;lements of logic \ s By CARDINAL MERCK Class _£ Book._ : CopyrigM^ .. COPYRIGHT DEPOSm Digitized by the Internet Archive in 2011 with funding from The Library of Congress http://www.archive.org/details/elementsoflogicOOmerc ELEMENTS OF LOGIC BY His Eminence Cardinal Mercier -*- THE THIRD EDITION Translated by EWAN MACPHERSON * NEW YORK THE MANHATTANYTLLE PRESS 1912 y\s V 2ftbU ©natal Remigius Lafort, D.D. Censor imprimatur John Cardinal Farley Archbishop of New York LC Control Number tmp96 026019 Copyright 1912 The Manhattanville Press o I \'<>\Y INTRODUCTION 1. Definition of Logic. — Logic is the systematic study of the order to be observed in judging, reasoning, and other processes of thought in order to arrive at the knowledge of truth. This' definiti< >n sh< iws us : ( 1 ) the materials (material cause) of the logical order; (2) their elaboration (formal cause) ; (3) the purpose of this elaboration (final cause). 2. Materials of Logical Order. — In some sense, these materials are acts of the mind, like apprehension, judgment, ratiocination (reasoning) ; but strictly speaking, only apprehensions are the material object of logical order (3). (1) By apprehension the mind represents to itself one thing or many things, without either affirming or denying anything. Concepts, the product of apprehension, are expressed by names or terms. (2) To establish a relation of identity or non-identity, of agree- ment or non-agreement, between the objects of two concepts, in affirming or denying one object of another is to judge. A judg- ment is expressed in a proposition. (3) To reason is to combine two or more judgments so as to form a new one. The complete ordinary expression of this simplest exercise of reasoning is the syllogism. 3. The Formal Cause of the Logical Order. — The formal object of logic, or the point of view from which logic regards the acts of the mind, is their adaptability to certain processes of thought which are called either particular sciences or philosophy. These processes imply stages. The mind must grasp the numer- ous aspects of reality one after another before co-ordinating the fragmentary explications. Judgment is the first step in com- bining ideas; judgments in their turn become the materials of reasoning; an isolated piece of reasoning does not suffice to produce adequate knowledge of things, but several reasonings become materials of a scientific system. This rational arrange- ment of ideas constitutes the logical order properly so called : ""the order which reason constitutes for its own acts". 3 .__: 4 LOGIC ■ 4. Difference between Psychology and 1 _,xC. — Many differ- ent sciences may be concerned with one and the same subject, if they study different properties in it, and, consequently, consider it from different points of view. They are then said to have a common (that is, undetermined) object, but each has its own formal (or determined) object. Psychology, too, has in part for its (material) object the act of human reason, but it does not study them under the same aspect (formal object) as logic does. Psychology sees in them vital acts, of which it seeks the nature and origin. Logic considers them in so far as they are cognitions of objects, objective representations, abstract and universal, fur- nishing the matter of the relations which reason formulates in judgments and reasonings, and arranges in a scientific system. In psychology, as in all the sciences of the real, order is the necessary condition of science; but logic has this order for its object. Its proper object is the form itself of this scientific con- struction. 5. Final Cause of Logical Order. — The systematization of the .process of reasoning has an ulterior aim: to make our knowledge true. Before explaining how logic directs its operations towards the true, it must be recalled that truth and error are qualities of the judgment, and not of the concept. As long as we merely speak of some one object by itself — e. g., the sun or a chimera — no one can say that we speak truly or falsely. Truth or error belongs to the statement that the sun exists, that the chimera exists. 1 Now, how can a science, logic, lead us to the knowledge of the truth? Evidently, logic could not in this sense supply the place of all the particular sciences. Each science enlightens the mind about the particular object with which it concerns itself; and consequently, anyone who had studied all of them would be marvellously equipped for always forming true judgments. But, besides this initiation into the whole of truth by the suc- cessive and collective study of the particular sciences, there is an initiation of another kind, viz., the preparation afforded by a more general science. Thought naturally proceeds from the simple to 1 See General Criteriology, n°. 6. INTRODUCTION 5 the complex. Now simplicity and universality always go to- gether in our knowledge. The most general sciences, then, are those the object of which is the most simple and, for that reason, best enables us to comprehend the more complex objects to which it is applicable. ■Logic is a general science in the sense that ii regulates the con- tent of all other sciences and subjects them to its laws in their construction. Its object, of extreme simplicity and boundless in extent, is the being of reason. 