1. If the true conclusion is affirmative, and the syl- logism in the first figure ; when the middle is appropriate, only the major can be false. 2. When the middle is inappropriate the major may be false and the minor true : 3. Or both false: 4. Or the major true and minor false. 5. In the second figure both cannot be contraries of the truth, but either may. 6. If the true conclusion is negative, when the middle is appropriate, only the major can be false. 7. When the middle is inappropriate, the major alone may be false. 8. The minor alone may be false. 9. Or both may be false. CONTENTS. ix Paoe Chap. XVIII. Beginning of Knowledge 70 § 1. All science is founded on Induction. Chap. XIX. Abe ant Tbuths by theib own natuee Indemonsteabie ? 70 § 1. Difference of Proper and Improper predication. 2. Is the process of Generalization finite ? 3. Is the process of Specification finite ? 4. Are the intermediates between two given extremes ~ finite ? 5. The same questions in negative proof. 6. In a circle of terms none are Antecedent or Ulti- mate. Chap. XX. When the Exibemes aee given, . . . . 72 § 1. the Intermediates are Finite, 2. and continuous. Chap. XXI. Negative Peopositions 72 § 1. If the trains of Generalization and Specification implied in the proof of an afiirmative proposi- tion are finite, those implied in the proof of a negative proposition are finite. 2. Shown in the first figure. 3. In the second figure. 4. In the third figure. 5. The trains would be limited, even though each conclusion were drawn in every possible mood and figure with different terms. Chap. XXII. The Teains aee Finite 75 § 1. Dialectical Proof: if the train of Generalization were infinite, Essences would be indefinable. 2. Distinction of Proper and Improper Predication. 3. Predication Proper is Substantive or Attributive. 4. Predication Proper is not Circular. 5. Rectilinear predication is finite : for both the generalization of Substances and that of Attri- butes is finite ; and therefore their sum is finite. 6. Second Dialectical proof: if no truths were Im- mediate, all conclusions would be Hypothe- tical. X CONTENTS. Paob § 7. Scientific proof: two kinds of essential predica- tion, Substantive and Attributive. 8. The Attributive nexus is finite. 9. The Substantive nexus is finite. 10. Demonstration is possible, and rests on indemon- strable truths. Chap. XXIII. Ultimate Laws 78 § 1. Two subjects may have an immediate connection with the same predicate. 2. Immediate laws are the Elements of Deduction, and cannot be discovered by a Deductive pro- cess. 3. Immediate laws are the ultimate Atoms of science. 4. The proof of a negative involves no term higher than the major. Example in the first figure in Celarent. 5. Example in the second figure in Camestres. 6. Example in the third figure in Bokardo. Chap. XXIV. Compaeison of Paeticuxab and Com- mensurate Pkoof 81 § 1. 2. 3. Particular proof may seem more perfect, as being Essential, and not Delusory. 4. 5. But Particular proof is not Essential, and Com- mensurate is not Delusory. 6. 7. It shows the Cause and ultimate Reason. 8. 9. 10. Is Antecedent : contains the particular vir- tually: and is an object of Reason not of Sense. Chap. XXV. Comparison op Appiemative and Nega- tive Peoop . . 84 § 1. Afiirmative proof employs fewer premisses. 2. Needs no Negative premisses. 3. 4. Is Prior and more Elementary. Chap. XXVI. Compaeison op Dieect and Indirect Proof 86 § 1 . Nature of Indirect proof. 2. It does not rest on absolutely antecedent pre- CONTENTS. xi Page Chap. XXVII. Compabative Peepection of Sciences. 87 § 1. A perfect science gives the Reason, not merely the Fact. 2. Is Abstract : 3. and Elementary. Chap. XXVIII. Unity of Science 87 § 1. Identity Generic or Specific. 2. Tests of Unity. Chap. XXIX. Diteksitt of Peoof 88 § 1. The same conclusion is susceptible of several proofs. Chap. XXX. Chance 88 § 1. A matter of chance cannot be proved. Chap. XXXI. Sensation 89 § 1. Sensation is not Science, because Incommensurate. 2. Yet is sometimes preferable to Science. 3. and might sometimes supersede Scientific inquiry. Chap. XXXII. Muitipmcity of Scientific Prin- ciples 90 § 1. Dialectical proof: some are true, others false. 2. Scientific proof: Heterogeneous terms cannot enter into the line of predication ; and the common principles, or Axioms, are insufiicient to prove the characteristic conclusions of a science. 3. The number of Premisses nearly equals the num- ber of Conclusions. 4. As conclusions are infinite, and homogeneous terms are finite, the heterogeneous terms must be infinite. 5. Some principles are contingent, others necessary. 6. 7. Every science has at least one Peculiar law. 8. Principles cannot be even Generically the same. Chap. XXXIII. Science and Opinion 93 § 1 . The conclusions of Science are necessary. 2. The ultimate grounds of Science are Definitions. 3. How far the objects of Science and Opinion may be the same. xii CONTENTS. § 4. Science and Opinion are incompatible in the same mind. Chap. XXXIV. Sagacity 95 § 1. is a rapid perception of the cause of a given phae- nomenon. BOOK II. Chap. I. Problems of Science 96 § 1. Four kinds of Problem: the problem of Fact, of Reason, of Existence, of Essence. 2. Problem of Fact. 3. Problem of Reason. 4. Problem of Existence. 5. Problem of Essence. Chap. II. The Object of Inquiry is always the Intermediate. 97 § 1. In the Problems of Fact and Existence we ask, Is there an Intermediate ? 2. In the Problems of Reason and Essence we ask. What is the Intermediate ? 3. The Problems of Fact and Existence are similar. 4. The Problems of Reason and Essence are similar. 5. The object of inquiry is always the Intermediate. Chap III. Definition and Demonstration have NOT the same province 98 § 1. 2. 3. 4. 5. 6. Definition and Demonstration cannot have the same province, for unity of truth im- plies unity of knowledge, &c. 7. And because Definitions are the basis of Demon- stration ; 8. and are assumed. 9. In Definition there is no subject and predicate. 10. Definition gives an Essence, Demonstration a Fact. Chap. IV. Categorical Proof of a Definition .... 101 % 1. Involves z, petitio principii. CONTENTS. xiii Paob Chap. V. Establishment of Definition by Division 102 § 1 . The proof of a Definition by Division involves a petiiio prindpii at every stage : 2. and at the end. 3. Its completeness may be ensured. 4. 5. Some conclusion results from a Division, but no Definition. Chap. VI. Hypothetical Pboof of Definition, and PBOOF BY Definition of the Opposite 103 § 1 . Hypothetical proof of a Definition involves a pe- tiiio prindpii. 2. As we do not quote the Axiom to prove, so we ought not to define Definition in order to de- fine a particular object. 3. Proof by Definition of the Opposite involves a petiiio prindpii. 4. Neither proof by Hypothesis nor proof by Division accounts for the Unity of the object defined. Chap. VII. Essence cannot be Pkoved .. .. .. 104 § 1. Essence is not the object of Deduction, Induction, nor Sensation. 2. Essence involves Existence, which cannot be the object of Definition, because Definition can only give a single truth. ■ 3. Besides, Existence is the object of Demonstration. 4. There is no cogency in Definition, either as to the Existence of the object, or as to the Significa- tion of the word. 5. Signification is not the object of Definition. 6. Definition is not demonstrative, nor can Essence be discovered by Definition. Chap. VIII. Two kinds of Definition . . ^ . . . 107 § 1 . Categorical proof of a Definition involves a peti- iio prindpii, and is Dialectical. 2. Knowledge of the Essence never precedes know- ledge of the Existence. xiv CONTENTS. Page § 3. Knowledge of Existence sometimes implies a par- tial knowledge of the Essence, sometimes is Accidental. 4. Knowledge of Existence may imply a knowledge of the causal part^of the Essence. 5. Or it may imply no knowledge of the Essence. 6. The Essence is the reason of the Existence. 7. The Definition of the Elementary is not ana- lyzable into cause and effect. Chap. IX. Foub kinds op Depinition 110 § 1 . Verbal Definition. 2. Unity of Statement. 3. Real Definition of the mediate, stating the cause. 4. Omitting the cause. 5. Definition of the Immediate. Chap. X. Causation .• Ill § 1 . Four kinds of cause. 2. The Material cause. 3. The Formal cause. 4. The Eificient cause. 5. The Final cause. 6. The Final cause inverts the chronological order. 7. The Final cause is reconcilable with the Mate- rial. 8. Two kinds of Necessity. 9. Chance. Chap. XI. Succession of Cause and Eppect 114 § 1 . Cause and Effect may be synchronous, 2. Or successive ; in which case the cause may be inferred from the effect, 3. But not the effect from the cause. 4. Present and Past events are discontinuous. 5. The media to infer an Antecedent from a Conse- quent are infinite, 6. Whether both events are past, or both future. 7. Example. CONTENTS. XV Page § 8. Natural occurrences proceed in Cycles similar to Circular Reasoning. 9. General premisses give General conclusions. Chap. XII.* Establishment or Definition 117 § 1. Essence consists of predicates confined to the genus, and distinguishing the species. 2. It may he proved Hyppthetically. 3. The foundation of Deductive Science Definitions of the Elementary. 4. Division shows the order of the essential ele- ments : 5. and ensures completeness. 6. Definition does not imply universal knowledge. 7. The essential character of the predicates included must be ensured by Dialectical topics. 8. Mode of determining their order ; 9. And of ensuring completeness. 10. Inductive mode of discovering the Definition. 11. Subgenera must be defined before the genus. Chap. XIII.* Antecedent Laws 121 § 1. Our data should be arranged according to their degree of generality. 2. We should endeavour to discover new genera : 3. and to trace new analogies. 4. Problems are the same generically or specifically : 5. or if related as antecedent and consequent. Chap. XIV. Relation of Cattse and Effect . . § 1. Cause and Efiect reciprocate as media of proof : 2. at least if the cause is commensurate. 3. The same effect has only one essential cause. 4. Acause,likeaneffect, may be generic or equivocal. 122 5. Example. 6. Or analogical. 7. Every Effect has a commensurate Cause. 8. The proximate Cause is the definition of the Effect. 9. Subjects which receive the same effect from dif- ferent causes are specifically different. * See Errata. xvi CONTENTS. Pass § 10. All the intermediates between a subject and its attribute are causes. 11. But the proximate intermediate is the cause to the subject. Chap. XV.* The Okgan oi' Pkimaey Tkttths 126 § 1. What is the mode and faculty of apprehending immediate truths ? 2. The organ by which they are apprehended is not originally perfect, but must be developed by an inferior power. 3. This power is Sense. 4. The process of development is Generalization. 5. The organ of immediate truths must be superior to Science, and therefore is Reason. APPENDIX A. AXIOMS 131 § 1. Forms of the Axiom. 2. Opponents of the Axioms. 3. Science that discusses the Axioms. 4. Defence of the Axioms. 5. Function of Ijhe Axioms. 6. Ubiquity of the Axioms. 7. Relation of the Axioms to Metaphysics and Logic. APPENDIX B. HYPOTHESES 139 § 1. An Hypothesis is a peculiar principle affirming the existence of an ultimate Cause. 2. It is defective in evidence. 3. Consequences of this character. 4. Art is Hypothetical. 5. Relative Hypothesis. 6. The Collocation of permanent causes is asserted in the Hypothesis. • * See Errata. INTRODUCTION. SKETCH OF THE ORGANON. § 1. In every Science may be found some general problem, to the complete solution of which all its inquiries converge; some central idea that unites all its members in an organic whole, however great their variety. It is by the Idea alone that we can determine into how many branches an inquiry should be divided, and what is the relative importance of these branches; what investigation is essential to the science, and what is nuga- tory or extraneous. The development of a particular Idea, curiosity to solve a par- ticular problem, is not a matter of accident in the history of in- dividuals or of nations. At one period the possession of a science becomes a want, its problems force themselves on the mind, and are importunate in their demands for a solution. At other times and under other circumstances the interest may be unfelt, and it may be almost impossible even to conceive the problem. This may be seen in the history of Theology, Philo- sophy, Political Science, Political Economy. In times unpropi- tious to a given study, a great and perhaps insoluble difficulty will be to determine what end it proposes, and what is its proper province. In more propitious times its questions will present themselves unbidden, and its old doctrines, if forgotten, will be re- discovered. This has been exemplified in the history of Logic. Its problem, the Conditions of Science, can only be a matter of curiosity to a scientific age : that is, either an age that actually B 2 MODERN WRITERS. possesses many sciences ; or an age that is strongly possessed by the Idea, and feels a restless aspiration to reduce it to a reality. The Logical problem at a certain period forced itself on the Greeks: it was attempted by Parmenides and others, and re- ceiyed a provisional solution at the hands of Plato and Aristotle. Some time had to elapse before the inadequacy of this solution could be felt: for a time the interest ceased; the idea was no longer a portion of the world's thought: if the old treatises existed, the life that once animated them was extinct; and from yarious causes men did not begin to demand a revision of the old solution till about the time of Bacon. Educated Europe then felt the same want that had been felt by Aristotle and Parmeni- des ; and the New Organon was produced by the same idea, by the same desire, that had before produced the Old. The men of one age, however, are not all moulded by the same influences, and there are numerous writers since this time whose treatises have not much beside their name in common with the works t)f Aristotle or Bacon. Not that there is any want of writers, who, with Bacon, felt the necessity of determining the Method of scientific inquiry; or who, living later, when so many sciences had been actually constructed, and thereby so many new and glorious phaeno- mena introduced into the world, were desirous to study the laws of these phsenomena, and to trace the processes by which they had arisen. That the reader may understand the nature of the following work, an account should be premised of the scope and drift of the general inquiry of which it forms a part. What this is has already been briefly intimated; but that the reader may become more familiarized with the conception, it may be expedient not to dismiss the question at once ; and as Aristotle's works are I incomplete and contain no such plan or deflnition, we may take a j rapid survey of some of the independent writers on the same I subject in modern times, whose view of the problem is essentially the same, however they may difiier in its treatment. Hereby we shall gain the authority of their names for the view we take, and, by noticing any questions which some of them may have handled and others neglected, may have an opportunity of bringing out into relief the main branches into which the inquiry is subdivided. § 2. In the Introduction to his System of Logic, Mr. Mill MILL. 3 announces that he is going to expound the Science of Evidence; and points out the limits that divide it from Metaphysics. Logic, according to his view, is not the science of Belief, but of Belief so far as it professes to be founded upon Proof. To determine what facts are ultimate, and what are resolvable into others, what are the propositions for the establishment of which Evidence is not re- quired, is the office not of Logic, but of the sister science of Me- taphysics. His definition is unobjectionable; but his limitation, which is adopted to avoid certain matters of controversy, appears to be erroneous. Relatives and Opposites, if we may be allowed to assume an Aristotelian maxim, fall under the same science : the scientific explanation of one Relative or Opposite is at the same time an explanation of its correlative. Now derivative truths and nnderived truths, concluded and unconcluded, pri- mary and secondary, are both Opposites and Correlatives, the one being the evidence and ultimate ground of the other. Logic then, if we admit the soundness of this principle, as it treats off the former, must also treat of the latter; as it treats of the nature of conclusions, must also treat of the nature of original premisses. Again, it is a reasonable maxim i that the same theory should i treat of the whole of a class. If then Logic examines Science, it must not separate it into two parts, examine the one and ne- glect the other, examine the superstructure, and neglect the basis or foundation. In other words, the same science which treats of one Criterion or truth-organ, must treat of all the Criteria or truth-organs : that which investigates the faculty of Inferences , must also investigate the faculty of Intuitions: that which/ examines the instrument of Mediate must examine the instrument of Immediate truth-apprehension. Or, to use Mr. MUl's own| term, the science of Evidence must not content itself with exa-! mining the nature of derivative or borrowed evidence, but must also ascertain the conditions of underived or unborrowed evidence. Mr. Mill allows that Logic and Metaphysics, according to his conception of them, will form the two halves of one whole body of truth; but his practice shows a closer connexion between them ;| than he allows in theory. His own treatise is an instance of the ' Post. Anal. I. 28. 4 MODERN WRITERS. limpossibility of going far into the conditions of Inference with- out entering into the question of truths unsusceptible of inference: for though he seems to have intended to avoid the topic, and in- deed announces that his theory will be such as the disciples of Hartley and Reid, of Locke and Kant, can equally accept; yet the topic is broached, and he himself clearly appears as an ad- herent of what is called the Sensational school. In Mr. Whewell's Philosophy of the Inductive Sciences the nature of Logic is described with great precision. It is a com- plete insight into the essence and conditions of all real know- ledge, and an exposition of the best methods for the discovery of new truths. Its province is to determine the difference be- tween true knowledge and its precarious or illusory semblances, and the conditions under which it is obtained. Still shorter, it is the theory which explains the nature of knowledge, and the process of discovery. These definitions are not so general as that given by Mr. Mill, which proposes for discussion all evidence whether scientific or unscientific ; nor do they profess to apply to more than one branch of Logic. Another branch investigates the conditions of legitimate and illegitimate Opinion, i Yet, as the highest element of an object chiefiy constitutes its essence, and should be given in its definition, and the investigation of Science is of higher rank and value than the investigation of Opinion, the above formulae would not be inadmissible as definitions of the whole genus. Logic. The discrimination between Scientific and Unscientific methpd has ever been the leading aim and inspiration of the genuine logician. We have traces of this antithesis in the fragments of Parmenides where he compares Reason and Opinion; in the Pla- tonic contrast of Dialectical and Rhetorical reasoning ; and Ari- stotle's distinctions between Science and Dialectics. The writers hardly deserve the name of logicians who confine themselves to examining the conditions of all reasoning, that is, the laws which are common both to Scientific and Unscientific or Dialectical me- thod, without going on to the inquiry to which this is merely ' 'Ekouttov yap to ptXnaTov iv ry — ^Topics vi. 12. ovaiij. fiaKiara, .... fiore tovto leal 'PtiHov oiv ij j-4 fSeXTurrov rj to Tov bpiaiibv tSn fiaXkov Bi\jiiaivtiv. laxarov. — Topics vi. 8. WHEWELL, BACON, KANT. 5 preparatory, what are the peculiarities which constitute the superiority of the former. This inquiry is the end proposed by the author of the Novum Organum. We have here indeed but the undeveloped germ, the rudimentary idea of the new method : but it is the idea, the germ, in its full vigour and power, safe to strike deep root in all minds fitted to receive it, and realize its mighty destiny. It may be doubted whether the spirit of the method may not even now be better caijght from the original work of Bacon, rough and inarti- cvdate as it is, than from the more finished treatises that have ap- peared after the instrument had been perfected and polished by practice. This work is an instance how much less a degree of precision is required for practical purposes than is demanded in speculation. It cannot be disputed, that, by acting on men like Newton, Bacon was to a certain degree the creator of the modem sciences. Yet how little is there in his works but the reiterated doctrine, a thousand ways illustrated and enforced, that if any thing like science was to be obtained, the preliminary observa- tions must be more exact, and more numerous ! That which chiefly displays the greatness of Bacon's mind, and most im- ) ; presses the reader with admiration, is the strong faith he places in the powers of the new method, and the almost prophetic insight 1 1 with which he hails the regeneration of the sciences that would ensue. And yet there were plausible objections to be urged against its success. There is printed among his works an in- structive letter from a certain Thomas Bodley ; which might afibrd consolation to any one who finds scepticism where he looks for encouragement. Bodley, though in a friendly manner, attempts, and that with great plausibility, to throw cold water on Bacon's hopes ; giving him credit for ingenuity, &c., but quoting old pro- verbs to the efiect that there is nothing new under the sun, and insinuating that there was nothing new in his method; that, if difierent, at most it was but different in degree : that philosophic creeds were- destined to revolve, and that he was now merely re- viving what had long ago been exploded: that before Bacon many ardent enthusiasts had arisen, who had hoped by more per- fect methods to increase the store of human knowledge, whose attempts had proved abortive, &c. &c. This was from a person whose judgment he respected. But he felt that the difference of 6 MODERN WRITERS. degree was a difference of kind, and continued to urge the world to adopt the new plan, and time has verified his anticipations. [ The Critic of Pure Reason, or Transcendental Logic, of Kant ;;' interests us so far as it is engaged with the same problem of ex- ' hibiting the structure of science: so far as it calls in question our knowledge of a spiritual world, it is beside our purpose. He divides the truths that compose the body of science into two classes : material truths that are derived from experience ; and those of a formative and organizing character, that are furnished a priori by the mind. The object of the Critic is to specify the latter, and the progress of the discussion discloses his views of ; the constitution of philosophy. He divides formal principles , into four classes, as contributed by Sense, Understanding, Judg- ' ment, and Reason. The pure or a priori Sense supplies the per- ception of Space and Time, creating the mathematical sciences, whose laws penetrate the future structure of truth in all directions. The Understanding furnishes certain generic conceptions and axioms, under which experiences must fall, and by which they must be governed. The Judgment, in what he calls its Reflective office, gives the precept of Generalization, or the command to look for Unity in Plurality, with the expectation of ultimately completing the pro- cess. In its Determining faculty it issues the precept of Specifi- cation, or the command to look for Plurality in Unity, whether in dividing and particularizing the above-named axioms and conceptions of the Understanding, or in subdividing the orders and laws discovered by Induction. ^ ' The Speculative Reason furnishes certain supreme Ideas, ne- cessary to complete the systematizing process, and to cement the whole of thought together in absolute unity. Practical Reason, besides supplying to Speculation its supreme Idea, creates itself the whole science of Morality. Thus we hare the outline and framework of the whole of philosophy, and of one portion of it something more. The re- mainder, the materials to fill up this outline, to fit into this frame- work, must be supplied by Sense and Induction. We see, then, that the purpose of Kant, as well as of the above-mentioned writers, was to exhibit the outlines and lineaments o^ Philosophy. We might quote others who have been engaged on the same PROBLEMS OF LOGIC. 