J ! Digitized by tine Internet Arciiive in 2007 witii funding from IVIicrosoft Corporation littp://www.arcliive.org/details/digestofdeductivOObarkricli A DIGEST OF DEDUCTIVE LOGIC A DIGEST OF DEDUCTIVE LOGIC FOR THE USE OF STUDENTS JOHNSON BARKER, B.A. METHUEN & CO. 36, ESSEX STREET, W.C. LONDON 1897 ^3 PREFACE This book does not pretend to be a treatise. It is a note book, intended to be used side by side with the ordinary Manual. My indebtedness to the ordinary Manual, as may be supposed, is con- siderable, for in large part these notes are little more than a summary of what any ordinary manual will contain : to summarise, however, was my main purpose. The book is designed, as stated in the title, for students preparing for examination. It offers them, firstly, an outline of that portion of the subject which the text book treats in full ; and, secondly, it provides a somewhat fuller discussion of points that are apt to be overlooked or omitted. It has been my aim throughout to bring into the relief of bare outline the essentials of deduction, and to elucidate obscurities. This book, then, differs from other works in being condensed where they are full, and in being supplementary where they are condensed, and thus it may claim a certain sort of freshness of treatment. 220697 vi PREFACE These notes have already been found useful in teaching. It is hoped that their usefulness may be extended by publication. The questions in Appendix I. are selected mainly from the B.A. examination papers set at the Universities of London and Durham. They are arranged, as far as possible, in sets correspond- ing to the subject matter of the chapters to which the Roman numerals refer. The number of ques- tions might easily have been multiplied : their purpose here, however, is not so much to supply an exhaustive praxis, but to indicate, all along the line of the study, the general standard required of those who take up Logic for examination. The Bibliography in Appendix II. is not in any sense complete. It is a list compiled in the course of my own reading, which for purposes of reference from time to time I have found useful. It is more complete than any similar list with which I am acquainted. Johnson Barker. CONTENTS CHAP. I. LOGIC, THOUGHT, AND LANGUAGE IL DEFINITION AND SCOPE OF LOGIC III. THREE PARTS OF LOGICAL DOCTRINE IV. TERMS V. CONNOTATION AND DENOTATION VI. PROPOSITIONS VII. PREDICABLES AND PREDICAMENTS VIII. DEFINITION AND DIVISION IX. IMPORT OF CATEGORICAL PROPOSITION QUANTIFICATION OF THE PREDICATE X. DIAGRAMMATIC REPRESENTATION XI. IM.MEDIATE INFERENCES XII. THE LAWS OF THOUGHT XIII. THE SYLLOGISM XIV. FIGURE AND MOOD : REDUCTION PAGE I 7 17 25 32 37 48 55 59 65 71 85 89 100 Vlll CONTENTS CHAP. I'AGE XV. IRREGULAR AND COMPOUND SYLLOGISMS 112 XVI. FALLACIES ... XVII. THE VALUE OF THE SYLLOGISM XVIII. SUMMARIES AND TABULAR STATEMENTS APPENDIX I EXAMINATION PAPERS APPENDIX II BIBLIOGRAPHY ... 123 129 A DIGEST OF LOGIC CHAPTER I LOGIC, THOUGHT, AND LANGUAGE REFERENCES Jevons, ch. iv. and vi. Keynes, Introduction. Welton, Vol, i., Introd., ch. i. Mill, Bk. i., ch. i. Logic is the science of the laws of valid thought. No such science is possible without a commonly received and understood means of expressing thought. The accepted means of expression is language. At the outset therefore we must take into account the nature and purpose of language in its connexion with thought. Matter of thought is suppHed b}^ sensory impres- sions, which act as stimuli to the mind and excite ideas. This raw material becomes know- ledge only through the activity of the mind itself. Mind has a power of synthesis which collects into 2 A DIGEST OF LOGIC one complex whole the various impressions received through the senses, and allocates them in one external object, of which we thus form a mental image or idea. This result of mental activity is perception. Perception, then, may be defined as that state of mind in which it becomes conscious of an individual sensible object. But we are capable of more than such simple acts of consciousness, and so much more that this is not commonly regarded as being thought at all. The first stage of thought is conception. Con- ception is the name for knowing generally, as opposed to perception in which we apprehend only the attributes of the individual thing perceived. The concept is to be regarded as an extract or deposit — either word is better than "abstract" — from a number of resembling percepts or images. It is a general notion formed by a comparison of individuals and the selection of attributes common to them all : in other words it is the discovery of likeness. Perception is apprehension of a thing : concep- tion is apprehension of a kind of thing. Percept is knowledge of a particular : concept is knowledge of a general. For perception naming is advan- tageous, but not essential. For conception language is indispensable. The name combines and registers in a fixed form a group of certain attributes, which otherwise would become disunited in thought when not attended to. It helps to recall that group and to keep it distinct from other groups. LOGIC, THOUGHT, AND LANGUAGE 3 The psychological concept is equivalent to the logical connotation or significance of a class name or general term. The general term thus formed need not refer to any actually existing class. It is enough that such a class can be conceived in thought, even though it have only one actual representative, or exist only in imagination. Naming, therefore, or some similar system of signs, is an essential factor in the progress and process of thought. The concept is the unit of thought, and without a name, would rapidly tend to disintegrate. Language may be defined as a system of signs for the purpose of facilitating or economising the process of thought and of recording and expressing its product. This definition includes gesture or imitative language, and conventional or verbal language. In conventional language the connexion between symbols and ideas is arbitrary and artificial. Speech is the universal medium of communica- tion because it is a natural method of expression. Men speak, not because they mean to speak, but because they are constituted as they are. It is also the most easily employed, as well as the most effective system of intercommunication. The chief functions of language may . thus be summarised — I. It is a means of intercommunication. II. It is a mechanical aid to thought, enabling us to form concepts and facilitating the process of thinking. 4 A DIGEST OF LOGIC III. It is an instrument of record and reference, demanding two main requirements, viz. — (i) Precision or definiteness of meaning, and (2) Completeness. Language is modified by two great and contrary processes, viz. — I. Generalisation, and II. Specialisation. I. Generalisation arises from detection of like- ness between a new object without a name, and some other object well known ; the old name is applied to the new object. This change is usually effected by a sort of unconscious instinct in a number of persons using the name. In the language of science such changes are often pur- posely made. Proper, or singular names, are constantly generalised both in popular and in scientific language. II. Specialisation is a change exactly the oppo- site, and equally important. A name originally applicable to a multiplicity of objects by usage comes to be applied only to a few ; or to put the same fact in another way, applied originally in a general sense it comes to have a special significance and application. One effect of special- isation is what is known as dcsyiionyiiiisatioii^ or the differentiation of synonyms. In addition to the changes effected b}^ generalis- ation and specialisation, vast enlargement and changes have also been made in language b}- the process of analogous or metaphorical extension of LOGIC, THOUGHT, AND LANGUAGE 5 the meaning of words. Practically this consists in generalisation, and differs only in proceeding by analogy rather than identity, that is, the ex- tension of meaning is based on imagined re- semblance rather than any actual likeness between the new object and the old after which it is called. Ambiguities of language are of frequent occur- rence. Very few words indeed have one and only^ one definite meaning. The exact meaning of a word depends for the most part upon the context in which it is used. This indeterminateness of meaning gives rise to confusion of thought and misunderstanding — technically called fallacy. Bear- ing this in mind, words have been classified as — L Univocal when they suggest no more than one definite meaning, IL Equivocal^ ambiguous, or Jiouionyiiioits when suggestive of two or more meanings, and II L Analogous when with the same meaning they have a different application. E.g. foot — of a mountain : of an animal : of a page : a measure of length. Equivocal words are further classified according as equivocation arises from their (i) Sound, (2) Spelling, or (3) both Sound and Spelling. These latter are grouped according as equivocation arises from {a) accidental confusion of different words, (^) transfer of meaning by association of ideas, or {c) logical transfer of meaning to analogous objects. An ambiguous word is in reality not one, but two or more words confused together. Language 6 A DIGEST OF LOGIC is full of ambiguities, and we cannot proceed far in logic until we have placed a precise interpret- ation upon certain forms of words as representing thought. If thought, and thought alone, were the subject matter of logic, there would be no such necessity. The fact that such necessity exists shows that to eliminate all considerations of language from logic is an impossibility. In dealing with such ambiguous words logically, we must first of all determine from the context one clear and definite meaning. Then, and not till then, can we proceed. CHAPTER II DEFINITION AND SCOPE OF LOGIC REFERENXES Jevons, Lessons, ch. i. Keynes, Introd., §§ i and 2. Welton, Vol. i., Introd., ch. ii., pp. 16 — 19. Mill, Logic, Introd. Mill, Exam, of Sir IVni. Hamilton, ch. xx., p. 373. Ray, Introd. and Appendix E, p. 302. Bain, Ded. Log., pp. 30— 37- Read, Carveth, Theojy of Logic, Introd. Logic is the science of the principles which regulate valid thought and its expression in language. Many other definitions of logic have been given which have varied greatly according to the view taken of the scope of the science. Of these Bain in his Deduction quotes and discusses the following — [rt:] The Art of Reasoning. \b'\ The Science and Art of Reasoning. [^] The Science of the Laws of Thought. \d\ The Science of the Operations of the Under- standing in the Pursuit of Truth. 8 A DIGEST OF LOGIC [c] The Science of the Operations of the Under- standing which are concerned in, or are subservient to, the Estimation of Evidence. Mill quotes and criticises the definitions [a], [d], and [d], giving [e] as his own. Reverting to the definition given at the head of this chapter, and accepting it as tolerably compre- hensive, the meaning of the words employed must be clearly- understood. Science is coherent or systematised knowledge. Its office is to detect and describe the natural laws inflexibly observed by the objects treated in the science. There is a science of.human reason or thought because there are uniform modes in which every one thinks and reasons, and must think and reason. A law or principle is uniformity of mode : also the statement of this uniformity. In other words it is the statement of a general truth. By laws of thought we mean "a certain uniformity or agree- ment which exists and must exist in the modes in which all persons think and reason, so long as they do not make what w^e call mistakes, or fall into self-contradiction and fallacy " (/evo/is). Psychology deals with these laws in the sense of uniformities, that is, laws in accordance with which men are found by experience normally to think and reason. It also investigates their genesis and development. Logic deals with them purely as statements which are regulative and authoritative, that is, as affording criteria by the aid of which DEFINITION AND SCOPE OF LOGIC 9 valid and invalid reasonings may be discrimin- ated. The word thought is used at least in three senses, viz. — {a) Any mental state : conceiving, judging, in- ferring. {b) Thought-process: conception, judgment, in- ference. (c) Thought-product : concepts, judgments, in- ferences. With regard to validity or truth, the most effective statement is that valid, true, or correct thought or thinking is that which is so recog- nised by all minds, that is, a thought is valid when it holds not only for the thinker, but for all others to whom he may communicate it. True thought has a general application : it is knowledge of a general kind for all alike. Logic investigates and determines the conditions under which the thought of one mind can stand for the thought of all minds ; it is concerned with the conditions under which a thinker can claim from all minds assent to his own thought. Validity is of two kinds : {a) formal, (J?) real. {ii) Formal validity is self-consistency, z. e. not self-contradiction. {U) Real validity is consistency with objective reality, i. e. with fact. Take, e.g. two propositions — (i) All men are mortal. (2) No man is immortal. lo A DIGEST OF LOGIC You cannot but think (i) when the thought ex- pressed is referred to the real and actual experi- ence of life, and it assures the validity of (2), that is, (2) is true in consistency with and because of (i). Some affirm that there is no other logic than that which has to do with making thought self- consistent. The Laws of Thought {q. v.), Identity, Contradiction, and Excluded Middle, are laws of consistency. The wider view of consistency requires the agreement of thought with fact. In the example above, (2) is consistent with (i), and is therefore logically valid. But does it also agree with fact ? If not, it must be rejected as invalid. It is to be noted that the conditions for determining the truth of self-consistency are different from those which determine the consistency of thought with fact. Since the time of Kant, it has been usual to call that treatment of logic which deals with the internal, intrinsic or self-consistency of thought by the name of pure or formal logic as opposed to applied or material logic which deals with the ex- ternal, extrinsic consistency of thought, /. f. of the agreement of thought with its object as actually existing either as something material or mental, real or imaginary. Formal logic takes no account whatever of the subject matter of thought. It deals with thought without any extrinsic reference, /. e. without refer- ence to fact or reality of any kind. Hence we may DEFINITION AND SCOPE OF LOGIC ii represent thoughts by bare and empty symbols. Thus in the empty schema — All M is P All 5 is M All 6" is P S, M, and P may stand for anything. The reasoning proceeds and the conclusion follows irrespective of the matter denoted by the terms involved or our knowledge of their meaning ; the intrinsic consistency of the thought remains un- altered however we interpret the terms. The distinction between formal and material logic does not correspond with the distinction between Deduction and Induction. Some writers wrongly make this distinction, e.g. Bain and Fowler. There is a Logic of Formal Induction as much as a Logic of Formal Deduction, just as there is also a Logic of Material Deduction. The laws of thought have been called necessary. Their " necessity " consists in the impossibility of ev^ading them without inconsistency. In the defin- ition of logic therefore as "the science of the necessary laws of thought," necessary means valid in the sense of being self- consistent. As with the definition of logic the scope and purpose of the science is variously stated accord- ing to the aspect in which it is regarded. If a man holds that general knowledge or thought pro- ceeds only by way of language, he may treat of 12 A DIGEST OF LOGIC it by its expression and he is called a nominalist. If he holds that you may think without language, he may treat of it by concepts, judgments, infer- ences, and he is called a conceptualist But by talking of names and concepts indifferently no inconsistency is involved, for nominalism need not be accepted so as to deny conceptualism, nor need conceptualism be accepted so as to affirm the possibility of thought without language. Again, thought is always of something, i. e. has an objective reference, though not necessarily of anything which actually exists. But even when thinking of something which ' has no objective existence it is thought of as an object, i.e. the thought is objectified. Thus we may proceed further and say that logic is concerned with things in so far as they are the objects of thought, and with language in so far as it is the embodiment of thought. This is the view of the Realist. Though as pure logicians we deal with the form or manner of thought as opposed to its matter, yet in a sense log^ic is an objective science : in the sense, that is, of dealing with a certain aspect of things, viz. their thinkableness. There are then three aspects in which logic may be viewed, viz. — I. Subjectively, II. Objectively, III. Verbally. As previously stated the definition of logic adopted by any one logician will be modified DEFINITION AND SCOPE OF LOGIC according to the point of view taken. The defini- tions following are framed in accordance with one or other of these aspects, and exhibit the difference which the point of view adopted necessitates. I. Subjective aspect. Logic is the science of the regulative principles of thought ; or the science of the axioms and laws to which thought must conform in order to be valid. This definition may be read as either that of formal or material logic according to the meaning of the word valid. If valid be read as self-consistent the definition is of formal logic. But if as con- sistent with reality it is the definition of material logic. II. Objective aspect. Logic is the science of the most universal relations and correlations of things and attributes, i. e. the science of the prin- ciples and laws to which we must conform in order that a relation established by comparison of things and attributes, or inferred from one or more given relations between them, may be true. This is a definition of material logic. III. Verbal aspect. Logic is conversant about language, and is the science of the use of names, propositions and arguments ; or, logic is the science of the import and relations of propositions. As already noted, this treatment of logic is some- times called Nominalism, as opposed to Concep- tualism. These names are ambiguous, for they usually apply to certain doctrines concerning the true nature of concepts, or general names. Nom- 14 A DIGEST OF LOCUC inalism however, involves no more than a clear recognition that, as a matter of fact, all thought- processes of any complexity are carried on by the aid of language. It is here used to denote that view of logic which seeks to remove from it the matter of thought, and also the mode of thought, and limits the science to a consideration only of the expression of thought. In this sense logic is also sometimes spoken of as symbolic. Ill its relation to other sciences logic has been called ^^ scientia scientiannn'' because in their method the sciences are based upon logical prin- ciples. This is its general r&lation. There are other special relations of logic to (i) Metaphysics. (2) Psychology. (3) Rhetoric, and (4) Grammar. In general the difference between logic and the other sciences may be stated as follows : the laws of thought arc laws of things as thinkable and are subjective in so far as they relate to thinking : but objective in so far as they relate to the objects thought about. In the other sciences we never get so far away from the objective basis. In logic the subjective aspect is always prominent and immediate. More particularly the relation of logic to these four sciences may be briefly stated as follows : (i) Metaphysics is the most general and specu- lative of the mental sciences, and its office is to CHAPTER III THREE PARTS OF LOGICAL DOCTRINE REFERENCES Jevons, Lessons^ ch. ii. Welton, Vol. i., Introd., ch. ii., pp. 19 seq. Logic is usually regarded as consisting of three parts, which according to the point of view are : — I. ia) Concepts, {b) Terms, or {c) Things or attributes. Y II. {a) Judgments, (b) Propositions, or {c) Rela- tion between , things and attributes, things and things, or attributes and attributes. III. {a) Inference, {b) Syllogism, or {c) Inference of relation between things and attributes, things and things, or attributes and attributes from one or more given relations. In this partition {a) will be the phraseology of formal logic, {b) that of symbolic logic, and [c] that of material logic. Method is sometimes added as a fourth part of logical doctrine. It refers to the disposition or 1 8 A DIGEST OF LOGIC arranorement of a series of reasonincf in discourse, and is therefore a part of rhetoric rather than of logic. These three parts of logical doctrine call for further discussion, and though the following analysis of conception is strictly speaking psychological, it finds a place here in deference to tradition which includes in the treatment of logic notice of the dispute anent the nature of the concept. The practical purpose served by introducing a notice of this dispute is that it enables us to understand more clearly than we could do otherwise what is the subject matter about which logic is con- versant. I. Three views as to the nature of the concept have been formulated. They are known as (i) Realism, (2) Conceptualism, and (3) Nominalism. ( 1 ) The Realists hold that for every concept or general name there is somewhere in existence an objective, real something to correspond with it. They deny that the concept is a psychical pro- duct which grows out of a perception of singular or particular objects. This view is obsolete and has now only a historic interest. (2) The Conceptualist asserts that the concept is an intelligible synthesis of attributes, without any existing objective entity, and that thought proceeds without the accompaniment of definite images by means of the concept alone. THREE PARTS OF LOGICAL DOCTRINE 19 (3) According to the Nominalist view a class is constituted only by its name : and the general name has nothing to correspond with it either objectively or subjectively. It is held that every time a general name is used, an image, or a rapid succession of images of various members of the class, is present to the mind, and as these images are individual they cannot be concepts, for as we have already seen the concept is knowledge of a general. The Conceptualists and Nominalists (both are sometimes called Nominalists) agree in declaring that the development of the concept is by elabora- tion from perceptions. The Conceptualist declares that in the concept there is something more or less definitely represented by the mind, that the concept is not an image of a thing, but is some kind of image. The Nominalist holds that the concept is nothing before the mind at all, but is a symbol, generally vocal, as a word or name : and that any image you can have is the image always of one thing, and as that is not a concept the name of the thing must be. Bain as a Nominalist says that the true psychological aspect of the concept is the representation of a number of individuals in rapid succession. If so the concept would be a mere collection. In conception we have, as a matter of fact, no definite or distinct image before the mind at all. These two positions are both true in part. The truth appears to lie in a combination of the two 20 A DIGEST OF LOGIC views. No general statement about the concept which shall be fully applicable to all cases can be made, for it includes a great variety of different kinds of intellectual product. This variety is shown by such a list of words as follows : — tiger, iron, man, fatJier, symbol, murder, nationality, substance. What the concept is as before the mind depends greatly on the number and kind of experiences brought together under it. If these experiences have been limited in number, or have been ex- tremely uniform, departing little from a certain sort of medium character, then some kind of repre- sentation is possible : yet not the representation of any one object, since then it would not be a concept, but a representation having something only of the definiteness of an image. If a variety of perceptions with few resemblances and predominant differences are brought together, it is impossible to have any sort of representative image, nevertheless there is the concept, for we can still conceive. E.g. Of the concept tiger a certain image comes before me representative of each tiger of the class of animals so named : it has a certain colour, size, stripes, yet none of these definitely represented — at any rate there is more than the mere name. No one tiger in particular is represented, nevertheless there is an image, not altogether indefinite and yet not definite. The Conceptualist rightly holds in opposition to the Nominalist that although vague there is represent- THREE PARTS OF LOGICAL DOCTRINE 21 ation, in other words that to some extent we do visualise. Of concepts such as nvn the case is different. There is no image as with f/^-er, man, etc. It is easy for the ConceptuaHst to instance such examples as tiger, etc., and apply them universally : it is also easy for the Nominalist to instance others such as iron and apply them in like manner. As a matter of psychical fact, the human mind, impressed by a variety of experiences, simultaneous or successive, and trying to reduce them to unity, almost inevitably resorts to muscular expression and notably to a movement of the larynx, which results in sound. Words are sounds available for language, and they start forth naturally from human beings merely on occasion of the reception of a multitude of similar impressions, and so use- ful are words found to be that even percepts come to possess names, and in the end we don't properly perceive unless the percept is named. As previously stated, for general knowledge naming is indis- pensable, and it is to naming as a means of know- ing generally that the mind naturally resorts. Now concepts or general notions are of such variety that a statement equally applicable to all is impossible. The statement of the Nominalist is that all conceiving consists in naming. To imagine or to perceive there is no necessity for speech, but in order to conceive there is such necessity, and it is with a view to conceiving that language arose. But it must be also admitted 22 A DIGEST OF LOCilC that the concept is a something subjective apart from something objective, and apart also from its symbol as expressed in speech. II. A judgment is the apprehension of relation between two concepts. In judging or forming a judgment two concepts are brought together for the purpose of comparison. It is thus the psychical correlative of the logical proposition. In other words a judgment is a mental act, its expression in language is a proposition. As to the nature of a judgment widely divergent views are held. Our estimate of the scope of logic will determine the view we adopt. There are two main points of dispute, viz. — {a) Concerning the matter of the judgment the question arises ; between what is it that a relation is apprehended ? {b) Concerning the form of the judgment the question arises; what is the nature of the relation between the two terms } The second point is discussed under the head of the Import of Propositions {q, v.). With regard to the matter of the judgment there are again the three conflicting theories, (i) Nomin- alism, (2) Conceptualism, and (3) Realism or Ma- terialism. It must be remembered, however, that these names most commonly refer to the doctrine of the concept just discussed. (i) Nominalism identifies the judgment with the proposition, and holds that we deal with names and names alone. The judgment is only a statement THREE PARTS OF LOGICAL DOCTRINE 2 about names affirming or denying one or the other. According to this view the whole scope of logic is bounded by names and their relations. (2) Conceptualism, as the name implies, regards the judgment as the comparison of concepts purely as concepts. From this standpoint logic has been defined as the science of the pure (or formal) laws of thought, or as the science of thought as thought. It is the logic of consistency which takes no account of language as the expression of thought and no account of matter as that about which the thought is conversant. The extremists of this school, as Mansel, hold that all a judgment can express is that one concept is contained in, or forms part of another concept, and that the judgment cannot do more than unfold and make explicit the content of a concept. (3) Materialism explains judgment as a relation between two concrete objects having nothing to do with the mental abstraction of their attributes. Propositions do not express relation between con- cepts, but between the things these concepts repre- sent. When we say, e.g. grass is green : this does not mean that our concept grass contains or agrees with our concept green, but that the thing grass possesses the attribute greenness. The scope of logic thus becomes the investigation of the condi- tions of real validity. Th^'s is Mill's standpoint. The extremists of this school are known as Transcendental Logicians. III. Inference or Reasoning is a comparison of 24 A DTGESI' DI' \f)(]](' judgments resulting in another judgment differing from the first. According to the point of view it has been variously defined, and as before there are the three doctrines. (i) NominaHsm regards inference as the act of thought by which we proceed from one or more propositions to a third proposition, the truth of which necessarily follows from those previously given. (2) Concept-ualism regaids inference as the pro- duct of comparing two of more judgments with a view to arriving at another which is contained in, or warranted by, the judgments already in the mind. (3) Materialism regards inference as the estab- lishment of a relation between two things or two attributes or between things and attributes by means of a third thing or attribute, or the infer- ence of a relation between things and attributes or things and things or attributes and attributes from one or more such relations given. ciiai^ti^:r IV tp:rms RKI'KRKNCKS Jevons, Lessons^ ch. iii. and v. Keynes, Part i., pp. 7—51. Most useful. Mill less useful here than in the later part of his bk. Welton, Vol. i., 15k. i., ch. i and 2. A Term is one or more words forming the subject or predicate of a proposition: derived from the Latin tenniiins meaning a boundary. It is the verbal equivalent, in a proposition, of an object or f^roup of objects : or of a concept. In a wider sense it is synonymous with name. It is well to avoid thinking of names as terms, a name is only a term when it forms one element of a proposition. There are two terms in a proposition between which the proposition asserts a relation to exist. Hobbes' definition of a name is usually quoted in this connexion and runs as follows : " A name is a word taken at pleasure to serve for a mark 26 A DIGEST OF LOGIC which may raise in our minds a thought Hke to some thought we had before, and which, being dis- posed in speech and pronounced to others, may be to them a sign of what thought the speaker had or had not before in his mind." It is not accurate to describe a term or name as a concept expressed in language, for names are primarily names of things, by which is meant objects of thought, and only secondarily names of ideas. Words are of two kinds : — I. A categorematic word is a word capable of being used by itself as a term : tantamount to " term." II. A syncategorematic word is not capable of being used by itself as a term : tantamount to " not-term." Jevons speaks loosely of syncategore- matic terms. Categorematic words are nouns or their equiva- lents. By a suppositio materialis any word may be used categorematically, ^.