6. Difference between Logic and Metaphysics. — Another science, having all being for its object, also deserves to be called a general science, because it rules all knowledge: this is meta- physics. Metaphysics and logic are both concerned with all being (common material object), but under different aspects (proper formal object). The object of metaphysics is real being consid- ered formally in its real quiddity, invested with real attributes. Logic has for its object the same being, formally considered in its mental objectivity, invested with attributes of reason which it acquires in thought and in virtue of thought. Everything real (existing or possible) is intelligible. Now the real, when it becomes the object of a mental conception, inevita- bly participates in the attributes which are inherent in the exer- cise of thought: as a mental object, it becomes abstract and uni- versal. Between abstract, universal objects relations are estab- lished which under the concrete and particular conditions of ex- istent things are impossible : such a mental object becomes the attribute of another object of thought which plays the part of subject in regard to the former; the content and extension of ideas give rise to relations of identity or of exclusion; judgments are produced, chains of reasoning are forged, and all the while the material of these various intellectual operations is being, not real being, independent of thought, but the being of reason, i. e., being under the aspect and with the characteristics which mental conception communicates to it. Metaphysics is the universal science of the real. Logic is the science of the science of the real. 1 1 Tin* relations considered by this philosophical discipline are not the ontological relations upon which the attention of the mind falls im- 6 LOGIC 7. Is Logic to be Considered a Science or an Art? — Is logic a speculative or. a practical science? Speculative science stops at the knowledge of its object; practical science makes that knowl- edge subservient to an ulterior action or work. "The end of the speculative is truth ; the end of the operative, or practical, is ac- tion." The logician does not study acts of thought merely for the disinterested pleasure of knowing their co-ordination; he puts his science to the ulterior use of directing mental operations. In this sense some hold, and with reason, that logic is a practical science. — Others, taking a higher point of view, say that logic is a spec- ulative science, because the direction of mental operations is itself subordinate to the knowledge of truth. St. Thomas takes this view when he says : ' "In speculative matters the rational dialectic science is one thing . . . the demonstrative, another." 1 Logic is also an art, if by this we understand a body of practi- cal rules, for the guidance of action. 2 mediately, the prima: intentiones, objects of a first abstraction, but the logical relations springing from the combination of- abstract objects to which the reason reflecting returns, sccundce intentiones, objects of second abstraction. 1 Summa Theol, 2a 2* q. 51, art. 2, ad 3. 2 "Other animals", he says, "are prompted to their acts by a certain natural instinct, but man is directed in what he does by the judgment of his reason. For this reason various arts serve for the easy and orderly execution of human acts. For an art appears to be nothing else but a fixed disposition of reason by which human acts arrive at their due end by way of calculated means. Now reason not only can direct the acts of the subordinate parts, but is also adapted to direct its own function. For it is the property of the intellective part to reflect upon itself : the intellect understands itself, and in like manner the reasoning faculty can reason about its own act. As, therefore, the art of building or of car- pentry comes from the fact that the reasoning faculty reasons about the act of the hand, and man is thereby enabled to perform acts of this kind with ease and with well ordered effort, so, also, there must be some art by which the act of the reason itself may be directed, by zuhich man may proceed easily and correctly in the very act of reasoning. And this is the art of logic, i. e., the rational science. Nor is it rational only because it is according to reason, which is a common characteristic of all arts, but also because it deals with the very act of the reason as its proper matter. And therefore it seems to be the art of arts, because it directs us in the act of the reason, from which act all acts proceed." Post. Analyt., lect. I. INTRODUCTION 7 8. Divisions of Logic. — (1) It is usual to divide logic into two branches : formal and real logic. This division, which is of rela- tively recent date, is very questionable: (a) It is obviously inspired by certain arbitrary theories of Kant's philosophy. 