7 subject, but that we have ali-eady quoted enough. As these j writers have been adduced to throw light on the views of Ari- ,' stotle, we may further compare them on certain points suggested by his writings. We shall find that one problem of his Logic is the determina- tion of the formative truths or Axioms; or principles indepen- dent of Experience, and common to all the sciences. (A.) Another problem is the nature of the Theses, or principles » characteristic of their appropriate science ; their relation to the conclusions ; and the shape and constitution of the whole body of truth in which they are incorporated. (B.) A third problem is the method of Induction, or the process by >■ which principles are discovered. (C.) Kant's Critic of Pure Reason discusses A, which is indeed its great object; throws light incidentally on B; and omits C, which is foreign to his plan. It did not belong to Bacon to recognize A ; he will not antici- pate a very definite solution of B ; and is chiefly employed on C Mr. WheweU treats of B and C, and apparently of A ; but it is not clear where he draws the line between a priori and a pos- teriori conceptions : his Axioms are not similar to those of Ari- stotle, and contain what is characteristic of particidar sciences. Mr. Mill investigates B and C, but does not recognize A ; al- though he seems unsuccessful in explaining the principle of Uni- formity by Experience, and his account of the Canons of Induc- tion assumes the principle of Causation. By this time it may be hoped that we have a tolerably clear conception of a certain subject matter which many writers have considered worthy of scientific investigation. To give however I such a definition of Logic as shall clearly show the limits that / part it from Metaphysics, is by no means easy. If, for instance, Logic is the science of Knowledge, there are some questions about Knowledge which Logic does not consider. The relation ' of Subject and Object, of the Mind and the World, of our con- ceptions of the world, and that which the world is in itself inde- pendently of our conceptions, are questions which must be as- signed to Metaphysics. Th? se may be excluded, by ascribing to Logic the theory of the internal, not the external relations of Knowledge. What is the final shape and organization of human 8 CONTENTS OF THE ORGANON. / Belief, what the relation of affiliation or interdependency between \ two portions of thought, whatever may be their relation to out- ward existences, will then constitute the problems of Logic. § 3. We may next give a rapid sketch of the contents of the Organon, in order to render more intelligible that portion of it which is here translated. If we assume that Logic has to deter- j mine what is the perfection of the intellectual faculties, and what are the measures to be taken for this end, it wUl inquire what is the nature of Science, and how it is to be pursued ; and what is Opinion, for this is often the utmost we can obtain, and how se- ' curable, as far as may be, from error. The formation of Science and of Opinion, by which we mean any unscientific belief, is partly similar, partly dissimilar. Logic, then, will naturally fall ' into three di^'isions : — I (A.) The generic branch, which treats of reasoning in general, i whether the result is Opinion or Science. (B.) The specific branch, which treats of reasoning the result of which is Science, Inductive or Deductive. (C.) The specific branch, which treats of Dialectical reasoning, the result of which is Opinion. (A.) This branch is contained in the Prior Analytics, to which we may append the Hermenia and Categories. The first of these treats of Syllogism, the second of Propositions, the third of Terms. Their contents are well known, having been transfused into the works of the scholastic logicians, whose only fault was that they did not sufficiently perceive that these were merely preliminary inquiries. The principle involved in all Syllogism is the dictum de omni et nullo^ which it will appear is identical with the Axiom, or the principle of Contradiction. When Dugald Stewart observes that the whole of the science of Syllo- gism is comprised or implied in the terms of one single Axiom, his assertion is quite correct ; the doctrine of Syllogism merely determining, on the authority of the Axiom itself, under what conditions the Axiom is applicable. His assertion, however, (Philosophy of the Human Mind, part 2, chapter 3,) that the object of Aristotle is to demonstrate by abstract reasoning the conclusiveness of demonstration, to ' See Appendix, (A.) MODALITY. 9 demonstrate by the syllogistic theory the validity of the syllo- gistic theory, is totally unfounded. No doctrine is enforced with more emphasis by Aristotle than this, that some truths are indemonstrable : and the very proposition he instances as being plainly indemonstrable, both as possessing already the highest possible evidence, and as required for the demonstration of other truths, is the A:xiom or principle of Syllogism.' To show the limits of its application, he employs the principle itself, because it is supreme, and there was no higher authority to which he could appeal. The laws of Modality are investigated in an inquiry that is preliminary to the theory of Science, as a certain modality of premisses and conclusions is an essential characteristic of science. Modality is sometimes called Matter, and it is a com- \ mon doctrine that matter is extralogical, and this would seem j to exclude modality from the consideration of Logic. Now the expression, that matter is extralogical, may mean, that, though Logic examines Science, Astronomy for instance, yet it teaches nothing about the stars, the subject-matter of Astronomy. For every science has its own subject-matter or province with which no other science interferes. But though Logic teaches nothing about the matter of Astronomy, yet, as a science, Logic has its own subject-matter, to which Astronomy is equally a stranger. So the matter of Chemistry is extralogical, and the matter of Logic is extrachemical. However, it is too evident a f fallacy to infer, that because the matter (of other sciences) is \ extralogical, therefore Modality, sometimes called Matter, is ! extralogical. But it may perhaps be urged, that none but the professor of a particidar science can know the modality of a par- ticular proposition ; and therefore it cannot be treated of by Logic. But Logic is equally ignorant of the quantity and quality of the proposition arising from the connection of two terms, and yet it investigates the laws of quantity and quality: it will therefore investigate Modality as it does quantity and quality, that is, hypothetically. If the words Matter and Form are used in the Kantian sense, then it must be remembered that the notions of necessity and ' See Appendix, (a.) C 10 CONTENTS OF THE ORGANON. contingency compose, according to Kant, part of the formal furniture of the mind, and in this view Modality would fall under the province of Logic. i Another subject discussed in the Prior Analytics is the fact, [that false premisses may give a true conclusion, i. e. that an hypothesis is not sufficiently established by showing that its con- sequences agree with phsenomena : and the mode in which pre- misses and conclusions may reciprocate : inquiries which seem to be a preparation for explaining the nature of Analytical and Synthetical reasoning, i and the method of testing Hypotheses. Also a slight and inadequate account of Induction is given. In general it must be confessed of these treatises, that the investi- gations are carried out with a minuteness that may be curious, but is not otherwise either interesting or valuable. § 4. Having concluded the generic theory of Syllogism, we proceed to its specific peculiarities. B. We treat at first of Deductive Science : and this division leads us naturally to inquire, to which class does Logic itself belong, Deductive or Inductive ? Aristotle treats it deductively, for he begins ^^ by defining Science to be the teference of the laws of phsenomena to their causes. We must not suppose I however that he was entitled to assume a definition, as in the I simplest mathematical sciences, without any justificatory inquiry. Logic, like Politics, is a practical science ; its reasoning is Ana- lytical, and the basis of its reasoning the conception of an end to be attained. As the end of Politics is happiness, or some- thing similar, and its problem the measures and machinery by which it may be promoted ; so the end of Logic is science, and ,iits problem the process of discovery : and the justification of the Iprinciple it assumes, that is, of the end it proposes, would ap- pear to consist in the proof of two propositions : these proposi- ti tions are : that no higher end is practicable, and that there is no linsurmountable obstacle to the attainment bf the end proposed. 'When these are proved, we may assume that the end is rightly selected, and that the theory rests on its appropriate basis. ' For an explanation of these pro- Bophy of the Human Mind, part ii. cesses see Dugald Stewart's Philo- chap. 4. ' Post. Anal. i. 2. SCIENCE INVESTIGATES CAUSES. 11 Now with regard to the former point, there are none who maintain that the aim selected is not sufficiently high : for the dissentient school contends that it is only too ambitious, insist- ing that science must renounce the hope of discovering Causes, and content itself with a humbler aim, the knowledge of Laws. The legitimacy of the hypothesis then depends on the otherj point, the truth of the suppositions analytically involved, or the' feasibility of the steps demanded : what these are we shall pre- sently examine. Meantime it .must be observed, that the main characteristic of j Aristotle's Logic, which is both the foundation of the rest of his ' own theory, and brings him into contrast with a modern school, is his attributing to science the investigation of Causes. Many writers — ^for instance, Hobbes, Berkeley, Hume, Brown, Dugald Stewart, Comte — deny the existence of any thing like causation, maintaining that what is so called is merely the invariable, but, f for all we know, arbitrary, conjunction of antecedent and conse- quent. The maintainers of this theory confess that the belief in natural causation is an universal instinct, which has been the great impulse to scientific research. They seem to have for- gotten the mathematical sciences ; for no one could maintain that the attributes of figure and number — for instance, that the interior angles of a triangle are equal to two right angles, or that three is the cube root of twenty-seven — are merely arbitrary and fatal ; and it has not been shown why physical cause and effect are not as naturally connected as mathematical subjects and attributes.^ To abandon the notion of Causation is to abandon the notion of Necessity as a characteristic of knowledge : for however con- stant and fatal the conj unction of two terms may be, yet if we only perceive them in juxtaposition, unless we perceive the manner in which they are locked and linked together by their essences, we cannot recognize the necessity of their connection. If however we introduce the notion of Causation and intelli- gible Necessity,* we are inevitably led to rest science on defini- tions : for in order to perceive the essential interpenetration 6f ' See Whewell, PhUosophy of the book xi. 16. Inductive Sciences, book iii., also ' Post. Anal, book i. 4, 6. v^ 12 SCIENTIFIC PRINCIPLES. any two terms, we must have a distinct conception of their essence, and the expression of such a conception is Definition. From this consideration some characteristics of scientific pro- positions might be deduced, which will be found to distinguish them from dialectical propositions. The terms of a scientific proposition, being essentially connected, will be coextensive or commensurate. ' Again, if the diversity of sciences depends on the diversity of the genus investigated, and Nature is heteroge- neous, there will be a multiplicity of sciences ; ^ and as the same predicate cannot be homogeneous to two heterogeneous subjects, the same predicate will not enter two difiierent sciences, but every scientific proposition will be confined to its one appropriate science. Whilst these are necessary, essential, coextensive, appropriate; dialectical predicates and propositions are contin- gent, accidental, incommensurate, and promiscuous or indeter- minate. If the conclusions of science must satisfy these conditions, it is not difiicult to see what must be the nature of its foundations. (1.) Definitions wiU be required, both of subject and of attri- bute, both of the compound and of the elementary. 3 The defi- nition of the elementary will not be further analyzable ; the definition of the compound and dependent must contain its elements and antecedents : and thus its parts will correspond to the premisses and conclusions of a syllogism. (2.) But we need more than Definitions : if we have merely these, our conclusion will be merely hypothetical. To give it a categorical character, we must be able to assert the real existence of the subject in which the attribute inheres, or of the primary power or elementary substance which generates the remote con- sequence. The proposition containing this assertion is called the Hypothesis. (3.) If we are not sensible of wanting more than these, still there is another principle which we always tacitly assume. In passing from any premisses to a conclusion, we rest upon the Axiom, or the principle of syllogism. The intuition of this principle constitutes the reasoning faculty. It is not always ■ Post. Anal, book i. 4, 5. ' Post. Anal, book i. 7, 9, '27, 32. ' Post. Anal. ii. 8. THERE MUST BE FIRST CAUSES. 13 used in its widest extent, in which it is a predication of identity: in mathematics it is merely regarded as a predication of equality. The Topics of Dialectics and Rhetoric are mostly particular cases of the Axiom. These elements of knowledge, which form the basis of Deduc- tive science, will form the conclusions of Inductive inquiry: ifor in general the problems of all sciences may be divided into four classes : — (1.) Is it a fact, that a given subject possesses a given attri- bute? (2.) What is the reason of the fact, that a given subject pos- sesses a given attribute ? (3.) Is a given conception of an elementary substance or power imaginary, or real ? (4.) "What is the character of a certain primary substance or power ? Of these the third and fourth are Hypothesis and Definition, the result of Inductive inquiry, and the basis of Deduction. The second problem should be answered by Demonstration, and its answer will contain the solution of the first. We may now consider the question suggested above, what suppositions are involved analytically in the hypothesis, in the possibility of science such as we defined. They are two : the one may be called an ontological, the other a psychological pos- tulate. As science ^ professes to explain causes and answer every Why ?, the series of genera and difierentiee that enter into the composition of an object must be finite, for the cause of a generic property is to be found in the definition of the genus ; and there would be no exhausting the series of possible ques- tions, why a subject possesses a given generic property, unless the number of genera and difierentiae contained in the subject is finite. And as the series composing the formal cause of a sub- ject must come to an end, in order that we may reach the formal element that is immediately connected with the predicate ; so must the series of material, efiicient, and final causation come to an end, in order that we may exhaust the questions Why?, when the immediate antecedent happens to be a term in the ' Post. Anal. ii. 1. ' Post. Anal. i. 19, 20, 21, 22. 14 THERE MUST BE AN INTUITIVE FACULTY. material, efficient, or final series. On these suppositions de- pends the possibility of realizing the scientific idea. Unless we have first Causes, and unless the series of Generalization is finite, we have no basis of Demonstration. Both of these suppositions — that the chain of antecedent causes to any consequent, and the number of specific elements in any essence, are finite — are ex- pressed by Aristotle in the assumption, that every object is definable, for the definition includes every kind of cause ; and this may be called an Ontological hypothesis. This supposition however thai; there are indemonstrable truths is not alone sufficient to show the possibility of Demonstration: we must further assume that we have some faculty or faculties corresponding to these truths, and capable of apprehending them : Aristotle asserts* that Sense and Reason are such facul- ties : and this may be called a Psychological hypothesis. These two hypotheses, then, are indispensable to the theory of science. Let us first consider the Psychological hypothesis. Upon this subject bear the controversies about the Criterion or Organ of truth. Philosophers were divided into those who denied and those who maintained the existence of a Criterion : the former were the Sceptics. Those who maintained a Crite- rion either advocated a simple or a mixed Criterion : the ad- vocates of the former were divided into Sensationalists and Rationalists, as they advocated Sense or Reason ; the advocates of the latter accepted both Sense and Reason. Democritus and Leuoippus were Sensationalists : Parmenides and the Pytha- goreans were Rationalists : Plato and Aristotle belonged to the mixed school. Among those who advocated Reason as a Crite- rion there was an important difierence : some advocating the common Reason, as Heraclitus and Anaxagoras: others the scientific Reason, or the Reason as cultivated and developed by education, as Parmenides, the Pythagoreans, Plato and Aristotle. In the Republic, 2 Plato prescribes a training calculated to prepare the Reason for the perception of higher truths. Aristotle re- quires education for the Moral Reason. The older Greeks used ' Post. Anal. i. 3, and ii. 15. Baiperai Tt xal dvaZuirvpurai. — De ^ EV TovToig Totg iiadrj/iaaiv Hepublica, vii. § 9. £(caffrot£ opyavov n ^vxve kKxa- THERE MUST BE AN INTUITIVE FACULTY. 15 the word Measure instead of Criterion : and Protagoras had said that Man was the Measure of all truth. This Aristotle interprets to mean that Sense and Reason are the organs of truth ; i and he accepts the doctrine, if limited to these faculties in a healthy and perfect condition. These names then cannot properly be ranked among the Common Sense philosophers, where they are placed by Sir WiUiam Hamilton. The manner in which the WiU is the Criterion of moral truth may be left to the theory of Morality. It is where the faculty has to be trained before it is Capable of perception, as in the fine arts and morals, that the theory of the Criterion is most difficult, and it is here that the Sceptics find it most advan- tageous to maintain the controversy. There is nothing on the subject in the Organon. When Reason is said to be an Organ of truth, we must include, besides the intuitive, the syllogistic faculty. This is the in- strument of the mediate or indirect apprehension of truth, as the other of immediate. The examination of these instruments, in order to discover their capabilities and right use, is Logic. This appears to be the reason why Aristotle gave the title of Organon to his Logic. So Epicurus called his the Canon or Criterion. The controversy on the Criterion is to be found at length in Sextus Empiricus De Criterio. What we have denominated the Ontological hypothesis ofi Deductive Logic, the finiteness of generalization, appears to be ; the same as the hypothesis demanded by General Logic, the existence of universals, and the hypothesis of Inductive Logic, the uniformity of nature. General Logic demands the exist- ence of universals*: for though it would be possible to reason, as Aristotle observes, without the Platonic Ideas, it would not without universals ; for without these there could be no middle term (which is always universal), and without a middle term no syllogism. Inductive Logic also makes a similar hypothesis, imder the name of the Inductive principle, the belief that Na- ture is a " tissue of laws," or that she is " stable and uniform." These hypotheses, which are necessary for Syllogism and In- duction, do not appear essentially distinct from the hypothesis • Metaph. x. 2, and xi; 6. ' Post. Anal. i. II. 16 THERE MUST BE FIRST CAUSES. ■which is necessary for Demonstration. For the same tendency that made us reduce the number of particulars by ranging them under universals would impel us to reduce those universals by ranging them under others still higher ; and the simplifying process, which began by reducing the Infinite to the Many, ■would not desist tiU it had reduced the Many to the One, Besides the existence of universals, Deductive Logic makes the hypothesis that every event has a cause, and that the chain of causation is finite. As, however, the reduction of univer- sals to the one appeared the work of the same principle that reduced the infinite to universals, and was not the matter of a distinct postulate, so the principle of looking for an absolute primary may be considered the same as that of looking for an antecedent, and does not require a separate hypothesis. The principle of the finiteness of the chains of generalization and causation belongs to the science of Being. In the Orga- non the argument is led so far, and then dropped. The prin- ciple is asserted and briefly considered in the Metaphysics, i [■ These hypotheses of Deductive Logic — the necessity of I assuming an absolute termination to the generalizing series, and an absolute beginning to the chain of antecedent and consequent, if science is to be possible — are recognized by Kant, and ascribed to the Reflective Judgment and Reason. The fact that laws can thus be given to Nature by the mind, he calls its autonomy or legislative power. He connects the law of Generalization and Specification with the teleological principle, by which we introduce final causes into natural science. As the organization of objects is determined by their end or destiny, so, if the end of Nature is to be known, she will obey any laws which are the conditions of being known : and as the condition of her com- prehensibility is the finiteness of the above-mentioned processes, it follows that these processes are finite. § 5. The Inductive method shall be considered after we have discussed the nature of Dialectics. (C.) Dialectics is defined^ to be the method of arguing with ' Metaph. ii. 2. avroi \6yov VTrixovrcg fi^Oiv ipov- ^ MI9o Joe d0' riQ SvvtiaofuBa av\- jiev virtvavTwv. — Topics, i. 1 . A \oyiZ,iv ■>) 0i\o(7o0ia yvdipia- Logic seems to be called a part of TiKT]. — Metaph. iv. 2. Dialectics. This latter statement " This may explain the passage in must be inaccurate : for General the Rhetoric, Trepf ovKKoyLa/tov o/ioi- Logic is a preliminary to the theory CONTRAST OF DIALECTICS AND SCIENCE. 19 light the theory of Dialectics may be considered to be an inte- gral part of Dialectics: and thus it happens that, though Dia- lectics and Logic are related as Logic and Science, yet there is a closer connection between the former than between the latter. At the risk of creating confusion, we must notice that the word Logic, as applied to the Science of Evidence, and as we have hitherto used it, is modern. Aristotle's term for this theory is Analytical Science.^ When he uses the word Logical, he uses it as equivalent to Dialectical; and he generally uses it when he wishes to oppose the Dialectical to the Scientific. It, or some cognate, will occur in several of the passages we shall proceed to quote, but to avoid confusion we shall always translate it by the word Dialectical. (1.) An argument is Dialectical that rests on Inappropriate principles, that pursues an Inappropriate method. As in Physical science the Appropriate method is Inductive, Dialectical is often opposed to Inductive. Democritus reasoned inductively, and is instanced as using a Physical and Appropriate, not a Dialectical, method. Others were great dialecticians but no observers, and therefore unsuc- cessful in their physical theories. Great familiarity with phae- nomena is necessary for the Physical philosopher.^ The forced and strained theories of philosophers are due to their perverse method. They make every thing bend to certain assumed dogmas, instead of being guided by observation.* The more abstract a Dialectical proof is, the wider it departs from the Appropriate principles.* of Science, jiist as much as to the ' tovtov S" ainov rb /irj KaXuJg theory of Dialectics : but it is possi- Xa^uv r&g irpwraq apxitg, aWA. ble that Dialectics is here not used navra ^ovXtaBai irpoQ nvag So^ag in its proper sense, but as a synonym mpKr/iBvag civayeiv' Set yap icrbig for Analytics or Logic. tSv jiiv aMrirdv aiaOr/TAg, tSiv ' Khet. i. 4 ; Anal. Post. i. 22. Si aiSiuv diSiovg, tS>v Si fQapT&v " ISoi S' av Tig KoX Ik tovtiov '6aov (jSaprag Aval rhg apxcig, oXiag S" Sia^kpovaiv ol (pvatieSig xai Xoyucfis ofioyeveig Tolg iiTroiceifiBvoig. — De aKOTTOVvrag AriiioKpiTog 3" &v Coelo, iii. 7. ^avtii) oiKitoig (cat ^vaiKoXg Xoyoig * 'AiroSei^tg \oyiK^ . . . '6(T(f Ka96- irfTriiadai. Neglect of Observation \ov nSXKov iroftpiorkpio tS>v oiKcioiv is called Smipia. — De Gen. et apxv. — De Gen. Anim. ii. 8. Corp. i. 3. 20 LOGIC OF OPINION. The theory of the Platonists arose from their Dialectical method, for they were the first great dialecticians. i Dialectical method is, however, not always opposed to Induc- tion : it is applied to unscientific argument when the appropriate principles are Deductive. There are two ^ examples of this in the following treatise. So far as a Dialectician or Rhetorician employs the appropriate principles or appropriate method, he ceases to be a Dialectician, and his argument becomes scientific.^ (2.) Another mode of expressing the peculiarity of Dialectics as opposed to Science we have in the Rhetoric; that it has no peculiar or appropriate subject genus.* Its arguments will apply to heterogeneous subjects:* whereas no scientific proof can migrate from its original science -fi for every science has a deter- minate province, and, while there is but one Dialectics, there are as many sciences as there are provinces. This property of Dialectics is equivalent to the former, that it disregards the Appropriate method. (3.) Or we may characterize Dialectics by saying that its treatment of any particular matter will be accidental,'' whereas scientific .propositions are all essential to their subject-matter.^ This follows from the preceding: for any argument or medium ^ 7] tS)V hSCjv eltraytoyrf 5«i Trfv ov iripi ri ykvoQ i^iov aiphipicnk^ Iv toXq Xoymg eyevero ff/csi/ziv ol yap vov. — Rhet. i. 2. npoTspoi AiaXcKTiKijg ov fisTtixov. — wepi tov SoBivrog. — Ibid. Metaph. i. 6. ov ■Kovriau inpl oiSiv ysvog ifi- ' Anal. Post. i. 23, and 32. ippova. — Rhet. i. 4. ' dv yap ivTVXV "PX^'S oiiKen Trepi wavTiov. — Soph. EI. II. Trepi AiaXEBj-iK^ oiiSi 'VtiTopiKfj aW ixti- irav yevog. — Ibid. vr) iarai fig Ix^i Tag dpxdg. — Rhet. = Bi6 Kal iir' oKKtav e^apfiorrovaiv i. 2. 