^. This "that" is a demonstrative pronoun. Names are common, applicable to more objects than one, or Individual, applicable to one object only. Common navies are General or Col- lective. Individual names are Singular or Proper. A general name is the name of a group of things or attributes, whether real or imaginary, and applies both severally and collectively; /.r. to all TERMS 27 and each. It is distributive : oriines as opposed to cuncti. A general name is applicable to a number of things in virtue of their being similar, or having something in common. This means in effect that it is the name of a concept as well as of individual things. A collective name is the name of a group taken together, i. e. collectively only. It refers to all {cuncti) not each. A collective name may be singular or general. There is no antithesis between general and collective as is sometimes implied. The classes overlap. The important logical antithesis is between the collective and distributive use of names. E.g. — Collective: All the angles of a triangle are eqjial to tivo rig] it angles. Distributive: All the angles of a triangle are less than tivo right angles. A singular name is capable of being applied only to one individual object. In dealing with singular names we are dealing with objects in the sense of percepts. A proper name is a singular name given to an indi- vidual merely as a mark to distinguish it from others. It is an arbitrary and unmeaning verbal sign, fohn is a proper name which can be correctly affirmed of more than one individual, but this does not make it general. The test of a proper name is insignificance, lack of meaning. Are substantial names singular or general ? Substantial is a \\-ord suggested by Jevons to 28 A DIGEST OF LOGIC describe the names of materials, as eartJi, oii, ivater^ flame. They are a pecuHar kind of collective name with the special characteristic of theoretically in- finite divisibility, and at the same time they possess perfect homogeneity or uniformity of structure. The test of generality is the mark of quantity, some, which can be prefixed in a meaning sense to all names that are general. Some cannot be attached to a really singular name. We can say, e.g. " some water is not good to drink : " the substantial name water therefore is general, not singular. Names are Concrete or Abstract. A concrete name denotes ^n object in virtue of special qualities which it possesses ; or a class of things in virtue of some quality, or set of qualities, which they have in common. Adjectives are therefore concrete, being epithets, descriptive of things. An abstract name " is the name of a quality, attribute, or circumstance of a thing." It only permits of one judgment, viz. that it is the pro- perty of its corresponding concrete. In the case of every concrete there is, or may be constructed, a corresponding abstract ; and also of the abstract there is, or may be constructed, a cor- responding concrete. Many names are abstract or concrete according to the precise signification attached to them. A general name, as such, is concrete : the name of the attribute connoted by the general name is abstract. The general name denotes TERMS 29 concrete things and connotes certain common attributes. The names concrete and abstract correspond in a certain way to the distinction between denotation and connotation {see next chapter). The question has been asked whether the dis- tinction between general and singular names can be applied to abstracts. In reply it must be re- membered that an abstract name is not merely the name of a quality, but of a quality considered entirely apart from the thing possessing it. When we begin to distinguish kinds and differences, and hence to use abstract names in the plural number, we render them practically concrete, and therefore so far general. Every abstract name that is the name of a single quality (e. g. squareness, different species oi squareness being unimaginable) is singular. Names are Positive, Negative, or Priva- tive. A positive name implies the existence or posses- sion of certain definite attributes. A negative name implies the absence of one or other of certain definite attributes. Theo- retically every positive name has a corresponding negative, and between them they exhaust the whole universe of thought. The true logical op- position is between affirmative (not positive) and negative. Terms having a thorough-going negative character are called Infinite, Indefinite, or Indeter- minate : e.g. such terms as not-white, understood as covering with zvhite the whole universe of discourse. 30 A DIGEST OF LOGIC A privative name implies the absence of qualities usually possessed. This distinction is logically of no importance. Names are contradictory or contrary. An affirmative and its corresponding negative are called contradictories. Terms thus related exhaust between them the entire area of thoug^ht : there is nothing that can be thought of to which one or other of them will not apply. Aristotle first thought clearly in this matter, and since his time dates this distinction of opposite notions and names. In propositions this opposition is still more clearly marked. Contraries are terms the farthest apart in the same area of thought : e. g. zvJiite, black. They admit of a positive expression. They are terms most opposed in the same class. With the contradictory you deny : with the contrary you not only deny, but posit something else. The contrary opposite is more than a bare negative. The contrary of any assertion is counter- assertion : the contradictory of an assertion is its negation. Names are Relative, Correlative, oy Absolute. Relative names are those which imply in their signification some object over and above the one named : this other object is called its Correlative. Absolute names arc names not-rclativc. Relative and Absolute in the Manuals are merely defined. Their opposition is not clearly brought TERMS 31 out. Relatives are only a class of oppositcs, and may be identified as contrary opposites : e. g. child is the contrary oi parent. Logically no name is so absolute as not to have a correlative, which, wanting any other, is its negative. Any name is relative in relation to its contradictory, and the relation of contradiction is the only one we can be sure about in the form of thought. The opposition of positive and negative lies at the very foundation of thought, and in talk- ing of relatives we go beyond the sphere of pure logic as such. So-called absolutes are names whose opposites are indeterminate : e. g. inan^ the indeterminate term is not-inan. 32 CHAPTER V CONNOTATION AND DENOTATION REFERENCES Jevons, Lessons, ch. v, Welton, Vol. i., Bk. i., t;h. ii., pp. 62 scq. Mill, Bk. i., ch. ii. Keynes, Part i., ch. ii. Ray, Part i., ch. ii. The meaning of a name in reference to the concrete is called its denotation or application. The meaning of a name in reference to the abstract is called its connotation or implication. If concepts rather than names be regarded as the logical unit instead of denotation, the word extension or extent is used : and instead of con- notation, the word intension, intent, content, or comprehension is used. The mnemonic Ex. AND De., In. and Con. will help to fix this in the mind. The connotation of a name comprises the attributes on account of which any individual is placed in the class called by the name ; that is, those attributes CONNOTATION AND DENOFATION S3 which are regarded as essential to the class, in the absence of any one of which we should refuse the name to any individual : or, in short, the qualities which give meaning to a name. It may be called the characteristic of a name. The denotation of a name is made up of all the individuals which the name connotes : that is, those objects, real or imaginary, to which the name is given. The denotation and connotation of a name are mutually related, and the general law of their relation is thus stated — C'^ ^-^ If connotation increases denotation decreases : if denotation increases connotation decreases. This variation is not in mathematical ratio, and the law therefore is not accurately stated when denotation and connotation are said to " vary in- versely," for there is no definite measure of increase or decrease in the variation. If a short statement be needed, the connexion may be described as one of opposite mutation. We must be careful to notice how connotation is assigned ' and determined. All the attributes implied by the name form its connotation. Con- notation consists in the implication : in other words, the connotation of a name embraces THOSE ATTRIBUTES, and those only, ON ACCOUNT OF WHICH THE NAME IS GIVEN, and wanting any of which the name would be denied. Other views have been held. It has been maintained that connotation embraces — 34 A DIGEST OF LOGIC (i) TJic viaxinimn of attributes common to members of a class ; if so, no one would know the meaning of a term, for no one can know every quality. (2) TJie ascertained attributes which members of a class possess in common ; if so, connotation would depend upon each thinker's personal know- ledge, and vary moreover as knowledge increased. (3) The miniimnn of common attributes sufficient to distinguish the class from other classes ; this is too narrow, and fails to give the import of a term. (4) The fundamental attributes common to a class ; in this case only a speciarlist could know the connotation of a term. Denotation, which is the meaning of a term in reference to the concrete, since it includes all the individuals to which the name is applicable in the same sense, is possessed by all names, whether they have connotation or not, though in the case of proper names, and of some abstract names, the denotation is reduced to the least possible limit, viz. unity. This twofold meaning of names is sometimes expressed somewhat differently. Names are classed as connotative and non-connotative. A connotative name is one which denotes a subject and implies an attribute or attributes. A non-connotative name is one which merel}^ denotes a subject or an attribute. It is also called absolute. This is the classification adopted b}- Mill, whose CONNOTATION AND DENOTATION 03 definitions have been given : it will be seen that a connotative name, thus defined, must possess both denotation and connotation. By the word subject he means anything that can possess an attribute. By attribute he means not only the outward marks by which it is known, but all its properties and relations whatsoever. These definitions are noteworthy on account of the discussion to which they have given rise, and which is briefly indicated as follows. General names are connotative, i. e, have meaning ; and they must have meaning, for the name is given to each of a multitude of particulars upon some general ground of likeness. It is the likeness that makes the name expressive. The general name, according to Mill, denotes a number of particulars, and connotes the resembling attributes in each of them. Whately in different language brings out the same point. He says, '' p-eneral names have an attributive character." Proper names, as such, are meaningless, and therefore non-connotative, not that they are given for nothing, every name is given for discrimination, but this is the only purpose of a proper name, and this purpose does not constitute meaning. The proper name is a sign arbitrarily put upon an object to mark it out from others. A connotative name is given for a definite reason that can be assigned, because of certain attributes possessed. Proper names may suggest certain qualities [e.g. Gladstone), but the name itself was not given 36 A DIGEST OF LOGIC because of those qualities, and suggestion is not significance. Proper names are not given because attributes are possessed ; if that were so, they would become general. A connotative name, by Mill's definition, is one that denotes a subject and connotes an attribute. Every name given to a class of things in virtue of some quality or qualities possessed by them in common is concrete, and the name of the quality abstract. Therefore all connotative names are con- crete. Abstracts and concretes go in pairs. What is connoted by the concrete is denoted by its cor- responding abstract, i.e. there is nothing left for the abstract to connote. Abstracts are therefore in Mill's phraseology non-connotative. 37 CHAPTER VI PROPOSITIONS REFERENCES Jevons, Lessons, ch. viii. Welton, Vol. i., Bk. ii., ch. i. Keynes, Part i., ch. i. Mill, Bk. i., ch. iv. A proposition is a combination of names. It cor- responds with the judgment in the conceptualist view of logic, which is a combination of concepts. The proposition may be defined as — A statement of relation between objective facts, which are apprehended in thought and expressed in language ; or the expression of an act of judg- ment ; or the assertion or denial of agreement between two terms. It consists of two terms connected by the present tense of the verb " to be " ; and takes the form of Subject + Copula -}- Predicate. Grammatically the proposition answers to a sen- tence indicative. All propositions are sentences, but not all sentences are propositions. 38 A DIGEST OF LOGIC The copula — is, is not — is simply a lingual con- trivance for linking the terms of a proposition together for the purpose of comparison, and does not necessarily imply existence. Hamilton and Fowler insist upon a imiform copula, is or is not, according as we affirm or deny. In the working of problems which involve propositions it is a great and important safeguard against error to re-express, if necessary, the propo- sition so that this uniform copula shall appear, for it helps to ensure the correct interpretation of the proposition in question. The traditional view of the proposition has four aspects known as Relation, Quality, Quantity and Modality. The current classification takes no account of Modality, which is therefore lacking in the scheme subjoined. I. Relation. Categorical. Contingent: — Conditional. If S is J/, t/ie?i S is P. Hypothetical, //"A is true, then B is true. Disjunctive. vS' is either III or P. II. Quality. Affirmative. Negative. HI. Quantity. Universal. Particular. In this scheme, and wherever else they may PROPOSITIONS 39 occur, the letters ^\ M, P^ etc., stand for terms, either subject or object as the case may be: the letters in faced type, A, B, etc., stand for statements, which are given either true or not true. The names conditional and hypothetical are used by the majority of writers on logic indifferently for the class which is above called contingent. Con- fusion has naturally resulted. To avert confusion the name contingent is suggested to include the two classes of conditional proposition, and as co-ordi- nate with the class disjunctive. Welton has sug- gested the name inferential^ but on etymological grounds the name contingent seems preferable. Categorical propositions are those which are not conditional. Their empty form is exhibited as under. The vowels A and I in the word affinno are used to denote affirmative propositions, and the vowels E and O in the word nego to denote the negatives ; A and E are used for the universals, and I and O for the particulars. AFFIRMATIVE NEGATIVE Universal Particular 1 A. all S is P. I. some S is P. E. no 5 is P. O, some S is not P. Categorical propositions are either analytic or synthetic. I. Analytic or verbal propositions express only the connotation, or part of the connotation of a term. 40 A DIGEST OF LOGIC Definitions are the best examples that can be given of analytic propositions. II. Synthetic or real propositions are those which express only, or in addition to part of the connotation, the properties or accidents of a term. E.g. tJie power to laugh is no part of the definition of man ; it is a property. The proposition man is a rational animal is analytic : man is an animal with the pozver to langh is synthetic. Analytic or verbal propositions have also been called explicative, identical or essential ; synthetic or real propositions have also been called ampliative, accidental or non-essential. There are otherclasses of propositions as follows — EXPONIBLE, those that are resolvable into more propositions than one : and these arc Copulativ^e, Remotive, or Exceptive, viz, — Copulative when two affirmative propositions are directly combined : the form is. All S is both M and P, i. e. All S is M and all S is P. Remotive when two negative propositions are directly combined : the form is, 5 is neither AT nor P, i. e. vS is not M and S is not P. Exceptive when the subject is limited by some qualifying word, e. g. exeept : the form is, vS' is M tinless it is P. Exclusive propositions limit the predicate to the subject by some qualif}'ing word such as only or alone : the form is, Only S is P. Indefinite or Indeterminate Propositions contain no explicit mark of quantity ; the only PROPOSITIONS 41 safe interpretation of them is to treat them as particulars. Infinite or Limitative propositions have a predicate of a thorough-going negative character : i. e. are of the form, .S" is not P. Tautologous propositions affirm the subject of itself. vS is S. Modal propositions are assertions cuiii inodo : adverbs confer modality. This classification of the various kinds of propo- sition is not very important, except perhaps as a guide to interpretation in cases of doubt. Doubt as a rule arises respecting quantity, and in this connexion it is well to notice certain quantitative words in current speech which lack definiteness of meaning. Before the propositions containing them can be accurately interpreted, the meaning of these words must be clearly defined. Such are the words following — Some means logically, some at least : not none : one at any rate, it may be more than one, or it may be all. In popular usage some means some at most : not all : more than one but less than all. Most means in popular usage, at least one more than half In logic it must be regarded as the equivalent of sonic, for formal logic pays no heed to degree in quantity. Few means popularly, most are not, or at any rate less than half are. In logic its equivalent is, some are not. All is used in two senses — (i) all and each : 42 A DIGEST OF LOGIC every: onuies : distributlvely : and (2) all together, not each : cuncti: collectively. Any is equivalent to all used in the distributive sense when it quantifies the subject of a categorical proposition. When the proposition is not categori- cal it is to be read as some : e. g. if any S is M, then S is P ; means, if some S is My etc. Contingent Propositions are statements with quali- fication. The contingent proposition therefore con- sists of two parts which are called respectively antecedent ox protasis ^ which is the statement of the condition or hypothesis, corresponding to the subject of the categorical : and consequent or apodosis, which is the statement of the result, corresponding to the predicate of the categorical. The names conditional diwd hypothetical of the two classes of contingents are used by various writers indiscriminately for the whole class. Care must be taken to keep the two forms distinct : the differ- ence between them is well marked though not always recognised. The general symbolic form for the contingent is, // ^" is X, P is V. This form is better reserved for conditionals alone. In this case the formula for expressing hypotheticals will be, If A is true, B is true. Here, as previously pointed out, A and B stand for statements, not terms. PROPOSITIONS 43 Conditional Propositions assert that if an object be found to have certain attributes it will also have, or not have, certain other attributes. The relation is between two combhiations of properties. Condition- als have both quality and quantity, and the four forms may be symbolically expressed thus — If S is M^ then S is P. A. Sometimes if S is J/, then S is P. I. If S is M, then S is not P. E. Sometimes if S is M, then S is not P. O. It will be seen that the quality is determined by the consequent. In a conditional proposition there often seem to be four terms : they can however always be reduced, with more or less ease, to three, so as to fit the general symbolic form, if S is AI, then S is P. Thus — If the standard of an examination \ is \ loiu, the percentage of passes \ is \ high. There are seem- ingly four terms. Instead of the word passes read failures^ and lozv instead of Jiigh. We thereby reduce the terms to three. Or we may read not low instead of the word high^ and, by a single alteration of phrasing, obtain the same result. The statement will thus run — If the standard of an examination \ is \ loiu, the percentage of passes \ is not I low. Another example — If the barometer falls, we shall have rain, may be re-expressed thus — If any atmospheric state causes a barometric fall, that state will bring rain. Conditionals may be reduced to categoric form. 44 A DIGEST OF LOGIC Some logicians assert that both classes of con- tingents are in reality identical with categoricals. With certain limitations this assertion is accurate : the limitations, as will be seen, apply to hypo- theticals. Taking the illustrations above, their categorical expression will be — Examinations in wJiich the standard is loiv \ are \ those in ivJiich the percentage of passes is high: Ail atmospheric states causing barometric fall \ are \ those ivhich bring rain. Hypothetical propositions assert relationship be- tween two statements, so that if one is true the truth of the other is determined. Thus, though the symbolic form may be the same as for con- ditionals, the distinction can be better marked by using letters for the statements in the antecedent and consequent respectively : hence the preferable form is — If A is true, then B is true. Hypotheticals have quality, but not quantity. The antecedent is not an event which may occur always or sometimes, but a proposition which is simply true or false. In the hypothetical there is a relation of two absolute and self-contained assertions, each of which can be used alone without change of meaning. It is this self-sufficiency of both antecedent and consequent that differentiates the hypothetical from the conditional. Thus in the proposition — If all candidates for examination luere luell prepared sojne zcould certainly be success- PROPOSITIONS 45 fiil^ the assertion is not about all and some candidates, but about their adequate preparation and their success. Hypotheticals can be reduced only to A and E categorical forms, for the reason that they consist only of singular terms and do not therefore admit of distinction in quantity. Some logicians would dispute the possibility of reducing the hypothetical to the categorical form on the ground that the dependence of one proposition upon another is not analogous to that existing between 5 and P of the categorical, and also on the ground that all hypo- theticals involve an element of doubt. This view however seems to be erroneous. Taking the illustration given above in reduced form it will stand — all cases of candidates being well prepared \ are \ cases in ivJiich some would certainly be snc- cessfid. Disjunctive propositions give the subject no definite predicate, but prescribe for it an alter- native between two different predicates, or it may be more than two. The general symbolic form is — 6^ is either M or P. These predicates may always be brought under a wider predicate, which shall include all the others ; this however is seldom done in practice. Thus — He is either a doctor^ a lawyer^ a clergyman^ or a teacher^ may be expressed — He is a member of a learned profession. 46 A DIGEST OF LOGIC Disjunctives have quantity but not quality, the quahty is ahvays affirmative. Universal — /;/ all cases S is P, or X is Y. Particular — In some cases S is P, or X is V. There is difference of opinion as to whether the disjunctive form necessitates the mutual exclusion of the alternative predicates. In many cases the alternatives are as a matter of fact exclusive ; exclusion however is not due to the disjunctive form, and in the logical treatment of these pro- positions it must not be assumed. The disjunctive is in fact a complex conditional, and the logical rule for its treatment is — Given a disjunctive with two alternatives, by taking away either of the alternatives you posit the other, but it cannot be said that by positing one you sublate the other. Disjunctives are reducible to conditionals of the form, if S is not M, it is P. They can therefore be reduced also to categoricals. E. g. All artificial tront flies are either zvinged or hackled. This yields in reduction the two conditionals as follows — (i) If any artiflcial tront fly is not zvinged it is hackled ; and (2) If any artiflcial tront fly is not hackled it is winged. These reduced to categorical form become, (i) All artiflcial tront flies not winged \ are \ hackled ; and (2) All artiflcial tront flies not Jiackled I are \ winged. According to a previous definition it is thus seen that disjunctives arc exponibles. One of the most important points in dealing PROPOSITIONS 47 with propositions is to grasp clearly what is meant by the distribution of terms. A term is said to be distributed when reference is made to each and every individual denoted by that term. Thus in the A proposition, all men \ are \ mortal^ the subject all men means each and every individual denoted by the term men, and according to the definition given it is distributed. The predicate mortal does not mean each and every being of which mortality can be asserted. There may be mortal beings that are not men, as indeed from material considerations we know there are. The predicate therefore is not distributed, reference not being made to every part of it. Similarly the distribution of the terms in each of the other categorical forms may be worked out. The distribution of the terms will be found to be as follows — A distributes subject not predicate ; E distributes both subject and predicate ; I distributes neither subject nor predicate ; O distributes predicate not subject. This distribution of terms may be fixed in the mind by remembering the mnemonic word AsEbInOp, which must be read v4, j-ubject; E, <5oth ; /, /neither ; 6^, /redicate. It will be noticed that universals distribute their subject, and nega- tives their predicate. The importance of thoroughly understanding the point rests on the fact that the validity of every argument depends upon the proper distribution of the terms occurring in it. 48 CHAPTER VII PREDICABLES AND PREDICAMENTS REFERENCES Jevons, Lessons^ ch. xii. Welton, Vol. i., Bk. i., ch. iii. and iv. Mill, Bk. i., ch. iii. and vii. Bain, Dcductio?i, pp. 73—77 ; 263 — 266. A predicate is something which is affirmed or denied of a subject ; A predicable is something which CAN BE so affirmed or denied. That is, predicables are possible predicates. The doctrine of the predicables is a consideration of the number of different kinds of statement which can be made about a subject. The heads of predicables are a classification of the various relations the subject and predicate of a proposition may sustain one to the other. At root the doctrine of the predicables is not logical, but metaphysical. The scheme is as follows ; — Heads of Predicables PREDICABLES AND PREDICAMENTS 49 Genus Species Differentia -n • fsjeneric Proprium< ^ i specific . ., (separable Accidens-{ ^ (niseparable Genus is a class made up of smaller classes. Species, with reference to genus, is the smaller class included ; with reference to an individual, it is the class including it. Differentia are the attributes, or attribute, by which one species is distinguished from all others contained in the same genus. Proprium is any quality common to the whole of the class, but not sufficient to distinguish that class from others. It is called generic when it belongs to the whole of the genus, and specific when belonging to the whole of the species. Jevons' nomenclature differs : property belonging to the whole species he zd^s peculiar, and he limits specific property to the infima (or lowest) species. Accidens is a quality which may or may not belong to an individual in relation to a species : or to a species in relation to a genus. It is called separable when it can be changed ; inseparable when, belonging to all the members of a class, it cannot be changed. Thus, e.g. taking triangle as species: genus, differentia, property, and accident will be respect- ively as follows : — Plane figiwe ; having three sides ; E 50 A DIGEST OF LOGIC having three internal angles equal to tzvo right angles ; having sides tJiree inches long. Genus and species are correlative terms ; the same term may be both a genus and a species, genus with regard to lower classes under it ; species with regard to a higher class above it. Sunimum genus is a term so general that it cannot be a species. The summum genus gives connotation at its lowest, denotation at its highest point. Infima species is a term so narrow that it cannot be a genus, and can only be divided into indi- viduals. It gives connotation. at its highest point, denotation at its lowest. The Aristotelian logicians held that there were ten summa genera which they called predicaments or categories. The connotation of a species is greater than that of the genus under which it is included. This excess of connotation is the difference of that species. Thus in connotation species = genus + difference. A proprium is an attribute which does not form part of the connotation of a term, but which does of necessity follow from it. Thus, whether an attribute is a difference or a proprium, depends upon the definition of the term. Accidens can only be determined by what it is not. It is a quality that does not of necessity belong to any class ; if however it docs, and if it belongs to every member of the class, it is called PREDICABLES AND PREDICAMENTS 51 inseparable ; if not common to every member it is known as separable. In this scheme of predicables no provision is made for singular terms, which by the older logicians were looked upon as outside the sphere of the science. When genus or difference is predicated, the pro- position is called analytic ; when proprium or accidens is predicated, the proposition is called synthetic. Equivalent names for analytic and synthetic propositions have been given on p. 40. Species is strictly speaking only predicable of an individual. It is thus seen that embedded in the doctrine of the predicables, we have the difference between formal and material logic. In the categorical proposition, where 5 and P are subject and pre- dicate respectively, S and P may be taken to represent distinguishable terms which are not how- ever necessarily distinct. But when we have terms which are distinct as well as distinguishable, we have to deal with material considerations, and though the proposition may still be written in the form S is P, we are no longer working with symbols but with the actual notions themselves. In the proposition man is a rational animal, the terms are distinguishable but not distinct. The same notion is marked by each of the terms. Rational animal is a synonym for man. Under the concept man you think rational and vice versa. In other words, we have nothing more than a concept 52 A DIGEST OF LOGIC under the guise of a judgment. But in the pro- position man is moi'tal^ the terms are distinct as well as distinguishable. Mortal \^ no part of the meaning of man. It is a material consideration, neverthe- less the conjunction of such terms may still be formulated as vS is P. This distinction is marked in the predicables as above ; it is essential or analytic as opposed to non-essential or synthetic predication. Formal doctrine takes no notice of this difference, but in material logic it is taken into account. We have to consider our predicate as sometimes obtained by analysis of the subject, and sometimes by synthesis. The