01 XSyoi oil trvyyevdv. — Post. An. Xriazrai T'fiv fvaiv avToiv afavi- i. 9. aag Tif fura^aivtiv liriaKiva^iiiv tig Tcpbg ■KoXXoiig 'iari fiEreveyKtiv. — tTnarrifiag vTroKUjikviiiv rivwv wpa^ Soph. El. II. yfiariov dWa firj jadvov \6yv. — ^ ovk tariv 15 aXXov yevovg /ura- Rhet. i. 4. jSavTa Sei^ai. — Post. An. i. 7. Kal fiaXXov airrofitvoi Kara, rpoirov oiiK strri fisrsveyKeXv Sid to sk twv (Bard rfiv o'lKuav jiiOoSov (?) ) iicTa- iSiav ilvai dpx AiaXeKTUcri ng . . . v Sewpet oil -/dp f^xpt Tivbg iyxtipovnv dvaKpi- rbv diora dWd rbv dyvoovvra Kai vuv Tovg ivayyiWoidvovg. — Ibid. 22 LOGIC OF OPINION. If the examiner is himself ignorant of a science, by what premisses can he expose the false pretensions of another who professes to know the science ? i The propositions he employs must be conclusions or dependent truths, which would be known to one who was master of the science,'^ but which also may be known to one who cannot deduce them from their ap- propriate principles,' without which knowledge is unscientific. The process was finally subjected to strict rules, chiefly calculated to secure the division of labour, by confining one party to the defensive, the other to the oflTensive, to avoid confusion, and prevent the dispute from becoming interminable. The Answerer, the person who maintained the defensive, began by enouncing some dogma or Thesis * which he was willing to defend. This Thesis must not be confounded with the scientific principle ; though, as the first truths of a science were submitted to a Dialectical examination before they were recognized, the two meanings would often coincide. It was the oifice of the Questioner to show that this Thesis led to obviously false consequences, or could not be defended without an inconsistency. For this purpose he had not the licence of the Orator, who may argue triumphantly from as- sumptions his adversary would never concede, and obtain invin- cible data from unscrupulous witnesses, but was confined to propositions allowed by his opponent, and extracted by ques- tioning, which made the process a series of Questions and An- swers. And the Question was to be such as could be answered by a simple affirmative or negative.^ If obvious, the proposition ought to be conceded ; if otherwise, the Questionefhad to adduce examples and claim it inductively. ^ The Answerer was not ' Sivarai truXXoyiJeffSai ypevSog Si eiSsvai Trjv Tsxvriv, /j,^ dSoTa Sk ayvoiav Tov SiSovroQ rbv \6yov . . . avdyKtj ayvouv. — Soph . El. 11. tiiffre TTOicT SfiKov d dyvoei. — Soph. ■* Topics, i. 9. El. 8. ' irpbg ijv tanv AiroKpiveaBai, ^ SK ruiv doKovvTuiv Tt^ anoKpt- valj rj ov, — Topics, viii. 2. vofiiv Kai dvayKaiav uSkvai Tv Xoywy nXrifiiiivai do- '■' a/iipiirliriToviiEva, — Rhet. iii. 5ai Kal irpoTaauQ. — Rhet. ii. 18. * o civ 'iv bv Kai ftiKpdv £7ri TToWd ® Koivd. y xp'h<"-l'-ov. — Metaph. v. 3. ' "iBia. ^ ASr). The word ykvoQ is used of ° t& i^ vrroyviov. the Organa, Topics, i. 12, but it is PIRASTIKE. 25 As the Organa or Generic propositions of Dialectics were di- vided into three classes, Ethical, Physical, and Metaphysical; so the Specific propositions of Rhetoric are ranged under three chief heads. Honour, Justice, Expediency. It may be observed, that Aristotle always uses the same or similar terms to express the collection of Scientific, Dialectical, and Rhetorical propositions. ^ After the enumeration of the Topics, directions are given to the Questioner as to the order in which the questions shoidd be arranged, and the manner in which they should be put.? As the Answerer will be disinclined to make any concessions, the bear- ing of which on the Thesis he perceives, it wiU be an object to conceal the drift of each particular proposition. This may be eflfected by mixing the essential propositions with others irrele- vant, and by deranging the order of the essential propositions, that is, proposing them unconnectedly and incoherently, not in the sequence in which they will finally enter the syllogism. The concealment is completely successful when the Answerer does not suspect that he has lost his cause after the fatal concessions have been made, till his opponent extricates and rearranges them, and shows that they involve the contradictory of the Thesis. The character of the opponent should be studied: some from confidence in themselves and contempt of their adversary will make any concessions at first, but afterwards grow more Cautious : from such the necessary propositions should be drawn before their fit of circumspection comes on. Others are excess- ively cautious at first, but afterwards grow ashamed of making so many difficulties, and become more liberal in their concessions. The jealousy of these persons, says Aristotle, should be exer- cised on indifferent matters, and the important propositions kept back till they begin to suspect themselves of over-timidity. Similar artifices are suggested, and some represented as fair, others as Sophistical.' One of these is, to rouse the anger of ' licXIyeij/, kKXanPivuv. — AnaL irpoTaaeigiKKeKTEOv. — Topic8,i.l2. Post. ii. 13. ^X"" i^eiKeyjiiva. — Bhet. ii. 23. ■TTporAaeig kKXafi^dvuv. — Anal. rpovog rfjg iKS.oyrjg TomKog (1. e. Prior, i. 27. ttdiKog). — Ibid. TrpoT&aug J/cMytii'.— Anal. Prior. = Topics, viii. 1. i. 30. 'Soph. El, 12 and 15. 26 LOGIC OF OPINION. your adversary by barefaced attempts at unfairness, as a dis- putant is not so formidable when lie loses his temper! These nefarious practices are pointed out of course for our avoidance: besides, we have scarcely a right i to speak with reprobation of Sophistry, unless we understand its character. Some artifices, though unjustifiable against a fair adversary, are j ustifiable against one who is unscrupulous himself: * but however fair, as far as he is concerned, we must avoid them from respect for ourselves : ' and, if we follow Aristotle's advice, instead of meeting Sophistry with Sophistry, we shall exercise a discrimination in choosing our adversary, and avoid engaging with those who cannot ob- serve the laws of honourable war&re.* We now proceed to the duty of the Answerer : for though the original province of Dialectics was merely the offensive pro- cess, that of assailing a given Thesis,^ it soon proceeded to in- vestigate the art of defence, and this province accordingly is included in its definition. The theory of Solution is contained in the short treatise on the Sophistical Elenchus, which ought to be regarded as the last book of the Topics. We may first, however, determine what propositions the An- swerer may be expected to concede, and what he may claim to withhold : ^ and the determination depends on the nature of the Thesis he advocates; which must be either probable, improbable, or indifferent, neither highly probable nor highly improbable. If the Thesis is improbable, its contradictory, the conclusion of the Elenchus, will be of itself probable; and as the premisses of a syllogism ought always to be more probable than the conclu- sion, the Answerer is not bound to grant propositions, however probable, unless their probability is greater than that originally possessed by the conclusion they have to establish. If the Thesis is probable, the conclusion of the Elenchus wiU be the reverse ; and then the Answerer ought to allow premisses which ' Soph. El. 16. ^ wairip yap ij Iv dyiSvi ASida ^ Soph. El. 17. eXdog n exei, koi sanv dStKOfiaxia ' SUaiov jiiv oiiK tvaxrinov ik. — ng- ovrag r/ tv dvTiKoyty, dSucoiia- TopicB, viil. 13. X'« ioTtv kpiaTiKr/. — Soph. El. 11. ov del avvtaravai evxipiSg irpbg ' Soph. El. 34. Tovg TV%6vTag' avayxri yap jrovripo- * Topics, viii. 4. Xoytav ffvfiPaiveiv, — Ibid. SOLUTION. 27 though not highly probable, still possess a higher degree of pro- bability than the conclusion. If the Thesis is neither probable nor improbable, its contradictory is of the same character, and propositions of but slight positive probability may be fairly claimed. The same rule will hold, whether the probability or improbability is absolute or relative to the creed of the particular Answerer: and if the Thesis is not a tenet of his own, but of some celebrated school or philosopher, reference must be had to what was probable or improbable in that school, or in the views of that philosopher : and if a third person succeeds to the cause of one of the original disputants, he should govern himself by the opinions of the person whom he superseded. Before we proceed to Solution we will explain certain terms : and we may observe, that there is great precision in the Dialec- tical nomenclature. Eristic and Sophistical reasoning are the same, but differ in the motives from which they are employed. A fallacy is Eristic, if prompted by the heat of dispute and the desire of victory: Sophistical, ^ when employed from mercantile motives by a pseudo-philosopher, who makes a trade of imaginary wisdom. A Sophistry must be distinguished from a Pseudographema: both are fallacies, ^ but the first is Dialectical, the second Scien- tific. As a sound Dialectical argument differs from a sound Scientific proof, becaiise the latter is confined to a particular subject-matter, while the former is indiscriminately applicable to several; so a Pseudographema is only practicable in a parti- cular department, while a Sophistry is of a Protean character. A Pseudographema* then, is defined to be a fallacy constructed of the false principles peculiar to a particular science, and is consequently intransferable.* ' aoipiaTiKol o\ So^ris x^P''" ^VS "£ ^ napaXoyttriioi. XpriiiaTiaiiov' tj yap ao^uTTiierf ean ' ol ek ruiv irepi tivuq iiriaTrjiiaQ XprilxaTiaTucri ng airb ao^iaq ipaivo- oiVeiwv yivofuvoi TrapoKoyuTfioi. To- fikvrig. — Soph. El. 11. pics, 1. 1. kK riiSv dpx<^v Kal riiSv Kal yap rj ao^uiTmri ian ipaivojii- ovinrcpatriidTwv riSv virb tijv tcx- vri aofia ng dKX oiiK onjaa. — Ibid. vriv \(/evSoypa€i. — Soph. Blench. II. ean ycip ri aotpiarixri ipaivopivfi It does not appear that the name was e Sii, rt ypafiiiaQ nvaQ ayuv jif) i>e ctv dxOetTjffccVf rdv -jrapaXoyifffibv TroteT- Tai. — Topics, i.l. ' ipsvSyg \6yog KoXuTai. (') edv did if/evSuSv avjiiTtpaivii)Tai' (') orav (paivrjTai (jviiinpaiveaBai fufl avjiirtpaivoiiivog' (') 'drav avjiirspaivriTai fiiv, fifi fjivToi irpbg r6 TrpoKsifievov C) 'oTav irpbg to TrpoKiifievov fiiv avfiTripaivtirai, /irj jiivToi Kara tjjv oiKelav jikBoSov. — ^Topics, viii. 10. As the third is a case of Ignoratio Elenchi, in the book on Fallacies (chap. 11), it is included among the second. The fallacy of non causa pro causa would also fall under the third of these heads. — Soph. El. 5. ^ As the preposition icnrd desig- nates the cause of an attribute, so the preposition irapa designates the cause of a fallacy. i^uTiv ri Avffig kfi^duiffig ^evSovg ffvXKoyifffzod Trap OTToiav kptJTtjfftv avfifiaivei rb \f/£vSog' Kal 77 tov to a genuine Elenchus, or else there could be no deception : its Solu- tion therefore consisted in Distinction,^ or pointing out where this resemblance failed. There were thirteen different heads of these delusive resemblances, well known under the name of Logical Fallacies, and to be found in the common books of Logic, which we therefore need not explain. The other kind of Enstasis is Denial, or Rejection. If the reasoning is conclusive and the Answerer refuses to abandon his Thesis, his only alternative is, to show reason why one of the premisses should be Rejected: of course it would have been better never to have made the concession, but if made, nothing is now left but to retract it. His bare negation was insufficient : he had to adduce an Homogeneous, Analogous, or Opposite case, or might appeal to Authority.' Enstasis seems to have been re- strained to these four topics, because it was desired, as far as possible, to confine the reasoning to the Questioner, and to place avu^aivei tiSv Xoyuv Toiig fiiv Phya. Anse. i. 3. See also the defi- avWeKoyuT/uvovQ dvcXovra roig Sk nition of Ximg. ^aivojiivovg SuXovra \veiv. — Soph. ' yiverai Sid nvog o/toioTijTos. — El. 18. Soph. El. 1. bjrws r) dvaipovvreg r) Siaipovvreg ' Siaiptmg. Xvaiiiev.—lbid. ' Anal. Prior, ii. 28. Rhet. il. 25. tl yap dvaipei f) Siaipei 6 kvurra.- The same laxity was allowed to the ixevog. — Topics, viii. 12. tpittriKSig Questioner in making a direct pro- avXKoyiKovrai, xal yap ^ivSn Xafi.- position.— Topics, i. 8, and 12. Pdvovai Kai davWoyiaroi ft'eri. — 30 LOGIC OF OPINION. the Answerer in a purely defensive attitude. Why a preference should he given to these particular four is not inconceivahle, Authority was a topic peculiarly Dialectical, as appears from the definition of a Dialectical proposition: Propositions relating to Opposites are closely connected, and, mutatis mutandis, may be considered identical: and Analogy or Induction is one of the simplest modes of reasoning. An Homogeneous case is either generic, or specific to the subject of discussion. Yet there was no reason why the other topics should be abso- lutely excluded : they were admitted, then ; but this mode of objecting to a premiss was not considered Enstasis, but Anti- syllogism.i This latter term then is not only applied to a syllo- gism framed by the Answerer against the conclusion of the Elenchus, but also to a syllogism directed against a premiss, when it falls under any topic other than the four that constitute the Enstasis. What is said of Enstasis in the Prior Analytics only applies to Enstasis by Rejection, and only to one of the four forms of this. In the Rhetoric we have a similar account of Solution,^ which is divided into Enstasis and Antisyllogism : ' and we have some further observations on the mode in which the Sign, Tekmerion, Induction, and Verisimilitude are enstatized. Signs can be always enstatized by Distinction, as they are always inconclusive : the Tekmerion can only be enstatized by Rejection, as its sequence is unexceptionable. It is not a sufiicient Rejection of Inductive propositions and Verisimilitudes, to ad- duce singular exceptions; this only shows they are not universal: but we must also show that they are not general ; for generality is enough for the opponent. The account that has been given of Pirastike will apply with but slight modification to Dialectics in general : the former employs any premisses that the Answerer chooses to grant,* be- ' This appears from the following li. 25. El oiv iiijTE dvTemx^ipsXv ' v 'ivaraaiQ rb i'nruv do^av nvd E%wi/ firiTe kvi(TTaa6ai oi riOjjfftf Sij- e? r/g 'itrrat SijXov '6ti ov cwWeXoyt- \ov oTi SvdKoXaivtt. — Topics, viii. 7. arai fj '6n TpsvSog ri t'iKtiv iv Tip ykvcf tovto tion of Conceptions and Colligation S' lariv iK Tov Trdaag TeBiuiptiiekvai of Facts, book ii. j De Coelo, i. 10 ; Tag Siafopdg. — Do Ceelo, ii. 13. Met. i. 3 ; Met. iii. 1 ; De Anima, ' See the Philosophy of the In- i. 1 and 2. ductive Sciences : on the Explica- ' Post. Anal. ii. 18. DEFECTS OF THE SYSTEM. 33 Methods of Agreement and DiiFerence ; and if, instead of Topics to establish the various kinds of Predicable, Aristotle had set himself to ascertain rigorous methods for the determination of such propositions, he might have approximated much nearer to the perfection of the modern Logic. Although the ultimate laws may appear in the form of Definitions, it is a great mis- take, as Bacon often observes, to proceed too precipitately to the discovery of these, instead of gradually advancing to them through laws of increasing generality from the primary laws, the immediate generalizations of phsenomena. Rules for the ascertainment of causal connections would have been more valuable than methods for the establishment of the Predicables : but though a scientific definition should express the cause of the object defined, no notice is taken of this in the Dialectical Topics for the establishment of Definition. A proposition expressing a Property is commensurate, but if we examine the Topics for Property, we shall find that they rather relate to the incidents of verbal controversy, than to the establishment of scientific laws. Plenty of writers have declaimed in vague terms against the old method of investigating principles, but none has indicated the exact points in which it difiered from the new. And yet our knowledge of the latter would be more complete, if we knew its relation to the one it superseded ; and now that the true method is so firmly established, there is no reason for exagger- ating the defects of the old, or danger in acknowledging the degree, whatever it was, in which it approximated to the truth. Besides the circumstance already mentioned, the laxity of the Topics, or methods of arguing from phsenomena, and the infeli- citous choice of the ends proposed to these Topics, another vice in the old system was the paucity of these original phaenomena, and the carelessness with which they were collected. We have a general recognition of the fact that the Physical i sciences must rest on induction, both in the passages already | cited, and in others that might be adduced ;i for Aristotle \ • clpiiKaai fiiv, ov KoKuie Si, dW r&e irepi iKaarov Ifiinipiag tan Tta- cLWUporkpiDQ tSv avu^aivovTiov. — paSovvai .... XriipOkvTiav yip Ua- De Respir. 1. iib ris fiiv apxaq vS>q tSiv ipaivo/iivuiv ovtoiq evpiOi]- F 34 LOGIC OF INDUCTION. stands in about the same relation to his predecessors in which Bacon stands to himself, and the expressions he uses in criti- cising their method often reminds us of the language of Bacon.' Indeed the apparent similarity of Bacon's method to that which it proposed to supplant, was one of the greatest obstacles to its introduction. For it appeared to have already had its trial, and if theoretically it might corrtain some minute points of difference, it was expected that these would vanish in the un- avoidable shortcomings of practice. StiU the prejudice against Sense created by the enthusiastic declamations of the ancient Rationalists was perhaps not completely eradicated, and the mathematical precision with which phsenomena are now mea- sured, and the method with which they are registered, did not enter into the Aristotelian conception of Induction : and we have an example how near the mind may approach to the recog- nition of a principle, and yet remain in darkness ; and how enormous a difference results from the complete possession of a great idea, and the half-true state of mind, that has partly given in its adherence to the truth, and partly remains in compromise with error. 'j But a still greater defect than the faultiness of its Observation I was the complete absence from the system of the idea of Ex- J periment. Observation takes cognizance of the phsenomena which nature presents of her own accord; whereas Experiment creates others for itself, and has the advantage, where it is ap- plicable, of selecting the conditions under which it wiU view the subject-matter, under which perhaps it is never presented by nature; and of knovnng precisely what these conditions are, as they proceed from our own arrangement : whereas in Observation we are often uncertain whether we have noticed all the antece- dents and concomitants of a given phaenomenon. Hence it is that Aristotle's success is very different in the sciences that rest on Observation and those that rest on Experiment. In the Poli- aav ai auTpoXoyiKal oiTroSii^tiQ .... Xdywv iStwpijroi rwv inrapxovTuiv £1 yap firiSlv Kara, riyv iaropiav va- &vTtg irpbg bXiya STn^Xs^avrce Awo- paXeiipBeiri twv aKj]6u)s {nrapxovrojv tpaivovrai p^oK, De Gen. et Cor. i. rote irpdyfiaai, &c. — Prior. Anal. 2, with Bacon's : Istud respicere pau- i. 30. ca et pronunciare secundum pauca ' Compare : ol S' ek tSiv ttoWHv perdidit omnia. DEFECTS OF THE SYSTEM. 35 tical sciences which rest on Ohservation, or rather on Experience, that is, where under any tolerable state of society Nature herself is sure to supply the sensations requisite for eliciting the ulti- mate laws and dominant ideas, it would be difficult to find any writer in later times by whom he has been surpassed or equalled : and his Zoological treatises, where Observation rather than Ex- periment was required, are spoken of with high praise by modern naturalists. In Chemistry, on the other hand, of which the beginning, middle, and end is Experiment, he was completely unsuccessful ; and an error in so elementary a science could not fail to bp widely felt in the other branches of his Philosophy. He complains of the difficulty of discovering primary laws, and seems to confess the unfinished state of Inductive Logic. ^ So much for his Inductive Method. The treatises contained in the Organon, though incomplete, perhaps take us over most of the ground that should be explored by Logic. One important deficiency is the method of the Meta- physical sciences : for the evolution of Metaphysical ideas cannot be inductive, as their objects do not belong to the sensible world. Aristotle may have acquiesced in the views of Plato, who seems to hold that the highest ideas of Reason are developed by lower but analogous perceptions.'' Some Logical doctrines might be gathered from the other works of Aristotle, such as that which Kant calls the Maxim of Parsimony.^ The Organon is by no means all that Aristotle wrote on the subject of Logic. In the list of his works given by Diogenes Laertius we find about twenty other Logical treatises : among them the Methodica, quoted in the Rhetoric, and consist- ing, according to Laertius, of eight books; which probably con- ' TrdvTti Sk Kul TravTbiQ sari tSiv jShv Trepi SKaarov rig o rpoiroQ. — De XaKi'torraToyv Xa^tlv nvh vianv Anim^, i. 1 . wipi TJjg ^xve' I'"-'- y^P ™X' ^'' '''V ' iiravAvai. &aircp ivava^aQiiols S6%eu fiia ng dvai iisBoSog xard. xP<*/*''"»'- — ^1**- Symposium. iravTiav Trepl Hv PovXa/ieOa yvCtvai ' ^avipbv '6n jiaKpif PsXrtov we T^v ovaiav, iivirep «ai t&v sark iXaxiarag troulv T&g ipx^Q, vav- (rv/ijSe/SijKoe iSiuv AiroSuKiV d Sk fii) ruv ye t&v avrav ntWovTiirv Stl- iari Ilia koX Koivi] Tig piOoSog irtpi Kvvadai, Kadamp d^wvn xai ol iv TO ri iariv, in xaXfTTiliTtpov yiverai ToXg fiaBrinamv. — De Coelo, ili. 4. TO irpaynaTiieirBai' Stijvn y&p \a- 36 LOGIC OF INDUCTION. tained a more systematic view of the whole of Logic than any of those that survive. We now conclude our sketch of the Organon, which we have divided into four parts; General Logic, the Logic of Deduction, the Logic of Induction, and the Logic of Opinion: the third indeed not sufficiently articulated and disengaged from the fourth, and hence the necessity of a Novum Organum. THE POSTERIOR ANALYTICS BOOK I. CHAPTER I. ON REASONING. § 1 . All teaching and learning by way of inference proceed from pre-existent knowledge. Of this we may be satisfied by examination of instances : it is thus that the Mathematical sciences and the Arts are acquired ; the Dialectician's Induction and Syllogism both appeal to previous knowledge, the one of the phaenomenon, the other of the law : and the Orator per- suades by Example and Enthymeme, the one a kind of Induc- tion, the other of Syllogism. § 2. The previous knowledge is twofold : it is a Judgment, and afiirms the existence of an object : or it is a Conception, and comprehends its nature : or it is a union of both. That one or the other of two contradictories is necessarily true, must be affirmed in a Judgment:' the nature of the triangle must be comprehended in a Conception : and we must both comprehend the nature of the Unit and affirm its existence : and these ele- ments of knowledge have not always the same evidence. § 3. When, however, implicit knowledge is rendered ex- plicit, the universal premiss may be antecedent to the conclu- sion, while the singular is simultaneous.* If, for instance, the equality of the interior angles of every triangle to two right angles is antecedently known, ^ as soon as the existence of a particular triangle in the semicircle is given by observation, (for ' We have here the three kinds of plicit knowledge. See Prior. Anal, scientific principle, which we shall ii. 23. and Nic. Eth. vii. 3. presently find are Axioms, Defini- ^ rjij,g g^mg gxample of immediate tiona, and Hypotheses. perception is adduced, Nic. Ethic. » yvapiZuv, actual knowledge, is vi. 8. opposed to EX"" T^v yvSaiv, iva- 40 ON REASONING. singTilar premisses are objects not of inference, but of observa- tion,) our knowledge of the conclusion is simultaneous. § 4. Before the minor is observed and the syllogism con- structed, the conclusion is in one point of view known, in another unknown. Before we know the existence of a subject, we cannot without qualification be said to know what attribute it possesses : we may be said to know it implicitly, or in the universal ; but only with such a limitation. This is the way we must solve the dilemma in the Meno, by which it is argued that we can learn nothing, or else only what we already know, i The other solution (which denies that we know the universal when ignorant of the particular) is inadmissible. If you pro- fess to know a universal, for instance, that all Twos are even, they refute you by producing a Two whose existence was un- known to you, and whose evenness consequently, they argue, you cannot have known ; maintaining, that you knew, not that all Twos were even, but that every Two, whose existence was known to you, was even. This is inadmissible ; for your know- ledge was derived from demonstration; and demonstration makes no reserve of the kind, but pronounces upon all triangles and numbers without exception. The true solution then is, that you knew in one sense what you were ignorant of in ano- ther. It is not inconceivable that we should learn what we u already know in a different point of view : but it would be, " that we should know and not know one and the same thing in one and the same point of view. ' See Meno, § 14. It was argued Axiom which asserts that no sub- that inquiry is useless, and that ject is capable of contradictory pre- nothing can be learnt: for what is dicates. known is not an object of inquiry ; In modem times, the fact that we and what is unknown it is useless to have an implicit knowledge of the search for, as it could not be recog- conclusion when we know the pre- nized even if found : and to say that mioses, has brought on the syllogism the same thing might be both known the charge of petitio principii. and unknown, seemed to violate the [41] CHAPTER II. SCIENTIFIC PRINCIPLES. § 1. Absolute science, as distinct from the Sophist's^ acci- dental science, is, according to the common conception, Know- ledge of the necessity and the reason of a law. Science must be this : for both the real and the fancied possessors of absolute science ascribe to it the investigation of necessary laws. We may afterwards see if there is any other kind. It is certain there is such a thing as demonstrative knowledge: demonstration means scientific proof: and the possession of scientific proof is science. I Assume this definition, and the premisses of demonstrative science must be true, elementary, immediate, clearer than the conclusion, antecedent, and causal; and then the principles will be appropriate to the conclusion. Proof may exist without these conditions, but not science nor demonstration. § 2. The premisses must be true. Science cannot be false : we cannot know that the diameter is commensurate. § 3. They must be elementary, and indemonstrable; else they wiU need demonstration: for the demonstrable is only es- sentially known by demonstration. § 4. They must be causal of the conclusion, clearer, and antecedent: causal, because to know the cause is the very es- sence of science : antecedent, both as causal and as foreknown : foreknown, not only as conceptions, but also as propositions.