analytic has a predicate obtained from the subject merely under the laws of thought ; in the proposition given dhowQ, rational ajiimalis logically implicated in maji. Hence these propositions are also called explicativ^e, the explication taking place under the laws of thought {q. v.). The predicate of a synthetic proposition can never be obtained merely from the laws of thought. Such pro- positions are therefore called ampliative, the am- plification taking place by reference to the matter concerning which the statement is made. Analytic propositions are also sometimes called identical, that is, there is an identity between subject and predicate. Identical propositions therefore may be defined as those in which the predicate gives the subject over again, but not as a distinct and separate thought. Definitions are instances in point. As a test we may substitutt.' PREDICABLES AND PREDICAMENTS 53 means for the formal copula is whenever we have an analytic proposition. In a synthetic proposition this substitution of means for is cannot be made, for is in this case has a totally different force. Classification depends entirely upon this scheme of predicables, consisting as it does of the formation of genera and species. The predicaments or categories of which mention has already been made, were intended by Aristotle as a classification of all possible predicates accord- ing to their own meaning and not in relation to the subject. These Aristotelian predicaments are now universally discredited, being usually regarded as a classification of all possible things with no reference to their use as predicates of a proposition. They are therefore of metaphysical rather than logical import. It is to be noted that no satisfactory scheme exists. Aristotle's scheme is as follows — ouaia substantia substance TTOcrhv TTOIOP Trpos Tl quantitas qualitas relatio quantity quality relation Ttoitiv actio action Trdaxitv TTOV passio ubi passivity where TTOTi quando Avhen KtiaOai t\nv situs habitus position condition Sir Wm. Hamilton has thus classified the above scheme — 54 A DIGEST OF LOGIC I. Substance (Quantity f Situs Actio I Passio Mill states and criticises this Aristotelian scheme, and gives the following classification of all nameable things as his own : — 1. Feelings or states of consciousness : 2. The minds which experience those feelings : 3. The bodies or external objects which excite certain of these feelings together with the po\v«r or property whereby they excite them : 4. The successions and co-existencies, the likenesses and unlikenesses, between feehngs or states of consciousness. There have been other schemes suggested by others, but the matter is not one of great logical importance, if indeed it has any claim to a place of treatment in logic at all. 55 CHAPTER VIII DEFINITION AND DIVISION REFERENCES Jevons, Lessons^ ch. xii. Welton, Vol. i. Bk. i., ch. v and vi. Mill, Bk. i., ch. viii. Bain, Inductioi-i^ pp. 153 — 170 and 195 — 198. Definition and division have to do with names, and though expressed in proposltional form they are not concerned with the proposition as such. Hence their proper place of treatment is under the heading of terms. Definition is the exposition of the connotation of a term expressed in the form of a proposition. Distinguish definition, dcsa^iption, and explanation, A name is defined : a tiling is described : ?i process is explained. The strictly logical form of definition is per g'enua et differentiam. To define a name does not involve statincr all 56 A DIGEST OF LOGIC that is known about the thing of which it is the name, for that would in most cases include attri- butes which are purely accidents. A definition is an analytic or verbal proposition. Rules of definition are not directions for defining, but criteria for testing definitions when made. Formal logic tests or proves, it does not discover or bestow knowledge. When a man has know- ledge and sets it out, logic tells him whether he has done so correctly. Formal definition is not always applicable, e.g. simple sensations cannot be defined. When we cannot define we can re-expres-s and give examples or fall back on description, or give an enumeration of constituent properties. E. g. miiid is that which feels, thinks, wills, and desires. This is definition by complete enumeration : it sets out the various functions of mind and is the only means of defini- tion in this particular case that we have. Definition is impossible when nothing else of the same class can be found : where the thing whose name is to be defined cannot be discovered as an object amongst similar objects or as an attribute amongst attributes. This is the case with the example mind. The rules of definition are usually thus stated : — I. A definition should not be redundant, i.e. contain either more or less than the connotation of the term defined. II. A definition should not be expressed in ob- scure, figurative, or ambiguous language. III. A definition should not be tautologous, i.e. DEFINITION AND DIVISION 57 should not contain the term defined, nor a synonym, nor its opposite. Violation of this rule is called circiilus in dejiniendo. IV. A definition should not be negative when it can be affirmative. Division is the exposition of the denotation of a term expressed in the form of a proposition. Logical division must be distinguished from physical partitioft, and metaphysical analysis. The test of a logical division is that the term divided and the definition of the term divided can be predicated of each dividing member. This is its distinction from hoih. paj^iition and analysis. Every division must be progressive. The old rule is Divisio non facial saltuni. This precaution is against proceeding from high generalisation to narrow particulars at a bound, or in logical terminology emuneration of species mnst be from proximate genera. The constituent species must together make up the genus divided : if any of them can be brought under a genus itself subal- tern to that which had to be divided, we know that a saltiis has been made and our division is at fault. The rules for division may be stated thus : — I. Division must be distinct, the constituents must exclude one another, otherwise the species overlap and produce confusion called cross-division. II. Division must be adequate, the constituent species must exhaust the genus, i. e. when added together they must make up the genus. 58 A DIGEST OF LOGIC III. Division must be founded upon one principle or basis, called \h(^ fundainentiiin divisionis. These rules may be summarised in the single statement that division must be exclusive and exhaustive. Cross division may be avoided by adopting the method known as dichotomy or exhaustive division. This is the only process strictly to be called logical division. Dichotomic division is division by affirmative and negative names under the laws of contradiction and excluded middle. E.g. Take any notion A. Divide by decrease of denotation and addition to connotation. \i B, C, etc. be the added connotation and b, c, etc. their contradictories, the scheme stands thus : — AB Ab ABC ABc AbC Abe AbCD AbCd This process may be carried out to any number of terms, but has the demerit of being cumbrous, and in many cases there is no need to resort to it. In branches of knowledge where our informa- tion is uncertain, then it becomes useful as a safe- guard against possible oversight in making our divisions. 59 CHAPTER IX IMPORT OF CATEGORICAL PROPOSITIONS QUANTIFICATION OF THE PREDICATE REFERENCES Jevons, Lessofzs, ch. xxii. Welton, Vol. i., Bk. ii., ch. ii. Mill, Bk. i., ch. v., and Exam, of Sh' Wm. Hainilfo?!^ ch. xviii. and xxii. Keynes, Part ii., ch. viii. In the discussion of the meaning involved in predication answers to the following questions are considered :— (i) What is related? or what is the meaning of 5 and P ? (2) What is the nature of the relation ? (3) Is existence implied? Here again in the question of import we are on extra-logical ground : as this subject has strictly speaking no place in formal logic. According to the traditional treatment of logic it is here in- cluded, but though full of interest it may be left for second reading. 6o A DIGEST OF LOGIC 1 . What is related ? Words, things, or ideas ? The proposition is a statement and therefore so far verbal : the statement is of a relation existing between objective facts, and therefore so far real : the relation is apprehended in thought and is therefore so far conceived. The point has already been discussed in determining the definition and scope of logic as a science. Two questions therefore only remain : — 2. What is the nature of the relation expressed in predication? In what aspect are the terms to be regarded ? Various answers have been given. ia) The Predicative Theory. S — P (which is the empty form for a categorical proposition), read predicatively, means that the attributes pos- sessed by P also belong or do not belong to the object or to the group of objects denoted by .S. That is, it reads 6" in denotation, and P in conno- tation. It is a relation equivalent to that which exists between subject and attribute. This is the common and natural reading : it is psychologically correct. {b) The Extensive Theory reads both terms in denotation, viz. that objects denoted by 6" are or are not among the objects denoted by P. It regards 5 as included in the class P. As a theory of predication this is psychologically' false. More- over on this view it is not P that is predicated, but inclusion in P. (c) The Attributive Theory reads both terms in connotation. This is Mill's position. (Bk. I. ch. v. CATEGORICAL PROPOSITIONS 6i § 4.) E. g. 7/iau IS mortal means whatever has the attributes of man has the attribute of mortality. This theory is psychologically false, and moreover on this view particular jDropositions are wanting in interpretation. {d) The Equational Theory regards 5 and P in a proposition as corresponding to the two sides of an equation, the copula being nothing more than the sign of equality between them. The act of judgment expressed in the proposition is thus held to be a mere assertion of identity. This view is developed by Jevons in his Prin- ciples of Science (p. 41). It was also in his later work adopted by Sir W. Hamilton as an outcome of the doctrine of the Quantification of the Predicate. 3. Does the categorical proposition imply the existence of the objects denoted by the terms? Logical existence may be in any sphere, fiction, mythology, imagination, fact. Logical terms re- present something thought of, that is, they imply the existence in thought of that of which they are the name. More than this cannot be asserted. The implication of existence to this extent also follows from the nature of the proposition, which is a statement of relation between concepts that exist at any rate in the mind. It is usually and properly considered however that if existence in re is intended it must be specially predicated. The real existence of the subject can never be implied in the mere form of the proposition. Quantification of the Predicate. To quantify the 62 A DIGEST OF LOGIC predicate is to place a sign of quantity before it as well as before the subject. This doctrine was in this century stated by Hamilton and George Bentham. There are earlier cases of its notice both by English and continental writers. They urge that — (i) There is no thinking in the definite form which is necessary without having a definite notion as to the quantity of the predicate, i. e. they assert that what is implicit in thought must be made explicit in language ; and further that (2) In the process of conversion this explication is practically assumed. With the quantified pre- dicate therefore conversion as a doctrine falls away. The proposition in effect becomes an equation. Hamilton proposed four new categorical forms in addition to those in common use. The symbols to mark them usually given are those suggested by Abp. Thomson and are shown on the left hand margin. Hamilton's notation is that on the right. U AH .S is all P afa A All 5 is some P afi E No 5 is any P ana 1] No 5 is some P ani T Some 5 is all P ifa 1 Some S is some /' ifi O Some 5 is not any P ina o) Some vS is not some P ini The letters /and n in Hamilton's notation indicate affirmation and denial respectively. QUANTIFICATION OF THE PREDICATE 62, The objections to the doctrine may be summarised as follows : — (i) Getting rid of conversion really means that we have done so by getting rid of the proposition. The old A, E, I, O no longer remain. The quantified forms can each be shown to be complex not simple statements. All S is all Pis exponible and is equivalent to All S is P -\- All P is S. It is a compendious statement of two propositions. It is clear that All S is all P is not so simple a thought as All S is P. We think All S is P with- out reference to some or all P, and so we see that All S is all P ceases to be the expression of a simple thought. To aver that All S is all P is a simple thought is to deny that All S is /* is a thought at all. Hamilton declares (as he must do to maintain his position) that implicitly we do think all or some P. He calls U a toto-total pro- position, and A a toto-partial proposition. (2) Another objection, advanced by De Morgan, is that the doctrine alters the logical sense of sojne, or uses it ambiguously. Some becomes some but not ally or sojne at most : at least it becomes so in the predicate. If the meaning be thus changed we may get rid of the " disgusting rules of con- version," but we also get rid of the square of op- position, for if some mean sojne at most^ contrariety and contradiction are swept away. (3) Further in All S is all P we get a use of all which is not intelligible unless we take it collectively. The doctrine has grown out of a 64 A DIGEST OF LOGIC misconception as to the quantity of propositions, which has been taken to be the quantity of the subject, but it is only a matter of convenience that the mark of quantity is attached to the subject. The predicate is that which is univers- ally or particularly affirmed or denied of the subject. 65 CHAPTER X DIAGRAMMATIC REPRESENTATION REFERENCES Jevons, Lessons^ ch. ix and xxii. Welton, Vol. i., Bk. ii., ch. iii. Keynes, Part ii., ch. vi. The value of any scheme for the diagrammatic representation of propositions depends upon the following requirements : — (i) The diagrams must be self-explanatory so soon as the principle on which they are constructed is understood. (2) Each diagram must be capable of one and only one interpretation. (3) Each proposition should be represented by one and only one diagram. Various methods have been suggested by differ- ent writers. Such methods are Euler's Circles, Lambert's Lines, Hamilton's Wedges, Venn's Diagrams, and, the most recent, Welton's Scheme. Euler's Circles. This is the method most com- monly given in the Manuals. Representing the F 66 A DIGEST OF LOGIC Individuals included in any class by a circle, there are between two classes five diagrams to indicate all the possible relations. These relations may be described as I. Coincidence : 11. Inclusion of wS by P: III. Intersection : IV. Inclusion of /^ by S: V. Exclusion. The circles then are combined thus : — IV. II. III. (3B V. The method adopted in most text-books (c.^-, Jevons' Lessons), of using only a single diagram for each propositional form, is misleading. The E pro- position, being the figure of exclusion, is the only form for which one and only one diagram will suf- fice. Although we have not a single diagram for each fundamental form of proposition, the circles DIAGRAMMATIC REPRESENTATION 67 are useful as indicating the real knowledge given by the propositions themselves. The circles treated as below, by shading, show in each of the forms that part of the predicate concerning which knowledge is given us. Venn's Diagrams. In this scheme the figure given does not represent a proposition. It is the framework into which the pro- positions are fitted. We are deal- ing with two terms, each of which has a contradictory. By combin- ing these terms and their contra- dictories we obtain four separate classes: viz. 68 A DIGEST OF LOCUC S that is P : 5 that is not-P: not-S that is P : and not-S that is not-P. Shortly they may be written S P, S P, S Py S P. The Hne over a letter is a common and convenient way of marking its contradictory. These four compartments are shown in the skeleton diagram. Every universal proposition denies the existence of one or more of these classes, and is indicated by a shading out of the compartment denied. Thus A and E are thus figured : — The weakness of this scheme is that it is not adapted to particular propositions. Dr. Venn proposes that a bar should be drawn across the compartment which the particular declares to be saved. The scheme has the advantage, however, of being good for propositions involving more terms than two, and it can also be used to repre- sent the categorical syllogism. Sir W. Hamilton uses heavy wedge-shaped lines which at best arc cumbrous and arc also somewhat confusing. Welton suggests a method which is a combin- DIAGRAMMATIC REPRESENTATION 69 ation of Lambert's lines and Venn's four com- partments. It has an advantage over Venn's circles in being applicable to particulars. Lambert's Scheme is with lines to jnark the ex- tent of the terms, and it represents the inclusion of one term in another by drawing the lines parallel to one another. With modification it can be made useful and graphic. Thus draw three columns, the first to contain S P, the second for 5 P, and the third for 6' P. Use lines to indicate the extent of 5 and P : make them unbroken for the amount definitely referred to, dotted for what is left un- certain in the statement. Let 5 be the upper line, and P the lower. Then we shall get the subjoined diagram : — s SP p It will be noted that lines wholly unbroken mark terms which are distributed. Yet another method may be employed, a com- bination of circles and lines, the lines unbroken and dotted to be interpreted as in the previous diagram. Here the predicate is figured by the 70 A DIGEST OF LOGIC circle, and the subject by the line, thus indicating the reading of them respectively in intension and extension. Distribution of P is marked by circles which do not contain an unbroken line : of .S by lines wholly unbroken. This scheme pictures one view of the import of the proposition. 71 CHAPTER XI IMMEDIATE INFERENCES REFERENCES Jevons, Lessons^ ch. ix. and x. Keynes, Part ii., ch. ii., iii., iv., v., and vii Welton, Vol. i., Bk. iii. Mill, Bk. ii., ch. i. Inference is the derivation of one truth from another, and involves a mental process. Inference in short is passage from thought to thought. Inference is immediate when the conclusion is derived from one premiss only : immediate infer- ences may be regarded as the application of the laws of thought to two given terms. There are two main classes of such inferences, viz. — I. The opposition of propositions, and II. Eductions. The reduction of contingents and disjunctives to categorical form might be added as a third class, for this reduction is really a form of immediate Inference. I. Opposition. Two propositions are said to be in opposition, or to be opposed, when they have the same subject and predicate but differ in quantity 72 A DIGEST OF LOGIC or quality or both. They are usually arranged in what is called the Square of Opposition as below : — Contraries. Co. sP" in c cr ft- I Subcontraries. -4-J CO o The inferences based on the square of opposition may be considered to depend exclusively on the three fundamental laws of thought {(/.v.). These inferences are summed up as follows : — Of Contradictories one must be true, one must be false. Of Contraries both cannot be true, both may be false. Of Subcontraries one may be false, both may be true. Of Subalterns the particular is true if the universal is true : the universal is doubtful when the particular is true. Aristotle arranged the square thus — IMMEDIATE INFERENCES 73 Seeing that A and E were more opposed than A and O, he put them further apart in the figure. This square, however, broke down with I and O. Diametric opposition is another name for con- tradiction ; it means assertion and its negation, counter-assertion, no medium admitted. It has the same meaning as when apphed to terms. If we cannot go beyond the simple denial of a proposition, then it has no contrary distinct from its contradictory. The opposition of singular propositions is called by Mansel Secondary contradiction (Mansel's Aldrich, p. 56). Singulars have no contraries distinct from their contradictories. E.g. Socrates is zuise, has the contradictory Socrates is not wise. There is no distinct contrary. By another method of treatment, however, the proposition may be read as a general proposition in the guise of a singular. In this case Socrates will stand for the acts or judgnients of Socrates, and this gives us the contra- dictory Some of the acts of Socrates are not zvise, and the contrary None of the acts of Socrates are tvise. Conditionals admit of distinction both in quantity and quality, and therefore the doctrine of opposi- tion is entirely applicable. Hypotheticals admit only distinction of quality, and therefore the only opposition is that of con- tradiction. Disjunctives do not admit difference of quality but only quantity, and moreover all disjunctives 74 A DIGEST OF LOGIC are affirmative. Contradiction, however, is possible as well as contrariety, but both contradictory and contrary are categorical. E. g. Every S is M or P gives the contradictory Some S is jieitJier M nor P, and the contrary No S is either M or P. II. Eductions. Immediate inferences by which from a given proposition (posited true) we deduce others that differ from it in 5 or P or both, and whose truth is assured by the truth of the original, are called eductions. They are classified as follows : — 1. Conversion.- 2. Obversion. 3. Contraposition. 4. Inversion. 5. Added Determinants. 6. Complex Conception. 7. Converse Relation. 8. Reversion. It is well to note here that m working out exercises involving the statement of propositions they should always be brought first into the strict logical form with the uniform copula is or is not. It is most convenient to symbolise the terms by letters S, J\ etc., the contradictories of which may be marked by a line over them. Thus S, P will stand for not-S, not-P respectively. The symbols can be re-translated into the original terms, if desirable, in setting down the results. To remember this not only shortens the labour of working, but IMMEDIATE INFERENCES 75 it is also a distinct aid to accuracy. It is astonishing what difficulty students often find in converting a simple proposition like the following P struck Q. If the rule be remembered, the difficulty disappears. In strict logical form it may be written P \ is \ a person ivJio struck Q. The converse will therefore be Some person zvho struck Q \ is \ P. Conversion in a broad sense means change in the position of the terms of a proposition. Logic is concerned with conversion only as a process of inference: "no conversion is employed for any logical purpose unless it be illative" (Whately, Log. p. 74). The distinct mental act in conver- sion and other immediate inferences lies in the different readings given to 6^ and P. In any judgment the natural reading of the subject is extensive and of the predicate intensive. In con- verting a proposition the attributive force of the predicate is dropped, the proposition is taken in extension. The difficulty sometimes found in con- version lies probably in this passage from the predicative to the " class " reading. I. Ordinary Conversion is transposition of 5 and P. Conversion is simple when converse and con- vertend have the same form as in the case of E and I. Conversion is per accidens or by limitation when part of the information given in the convertend is lost, as in the case of A. O propositions do net admit of ordinary conversion. 76 A DIGEST OF LOGIC Simple conversion and conversion per accidens have also been called conversio pura and conversio iinpura (cf. Lotze, Log.^ § 79). That particular negatives do not admit of ordinary conversion follows from the rule that no term must be distributed in the converse which was not distributed in the convertend. No difficulty can be found in converting or per- forming other immediate inferences upon any given proposition when once brought into strict logical form, and its predicate as well as its subject read in extension. 2. Obversion is change of quality. It is a process of immediate inference, in which from one pro- position we infer another, having for its predicate the contradictory of the predicate of the original proposition. The name obversion was introduced by Bain. Other names for this process are — (i) Permutation, Foivler. (2) ^quipollence, Ueberiveg. (3) Infinitation, Boiuen. (4) Immediate Inference by Private Conception, Jevons. (5) Contra version, De Morgan. (6) Contraposition, Spalding. Bain, after dealing with formal obversion, follows with a statement of material ob\'crsion. This is extra-logical. From 5 a P, I may by formal ob- version infer vS" e P, but the material obverse, .S" is P, docs not follow, except as the result of actual IMMEDIATE INFERENCES 77 observation and independent investigation. The only information I can infer about 5 from 5 a P is, S i P or S P. The meaning of obversion is explained by Bain in his Deductio7tJ ^^. 109, no ). " In affirming one thing we must be prepared to deny the opposite." Thus, the road is level, it is not inclined, are not two facts, but the same fact viewed from opposite sides ; this process is called obversion. All four pro- positional forms admit of an obverse. 3. Contraposition is obversion followed by con- version. It is a process of immediate inference, in which from a given proposition we infer another proposition, having the contradictory of the original predicate for its subject, and the original subject for its predicate. Another name for this process is conversion by negation. Logicians differ as to whether the contrapositive of All S is P is No not-P is S, or All not-P is not-S, i. e. as to whether the quality should be preserved. The solution of the dispute is in the definition above, which rules that the original subject is to stand as the new predicate. Hence the contrapositive is No P is S. 4. Inversion yields the original subject nega- tived. It is inference of a proposition having the contradictory of the original subject for its subject, and the original predicate for its predicate. This is the meaning given by Keynes, and it fits in best with the general scheme of eductions. Jevons uses the word in a different sense. 78 A DIGEST OF LOCxIC Taking as the original proposition All S is P, Jevons classifies the related propositions thus — INFERABLE Converse Some 5 is P. Obverse No 5 is P. - Contrapositive No P_ is S, or All P is 5^. NON-INFERABLE Inverse All P is 5. Reciprocal All 5 is P. In this scheme the inverse as defined above finds no place, and indeed it is not recognised by Jevons at all. The inverse may be obtained from the original by converting and obverting, or by obverting and converting alternately. Each of the inferences above named takes two forms, one with a positive predicate, and the other with a negative predicate. The simplest forms are those with the positive predicate, and to these have been given the simple names converse, contra- positive, and inverse. The corresponding negative forms are called the obvcrted converse, obvcrted con- trapositive, and obvcrted inverse of the original proposition. The rule in all conversion is that no term shall be distributed in the converse that was not distributed in the convertend. IMMEDIATE INFERENCES 79 Given two terms and admitting their contra- dictories, the possible combinations are as follows — SP SP S P PS PS PS PS In the universals all these forms are obtainable. The table below shows the immediate inferences from each of the propositions A, E, I, O. A E I o ' Original Proposition SaP SeP SiP SoP % Obverse Sep SaP SoP SiP ^ Converse ... ^ Obverted Converge' Pis PoS Pes PaS PiS PoS — J^' Contrapositive Pes PiS — Pi s. ^7 Obverted Contrapositive PaS PoS — PoS ^ Inverse SoP SiP — Obverted Inverse SiP SoP — The treatment of contingents and disjunctives remains to be noticed. In a conditional pro- position the antecedent and consequent correspond respectively to the subject and predicate of the categorical. They may be written — A. If any 5 is Af then always that 5 is P. E. If any S is M then never that 5 is F. I. If any 5 is M then sometimes that 5 is P. O. If any 5 is Jll then sometimes not that .S is P. Or more briefly — 8o A DIGEST OF LOGIC A. All 5 M is 5 P, E. No i)^ M is 5 P. I. Some 5 M is 5 P. O. Some 5 M is not 5 P, Hypotheticals are to be treated similarly, except that here we have no distinction of quantity. The propositions are either A or E, viz. All cases A are^ or are not^ cases B. Disjunctives admit quantity and bar quality : they are always affirmative. Obversion and con- traposition are possible, but the disjunctive form disappears and becomes contingent. E. g. 5 is either M or P, this is equivalent 'lo If S is not M it is P. We have then as — Contrapositive If vS is not P it is not J/. Obverted contrapositive If 5 is not P it is M. Obverse If 5 is J/ it is not P. 5. By added determinants is meant addition of qualification to both 5 and P, in order that the meaning of the term may be more exactly de- termined. In making this inference both 5 and P must be limited in the same way. The limitation is called determination, and the limiting word the deternii)iant. Inference by added determinants is not a typical case of immediate inference. The process is valid enough if both 5 and P are determined alike ; thus although from A cottage is a building we cannot infer that A huge cottage is a huge building, yoX it IMMEDIATE INFERENCES 8i is true that A cottage, Jmge as it is as a cottage is a building huge as it is as a cottage. A similar re- mark applies to complex conception, the process is valid if 5 and P are alike implicated. The reason for care in adding determinants is that meaning is apt to vary with context, and therefore render this sort of inference liable to fallacy. E. g. All negroes are ineriy therefore An honest negro is an honest man. This is true, for in each case the determinant agrees. It is, however, not true that because A bass singer is a man, that therefore A bad bass singer is a bad tnan. 6. Complex Conception consists in the addition of a name to both 5 and P. The difference in this eduction and added determinants is that in this case 6^ and P become the determinants of a new name added. 6* and P qualify instead of being qualified. E. g. Honesty is the best policy, therefore Acts of honesty are acts of the best policy. There is the same liability to fallacy as before. It does not follow, e.g., that because All horses are animals, therefore A majority of horses is a majority of animals. y. Converse Relation is an inference made when in a proposition stating a relation of two things, the relation being expressed by a relative word, the same relation is expressed by transferring the names of the related objects and replacing the relative word by its correlative. Using symbols this eduction may be written (Q and Q}- being a pair of correlatives) 5 is Q of P, therefore P is 0} of S. 82 A DIGEST OF LOGIC E.g. The Prince of Wales is tJie son of Queen Victoria, therefore Queen Victoria is the mother of the Prince of Wales. Or DnrJiani is north of London, therefore London is sotttJi of DurJiani. This educ- tion is based on purely material considerations. 8. Reversion consists in passage from the ex- tensive to the intensive reading of a proposition, in other words both the terms being read in denotation the inference lies in changing the proposition so as to exhibit the mutual relation of the terms in con- notation. Reversion is most readily performed upon the universal affirmative, for in this form of proposition subject and predicate most clearly stand to one another in the relation of species and genus. For this reason the other three forms have scarcely received due consideration. The inference can best be illustrated and explained by examples. Thus All metals \ ai^e \ elements when read in ex- tension means TJie species metal is included in the genus element. The problem is to frame a proposi- tion which shall express the relation of the terms in respect of their connotation. Now the law of connexion between denotation and connotation is one of opposite mutation, hence it follows that the species having the smaller deno- tation possesses the larger connotation, or in other words the connotation of the species includes that of the genus. The required proposition therefore is, All tJie attributes wJiicJi are characteristic of elevient I are \ attributes which give meaning to the name metal: or all qualities of genus clement \ are \ quali- IMMEDIATE INFERENCES 83 ties of species metal. To express this eduction symbolically it will be convenient to use a new sign. The mathematical sign for the root of a quantity seems to be suitable : it denotes that the term to which it is attached is to be read inten- sively. Thus if the term A mean objects, real or imaginary, called A, J A will mean attributes giving meaning to the name A, and the reverse of S a P will appear as sj P ct sjS. The universal negative and the particular pro- positions are less readily dealt with. It must be remembered that in naming a class, whilst it is possible to refer to all or only some of the things included, the connotation of the class name is a fixed quantity, and the whole of it is always in- volved, that is, the connotation of a name is the same whether all of the objects denoted by it are referred to or only some of them. Put shortly we may say that reference in denotation may be either entire or partial, in connotation it is always entire. Hence it seems that there can be no particular reversions. This is not the view taken by Jevons (^Studies, p. 128), who regards the connotation as including all the qualities belonging to the individuals of a class, and seeing that all the qualities are not always involved in predication a particular of the regular form may be obtained. Setting aside this view and reading connotation in the way previously defined (p. 32) the reversions for E, I, and O will be as follows : — 84 A DIGEST OF LOGIC E. No metals are compounds^ therefore The char- acteristic of compomids is not a quality of metals. Symbolically sjPe JS. I. Some elements are metals, therefore Sometimes the characteristic of metals is a quality of elements. Symbolically sjP i \fS. O. Some elements are not metals, therefore Some- times the characteristic of metals is not a quality of elements. Symbolically JP o JS. The matter of predication being concomitance of quality with quality the sign of quantity in the particulars will be sometimes. It may be urged that in reversion we drift away from the sphere of formal logic, nevertheless it is in ordinary speech a very common form of inference and deserves fuller attention than it has yet received in the Manuals, where usually it escapes attention altogether. B5 CHAPTER XII THE LAWS OF THOUGHT REFERENCES Jevons, Lesso7is^ ch. xii. Welton, Vol. i., Introd., ch. iv. Bain, Deduction^ pp. 14 — 21. Ray, Introd., ch. ii. About these laws there has been endless discus- sion and the various points that have been raised are difficult to summarise. Full treatment is outside the plan of these notes, reference therefore must be made to the Manuals in which they are adequately- stated and expounded. The laws of thought are usually given as three, viz. The law of I. Identity all A is A : II. Contradiction no A is not-^ : III. Excluded middle all A is either A or not-^. Leibnitz supplemented these three with a fourth which he called the Law of Sufficient Reason. The laws of thought have also been called Regu- 86 A DIGEST OF LOGIC lative Principles of Thought : Axioms of Consist- ency : and Criteria of Truth or Validity. They are a priori mental laws in agreement with which all valid thought must be conducted, hence they are laws in the scientific sense of being uni- formities ; they are also laws in the secondary sense of being regulative when applied to govern and test arguments. I. The principle of identity is most simply stated as A is A. Other statements are, Whatever is, is : or Everything is what it is. It demands during any argument that each term shall be used in one unvarying sense, that what is posited true in one context shall be held true in another. Such propositions as A is A command instant assent, but convey no information : the law must therefore be interpreted to cover such propositions as A is B. Such forms are statements, not of the same fact in the same language as A is A is, but of the same fact in different language, and it is in this that the iden- tity consists. The two names, though both appli- cable to the same thing or fact, differ in signification, and we have therefore an identity amid diversity of meaning, and the proposition in which they are conjoined is capable of giving information. II. The principle of contradiction states that tJie same thing cannot be both A and not- A : other- wise expressed, A is fiot not- A : or Nothing can both be and not be. By this law it is laid down that the same attribute cannot be affirmed and denied of the same subject at the same time. This, and the THE LAWS OF THOUGHT 87 preceding principle, are the basis of all immediate inference: e.g. in opposition, for judgments to be contradictory they must refer to the same subject at the same time, and, if they do, they cannot by this law both be true. Thought in the last resort must agree with reality, and put to the test of material consideration we cannot conceive a thing as at once possessing an attribute and not possessing it. In argument this principle demands that having made a statement we must abide by it, for our consistency will be at fault unless we are prepared to deny the contra- dictory of the statement originally made. III. The principle of excluded middle is enunci- ated A is either B or not-B. Otherwise stated, Either a given judgment must be true or its co7itradictory ^ there is no middle course. Bain calls this law " an incident of partial or incomplete contrariety . . . too much honoured by the dignity of a primary law of thought." The principle has been questioned by other writers who have confused contradiction and contrariety. Contraries mark the utmost possible divergence. Contradictories are simple negations, they admit no intermediate course, they exclude all questions of degree. Care is necessary to avoid this confusion. Lotze objects to the for- mula A is either B or not-B on the ground that not- B embraces everything in the universe except B and is therefore meaningless : he would say Every A either is or is not B. Practically however negative terms are usually limited in application, SS A DIGEST OF LOGIC The axiom of excluded middle does not decide which of the two contradictory terms is true, but declares only the necessity of affirming one or other of them. By the principle of contradiction we are prohibited from thinking that two contradictory attributes can both be simultaneously present : by the principle of excluded middle we are prohibited from thinking that they can both be simultaneously absent. IV. The principle of sufficient reason, first distinctly formulated by Leibnitz, means that no fact is real, no proposition true, without a sufficient reason why it is so and not otherwise. The principle is not a fundamental law of thought. Valid arguments need not be based on the prin- ciples of identity, contradiction, and excluded middle entirely although they must be in conformity with them. Those that are founded on mathematical axioms are equally cogent, such as the argument a fortiori, If A is greater than B, and ^ is greater than 6", therefore A is greater than C: or If A is equal to B, and B is equal to C, therefore A is equal to C. Arguments however of this character are not in the form of reasoning recognised in formal logic. 89 CHAPTER XIII THE SYLLOGISM REFERENCES Jevons, Lessons^ ch. xv. Keynes, Part iii., ch. i. and ii. Most useful. Mill, Bk. ii., ch. iv. Welton, Vol. i., Bk. iv., ch. i. and ii. Bain, Dediictioji^ pp. 133, seq. Mediate inference is of two kinds, viz. — I. Deduction, or method of argument from general to particular, and II. Induction, or method of argument from particular to general. Syllogism is a common name for mediate infer- ence, in Latin called coinpiitatio, which means a reckoning or summing up. It is the summing up of two terms in a conclusion through the medium of a third term. It is an act of thought by which we proceed from two judgments to a third, the truth of which follows from those already given. It is an inference in which one proposition is derived from two others conjointly. These various definitions fairly describe the nature of the syllogism. 90 A DIGEST OF LOGIC In form the syllogism consists of three pro- positions, of which the first two are called pre- misses, and the last the conclusion. Syllogism is of two kinds — (i) Deductive and (2) Inductive. The deductive s3^11ogism has received the fuller treatment. Aristotle spent most of his labour upon it. The genus syllogism has indeed been taken for the species deductive syllogism. Dealing now with the deductive syllogism, S, M, P are the usual symbols for minor, middle, and major terms respectively. The Major Term is the predicate of the con- clusion : The Minor Term is the subject of the con- clusion : and The Middle Term is the medium of comparison of two propositions. The Major Premiss is the proposition containing the major term : The Minor Premiss is the proposition containing the minor term. We are concerned in syllogism not with the truth or falsity of any one of the individual propositions which compose it, but simply with the dependence of one of them upon the other two, so that if we grant the latter we necessarily accept the former. The derived proposition called the conclusion, there- fore propounds no truth which was not contained in the data, and the propositions must contain a THE SYLLOGISM 91 common element as the ground of comparison from which the conclusion is derived. The three propositions which compose a syllogism are called its proximate matter, and the terms united its remote matter. The conclusion put first as a thesis was called by the old logicians the question^ and the propositions establishing it, the reason. The common element is the middle term, the other two terms are called the extremes. We have already seen that the terms of a pro- position may be viewed in respect of quality, quantity, relation, and modality, giving rise to the classification set out on p. 38. The two premisses of a syllogism may be viewed In a similar way, giving rise to a corresponding classification of the syllogism. The moods of a syllogism spring from difference in the quantity and quality of the two premisses. In view of relation when the premisses are both of the same kind, both categoricals or both contingent, syllogism is said to be pure. If the premisses are of different relations the syllogism is said to be mixed. The following Is a tabular view — {a) Categorical. Syllogism (i) Pure - iU) Conditional. I {c) Hypothetical. (2) Mixed ( {a) Hypothetico - catc- } gorlcal. 1 {]?) Disjunctive. \ {c) Dilemma. Syllogistic reasoning rests upon the laws of 92 A DIGEST OF LOGIC thought : identity is at the root of every affirm- ative, contradiction is at the root of every negative categorical. Pure contingent syllogisms rest on these principles together with that of sufficient reason. Logicians have usually developed the laws of thought into Axioms of Syllogism. These axioms are therefore not ultimate, but secondary or derived: and so called axiomata media or middle axioms. Aristotelian logicians regarded the first figure as the type of categorical syllogism. The empty ^r/?^;//^? of this is — M P S M therefore 5 Other forms of syllogism were tested by reduction to this form. These logicians therefore gave one axiom, viz. the Dictum de omni et nidlo, as they called it, which applied to this one form, and was stated as their fundamental principle of syllogistic reasoning. The Dictum may be thus stated — " Whatever may be said affirmatively or negatively of a class may also be said affirmatively or negatively of any- thing within that class." Or more shortly the state- ment may stand, " Whatever may be distributively predicated of a whole may in like manner be pre- dicated of each of a whole." The Latin form usually given by the older logicians is — " Quicquid THE SYLLOGISM 93 de omni valet, valet enhn de quibiisdam et de singulis. Qiiicquid de nulla valet, nee de quibusdani valet, nee de singulis'' It is to be noted that the word class in the statement first given means the class name read distributively, the dictum is de omni, not DE CUNCTO. The dictum presupposes the class or extensive theory of judgments or propositions which is ap- plicable to all propositions having general terms, but those who regard the connotation of each term as being the important element formed an axiom corresponding to the dictum to express this conno- tative view, viz. ^^ Nota notae est not a rei ipsius. Re- pugnans notae, rep2ignat rei ipsi!' Mill adopts this statement in his Logic. It means wS Jias the mark M which is tJie mark of P, therefore 5 Jias P : ox S is ^a mark of M zvhich is a mark of P, therefore 6^ is a mark of P. Mill renders, " Whatever Jias any mark, has that zvhich it is the mark of. Or when the minor premiss as well as the major is universal we may state it thus : Whatever is a mark of any mark, is a mark of that which this last is a mark of." There are certain rules of mediate inference known as Canons of Syllogism, and according to tradition they are Six in number, as follows : — Relating to the nature of the syllogism. I. There must be three and only three terms. II. There must be three and only three pro- positions. Relating to quantity. 94 A DIGEST OF LOGIC III.vThe middle term must be distributed once at least. IV. No term not distributed in a premiss must be distributed in the conclusion. Relating to quality. V. One premiss must be affirmative, for from two negatives nothing can be inferred. VI. If one premiss be negative the conclusion must be negative, and vice versa, to prove a negative conclusion one premiss must be negative. It is usual to give in addition to the canons the fpllowing corollaries derived from them. / I. From two particulars nothing can be inferred. ./ 2, If one premiss be particular the conclusion must be particular. 3. From a particular major and a negative minor nothing can be inferred. It is to be noted that Canons I. and II. are not rules of inference but rules for deciding whether or not we have a syllogism. I. forbids ambiguity, for if any term is used ambiguously it becomes in effect two terms, and so there are four terms instead of three present. Hence there is no need to add, as is sometimes done in Rule III., " the middle term must not be used ambiguously." The fallacy arising from ambiguity of one of the terms is called quateniio tcniiinoniin or fallacy of four terms. There must be a common element as a connecting link between major and minor terms, and this must be identical in the two premisses. Breach of Rule III. is called fallacy of the un- THE SYLLOGISM 95 distributed middle. It is absolutely necessary for the middle term to be once distributed, for other- wise there is no bond of connexion between major and minor terms. The real mediation lies in that part of M which is common, and there can be no assurance that any part of M is common unless once at least the whole of J/ is referred to, and this is what distribution means. Breach of Rule IV. is called fallacy of illicit process, of the major or minor as the case may be : more shortly it is called illicit major or illicit minor according to the case in question. The Rule V. that two negatives yield no conclu- sion follows from the fact that in neither premiss is M in connexion with 5 and P. The accuracy of the rule has been questioned by Jevons {Princi- ples of Science, ch. iv., § lo), and on the same grounds by Bradley {Principles of Logic, p. 254). It is also noticed in the Port Royal Logic (p. 211). Jevons answers his own objection in his Lessons (P- 134). As a matter of fact the rule only applies so long as we keep strictly to syllogistic reasoning. Using the methods of immediate inference two negatives may yield a valid conclusion. By means of obver- sion and conversion the conclusion may be drawn. Keynes instances a syllogism in Barbara which may be written in the negative form. The following case seems more convincing. Given the premisses Mo P, SeM ; a conclusion is possible, viz. Si P. It is obtained thus — 96 A DIGEST OF LOCxIC Some M is not P yields obverse Some ]\I is not-/*. No 5 is J/ yields the ob-) . ., __. ^ „ ^ , ^All M IS not-5. verted conversej therefore Some not-5 is not-/*. As a concrete example take the following — (i) Some insects \ are not \ ivinged. (2) No vertebrates \ are \ insects. These premisses (i) obverted and (2) converted and then obverted, become (i) Some insects \ are \ wingless, (2) All insects \ are \ invertebrate. Some invei'teb rates \ are \ wingless. By a process similar to the above E E as well as O E can be shown to yield a valid syllogism : E O is intractable. E E is worked thus — Given two premisses, (i) M e P and (2) 5 e M. Take (2) and by inversion it becomes 5 i M. With this new minor construct the syllogism, and we have M_ e P S i M S P As a concrete example take the premisses, (i) No criminals are deserving of pity, and (2) No innoccjit persons are criminals. When wc have inverted the premiss (2) our syllogism will stand thus — THE SYLLOGISM 97 (i) No criminals are deserving of pity. (2) Some guilty persons are criminals. . ' . Some guilty persons are not deserving of pity. Using the methods of immediate inference upon the premisses of the invalid syllogistic moods there is no reason why the majority of them cannot be made to conform with moods that are valid. This, as shown above, can certainly be done with E E and OE. The rule that two negatives yield no conclusion holds good only so long as we deal with the premisses as negative in the syllogism, i. e. do not go outside the syllogism to alter the form of the premisses. The premisses treated as here suggested cease to be negative, but if indirect reduction is allowable in any case, as it is, it is certainly allowable here also. The canons of the syllogism may be compressed ' — "simplified" according to the Manuals — but it can hardly be called simplification, since they cease to be simple in the sense of being easily understood. The simplification is as follows — Canons L and IL are omitted as being not rules but description of syllogism, and thus we are left with four. These four are not independent, for breach of IV., V., or the first part of VI. involves indirectly a breach of III. The independent rules of the syllogism are thus reduced to two — 1. The middle term must be distributed once at least in the premisses. 2. To prove a negative conclusion one of the premisses must be negative. 98 A DIGEST OF LOGIC It may be noted that the only syllogism rejected by (2) and not also rejected directly or indirectly by (i) is A A O in Figure IV. So far as the first three figures are concerned, therefore, we are left with the single rule of the undistributed middle. This compression is not of any practical im- portance. The Connexion between the Dictum and the Syllo- gistic Canons is to be carefully noticed. The dictum applies to syllogisms in the first figure and was not intended to apply beyond that figure, but as all syllogisms may be reduced to the first figure the dictum applies indirectly to those also in Figures II., III., and IV. (i) The dictum provides for three and only three terms — I. Whatever is predicated = major term, II. of a whole = middle term, III. of each of a whole = minor term. (2) The dictum provides for only three pro- positions — I. Predication of something of a whole, II. statement that each is contained in the whole, III. making the original statement of the con- tained each. (3) The dictum provides not only that the middle term shall be distributed, but more definitely that it shall be distributed in the major premiss. Whatever is predicated of a whole means a distri- THE SYLLOGISM 99 buted whole. The middle term in Figure L is the subject of the major premiss, and as this is A or E it is as a matter of fact always distributed. (4) The dictum provides for one affirmative pre- miss, since the declaration that the each is contained in the whole can only be affirmation, not denial, i. e. the minor premiss must be affirmative. (5) The dictum provides for a negative conclusion from a negative premiss, and vice versa by the words " in like manner." (6) Illicit process is provided against indirectly. We are limited by what has preceded to the follow- ing cases, A A, A I, E A, E I, and these separately examined are seen to fall under the rule. [OO CHAPTER XIV FIGURE AND MOOD. REDUCTION ' REFERENCES Jevons, Lessons^ ch. xvi., xvii. Keynes, Part, iii., ch. iii., iv. Mill, Bk. ii., ch. ii. Welton, Vol. i., Bk. iv., ch. iii., iv. Figure of syllogism is syllogism with a definite position of M. Moods of figure of syllogism are the possible combinations of the premisses in that position oi M. There are four figures corresponding to the different ways in which S, M, and P may be arranged. These letters as before are used to denote the minor, middle, and major terms respect- ively. The point of note in the subjoined table is the position of M. FI GU R E. r. II ni rv. MAJOR PREM155. jniNOR PREM15S. ^ p 5 P s ^ C ONCLUSION. S P S P S P S P FIGURE AND MOOD: REDUCTION loi Account may be taken of the premisses without regard to the position of M, and this is called unfigured syllogism. Aristotle took account only of Figures I., II., and III. He regarded the first figure as the normal form and called it in consequence the perfect figure. The fourth figure was first explicitly recognised by Galen, and hence it has been called the Galenian figure. By some logicians the fourth figure is rejected. The first figure gives conclusions in all four pro- positional forms A, E, I, and 0. The second figure only proves negatives : the third only particulars. Hence the first figure is fairly called perfect. It proves moreover in the most clear and transparent manner. Special rules have been formulated for the figures as follows — I. (i) The minor premiss must be affirmative. (2) The major premiss must be universal. II. (i) One premiss must be negative. (2) The major premiss must be universal. III. (i) The minor premiss must be affirmative. (2) The conclusion must be particular. IV. (i) If the major is affirmative the minor is universal. (2) If either premiss is negative the major is universal. (3) If the minor is affirmative the conclusion is particular. There are certain characteristics peculiar to each figure that may be noted, viz. — 1 I02 A DIGEST OF LOGIC Fig. I. proves A, E, I, and O : it is the perfect figure. It is the only figure proving A. This alone makes it the most useful and important of all the syllogistic figures. All deductive science tends to work in A A A of this figure. Only in this figure have we the subject and pre- dicate of the conclusion occupying the same position as ^ and P in the premisses. This accounts in part for argument in Figure I. seeming more natural than in other figures. The dictum de oinni et iudlo as already pointed out applies directly to this figure only. Fig. II. proves E, O, — negatives only. As the middle term is predicate in both the pre- misses, unless one premiss were negative the middle term would be undistributed. This figure is chiefly used for purposes of dis- proof. It has also been called the exclusive figure because by means of it we may go on excluding various suppositions as to the nature of something under investigation whose real character we wish to ascertain. This process is called absciss io infiniti. (See Whately, Log., p. 60.) Fig. III. proves I, O — particulars only. If the con- clusion were universal it would involve illicit minor. This is the most natural figure when the pre- misses are singular propositions. It is also useful in taking exception to a universal proposition laid down by an opponent as establishing an instance in which such universal does not hold good. Fig. IV. proves only E, I, 0. It is seldom used FIGURE AND MOOD: REDUCTION 103 and by some rejected. It is not recognised by Aristotle. De Morgan calls it nothing but " the first with a converted conclusion." The natural order of thought in it is completely reversed. When a conclusion is weaker than the premisses warrant, i. e. when I or O is inferred where A or E are possible, the syllogism is said to be weakened and the mood is called subaltern. If a conclusion remains unaltered although we substitute for one of the premisses the subaltern of that premiss, the syllogism is said to be strengthened. Mood is the form of a syllogism as determined by the quantity and quality of the premisses, i. e. the arrangements of A, E, I, in sets of three, each triplet of propositions is called a mood, or form of the syllogism. The combinations of 3 out of 4 things are as follows : — (i) All three alike = 4 (2) Two alike, one different = 4x3x3 =36 (3) All three different = 4x3x2x1 =24 Total 64 Of these sixty-four possible arrangements only nineteen are valid. In Figure I. there are 4 II. >; 4 [II. » 6 IV. ,, 5 Total 19 104 A DIGEST OF LOGIC TABLE OF FIGURES AND VALID MOODS. B D c F L AAA V All EA£ EIO II. AOO EAE AEE EIO III. OAO All AAI lAI EIO EAO IV. AAI lAI AEE EIO EAO The valid syllogistic forms may be determined either directly or indirectly; directly by appeal to the fundamental laws of thought, indirectly by examina- tion of all possible combinations and the exclusion of those which break any of the canons of syllogism. The indirect method is the one usually resorted to. Reduction is the name given to the process of expressing in Fig. I. the syllogisms which appear in other figures, or, more generally stated, it is change of mood or figure. Unless specified, reduction is always taken to mean change of imperfect figure to the perfect. Questions on reduction depend upon immediate inference and the transposition or metathesis of the premisses. Reduction is of two kinds. I. Direct or Ostensive, which means proof of the same conclusion by an argument in Fig. I. II. Indirect or Reductio ad absurdum (also called Reductio ad or per vnpossibile, or Deductio ad iin- possibile or ad absurduni) consists in proof of the contradictory of the original conclusion to be false by syllogism in Fig. I. Unless specially asked for, FIGURE AND JSIOOD: REDUCTION 105 it is always understood that reduction is to be made ostensively. Note, eduction applies to propositions ; reduction to syllogism. The doctrine of reduction is only intelligible on the ground that figures differ in cogency and efficiency in a marked way. It is conceivable that a man may grant a conclusion in the first figure and not in the second or third. Reduction is proving in the first figure, which is unexceptionable, that which may be excepted against in the other figures. Both kinds of reduction apply equally to every mood, but it was formerly usual to limit reductio per impossibile to the cases of Baroco and Bocardo. These moods the older logicians failed to reduce ostensively because O is not amenable to conversion. We now treat O by obversion, and by this means both these moods can be ostensively dealt with. The value of reduction has been disputed. The moods are usually designated by the names which occur in the following hexameters. It is most important to know these mnemonic lines thoroughly for the accurate working of problems in reduction. Note that the names Baroco and Bocardo are sometimes spelt with a " k." This is a mistake : " c " is the original form. Barbara, Celarent, Darii, Ferioque prioris : Cesare, Camestres, Festino, Baroco, secundae : tertia, Darapti, Disamis, Datisi, Felapton, Bocardo, Ferison, habet : quarta insuper addit Bramantip, Camenes, Dimaris, Fesapo, Fresison. io6 A DIGEST OF LOGIC Each valid mood in every figure — except sub- altern moods — is here represented by a separate word, which in the imperfect moods contains directions for reduction. Vowels give the quantity and quality of the propositions : Initials connect the moods of each figure. The consonants are thus to be interpreted — V s, the proposition denoted by the preceding vowel is to be converted simply : . /, the proposition denoted by the preceding vowel is to be converted per accidens : 7;/, muta, i.e. metathesis or tTansposition of the premisses : c, indirect reduction, /. e. substitute for the pro- position whose vowel precedes its contradictory. The meaningless letters are /; (not initial), d (not initial), /, 71, r, and t. Note that s and / at the end of a word show that the conclusion of the new syllogism must be treated as the letters indicate. The syllogistic mnemonic appears in various forms. The lines given are from Aldrich and are those in general use. Modifications have been suggested in order to make all the letters significant. C. Read in Mind, No. xxvii., p. 440, seeks to obviate the disadvan- tages of — (i) The mood not being indicated by a letter : (2) meaningless letters : and (3) no indication of ostensive reduction of Baroco and Bocardo by obversion and contraposition. FIGURE AND MOOD: REDUCTION 107 He takes /, n, r, and t as signs of I., II., Ill , and IV. figures respectively, and makes the lines run thus : — Ballala, Cellalel, Dalii, Felioque prioris : Cesane, Camesnes, Fesinon, Banoco secundae : Tertia Darapri, Drisamis, Darisi, Ferapro Bocaro, Ferisor habet : quarta insuper addit Bamatip, Gametes, Dimatis, Fesapto, Fesistot. On the same principle Miss Christine Ladd in her Studies in Log., p. 40, suggests that difference of figure might be marked by r, /, /, and ;/ re- spectively. Dealing now with Baroco and Bocardo we note that— c indicates reductio per inipossibile. The position of the letter shows that the first step is the omission of the premiss preceding it, i. e. the other premiss and the contradictory of the conclusion are to be combined in a new syllogism, which gives a false conclusion and therefore indirectly establishes the truth of the original. The indirect reduction of Baroco is effected thus — Baroco P a M = All P 1 is \M S ni = Some 5 1 is not \M .' . S P = Some 5 | is not | P If S P \s false, its contradictory S a P is true. Substitute S a P for the minor premiss and we have the syllogism in Barbara thus — ■ io8 A DIGEST OF LOGIC p a M s a P . 5 a M but in the minor of the original syllogism 5 o M is posited as true, therefore our new conclusion S a M \?> false ; but being the conclusion from two premisses, one of which, viz. P a M, is posited true, the other premiss, viz. S a P, must be false, that is, its contradictory, viz. S o P/\s true, and this is the conclusion of the original syllogism which was to be proven. The indirect reduction of Bocardo is effected similarly — Bocardo M o P M a S S P If this conclusion be false, then its contradictory, viz. S a P, must be true. Substitute S a P for the major premiss M o P and we have a syllogism in Barbara thus — 5 a Ma P S M a P But this conclusion must be false since it con- tradicts the original major, M o P, which is admittedly true. But in the second syllogism, M a P \<, a conclusion drawn from two premisses, FIGURE AND MOOD: REDUCTION 109 of which the minor is posited true, therefore if our new conclusion, viz. M a P, is false, the major pre- miss of the second syllogism must also be false, that is, its contradictory, viz. S P, must be true, and this is the original conclusion which was to be proven. Both Baroco and Bocardo may be reduced osten- sively, and the following names have been suggested as substitutes to indicate the method — Baroco Facovo, Faksoko, Faksnoko, Facoco^ or Fakoro. Bocardo Docamovs, Doksamosk, Doksauirosk, Docajiioc, or Doksamo. Of these Faksoko and Doksamosk are the best. In the other substitutes the letters are open to misconstruction. k indicates obversion ; ks indicates obversion and then conversion, i. e. contraposition. In Facovoand Docamovs, <: means contraposition and V obversion. Baroco or Faksoko P a M S M .', S P Contraposition of the major and obversion of the minor premiss yield the syllogism — Ferio M e P S i M .'