^ Priority and pre-evidence are of two kinds. What isnaturally prior and clearer is not prior and clearer to man : the objects which are farther from sense are absolutely prior and clearer: those which are nearer to sense are prior and clearer to man. ' The predicate of a scientific pro- scientific, is Sophistical, position is Essential : the predicate " That is, the principles of Science of a dialectical proposition is Acci- must include Hypotheses, or Postu- ilental : a proof founded on dialecti- lates, as well as Definitions, cal propositions and professing to be 42 SCIENTIFIC PRINCIPLES. The latter are particulars, the former universals, so that they are opposites to one another. § 5. They will be elementary because they are the appro- priate principles : for Element and Principle are synonymous. A demonstrative principle is an immediate or proximate proposi- tion. A proposition is either of two enunciations, and has a single subject and predicate : if dialectical, it offers an alternative: if demonstrative, it determines which is true. Enunciation is either of two contradictories. Contradiction is opposition which excludes an intermediate: the side which conjoins subject and predicate is affirmative ; that which disjoins them is negative. § 6. Immediate syllogistic principles are either Theses;' that is, are indemonstrable, but not the necessary antecedents of all inference : or Axioms ; that is, are indispensable for any progress in knowledge. Such principles as the latter there are, and this is the name we generally give to them. A Thesis may be one side of an enunciation, and assert the existence or non-existence of a subject; and is then called an Hypothesis : or it makes no assertion, and is called a Definition. The arithmetician, when he defines the Unit as an indivisible quantity, makes a Thesis, but not an Hypothesis : for to unfold the essence of a subject is not the same as to affirm its existence. § 7. Belief and knowledge of the law being grounded on de- monstration, and this standing in the strength of elementary laws, some or all of the elementary laws must be not only fore- known, but with a higher knowledge than the conclusion :, the cause which imparts a predicate to a subject always possessing that predicate in a more eminent degree: as the primary object of affection is dearer than another object which is loved for its sake. The primal laws, the origin of our knowledge and belief, must be the object of higher knowledge and belief than the deri- vative laws of which they are the vouchers. Now a truth cannot be believed more than other truths whicR are known, unless itself the object of knowledge: the grounds of demonstration are therefore the objects of knowledge, as some or all of them must ' The Theses correspond to the or Topics of Rhetoric and Dialectics, specific principles of Rhetoric, and For an account of the Axioms and to the Organa of Dialectics: the Hypotlieses, see Appendix A and B , Axioms correspond to the Maxims FIRST TRUTHS. 43 be grasped with a firmer faith than the demonstrated law. And knowledge and faith in the primary truths must not only be greater than that in the conclusion, but also than that in any of the opposite principles, from whence the antagonistic errors might be educed. For perfect science must be impregnable. CHAPTER III. THE FIRST TRUTHS* ARE KNOWABLE, BUT NOT DEMONSTRABLE. § 1. From the necessity of knowing the primary laws, some have maintained that science is impossible ; others, that science is possible and all laws demonstrable : neither of which doctrines is necessary or true. The impossibility of science is maintained by a dilemma: Either there is no limit to the regression, no primary law; and then, as we cannot traverse an illimitable series of antecedent laws, there can be no science : or, if there is a limit to the re- gression, as demonstration is the only source of science, the primary indemonstrable laws must be unknown, and the conclu- sion merely hypothetical, not categorical and scientific. The others, though they hold, with these, that demonstration is the only source of science, contend that all laws are demon- strable by a reciprocal and circulating evidence. We maintain that demonstration is not the sole source of science ; that the science of immediate truths is not demonstra- tive. If we demonstrate by prior and more elementary laws, the immediate laws, where regression ceases, must be indemon- strable.^ Further, we assert that, besides science, man possesses a faculty that begins science, the faculty of Ideas. § 2. Absolute demonstration cannot be circular, for these reasons. Firstly, the ground of demonstration is prior and more evident than the conclusion ; and one and the same law cannot be both prior and more evident, and posterior and less evident. It may possess the one character absolutely, and the ' This question is resumed chap, xix — xxii. 44 UNIVERSAL, ESSENTIAL, COMMENSURATE. other relatively to man : and it is its relative character which determines its position in Induction. But our definition of ahsolute science need not be enlarged ; for that which is merely prior to man cannot be the ground of absolute demon- stration. ^ Secondly, circular demonstration only proves that a theorem is true, if it is true : in which manner any theorem may be established. Assume three terms (for it is immaterial how many or few terms compose the circle). In regular proof, when theorem A establishes theorem B, and this again theorem C, we have theorem A in warrant for theorem C. In circular proof, A recurs instead of C ; so that theorem A is warrant for theorem A. Any theorem may be thus warranted. Thirdly, even this proof is impossible except for reciprocals, such as pro- perties. One term or premiss gives no conclusion : two pre- misses make an elementary syllogism. We showed, when speaking of syllogism, that if the terms A, B, C, reciprocate, all their possible conjunctions are capable of circular proof in the first figure : and we also showed that it could not be constructed in the other figures. Only propositions that are simply con- vertible are capable of circular proof; and as these are rare, it is an idle and untenable assertion that demonstration is circular, and all truths demonstrable. '^ CHAPTER IV. UNIVERSAL, ESSENTIAL, COMMENSURATE. § 1. The conclusions of absolute science are necessary: the premisses of demonstration therefore are necessary. In order to examine their character, let us define Universal, Essential and Commensurate. § 2. An attribute is universal that is possessed by a class, without exception of individuals or of times. Animal is a uni- versal predicate of Man i^ and wheresoever and whensoever we can predicate Man, we can also predicate Animal. Point is a ■■ Knowledge is not Science till it ' See, however, book ii. 11. has reached the deductive state. UNIVERSAL, ESSENTIAL, COMMENSURATE. 45 universal attribute of Line. For we assail a universal proposition by adducing an individual of which, or a time when, the predi- cate is not true. § 3. An attribute is essential that enters into the concep- tion ofthe subject;! as Line enters into the conception of Triangle, and Point into the conception of Line. It helps to compose the essence of the subject, and it is found in its definition. Or, it is an attribute in whose definition the subject is con- tained.2 Straight and Curved are attributes of Line; and even and odd, prime and compound, square and scalene, of number: and we cannot define them without mentioning the subjects they attach to, line and number. Those predicates which satisfy neither of these conditions are accidental : as White and Musical with reference to Aninial. In another sense, that is essential which is not ascribed to any subject as an attribute : as Substance, which requires nothing else as substratum of its existence. What is thus ascribed is accidental. White and Walking are ascribed to a subject that is white and walks. In another sense, a concomi- tant that is caused by an antecedent is essential. Death is an essential concomitant of Beheading. But it is accidental that it lightens while you walk. In the essential propositions of absolute science, the sub- ject is either contained in the definition of the predicate, or contains the predicate in its own definition; the essence of the terms is the cause of their conjunction : and their conjunction is necessary. The subject necessarily possesses a determinate pre- dicate, or at least the alternative of two contraries. Line must be either Straight or Curved ; Number must be either Odd or Even. Contrariety is the privation or contradiction of a, quality, in a subject of the same kind as another which possesses the quality. That which is not odd, and belongs to number, the class, to which oddness attaches, is even. Therefore, as ' From the force of the preposi- x" """■' ovaiav xai xard to (ldo£, tion, Kaff avrb includes the notion ch. xxxiii. if ycip Kaff avrovirapxu of Causation. A predicate is essen- « tovto avrb avTif oLnov, ch. xxiv. tial when the subject itself {airh), "^ Met. vii. 5 ; Phys. Ausc. i. 3 ; or its essence, is the cause of its con- ov vira^xii iv rif Ady^i tovto if nection with the predicate : vTrap- avfi^kfiriKe. Also Post. Anal. i. 22. 46 COMMENSURATE. one or the other of two contradictories must be true, one or the other of such essential predicates must be true.^ § 4. A ^commensurate attribute is universal and essential, and belongs to the subject as it is what it is, and is therefore neces- sary. The term, Essential, is equivalent to the term. As it is what it is. A line Essentially, and As it is what it is, contains a point, and is straight. A triangle Essentially, and As it is what it is, contains angles equal to two right angles. An attribute is commensurate to the primary or highest genus of which it is universally predicated. The attribute of containing angles equal in sum to two right angles is predicable of Figure, but not universally. It is predicable of Isosceles tri- angle, universally but not primarily. It is universally, and pri- marily predicated of Triangle. Where it is both universally and primarily predicable, it is commensurate. Of Triangle it is de- monstrated primarily, commensurately, and essentially. To Isosceles triangle it is not commensurate nor essential. CHAPTER V. COMMENSURATE. § 1. It often happens that a conclusion is not primary and commensurate, when it seems to be. When there is no genus of the individual or individuals ; or when there is a genus, but a nameless one, and the individuals differ in species ; or when the predicate has been proved of a species ; we are liable to this mistake. The conclusion, though not primary and commensu- rate, is universal. If not primary and commensurate, the de- monstration is not essential. Perpendiculars to the same line are parallel ; but this is not an essential proposition ; for not ' This principle is the Axiom. used as synonyms : and even in the ' Ka9d\ov is generally translated present his practice is not uniform, Universal, but it was necessary to so that sometimes it is uncertain use another word, in order to distin- how Ka66\ov should be translated, guish it from xard ■jravrog. In In book ii. 14 the definition is ex- Aristotle's other works they are pressly abandoned. COMMENSURATE. 47 only perpendiculars, but all lines that meet another at equal ■ angles, are parallel. Were the isosceles the only triangle, the property of containing angles equal to two right angles would seem essentially connected with isoscelism. The permutation of proportionals, numbers, lines, solids, times, is not essentially connected with number, time, dimension, but can be demon- strated at once of the commensurate genus. It was formerly proved in detail. They differ in species, and there was no name for their genus. When you prove in detail of each species of triangle, equilateral, scalene, isosceles, the equality of their interior angles to two right angles, you may exhaust the possible cases, but your predicate is not essential and com- mensurate, and you have only a sophistical science. Your Uni- versal, though numerical, is not Essential.^ § 2. What is the criterion of a scientific and commensurate conclusion ? If Triangle is essential to the predicate, and the essence of Isosceles is the same as the essence of Triangle, the conjunction of Isosceles and the predicate is Scientific. What subject is essential, primary, and commensurate ? The primary or lowest genus, that cannot be eliminated without the destruc- tion of the predicate.^ The interior angles of a brazen isosceles triangle are equal to two right angles. Brazenness and Isoscel- ism maybe eliminated, but not Figure. But lower genera than Figure are also ineliminable. If Triangle is the primary or lowest ineliminable genus, it is essential and commensurate. ' Essential propositions are found- tlieir difference of view on this sub- ed on definitions (see chap, iv), and ject affects their Metaphysics, not the object of definition is the clSog. their Logic. See also chap, xxxiii, {/■jrokriipeTai ' Commensurate propositions ijrapx"*" K'"'' ovaiav Kai xarct to should be the objects proposed for tlSoQ. The knowledge, then, of the discovery by the methods of Induc- «Z5oe is necessary for science, accord- tion. See Mr. Mill's System of ing to Aristotle as well as Plato ; Logic, book ii. [48] CHAPTER VI. SCIENTIFIC PRINCIPLES NECESSARY, THEREFORE ESSENTIAL. § 1. Scientific conclusions are necessary, and are therefore educed from similar premisses. This condition is not satisfied by accidental attributes, but is by essential : for here the predi- cate enters into the definition of the subject ; or the subject enters into the definition of the predicate, and must exhibit one of two contraries. The premisses of demonstration are therefore essential. § 2. Or we might have proved the necessity of demonstrative premisses by assuming the necessity of the demonstrative con- clusion. And if the premisses are necessary, not merely true, the proof is demonstrative. We imply the necessity of demon- strative premisses, when we assail a supposed demonstration by urging that there is no necessity in the conclusion, or none evinced by the proof. It is therefore a great mistake to suppose that our principles are rightly selected, if only probable and true : as the Sophists assume, that to know is the possession of knowledge.! A principle requires more than probability and truth ; some truths are inappropriate. A principle is the ele- mentary law appropriate to a particular subject-matter. Another consideration will prove the necessity of the pre- misses. You have no science of the demonstrable till you can explain its reason. If the major term is a necessary predicate of the minor, and the middle term of your demonstration is not necessary, you cannot explain the reason. If your middle term is not necessary, it cannot explain the necessity of the conclusion. Again, if "at present you have no knowledge of a truth, which remains unaltered, while you remember your former rea- son ; you had no knowledge before.^ If your middle term is not necessary, it may cease to be predicable : then, remembering your former reason, you will not know the truth, which remains unaltered. If the middle has not actually ceased, but may ' See Plato, Euthydemus, § 16. ' This argument is taken fi-om the Theaetetus, 4 55. 'IT' SCIENTIFIC PRINCIPLES NECESSARY. 49 sibly cease, such a situation is possible, and such possibility is inconsistent with science. A conclusion may be necessary, though the middle by which we prove it is contingent ; just as it may be true, though the premisses by which we establish it are false. But if the middle is necessary, the conclusion must be necessary ; as it must be true, if the premisses are true. A is a necessary predicate of C, if A is necessary to B, and B to C. If the conclusion is con- tingent, the middle cannot be necessary. Let A be a contingent predicate of C. If A were necessary to B, and B to C, A would be necessary to C : which is contrary to hypothesis.. In de- monstrative science the conclusion is a necessary law ; and if your middle term is not necessary, you will not know the rea- son of the necessity, nor even the necessity, of the law. Should you indeed mistake contingent premisses for necessary, you will believe without knowledge the necessity of the conclusion : without this mistake, you cannot even believe in the necessity of the law, neither knowing the fact from mediate, nor the rea- son from immediate premisses. § 3. Unessential attributes are not objects of demonstrative science : they cannot be necessarily concluded. It may be asked of what use they are as premisses in Dialectics, if they do not necessitate the conclusion. Do we not first make some irrelevant remarks, and then assert the conclusion, when we argue from contingent premisses ? To which we answer, that they are not propounded as grounds of a categorically necessary conclusion ; but because, if they are conceded, by a hypothetical necessity the conclusion is conceded ; and if they are true, by a hypothetical necessity the conclusion is true. § 4. Essential attributes, then, are necessary to their peculiar subject-matter, and form the conclusion and premisses of scien- tific demonstration. Accidents, not being necessary, and even if universal, not essential, do not teach the reason of a law. This happens in proof by signs. The conjunction may be essential, but you do not know it as such, nor do you know its reason. You know the reason when you know the cause ; and when the j^l^^inction of the terms of your syllogism, major and middle, iB^^ and minor, is caused by their own essence. [50] CHAPTER VII. SCIENTIFIC PRINCIPLES ARE APPROPRIATE AND INTRANSFERABLE. § 1. One science cannot employ proofs borrowed from another. 1 Geometrical truth cannot be proved by Arithmetic. For demonstration is analyzable into three elements ;2 the demonstrated major, an attribute essential to a particular mat- ter ; the axioms, or syllogistic canons ; and the subject-genus, whose properties and essential attributes are proved. Of these the axioms, or syllogizing powers, are common to all sciences. But if the subject-genus of Geometry is different from the sub- ject genus of Arithmetic, Geometrical attributes cannot be proved by Arithmetical demonstration. Such transference ' " But, in order that we may make any real advance in the discovery of truth, our ideas must not only be clear; they must also be appropriate. Each science has for its basis a different class of ideas ; and the steps which consti- tute the progress of one science can never be made by employing the ideas of another kind of science. No genuine advance could ever be obtained in Mechanics by applying to the subject the ideas of space and time merely; no advance in Che- mistry by the use of mere Mechani- cal conceptions ; no discovery in Physiology by referring facts to mere Chemical and Mechanical principles. Mechanics must involve the conception of Force ; Chemistry the conception of Mlementary Com- position ; Physiology the concep- tion of Vital Powers. Each science must advance by means of its appro- priate conceptions. Each has its own field, which extends as far as its principles can be applied." — Philo- sophy of the Inductive Sciences, book ii. 2. ^ £t Sk OiTroSuKTLKTJ 'jr€pi ai/Tixiv lari, Seiim ri yevog tlvai viroKetne- vov, Kal T& fikv TraOri rd Sk A^iMiiaTa airiSv avayKti y&p £k tivmv ilvdi Kai TTEpi ri Kal riviiiv rryii dTTodei^iv. Met. iii. 2. emep vaaa cnroStiKTuerl irtpi n inroKiipsvov Osdtpti rd Kad' avrd avfiPe^riKora h tS>v koiviSv oo^iiSv' Trepl ovv rh avrb yevog rd (TvpfiijiriKora Kaff avrd rffQ airfiQ koTi 9sti)pi](Tai Ik rdv airStv So^&v . — Ibid. See Post. Anal. ii. 12. SCIENTIFIC PRINCIPLES ARE ETERNAL. 51 would be possible, as will be shown, if Number were the genus of Magnitude ; for Arithmetical and all scientific demonstration always expresses its peculiar subject ; and unless the subject is wholly or partly the same, the demonstration is in transferable and incommunicable to any other genus : i for if the middle and major are not homogeneous to the minor, they are accidental attributes and unessential. § 2. Geometry, therefore, will not demonstrate that Con- traries are simultaneously known ; nor that the product of two cube numbers is a cube : nor will any- science establish a theorem for another, unless they stand in the relation of genus and species, as Geometry and Optics, Arithmetic and Harmonics. Geometry will not even investigate aU attributes of Lines ; not those which are unessential, and do not derive from her pecu- liar and appropriate principles. It will not discuss whether the straight line is the line of beauty, or whether it is contrary to the circular ; these attributes not attaching to their particular genus, but to something it holds in common with other genera. CHAPTER VIII.* SCIENTIFIC PRINCIPLES ARE ETERNAL. § 1. If the premisses of absolute demonstration and science are commensurate, the conclusion must be eternal. Transient ' A dialectical proposition or proof 5i£ icat Iw' aXXo yivoQ. — Ibid, iregai differs from a scientific in being ap- Tif yivu aX dpxal ical oiiS" iw(riKi7, ovSh MaBrjpaTiKfiQ, aSXd ei S" inrdpxu Tig oiiaia x'^pi^T^ "ai irporkpag d/ifoXv. 'H jiiv yap *«- dxivfirog, hirep inipaaojjitBa Seikvv- BiK-q irepi axcipwrra piv, dW ovk vai, ivravQa &v ciij irov Kai t& BiTov. dxivTjTa' Trig ^^ Ma9)ipanK^e ivia SijXov Toivvv on Tp'ia ykvri tS)v 6eo)- Trepi dxivriTa /lev, ov xiapiard le pi/riKoiv iiriffrij/ioiv Ian, ^vaiKti, iauig, dXK' iig iv v\y ri Si Ilpiinj MadtjpaTiKr), 0£o\oyiK^. Kai TTfpi i^wpKTrd Kai dKivr)Ta' iiari THE FIRST FIGURE IS MOST SCIENTIFIC. 63 of the Rainbow. The explanation strictly belongs to Optics : the facts to Physical science. Many sciences not subordinate are in particular points thus related. The fact, that circular wounds are slow to heal, belongs to the Physician; the expla- nation to the Geometer. CHAPTER XIV. THE FIRST FIGURE IS MOST SCIENTIFIC. § I . Of all the figures the first is most employed in science. It is employed by all the mathematical sciences. Arithmetic, Geometry, Optics, for instance r and a reasoned conclusion, the most characteristic point of science, is generally if not univer- sally drawn in this figure. Secondly, it is the only one adapted for establishing a defini- tion, which is universal and affirmative, the conclusions of the second and third being negative and particular. Thirdly, the intercalation of more and more elementary laws, and finally of the immediate, by which the premisses of the lat- ter figures are deduced, must take place in the first figure.' The first is self-sufS.cient, and appears on these accounts to play the chief part in science. 1 Deduction is called condensa- All C is D. tion, (KarairvKvovTai,) because it .'.AUCisE. consists of the interposition of mid- And die terms. The proposition, all A is All B is C. £, is thus deduced : — All A is B. AllCisE. .-.AUAisC. All A is C. The deduction is complete when -•.All A is E. all the premisses, AB, BC, CD, Both of these premisses may be D E, are immediate propositions, thus deduced : — dd rb fiiaov irvKvovrai 'io)Q dSiat- AU D is E. pira yivrirai Kai cv, chap. XXIII. [64 ] CHAPTER XV. NEGATIVE PEOPOSITIONS MAY BE INDEMONSTRABLE. The proposition, B is not A, as well as the proposition, B is A, may be an atomic truth. A proposition is an atom or indi- visible, whose terms are divided by no intermediate link, and connected or disconnected by no foreign cause. If either A, or B, or both, have a genus, the disjunction of A and B cannot be primary. For, if C is the genus of A, it per- haps is not the genus of B : then, because A is C, and B is not C, we may infer that B is not A. Or if D were a genus of B, so that all B were D, and no D were A, we might infer that no B is A. And similarly, if both B and A have a genus. The possibility that the genus of A should not be a genus of B, or the genus of B not a genus of A, is clear from the contra-dis- tinguished categories or orders. If nothing in the category A, C, D, is predicable of any thing in the category B, E, F, and G in the first group is genus of A, it cannot be genus of B, or the groups would not be mutually exclusive; and similarly if B had a genus. If neither has a genus, and B is not A, the proposition is an atomic negative. Were there a middle term and proof, one of them must have a genus : for the proof must fall into the first or second figure. If in the first, B has the genus, for the minor premiss of this figure must be affirmative : if in the second, one or the other must have the genus, for either premiss may be negative, but not both. Under these conditions a negative proposition may be indivi- sible or atomic. [65 ] CHAPTER XVI. ERROR IN PRINCIPLE. § 1. Ignorance, that is not merely the negative but the eon- trary of knowledge, is either direct or concluded ; and either of mediate or of immediate propositions. Ignorance of immediate or primary propositions, whether aiErmative or negative, if a direct belief, admits of no varieties : if a concluded error, it may arise under several conditions. § 2. Let the proposition, no B is A, be an indivisible or atomic truth. If you conclude that all B is A, by a middle term C, you are deceived by deduction : and either both, or only one of your premisses, all C is A all B is C, may be false. Both may be false : for it is possible that the statement, all C is A, is false ; and, as the proposition, no B is A, is primary, and B can therefore have no genus, the state- ment, all B is C, is also false. Or one of the premisses may be true : but this can only be the major, aU C is A. The minor, all B is C, must be false ; for, if the proposition, no B is A, is primary, B can have no genus. The major, all C is A, -may- be true; for the propo- sitions,^ all C is A no B is A, whether mediate or immediate, are quite consistent with the proposition, no B is C. § 3. This is the only manner in which we can conclude a false affirmative, for only the first figure concludes an afiirmative universal. A false negative may be drawn either in the first" or ' This passage and another in the where KartiyopeXaBai and virapx^iv following chapter {iyxiapii yip ri are used generically of affirmative A irXtiomv virapx^iv S, oiie ianv and negative propositions. wTraWijXo) are the only places K 66 ERROR IN PRINCIPLE. in the second figure. Let us examine under how many condi- tions a false conclusion, no B is A, may be drawn in the first figure. Both the premisses, no C is A all B is C, may he false : for the assumption, that all C is A, and no B is C, does not contravene the hypothesis, that all B is A. Or one or the other indiscriminately may be false : The major, no C is A, may be true ; and then the minor, all B is C, must be false : for, firstly, the propositions, all B is A all B is C, would give the conclusion, some C is A, which contradicts the major we have just assumed to be true ; and, secondly, the premisses, no C is A all B is C, give the conclusion, no B is A, which contradicts the hypothesis. Or the minor, all B is C, may be true ; and then the major, no C is A, must be false : for, from the hypothesis and minor, all B is A all B is C, it follows that some C is A, and therefore the major, no C is A, is false. In the first figure, then, a false conclusion may proceed from either one or two false premisses. § 4. If the false conclusion, no B is A, is drawn in the second figure, the premisses cannot both be wholly false or contrary to the truth. If all B is A, no middle term can be universally affirmed of one extreme, and universally denied of the other: for the false conclusion, no B is A, tnust result from such premisses. But they cannot both be contrary to the truth ; for then the contraries of both ought to be true propositions ; but we should again have a middle term universally denied of one extreme, and universally afiirmed of the other. § 5. Both premisses may be partly false or contradictory to the truth. Whether the premisses are, all A is C, and no B is ERROR IN PRINCIPLE. 