. S P no A DIGEST OF LOGIC Bocardo or Doksamosk M o P J/ a S .'. S P Contraposition of the major and metathesis of the premisses yield — Darii M a S P i M .- , P i S This conchision by conversion and obversion becomes J^^ o P or the conclusion of the original syllogism, which was to be proven. Indirect reduction is applied usually only to Baroco and Bocardo, but it is equally applicable to the moods which are dealt with as a rule ostensively. Indirect reduction is a way of proving in the first figure that a conclusion is true because its contra- dictory is false. The assumption upon which the process is based, is that if a premiss leads to a false conclusion it must itself be false. There is nothing special to Baroco and Bocardo in this, for the process will apply to all the moods. Euclid uses reductio ad absurduni on the same fundamental principle that aiiytJiing, being used cor- rectly, which leads to fallacy must itself be fallacious. Aristotle was the first to see that a false con- clusion could never be got correctly from true premisses, and also that a materially true conclu- sion can be obtained from premisses one or both of FIGURE AND MOOD: REDUCTION iii which may be false, i. e. from true we can only get true, but from false we may get true. E.g. — All stones are animals All cozvs are stones All cows are animals. A conclusion never proves its premisses, but the falsity of a conclusion overturns the premisses. There is an aspect of material investigation called plurality of causes ; this and the validity of scientific hypothesis repose on the principle that a materially true conclusion may be drawn from false premisses. 112 CHAPTER XV IRREGULAR AND COMPOUND SYLLOGISMS REFERENCES Jevons, Lessons^ ch. xviii., xix. Keynes, Part iii., ch. vi. Welton, Vol. I., Bk. iv., ch. v.^ The table subjoined gives at a glance the irregular syllogisms. i First Order — omission of major premiss. ENTHYMEME x Second Order — omission of minorpremiss. ( Third Order — omission of conclusion. T- 11 i. i. J ( Prosyllogism Fully stated | Episyllo|ism ( Curtailed \ f£f '"^^''^ S Aristoteli \ Sorites I Goclenia, The word enthymeme is derived from the Greek ivOviJLijiJLa, which means a suggestion or argument. It is defined by Aristotle as {n;A.A.oyto-juos e^ dKorcov ?y (njixeicov. The €Ik6s and o-T^/xeior themselves are propositions : qlkos states a general probability, and (Tiiixdov a fact which is known to be an indication more or less certain of some further statement, SYLLOGISMS— IRREGULAR, COMPOUND 113 whether of a single fact or a general belief In short, an enthymeme meant originally a syllogism with probable premisses. Aristotle's use of the word is entirely different to present usage, and has now only historical interest. The enthymeme is now usually defined as an abridged syllogism. The syllogism instead of being stated in full is truncated by the omission of one or other of the constituent propositions. Ac- cording to the proposition omitted, enthymemes are ranked in three orders, viz. — first order, major premiss omitted : second order, minor premiss omitted : third order, conclusion omitted. The following are examples — 1st. We are mortals^ and tJierefore liable to ei'ror. 2nd. Mortals are liable to error, and therefore zve are liable to error. 3rd. Mortals are liable to error, and we are mortals. In dealing with an enthymeme, care should be taken to express the omitted proposition. It is to be noted that according to the definition now current, the enthymeme differs in no way at all from the ordinary syllogism except in its expression. By a polysyllogism is meant a conjunction of syllogisms so stated that the conclusion of one becomes a premiss of another. The syllogism whose conclusion becomes the premiss of the syllogism that follows it is cdXXoidi^A prosyllogisni. 114 A DIGEST OF LOGIC The syllogism whose premiss is the conclusion of the syllogism preceding is called an episyllogism . When in these conjoined syllogisms the full statement is abridged by omission of any of the constituent propositions, it is called^an epicheirenia. In other words, the epicheirema is a polysyllogism in which the prosyllogisms are enthymemes. The following are examples. Polysyllogism fully stated. (i) All voyages of discovery have a scientific value. (2) All arctic expeditions are voyages of discovery. (3) .'. All arctic expeditions have a scientific value. (4) But Nansen's search for the North Pole zuas an arctic expedition. (5) .*. Nans ens search for the North Pole has a scientific value. In symbol the above argument may be written — Q a P R a Q R a P but S a R .' . S a P Note propositions (i), (2), and (3J form the prosyllogism : propositions (3), (4), and (5) form the episyllogism. Epicheirema or Polysyllogism curtailed. All arctic expeditions have a scientific value because they are voyages of discovery. Nansen's search for the North Pole therefore has a scientific value. SYLLOGISMS— IRREGULAR, COMPOUND 115 Sorites (from o-Mpos a heap) is a chain of syllogisms curtailed in statement and differing from the epicheirema in being curtailed in a definite and uniform manner. Or more shortly put, the defini- tion may be given as follows — A sorites is a chain of enthymemes all of the third order terminating in a fully expressed syllogism. There are tzvo kinds of Sorites — (i) In the ordinary or so-called Aristotelian Sorites the suppressed conclusion of each syllogism becomes the minor premiss of the next. It is more easily remembered by noting that the subject of the conclusion is the subject of the first proposition. Thus — 6" is R R \s Q Q is P .-. S \s P (2) In the Goclenian Sorites the suppressed con- clusion of each syllogism becomes the major premiss of the next. It may be remembered by noting that the predicate of the conclusion is the predicate of the first proposition. Thus — g is P R IS Q S is R . S Is P In the ordinary sorites there are two special rules, viz. — ii6 A DIGEST OF LOGIC (i) The last and only the last premiss can be negative. (2) The first and only the first premiss can be particular. In the Goclcnian sorites these rules must be reserved in statement. (i) The first and only the first premiss can be negative. (2) The last and only the last premiss can be particular. An O proposition is therefore by these rules ex- cluded as a premiss, although an O conclusion can be drawn if the final syllogism is in Ferio. There is no difficulty in deducing these special rules from the general canons of syllogism : (i) one negative premiss only, or else with a second we shall have a syllogism wdth two, and so the chain will be broken : (2) one particular premiss only, or else with a second w^e shall have a syllogism with two, w^iich will break the chain. The position of these premisses is determined by the rule relating to distribution. Pure contmgent syllogisms do not call for special treatment, for in every case the premisses can be expressed in categorical form and dealt with as regards mood, figure, and reduction in the usual way. They are syllogisms in which both the premisses are conditional or both hypothetical, giving respectively a conditional or hypothetical conclusion, and called respectively conditional or hypothetical syllogisms. SYLLOGISMS— IRREGULAR, COMPOUND 117 Thus the following argument is a hypothetical syllogism in Barbara — If M is P is If S is M is . • . If S is P is. No difficulty is experienced in transforming the premisses into categoricals and obtaining a cate- gorical conclusion. Treated thus it becomes — Every coincidence of M is a coincidence of P Every coincidence of S is a coincidence of M . • . Every coincidence of S is a coincidence of P. The name hypothetical syllogism, however, is commonly restricted, as by Jevons, to a mixed syllogism in which one of the premisses only is hypothetical, the other being categorical. A more accurate nomenclature would be to call these syllogisms Jiypothetico-categoricaL- In these syllogisms — the major premiss is hypothetical : the minor premiss is categorical : and the conclusion is categorical. The hypothetico- categorical syllogism has two moods — (I.) Modus ponens, and (II.) Modus tollens. I. The modus ponens or Constructive hypothetical syllogism is the mood of affirmation. If S is P is, but vS is, . • . P is. The antecedent of the hypothetical is affirmed, and thereby the consequent is established. ii8 A DIGEST OF LOGIC II. The modus tollens, or Destructive hypo- thetical syllogism is the mood of negation. If S is P 7Sy but P is not, .' . S is not. The consequent of the hypothetical is denied, and thereby the antecedent is found wanting. The rule for deahng with these syllogisms is commonly stated thus : " The antecedent must be affirmed, or the consequent denied." More shortly it may be put, posit antecedent, or snblate consequent. It has been urged by Bain, Mansel, and others that this form of syllogism is not mediate, but immediate reasoning, i. e. it is not syllogism at all. Immediate reasoning, however, always leaves off with a conclusion resembling in form the original proposition. Thus starting with the hypothetical, if the reasoning were immediate, the conclusion would be hypothetical : it is on the contrary, how- ever, categorical. We cannot from our hypothetical get any conclusion without either positing the ante- cedent or sublating the consequent, that is, given one proposition (viz. the hypothetical major), we pass from it throuc^h another (viz. the categorical minor) to a third (viz. the categorical conclusion), and this is as clearly mediate reasoning as in categorical syllogism. It is urged by Mansel that there is no middle term. In answer it may be said that the categori- cal minor is a proposition such as includes a middle term. Thus transform the categorical to the h)'po- thetic form as follows — SYLLOGISMS— IRREGULAR, COMPOUND 119 M is P S is M . • . ^ is /^ If M is P is but M is (in the form of S) .-. P is. It appears then that it is not the middle term that is wanting, but the minor term in not being separately expressed. Bain's objection is different and is based on the ambiguity of the word if (see Mind, Logic of If 1877, p. 264, and Bain, Ded., p. 116). He argues that the hypothetical, e. g. " If it is fine ivc ivi/l go azuay to-vwrrowl' is nothing more than a con- junction of two statements into one, viz., that zve will go away to-morrow and it is fine. He is read- ing into the word if the meaning since or because^ whereas it properly denotes bare hypothesis with the meaning suppose or granted that. In symbol Bain's hypothetical must be written. If S is {and it is) P is. In this case the conclusion is certainly deduced immediately. In answer it may be said that the same is true in the case of the categorical syllogism. If both the premisses are conjoined and read together the conclusion follows immedi- ately. They are however read separately and so from either of the premisses taken separately the conclusion is mediately drawn. In short whatever argument can be brought against the mediacy of I20 A DIGEST OF LOGIC the hypothetical syllogism can also be brought against the mediacy of the categorical. A disjunctive syllogism is one in which the major premiss is a disjunctive proposition. The minor premiss and the conclusion are categorical. Many logicians recognise two moods : I. Modus tollendo ponens^ II. Modus ponendo tollens. I. The Modus Tollendo Ponens is equivalent to the constructive JiypotJietical into which it may be resolved. One of the alternatives is denied and thereby the other is established as — 5 is either Q or P but S is not Q . • . 5 is P. Stated in hypothetical form the syllogism stands — If 5 is not 0, 5 is P but 5 is not Q .'. S is P. II. The Modus Ponendo Tollens is regarded by many logicians as a valid mood and equivalent to the destructive JLypotJietical. It consists in affirmation of one of the alternatives whereby the other is negatived and forms the conclusion. Thus ^' is cither Q or P but 5 is Q .-. S is not /'. The validity of this mood depends entirely upon the interpretation of the disjunctive that in it the alternatives are mutuall)' exclusive. If however SYLLOGISMS— IRREGULAR, COMPOUND 121 we take the opposite view, held by many, that the alternatives are not of necessity mutually exclusive, then the validity of this mood is vitiated. As will be seen it depends in any case upon how the dis- junctive premiss is read. The only case therefore in which we can be sure of the validity of this mood is that in which the terms of the alternatives are contradictories : 6" is either P or P. With regard to the dilemma logicians are not agreed either as to its form or nature : hence defi- nitions have varied considerably. It may perhaps be fairly called a contingent- disjunctive syllogism in which the major premiss is a contingent contain- ing a plurality, either of antecedents or con- sequents, and the minor premiss is a disjunctive. These premisses will yield either a categorical or disjunctive conclusion. As in the previous classes of mixed syllogism there are two moods, (I.) Modus Ponens, or Con- structive in which the conclusion is affirmative : called simple when categorical : complex when disjunctive. And (TI.) Modus tollens^ or Destructive in which the conclusion is negative, and (according to the view of the majority) always disjunctive : called therefore complex. The schema for the three forms may be written as follows : — I. Modus ponens. (i) Simple Constructive. If A then X, and if B then X: But either A or B : . • . X 122 A DIGEST OF LOGIC (2) Complex Constructive. If A then X, and if B then Y : But either A or B : .' . X or Y. II. Modus toUens. Complex Destructive. If A then X, and if B then Y: But neither X nor Y : .' . Neither A nor B. The dilemma is rather a device of rhetoric than a sound logical method. Its purpose is to force an opponent to a choice of alternatives both of which are damaging to his argument, hence the proverb, " to be on the horns of a dilemma." The rule for rebutting a dilemma is to change the position of the consequents and make them nega- tive. Thus e.g. against the complex constructive it may be retorted — If A tJien 710 t-Y, and if B then not-X : But either A or B : . ' . not- Y or not-X. The weakness of dilemmatic argument lies in the fact already noticed, that in a disjunctive pro- position the alternatives are not of necessity mutually exclusive. 123 CHAPTER XVI FALLACIES REFERENCES Jevons, Lesso7ts^ ch. xx., xxi. Mill, Bk. V. (all). Whately, Elejiients of Logic, 9th ed., Bk. iii., pp. loi seq. Welton, Vol. ii., Bk. viii. (all). De Morgan, Fo?inal Logic, ch. xiii. The word fallacy is used in three distinct senses, meaning — (i) error in an argument, (2) violation of any logical principle, and (3) any kind of mental confusion whatever. The meaning should be restricted to violation of any logical principle, and this will include the breach of the rules of inference. By Aristotle fallacies were classed according as the error lay — I. in the form — in dictione — or IL in the matter — extra dictione. 124 A DIGEST OF LOGIC Subsequent logicians have rejected or modified this classification. Whately divides fallacies into — I. Logical which are (a) purely logical and {d) semi-logical. II. Non-logical or material — corresponding with Aristotle's exlra dictione. I. {a) The purely logical fallacies relate to the syllogism and are the fallacies of undistributed middle and illicit process whether of major or minor. ih) The semi-logical correspond with Aristotle's in dictione. Mill greatly enlarged and modified the scheme to include all possible errors liable to invalidate inference. The whole question is discussed at great length in Book V. of his Logic, and to this reference must be made for full treatment of the subject. No thoroughly satisfactory classification of fallacies has yet been made, although frequently attempted, and De Morgan doubts whether such a classification is possible. The fallacies of deduction have already been noticed and described. Those of induction are beyond our present scope. Material fallacies are strictly speaking outside the sphere of logic alto- gether. The following summary of the more im- portant fallacies is given in accordance with the traditional treatment of the subject. FALLACIES 125 Semi-Log^ical Fallacies. I. Equivocation or Ambiguous Middle is use of the same word in a varying sense. E. g. The dog is an animal. Sir ins is the dog.. . ' . Sirius is an animal. A man zvho is deaf in one ear zvas rejected from a jury the other day because it was argned he couldn't Jiear both sides. 2. Amphibology is doubtful grammatical structure of a sentence. E. g. / Jiave come from a country where mosquitoes abound. Majiy of them lueigh a pound, and they settle on the trees and bark. The stock illustration is: Aio te, Aeacida, Romanos vincere posse. 3. Composition is the fallacy of using a middle term distributively in a major premiss and collec- tively in the minor. E. g. 3 and 2 are odd and even, 5 is 3 and 2, . • . 5 is odd and .even. 4. Division is the fallacy of using a middle term collectively in the major and distributively in the minor. E. g. The planets are seven, Venus and Mars arc planets^ . ' . Venus and Mars are seven. 5. Accent is a fallacy arising from false emphasis in speaking. E. g. {She.) " Do you think that I could get a donkey to take me up the mountain ? " (He^ *' Lean on ME." 6. Figure of speech is the assumption that words 126 A DIGEST OF LOGIC similar in form are similar in meaning. Essentially this fallacy is one of equivocation. The traditional example is : IV/iat a man walks on he tramples on. He zvalks on the zvhole day, .', He tramples on the zvhole day. The material fallacies. These, also called non-logical, arise from the subject matter not the form of the argument, and of these the following are usually enumerated. 1. A dicto simpliciter ad dictum secundum quid, or Fallacy of Accident. It is a false argument from general to particular. E. g. To inflict pain purposely is the mark of a brutal nature. The surgeon inflicts pain purposely. . ' . The surgeon is a man of brutal nature. 2. A dicto secundum quid ad dictum simpliciter or Converse Fallacy of Accident is a false argument from particular to general. E. g. Miracles ivere not stibjected to a thorougJi scientific examination at the time they ivere wrought, and. miracles have never been known to occur within modern times. . * . Miracles are altogetJier impossible. . 3. Ignoratio Elenchi or Fallacy of Irrelevant Con- clusion, literally ignorance of the refutation, the elencJius being the contradictory of the assertion of a supposed opponent. It is refutation of the wrong point. It includes all kinds of irrelevancy and assumes three main forms, viz. — {a) Mistake in the point at issue. E.g. ''Here, zuaitery take away these oysters. They arc badT FALLACIES i^l " Vesszr, but we've given you tzvo more than you asked for to make upT (b) The imputation of consequence or motive. E. g. The doctrine of the High Church party in the Church of England leads to Romanism .' . it must be false. {c) Introduction of rhetorical expedients such as the argumenta ad hominem, ad populum, etc. E, g. TJiis proposal is tJiorougJdy bad, as may readily be supposed from the cJiai'acter of the man zvho makes it. 4. Petitio Principii or Begging the Question or Circulus in Probando. A form of fallacy in which the conclusion is either itself one of the premisses or is required to establish one of the premisses. The fallacy occurs generally in protracted argu- ments. It is analogous to t\\Q circulus in definiendoy viz. that fault in definition which seeks to define a word by itself or its synonym. E. g. Consumption is tuberculosis : we are able to diagnose consumption in a patient luhenever lue observe the symptoms of tubercular disease. 5. Non sequitur or a conclusion not adequately supported by the premisses and which therefore " does not follow." This fallacy can always be reduced to some other form. E. g. {Professor of Chemistry.) " The substance you see in this vial is the most deadly of all poisons. A single drop placed on the tongue of a cat is enough to kill tJie strongest man!' This for instance might be classed as Ignoratio Elenchi. 128 A DIGEST OF LOGIC 6. Noil causa pro causa or Post hoc ergo propter hoc or False Cause. The attribution of any event to some antecedent with which it has no sort of connexion. E. g. The Norivegians once at tr United a disap- pearance of fish from their shores to the introduction into Norzvaj/ of vaccination. 7. Fallacia plurium interrogationum or Fallacy of Many Questions, i.e. a combination of two or more questions, each requiring a separate answer, into one, the single question asked not admitting of only one answer. The fallacy is refuted by answering separately each particular. P>. g. {Editor, to aspiring writer) " You shoidd write so that the most ignorant can understand zuhat you mean!' (^Aspirant.) " Well, wJiat part of my paragraph don't you understand ? " 129 CHAPTER XVII THE VALUE OF THE SYLLOGISM REFERENCES Welton, Vol. i., Bk. iv., cli. iii., p. 37: Ray, p. 250. Mill, Bk. ii., ch. iii. Bain, Deduction^ Bk. ii., ch. iii. The value of the syllogism as a method of infer- ence has been disputed, in the seventeenth century by Locke, Descartes and others, in more recent times notably by Mill followed by Bain and others. Mill's objection is twofold. He urges that (i) syl- logistic reasoning is not a process of inference, and (2) it involves the fallacy oi petitio principii. The objection may be met if we are careful to bear in mind that syllogistic reasoning does not pretend to be more than a process of formal logic. Now formal logic does not provide us with the mat- ter of argument ; this is otherwise gained, but being gained the office of formal logic is to ensure its being used with self-consistency. Propositions are dealt with simply as relations between terms. The I30 A DIGEST OF LOGIC question of their material truth lies outside the limit of formality. Syllogism deals with the application of two pro- positions that have a common or middle term, com- bining them under the laws of thought in a third proposition called the conclusion ; and once more, it is not the province of the syllogism to test this conclusion by reference to the matter about which it is concerned so long as the self-consistency of the syllogism itself is assured. If it is useful and important to combine our judgments so as to avoid fallacy, then in so doing syllogism has a very distinct value. Most of what we call knowledge is communicated by general statements. It is by the process of deduction that the general statement is applied to particular cases, or in other w^ords that inference is made from the more to the less general : and syllogism is the form of deduction. Mill's argument proceeds on the assumption that we argue from particulars to particulars and do not as a rule pass through a general proposition to reach the conclusion. He regards syllogism there- fore not as a necessary mode of reasoning but only as a permissible form into which an argument may be thrown. It serves as a test of validity in an argument, and so far it is a safe-guard against fallacy. But even if it be no more than this syllo.- gism is obviously valuable. The true ground that Locke, Descartes, and others had for their attack, was that for ages it had come THE VALUE OF THE SYLLOGISM 131 to be thought that by mere combinations of state- ments it was possible to determine matters of fact. It was in this way that the schoohnen dogmatised about facts from statements borrowed from others or hastily assumed. Consequently syllogism fell into disrepute because it had come to be falsely re- garded as determining truth in relation to fact. In discussing therefore the question of the value of syllogism the key to its defence lies in remembering its proper function. It does not pretend to be anything more than a mere process of formally explicating what is already implicitly granted. It is concerned only with self-consistency. The con- sistency of thought with fact is a consideration entirely different and lies outside its sphere. Granting then that syllogism is a mere process of formal reasoning, it remains to be seen whether it is of any account for purposes of real inference. This is the question proposed by Mill, who deals with it in Book II. of his Logic. Mill's position is that all inference is ultimately deductive. Hence syllogism is not a process of inference at all. It is rather a process of interpret- ation. He writes — " All inference is from particu- lars to particulars : general propositions are merely registers of such inferences already made, and short formulae for making more. The major premiss of a syllogism consequently is a formula of this de- scription, and the conclusion is not an inference drawn from the formula but an inference drawn according to the formula, the real, logical antecedent 132 A DIGEST OF LOGIC or premiss being the particular facts from which the proposition was collected by induction." Mill in his analysis of the syllogism takes the moods Barbara and Celarent as the universal types for affirmative and negative conclusions respectively. Thus in the syllogism e. g. All mammals have hmgs, WJiales are mammals ,' . Whales have lungs, he argues that between the premisses and the con- clusion there is nothing that can be called real inference. By mere consistency the conclusion cannot be avoided. Unless it be known that whales have limgs we have no business to start with All mammals have lungs ; there is no passage here from known to unknown, and in any case if the conclusion of a syllogism is regarded as a new truth derived by a process of inference, that inference does not lie between the conclusion and the premisses, but between the conclusion and certain other data at the back of the syllogism, which other data are the actual foundation of the argument. The conclusion may involve a process of real inference but not from the premisses, and if from other data through the premisses it is because in getting to the major premiss a material inference was performed of such scope as to include the conclusion. The syllogistic process therefore is never more than explication or interpretation. Taking this view it follows further that the fallacy o{ petztio priiicipii {^.'wwfoXvcd. Syllogism is the form of deduction: deduction consists in deriving a parti- cular from a general : but since we cannot infer from THE VALUE OF THE SYLLOGISM 133 a general any particular not included, therefore the conclusion of a syllogism simply re-asserts what was included in the major premiss. This re-asser- tion is according to Mill \h^ petitio principii. Mill's standpoint is open to criticism. Amongst other points these may be noted : — 1. The discussion has been complicated by a confusion in the use of the words reasoning and inference. Reasoning or inference in the widest sense may be defined as progression in thought. But a distinction lies between formal and real reasoning or inference. In formal reasoning the thought to which we pass is implicated in what we start with. In real inference what we arrive at, however it may be connected with the starting- point, is not impHcated therein. Real inference, says Mill, "is passage from the known to the unknown." In formal reasoning the passage is from the implicit to the explicit, from what is implied in the premiss to what is explicitly stated in the conclusion. But this passage of thought is just as much inference as passage from known to unknown. To describe syllogism therefore as a mere process of interpretation does not by any means remove it from the sphere of reasoning, for interpretation after all is a short expression for the process of explicating what has already been implicitly given, and as we have already seen, this is all that syl- logism pretends to do. 2. Mill, in his attack on the syllogism, leaves out 134 A DIGEST OF LOGIC of account the part played by the minor premiss. If the major premiss contained the conclusion in the sense that he assumes, then the conclusion could at once be gained per saltum, without a minor premiss intervening. The minor premiss, however, has a distinct and important part in the argument. It ensures the correct application of the major to the case under consideration, and, unless the minor affirms it to be included in the general statement of the major, there can be no passage of thought leading to the conclusion. In effect the minor is the essential factor in the process of interpretation. The conclusion is not, and cannot be, reached except through the two premisses taken jointly, and it is this that constitutes the reasoning. 3. If Mill's view be accepted, it must be on the assumption that the mind cannot accept the premisses, and not at once deduce the conclusion. With omniscience and a perfect intellect the as- sumption would doubtless hold good, but with limited powers of attention, and imperfection of knowledge, and in the face of the complexity of nature, it is quite possible that while admitting M to be under P, and wS to be under AT it is not instantly seen that .9 is consequently under P. As a matter of fact it constantly happens that starting from a given proposition, and using only the syllogistic method we reach a conclusion which to lis is an entirely new judgment, and therefore the argument is not at any rate to us a petitio principii. The truth is that the petitio principii (as THE VALUE OF THE SYLLOGISM o; seen and argued by Martlneau) is entirely relative, depending upon whether the data forming the major premiss are near or too remote to be readily recognised, or in other words depending upon the range of knowledge and observation of the reasoner. This point is obscured by the simplicity of the examples commonly given in the Manuals to illus- trate the syllogism. Compare Mill's own favourite example — All men are mortal, Socrates is a man . * . Socrates is mortal^ with a deductive argument expressed in the current language of literature, for instance, the following passage from Drummond's Natural Law in the Spiritual World (Ed. 1888, p. 249). " The part of the oj'ganism zvhich begins to get out of correspondence with the Organic Environ- ment is the only part which is in vital coj^respond- ence luith it. Though a fatal disadvantage to the natural man to be thrown out of correspondence with this Environment, it is of inestimable import- ance to the spiritual man. For so long as it is mai7itained the ivay is barred for a further Evohttion. And hence tJie co7tdition necessary for the further Evolution is that the spiritual be released from the natural!' The syllogistic forms in this argument are concealed by inversion, qualification, enlargement, and suppression of terms, so that the conclusion by no means appears merely on inspec- tion as it does in the unencumbered text-book ex- amples. It is, indeed, very rarely that we find in ordinary intercourse or composition that simplicity of form which the Manuals might lead us to expect, 136 A DIGEST OF LOGIC yet practically it is with these forms of everyday life that we must be practically prepared to deal, and it is in these forms that we best realise the actual passage from thought to thought involved in de- duction equally as in induction. 4. Yet another answer has been given to Mill's objection. It was formulated by Whately, who saw that an inductive argument itself involves syllogism, and therefore syllogism cannot be described as only a special mode of treating an induction. In other words deduction is a necessary factor in induction. The reply is a just one, for it is impossible to formulate general truths until we have deduced from instances already observed those qualities or attributes which warrant inclusion under the general notion in its course of development. 5. The truth is that in all reasoning neither the one process nor the other stands alone. Modern thought assigns greater prominence to the methods of induction since its results have reference to new matter, whilst deduction plays the humbler part of combining notions previously formed. In ordinary argument, however, even in a single proof, we pass continually from one process to the other. Both have their proper place, and the utmost that can be said is that they are interdependent. In- duction is a factor in all deduction, for our premisses are inductively derived. Deduction is a factor in all induction, for the principles induc- tively obtained can only deductively be applied to particular cases. CHAPTER XVIII SUMMARIES AND TABULAR STATEMENTS Logic is the science of the valid laws of thought. Science is systematised knowledge : coherent system depends upon logical method. Logic is therefore connected with all the sciences, but notably with — 1. Metaphysics, 2. Psychology, 3. Rhetoric, 4. Grammar. Logic deals with language as the instrument of thought. Language — 1. assists the process of thought, 2. records the products of thought, 3. is the natural vehicle for expressing thought. 138 A DIGEST OF LOGIC Language is modified by — 1. Generalisation, 2. Specialisation. Language is sometimes ambiguous, and according to the meaning suggested words are classified — Words - fUnivocal Equivocal or Ambiguous Analogous in sound only, in spelling only, both in sound and spelling. Thought is the subject-matter of Logic in rela- tion to — 1. thought, 2. things, or 3. language. Validity is — 1. Self-consistency, or 2. Consistency with objective reality ; and according to the validity dealt with, logic is — 1. Pure or Formal, or 2. Applied or Material. SUMMARIES, TABULAR STATEMENTS 139 There are three points of view relating to the nature of the concept, known as — 1. Conceptualism, 2. Materialism, 3. Nominalism. These points of view, though primarily relating to the nature of the concept, affect the entire view taken of the nature and scope of logic. A concept is the product of comparing two per- cepts in order to discover their points of agreement. Objectively it is an attribute, or a group of attributes, possessed in common by a number of individual objects. Subjectively it is an idea which corresponds with the attribute or group of attributes. In language it is a name, i. e. a word or combina- tion of words, by which it is denoted and expressed. Any sign whatever may, as a matter of fact, stand as its symbol: its most natural expression, however, is articulate speech. Three parts of Logic 'Names or Words as "counters of thought." Propositions or Names as terms in comparison. Inferences or Propositions as ground for argument. I40 A DIGEST OF LOGIC NAMF^ JCategorematic = terms. \Syncategorematic = not-tcrms. Terms or categorematic words are — Univocal one meaning : Equivocal double meaning : same meaning differently applied : class name ; all and each ; distribu- Analogous General or^ Common/ Collective Singular or ^ Individual.) Proper Concrete Abstract Positive Negative Privative Contradictory Contrary Relative Correlative Absolute all, not each ; cuncti as opposed to oinnes: a single object ; significant : a verbal mark'; insignificant : thing ; adjectives are concrete : attributive : existence or possession of a quality : denial of a quality : absence of a quality usually pos- sessed : area of thought divided : most opposed in the same class : suggestive of some other object : the other object suggested : non-relative. Heads of predicables Genus Species Differentia ,. . fq-eneric. rroi)rium -\^ .r ^ (specific. A . , fseparable. Accidens -[ . '■ , , [m separable. SUMMARIES, TABULAR STATEMENTS 141 Connotation comprises the qualities that give meaning to a name : Denotation, all the individuals possessing these qualities. Connotation and Denotation vary in OPPOSITE mutation. PROPOSITIO] ^S or Names as Terms in Comparison — f Analytic Synthetic rCopulative fA| Exponible] Remotive ]7 I. Categorical^ j > - [Exceptive Exclusive oj Indefinite Infinite Tautologous Modal ^ ^A 'Conditional - E I IT. Contingent - .0 Hyp othetical - IE fA III. Disjunctive-^ y Immediate Inferences- I. Opposition. II. Eduction. 142 A DIGEST OF LOGIC EDUCTIONS T r- • ftransposition fsimple. I. Conversion ^ ^ {^^^ ^ {per accidens. II. Obversion — change of quality. III. Contraposition — obversion + conversion. IV. Inversion — subject negatived. The rule — No term must be distributed in the con- verse which was not distributed in the convertend. The less important eductions are — 1. Added Determinants. 2. Complex Conception. 3. Converse Relation. 4. Reversion. THE LAWS OF THOUGHT arc— I. Identity— all A is A. II. Contradiction — no A is not-A. III. Excluded Middle—all ^ is y^ or not-A. INFERENCES or Propositions as Ground for Argument. I. lMMEDIATEJOPl^°f.'"°" Eduction TDeduction o\'(Pitrc 1 1. Mediate ^ Syllogism fnrgul.rr \ Traduction yMixed Induction SUMMARIES, TABULAR STATEMENTS 143 SYLLOGISM ^Categorical I. PURE^ Conditional [Hypothetical II. Irregu- lar 'Enthymeme ^Polysyllogism f Fully { P rosy llogis 111 I sidiiQdyEpisyllogisvi I Cur- (Epickeirenia Ki^iltdySo rites /"Contingent-categorical III. MlXED^' Disjunctive [Dilemma FALLACIES I. Logical (illicit major *^ l*^ Purely logical- illicit minor ^ \undistitrbed middle .Semi-logical II. Non-Logical or Material (equivocation I amphibology \ composition j division accent Kfigitre of speech ^Accident Converse accident Ignoratio Elenchi Petitio principii Non sequitur False cause ^ Many questions. APPENDIX I EXAMINATION QUESTIONS I. Logic, Thought, and Language 1. Distinguish between the psychological and the logical treatment of thought, with special reference to the question whether all our thinking is carried out by con- cepts as the logician understands them. 2. What is the central function of thought, and how are its activities regulated and classified ? 3. Why and in what manner is logic concerned with the use of language? Distinguish accurately between the logical proposition and the grammatical sentence, giving examples. 4. Define language ; and point out the main functions which it performs. How is it that spoken language has become the only universal one amongst mankind ? 5. '■^ No reason without language'' ^'' No language ivithoiit reason ^ Comment critically on these aphorisms. 6. Discuss the ways in which the process of thought may be affected by language, and bring out in your answer the requisites of a philosophical language. IL Definition and Scope of Logic 7. Compare any definitions of logic tliat may be known to you, and estimate their merits. 8. ^^ Logic is entirely conversant about language.''' EXAMINATION QUESTIONS 145 (Whately.) Is this a satisfactory account of the subject matter of logic ? 9. What is meant by saying that logic deals only with the form of thought ? Show how the use of symbols enables us to examine the form of our thought. 10. Bring out the exact scope of logic, defining its relation to {a) the special sciences ; {b) psychology ; {c) philosophy, or theory of knowledge. 11. How is logic related to grammar, psychology, and metaphysics ? 12. In what different ways has the relation of logic to psychology been conceived? Give your own view of the distinction and of the connexion between them. III. The Three Parts of Logical Doctrine 13. '' The doctrine of terj?is is really a composite and for the most part extra-logical body of doctrine T Ex- amine this statement, and consider the differences that ensue according as this body of doctrine is regarded as treating of (i) concepts, (2) terms, or (3) classes. 14. The origin of concepts. Give a brief account of the chief theories of modern philosophers on this question. 15. Explain the point at issue between Realists, Nominalists, and Conceptualists. IV. Terms 16. State the different ways in which terms may be classified, giving an illustration of each. Have all the distinctions equal logical importance ? 17. Give the principal division of names needed for logical purposes. Why does not logic recognise the distinction between substantives, adjectives, and verbs ? L 146 A DIGEST OF LOGIC 1 8. Discuss the meaning and the logical importance of the distinction between concrete and abstract terms. Explain fully how it happens that it is sometimes difficult to say to which of these classes a particular term should be referred. 19. Explain the distinctions that have been drawn by logicians between (a) general and collective names, (l?) abstract and concrete terms. How far do you think them correct and important? Do the distinctions appear in any form in the treatment of judgments? 20. Define and illustrate the distinctions {a) of con- tradictory, contrary, and indefinite terms ; (Z*) of contra- dictory, contrary, and indefinite propositions. Has some a contradictory? If so, what is the joint extent of some and not-some ? 21. Is there any distinction to be drawn between singular and proper names ? What views are or may be held as to their being mere unmeaning marks in logic ? 22. Describe the logical characters of the following terms — Equal, Equation, Equality, Equalness, Inequality, and Equalisation. V. Connotation and Denotation 23. State the various ways in which terms may be divided, dwelling more in detail on the distinction between denotation and connotation. Which of these divisions of terms do you regard as of fundamental sig- nificance in logical theory ? Give your reasons. 24. What are connotative names ? What are the principal difficulties by which we are beset in determining the connotation of any given name ? 25. Analyse the following terms in the counter quantities or wholes of extension and intension — Ala/i, govenimejit^ law, triangle, vegetable. EXAMINATION QUESTIONS 147 26. Argue at length the question whether {a) Proper names, {b) Abstract names have a connotation. 27. State, in carefully chosen language, the logical law of the relation between extension and intension of con- cepts, giving illustrative examples. How do you reconcile with it the fact {a) that there are as many mortal men as there are men, {b) that the notion trilateral triangle imports nothing more than triangle? 28. Define a term; and explain what is meant by the denotation and connotation of terms. Discuss the following — " T/iei'e is 7iothi?ig ifi the import of a proposition of which the terms a7'e abstract, but what there is in some proposition which can be framed of concrete terms. VI. Propositions 29. Exemplify conditional propositions. How are such propositions reduced and converted ? 30. Discuss the relation of the disjunctive proposition to {a) the hypothetical, {b) the categorical. 31. Distinguish between ampliative and explicative propositions and give several examples of each kind. 32. What is an essential proposition? and in what cases is it difficult to draw the line between essential and real propositions ? ZZ' (^) Unfold as completely as possible the implica- tions of the proposition, " None can be happy without virtue,^' naming in each case the process used. {b) Given the proposition, " Whatever is either B or C and at the same time either D or E, is A'' What can be asserted respecting not-A ? VII. Predicables and Predicaments 34. Give an account of the predicables. In what part of logic are they properly placed ? 148 A DIGEST OF LOGIC 35. Distinguish a genus and a type. 36. Give some account of the predicables. How may they be adjusted to modern thought ? 37. Mention the various heads of predicables, and explain their connexion with definition. Give in- stances of definitions, pointing out what are the genus and differentia in each case. In what cases may it be impossible to define a term ? 38. Distinguish between verbal and real predication, and show how the five predicables bring out the distinc- tion. 39. Explain what you understand by a category, and discuss some scheme of categories known to you. VIII. Definition and Division 40. What is definition and of how many kinds does it consist? How would you proceed in order to define such a term as virtue ? How far does definition in all cases imply a reference to the things denoted by the terms ? 41. State the currently accepted rules of logical defini- tion. Examine their worth and discuss the view that all definitions are of names only. 42. Compare the following notions with respect to their definability — Iro7i, Steel, Murder-, Red, Grey. How would you proceed to give a definition of {a) Iron, (/>) Alurder? 43. Discuss the requirements of definition as applied to scientific terms. How far do the rules of formal definition carry us in this case ? 44. Explain clearly with examples how definition and division are related to each other. 45. What is meant by saying — Divisio ?wn faciat saltuml How are you to know that a saltus has not been made? EXAMINx\TION QUESTIONS 149 Draw up a logical scheme of divisions so as to indicate the places of the following — AB, Abe, ahcD, aBC^ abCD ; a, b, r, d, representing privative terms. IX. Import of Categoricals — Quantification of THE Predicate 46. What is predication ? Does it ever involve exist- ence, or must existence be always specially predicated ? 47. Assign precisely the meaning of the assertion that it is false to say that sotfie English soldiers did fiof behave discreditably in South Africa. 48. How does the quality of a proposition affect its quantity ? Is the relation a necessary one ? 49. Explain and discuss the following : — {a) In a judgment the subject is naturally interpreted in denotation and the predicate in connotation. {b) Every proposition is an assertion that two names are or are not applicable to one and the same object. 50. On what grounds has the quantification of the pre- dicate been maintained? Estimate these grounds critically. 51. Set forth the doctrine of the quantified predicate, and estimate the claims made for it. How far do you find that it maintains or departs from the traditional meaning of some in logic ? 52. Is logic bound by the ordinary usages of language? Discuss the question in connexion with the following topics — {a) The quantification of the predicate, {b) the proper logical interpretation of the form Some S is P. 53. Bring out clearly the grounds of difference of view between Hamilton and Mill in regard to quantification of the predicate. X. Diagrammatic Representation 54. Give a concise account of any schemes of dia- ISO A DIGEST OF LOGIC grammatic representation of propositions and discuss their value. 55. What are the possible distinct forms of syllogism that can be illustrated by Eulerian diagrams ? Discuss the propriety of this mode of representing propositions and syllogisms. XL Immediate Inferences 56. Give the contradictory, the obverse, the converse, and the contrapositive of the following : — (n) Private vices are public benefits. (b) Not to kiioiu me argues thyself unknoicm. (c) Beauty aiid use are identical, {d) No mail is always cojisistent. 57. ^'' Previsio7i is a test of true theory .^'' '•''Prevision is the test of t^'ue tJieory.^' Describe the forms of proposition to which the above belong and give their converses, contradictories, and obverses. 58. Assuming that no organic beings are devoid of carbon, what can we thence infer respectively about beings which are not organic and things which are not devoid of carbon ? 59. Prove the rules of obversion, conversion, and con- traposition by reference to the laws of tliought ; or show what other proof you would give of them. Convert and contraposit the proposition — For evefj wrong there is a legal remedy. 60. State and illustrate what you understand by obversion. On what laws or axioms docs the validity of this process depend ? 61. What is meant by obversion, formal and material ? How is obversion related to conversion by negation or contraposition ? EXAMINATION QUESTIONS 151 Give the obverse and contrapositive of the following propositions : — {a) All animals feed, ip) No pla7tts feed, (c) Only a^iimals feed. 62. What do you consider to be the real distinction between a categorical and a hypothetical proposition ? Are the processes of immediate inference applicable to hypothetical propositions ? 63. From all Sis P\y['^dX can you infer concerning not-S and 7iot-P ? Show how you justify any inference you make. Illustrate by concrete examples what is called im- mediate inference by added determinants. If A = B and Z = M, A + Z = B + M. Is such a theorem logically valid either extensively or intensively ? 64. Can all kinds of propositions be exhibited in the intensive as well as the extensive form ? Give reasons in support of your answer. In the event of its being in the negative, draw up a Hst distinguishing between those kinds of propositions which can and those which cannot be so exhibited. XII. The Laws of Thought 65. Bring out the meaning and estimate the logical value of the three laws of thought. 66. Enunciate, in the form that seems to you most suitable from the point of view of logical theory, the primary laws or axioms of thought, and discuss their relation to the processes of reasoning. 67. State and explain the three formal laws of thought and discuss their connexion (a) with immediate and -{d) with mediate inference. In what sense are these laws called necessary ? How do you reconcile their necessity with the existence of fallacies ? 152 A DIGEST OF LOGIC 68. What is a law of thought ? State the three primary laws of thought. Have they a real importance in logic ? or are they " absurdly obvious " ? 69. Explain how the universal laws of thought give rise to dichotomous or bifid classification. 70. Explain the relation between the universal laws of thought, the canons of syllogism, the dictum de omni et nullo, and any other forms of the fundamental axioms of inference that occur to you. XIII. The Syllogism 71. Explain the syllogistic rule respecting two negative and two particular premisses, pointing out the grounds on which they rest. Do the following break either of these rules ? {a) This person is very learned and also very sociable^ consequently some very sociable persons are very learned. (b) No man is a proper object of contempt, at the same time no mail is perfectly admirable, cofisequently some bei?igs who are 7iot perfectly admirable are not proper objects of co7itempt. if) The majority of English people have but little literary taste, and the majority of English people read, fro?n which it follows that some who read have but little literary taste. 72. Give a clear and precise explanation of the rule concerning the middle term of a syllogism. 73. If the major term of a syllogism be the predicate of the major premiss, what do we know about the minor premiss ? 74. ((?) Deduce from the general principles of tlie categorical syllogism tJie special rules of the second figure. {I)) What can be determined respecting a syllogism EXAMINATION QUESTIONS 153 under each of the following conditions? — (i) that only one term is distributed, and that only once, (2) that only one term is distributed, and that twice, (3) that two terms only are distributed, each only once, (4) that two terms only are distributed, each twice. 75. Invent a syllogism in Barbara, and state it both in the extensive and intensive form. XIV. Figure and Mood of the Syllogism. Reduction 76. Ascertain how many universal terms there may be in the premisses of a syllogism more than in the con- clusion. 77. How much can you tell about a syllogism when you know, (i) that only the middle term is distributed, (2) that all the terms are distributed ? Show directly^ i. e. using only the general rules of syllogism and the forms of immediate inference, in how many ways an E conclusion may be drawn. 78. Show by deduction from the rules of the syllogism that there are five and only five ways of proving a universal conclusion. 79. Write down the dictum de omni et nuUo. What is the connexion of this dictum with the process of re- duction ? Is reduction of any practical use ? 80. Taking a syllogism of the third figure, and assum- ing one of the premisses to be false, show whether or not, with the knowledge of its falsehood thus supposed to be in our possession, we can frame a new syllogism ; if so point out the figure and mood to which it will belong. 81. Explain fully the limitations of the conclusions obtainable in the third figure of the syllogism. Are these limitations got rid of by ob version (permutation) of the premisses ? 154 A DIGEST OF LOGIC 82. State briefly the various opinions that have been held by logicians regarding figure, and in particular discuss the reasons for and against the admission of the fourth figure. 83. What is a subaltern mood, and why is it so called ? In what figures do AA and AE yield subaltern moods at all ? Show why. In what cases, if any, is it impossible to weaken one of the premisses in a subaltern mood with- out affecting the conclusion ? 84. Using any of the forms of immediate inference (including obversion), show in how many moods the following argument can be expressed — Every law is not bindings for some laws are morally bad, and nolJiing which is so is bindifig. XV. Irregular and Compound Syllogism 85. Give instances of the various forms of conditional arguments. 86. Does the mode of reasoning in a hypothetical syllogism differ from ordinary deduction ? 87. Show that the reasoning in a sorites is strictly syllogistic. 88. What is a dilemma ? Can it take more than one form? 89. Define the dilemma. What are its various forms ? On what does its validity depend ? 90. What is dilemma and why is it a treacherous form of argument ? XVI. Fallacies 91. State and compare the most important methods of classifying the fallacies known to you. 92. Explain the following fallacies, giving an example EXAMINATION QUESTIONS 155 of each — ignoratio elenchi^ non causa pro causa, a dicta secundum quid, amphibology , false a?ialogy, malobserv- ation. 93. On what ground would you base a classification of fallacies ? Compare critically various classifications that have been proposed. Explain exactly the nature of the fallacies called — Accident, Non causa pro causa, Argu- mentum ad hoi7iine7n. How far do the rules of formal logic suffice for their detection ? 94. Mention any arrangements or classifications of fallacies commenting on the principle of classification involved. Explain and exemplify the following : — A dicto sif?tpliciter ad dictum secundum quid, ig?wratio elenchi, non causa pro causa, and petitio principii. 95. Point out the exact nature of the fallacies called severally — Composition and division, A dicto secundujn quid ad dictum sinpiiciter, Post hoc trgo propter hoc. False analogy. XVII. The Value of the Syllogism 96. Define induction, and state with reasons your view of its relation to syllogism. 97. What is Mill's view of the function and value of the syllogism ? How has it been criticised ? 98. Discuss tlie value and function of the syllogism. 99. How does it come to pass that there can be any dispute as to whether the syllogism is a petitio principii ? 100. It is maintained, on the one hand, that no in- ference is valid in which the conclusion is not contained in the premisses, and, on the other hand, that no move- ment of thought deserves to be entitled inference in which there is not progress from the known to the unknown. Examine the grounds for these two state- ments, and discuss the possibility of holding them jointly. 156 APPENDIX II Abbott, T. K. ... Adamson, R. ... Aldrich Aristotle Arnaud and Nicole ... Bacon, Sir Francis ... Bagot, Daniel, Dean Bain, Alex Baker, A Balfour, Rt. Hon. A. J. BIBLIOGRAPHY ,.. Elements of Logic. Dublin, 1885. ... Art. " Logic" in Ejicyclo. Brit.^ ed. ix. Published separately. ... See Mansel. ... Logical woi'ks comprised under the title Organon. They are as follows : — Kategoriai (Predicamenta). Peri Hermeneias (De Interpre- tatione). Analytica Priora -^ , , ,. / . ^ . -Analytics. Analytica PosterioraJ Topika (Dialectics). Peri Sophisticon Elenchthon. ... La Logique, ou Fart de Penser. Paris, 1662. See Baynes, Port Royal Logic. ... De Argumentis Scientiarum, libri ix. 1623. Novum Organon. October 1620. Explanatory Notes on the Principal Chapters of Murray's Logic. Dublin, 1826. Deductive Logic. Longmans, 1879. Inductive Logic. Longmans, 1879. Outlines of Logic, Psychology, and Ethics. Lond., 1891. Philosophic Doubt. Lond., 1879. BIBLIOGRAPHY 157 Banett, T. S Baynes, Thos, Spencer )? 55 ?? Bentham, Geo. Boole, Geo J) 55 Bosanquet, B Bowen, Francis Bradley, F. H. Calderwood, Hy. Chase, D. P. ... Clarke, R. F. .. Coleman Davis, N. K. ... Devey, Joseph Drummond, P. C. ... Examination Ques- tions and Papers ... Logic and Metaphysics. Lond., 1875. Port Royal Logic. Lond., 1872. New Analytic of Logical Form. Edin., 1850. Outline of a new system of Logic. Lond., 1827. Pure Logic. Lond., 1864. Mathematical Analysis of Logic. Lond., 1847. Investigation of the Laws of Thought. Lond., 1854. Logic, or the Morphology of Know- ledge, 2 vols. Oxf, 1888. Lotze's Logic, Translation. Clar. Press, Oxf, 1889. Essentials of Logic. Lond., 1895. Treatise on Logic, or the Laws of Pure Thought. Camb. U.S.A. and Triibner, 1866. Principles of Logic. Lond., 1883. Fleming's Vocabulary of Philosophy. Griffen, Lond., 1887. A First Book of Logic. Oxf, 1879. Logic. Manuals of Catholic Philo- sophy. Lond., 1889. Notes on Logic. Oxf, 1880. Theory of Thought, Deduction. New York, 1880. Syllabus of a proposed System of Logic. Lond., i860. Art. " Logic,'' Engl. Cyclo. Formal Logic. Lond., 1847. A Bundle of Paradoxes. Logic, or the Science of Inference. Bohn's Library, Bell, 1852. A First Logic Book. Oxf, 1875. Sec Questions. 158 A DIGEST OF LOGIC Fitzgerald, P. F. Fowler, Thos, ... Gilbert, J. W Gilmore, J. H. Hamilton, Sir W. 55 55 Harris, W. T Hegel Hill, D.J Hughlings, J. P. Jevons, Wm. Stanley Jones, Miss E. E. C. Kant, 1 Treatise on the Principle of Suffi- cient Reason. Lond., 1887. Deductive Logic. Clar. Press, Oxf., 1870. Last ed., 1895. Inductive Logic. Clar. Press, Oxf., 1870. Last ed., 1895. Logic for the Million. Lond., 1851. Outlines of Logic. New York, 1879. Lectures on Logic, 2 vols. Lond. Exam, of Sir W. Hamilton's Philos. See Mill. Hegel's Logic. A critical exposi- tion. Chicago, 1890. Logic translated by Wallace, 2 \'ols. Oxf., 1892-94. Jevons' Logic recast. New York, 1883. _ The Logic of Names : an Introd. to Boole. Lond., 1869. Elementary Lessons in Logic. Mac- millan, 1886. Studies in Deductive Logic. Mac- millan, 1880. Principles of Science. Macmillan, 1877. Substitution of Similars. I\Lacmillan, 1869. Pure Logic, z. e. The Logic of Quality. 1864. The Philos. of Induction. Contemp. Rev., vol. xiv., p. 457. The use of Hypothesis. //vV/., p. 778. Elements of Logic. Edin., 1890. Introd. to Logic. Translated. Lond., 1885. BIBLIOGRAPHY 159 Keynes, J. N Studies and Exercises in Formal Logic. Macmillan, 1894. Ladd, Miss Christine Lambert, Joliann H. Latham, R. G. Liard, L. Lotze , Studies in Logic. Lond,, 1883. Neues Organon. Leipzig, 1764. Logic in its application to Language. Lond., 1856. Les logiciens anglais contemporains. Paris, 1878. Logic translated by Bosanquet, 2 vols. Clar. Press, Oxf., 1888. Mansel, H. L. Aldrich's Artis Logicae Rudimenta. Martineau, Jas. M'Cosh, Jas. ... Mill, John Stuart Prolegomena Logicae. Oxf., i860. Theory of Reasoning, Essays Philos., etc., vol. ii., 1869. Laws of Discursive Thought. Lond., 1870. System of Logic, i vol. ed. Long- mans, Lond., 1884. Analysis of the above by Killick, q.v. „ „ „ Stebbing, ^.-6/. Exam, of Sir W. Hamilton's Philos. Longmans, 1865. Elementary Notions of Logic. Lond., 1884. Miiid^ A Quarterly Magazine, Arts, by various authors. Minto, Wm. Murray, Richard Mussehenbroek, P. Logic, Inductive and Deductive. Murray, 1893. Introd. to Logic. Dublin Univ. Press Series. Dub., 1890, Compendium of Logic. Lond. and Dub., 1847. Explanatory Notes on, by Dean Bagot, q.v. Commentary on by J. Walker, q.v. Institutiones Logicae. 1748. ;6o A DIGEST OF LOGIC Newman, F. W. ... Lectures on Logic. Lond., 1838. Nicole et Arnaud ... See Baynes, Port Royal Logic. Oxford Handbook of Logic. Oxf., 1880. Pcirce, C. S Proceedings of the American Academy of Arts and Sciences, on Intension and Intensive reading of Propositions, vol. iii., pp. 4i5— 432, 1867. „ „ Studies in Logic. Boston, 1883. Questions, Examination Papers, etc. — Palaestra Oxoniensis: Questions and Exercises. Oxf., 1875. Jevons, W. S., Studies in Deductive Logic. Macmillan, 1880. Advanced Logical Questions. Simp- kin, Lond., 1 88 1. Holman, Questions on Welton's Logic. Clive, Lond., 1893. B.A. Mental and Moral Science Papers. Clive, Lond., 1889. Weatherly, F. E., Questions in Logic. Oxf, 18S3. Ray, P. K Read, Carvcth Robertson, Croom ... Royce, J. Ryland, F Sheldon Siduwick, A Si^jwart, C. Text Book of Deductive Logic. Macmillan, 1886. Theory of Logic. Lond., 1878. Articles in Mi?id, various dates. Primer of Logical Analysis. San Francisco, 1881. Logic. An introductory manual. Bell, Lond., 1896. Elements of Logic. Lond., 1864. The Process of Argument. Lond., 1893- Fallacies. International scientific series, vol. xlviii. Lond., 1883. Logic, 2 vols., translated by H. Dendy. Lond., 1895. BIBLIOGRAPHY i6i Solly Spalding Stebbing, W Stewart, D Stock, St. G Thomson W ., Archbp . Trendelenburg, F. A. Ueberweg Veitch, J. Venn, John Walker, J Wallace W^allis W^atts, Isaac Weatherly, F. E . ... 53 51 Welton, J Whately, Richd., Abp. 55 55 55 Whewell Syllabus of Logic. Art. " Logic" in the Encyclo. Brit. ed. viii. Analysis of J. S. Mill's System of Logic. Lond., 1864. Handbk. of Ded. Logic. Edin., 1885. Deductive Logic. Lond., 1888. Outline of the Laws of Thought. Lond., 1882. Elementa Logices Aristotele^. 1852. Outlines of Logic. The above translated. Lond., 1881. System of Logic translated by Lind- say. Institutes of Logic. Edin., 1885. Symbolic Logic. Lond., 1881. The Logic of Chance. Lond., 1881. Commentary on Murray's Com- pendium. Lond. and Dub., 1852. Hegel's Logic translated. Lond., 1874. Institutio Logicae. 1684. Logic, or the right use of reason. Lond., 1811. Rudiments of Logic. Oxf., 1879. Logic Tables. Oxf., 1879. Questions in Logic. Oxf., 1883. A Manual of Logic, 2 vols. Clive, Lond., 1 89 1. Lessons in Reasoning. Elements of Logic. Longmans, ed. ix., 1865. On the Philosophy of Discovery. 1841. History of the Inductive Sciences. 1840. M Richard Clay & Sons, Limited, London & Bungay. A CATALOGUE OF BOOKS AND ANNOUNCEMENTS OF METHUEN AND COMPANY PUBLISHERS : LONDON 36 ESSEX STREET W.C. CONTENTS FORTHCOMING BOOKS, PAGI 2 POETRY, ..... lO BELLES LETTRES, .... II ILLUSTRATED BOOKS, .... 13 HISTORY, ...... 14 BIOGRAPHY, ...... 16 TRAVEL, ADVENTURE AND TOPOGRAPHVj x8 GEJ^ERAL LITERATURE, 19 SCIENCE, ..... 21 PHILOSOPHY, ..... 22 THEOLOGY, ...... 22 LEADERS OF RELIGION, 24 FICTION, . . • . 25 BOOKS FOR EOYS AND GIRLS, . 34 THE PEACOCK LIBRARY, 35 UNIVERSITY EXTENSION SERIES, 35 SOCIAL QUESTIONS OF TO-DAY, 36 CLASSICAL TRANSLATIONS, 37 EDUCATIONAL BOOKS, . .^ 38 SEPTEMBER 1897 September 1S97. Messrs. M et h u e n ' s ANNOUNCEMENTS Poetry SHAKESPEARE'S POEMS. Edited, with an Introduction and Notes, by George Wyndham, M. P. Crown Zvo. Buckram. 65-. This is a volume of the sonnets and lesser poems of Shakespeare, and is prefaced with an elaborate Introduction by Mr. Wyndham ENGLISH LYRICS. Selected and Edited by W. E. Henley. Crown 2>vo. Bnckraui. ()s. Also 15 copies on Japanese paper. Demy ^vo. £2, 2s. net. Few announcements will be more welcome to lovers of Ens;lish verse than the one that Mr. Henley is bringing together into' one book the finest lyrics in our language. NURSERY RHYMES. With many Coloured Pictures. By F. D. Bedford. Small ^to. 6s. This book has many beautiful designs in colour to illustrate the old rhj'mes. THE ODYSSEY OF HOMER. A Translation by J. G. Cordery. Crown %vo. \os. 6d. Travel and Adventure BRITISH CENTRAL AFRICA. By Sir II. H. Johnston, K.C.B. "With nearly Two Hundred Illustrations, and Six Maps. Croivn ^io. 30 j. net. Contents.