67 C ; or, no A is C, and no B is C ; we may suppose them both contradictory to the truth, without contravening the hypothesis, all B is A. § 6. Either premiss singly may be contrary to the truth. Let the premisses be, all A is C no B is C ; then, if the major is true, we have the true propositions, all A is C all B is A; so that the minor, no B is C, is contrary to the truth. Or, if the minor is true, we have the premisses, no B is C all B is A; from which it follows that some A is not C ; and therefore the major, all A is C, is contradictory to the truth, and may be contrary. Or, let the premisses be, no A is C all B is C; then, if the major is true, we have the propositions, no A is C all B is A J from which it follows that the minor, all B is C, is contrary to the truth. Or, if the minor is true', then we have the propositions, all B is C all B is A, which give the conclusion, some A is C : therefore the major, no A is C, is contradictory to the truth, and' may be contrary. An atomic or elementary error may therefore result from one or from two erroneous premisses. [68] CHAPTER XVII. ORIGIN OF ERROK IN DEMONSTRABLE PROPOSITIONS. § 1. With respect to mediate or deducible propositions, aflirm- ative or negative, if the middle by which they are falsely con- cluded is appropriate, both premisses cannot be fake, but only the major. The appropriate middle is that by which the truth might be concluded. Let the true conclusion, all B is A, be deducible from the middle C. The minor premiss must always be affirmative and true ; if it were negative, there would be no conclusion : but the major may be false, for, converted into its contrary, it gives a contrary conclusion.* § 2. When the true premisses are, ' ' ' all D is A ■ - all B is D; where the middle D is inappropriate, and taken from a distinct category; we leave a conclusion if we change the quality of the major, but not if we change the quality of the minor : so that the one must always be true, the other always false : and this case resembles that of the appropriate middle. § 3. Supposing the true premisses to be, all t) is A no B is D, both .premisses of our deduction must be false: for we must change the quality of both in order to make a syllogism : we must assume, no D is A all B is D J both which propositions are false. ' avnaTpofii here means change signifies the substitution of the con- of quality; in Prior. Anal. ii. 8, it elusion for one of the premisses. ORIGIN OF ERROR. 69 § 4. In this last syllogism, if the major is true, the minor must be false ; for it leads to the conclusion, no B is A, which is false by hypothesis. § 5. When the erroneous conclusion is in the second figure, both premisses cannot be wholly false or contrary to the truth : for, as we observed before, when all B is A, no middle can be universally affirmed of the one extreme, and universally denied of the other ; but either singly may be contrary to the truth. If the true propositions are all A is C all B is C; and we assume the premisses, all A is C no B is C; ' the major premiss is true, and the minor false : if we assume the premisses, aU B is C no A is C : the minor is true, and the major false. When the conclusion is negative, these are the sources of error. § 6. When the conclusion is affirmative, and drawn from the appropriate middle, both premisses cannot be false, for the minor must be affirmative to give any conclusion ; so that the error must be in the major : for this is the only premiss whose contrary affords a conclusion. § 7. Similarly, if the middle be inappropriate and heteroge- neous, as we observed in the case of the negative conclusion, the minor cannot be converted into its contrary, but the major can : and the deception is the same as when the middle is ap- propriate and homogeneous. § 8. When all D, the inappropriate middle, is A, our major premiss, all D is A, is true, and the minor, all B is D, is false. For it does not follow from the propositions, all D is A no B is A, that all B is D. 70 NEGATIVE IGNORANCE. § 9. If no D is A, our major premiss, being affirmative, is false ; while the minor» all B is D, may be either true or false. While no B is A, it may be true that no D is A, and all B is D : for example ; music is a science, and neither music nor science is an animal : or, it may be true that no D is A, and no B is D. If, then the major premiss is negative, one or both the pre- misses may be false. We have seen in how many ways it is possible to be misled either in demonstrable or in indemonstrable propositions. CHAPTER XVIII. NEGATIVE IGNORANCE. If man has lost any sense, he has lost a corresponding science, now unattainable. We acquire knowledge by induction or de- monstration, the one based on phsenomena, the other on laws, which are only discoverable by induction. Even the materials of mathematics are furnished by induc- tion;' which shews us throughout nature certain attributes, which, though not self-existent and substantive, are insulable in thought. The cognizance of phsenomena belongs to sense, not to reason. Sense, then, is indispensable to induction, and induction to discovery of the law. CHAPTER XIX. ABE ANY TRUTHS IN THEIR OWN NATURE INDEMONSTRABLE ? § 1. AH deduction involves three terms, and either connects a predicate A with a subject C, by predicating A of B, and B of ' o fiaBtiitanKbg Trepi rd k^ A^ai- aWag aiaOtiTdg ivavTiiaasiQ' fiovov peacue rrjv dewpiav irouirai' irepi- Sk KaTaKeiirn rb iroabv Kai am/ex^^j eXiav ydip wdvra rd alaOtjtd dciujoct, rfiv fikv k^' ev Tutv S' k-jrl Svo twv olav jSapoe Kai Kovf 6Ti]Ta Kai axXt)- S" kjri rpla, Kai r<4 iraSij rd tovtuv, poTijra Kai Toivavr'wv, In Sk Kai y itoaa. kari Kai avvixd Kai oh kuO' 6fpn6TtjTa Kai ypvxportira Kai rag 'irepSv ri, Beiapci. — Met. xi. 3. LIMIT OF ANALYSIS. 71 C ; or disconnects them by ascribing a predicate to the one and withholding it from the other. Such statements are the ele- ments and hypotheses of deduction. We condade that A is predicated of C by the middle B ; and that A is predicated of B by some other middle ; and that B is predicated of C by another. Dialectics only aiming at belief, credibility, as far as circum- stances allow, is the only requisite of its premisses. If a middle term between A and B is credible, though not real, it is suffi- cient for dialectical proof, but not for science. When we predicate whiteness of man, the predication is es- sential : whiteness is not ascribed to man, because man is ascribed to any other substance.^^ When we predicate man of whiteness, the predication is accidental : man is ascribed to the whiteness, because the whiteness is ascribed to a man, § 2. Let C be the attribute of no subject, but the primary subject of B, without any intermediate ; and let B be the pri- mary subject of F, and F the primary subject of E : must such a series terminate, or is it illimitable ? § 3. Again, if there is no essential predicate of A, and A is a primary predicate of H, with no antecedent intermediate ; and H of G, and G of B ; must such a series terminate, or may this too be illimitable ? This question differs from the former : the former asked, if we begin from a primary subject, can we go upwards along an illimitable series? The second, if we begin from a primary predicate, can we go downwards along an illimitable series ? § 4. Again, Lf the extremes are fixed, can the intermediate links be infinite ? When B is intermediate between A and C, and others between A and B, and others between these ; can this intercalation be endless ? This is to ask, is there any end to demonstration? is everything demonstrable, or are the con- necting intermediates finite ? § 5. The same question arises in negative syllogisms and propositions. When no B is A, A is either denied primarily of < This kind of essential or proper predication mentioned in chap. iv. predication, which occurs again at and at the end of chap. xxil. which the beginning of chap. xxii. must is characteristic of science, and is only not he confounded with the essential one species of proper predication. 72 LIMIT OF ANALYSIS. B ; or antecedently of some other term G, which is predicated of all B ; and either primarily of G, or antecedently of some other term H. There is either an endless series of terms of which A is antecedently denied, or there is a primary term that ends the series. § 6. In a reciprocating series there can he no primary nor ultimate term ; for there is no antecedence nor subsequence, even though both the ascending and the descending series are limitless ; their reciprocation, however, may be dissimilar, giv- ing- sometimes an essential, and sometimes an accidental pre- dicate. CHAPTER XX. INTERMEDIATES OF GIVEN EXTREMES ARE FINITE. § 1. If the series of ascending or more universal predicates, and descending or more particular subjects, is limited in both directions, the number of intermediates must be finite. If the terms interposed between the extremes of the proposition, F is A, were innumerable, we might start from F, and travel up an endless succession of predicates without reaching A ; or start from A, and travel down an endless succession of subjects, without reaching F. This by hypothesis is impossible : the intervening links between F and A are therefore finite. § 2. It is equally impossible that some should touch and be undivided, and others severed by an impassable chasm. Select any intervening term whatever, and the number of intermediates that divide it from A and F must either be finite or infinite. Where the chasm occurs is immaterial. The hypothesis is violated, if any term is severed by an infinite series from either extreme. CHAPTER XXI. NEGATIVE PROPOSITIONS. § 1. If the retrogression of subjects and progression of pre- dicates is limited in the analysis of affirmative propositions, it must be so in the analysis of negative. LIMIT OF ANALYSIS. 73 Let us examine the proof of a negative conclusion in the three figures ; and assume that, ia affirmative propositions, we cannot progress from a primary subject, nor retrogress from an ultimate predicate, without arriving at a limit. § 2. If we prove the negative, no C is A, in the first figure, by the premisses, no B is A all C is B, the number of intercalated terms in the minor interval or pro- position, C is B, is by hypothesis finite ; for this interval is always affirmative. The major may be proved by the antece- dent premisses, no D is A all B is D; and this major by the antecedent premisses, no E is A all D is E: so that every antecedent proof adds a higher predicate of C ; and,^^ as their progression is by hypothesis limited, the subjects of A must be also limited ; and there must be some term of which A is primarily denied. § 3. In the second figure, if we prove the conclusion, no C is A, by the premisses, all A is B no C is B^ the minor premiss may either be proved in the first or in the second figure : let us prove it in the second ; and we require the premisses, all B is D no C is D : ' Siar iird n lirt to avw "laraTai the line from A down to B. In the bibe, KoX n liri rb kutui arrjatTai. rj Tauchnitz edition the avia and icdrw M rb avw bSoe is the line of terms are transposed, from B up to A ; »; etti rb kuto) is li 74 LIMIT OF ANALYSIS. if we again prove the minor, we require tlie premisses, all D is E no C is E : so that every antecedent proof adds a higher predicate of A ; and, if these are limited, the antecedent negatives are also limited.! § 4. In the third figure, if we prove the conclusion, some C is not A, by the premisses, some B is not C aU B is A: the major premiss may either be proved in the former figures, in which we saw the progression was limited ; or, if we prove it in the third, we require the premisses, some D is not C all D is B: and to prove this major, we require the premisses, some E is not C all E is D: so that every antecedent proof adds a lower subject of A; and therefore, as the retrogression of affirmative subjects is as- sumed to be limited, the retrogression of negative subjects is also limited. § 5. As, then, the number of proofs in each figure is limited, and the number of figures is limited ; and as the product of two finite numbers is finite ; the number of antecedent nega- ' The syllogisms examined are in and this major by the premisses, Camestres ; if we examine them in no D is E Cesare, the result is slightly differ- all B is E. ent. We may prove the negative, From which it appears that the de- no C is A, by the premisses, duction in Cesare does not always no A is B add"a higher predicate of the major all C is B, term, as in Camestres, but alternately the major may be proved by the pre- a higher predicate of the minor and misses, major, no B is D all A is D ; LIMIT OF ANALYSIS. 73 tives wUl be finite, even though the conclusion should be drawn in every figure. If, then, the succession of subjects and predicates is limited in the analysis of an affirmative proposition, it is limited in the analysis of a negative. CHAPTER XXII. THE TRAINS OF PREDICATION ARE FINITE. § 1. First let us give a dialectical proof. Predicates that compose the essential character must be finite : else, as infinite elements could not be enumerated, such character would be indefinable. Before we can complete this proof we must make some pre- liminary remarks. § 2. Predication is essential or proper, when I afiirm that wood is white, or that a man walks. Wood is the subject of whiteness : whiteness is an attribute possessed by wood or a species of wood, not by another subject to which wood is also ascribed. Predication is accidental or improper, when I afiirm that the white is wood, or that the white is musical. White is not the subject of wood, wood is not an attribute ascribed to white or to a species of white, but is a subject to which the attribute whiteness is ascribed. When I affirm that the white is musical, white is not the subject of musical ; musical is not an attribute ascribed to white nor to a species of white, but to man, a subject to which the attribute whiteness is also ascribed. § 3. The predicates that enter demonstration are proper, not accidental, and fall under the categories of substance, quality, quantity, relation, action, passion, place, or time. When substance is predicated, the subject is either the pre- dicate or a species of the predicate, as when animal is predi- cated of man. When accident is predicated, it is neither identical with the subject, nor its genus : as white is predicated of man. No accident can exist but by inherence in a substance. The Platonic Ideas are imaginary, and, even if they existed, would 76 LIMIT OF ANALYSIS. be nothing to our purpose, not being concerned in demonstra- tion. § 4. If A is a quality of B, B cannot be a quality of A, and they cannot precipitate with absolute predication. Such predication cannot be circular or reciprocal. If the terms reciprocate as genera ; firstly, no essence would be de- finable, for we could not exhaust an infinite series of genera ; secondly, a genus would be a species of itself. If the terms reciprocate as substance and accident, their pre- dication is only accidental. § 5. Rectilinear predication cannot proceed without a limit.* For the predicates are either substantive genera, and this series we know to be finite ; or they are accidents, essential or unes- sential. Every accident inheres in some term of the substan- tive succession : their descending or subject series, therefore, is limited by the limit of this succession : and, as their genera are finite like those of substance, their ascending or predicate series is also limited. The scale, therefore, has both a basis or pri- mary subject, and an apex or ultimate predicate. § 6. Another dialectical proof is as follows : antecedent pre- dicates make a proposition demonstrable ; and the demonstrable cannot be apprehended better than by knowledge, and cannot be known without demonstration. If the antecedents are nei- ther known nor apprehended better than if they were known, the consequents cannot be the objects of knowledge. The number therefore of intermediate predicates must be limited, if demonstration is categorical, and not merely hypothetical. If the succession of higher predicates is unlimited, every truth is demonstrable, but, as an endless preceding series has to be passed, cannot be demonstrated ; and, as we do not apprehend them with any thing better than knowledge, our science is not categorical, but merely hypothetical. § 7. These proofs are dialectical -.^ a scientific and shorter ' aWd lii Otis' (ig rb avo) avtipa and most obscure, somewhat more iarai. As this chapter, though one liberty has been taken in departing of the most important in the trea- from the letter of the original than tise, as asserting the Logical Hypo- elsewhere. thesis, the existence of first truths, is ' The first proof appears to be also one ofthe most carelessly written Dialectical, because it applies to LIMIT OF ANALYSIS. 77 proof that the series of essential predicates (which demonstrative science alone regards) must terminate in both directions, is as follows : — A predicate is essential if it enters into the definition of the suhject, as divided into the definition of number : or if the subject enters into the definition of the predicate, as num- ber into the definition of odd. § 8. A succession of this latter kind of predicates must be finite : for if there be a further predicate of odd, into whose definition odd enters, number will be the primary subject in the definition of that further predicate, and a limit of its de- scending series. The terms of the ascending series must be finite, for the whole nexus of properties must inhere in the original subject, and the whole nexus of subjects, which is of 'equal length, must enter the definition of the ultimate property : and as no predicate can have an infinite line of such subjects, nor any subject an infinite line of such predicates, the ascend- ing series must also eventually terminate. § 9. A succession of the former kind of predicates, found in the d finition of the subject, must be finite : else the subject would be indefinable : so that here too the ascending, and con- sequently the descending, series is finite. § 10. If so, two extremes can only have a finite number of intermediates,^ and demonstration has an absolute basis and contingent predicates, as well as to belongs to Analytical Science, or essential or necessary, and it leaves Logic,) because it rests on appro- us in doubt whether the second kind priate principles, the definition of of essential predicates, whose defi- essential propositions, nition includes their subject, may It is, however, not so much a not extend in a lateral direction proof, as a more accurate deteiTQi- without limit ; so that the proof is nation of the principle that must be both too extensive and too narrow. postulated. This postulate, the ex- The second proof is merely Hypo- istence of first principles, as concern- thetical ; there must be first truths ing the constitution of the world, if there is science. This is a petitio appears to belong properly to Meta- principii; for the object of proving physics, and is merely borrowed by the existence of first truths is to Logic— See Metaph. ii. 2, and In- prove the possibility of science ; tlfew^jjjj^ij^^ latter, therefore, must not be as- ' "CoinpS^'«iJ?OTivative laws are sumed as a proof of the former. such as are dedu«bl|!teom, and may The third proof is Analytical, that be resolved into, other%id more ge- is Scientific, (for the present treatise neral ones. Ultimate ]a\t;s are those 78 ULTIMATE LAWS. point of departure ; and they were mistaken who, we said, denied the existence of indemonstrable truths. If demonstra- tion has an absolute point of departure, all truths are not de- monstrable, and the chain of deduction is not endless : other- wise there would be no atomic and irreducible law, but every law would be capable of resolution. Deduction does not add a term, but interpose it between the extremes : and if deduction were endless, two extremes would be sundered by an infinite number of intermediates ; which, as we have shown by both dialectical and logical proof, cannot be, as both the ascend- ing and descending series of predication are determinate and bounded. CHAPTER XXIII. ULTIMATE LAWS. § 1. It follows, that if two terms, neither of which is univer- sally predicable of the other, possess the same predicate, they need not possess it in virtue of a common intermediate. The isosceles and scalene triangles both contain angles equal to two right angles, and in virtue of a common character : but the case is not always similar. If a predicate A is connected with the subjects C and D bj' the intermediation of B, B will require another intermediate, and this another ; and the terms sepa- rating the extremes will be infinite. This we have shown can- not be ; and we need not always look for a common link to connect a predicate with several subjects, if we recognize the existence of immediate laws. If, however, the predicate is es- sential, the subjects must be homogeneous, and comprise the same individuals ; for we have seen that one and the same de- monstrative attribute cannot attach to the matters of heteroge- neous sciences. § 2. If the proposition, B is A, has an intermediate, it is de- monstrable ; and the elements of its deduction will equal in which cannot. We are not sure that resolution of a derivative law into any of the uniformities which we more general laws, brings us nearer are yet acquainted with are ultimate to them." — Mill, System of Logic, laws; but we know that there must lii. 14. be ultimate laws, and that every ULTIMATE LAWS. 79 number the intermediates, being composed of the immediate laws, or such of them as are universal. Immediate and pri- mary laws are incapable of deduction, and require a diiFerent method of discovery.* The deduction of negative theorems also depends on the existence of antecedent negations : and the an- tecedent intermediate laws compose the elementary principles of their deduction ; so that primary and indemonstrable truths win be negative as well as affirmative. § 3. We demonstrate that A attaches to B, by showing that A attaches to C, and C to B : and thus we never introduce a class higher than A; but continually condense the middle ■ terms,2 till the theorem is resolved into its indivisible laws, or the units of truth.