— (i) The History of Nyasaland and British Central Africa generally. 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With 80 Illus- trations and 6 Maps. Crown d^to. 2^s. The travels of Prince Henri in 1895 from China to the valley of the Bramaputra covered a distance of 2100 miles, of whith 1600 was through absolutely unexplored country. No fewer than seventeen ranges of mountains were crossed at altitudes of from 11,000 to 13,000 feet. The journey was made memorable by the discovery of the sources of the Irrawaddy. To the physical difficulties of the journey were added dangers from the attacks of savage tribes. The book deals with many of the burning political problems of the East, and it will be found a most important contribution to the literature of adventure and discovery. THREE YEARS IN SAVAGE AFRICA. By Lionel Decle, \Yith an Introduction by H. M. Stanley, M.P. With 100 Illus- trations and 5 Maps. Demy^vo. 2\s. Few Europeans have had the same opportunity of studying the barbarous parts of Africa as Mr. Decle. Starting from the Cape, he visited in succession Bechuana- land, the Zambesi, jMatabeleland and Rlashonaland, the Portuguese settlement on the Zambesi, Nyasaland, Ujiji, the headquarters of the Arabs, German East Africa, Uganda (where he saw fighting in company with the late Major ' Roddy' Owen), and British East Africa. In his book he relates his experiences, his minute observations of native habits and customs, and his views as to the work done in Africa by the various European Governments, whose operations he was able to study. The whole journey extended over 7000 miles, and occupied exactly three years. WITH THE MOUNTED INFANTRY IN MASHONA- LAND. By Lieut. -Colonel Alderson. With numerous Illustra- tions and Plans. Demy 8?v. 12s. 6d. This is an account of the militarj?' operations in Rlashonaland by the officer who commanded the troops in that district during the late rebellion. Besides its Interest as a story of vv-arfare. 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Edited by Professor Leon Parmentier of Liege and INI. BiDEZ of Gand. De/iij/ Svo. ys. 6(1. [Byzaitiine Texts. THE ODES AND EPODES OF HORACE. Translated by A. D. GODLEY, ALA., Fellow of Magdalen College, Oxford. Crown Svo. biukrain. 2s. ORNAMENTAL DESIGN FOR WOVEN FABRICS. By C. Stephenson, of The Technical College, Bradford, and F. SUDDARDS, of The Yorkshire College, Leeds. With 65 full-page plates, and numerous designs and diagrams in the text. Demy Svo. 75. 6d. The aim of this book is to supply, in a systematic and practical form, information on the subject of Decorative Design as applied to Woven Fabrics, and is primarily intended to meet the requirements of students in Textile and Art Schools, or of designers actively engaged in the weaving industry. Its wealth of illustration is a marked feature of the book. ESSENTIALS OF COMMERCIAL EDUCATION. By E. E. Whitfield, M.A. Croivn Svo. is. 6d. A guide to Commercial Education and Examinations. 8 Messrs. Methuen's Announcements passages for unseen translation. by e. c. Marchant, M.A., Fellow of Pelerhouse, Cambridge; and A. M. Cook, INI. A., late Scholar of Wadham College. Oxford: Assistant Masters at St. Paul's School. Crown 2>vo. 3.f. bd. This book contains Two Hundred Latin and Two Hundred Greek Passages, and has been very carefully compiled to meet the wants of V. and VI. Form Boys at Public Schools. It is also well adapted for the use of Honour men at the Universities. EXERCISES ON LATIN ACCIDENCE. By S. E. Win- bolt, Assistant Master at Christ's Hospital. Croivn Zvo. \s. 6d. An elementary book adapted for Lower Forms to accompany the shorter Latin primer. NOTES ON GREEK AND LATIN SYNTAX. By G. BucKLAND Green, M.A., Assistant Master at the Edinburgh Academy, late Fellow of St. John's College, Oxon. Cr. Svo. 2s. 6c/. Notes and explanations on the chief difficulties of Greek and Latin Syntax, with numerous passages for exercise. A DIGEST OF DEDUCTIVE LOGIC. 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Crown Svo. 6s. SECRETARY TO BAYNE, M.P. By W. Pett Ridge. Crown Svo. 6s. TPIE BUILDERS. By J. S. FLETCHER, Author of 'When Charles i. was King.' Crown Svo. 6s. JOSIAH'S WIFE. By NORMA LORIMER. Crozan Svo. 6s. BY STROKE OF SWORD. By Andrew Balfour. Illus- trated by W. CuBiTT Cooke. Crown Svo. 6s. A romance of the time of Elizabeth THE SINGER OF MARLY. By Ida Hooper. Illustrated by W. CuBiTT Cooke. Crown Svo. 6s. A romance of adventure. KIRKHAM'S FIND. By Mary Gaunt, Author of 'The Moving Finger. ' Crown Svo. 6s. THE FALL OF THE SPARROW. By M. C. BALFOUR. Crown Svo. 6s. SCOTTISH BORDER LIFE. By James C. DiBDiN. Crown Svo. ^s. GJ. A 2 A LIST OF Messrs. Methuen's PUBLICATIONS roetry RUDYARD KIPLING'S NEW POEMS Rudyard Kipling. THE SEVEN SEAS. By Rudyard Kipling. Third Edition, Crown %vo. Buckram, f^ilt top. 6j. 'The new poems of Mr. Rudj-ard Kipling lip.ve nil the spirit and swing of their pre- decessors. Patriotism is the solid concrete foundation on which Mr. Kipling has built the whole of his work.' — Times. ' Full of passionate patriotism and the Imperial spirit.' — Yorkshire Post. 'The Empire has found a singer ; it is no depreciation of the songs to say that states- men may have, one way or other, to take account of them.' — Manchester Guardian. ' Animated through and through with Indubitable genius.' — Daily Telegraph. 'Packed with inspiration, with humour, with pathos.' — Daily Chronicle. ' All the pride of empire, all the intoxication of pov.-er, all the ardour, the energy, the masterful strength and the wonderful endurance and death-scorning pluck which arc the very bone and fibre and marrow of the British character are here." —Daily Mail. Rudyard Kipling. BARRACK-ROOM BALLADS; And Other Verses. By Rudyard Kipling. Elevenlh Edition. Crown Svo. 6s. ' Mr. Kipling's verse is strong, vivid, full of character. • . . Unmistakable genius rings in every line.' — Times. The ballads teem with imagination, they palpitate witli emotion. We read them with laughter and tears ; the metres throb in our pulses, the cunningly ordered words tingle with life ; and if this be not poetry, what is?' — Pall Mall Gazette. *Q." POEMS AND BALLADS. By '^Q.," Author of ' Green Bays,' elc. Crown Svo. Bnckram. "^s. 6d. * This work has just the faint, ineffable touch and glow that make poetry ' Q." has the true romantic spirit.' — Speaker. "Q." GREEN BAYS : Verses and Parodies. By " Q.," Author of 'Dead Man's Rock,' etc. Second Edition. Crown Svo. -^s.Sd. 'The verses display a rare and versatile gift of parody, great command of metre, and a very pretty turn of humour.' — Times. E. Mackay. A SONG OF THE SEA. By Eric ]\L\ckay, Author of 'The Love Letters of a Viohnist.' Second Edition. Fcap. "^vo. «^j. G. W. Steevens. MONOLOGUES OF THE DEAD. By G. W. Steevens. Foolscap Zvo. ^s. 6d. A series of Soliloquies in which famous men of antiquity — Julius Csesar, Nero, Alcibiades, etc., attempt to express themselves in the modes of thought and language of to-day. The edcct is sometimes splendid, sometimes bizarre, but always aaia^In^ly clever. — rull Mall Cu^c i^c. 12 Messrs. Methuen's List Victor Hugo. THE LETTERS OF VICTOR HUGO. Translated from the French by F. Clarke, M.A. In Two Volumes. Demy 2>vo. IQS. 6d. each. Vol.1. 1815-35. This is the first volume of one of the most interesting and important collection of letters ever published in France. The correspondence dates from Victor Hugo's boyhood to his death, and none of the letters have been published before. The arrangement is chiefly chronological, but where there is an interesting set of letters to one person these are arranged together. The first volume contains, among others, (i) Letters to his father ; (2) to his young wife ; (2)^ to his confessor, Lamennais ; a very important set of about fifty letters to Sainte-Beauve ; (5) letters about his early books and plays. 'A charming and vivid picture of a man whose egotism never marred his natural kindness, and whose vanity did not impair his greatness.' — Standard. C. H. Pearson. ESSAYS AND CRITICAL REVIEWS. By C. H, Pearson, M.A., Author of 'National Life and Character.' Edited, with a Biographical Sketch, by H. A. Strong, M.A., LL.D. With a Portrait. Demy Svo. 10s. 6d. ' Remarkable for careful handling, breadth of view, and knowledge." — Scotsman. * Charming essays. ' — Spectator, W. M. Dixon. A PRIMER OF TENNYSON. By W. M. Dixon, M.A., Professor of EngHsh Literature at Mason College. Crown Svo. 2s. 6d. ' Much sound and well-expressed criticism and acute literary judgments. The biblio- graphy is a boon.' — Speaker. W. A. Craigie. A PRIMER OF BURNS. By W. A. Craigie. Crown Svo. 2s. 6d. This book is planned on a method similar to the ' Primer of Tennyson.' It has also a glossary. 'A valuable addition to the literature of the poet.' — Times. ' An excellent short account.' — Pall Mall Gazette. 'An admirable introduction.'— G/tf3^. Sterne. THE LIFE AND OPINIONS OF TRISTRAM SHANDY. By Lawrence Sterne. With an Introduction by Charles Whibley, and a Portrait. 2 vols. ^s. 'Very dainty volumes are these; the paper, type, and light-green binding are all very agreeable to the eye. Simplex munditiis is the phrase that might be applied to them.' — Globe. Congreve. THE COMEDIES OF WILLIAM CONGREVE. With an Introduction by G. S. Street, and a Portrait. 2 vols. ^s. ' The volumes are strongly bound in green buckram, are of a convenient size, and pleasant to look upon, so that whether on the shelf, or on the table, or in the hand the possessor is thoroughly content with ih^m.' —Guardian. Morier. THE ADVENTURES OF HAJJI BABA OF ISPAHAN. By James Morier. With an Introduction by E. G. Browne, M.A., and a Portrait. 2 vols. ys. Walton. THE LIVES OF DONNE, WOTTON, HOOKER, HERBERT, AND SANDERSON. By Izaak Walton. With an Inlroduclion by \'lrnon Blacklurn, and a Portrait. 31. 6d. Messrs. Methuen's List 13 Johnson. THE LIVES OF THE ENGLISH POETS. By Samuel Johnson, LL.D. With an Introduction by J. H. Millar, and a Portrait. 3 vols. \os. 6d. Bums. THE POEMS OF ROBERT BURNS. Edited by Andrew Lang and W. A. Craigie. With Portrait. Demy Svo, gilt top. 6j-. This edition contains a carefully collated Text, numerous Notes, critical and textual, a critical and biographical Introduction, and a Glossary. ' Among the editions in one volume, Mr. Andrew Lang's will take the place of authority. ' — Times. F. Langbridge. BALLADS OF THE BRAVE: Poems of Chivalry, Enterprise, Courage, and Constancy. Edited, with Notes, by Rev. F. Langbridge. Croivn Zvo. Bttckram. 35. 6d. School Edition, is. 6d. 'A very happy conception happily carried out. These "Ballads of the Brave" are intended to suit the real tastes of boys, and will suit the taste of the great majority.' — Spectator. ' The book is full of splendid things.' — World, Illustrated Books Jane Barlow. THE BATTLE OF THE FROGS AND MICE, translated by Jane Barlow, Author of ' Irish Idylls,' and pictured by F. D. Bedford. S7nall \to. ds. vet. S. Baring Gould. A BOOK OF FAIRY TALES retold by S. Baring Gould. With numerous illustrations and initial letters by Arthur J. Gaskin. Second Edition. Crown Svo. Buch-avi. 6s. 'Mr. Baring Gould is deserving of gratitude, in re-writing in honest, simple style the old stories that delighted the childhood of " our fathers and grandfathers." As to the form of the book, and the printing, which is by Messrs. Constable, it were difficult to commend overmuch. — Saturday Revie^v, S. Baring Gould. OLD ENGLISH FAIRY TALES. Col- lected and edited by S. Baring Gould. With Numerous Illustra- tions by F. D, Bedford. Second Edition. CrozvjtSvo. Buch'am. 6s. 'A charming volume, which children will be sure to appreciate. The stories have been selected with great ingenuity from various old ballads and folk-tales, and, having been somewhat altered and readjusted, now stand forth, clothed in Mr. Baring Gould's delightful English, to enchant youthful readers.' — Guardian. S. Baring Gould. A BOOK OF NURSERY SONGS AND RHYMES. Edited by S. Baring Gould, and Illustrated by the Birmingham Art School. Buckram^ gilt top. Croivn Svo. 6s. ' The volume is verj' complete in its way, as it contains nursery songs to the number of 77, game-rhymes, and jingles. To the student we commend the sensible intro- duction, and the explanatory notes. The volume is superbly printed on soft, thick paper, which it is a pleasure to touch ; and the borders and pictures are among the very best specimens we have seen of the Gaskin school.' — Bir7ninz- ham Gazette. 14 Messrs. Methuen's List H. C. Beeching. A BOOK OF CHRISTMAS VERSE. Edited by H. C. Beeciiixg, INI.A., and Illustrated by Walter Crane. Crown 8vo, gilt top. ^s. A collection of the best ver<;e inspired by the birth of Christ from the Middle Ages to the present day, A distinction of the book is the large number of poems it contains by modern authors, a few of which are here printed for the first time. 'An anthology which, from its unity of aim and liigh poetic excellence, has a better right to exist than most of its fellows.' — Guardiatt. History Gibbon. THE DECLINE AND FALL OF THE ROMAN EMPIRE. By Edward Gibbon. A New Edition, Edited with Notes, Appendices, and Maps, by J. E. Bury, M.A., Fellow of Trinity College, Dublin. In Seven Volumes. Demy %vo. Gilt top. %s. 6d. each. Also crown 2>vo. 6s. each. Vols. /., //., and III. ' The time has certainly arrived for a new edition of Gibbon's great work. . . . Pro- fessor Bury is the right man to undertake this task. His learning is amazing, both in extent and accuracy. The book is issued in a handy form, and at a moderate price, and it is admirably printed.' — Thiics. ' The edition is edited as a classic should be edited, removing nothing, j'et indicating the value of the text, and bringing it up to date. It promises to be of the utmost value, and will be a welcome addition to many libraries.' — Scots»ian. 'This edition, so far as one may judge from the first instalment, is a marvel of erudition and critical skill, and it is the very minimum of praise to predict that the seven volumes of it will supersede Dean Milman's as the standard edition of our great historical classic' — Glasgow Herald. * The beau-ideal Gibbon has arrived at last.* — Skeich, 'At last there is an adequate modern edition of Gibbon. . . . The best edition the nineteenth century could produce." — Manchester Guardian. Flinders Petrie. A HISTORY OF EGYPT,fromthe Earliest Times to the Present Day. Edited by W. M. Flinders Petrie, D.C.L., LL.D., Professor of Egyptology at University College. Fnlly Illustrated. In Six Volumes. Crown 8vo. 6s. each. Vol. I. Prehistoric Times to XVI. Dynasty. W. M. F. Petrie. Third Editioji. Vol. IT. The XVIIth and XVIIIth Dynasties. W. ^\. F. Petrie. Second Edition. ' A history written in the spirit of scientific precision so worthily represented by Dr. Petrie and his school cannot liut promote sound and accurate study, and supply a v.acant place in the English literature of Egyptology.' — Times. Flinders Petrie. EGYPTIAN TALES. Edited by W. M. I'^linders Petrie. Illustrated by Tristram Ellis. In Two Volumes. Cj-owii Zvo. ^s. 6d. each. 'A valuable addition to the literature of comparative folk-lore. The drawings arc really illustrations in the literal sense of the \\ox<\.'— Globe. ' It has a scientific value to the student of history and ?i.\c\\2^cAo%y .' —Scotsman. 'Invaluable as a picture of life in Palestine and Egypt." — Daily Neivs. Messrs. Methuen's List 15 Flinders Petrie. EGYPTIAN DECORATIVE ART. By W. M. Flinders Petrie, D.C.L. With 120 Illustrations. Crown '- Professor Flinders Petrie is not only a profound Egyptologist, but an accomplished student of comparative archseology. In these lectures, delivered at the Royal Institution, he displays both qualifications Vflth. rare skill in elucidating the development of decorative art in Egypt, and in tracing its influence on the art of other countries.' — Titnes. S. Baring Gould. THE TRAGEDY OF THE C^SARS. The Emperors of the Julian and Claudian Lines. With numerous Illustrations from Busts, Gems, Cameos, etc. By S. Baring Gould, Author of 'Mehalah,' etc. Fourth Edition. Royal %vo. i^s. ' A most splendid and fascinating book on a subject of undying interest. The great feature of the book is the use the author has made of the existing portraits of the Caesars, and the admirable critical subtlety he has exhibited in dealing with this line of research. It is brilliantly written, and the illustrations are supplied on a scale of profuse magnificence.' — Daily Chronicle. ' The volumes will in no sense disappoint the general reader. Indeed,_ in their way, there is nothing in any sense so good in English. . . . Mr. Earing Gould has presented his narrative in such a way as not to make one dull page.' — Athenceunt. H. de B. GibMns. INDUSTRY IN ENGLAND : HISTORI- CAL OUTLINES. By H. de B. Gibbins, INI.A., D.Litt. With 5 Maps. Second Edition. Demy Svo. los. 6d. This book is written with the view of affording a clear view of the main facts of English Social and Industrial History placed in due perspective. Beginning with prehistoric times, it passes in re\aew the growth and advance of industry up to the nineteenth century, showing its gradual development and progress. The book is illustrated by Maps, Diagrams, and Tables. A. Clark. THE COLLEGES OF OXFORD : Their History and their Traditions. By Members of the University. Edited by A. Clark, M.A., Fellow and Tutor of Lincoln College. Svo. I2s. 6d. ' A work which will certainly be appealed to for many years as the standard book on the Colleges of Oxford.' — Atlienceum. Perrens. THE HISTORY OF FLORENCE FROM 1434 TO 1492. By F. T. Perrens. Translated by Hannah Lynch. Zvo. \2s. 6d. A history of Florence under the domination of Cosimo, Piero, and Lorenzo de Medicis. ' This is a standard book by an honest and intelligent historian, who has deserved well of all who are interested in Italian history.' — Manchester Guardian. J.Weils. A SHORT HISTORY OF ROME. By J. Wells, M.A., Fellow and Tutor of Wadham Coll., Oxford. With 4 Maps. Crown 2>vo. y. 6d. This book is intended for the INIiddle and Upper Forms of Public Schools and for Pass Students at the Universities. It contains copious Tables, etc. 'An original work written on an original plan, and with uncommon freshness and vigour. ' — Speaker, i6 Messrs. Methuen's List E. L. S. Horsburgh. THE CAMPAIGN OF WATERLOO. By E. L. S. Horsburgh, B.A. JVi'fh Plans. Crown 8vo. ^s. * A brilliant essay — simple, sound, and thorough.' — Dally Chronicle. ' A study, the most concise, the most lucid, the most critical that has been produced. — Birmingham Mercury, H.B. George. BATTLES OF ENGLISH HISTORY. ByH.B. George, M.A., Fellow of New College, Oxford. With numerous Plans. Third Edition. Crown Svo. 6s. * Mr. George has undertaken a very useful task — that of making military' affairs in- telligible and instructive to non-military readers — and has executed it with laud- able intelligence and industry, and with a large measure of success.' — Times. 0. Browning. A SHORT HISTORY OF MEDIEVAL ITALY, A.D. 1 250- 1 530. By Oscar Browning, Fellow and Tutor of King's College, Cambridge. Second Edition. In Two Volumes. Crown Svo. 5^. each. Vol. I. 1250-1409. — Guelphs and Ghibellines. Vol. n. 1409- 1530. — The Age of the Condottieri. 'A vivid picture of mediaeval Italy.' — Standard. ' Mr. Browning is to be congratulated on the production of a work of immense labour and \&z.xv\x\g.''— Westminster Gazette. O'Grady. THE STORY OF IRELAND. By Standish O'Grady, Author of ' Finn and his Companions.' Cr. %vo. 2s. 6d. 'Most delightful, most stimulating. Its racy humour, its original imaginings, make it one of the freshest, breeziest volumes.' — Methodist Times. Biography Baring Gould. THE LIFE OF NAPOLEON BONA- PARTE. By S. Baring Gould. With over 450 Illustrations in the Text and 12 Photogravure Plates. Large quarto. Gilt top. 36J. ■ The best biography of Napoleon in our tongue, nor have the French as good a biographer of their hero. A book very nearly as good as Southey's " hife of Nelson." '—Manchester Guardian. 'The main feature of this gorgeous volume is its great wealth of beautiful photo- gravures and finely-executed wood engravings, constituting a complete pictorial chronicle of Napoleon I.'s personal history from the days of his early childhood at Ajaccio to the date of his second interment under the dome of the Invalides in Vaxis.'— Daily Telegraph. ' The most elalwrate account of Napoleon ever produced l)y an English writer.'— Daily Chronicle. ' A brilliant and attractive volume. Never before have so many pictures relating to Napoleon been brought within the limits of an English book.' — Globe. ' Particular notice is due to the vast collection of contemporary illustrations.' — Guardian. 'Nearly all the illustrations are real contributions to historj'.' — IJ'esf minster Gazette. 'The illustrations arc of supreme inteTv<.t.' Standard. Messrs. Methuen's List 17 Morris Fuller. THE LIFE AND WRITINGS OF JOHN DAVENANT, D.D. (1571-1641), President of Queen's College, Lady Margaret Professor of Divinity, Bishop of Salisbury. By Morris Fuller, B.D. Crown %vo. 'js. 6d. ' A valuable contribution to ecclesiastical history.' — Birniinghain Gazette. J. M. Rigg. ST. ANSELM OF CANTERBURY: A Chapter IN THE History of Religion. By J. M. Rigg. DeviyZvo. ^s. 6d. ' Mr. Rigg has told the story of the great Primate's life with scholarly ability, and has thereby contributed an interestingchapter to the history of the Norman period.' — Daily Chronicle. F. W. Joyce. THE LIFE OF SIR FREDERICK GORE OUSELEY. By F. W. Joyce, M.A. With Portraits and Illustra- tions. Crown Zvo. *]s. 6d. ' This book has been undertaken in quite the right spirit, and written with sympathy insight, and considerable literary skill.' — Times. W. G. Collingwood. THE LIFE OF JOHN RUSKIN. By W. G. Collingwood, M.A., Editor of Mr. Ruskin's Poems. With numerous Portraits, and 13 Drawings by Mr. Rusk in. Second Edition. 2 vols. S-vo. 32^. ' No more magnificent volumes have been published for a long time,'— Tidies. * It is long since we had a biography with such delights of substance and of form. Such a book is a pleasure for the day, and a joy for ever.' — Daily Chronicle. 0. Waldstein. JOHN RUSKIN : a Study. By Charles Waldstein, M.A., Fellow of King's College, Cambridge. With a Photogravur Portrait after Professor Herkomer. Post Svo. ^s. 'A thoughtful, impartial, well-written criticism of Ruskin's teaching, intended to separate what the author regards as valuable and permanent from what is transient and erroneous in the great master's writing.' — Daily Chronicle. W. H. Hutton. THE LIFE OF SIR THOMAS MORE. By W. H. Hutton, M.A., Author of ' William Laud.' With Portraits, Crown Svo. ^s. ' The book lays good claim to high rank among our biographies. It is excellently, even lovingly, written." — Scotsman. ' An excellent monograph.' — Times. Clark RusselL THE LIFE OF AD]\IIRAL LORD COL- LINGWOOD. By W. Clark Russell, Author of ' The Wreck of the Grosvenor.' With Illustrations by F. Brangwyn. Third Edition. Crown Svo. 6s. •A book which we should like to see in the hands of every boy in the country.' — .S"^. James's Gazette. ' A really good book.' — .Saturday Review. A3 1 8 Messrs. Methuen's List Southey. ENGLISH SEAMEN (Howard, Clifford, Hawkins, Drake, Cavendish). By Robert Southey. Edited, with an Introduction, by David Hannay. Second Edition. CrownSvo. 6s. 'Admirable and well-told stories of our naval history.' — Artny and Navy Gazette. 'A brave, inspiriting book.' — Black and White. Travel5 Adventure and Topography R. S. S. Baden-Powell. THE DOWNFALL OF PREMPEH. A Diary of Life with the Native Levy in Ashanti, 1895. By Colonel Baden-Powell. With 21 Ilkistrations and a Map. Demy Zvo. \os. 6d. '• A compact, faithful, most readable record of the campaign.' — Daily News. ' A bluff and vigorous narrative.' — Glasgoxv Herald. R. S. S. Baden-Powell TPIE MATKBELE CAMPAIGN 1896. By Colonel R. S. S. Baden- Powell. With nearly 100 Illustrations. Second Edition. Deniy^vo. 155. 'Written in an unaffectedly light and humorous style.' — The World. 'A very racy and eminently readable book.' — St. James's Gazette. * As a straightforward account of a great deal of plucky work unpretentiously done, this book is well worth reading. The simplicity of the narrative is all in its favour, and accords in a peculiarly English fashion with the nature of the subject.' Times. Captain Hinde. THE FALL OF THE CONGO ARABS. By Sidney L. Hinde. With Portraits and Plcns. Defuy Svo. i2s. 6d. * The book is full of good things, and of sustained interest.' — St. James's Gazette. A graphic sketch of one of the most exciting and important episodes in the struggle for supremacy in Central Africa between the Arabs and their_ Europeon rivals. Apart from the story of the campaign. Captain Hinde's book is mainly remark- able for the fulness with which he discusses the question of cannibalism. It is, indeed, the only connected narrative— in English, at any rate — which has been published of this particular episode in African history.' — Tima. * Captain Hinde's book is one of the most interesting and valuable contributions yet made to the literature of modern Africa.' — Daily Nczvs. W. Crooke. THE NORTH-WEST PROVINCES OF INDIA : TiiEiR Ethnology and Administration. By W. Crooke. With Maps and Illustrations. Demy Svo. 10s. 6d. ' A carefully and well-written account of one of the most important provinces of the Empire. In seven chapters Mr. Croote deals successively with the land in its physical aspect, the province under Hindoo and Mussulman rule, the province under British rule, the ethnology and sociology of the province, the religious and social life of the people, the land and its settlement, and the native peasant in his relation to the land. The illustrations are good and well selected, and the map is excellent. ' — Manchester Guardian. Messrs. Methuen's List 19 W. B. Worsfold. SOUTH AFRICA : Its History and its Future. By W. Basil Worsfold, INI. A. IVich a Map. Second Edition. Crown Svo. 6s. 'An intensely interesting book.' — Daily Chronicle. ' A monumental work compressed into a very moderate compass.' — World. General Literature S. Baring Gould. OLD COUNTRY LIFE. By S. Baring Gould, Author of ' Mehalah,' etc. With Sixty- seven Illustrations by W. Parkinson, F. D. Bedford, and F. Masey. Large Crown Svo. los. 6d. Fifth and Cheaper Edition. (>s. '"Old Countrj' Life," as healthy wholesome reading, full of breezy life and move- ment, full of quaint stories vigorously told, will not be excelled by any book to be published throughout the year. Sound, hearty, and English to the core.' — World. S. Baring Gould. HISTORIC ODDITIES AND STRANGE EVENTS. By S. Baring Gould. Third Edition. Crown ^vo. 6s. ' A collection of exciting and entertaining chapters. The whole volume is delightful leading.'— Times. S. Baring Gould. FREAKS OF FANATICISM. By S. Baring Gould. Third Edition. Crown Svo. 6s. 'Mr. Baring Gould has a keen eye for colour and effect, and the subjects he has chosen give ample scope to his descriptive and analytic faculties. A perfectly fascinating book. ' — Scottish Leader. S. Baring Gould. A GARLAND OF COUNTRY SONG : English Folk Songs with their Traditional Melodies. Collected and arranged by S. Baring Gould and H. Fleetwood Sheppard. Demy ^to, 6s. S. Baring Gould. SONGS OF THE WEST: Traditional Ballads and Songs of the West of England, with their Traditional Melodies. Collected by S. Baring Gould, M.A., and H. Fleet- wood Sheppard, M. A. Arranged for Voice and Piano. In 4 Parts (containing 25 Songs each), Parts I., //., ///., 3j\ each. Part IV., ^s. In one Vol., French morocco, \^s. ' A rich collection of humour, pathos, grace, and poetic fancy.' — Saturday Review, 20 Messrs. Methuen's List S. Baring Gould. YORKSHIRE ODDITIES AND STRANGE EVENTS. Fourth Edition. Crown %vo. 6s. S. Baring Gould. STRANGE SURVIVALS AND SUPER- STITIONS. With Illustrations. By S. Baring Gould. Crown ^vo. Second Edition. 6s. ' We have read Mr. Baring Gould's book from beginning to end. It is full of quaint and various information, and there is not a dull page in it. ' — Notes and Queries. S. Baring Gould. THE DESERTS OF SOUTHERN FRANCE. By S. Baring. Gould. With numerous Illustrations by F. D. Bedford, S. Hutton, etc. 2 vols. Demy Zvo. 325. ' His two richly-illustrated volumes are full of matter of interest to the geologist, the archaeologist, and the student of history and manners.' — Scotsvian. G. W. Steevens. NAVAL POLICY: With a Descrip- tion OF English and Foreign Navvies. By G. W. Steevens. Demy 8vo. 6s. This book is a description of the British and other more important navies of the world, with a sketch of the lines on which our naval policy might possibly be developed. It describes our recent naval policj', and shows what our naval force really is. A detailed but non-technical account is given of the instruments of modern warfare — guns, armour, engines, and the like — with a view to determine how far we are abreast of modern invention and modern requirements. An ideal policy is then sketched for the building and manning of oUr fleet ; and the last chapter is devoted to docks, coaling-stations, and especially colonial defence. ' An extremely able and interesting work.' — Daily Chronicle. W. E. Gladstone. THE SPEECHES AND PUBLIC AD- DRESSES OF THE RT. HON. W. E. GLADSTONE, M.P. Edited by A. W. Hutton, M.A., and H. J. Cohen, M.A. With Portraits, '^vo. Vols. IX. and X. \2s, 6d. each. J. Wells. OXFORD AND OXFORD LIFE. By Members of the University. Edited by J. Wells, M.A., Fellow and Tutor of Wadham College. Croivn 8vo. 3^. 6d. ' We congratulate Mr. Wells on the production of a readable and intelligent account of Oxford as it is at the present time, written by persons who are possessed of a close acquaintance with the system and life of the JJniytrsity.'—Ai/iencrum. L. Whibley. GREEK OLIGARCHIES : THEIR ORGANISA- TION AND CHARACTER. By L. Wiiiblev, M.A., Fellow of Pembroke College, Cambridge. Crown Zvo. 6s. ' An exceedingly useful handbook : a careful and well-arranged study of aii obscure subject.' — Tiiucs. ' Mr. Whibley is never tedious ur pedantic' — Fall Mall Gazette. Messrs. Methuen's List 21 L. L. Price. ECONOMIC SCIENCE AND PRACTICE, By L. L. Price, M.A., Fellow of Oriel College, Oxford. Crown Svo. 6s. ' The book is well written, giving evidence of considerable literary ability, and clear mental grasp of the subject under consideration. ' — ^Fi^j-^'grw Morning News. C. F. Andrews. CHRISTIANITY AND THE LABOUR QUESTION. By C. F. Andrews, B.A. Crown ^vo. 2s. 6J. ' A bold and scholarly survey.' — Speaker. J. S. Shedlock. THE PIANOFORTE SONATA: Its Origin and Development. By J. S. Shedlock. Crown Svo. 5^. 'This work should be in the possession of every musician and amateur, for it not only embodies a concise and lucid history ot the origin ofoneof the most im- portant forms of musical composition, but, by reason of the painstaking research and accuracy of the author's statements, it is a very valuable work for reference.' — A theHCB7i}n. E.M. Bowden. THE EXAMPLE OF BUDDHA: Being Quota- tions from Buddhist Literature for each Day in the Year. Compiled by E. M. Bowden. With Preface by Sir Edwin Arnold. Third Editiofi. iGf/io. 2s. 6d. Science Freudenreich. DAIRY BACTERIOLOGY. A Short Manual for the Use of Students. By Dr. Ed. von Freudenreich. Translated from the German by J. R. Ainsworth Davis, B.A., F.C.P. Crown Svo. 2s.6d. Chalmers Mitchell. OUTLINES OF BIOLOGY. By P. Chalmers I\Iitchell, M.A., F.Z.S. Fully Illustrated. Crown %vo. 6s. A text-book designed to cover the new Schedule issued by the Roj-al College of Physicians and Surgeons. G.Massee. A MONOGRAPH OF THE MYXOGASTRES. By George Massee. With 12 Coloured Plates. Royal Svo. iSs.net. 'A work much in advance of any book in the language treating of this group of organisms. It is indispensable to every student of the Myxogastres. The coloured plates deserve high praise for their accuracy and execution.'— iV«^Krvo. I'^s. * Learned and reverent : lucid and well arranged.' — Record. 'Accurate, well ordered, and judicious.' — National Observer. ' A clear and remarkably full account of the main currents of speculation. Scholarly precision . • . genuine tolerance . . , intense interest in his subject — are Mr. Ottley's merits, ' — Guardiati. F. B. Jevons. AN INTRODUCTION TO THE HISTORY OF RELIGION. By F. B. Jevons, M.A., Litt.D., Principal of Bishop Flatfield's Hall. Demy Svo. los. 6d. Mr. F. B. Jevons' 'Introduction to the History of Religion' treats of early religion, from the point of vaew of Anthropology and Folk-lore ; and is the first attempt that has been made in any language to weave together the results of recent investigations into such topics as S^'mpathetic Magic, Taboo, Totemism, Fetishism, etc., so as to present a systematic account of the growth of primitive religion and the development of early religious institutions, ' Dr. Jevons has written a notable work, and we can strongly recommend it to the serious attention of theologians, anthropologists, and classical scholars.' — 3fan- Chester Gtiardian. ' The merit of this book lies in the penetration, the singular acuteness and force of the author's judgment. He isat once critical and luminous, at once just and suggestive. It is but rarely that one meets with a book so comprehensive and so thorough as this, and it is more than an ordinary pleasure for the reviewer to welcome and recommend it. Dr. Jevons is something more than an historian of primitive belief— he is a philosophic thinker, who sees his subject clearly and sees it whole, whose mastery of detail is no less complete than his view of the broader aspects and issues of his subject is convincing.' — BirmingJiam Post. S. R. Driver. SERMONS ON SUBJECTS CONNECTED WITH THE OLD TESTAMENT. By S. R. Driver, D.D., Canon of Christ Church, Regius Professor of Hebrew in the Uni- versity of Oxford. Crown Svo. 6s. * A welcome companion to the author's famous ' Introduction.' No man can read these discourses without feeling that Dr. Driver is fully alive to the deeper teaching of the Old Testament.' — Guardian. T. K. Cheyne. FOUNDERS OF OLD TESTAMENT CRITI- CISM : Biographical, Descriptive, and Critical Studies. By T. K. Cheyne, D.D., Oriel Professor of the Interpretation of Holy Scrip- ture at Oxford. Large crown Svo. 'js. 6d. This book is a historical sketch of O. T. Criticism in the form of biographical studies from the days of Eichhorn to those of Driver and Robertson Smith. ' A very learned and instructive work.' — Times. C.H.Prior. CAMBRIDGE SERMONS. Edited by C.H. Prior, M.A., Fellow and Tutor of Pembroke College. Crown Svo. ds. A volume of sermons preached before the University of Cambridge by various preachers, including the Archbishop of Canterbury and Bishop Westcott. A representative collection. Bishop Westcott's is a noble sermon.' — Guardian. E. B. Layard. RELIGION IN BOYHOOD. Notes on the Religious Training of Boys. With a Preface by J. R. Illing- WORTH. By E. B. Layard, M.A. \Smo. \s. 24 Messrs. Metiiuen's List W. Yorke Faussett. THE DE CATECHIZANDIS RUDIBUS OF ST. AUGUSTINE. Edited, with Introduction, Notes, etc., by W. Yorke Faussett, M.A., late Scholar of Balliol Coll. Crown 8vo. ^s. 6d. An edition of a Treatise on the Essentials of Christian Doctrine, and the best methods of impressing them on candidates for baptism. 'Ablj' and judiciously edited on the same principle as the ordinary Greek and Latin texts.' — Glasgow Herald. 2Det3Dtional ©oofe^. With Full-page Illustrations. Fcap. 8vo. Buckra?n. 3^. 6d. Padded morocco^ 55. THE IMITATION OF CHRIST. By Thomas A Kempis. With an Introduction by Dean Farrar. Illustrated by C. M. Gere, and printed in black and red. Second Edition. 'Amongst all the innumerable English editions of the "Imitation," there can have been few which were prettier than this one, printed n strong and handsome type, with all the glory of red initials.' — Glasgow Herald, THE CHRISTIAN YEAR. By John Keble. With an Intro- duction and Notes by W. Lock, D.D., Warden of Keble College, Ireland, Professor at Oxford. Illustrated by R. Anning Bell. ' The present edition is annotated with all the care and insight to be expected from Mr. Lock. The progress and circumstances of its composition are detailed in the Introduction. There is an interesting Appendix on the MSS. of the "Christian Year," and another giving the order in which the poems were written. A "Short Analysis of the Thought" is prefixed to each, and any difficulty in the text is ex- plained in a note.' — Guardian. ' The most acceptable edition of this ever-popular work.' — Globe. 3/6 Leaders of Religion Edited by H. C. BEECHING, M. A. With Portraits, crown 8zv. A series of short biographies of the most prominent leaders of religious life and thought of all ages and countries. The following are ready — CARDINAL NEWMAN. By R. H. HUTTON. JOHN WESLEY. By J. H. Overton, M.A. BISHOP WILBERFORCE. By G. W. Daniel, M.A. CARDINAL MANNING. By A. W. HuTTON, M.A. CHARLES SIMEON. By H. C. G. MOULE, M.A. JOHN KEBLE. By Walter Lock, D.D. THOMAS CHALMERS. By Mrs. Oliphant. LANCELOT ANDREWES. By R. L. Ottley, M.A. AUGUSTINE OF CANTERBURY. By E. L. CUTTS, D.D. WILLIAM LAUD. By W. H. HuTTON, B.D. Messrs. Methuen's List 25 JOHN KNOX. By F. M'CUNN. JOHN HOWE. By R. F. HORTON, D.D. BISHOP KEN. By F. A. Clarke, M.A. GEORGE FOX, THE QUAKER. By T. Hodgkin, D.C.L. Other volumes will be announced in due course. Fiction SIX SHILLING NOVELS Marie Corelli's Novels Crown Svo. 6s. each. A ROMANCE OF TWO W^ORLDS. Sixteenth Ediiio?i. VENDETTA. Thirteenth Edition. T H E L M A. Seventeenth Edition. ARDATH. Tenth Editimi. THE SOUL OF LILITH Nijith Edition. WORMWOOD. Eighth Edition. BARABBAS : A DREAM OF THE WORLD'S TRAGEDY. Thi)-ty-first Edition. ' The tender reverence of the treatment and the imaginative beauty of the writing have reconciled us to the daring of the conception, and the conviction is forced on us that even so exalted a subject cannot be made too familiar to us, provided it be presented in the true spirit of Christian faith. The amplifications of the Scripture narrative are often conceived with high poetic insight, and this "Dream of the World's Tragedy " is, despite some trifling incongruities, a lofty and not inade- quate paraphrase of the supreme climax of the inspired narrative.' — Dublin Review. THE SORROW^S OF SATAN. Thirty-sixth Edition. ' A very powerful piece of work. . . . The conception is magnificent, and is likely to win an abiding place within the memory' of man. . . . The author has immense command of language, and a limitless audacity. . . . This interesting and re- markable romance will live long after much of the ephemeral literature of the day is forgotten. ... A literary phenomenon . . . novel, and even sublime.' — W. T. Stead in the Review of Reviews. Anthony Hope's Novels Crown ?)Vo. 6s. each. THE GOD IN THE CAR. Sevmih Edition. . _ ' A very remarkable book, deserving of critical analysis impossible within our limit ; brilliant, but not superficial ; well considered, but not elaborated ; constructed with the proverbial art that conceals, but yet allows itself to be enjoyed by readers to whom fine literarj' method is a keen pleasure.'— The World. A CHANGE OF AIR. Fourth Edition. 'A graceful, vivacious comedy, true to human nature. The characters are traced with a masterly hand.' — Times. A MAN OF MARK. Fourth Edition. ' Of all Mr. Hope's books, "A Man of Mark " is the one which best compares with ' ' The Prisoner of Zenda." ' — National Observer. 26 Messrs. Methuen's List THE CHRONICLES OF COUNT ANTONIO. Third Editum. 'It is a perfectly enchanting story of love and chivalry, and pure romance. The outlawed Count is the most constant, desperate, and withal modest and tender of lovers, a peerless gentleman, an intrepid fighter, a very faithful friend, and a most magnanimous foe. ' — Guardian. PHROSO. Illustrated by H. R. MiLLAR._ Third Edition. ' The tale is thoroughly fresh, quick with vitality, stirring the blood, and humorously, (l2ish.\x\g\yto\A.'— St. James s Gazette. ' A story of adventure, every page of which is palpitating with action and excitement.' —Speaker. ' From cover to cover " Phroso " not only engages the attention, but carries the reader in little whirls of delight from adventure to adventure." — Academy. S. Baring Gould's Novels Crozvn 2>vo. 6s. each. 'To say that a book is by the author of " ISIehalah" is to imx)ly that it contains a story cast on strong lines, containing dramatic possibilities, vivid and sympathetic descriptions of Nature, and a wealth of ingenious imagery.' — Speaker. ' That whatever Mr. Baring Gould writes is well worth reading, is a conclusion that may be very generally accepted. His views of life are fresh and vigorous, his language pointed and characteristic, the incidents of which he makes use are striking and original, his characters are life-like, and though somewhat excep- tional people, are drawn and coloured with artistic force. Add to this that his descriptions of scenes and scenery are painted with the loving eyes and skilled hands of a master of his art, that he is alwaj'S fresh and never dull, and under such conditions it is no wonder that readers have gained confidence both in his power of amusing nnd satisfying them, and that year by j'ear his popularity widens. ' — Court Circular. ARM I NELL : A Social Romance. Fourth Edii:o7i. URITH : A Story of Dartmoor. Fifth Edition, ' The author is at his best.'— T/w^j. IN THE ROAR OF THE SEA, Sixth Edition. 'One of the best imagined and most enthralling stories the author has produced. — Saturday Review. MRS. CURGENVEN OF CURGENVEN. Fourth Editio7i. ' The swing of the narrative is splendid.' — Sussex Daily Neivs. CHEAP JACK ZITA. Fourth Edition. ' A powerful drama of human passion.' — IVesttninster Gazette. 'A story worthy the author.' — National Observer. THE QUEEN OF LOVE. Fourth Edition. ' You cannot put it down until you have finished it.' — Punch. ' Can be heartily recommended to all who care for cleanly, energetic, and interesting fiction.' — Sussex Daily News. KITTY ALONE. Fourth Edition. ' A strong and original story, teeming with graphic description, stirring incident, and, above all, with vivid and enthralling human interest.'— Daily Telegraph. NOEMI : A Romance of the Cave-Dvvellers. Illustrated by R. CaTON WOODVILLE. Third Edi(io7l. ' " Nocmi " is as excellent a tale of fighting and adventure as one may wish to meet. The narrative also runs clear and sharp as the Loire itself.' — Fail Mall Gazette. 'Mr. Baring Gould's powerful story is full of the strong lights and shadows and vivid colouring to which he has accustomed us.' — Standard. Messrs. Methuen's List 27 THE BROOM- SQUIRE. Illustrated by Frank Dadd. Fourth Edition. ' A strain of tenderness is woven through the web of his tragic tale, and its atmosphere is sweetened by the nobility and sweetness of the heroine's character.' — Daily Neivs. * A story of exceptional interest that seems to us to be better than anything he has written of late.' — Speaker. THE PENNYCOMEQUICKS. Third Edition, DARTMOOR IDYLLS. 'A book to read, and keep and read again ; for the genuine fun and pathos of it will not early lose their effect. ' — Vanity Fair. GUAVAS THE TINNER. Illustrated by Frank Dadd. Scco?id Edition. ' Mr. Baring Gould Is a wizard who transports us into a region of visions, often lurid and disquieting, but always full of interest and enchantment.' — Spectator, ' In the v/eirdness of the story, in the faithfulness with which the characters are depicted, and in force of style, it closely resembles " Alehalah. '" — Daily TelegrapJi. ' There is a kind of flavour about this book which alone elevates it above the ordinary novel. The story itself has a grandeur in harmony with the wild and rugged scenery which is its setting/ — A thenceiini. Gilbert Parker's Novels Crown %vo. 6s. each. PIERRE AND HIS PEOPLE. Fourth Edition. ' Stories happily conceived and finely executed. There is strength and genius in Mr. Parker's style.' — Daily Telegraph. MRS. FALCHION. Fourth Edition. ' A splendid studj' of character.' — Athencsutn. ' But little behind anything that has been done by any writer of our time. ' — Pall Mall Gazette. 'A verj' striking and admirable novel.' — St. James's Gazette. THE TRANSLATION OF A SAVAGE. ' The plot is original and one difficult to work out ; but Mr. Parker has done it with great skill and delicacy. The reader who is not interested in this original, fresh, and well-told tale must be a dull person indeed.' — Daily Chronicle. THE TRAIL OF THE SWORD. Fifth Edition. 'Everybody with a soul for romance will thoroughly enjoy "The Trail of the Sword." ' — St. Ja7itess Gazette. ' A rousing and dramatic tale. A book like this, In which swords flash, great sur- prises are undertaken, and daring deeds done, in which men and women live and love in the old straightforward passionate way, is a joy inexpressible to the re- viewer.' — Daily Chronicle. WHEN VALMOND CAME TO PONTIAC : The Story of a Lost Napoleon. Fourth Edition. ' Here we find romance — real, breathing, living romance, but it runs flush with our own times, level with our own feelings. The character of Valmond is drawn un- erringly ; his career, brief as it is, is placed before us as convincingly as history itself. "The book must be read, we may say re-read, for any one thoroughly to appreciate Mr. Parker's delicate touch and innate sympathy with humanity.' — Pall Mall Gazette. 'The one work of genius which 1895 has as yet produced.' — A^eiv Age. AN ADVENTURER OF THE NORTH: The Last Adven- tures of ' Pretty Pierre.' Second Edition. 'The present book is full of fine and moving stories of the great North, and it will add to Mr. Parker's already high reputation.'— G/rti-^^w Herald. 28 Messrs. Methuen's List THE SEATS OF THE MIGHTY. Illustrated. Eighth Edition. ' The best thing he has done ; one of the best things that any one has done lately.' — St. Javiea's Gazette. ' Mr. Parker seems to become stronger and easier with every serious novel that he attempts. . . , In " The Seats of the Mighty " he shows the matured power which his former novels have led us to expect, and has produced a really fine historical novel. . . . Most sincerely is Mr. Parker to be congratulated on the finest novel he has yet written.' — Athentpum. 'Mr. Parker's latest book places him in the front rank of living novelists. "The Seats of the Mighty" is a great book.' — Black and White. 'One of the strongest stories of historical interest and adventure that we have read for many a daj'. . . . A notable and successful book.' — Speaker. Conan Doyle. ROUND THE RED LAMP, By A. Conan Doyle, Author of ' The White Company,' ' The Adventures of Sherlock Hohnes,' etc. Fifth Edition. Crotvn 2>vo. 6s. ' The book is, indeed, composed of leaves from life, and is far and away the best view that has been vouchsafed us behind the scenes of the consulting-room. It is very superior to " The Diary of a late Physician." ' — Illustrated London JVews. Stanley Weyman. UNDER THE RED ROBE. By Stanley Weym AN, Author of ' A Gentleman of France. ' With Twelve Illus- trations by R. Caton Woodville. TiveJfth Edition. Crown %vo. 6s. 'A book of which we have read every word for the sheer pleasure of reading, and which we put down with a pang that we cannot forget it all and start again.' — Westtninstcr Gazette. ' Every one who reads books nt all must read this thrilling romance, from the first page of which to the last the breathless reader is haled along. An inspiration of " manliness and courage." ' — Daily Chronicle. Lucas Malet. THE WAGES OF SIN. By Lucas Malet. Thirteejith Edition. Crown '^vo. 6$. Lucas Malet. THE CARISSIMA. By Lucas Malet, Author of 'The Wages of Sin,' etc. Third Edition. Crown Svo. 6s. Arthur Morrison. TALES OF MEAN STREETS. By Arthur Morrison. Eojtrth Edition. Croiim 8vo. 6s. ' Told with consummate art and extraordinary detail. He tells a plain, unvarnished tale, and the very truth of it makes for l)eauty. In tlie true humanity of the book lies its justification, the permanence of its interest, and its indubitable triumph.' — A thentpunt. ' A great book. The author's method is amazingly effective, and produces a thrilling sense of reality. I'he writer lays upon us a master hand. The book is simply appalling and irresistil)le in its interest. It is humorous also ; without humour it would not make the mark it is certain to make.' — World. Arthur Morrison. A CHILD OF THE JAGO. By Arthur ]MoRRiSON. Third Edition. Croivn %vo. 6s. This, the first long story which Mr. ^Morrison has written, is like his remarkable ' Tales of Mean Streets,' a realistic study of East End life. ' The book is a masterpiece.' — Pall I\fall Gazette. 'Told with great vigour and powerful simplicity.' — AtJtettaum. Mrs. Clifford. A FLASH OF SUMMER. By Mrs. W. K. Cr.ir- FORD, Author of ' Aunt Anne,' etc. Second Edition. Crown Zvo. 6s. ' The story is a very sad and a very lif autiful one, exquisitely told, and enriched with many subtle touches of wise and tender insight. It will, undoubtedly, add to its author's reputation— already high — in the ranks of novelists.' — Speaker, Messrs. Methuen's List 29 Emily Lawless. HURRISH. By the Honble. Emily Law- less, Author of ' Maelcho,' etc. Fifth Edition. Crown ^vo. ds. A reissue of Miss Lawless' most popular novel, uniform with ' Maelcho.' Emily Lawless. MAELCHO : a Sixteenth Century Romance. By the Honble. Emily Lawless. Second Edition. Crown Zvo. (iS. ' A really great book.' — Spectator. 'There is no keener pleasure in life than the recognition of genius. Good work is commoner than it used to be, but the best is as rare as ever. All the more gladly, therefore, do we v.-elcome in " Maelcho " a piece of work of the first order, which we do not hesitate to describe as one of the most remarkable literary achievements of this generation. Miss Lawless is possessed of the very essence of historical genius.' — I\Ianchcsicr Guardian. J. H. Findlater. THE GREEN GRAVES OF BALGOWRIE. By Jane H. FiNDLATER. Third Edition. Crown Zvo. 6s. 'A powerful and vivid s\.oxy.' —Standard. ' A beautiful story, sad and strange as truth itself.' — Vanity Fair. ' A work of remarkable interest and originality.' — National Observer. ' A very charming and pathetic tale.' — Pall Mall Gazette. ' A singularly original, clever, and beautiful story.' — Guardian. ' " The Green Graves of Balgowrie" reveals to us a new Scotch writer of undoubted faculty and reserve force.' — Spectator. 'An exquisite idyll, delicate, affecting, and beautiful.' — Black and White. H. G. Wells. THE STOLEN BACILLUS, and other Stories. By H. G. Wells, Author of 'The Time Machine.' Crown Svo. 6s. ' The ordinary reader of fiction may be glad to know that these stories are eminently readable from one coverto the other, but they are more than that ; they are the impressions of a very striking imagination, which, it would seem, has a great deal within its reach.' — Saturday Review. H. G.Wells. THE PLATTNER STORY AND Others. By H. G. Wells. Second Edition. Croivn Svo. 6s. 'Weird and mysterious, they seem to hold the reader as by a magic spell.' — Scotstnan. 'Such is the fascination of this writer's skill that you unhesitatingly prophesy that none of the many readers, however his flesh do creep, will relinquish the volume ere he has read from first word to last.' — Black and iPhite. ' No volume has appeared for a long time so likely to give equal pleasure to the simplest reader and to the most fastidious critic' — Academy. ' Mr. Wells is a magician skilled in wielding that most potent of all spells — the fear of the unknown.' — Daily Telegraph. E. F. Benson. DODO : A DETAIL OF THE DAY. By E. F. Benson. Sixteenth Edition. Crown Zvo. 6s. ' A delightfully witty sketch of society.' — Spectator. ' A perpetual feast of epigram and paradox.' — Speaker. E. F. Benson. THE RUBICON. By E. F. Benson, Author of 'Dodo.' Fifth Edition. Crown Svo. 6s. ' An exceptional achievement ; a notable advance on his previous v/orV.'— National Observer. Mrs. Oliphant. SIR ROBERT'S FORTUNE. By Mrs. Oliphant. Crown Svo. 6s. ' Full of her own peculiar charm of style and simple, subtle chaxacter-painting comes her new gift, the delightful story before us. The scene mostly lies in the moors, and at the touch of the authoress a Scotch moor becomes a living thing, strong, tender, beaulii'ui, and changeful.' — Pall Mall Gazette. 30 Messrs. Methuen's List Mrs. Olipliant. THE TWO MARYS. 13y Mrs. Oliphant. Second Ediiio7i. Croivn Zvo. 6j-. V/.E.Norris. MATTHEW AUSTIN. By W. E. Norris, Author of ' iMademoiselle de Mcrsac,' etc. FoiD'th Edition. CrownZvo. 6s. "Matthew Austin" may safely be pronounced one of the most intellectually satis- factory and morally bracing novels of the current year.' — Daily Tclerraf'h. W. E. Norris. HIS GRACE. By W. E. Norris. Third Edition. Crown Zvo. 6s. ' Mr. Norris has drawn a really fine character in the Duke of Hurstbourne, at once unconventional and very true to the conventionalities of life.' — Atheticeum. W. E. Norris. THE DESPOTIC LADY AND OTHERS. By W. E. Norris. Crown Svo. 6s. ' A budget of good fiction of which no one will tire.' — Scotsman. W. E. Norris. CLARISSA FURIOSA. By W. E. Norris, Author of 'The Rogue,' etc. Crown Svo. 6s. ' One of Mr. Norris's very best novels. As a story it is admirable, as a. jt'u cE esprit it is capital, as a lay sermon studded with gems of wit and wisdom it is a model which will not, we imagine, find an efficient imitator.' — The World. 'The best novel he has written for some time: a story which is full of admirable character-drawing. ' — Tlie Standard. Robert Barr. IN THE MIDST OF ALARMS. By Robert Barr. Third Edition. Crozun ^vo. 6s. ' A book which has abundantly satisfied us by its capital humour,' — Daily Chronicle. 'ISIr. Barr has achieved a triumph whereof he has every reason to be proud.'— /"a// Mall Gazette. J. Maclaren Cobban. THE KING OF ANDAMAN : A Saviour of Society. By J. Maclaren Cobban. Crozvn Svo. 6s. ' An unquestionably interesting book. It would not surprise us if it turns out to be the most interesting novel of the season, for it contains one character, at least, who has in him the root of immortality, and the book itself is ever exhaling the sweet savour of the unexpected. . . . Plot is forgotten and incident fades, and only the really human endures, and throughout this book there stands out in bold and beautiful relief its high-souled and chivalric protagonist, James the Master of Hutcheon, the King of Andaman himself.' — Pall Mall Gazette. J. Maclaren Cobban. WILT THOU HAVE THIS WOMAN ? By J. M. Cobban, Author of ' The King of Andaman.' Crown Svo. 6s. ' Mr. Cobban has the true story-teller's art. He arrests attention at the outset, and he retains it to the and.'— Birmingham Post. H. Morrah. A SERIOUS COMEDY. By Herbert Morrah. Crown Svo. 6s. 'This volume is well worthy of its title. The theme has seldom beeu picocatcd with m'..re freshncas or more foico.' — .Scol^f/iuu. Messrs. Methuen's List 31 K. Morrali. THE FAITHFUL CITY. By Herbert Morrah, Author of 'A Serious Comedy.' Crown 8vo. 6s. ' Conveys a suggestion of welrdncss and horror, until finally he convinces and enthrals the reader with his mysterious savages, his gigantic tower, and his uncompromising men and v>-omen. This is a haunting, mysterious book, not without an element of stupendous grandeur.' — Athcnccnin, L. B. Walford. SUCCESSORS TO THE TITLE. By Mrs. Walford, Author of ' Mr. Smith,' etc. Second Edition. CrownSvo. 6s. ' The story is fresh and healthy from beginning to finish ; and our liking for the two simple people who are the successors to the title mounts steadily, and ends almost in respect.' — Scoisfuan. T. L. Paton. A HOME IN INVERESK. By T. L. Paton. Crown 8z^io. 6s. ' Mr. Corbett writes with immense spirit, and the book is a thoroughly enjoyable one in all respects. The salt of the ocean is in it, and the right heroic ring re- sounds through its gallant adventures.' — Speaker. L. Cope Cornford. CAPTAIN JACOBUS : A ROMANCE OF THE ROAD. By L. Cope Cornford. Illustrated. Crown^vo. 6s. ' An exceptionally good story of adventure and character.' — World. C. p. WoUey. THE OUEENSBERRY CUP. A Tale of Adventure. By Clive^'Phillips Wolley. Illustrated. Crown ^vo. 6s. ' A book which will delight boys : a book which upholds the healthy schoolboy code of morality.' — Scots niaji. L. Daintrey. THE KING OF ALBERIA. A Romance of the Balkans. By Laura Daintrey. Crown ^vo. 6s. ' Miss Daintrey seems to have an intimate acquaintance with the people and politics of the Balkan countries in which the scene of her lively and picturesque romance is laid.' — Glasgow He-raid. M. A. Owen. THE DAUGHTER OF ALOUETTE. By Mary A. Owen. Croivn %vo. 6s. A story of life among the American Indians. 'A fascinating story.' — Litcraty Jl'orld. Mrs. Pinsent. CHILDREN OF THIS WORLD. By Ellen F. Pinsent, Author of 'Jenny's Case.' Crozvn 8fi?. 6s. ^ ' INIrs. Pinsent's new novel has plenty of vigour, variety, and good writing. There are certainty of purpose, strength of touch, and clearness of vision.' — Aihcnteum. Clark Russell. MY DANISH SWEETHEART. By W. Clark Russell, Author of 'The Wreck of the Grosvenor,' etc. Illustrated. Fourth Edition. Crozvn Svo. 6s. G. Manville Fenn. AN ELECTRIC SPARK. By G. Manville Fenn, Author of ' The Vicar's Wife,' 'A Double Knot,' etc. Second Edition. Crown Svo. 6s, L. S. McChesney. UNDER SHADOW OF TPIE MISSION. By L. S. McChesney. Crown Svo. 6s. ' Those whose minds are open to the liner issues of life, who can appreciate graceful thought and refined expression of it, from them this volume will receive a welcome as enthusiastic as it will be based on critical knowledge.' — Church Times. Konald Ross. THE SPIRIT OF STORM. By Ronald Ross, Author of 'The Child of Ocean.' Crown %vo. 6s. A romaucc of the Sea. ' Weird, powerful, and impressive.'— i'/ac/t and White. Messrs. Methuen's List 33 R. Pryce. TIME AND THE WOMAN. By Richard Pryce. Second Edition. Crown Svo. 6s. Mrs. Watson. THIS MAN^S DOMINION. By the Author of ' A High Little World. ' Second Edition. Crown Zvo. 6s. Marriott Watson. DIOGENES OF LONDON. By H. B. Marriott Watson. Crown 8w. Btickram. 6s. M. Gilchrist. THE STONE DRAGON. By Murray Gil- christ. Crown Zvo. Buckram. 6s. ' The author's faults are atoned for by certain positive and admirable merits. The romances have not their counterpart in modern literature, and to read them is a unique experience.' — National Obscft'er. E. Dickinson. A VICAR'S WIFE. By Evelyn Dickinson. Crown Svo. 6s. E. M. Gray. ELS A. By E. M 'Queen Gray. Crozau Svo. 6s. 3/6 THREE-AND-SIXPENNY NOVELS Crown Svo. DERRICK VAUGHAN, NOVELIST. By Edna Lyall. MARGERY OF QUETHER. By S. Baring Gould. JACQUETTA. By S. Baring Gould. SUBJECT TO VANITY. By Margaret Benson. THE SIGN OF THE SPIDER. By Bertram Mitford. THE MOVING FINGER. By Mary Gaunt. JACO TRELOAR. By J. H. Pearce. THE DANCE OF THE HOURS. By 'Vera.' A WOMAN OF FORTY. By Esme Stuart. A CUMBERER OF THE GROUND. By Constance Smith. THE SIN OF ANGELS. By Evelyn Dickinson. AUT DIABOLUS AUT NIHIL. By X. L. THE COMING OF CUCULAIN. By Standish O'Grady. THE GODS GIVE MY DONKEY WINGS. By Angus Evan Abbott. THE STAR GAZERS. By G. Manville Fenn. THE POISON OF ASPS. By R. Orton Prowse. THE QUIET MRS. FLEMING. By R. Pryce. DISENCHANTMENT. By F. Mabel Robinson. THE SQUIRE OF W'ANDALES. By A. Shield. A REVEREND GENTLEMAN. By J. M. Cobban. 34 Messrs. Methuen's List A DEPLORABLE AFFAIR. By W. E. Norris. : A CAVALIER'S LADYE. By Mrs. Dicker. THE PRODIGALS. By Mrs. Oliphant. THE SUPPLANTER. By P. Neumann. A MAN WITH BLACK EYELASHES. By H. A. KENNEDY. A HANDFUL OF EXOTICS. By S. Gordon. AN ODD EXPERIMENT. By Hannah Lynch. 2/6 HALF-CROWN NOVELS A Series of Novels by popular AtUhors. 1. HOVENDEN, V.C. By F. Mabel Robinson. 2. ELI'S CHILDREN. By G. Manville Fenn. 3. A DOUBLE KNOT. By G. Manville Fenn. 4. DISARMED. By M. Betham Edwards. 5. A MARRIAGE AT SEA. By W. Clark Russell. 6. IN TENT AND BUNGALOW. By the Author of ' Indian Idylls.' 7. MY STEWARDSHIP. By E. M'Queen Gray. 8. JACK'S FATHER. By W. E. NoRRis. 9. JIM B. lo. THE PLAN OF CAMPAIGN. By F. Mabel Robinson. ir. MR. BUTLER'S WARD. By F. Mabel Robinson. 12. A LOST ILLUSION. By Leslie Keith. Lynn Linton. THE TRUE HISTORY OF JOSHUA DAVID- SON, Christian and Communist. By E, Lynn Linton. Eleventh Edition. Post Svo. is. Books for Boys and Girls olA A Series of Books by well-kno'iun Authors^ well illustrated. ^\ 1. THE ICELANDER'S SWORD. By S. Baring Gould. 2. TWO LITTLE CHILDREN AND CHING. By Edith E. CUTIIELL. 3. TODDLEBEN'S HERO. By M. M. Blake. 4. ONLY A GUARD-ROOM DOG. By Edith E. Cuthell. 5. THE DOCTOR OF THE JULIET. By Harry Colling- WOOD. 6. MASTER ROCKAFELLAR'S VOYAGE. By W. Clark RUSSKLL. 7. SYD BELTON : Or, The Boy who would not go to Sea. Cy G. Manville Fenn. Messrs. Methuen's List 35 3/6 The Peacock Library A Series of Books for Girls by well-known Authors, handsomely bound in bine and silver, and zvell illustrated. 1. A PINCH OF EXPERIENCE. By L. B. Walford. 2. THE RED GRANGE. By Mrs. Molesworth. 3. THE SECRET OF MADAME DE MONLUC. By the Author of ' Mdle Mori.' 4. DUMPS. By Mrs. Parr, Author of 'Adam and Eve.' 5. OUT OF THE FASHION. By L. T. Meade. 6. A GIRL OF THE PEOPLE. By L. T. Meade. 7. HEPSY GIPSY. By L. T. Meade, is. 6d. 8. THE HONOURABLE MISS. By L. T. Meade. 9. MY LAND OF BEULAH. By Mrs. Leitii Adams. University Extension Series A series of books on historical, Hterary, and scienlific subjects, suitable for extension students and home-reading circles. Each volume is com- plete in itself, and the subjects are treated by competent writers in a broad and philosophic spirit. Edited by J. E. SYMES, M.A., Principal of University College, Nottingham. Crown Svo. Price {with some exceptions) 2s. 6d. The following volumes are ready : — THE INDUSTRIAL HISTORY OF ENGLAND. By H. de B. Gibbins, D.Litt., M.A,, late Scholar of Wadham College, Oxen., Cobden Prizeman. Fifth Editio7i, Revised. With Maps and Plans, y. 'A compact and clear story of our industrial development. A study of this concise but luminous book cannot fail to give the reader a clear insight into the principal phenomena of our industrial history. The editor and publishers are to be congrat- ulated on this first volume of their venture, and we shall look with expectant interest for the succeeding volumes of the series.' — University Extension Journal, A HISTORY OF ENGLISH POLITICAL ECONOMY. By L. L. PmCE, M.A., Fellow of Oriel College, Oxon. Second Edition. PROBLEMS OF POVERTY : An Inquiry into the Industrial Conditions of the Poor. By J. A. HOBSON, M.A. Third Edition. VICTORIAN POETS. By A. Sharp. THE FRENCH REVOLUTION. By J. E. Sy^IES. M.A. PSYCHOLOGY, By F. S. Granger, M.A. 36 Messrs. Methuen's List THE EVOLUTION OF PLANT LIFE : Lower Forms. By G. TvLvssee. IVi^/i Illustratiotis. AIR AND WATER. Professor V. B. Lewes, M.A. Ilhistrated. THE CHEMISTRY OF LIFE AND HEALTH. By C. W. KiMMixs, M.A. Illustrated, THE MECHANICS OF DAILY LIFE. By V. P. Sells, M.A. Illustraied. ENGLISH SOCIAL REFORMERS. H. DE B. Gibbins, D.Litt.. M.A. ENGLISH TRADE AND FINANCE IN THE SEVENTEENTH CENTURY. By W. A. S. Hewins, B.A. THE CHEMISTRY OF FIRE. The Elementary Principles of Chemistry. By M. M. Pattison Muir, M.A. Ilhistrated. A TEXT-BOOK OF AGRICULTURAL BOTANY. By M. C. Potter, M.A.. F.L.S. Illustrated, y. 6d. THE VAULT OF HEAVEN. A Popular Introduction to Astronomy. By R. A. Gregory. With numerous Illustratlotis. METEOROLOGY. The Elements of Weather and Climate. By H. N. Dickson, F.R.S.E., F.R. Met. Soc. Illustrated. A MANUAL OF ELECTRICAL SCIENCE. By George J. Burch, M.A. With numerous I llustratio?is. 3?. THE EARTH. An Introduction to Physiography. By Evan Small, IvI A. Illustrated. INSECT LIFE. By F. W. Theobald, M.A. Illustrated. ENGLISH POETRY FROM BLAKE TO BROWNING. By W. M. Dixon, M.A. ENGLISH LOCAL GOVERNMENT. By E. Jenks, M.A., Professor of Law at University College, Liverpool. THE GREEK VIEW OF LIFE. By G. L. Dickinson, Fellow of King's College, Cambridge. Social Questions of To-day Edited by H. de B. 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