* An unit of truth is an immediate law, for such is absolutely One. ' The inductive method. ^ KaTairvKvovrai Kai av^CTat 'ipiafi,kvag. — Metaph. xiv. 1. Measure was the word used by the older Greeks for what was afterwards called the Criterion. The final Cri- terion or Measure of truth, accord- ing to Aristotle, are the immediate propositions, the elementary percep- tions of reason. The Measure of truth may be illustrated by compa- rison with analogous Measures. It must be homogeneous to the objects measured : the measuring unit of dimension, weight, sound, colour, will be a dimension, weight, sound, or colour; and as objects measured differ in kind, so will the measuring units. In like manner the measuring units of science, the first principles, must be homoge- neous to the conclusions, (Post. Anal, book i. 7, 9, 27, 32,) and wiU vary in different sciences. This was urged against the Platonists, who overrated the universality of first principles. The knowledge of the object mea- sured, length for instance, is indi- rect, by calculation, or reference to the standard unit of length: the knowledge of the unit is direct ap- prehension by Sense or Imagination. So the knowledge of scientific con- clusions differs from the knowledge 80 ULTIMATE LAWS. The beginning or basis of a system is simple and uncombined, and varies in different systems : in a system of weights the unit is a mina ; in musical sounds the unit is a semitone ; in demon- stration the unit is an immediate law : in science and deductive thought the unit is reason. Affirmative deduction, as we said, assumes no class higher than the predicate. § 4. A negative syllogism in the first figure assumes no term higher than the predicate. The conclusion, no B is A, is proved by the premisses, no C is A all B is C: and this major premiss, no C is A, by the antecedent premisses, no D is A all C is D: so that we never introduce a class higher than A. § 5. In the second figure we prove the conclusion, no E is D, by the premisses, all D is C no E is C: or the conclusion, some E is not D, by the premisses, all D is C some E is not C : so that the classes we introduce, though higher than D the major, are not higher than E the minor.' § 6. In the third figure we prove that some C is not A, by the premisses, some B is not A all B is C: so that the middle introduced is lower both than minor and than major. of principles : the former is Infer- Deductive Science, ence, the latter Reason or imme- ' The syllogisms examined are in diate intuition. The existence of Camestres and Baroko : in Cesare these measuring units in the mind and Festlno the middle term is and in nature is the hypothesis to higher than the minor, but not which we are driven by the idea of higher than the major. [81 ] CHAPTER XXIV. COMPARISON OF PABTICULAK AND COMMENSURATE PROOF. § 1. Proofs are commensurate or particular, affirmative or negative, direct or indirect ; and their comparative merits are disputed. Let us compare first commensurate and particular. § 2. Particular proof may seem to be preferable as conveying greater knowledge : for knowledge is the end and aim of proof; and our knowledge of a subject is greater when we know its attributes as essential, than when we know them as accidental. Our knowledge of the musician Coriscus is greater when we know that Coriscus is a musician, than when we know that a man is a musician. Commensurate proof connects the attribute essentially with a second subject, with the original only acci- dentally : it does not attach the attribute of containing angles equal to two right angles to the essence of isosceles, but repre- sents it as accidental. If essential proof deserves the prefer- ence ; as particular proof connects the subject essentially with the predicate, particular proof is preferable. § 3. Secondly, whereas commensurate proof treats of unreali- ties, and inspires us with an opinion of their reality ; leading us to believe in the existence of a triangle, figure, and number, distinct from individual triangles, figures, and numbers ; and in the definition of proportional, asserting that it transcends and is distinct from number, line, surface, and solid ; particular probf, being neither about unrealities nor delusory, is preferable to commensurate. § 4. It may be answered, that the first consideration is rather in favour of commensurate proof than of particular. If we prove of isosceles an attribute essential to triangle, the predicate is accidental. If the attribute of containing angles equal to two right angles is demonstrable of triangle, it is essential to triangle and accidental to isosceles. If triangle is a higher class, and univocal, and universally possessed of the attribute, it, and not isosceles, is essentially connected with the attribute. M 82 PARTICULAR PROOF. Commensurate proof, then, as engaged with essential predicates, is preferable to particular. § 5. If the commensurate is univocal, it has more of reality than some particulars, they being perishable, while it is im- perishable : and its unity does not compel us to believe its se- parate existence, any more than the separate existence of quality or quantity, or action or passion. If we believe it, we are to blame, and not the commensurate. § 6. A demonstration is a proof exhibiting the attribute's cause and reason : the cause is only exhibited by commensurate proof: for the commensurate subject is primary, and the pri- mary is essential, and the essence of the essential subject is the attribute's cause. Commensurate proof, therefore, is preferable, as exhibiting the attribute's cause and reason. § 7. Our inquiry into the cause of a change or state does not cease, and we do not consider it known, till no ulterior cause is assignable : the explanation is not finished and complete till it proceeds from the ultimate cause. What was A's motive in his departure ? The receipt of money. What was his motive in this ? The payment of his debt. What was his motive in this ? The performance of his duty to his neighbour. When no ulte- rior motive is assignable, the last motive is called the final cause of a state or change ;' and when we know this, we know the reason of an action. This is no peculiarity of the final cause : ' An instance of reasoning from vvapxti Sk rodl Swafief tovto £k the final cause, such as takes place ■^Sr/ sir' aiiTif. in art and practical deliberation, is Compare : ol yap avWoyuTfioi tSiv given, Metaph. vii. 7. rrpaKTui vapxfiv exovTie daiv, iTniSii d-nb TkxvriQ Si ylyvtrai S>v ri ilSog roiovSe to rsKoe, &c. — Nic. Eth. vi.l2. ev ry ^vxy. yivtrai ycip rb vyikg Resolve, as well as Science, implies voriaavTog, lireid^ roSc vyUia, 6,vay- a. conception of ultimate reasons, oi/c Kjj, ei vyiig iarai, Toll iirdp^ai, oiov inn iravriiiQ ixovTog ivOpdvov rj o/iaKoTiira- it Si tovto, BtpfioTnira- irpoaipemg, ovSi yccp ^ovXtiaaadcu Kal ovTiog ad voti, eug av dyayy dg oiS" viroXri^ig row SutTi. tan yap TOVTO b aiiTbg Svyarai icxarov ttoi- fiovXivriKbv Trjg ipvxrjg rA BtioptjTi- "v. Kbv airiag nvog- Tb yap ov 'ivcKa And again : d vyiavOriaeTai Sit fiia tSiv aiTiiov kari . . . Sib olg /iri- oiia\vv9rjvai- t'i ovv Ioti to bfiaXw- 9dg kutui axoirbg ov jSovXevTiKot. — Orjvai ; ToSi' tovto S' larai d 0ep- Ethic. Eudem. ii. 10, fiavOrjfTtrai. tovto Si ti Iuti, toSL' PARTICULA-R PROOF. 83 and as our knowledge of the motive is incomplete till no ulte- rior motive is assignable, so, in general, our knowledge of a cause is incomplete till no ulterior intermediate can be assigned. A given figure's exterior angles are equal to four right angles. Why ? Because it is an isosceles. Why has an isosceles this property ? Because it is a triangle. Why has a triangle ? Be- cause it is a rectilinear figure. If this reason is ultimate, it completes our knowledge. This ultimate explanation, which alone is adequate, is commensurate. § 8. Objects are knowable so far as they are determinate, and unknowable so far as they are indeterminate : now particular objects are infinite, while commensurate are simple and deter- minate, being the limits and determinations of the infinite. If then knowledge is greater, the more knowable its correlative objects, commensurate proof, as surpassing its rival in degree of knowledge and demonstrativeness, claims our preference. § 9. A proof of two propositions is better than the proof of one : commensurate proof, therefore, is better than particular : for the commensurate conclusion includes the particular, but the particular conclusion does not include the commensurate. § 10. In proportion as a proof is commensurate, the premiss approaches to an elementary law :i when we have reached the immediate premiss we have reached the' elementary law. De- duction is perfect when it commences from the primary law : in proportion, therefore, as our premisses approach the primary law, our deduction approaches perfection. If the proposition, ' " It is of importance to remark more to be relied on ; there are that when a sequence of pheenomena fewer chances of their being ulti- ia thus resolved into other laws, they mately found not to be universally are always laws more general than true .... They are more nearly un- itself. The law that A Is followed conditional ; they are defeated by by C is less general than either of fewer contingencies ; they are a the laws which connect B with C nearer approach to the universal and A with B . . . . Jfot only are the truth of nature .... There needs no laws of more immediate sequence more to show how much more ge- into which the law of a remote se- neral the elementary laws must be, quence is resolved laws of greater than any of the complex laws which generality than that law is, but (as a are derived from thera." — System of consequence of, or rather as implied Logic, by J. S. Mill, book il. 12. in, their greater generality) they are 84 NEGATIVE PROOF. D is A, has the intermediates C and B ; if B is a higher class than C, commensurate deduction will begin with B. § 11. Some of the above proofs are dialectical. The doctrine is clear, if we consider that a man who knows the commensu- rate virtually knows the particular. He who knows that every triangle contains angles equal to two right angles, though igno- rant that the isosceles is a triangle, virtually knows the predi- cate of the isosceles. But if he knows the particular conclu- sion, he neither actually nor virtually knows the commensurate. Again, the particular is an object of sense, the commen- surate of reason. CHAPTER XXV. COMPARISON OF AFFIRMATIVE AND NEGATIVE PROOF. § 1. We have shown that commensurate proof is better than particular : we proceed to show that affirmative is better than negative. Assume that proof from fewer petitions, hypotheses, or propositions, is, ceteris paribus, preferable to a longer deduc- tion : for if the conclusion conveyed is equally certain, the shorter proof conveys it with greater rapidity. To prove com- mensurately the proposition, that preference should be given to the shorter proof, suppose that the certainty of the premisses is equal, and that the certainty of the conclusions varies according to their order of sequence : and let the conclusion, E is A, be drawn either through the middles, D, C, B, or through the middles, G, F. The proposition, E is A, as concluded in the second deduction, is equally certain with the proposition, D is A, as concluded in the first deduction ; but, as concluded in the first deduction, it is not so certain as the proposition, D is A ; for a conclusioi) is not so certain as its ground and antecedent. A preference, therefore, is, ceteris paribus, due to the shorter deduction. Though both negative and affirmative deduction assume three terms and two premisses, yet, as the former only asserts exist- ence, the latter both existence and non-existence, the latter NEGATIVE PROOF. 85 requires more propositions, and is therefore inferior to the former.! § 2. Again, we know that one premiss must always be affirm- ative, as two negatives produce no conclusion : hence, in de- ducing the premisses from their ultimate laws, the affirmative propositions increase with greater rapidity. If you wish to demonstrate the premisses, no B is A all C is B, interpose the middles D and E : the proposition, no B is A, will follow from the premisses, no D is A all B is D; and the proposition, all C is B, will foUow from the premisses, all E is B all C is E: thus the deduction has added one negative and three affirmative premisses. And so in any further prosyUogisms ; every affirm- ative conclusion deriving from two affirmatives, and every ne- gative from a single negative. If then the ground of proof is more certain and credible than the conclusion ; and the affirmative is employed as ground of the negative, but the negative not as ground of the affirmative ; the latter, as antecedent and more evident, claims a preference. § 3. The element of deduction is a commensurate immediate proposition, and is affirmative or negative according to the con- clusion. As existence precedes non-existence, so the affirma- tive precedes and explains the negative. Affirmative proof, therefore, as composed of preferable elements, is preferable to negative proof. § 4. As implied in the existence of negative proof, and not implying it reciprocally, affirmative proof has a more primordial and elementary character. ' The commentators observe that premisses has nothing to do with this is a fallacy, as the number of their quality. [86 ] CHAPTER XXVI. COMPARISON OF DIRECT AND INDIRECT PROOF. § 1. Having shown that affirmative proof is better than ne- gative, we proceed to show that direct is better than indirect : and first let us examine their difference. The premisses, no B is A all C is B, furnish a direct proof of the proposition, no C is A. Indirect proof assumes the contradictory of the proposition it wishes to establish, and educes a confessedly false conclusion. If we wish to establish that some B is not A, we assume the pre- misses, all B is A all C is B: from these results the confessedly false conclusion, all C is A ; and as the minor premiss is unquestioned, the major must be false, and therefore some B is not A. The position of the terms in the two syllogisms is similar ; but there is a difference in the evidence of the propositions. In the former the propo- sition, no B is A, is more evident than the proposition, no C is A, and is employed in its direct proof: in the latter the propo- sition, some C is not A, is better known than the proposition, some B is not A, and is employed in its indirect proof. § 2. The proposition, no B is A, which constitutes the evidence in the direct proof, is naturally and absolutely antecedent to the proposition, some C is not A, which gives evidence in the indi- rect proof; the former being ground, the latter conclusion. The conclusion of indirect proof, some B is not A, is not a proper conclusion,^ and its evidence, some C is not A, is not the proper ground ; the subject of the latter proposition, C, not ' The ultimate conclusion of an and the premisses (ekeTvo) are not indirect proof (ft avfi^aivci ivaipn- naturally premisses (i? uv) : for the aOm Ti) is not naturally a conclusion ; former, some B is not A, is the sub- COMPARATIVE PERFECTION OF SCIENCES. 87 being related to the subject of the former, B, as a whole to a part ; which relation constitutes the ground and conclusion of a syllogism. As, then, direct proof employs absolutely antece- dent and clearer premisses, it is preferable to indirect, even when its conclusion is negative ; much more so when it is affirm- ative. CHAPTER XXVII. COMPARATIVE rtlRFECTION OF SCIENCES. § 1. A science which exhibits the reason of a fact is exacter and holds a higher rank than a science which exhibits the fact alone. § 2. The science of an abstract and insulated subject is ex- acter than a concrete science : as Arithmetic is exacter than Harmonics. § 3. The science of a more elementary subject is exacter than that which treats of several elements combined ; as Arith- metic than Geometry. There is a combination and complexity of elements in the subject of the one compared with the subject of the other : for points are placed, and units are placeless. CHAPTER XXVIII. UNITY OF SCIENCE.. § 1 . It is generically one and the same science which treats of the whole of a genus, including the specific derivatives from its elements, and their parts and essential attributes. i Sciences altern of one of the premisses of de- ' iraaai ai iiriaTfijiai vipi tv ri' moastrative proof; and one of the Koi yivog ri Trepiypa^dfuvai . . ovtu latter, some C is not A, is the subal- ret Kaff avrA, virap%ovTa r<^ yivu tern of the conclusion of demon- ■Kipi o daiv awodeucvvovin. — Met. vl. strative proof. rl> l| oJ avWoyiv- 1. at iirutrfinai piipoc n tov ojtoe fwe, means, a natural premiss. inonnvofuvai Biiapovai Trepi tovto 88 UNITY OF SCIENCE. have not this generic identity, if neither the elements of the one are derived from the elements of the other, nor the ele- ments of both from the elements of the same third science. § 2. This must be tested by examining the indemonstrable propositions on which they ultimately rest; for the principles should be homogeneous to the conclusions : and this again may be tested by examining whether the conclusions are homoge- neous to one another. CHAPTER XXIX. SEVERAL PROOFS OF THE SAME CONCLUSION. The same attribute is susceptible of several demonstrations, not merely by a remoter term of the same series, but by a term taken from a heterogeneous series. Pleasure may be proved to be change because it is excitement, or because it is supervening calm : which intermediates belong to different categories. They must, however, be mutually attributable,* as both are attributes of the same subject. We ought to examine under what condi- tions the other figures enable us to prove the same predicate by different intermediates. CHAPTER XXX. CHANCE. The effect of chance cannot be a conclusion of [demonstrative science, for .it is what remains when we exclude the necessary or general. The premisses of deduction are always either ne- cessary or general, and give respectively a necessary or general t6 ffu/*,8E/3)jKoe. — Met. iv. 1. liirav- iariv imaTr)fi7]Q rif yivu, to. re iXSti roe ^^ ylvoDg Kai aiaOtiinc jiia ivbg rS)v eiSSv. — Met. iv. 2. Kai eTrurTrtjirf olov ypap-fiariRri jiia i There will be a syllogism in ovaa irdaas Biiopii T&t ^o)vag. Sw Darapti. (B. St. Hilaire.) Kai rov ovtoq ^v oi- Kt'uov apx^v \6yoi Ktvoi' Ik Si rdv turapx""'"'"'' ''V y^"" ^tiiip&v av Tig ftaXkov \a.j3oi Tr)v airiav. De Gen. An. ii. 8.) This precept is the assertion of the inductive against the deductive tendency, and always requires to be re-enforced when a new department of nature is to be explored, as the first explanations are generally vain attempts to apply old laws to the solution of new phae- nomena. See Philosophy of the In- ductive Sciences, book ii. 3. Com- pare Cicero: Omnia hsec, quae su- pra et subter, unum esse, et un^ vi atque un^ consensione naturae con- stricta esse dixerunt. Nullum est enim genus rerum, quod aut avul- sum a cseteris per seipsum constare. aut quo caetera si careant, vim suam atque seternitatem conservare pos- sint. Est enim ilia Platonis vera vox, omnem doctrinam harum in- genuarum et humanarum artium uno quodam societatis vinculo con- tineri. — De Orat. iii. 6. The question is proposed by Mr. Mill : " Since we are continually discovering that uniformities, not previously known to be other than ultimate, are derivative, and re- solvable into more general laws; since (in other words) we are con- tinually discovering an explanation of some sequence, which was pre- viously known only as fact; it be- comes an interesting question, whe- ther there are any necessary limits to this philosophical operation, or whether it may proceed until all the uniform sequences in nature are re- solved into some one universal law. For this seems, at first sight, to be the ultimatum towards which the progress of induction, by the De- ductive method, resting on a basis of observation and experiment, is progressively tending." — System of Logic, iii. 14. He decides " that the ultimate laws of nature cannot possibly be less numerous than the distinguishable sensations or other feelings of our nature." MULTIPLICITY OF SCIENTIFIC PRINCIPLES. 91 Firstly, they differ like the conclusions in truth and false- hood : for though a true conclusion may result from false pre- misses;' this is the only case in which premiss and conclusion differ in character. The true conclusion, C is A, may result from false premisses, C is B, B is A : but if the latter are de- duced, the premisses of their deduction must be false ; for false conclusions can only derive from false premisses, as true pre- misses involve a true conclusion. Secondly, false principles differ among themselves, for they are inconsistent and contrary. § 2. The same may be evinced by an appropriate deduction. The elementary conceptions of many departments of nature are heterogeneous, and inapplicable beyond the limits of their ap- propriate science. The theory of points, which are placed, can- not introduce into its syllogisms the conception of units, which are placeless. The transferred conceptions would have to ap- pear as predicates of the major term of the science to which they were transferred, or as subjects of the minor, or as interme- diates to major and minor : or in all positions ; some as supe- rior to the major, others as inferior to the minor, and a re- mainder as intermediate to major and minor : but they cannot occupy any of these places. There are no common principles from which all truth can be deduced ; such as the canon, that either aifirmative or negative must be true.^ For subjects are heterogeneous ; and some pre- dicates are peculiar to the genus of magnitude, others to the genus of quality ; and subject and predicate must be both defined, and then conjoined by the general canon. § 3. Besides, the number of principles nearly equals the number of conclusions: and for every new conclusion a new proposition introduces a new conception, whether inferior to the minor, intermediate, or superior to the major. § 4. Again, as conclusions are infinite, and each succession of (homogeneous) terms is finite, (there must be an infinite variety of heterogeneous successions.^) § 5. -Again, some principles are contingent, others necessary. § 6. It is plain that, if conclusions are infinite, principles can- not be identical, as we have interpreted the expression. If it ' See Locke, as quoted in Appendix A. ' See chap. xxii. 92 MULTIPLICITY OF SCIENTIFIC PRINCIPLES. is only meant that there are principles of Geometry, principles of Arithmetic, principles of Medicine, and principles of every science, it is absurd to call them identical because they are what they are, for thus every thing is identical. § 7. It cannot be meant that every premiss will prove every conclusion ; for this is at once refuted by Logical theory, or by inspection of existing sciences : for principles are immediate propositions, and a fresh conclusion cannot be obtained without a fresh immediate proposition. If only primary immediate pro- positions are allowed to be principles, there is one peculiar pri- mary proposition to every heterogeneous matter.* § 8. If it is neither asserted that any premiss will prove any conclusion, nor allowed that the premisses of each science are peculiar ; it may be maintained that all principles are specifi- cally diverse, but identical in genus. This cannot be, for we have seen that the primary laws of heterogeneous matters are themselves heterogeneous. There are two classes of primary laws : the canons are common to all sciences ; the subject, as number, or magnitude, is the exclusive domain of a particular science. ' " For example ; since there is a tiny of the phsenomena, whatever phsBuomenon sui generis called co- number of hidden links we might lour, which our consciousness testi- detect in the chain of causation ter- fies to be not a particular degree of minating in the colour, the last link some other phsenomenon, as heat, or would still be a law of colour, not a odour, or motion, but intrinsically law of motion, nor of any other unlike all others, it follows that phaenomenon whatever .... White there are ultimate laws of colour; colour can in no manner be ex- that though the facts of colour may plained exclusively by the laws of admit of explanation, they never can the production of red colour. In be explained from laws of heat or any attempt to explain it, we cannot odour alone, or of motion alone, but but introduce, as one element of the that, however far the explanation explanation, the proposition, that may be carried, there will always some antecedent or other produces remain in it a law of colour . . . and the sensation of white." — Mill, Sys- however diligent might be our scru- tem of Logic, iii. 14. [93] CHAPTER XXXIII. SCIENCE AND OPINION. § 1. Knowledge or Science and its object differ from Opinion and its object. Knowledge is commensurate, and rests on necessary grounds. Contingent truths cannot be objects of knowledge, else they would both be necessary and non-necessary : nor can they be objects of Reason, for Beason is the beginner of Science ; nor of indemonstrative science, for this is the apprehension of im- mediate propositions -A and as all apprehension of truth is either Heason, Science, or Opinion, it follows that Contingent truths are the object of Opinion. This is confirmed by phsenomena : the truth of Opinion is precarious : this is explained, if its object is the mutable. When a man regards a fact as necessary, he regards himself as possessed of Knowledge, not of Opinion : when he regards it as actual but contingent, he regards himself ' as possessed of Opinion, not of Knowledge : confirming our position, that the contingent is the object of Opinion, the ne- cessary of Knowledge. § 2. Can the same thing in any sense be an object of both Opinion and Knowledge, and can we, without identification of Opinion and Knowledge, maintain that every object of Know- ledge may be an object of Opinion ? For then Opinion might follow the steps of Knowledge along the intermediates till it arrives at the immediate, and why should the one be Knowledge and not the other ? For the reason or intermediate kw, as well ' Beason, Science, and Opinion, Itrurriiiiri, Kai So^a, Kai ^pSvting are three species of intellectual ap- (vove). — De AnimS,, iii. 3. prehension : Reason apprehends first Swdfuie Kaff dg Kpivo/iEv, alaBi]- principles, Science necessary conclu- atg, So^a, vovg, iirurrijiiti. — Ibid, sions. Opinion contingent proposi- rb voiiv (Ji'noKaji^avuv) (ppovtimg, tioii5_ (voSj) Kai iiriBTrinr), Kai WJa. — Ibid. tiai Si Trje viroXffij/eiag Sia^opai, 94 SCIENCE AND OPINION. as the fact, may be the object of Opinion. Apprehension of a necessary conclusion, based on the definitions which form the legitimate grounds of demonstration, is Knowledge, not Opi- nion. Apprehension of a proposition as true, but not as educi- ble from essential and definitive theorems, is Opinion, not Knowledge.! if based on immediate propositions, it is Opinion both of fact and of reason : if not based on immediate proposi- tions, it is Opinion of fact alone. § 3. The object, then, of Science and Opinion is only iden- tical in a manner similar to that in which the object of true and false apprehension is identical. If the object of true and false Opinion were identical in the way in which some explain, among other strange results it would follow, that a false Opinion is no Opinion. But the word Identical is equivocal : the object of true and false Opinion is identical in one sense, and not in another. The commensurateness of diameter and circumfer- ence, which is an object of false belief, is not in the same man- ner an object of true belief. While the material element, the terms of the theorem, is the same, the formal elements are op- posed : so that the object of true and false belief must be partly identified and partly distinguished. The same holds with respect to the objects of Science and Opinion. They agree in the subject and predicate of their theorem, and agree in their conjunction, but difier in the mode of their conjunction ; the one connecting them necessarily and essentially, the other con- tingently and accidentally. § 4. It follows, that Knowledge and Opinion of the same fact cannot coexist in the same mind: for we cannot believe one and the same truth to be both contingent and necessary.'^ The object of Opinion and Knowledge may be identical in two dif- ferent minds, but not in the same mind : for we cannot at the same time entertain the two beliefs, that the conjunction of * W7rap;^€w war ovffiav Kai Kara, rtj^ to. Ka96\ov ov x*^p^f^^ eTroUt TO elSog. Science then rests on a oiSi roii£ bpia/jiovQ' oi S" Ixdipiaav, knowledge of the Idea according to Kai t& roiavra tUv ovriav 'iSkag both Plato and Aristotle. They dif- jrpoff^jyoptwtraj/. — Met. xiii. 4. fered, however, as to the nature of ' The Axiom states that nothing the Idea, though they would express can be the subject of contradictory it in the same definition. 6 JiwKpd- predicates. SAGACITY. 95 man and animal is accidental or contingent, and essential or necessary. § 5. Further distinctions between Inference, Reason, Science, Art, Wisdom, Philosophy, belong rather to Physical or Moral Science than to the present treatise.* CHAPTER XXXIV. SAGACITY. Sagacity is a talent of guessing rightly at the -intermediate when there is no time for consideration. A man observes that the bright side of the moon always faces the sun, and quickly divines the explanation that her light is borrowed : or observes a man in conversation with a capitalist, and conjectures that his object is a loan : or understands the friendship of two persons by referring it to a common enmity. In all these cases the extremes are observed, and at once deduced from the interme- diate causes. The moon, C, shines with light borrowed from the sun, B ; and therefore, its luminous face is opposite the sun, A. The conclusion, C is A, is noticed, and immediately analysed into its premisses, C is B, B is A. ' Psychology, or at least a per- ^vxr) Kivrjaeiog dpx4 ovSk ra /jiopia tion of it, belongs to Physical sci- Siravra . . . SrjXov ovv i>£ ov Trepi ence. \sktcOV av eiij ti^ 'jrtpi ^iktsuq 'Trdtnjg ^XVQ \eKTeov. oiiSs yap wa- 9iii>pr)nKff TTipl \l/vx^£ liaXKov rf Trig aa ifa)x>) ipvaig, aXKd ti fwpiov airrje vXris, '6a(f fidWov 17 iiXij Si iKeivrjv iv rj Kai TrXeiu). — De Part. Anim. i. j>vaig lar'tv ri dvairaXiv . . . diropj]- 1. Kal ircpi ^x^S iviag Btbiprjirai ff£i£ S" av Tig jrSTCpov irepl irdarig rov (jniaiKov, o(ra nf) dvev rrjg ii\)jg ^vxvg Trjg (pvaiKrig lore rb tiireiv, f) kariv. — Met, vi. 1 ; Nic. Ethic, vii. 3. TTepi Tivog . . . ^ ovK effTi 'ffdira iy BOOK II. CHAPTER I. PROBLEMS OF SCIENCE. § 1 . Problems and theorems are equal in number : problems are four : (1) The question of Fact : Has a given subject a certain attribute ? (2) The question of Keason : What is the cause that a given subject has a certain attribute ? (3) The question of Existence : Does a given subject exist ? (4) The question of Essence : What is the nature of a given subject ? 1 § 2. The ■word,'^ Whether, when we inquire Whether this or that of certain enumerated cases is true, as when we inquire, Whether or not the sun is eclipsed, generally indicates a ques- tion of Fact : for the inquiry ceases when the Fact is known ; and, if known at first, the word Whether does not enter the question. § 3. The inquiry into the Reason follows upon knowledge of the Fact : when we know that the earth is subject to earth- quakes, and the sun to eclipse, we inquire, what is the cause of earthquake and eclipse ? § 4. It is a different problem, when we inquire into the ex- istence or non-existence of an agency or substance : as when we ask. Is there, or is there not, a centaur ? Is there, or is there not, a God ? ' The two last of these are pro- i. 10), so that, to a certain degree, blems of Inductive, but first princi- the second problem also is assumed pies of Deductive Science ; the one among the principles of Demonstra- being the hypothesis, the other the tion. definition. The attribute, as well as ' kv rotj avTucu/dvoig dtl roO to- the subject, must be defined (bopk rkpov ij Kfirtjaig. — Met. x. 5. A MIDDLE TERM THE OBJECT OF INQUIRY. 97 § 5. When we know the Fact that an agency or substance exists, we inquire into its Essence or nature : What is the na- ture of man ? What is the nature of a God ? CHAPTER II. THE OBJECT OF INQUIRY IS ALWAYS THE INTERMEDIATE. § 1. Problems and theorems may be classed as above. When we inquire (1) the Fact, whether a subject possesses an attri- bute ; or (3) the simple Existence of the subject ; our inquiry is. Has it, or has it not, an Intermediate ? § 2. When we know (3) the Existence of a subject, or (1) the Fact that it possesses an attribute ; in other words, when we know the simple or modified Existence of the subject; and proceed to inquire (4) into the Essence of the subject, or (2) the Reason of its attribute ; then our inquiry becomes, What is the determinate Intermediate F § 3. The questions (1), Does the moon wax or wane? Is the moon eclipsed ? referring to a particular property of the moon, are questions of modified Existence : (3), the Existence of the moon or of night, if discussed would be a problem of simple Existence. Two of the problems inquire. Is there an Intermediate ? and two, WTiat is the Intermediate ? for the object of inquiry is al- ways a Cause, and the Cause enters as an Intermediate. To inquire. Is the moon eclipsed? is to inquire. Is there a Cause of the moon's eclipse ? When this is settled we proceed to in- quire. What is the Cause of the moon's eclipse ? The Cause of a subject's existence, or of its possessing an attribute essential or accidental, always enters syllogism as an intermediate. By the simply existing subject I understand the earth, the sun, the triangle : by their modifications or attributes, equality, in- equality, eclipse, interposition. § 4. The problem of Reason may be identified with the pro- blem of Essence. The problem and solution. What is the 88 DEFINITION INDEMONSTRABLE. nature of eclipse ? The deprivation of the moon's light by the earth's interposition ; are identical with the problem and solu. tion, What is the Cause of eclipse ? The earth interposing de- prives the moon of light. The question, What is the Essence of harmony ? and the answer, A numerical ratio of grave and acute, are identical with the question and answer. What is the Reason of grave and acute harmonizing ? Their having a cer- tain numerical ratio. The question. Is it a Fact, that grave and acute possess the attribute of harmonizing ? becomes the question. Have grave and acute a numerical ratio ? and after this is settled, ensues the question. What is the reason of their harmonizing ? or, What is their numerical ratio ? § 5. Sensible intermediates show that the object of search is always the intermediate ; for sensation would render inquiry unnecessary, by indicating the commensurate antecedent. A spectator on the moon would not need to inquire into the Fact or Cause of eclipse, for sense would connect the particular eclipse with the particular interposition.; and out of this he would elicit the commensurate conjunction. § 6. The knowledge of the Reason, then, is identifiable with the knowledge of the Essence. For the Essence of the subject is the Reason of its simple existence : and the Reason of the attribute constitutes its Essence. CHAPTER III. DEFINITION AND DEMONSTRATION HAVE NOT THE SAME PROVINCE. § 1. The object, then, of research is always the Interme- diate.! Let us next examine how the Essence or fundamental character is discovered and explained, and *hat is the nature ' Mr. Whewell asserts (Philoso- discovery of the major extreme; but phy of the Inductive Sciences, book he does not observe that what he ii. chap. 5.) that the discovery of calls the " second extreme" is really the middle is not so important a the middle of an original syllogism, step in the progress of science, as the The phtenomenon that Kepler ob-, DEFINITION INDEMONSTRABLE. 99 and the object of definition, beginning with a preliminary dis- cussion closely allied to what has preceded ; whether the same object under the same aspect is both demonstrable and de- finable. § 2. Some matters of deduction must be indefinable, for syl- logism in the second and third figure is negative and particu-> lar : but definition, stating what an object is, must always be afiSrmative and universal. § 3. The objects of affirmative conclusions in the first figure cannot all be definable : for, if all knowledge of the demonstra- ble results from demonstration, all the demonstrable must be indefinable ; else, possessing the definition and not the proof, we might know the demonstrable without demonstration. § 4. The same may be seen by induction ; there was never a case in which an attribute, essential or unessential, was learnt by mere definition. § 5. If definition is limited to the characterization of sub- stances, attributes are indefinable.* § 6. We have shown that some objects of demonstration are indefinable. To show that some objects of definition are inde- monstrable, we may repeat one of our former arguments. Unity of the truth implies unity of knowledge ; and to know a dedu- cible truth is to possess its deduction : a deducible truth, there- fore, cannot be known by definition. § 7. Again, definitions are the principles and foundation of deduction : and the principles are indemonstrable : else there woul4 be elements of the elementary, and foundations of the foundation, in endless regression. The primary or limiting truths, therefore, are definitions incapable of deduction. served, the conclusion of the original plained by what forces Mara was syllogism, was : impelled in his elliptical course, in Mars is seen in certain positions. which the forces would be the After many unsuccessful attempts, middle. Kepler explamed this by assuming : ' This, however, is not true. ^ 0a- Mars describes an ellipse about vepbv 'on i irpiirwg icoi enrXHc opia- the sun. * /«Ae Kal r6 rt ^v ilvat tSv oiaiOiv The elliptical motion of Mars is iariv ov firfv aXXd sai rHv dWutv here the middle; it would be the o/ioiws iffri, ttX^v oi 7rp(i™£.— Met. major of a syllogism, which ex- vii. 4. See Post. Anal. i. 10. 100 DEFINITION INDEMONSTRABLE. § 8. The objects of definition, then, and demonstration are not always identifiable : nor are they in any case. For the defined is the essence or fundamental character, and this is always postulated or assumed in science, not demonstrated:' as the mathematician assumes, not demonstrates, the nature of Unity, or the nature of Even. § 9. All deduction conjoins or disjoins a subject and predi, cate : in definition there is no subject and predicate. Animal is not attributed to Biped, nor Biped to Animal: Plain to Figure, nor Figure to Plain. § 10. Again, Essence differs from Fact : the definable is an Essence, the demonstrable a Fact : and as Essence* and Fact are not, like Triangle and Isosceles, related as part to whole, they require a different mode of explanation. § 11. We have seen that neither the whole classes of the de- finable and demonstrable can be identified, nor any of their members :" and the same difference that exists between the definable and demonstrable wUl exist between definition and demonstration. ' In the Greek we have viroTt9i- /itvai rb ri ean: this is an inaccu- rate expression : 6 yd.p opicr^bg Oefftg fj£v sffTiVf viroOecFig S" oiK iffri. — Book i. 2. ' The indemonstrability of first truths is expressed by Plato, when he makes Socrates as teacher pro- fess the obstetrical art. (dyovog ii/jii. ao^iag . . fiaievsffQai juf o Bebg dvayKa- Zsi, yivvav SI diriKwXvtr^v. Theajt. § 20.) Ideas and principles must be the spontaneous growth of the mind ; they cannot be imparted from with- out ; they are not, like deductive conclusions, implied in previous knowledge ; they require a new per- ceptive power, and the first genuine perception of a great principle is, as it were, a new birth. The only assistance to their development that it teacher can contribute, is the use of the Elenchus, the rejection of un- sound maxims and distorted views, by deducing their false consequences, or showing their discordance with acknowledged truth. (Paaavil^av TTOTtpov EiS(i}\av Kai ^evSog (iffo- TiKTU rov vkov 71 StdvoLa, rj yovifiov T€ Kai «s« ^^^™ properly the relations of opuT/wei chap. IX. species to genus and to specific pro- c. Cause and effect are essentially perty. connected, and two modes of essen- ' See Post. Anal. i. 8. 112 FOUR CAUSES. § 2. The necessitating antecedent cannot be traced in less than two propositions '.^ their common intermediate necessitates the conclusion. Let us take an example : Why is the angle in a semicircle a right angle ? What antecedent necessitates this predicate ? Let A represent a right angle : B the half of two right angles : C the angle in a semicircle. From the proposi- tions, C is B, B is A, we conclude that C is A ; which means, that the angle in a semicircle is a right angle : and B is the an- tecedent that necessitates this conclusion. The interpretation of symbols resembles verbal definition. § 3. The formal cause as intermediate has already been ex- plained. § 4. We inquire the efficient cause when we ask. What was the origin of the Persian war? Why were the Athenians attacked ? Because they assaulted Sardis with the Eretrians. Let A represent war, B unjust aggression, C Athens : A is con- joined with C, because A and B, B and C are conjoined. The assault on Sardis, the first movement or original impulse of the war, appears as the intermediate. § 5. When we ask. Why does a man take exercise ? For health : Why is a house built ? For the preservation of pro- perty : Health and Preservation are the motive or final cause. Suppose that exercise is the efficient cause of digestion, and digestion the efiicient cause of health : and let C represent ex- ercise, B digestion, A health. In the efficient-cause syllogism the intermediate that conjoins A with C is the efficient cause B, which enters into the definition of the final cause A. In the final-cause syllogism the existence of the fact, that C is B, is explained by the mediation of A the motive. The propositions of a sylloigism should be inverted,'^ and then the relation of the efficient and final causes will be clearer. ' ai viroBiatig Tov ffu/tTTtpair/taroE pics, viii, 12. to yap avTiarpiipiiv i>Q rb £? qv aXna iari. — Phys. Aus. soTi to fUTaXa^ovTa t6 avfnrkpaaiia. ii. 3. fiiTO. Twv XoHrwv ipuTtifiaTiav dve- " The inversion of a syllogism is Xtlv iv twv SoOivTuv. Tlie follow- when the conclusion and one of the ing is an example. The eye sees be- premisses change places. For the cause it is of a certain structure ; meaning of /itTaXpiilSavHp, see To- here the mechanism (B) of the eye FINAL CAUSE. 113 § 6. . The terms of the final-cause syllogism do not preserve the order of occurrence observed in the efficient-cause syllo- gism. In the syllogism that exhibited the eificient cause, the middle term. Aggression, was the earliest occurrence : in the syllogism explaining the motive, the minor term. Exercise, is the earliest occurrence : the middle terra. Health, the latest. § 7. A fact may be necessitated by the material cause, and yet have a design : ^ as light issues from a lantern in conse- quence of the material necessity that corpuscles escape through pores too large to retain them, (if we assume that bodies are (C) is the efficient cause of sight (A) ; and we have the following syllo- gism : all B is A all C is B . . all C is A. But the eye is of a certain structure in order that it may see.: sight is the final cause of the mechanism of the eye. In the syllogism by which this is expressed, all A is B all C is A .-. all C is B, the minor and conclusion of the former syllogism have changed places. • A lantern (A) emits Ught (C) because it is of a porous material (B), and in order to guide us in the dark (D). The proposition, A C, may be proved by either of the mid- dles, B or D ; the proposition, A D, may be proved by the middle B, and the proposition, A B, may be proved by the middle D. The difficulty of reconciling the efficient and mate- rial with the final cause, a question which is here so briefly dismissed, has been one of the chief points on which the schools of philosophy have split, some adopting the ma- terialistic, others the spiritualistic theory. Kant attempts a recon- ciliation in his Critic of the Judg- ment. See Plato, Phsedo, § 106 > also Trendelenberg's Logic. The conclusion deducted fi-om a final cause indicates the necessary con- dition for realizing a proposed end, and is said to possess an hypo- thetical necessity, tovto S" etrriv (Kffwfp l^ VTToQkatiaQ. & ^vayKri TrepiKVKKeiv Kai it'a- " ri^ Xinrofikvi^ Tpoviji avvejrXrj- Kajiirriiv . . . avriarpifuv Spa civdy- piiiae TO '6\ov o 9tbs, ivBiXsxrj ttoijj- kij tarai. — Ibid. li. 10. aac rfiv yivtmv . . . Sib Kai raWa, Set Si vor)trai tovtov &(nrcp rrora- offa jUcrrt^aXXtt dg dWrjXaj fitfietTat fibv piovra KVK\(p dvo) Kai KaTtt)' Kai rijv KiVXij) (j)opdv iiovri yap r) KiiKXif) tovt MeXexh iOiXu yiyvfoBai. — we should divide wholes into their parts, and genera into their species ; and place first the attributes of the whole genus ; if the inquiry is zoological, the characteristics of the whole animal kingdom ; next the characteristics of the immediate subdivisions ; of the whole subgenus bird for instance ; and the remainder in like manner. This will enable us to deduce or explain the charac- teristics of the subgenera. Let A represent animal, B animal characteristics, C D E particular animals, as man or horse. Then A wiU be the reason why B is predicated of C. § 2. We should not confine our observations to commonly recognized genera, but endeavour to detect other generic cha- racters, and ascertain what predicates are attached to them, and to what subjects they are attached. A class of animals is homed, and characterized by a ruminating apparatus and the absence of teeth in the upper jaw. If we know what animals are the subject of this predicate, the possession of horns, this character,^ the possession of horns, is the cause and explanation of their possessing the other characteristics. § 3. We must also observe analogies : there is no common ' The collection of premisses, whe- iii. 14. The explanation here given ther, as here, Scientific Theses, or is, that the horns exhaust the mate- Dialectical Organa, oi' Rhetorical rial that might have formed, the up- specific data, is expressed by the per teeth ; and, as thereby the mas- word hUyuv or iKXaii^avav. To- tication is incomplete, to assist the pics, i. 12; Prior. Anal. i. 27 ; Rhet. digestive process, nature provides jj_ 22_ the ruminating apparatus, a kind of '' See De Part. Anim. iii. 2. and secondary stomach. 122 RELATION OF CAUSE AND EFFECT. name for the spine of fish, the pounce of the sepia, and the common bone, but they all have the same concomitant attri- butes, evincing a unity of nature. § 4. Identity of problem is constituted by identity of the ex- planatory intermediate ;i as several problems are explained by the development of an opposite by its opposite ; and here the intermediate, though the same in genus, may differ in subject or in mode. The echo, the image in a mirror, the rainbow, are caused by refraction, generically the same, but different in species. § 5. Or problems are identical, if the explanatory middle of the one is subordinate to the explanatory middle of the other. The Nile swells at the close of the month, because the weather is stormy ; the weather is stormy because the moon wanes : these causes are subordinate. CHAPTER XIV. RECIPROCATION OF CAUSE AND EFFECT. § 1. As the presence of an efiect implies the presence of its cause : for if the fall of the leaf and the moon's eclipse do not imply the leaf's broadness and the earth's interposition, their origin must be due to other causes : and as the presence of the cause, the broadness of the leaf, or the interposition of the earth, implies the presence of the efiect, the fall of the leaf or the moon's eclipse : the cause and efiect are simultaneous, and the cause is deducible from the efiect as well as the efiect from the cause. Let A be the fall of the leaves, B broadness of the leaves, C the vine. Because A is predicated of B, and B of C, therefore A is predicated of C, and B the intermediate is the cause. Again, the broadness of the vine-leaves is deducible from their annual fall. Let D be broad-leaved, E shedder of leaves, F the vine. All F is E, and all E is D, therefore all F ' See the Meteorics, where he proposes to explain a great variety of pheenomena by very few causes. RELATION OF CAUSE AND EFFECT. 123 is D. In this case, however, the intermediate E is not the cause, for causation implies priority, and cannot be reciprocal. As interposition is the cause of eclipse, and not eclipse of inter- position, and a reasoned or explanatory proof employs the cause, a deduction of the latter kind is not a reasoned proof, but only a proof of fact. Interposition is the cause of eclipse, and not vice versa, for it enters into the definition of eclipse, and renders it cognizable. § 2. If, however, the same term may be the primary predi- cate of several subjects, may not the same effect arise from severed causes ? Let A be a primary predicate of both B and C, and B of D, and C of E. A then is a predicate of D and E by the respective causation of B and C. The existence, it would appear, of the cause involves the existence of the effect ; but the existence of the effect only involves the existence of one among several possible causes. If, however, the theorem is commensurate, the effect will be commensurate to the cause. The fall of leaves must be explained of its commensurate sub- ject, whether a whole class or a species, whether the whole vegetable kingdom or a particular province : so that the cause or intermediate will be equal in extent and convertible with the effect or major. If the fall of leaves is produced by coagula- tion, wherever there is a fall there must be coagulation, and wherever there is coagulation of sap there must be a fall of leaves. § 3. There is only one cause from which an effect can be de- duced, if the demonstration is essential ;^ for then the middle is ' "The ideal limit, therefore, of modes of production may be resolved the explanation of natural phseno- into another, or that all of them mena (towards which, as towards may be resolved into some more other ideal limits, we are constantly general mode of production not hi- tending, without the prospect of therto recognized. But when the ever completely attaining it) would modes of production are reduced to be to show that each distinguishable one, we cannot, in point of simplifi- variety of our sensations, or other cation, go any further . . . Accord- states of consciousness, has only one ingly the greatest achievements in sort of cause As long as there physical science have consisted in are several known modes of produc- resolving one observed law of the tion of a phenomenon, so long it is production of motion into the laws not impossible that one of these of other known modes of production. 124 RELATION OF CAUSE AND EFFECT. the definition of the efiect or major. The same effect is sus- ceptible of many deductions by sign or accident : both the ma- jor and the minor premiss, both the conjunction of effect and cause, and of cause and material, may be accidental ; but such propositions are useless in a scientific theorem. § 4. The premisses resemble the theorem ; if it is equivocal, the premisses are equivocal ; if it is incommensurate, they are incommensurate. The cause of the convertibility of a propor- tion is both different and identical for proportional lines and proportional numbers ; different so far as they are lines and numbers ; identical so far as they receive the same increments. § S. If one cause can be given why colour is similar to colour, and figure to figure, it must be equivocal ; for similarity of figure is analogy of sides and equality of angles ; and simi- larity of colour is production of the same sensation, or whatever else may be its definition. § 6. If effects are analogous, the intermediates by which they are deduced are analogous. § 7. There is a reciprocal sequence between the major, the middle, and the minor terms, the effect, the cause, and the ma- terial. The major is more extensive than any particular minor, but equal to the universal class : the equality of exterior angles to foar right angles is more extensive than triangle or square, but equal to the whole class of plane rectilinear figures : and the relation of the middle to the extremes is similar. § 8. The middle is the definition of the major; therefore definitions are the basis of a science. The fall of the leaf is an attribute of the vine, but more extensive ; of the fig, but more extensive : it is co-extensive to some class in which they are all embraced. The primary intermediate defines the fall of the leaf, the attribute or major : not Broad-leaved, the primary in- or the laws of several such modes shown to be produced by electrl- into one more general mode ; as city ; when the motions of fluids in when the fall of bodies to the earth, a lateral direction, or even contrary and the motions of the planets, were to the direction of gravity, were bi'ought under the one law of the shown to be produced by gravity; mutual attraction of all particles of and the like." — System of Logic, matter; when the motions said to bookiii. 14, be produced by magnetism were RELATION OF CAUSE AND EFFECT, 125 termediate next the subject, which is only a class including all leaf-shedding trees : but the intermediate next the effect or attribute — coagulation of sap, or whatever else it may happen to be. Leaf-shedding is defined by the coagulation of the sap at the junction of the stalk and stem. § 9. To examine with symbols the incommensurate sequence of cause and effect, assume the propositions, all B is A all D is B: where A the effect is universal to B the cause, but not its pri- mary or coextensive universal : and B the cause is universal to C the subject, but not its primary or coextensive universal. As B- is not the only cause of A, let us assume otjjer propo- sitions : all C is A all E is C; where the terms are similarly related. If neither B nor C is commensurate to A, they must be mutually exclusive : for any genus that contained all the causes of A would be commensu- rate to A, which is contrary to hypothesis. The same effect, then, may be produced by different causes, but only in subjects specifically different. Longevity may be due to the absence of gall in Quadrupeds : in Birds to the predomi- nance of solids, or whatever else the cause may be. § 10. If a subject does not fall at once under the term indivi- sibly connected with the attribute, but is separated from it by several intermediates, all these intermediates are causes of its possessing the attribute. § 11. Which is properly called its cause? the intermediate immediately adjoining the universal or attribute, or the one immediately adjoining the subject? The one adjoining the subject is the cause that the primary or subject falls under the universal or attribute. If D is C, and C is B, and B is A ; C is the cause that conjoins the effect A to the subject D, because it conjoins B to D ; B is the cause that conjoins the effect A to the subject C; and B is the cause of its own conjunction with A. [ 126 } CHAPTER XVI. THE ORGAN OF PRIMARY TRUTHS. § 1 . Suet is the nature and origin of syllogism and demon- stration, and, what is the same as the latter, of demonstrative science. Let us now proceed to consider the method and the faculty by which elementary principles are recognized. Demonstrative science, as we saw, is based on a knowledge of primary im- mediate principles. Is the mode of knowing the immediate identical with the mode of knowing the mediate ? Is it Science, or something different in kind? Are the appreciating faculties acquired, or are they innate, though unobserved ? § 2. They cannot be innate : we can scarcely have a know- ledge more perfect than demonstration, and yet be unconscious of it. If they are acquired, we saw, when treating of demon- stration, that we cannot learn and acquire knowledge without a basis of previous knowledge. As, then, they are neither in- nate, nor acquirable without a basis of previous knowledge and perceptions, some developed power must be innate of inferior perfection and excellence to the faculties of the im- mediate. § 3. Such we find in all animals : all have an innate percep- tive power which we call Sense. In some the sensation is tran- sient; and these have no knowledge, at least of the objects whose impression is transitory, beyond sensation. Others retain the sensation, and these are subdivided ; for in some of them a number of permanent 'sensations develop^s an intellectual con- ception. On sensation, then, ensues memory ; and on many memories of the same fact Experience : for many similar memories are one Experience : on Experience, or the whole unchanging uni- versal that has settled in the mind, the all-permeating One be- side the Many, ensues the beginning of Art and Science; of ORGAN OF PRIMARY TRUTHS. 127 Art if the end is production, of Science if the end is truth.» The faculties, then, are neither innate and originally developed, nor preceded by any higher cognizant power, but by Sense. § 4. In a battle, when an army is taking to flight, first one man makes a stand, and then another, and another, till they re- cover their original order :* the soul is adapted for undergoing a similar process : and we may now repeat more distinctly what we said before. So soon as an individual makes a stand in the mind, we have the primary or lowest universal ; for, though sensation perceives Callias, the individual, sense perceives Man, the universal : in these lowest universals, higher universals make a stand ; and finally the indecomposable and highest uni- versals : first a kind of animal, then animal, and then a higher genus. Man's knowledge of the elementary, it appears, is inductive ; for the way that sense imparts the universal is in- ductive. § 5. Our intellectual faculties are either fallible, as Opinion and Reasoning, or infallible, as Science and Reason. As all science implies conclusion, principles are not objects of science. As principles are more evident than conclusions, and no power except Reason has greater light and insight than Science, prin- ciples are the objects of Reason. Again, as the basis of demonstrated truth is not demonstrated truth, so science is not the basis of science. If Reason is the only infallible faculty besides Science, Reason must be the ' With ^pe/ifiaavTog tov Ka96\ov fiiv KaBoKov rjpeiiovira /laXKov, »/ Si compare, rip ydp ^pe/iriaai Kal aTrj- ov. — De Anima, iii. 11. vai Ttfi' Siavoiav iiriaraadai Kal ' The drift of this simile is ob- ^poi'cti' Xcyo/ieda , . . Tif ycip Kadi- seure : it may mean, that as order araaBai riji/ i^x^v Ik Trig •h^iKrJQ succeeds to the disorder of flight, ipeTrjg ijipdvifiSv ri yivcrai Kal ini- so the ordering ideas succeeds to the arrjiiov . . . KaBiararai Si Kal iravi- confusion of pheenomena ; and as rai TTJg rapaxije totc fiiv iiirb rrjg the routed army could not have as- ^vaciog Tore S" vir' dWoiv. Phys. sumed Its second array but for its Ausc. vii. 3. ruv aKivrjruJv '6pii>v Kal former organization, so the regu- vp&Tiav. Jfic. Ethic, vi. 11. 'iartjai lating ideas could not appear in the yelp Xtyuv t^v Siavoiav Kal b dKov- mind, unless there were in nature aag ^pk/uiatv. — De Interp. 3. behind the confusion of pheenomena afi^ot Kivovffiv al So^aif &\\' rj an original order and law. 128 ORGAN OF PRIMARY TRUTHS. basis or beginning of Science :* and the beginning of Science bears the same relation to the basis or beginning of truth, that the whole body of science bears to the whole body of truth. ' a'pX^" ^inaTriiitig clvai nva fiev jiva, iv Si iiiXti Sitatg, iv Sk ^afiiv, y Toiig '6povc yvuipU^o/iev. — avWoyia/iif ri 'iv irpoToaiQ a/ttaoe, Post. Anal. 1. 3. i) apx4 iv ^dpu iv S" linijrijiiy 6 vovg, — Ibid. i. 23. APPENDIX APPENDIX A. AXIOMS. § 1. An Axiom is a principle not limited to any one depart- ment of nature, but equally applicable to every subject-matter.* The leading Axiom is expressed under various formulae. In the Metaphysics we have,* One of two contradictories must be true ; and. The same thing cannot be and not be. In the Prior Ana- lytics,* The same subject cannot have contradictory predicates ; and, Every subject must have one of two contradictory predi- cates. In the Treatise on Fallacies,* Things which are the same as the same are the same as one another. § 2. It is clear that if this principle were not true, if it were possible that the propositions, A is B, and A is not-B, could stand together, there could be no reasoning and no thought. Accordingly those who denied the possibility of Knowledge or Philosophy, in order to do their work thoroughly, selected this principle as the object of their attack. To effect its overthrow various doctrines of celebrated philosophers were brought to bear. Heraclitus, for instance, had said that all nature is in a per- petual flux, so that nothing is in the same state for two succes- sive moments.^ From this it would follow that neither of two contradictories could be predicated with truth of any subject. * Koivov. — AndX, Post, passim. * rd. kvl Kal ravTi^ ravrd, Kal d\~ " irav avafKoiov r) ipavai ri airo- X^Xotg diiovjuv ilvai raira. — Soph. ifidvai, Kai dSvvaTov li/ia ilvai Kal Elench. 6. Perhaps the most au- ft^ tlvai. — Met. iii. 2. cient formula is the line of Parme- ^ (pane K"' airoipame oix vv&p- nides : oii yap firjiroTe tovto Says, Xovaiv al AvTixdiuvai a/juz rip aiiTig. elvai /*^ kovra. — ^Plato, Sophistes. . . . Kara iravrbs ivbg v ijictaiQ n * Met. iv. 5. anoipane a\i)6J7£. — Prior. An. i. 40. 13-2 AXIOMS. Anaxagoras held that the ultimate elements could never be entirely separated ;i that nothing in nature was pure or simple, or excluded opposite elements, but received its denomination according to the predominance of particular ingredients. It follows, that neither of two contradictories can be predicated absolutely of any subject. He maintained also, that whatever seems is true ;* an assertion similar to that of Protagoras, who taught that man is the measure of reality, which meant that opinion is the criterion of truth ;* and, as the same objects pro- duce different sensations and opinions in different men, it was inferred that truth may be self-contradictory. To avoid the consequences of the doctrine of HeracHtus,* Plato, who came from this school, maintained the existence of immutable Ideas. § 3. As all the sciences alike assume the truth of the Axioms,^ it does not appear to which of them the discussion properly belongs, and this is proposed as a question in the Metaphysics; where it is decided, that, as they are true of all Being, they belong to the science of Being, and accordingly they are dis- cussed by Aristotle in the Metaphysics. ^ § 4. The Axioms are indemonstrable ; for it is impossible ^ ofiov TTOLvra ;3^p^juara, uiffre lit]- also Met. iv, 5. Bat (Tot, lav Ti ^ovKy, Slv aXtjBSiQ tv VTrdpxuv. — Met. iv. kdv Te fjf^, dveKTsov '6vri fiirpty, — 4. ficfiixBai irdv iv Ttavri. — Met. Plato, Theaet. § 64. airapKr] exa- iv, 5. kv navri TravTog tlvai jioipav, firipivii>v ^ v eTepiDv rd aia9tjT'!]piov Kal Kpirjj- Koiov ix^iv Thv otiovv avvikvTa tSiv pioj/j Toi)q eTEpovg fiiv vTroXrjTrTeov bvriov, tovto oitK VTToQttriQ, — Ibid. fiETpov elvaij Toig d* Irkpovg oiix ovk egti d' vjroOeffig o dvdyKrj v7ro\ji-jrT£ov. oftoitog Ss tovto Xsyoi tlvai St avTb Kal Soxetv dvdyKrj, — Kal «7rt dya^ou Kal KaKov Kal koXov Post. Anal. i. 10. Koi alffxpov Kal Tutv aXKwv twv toL' ^ iijv dvdyKrj exEiV Tbv otiovv fia~ ovTiav. — Met. xi. 6. Btjaoiievov, d^iD/jui. — Post. Anal. i. * dii effTLV hvUTijvai rrpbg t6v e^oj 2. S dk yviopiZsiv dvayKoiov Tip OTt- \6yoVf dWd TTpbg rbv eVw \6yov ovv yvinpit^ovTif Kal ijKELv fi^oj/ra OVK dtl. — Anal. Post. i. 10, dvayKoiov. — Met. iv, 3. AXIOMS. 135 § 5. How do the Axioms enter science, of which they are said to be the common principles ? Not as' propositions or pre- misses, but as the principle of syllogism by which we pass from premisses to a conclusion. We may show that the Axiom : The same thing cannot have contradictory predicates, is equivalent to the dictum, de omni et nulla, by applying it to the two first moods of the first figure. For in the afiirmative syllogism, all B is A aU C is B .-. all C is A, the major premiss may be considered as assigning A, one of two contradictory predicates, to B ; the minor as recognizing the identity of B and C ; and the conclusion as affirming, in virtue of the Axiom, that C cannot possess the contradictory of A. A negative syllogism can be analyzed in the same manner. In the syllogism, no B is A all C is B .•.no C is A, the major premiss ascribes not-A, one of two contradictories, to B ; the minor recognizes the sameness of B and C ; and the conclusion, by faith in the Axiom, denies the other contradic- tory of C. The explanation wUl slightly vary according as we take different forms of the Axiom. Their equivalence to the dictum de omni et nulla appears to have been held by Aristotle from his calling them the Syllo- gistic principles, or the Demonstrative principles -A and he seems to mean that they are not employed as premisses, when he says that they are not expressed but only implied, unless the conclusiveness of an argument is called in question.^ " irepi tSv diroSeiKTiicwv dpx?>v ° oiSefiia Xafi^avH diroSuKig dW Xeyiit S' d'TroSuKTiKd.Q, Koi rag Roi.vd.q ri lav Sky Seiiai icai rh av/jfTrBpaa/ia So^ag £? (5v HiravTcg Sumivovai. — : ovTiiig. — Post. Anal, i. 11. Coin- Met, lii. 2. Trept tSv ovXKoyianKSiv pare oiS' iv avWoyur/iif Xa/ilSdverat dpxoiv Tov fi\oiT6v Anal. i. 32. oiov T ilvai Tivaq l^ 5iv diravra AXIOMS. 137 single step in deduction, as they constitute in fact the deductive faculty. Dugald Stewart recognized the distinction between Axioms and Theses, the latter of which he calls First Princi- ples, the former Laws of Belief. — (Philosophy of the Human Mind, part 2, chapters 1, 2.) Mr. Whewell's Axioms are very different from those of Ari- stotle. Sometimes they are equivalent to Hypotheses (book x. 5) : sometimes they contain more than the Hypothesis, being supplementary to the Definitions where these are inadequate j sometimes the word is used in the stricter sense. Yet, though thus peculiar in his use of the term, he censures Locke and Stewart, who affixed a very different meaning to it, for calling the Axioms barren truisms. This is true in the sense in which they employed the term. The Axioms are themselves barren and fruitless, their office being to cause the Theses to fructify. In Dialectics and Rhetoric a similar relation obtains between the Topics and the Organa, or specific premisses. § 6. The Axiom is not used in all its generality whenever employed, but only so far as it regards the subject-matter under discussion :i in Mathematics, for instance, it does not contain the notion of Identity, but only the Mathematical form of this. Equality. The existence and character of the Axioms is indicated by Logic ; and the laws of reasoning, as traced by General Logic, may be considered as the development of their simplest form : they are used by all the sciences -.^ they are discussed and de- fended by Metaphysics ; and are characteristic of Dialectics. The Dialectical Maxims or Topics are modifications of the Axioms, and obtainable by deduction •,^ for they appear to be the derivative Axioms to which Aristotle alludes. ' vpiivTai liiv iravTCQ, eiri roaov- \ov wtipi^ro iuKvvvai t& Koivd. — Tov di xpiavTai 'tip' 'oaov airolg Ixa- Anal. Post. 1.11. vov' TOVTO S' iariv '6aov iir'ix^i to ' ifivau yap cipxv t«^ ™»' aWiav yivoe irtpl ov ^ipovairdeavoSei^tig. dluaiiaTiov avrt) iravTiav. — Met. iv. ..Met. iv. 3; also Anal. Post. i. 10. 3. The same is asserted by Sir Wm. ^ imKoivaivovai SI T^aaai ai km- Hamilton. " For every maxim of arrjfiai dXKiiXaiE Bards rA Koivd, leah every Dialectical Place is itself cou- 9j StaKcKTiKV irdaaig, (cat ft ng Ka96- tained within the sphere of one or 138 AXIOMS. It is the Axiom, the principle that one of two contradictories must apply to every subject, that constitutes the necessity of Division. 1 § 7. Some have assigned all primary truths to Metaphysics : this cannot be, unless it is the sole science ; for all science rests on a basis of primary laws. But though, in resting on Theses, Metaphysics only resembles its sister sciences, it stands in a peculiar relation to the Axioms. The others investigate as well as use their respective Theses, but employ the Axioms without submitting them to an investigation ; for as these principles are laws of all Being, their investigation belongs to the science of Being, that is, to Metaphysics or Ontology : by Metaphysics, therefore, they are investigated as well as employed. Logic will take cognizance of the Axioms, as, to a certain degree, it takes cognizance of all truths. An Astronomical con- clusion, so f^r as it is a conclusion, obeys certain Logical canons ; so far as it regards the heavenly bodies, it belongs to Astronomy. In the same way Astronomical principles, so far as they are principles, exhibit certain Logical attributes : so far as they refer to the Stars, they are Astronomical. And Logic stands in a similar relation to the conclusions and principles of all other sciences. Metaphysics included, whether the principles are Theses or Axioms. Though the latter, then, are peculiarly the province of Metaphysics, yet to a certain degree, as well as all other truths, they would fall under the cognizance of Ijogic. But a much closer relation than this subsists between the Axioms and Logic. They are the principles involved in all reasoning, (called, as we have seen, by Aristotle, avWoyia-riKal apj^ai, and avoSeLKTiKai a.p)(a.i) that is, they are the very princi- ples whose consequences and limitations are traced by General Logic. Metaphysics undertakes their justification and defence against all assailants ; Logic assumes them as self-evident, and other of the four logical laws, of fesses to elicit a great variety of eon- Identity, Contradiction, Excluded elusions from the Axiom. Middle, and Reason and Conse- ' to 5* Unav ifiTciTrTHv eIq ri)v quent, of which it is only a subordi- Biaiptaiv av y dvrtKdfiiva, oiiK al- nate modification." — SeeSirW. H.'s rij^a, dvdyKrj yap. — Anal. Post. ii. edition of Held, p. 767. Fichte pro- 12. HYPOTHESES. 139 developes them into the forms of argument and the canons of syllogism. Through the Axioms, then, Logic is more closely related to Metaphysics than to the other sciences : it criticizes both it and them : but while independent of the latter, it bor- rows from the former some of its ultimate principles. APPENDIX B. HYPOTHESES. § 1. An Hypothesis is a peculiar principle,^ that is, it differs from an Axiom, in that it varies in different sciences ; and is the I element that gives a categorical character to the conclusions,/ by afiirming the reality of the first cause whose effects are de-/ duced, or of the substance whose attributes are proved.^ Had we merely definitions of the cause and the effect, of the sub- stance and the attribute, we might indeed demonstrate their respective connection. But such an effect and attribute would be purely ideal and imaginary : we should not know their reality or actual existence, a knowledge that is essential to the completeness of science. If, however, we know the actual ex- istence of the first cause or the substance, then by the aid of definitions we can not only evince the indissoluble connection of the effect and attribute with such cause and substance, but also their actual and real existence. The existence of the effect I and attribute is not assumed in the Hypothesis :' to prove it is 1 the work, and the sole work of Demonstration, for their nature, or essential character, is assumed in the Definitions. ^ § 2. It must be observed, that Hypothesis sometimes appears to signify the contrary of what has been stated ; for a conclu- ' iSia or oUeia dpxri- t^Ti S' ISia inaccurate to use Hypothesis for de- Kal a. XafijiavcToi ilvai. — Post.Anal. finition, as appears from Post. Anal. i. 10. i. 2. OTi S" tffri rag jiiv dpxdg dvdy- ' 0e(7ie ^ TO ilvai n fi firi iivai ti kt] XafiPdvuv. — Post. Anal. i. 10. Xafipdvovaa, vjroBeaig. — Post. Anal. ^ rd St rovriav irdQi] xaff avrd H i. 2. litv ar)jiaivu FxaaTov Xajifidvovaiv (Ivai rd &iif(ra koi rde dpxag viro- on 5* tan Sukvvovui. — Poet. Anal, eiffflat M. — Post. Anal. ii. 8. It is 1. 10. 140 HYPOTHESES. sion is said to be hypothetical in the absence rather than in the presence of the Aristotelian Hypothesis : in modern times a theory is called an Hypothesis before it is established as a Law — that is, while it consists of Definitions without Hypothe- ses ; and Aristotle himself calls conditional conclusions hypo- thetical.' This perhaps may be accounted for from acharacter- (istic of the Hypothesis that distinguishes it from the Axiom, its want of recognizable necessity.* Hence it seems to have been applied to propositions that have scarcely any evidence ; and a conclusion that rested on such a premiss would be so far conditional, and, in reference to this premiss, hypothetical. J There will be no confusion if we remember that when an Hypo- ' thesis is spoken of as a scientific principle, it means that ele- ment that renders conclusions unconditional and un-hypothe- tical. § 3. Three characteristics, then, are united in the conception f of the Hypothesis : it is an appropriate principle ; it asserts ; existence or reality ; and its necessity is deficient in evidence. From this last peculiarity of existential propositions, some mo- dern writers have maintained that the demonstrative sciences are hypothetical, not categorical.' Kant maintains that the ex- istence of Space and Time are inevitably believed, and hence gives the mathematical sciences a categorical character. He considers that the want of evidence or subjective necessity in the Hypothesis of Natural Theology is an important objection against that science. But there is no apparent reason why a Being should not be possessed of necessary existence, though the necessity of its existence be not discoverable to the human mind. Aristotle merely observes that existential propositions vary in degrees of evidence.* § 4. Arts will be founded on Definitions alone, not on Hypo- ' Categorical and conditional are tlvai Si aurh ical SokeXv dvayKt]. — opposed as airXiog and el viroBiaeiag. Post. Anal. i. 10. Post. Anal. i. 22. ' Dugald Stewart. See the distinction of categorical ' rb yivog pt-fi vtroTiOiaQai tlvai or absolute and hypothetical neces- hv y favtpbv on iarlv ov yip o/ioi- sity. De Part. Anim. i. 1 ; also lag SrjXov on o dpiBnog ean Kal 8n Physic. Ausc. ii. 9. Bcp/ibv Kal \l/vxpov. — Post. Anal. '' ovK etrn 5' vwoBiaig o dvayKri i. 10. HYPOTHESES. 141 theses : for the foundation of Productive reasoning is the con- ception of an end, which does not yet exist, but may exist if certain means are put into execution, i So the result of Moral deliberation is a conditional conclusion ; it only asserts that a certain measure must be adopted^ if we wish to realize a certain end. It is the duty, however, of Moral Philosophy to show the possibility of this end, that is, not its actual, but its poten- tial existence ; which duty is performed when she establishes the freedom of the will. The will is the efficient cause by which the end may be realized ; and the propositions which state its freedom may be regarded as the Ethical Hypothesis, asserting the potential existence of the Moral Good. § 5. Besides the Absolute Hypothesis, there is a Kelative* Hypothesis which is susceptible of proof, and therefore is not a | genuine first principle f it is assumed, however, as a principle, ' because the person to whom it is addressed is willing to accept it without proof. This appears to be the sense in which Plato uses the word, when he calls the principles of all but the pri- mary science Hypotheses, meaning merely arbitrary points of departure, capable of deduction from higher principles.' Under this head would come what Bacon has called the Axiomata Media. A primary law of -any science can be analyzed into two ele- ments ; one of which defines the character of an original power, and the other affirms its existence. Though the latter of these is, properly speaking, the Hypothesis, yet it is sometimes used to denote the whole truth ;* in which case, perhaps, greater prominence is given to the existence of the subject-matter than to its essence. § 6. The Aristotelian Hypothesis corresponds to what Mr. ' i} yelp apx4 Toie l>^v rb ov ToXg iiriPaaeiQ re Kai opfiag. — Ibid. 20. Sk Tb Iffd/tEvojA— De Part. Anim. i. 1. SiA. rb jxv iw' dpxw avcXedvTas » Post. Anal. i. 10. o-KOTreTv ctXK.' tS viroBktrvav, vovv ^ rb fiiv ^vxh ZwrtXr dvayKoZtrai ovk laxuv. — Ibid. i^ vvoBkaiiov, rb d" av 'drepov i-ir v SiaXiKTuefi rde v-iroOkait^ avai- apxvv dwiroGiTov t'oSffa.— Hep. vi. povaa kir' avrrtv rfivdpxhv vopcvi- 19. rat. — Ibid. vii. 13. rdc iiiroBkauc Trmovfievog oiiK dp- * Himip kv role p.a6iiimTiKoXi; ai X&g, dWA. Tif bvn iinoOkauQ, olov ivoOkaug.—mh. Nic. vii. 8. 142 HYPOTHESES. Mill has called the Collocation of Causes, which is explained in the following passages : — " This leads us to a conception which we shall find of great importance in the interpretation of nature ; that of a Perma- nent Cause, or original natural agent. There exist in nature a number of permanent causes, which have subsisted ever since the human race has been in existence, and for an indefinite and probably enormous length of time previous. The sun, the earth and planets, with their various constituents, air, water, and the other distinguishable substances, whether simple or compound, of which nature is made up, are such permanent causes . . . We can give, scientifically speaking, no account of the origin of the permanent causes themselves. Why these particular natural agents existed originally and no others, or why they are com- mingled in such and such proportions, and distributed in such and such a manner throughout space, is a question we cannot answer . . . All phaenomena, without exception, which begin to exist, that is, all except the primeval causes, are effects either immediate or remote of those primitive facts, or of some combi- nation of them . . . The whole of the phaenomena of nature were therefore the necessary, or in other words, the uncondi- tional, consequences of the original collocation of the Perma- nent Causes." — System of Logic, book iii. 5. " It is necessary here to remark, that in this resolution of the law of a complex effect, the laws of which it is compounded are not the only elements. It is resolved into the laws of the sepa- rate causes, together with the fact of their co-existence. The one is as essential an ingredient as the other ; whether the ob- ject be to discover the law of the effect, or only to explain it. To deduce the laws of the heavenly motions, we require not only to know the law of a rectilineal and that of a gravitative force, but the existence of both these forces in the celestial regions, and even their relative amount. The complex laws of causation are thus resolved into two distinct kinds of elements : the one simpler laws of causation, the other (in the aptly se- lected language of Dr. Chalmers) collocations ; the collocations consisting in the existence of certain agents or powers, in cer- tain circumstances of place and time." — Book iii. 12. " Derivative laws, therefore, do not depend solely upon the HYPOTHESES. 143 ultimate laws into which they are resolvable : they mostly de- pend upon those ultimate laws and an ultimate fact ; namely, the mode of co-existence of some of the original elements of the universe. The ultimate laws of causation might be the same as at present, and yet the derivative laws completely dif- ferent, if the causes co-existed in different proportions, or with any difference in those of their relations by which the effects are influenced." — Book iii. 16. The ultimate laws of the Permanent causes assume, in the Aristotelian Logic, the form of Definitions : the ultimate fact of the existence of these causes, that gives an unconditional con- clusion, is expressed in the Hypothesis ; both are called The- ses ; and, combined with the developing Axioms, tliey are a sufficient basis of categorical science. What Mr. Mill has called a Postulate is the Hypothesis. See note to Post. Anal. ii. 7. OXFORD : PRINTED BY E, W. MORRIS. Cornell University Library B441.A5 P85 Logic of science : a translation of the olin 3 1924 028 996 572 ^«/?^ --it ft iA>,\ '-^ ■•h yi' W' im 'f- 'iv,.- n 'If « ' M M V ' ^<'M.ii'it:ri'! ^*/^(