1 (b) The questions ordinarily discussed in real logic constitute for us the object of a treatise which comes next after psychology, and which we call critcriology (science of the criterion of truth and certitude), or analysis of certain knowledge. (2) Formal logic is generally divided into three parts, treating respectively of apprehension, of judgment, and of reasoning. This division, which is unimpeachable, is borrowed from the ma- terial object of logic. Without rejecting it, we prefer: (3) Another division, which squares better with the general distribution of every philosophic study 2 and is inspired by the study of logical order by its four causes, efficient, material, formal and final.'-' 1 The study of the efficient cause of logic belongs, properly speak- ing, to psychology. Here it forms the object of a Preliminary Chapter {Chap. I). The First Part of the treatise on logic will have for its object concepts and terms, the materials of logical order : The Material Cause of logical order (Chap. II). The Second Part will have for its object the arrangement of these materials, their deliberate disposition in judgments, reason- ing, system, to secure the knowledge of truth : Formal Cause of logical order (Chap. III). A concluding chapter will have for its object the employment of rational order in the service of science and philosophy: Final Cause of logical order (Chap. IV). 4 1 See Critcriology, n°. 42. 2 Ci. the beginning of an opusculum in logic reckoned among the works of St. Thomas: De totius Logics Aristotclis Summa. Op. XLIV, Procemium. Ed. Parm. 3 Cf. General Metaphysics, fourth part. 4 These four causes of logical order are mentioned in the definition of logic [I] and in the text of St. Thomas: Logic is the "art by which the act of the reason itself [material cause] may he directed [formal cause], by which man [efficient cause] may proceed easily and correctly in the very act of reasoning [final cause]." CHAPTER I The Efficient Cause of Logical Order 9. Principles and Nature of the Operations of Reason. — The remote principle of the operations of reason is the human sub- stance composed of body and soul ; the proximate, or immediate, principle is the intellectual faculty. 1 Psychology teaches us that every act has its origin in the senses. While the material thing, which is the object of our sen- sations, is always determinate, made of particular matter, en- dowed with particular properties, the object of the concept is abstract and universal, that is to say, is considered apari from the particular attributes which really belong to it in nature (abstra- here, to consider separately), and it thereby becomes universal, or applicable to an indefinite number of individual subjects. This bell, which I see and touch, is made of bronze, it is round in shape, it gives a pleasant sound, it is there on my desk at this moment as I look at it. All this is determinate. Now I am able to think of a bell which abstracts from all these peculiarities, and which will serve to represent to me, at least imperfectly, all bells of whatsoever material they may be made, whatsoever may be their peculiarities of shape or of tone, whatsoever the position in space or the moment of time in which they may exist. 10. Multiplicity of the Operations of Reason. Their Funda- mental Identity. — All the operations of reason — apprehension, judgment, and reasoning — are at bottom identical; they consist in the intuition that something is {quod quid est), but they never- theless present different accidental characters which it is of in- terest to determine. I. Apprehension assumes many formalities. (1) When the mind considers an object independently of its surroundings, the action is called attention. (2) The attention is directed sometimes to a single note in the object, independently of those with which it is united, sometimes 1 See Psychology, n°. 153. Till-'. EFFICIENT CAUSE OF LOGICAL ORDER 9 to the whole collection of notes which constitute the essence of the object, but apart from the notes which individualize it in reality: such acts of the mind arc called abstraction. (3) Abstraction is the basis of generalization. ( 1 ) Abstraction effects in the mind analysis, i. e., de-composi- tion of the notes of the object known. (5) When the mind reunites notes previously separated, it makes a synthesis. (6) When we represent to ourselves two objects in succession and perceive a relation between them, the apprehension — or rather, the double apprehension— is called comparison. (7) The perception of an existing reality is an intuition. We call it perception as opposed to the conception of things said to be ideal, i. e., things considered apart from their existence. (8) When the intelligence has for its object the acts of one's own soul, chiefly its spiritual acts, the apprehension takes the name of consciousness. (9) Distinction is an act by which the mind represents one ob- ject to itself as not being the same as a second object. By object we are to understand anything that can be the term of an act of thought (id quod ob-jicitur cognoscenti). 1 II. Judgment consists in attributing one object to another, in seeing that two objects, previously apprehended, have, or have not, anything in common. It is an act of apprehension of which the formal object is the identity between the terms of two ante- cedent apprehensions (appreheusio complexa, or complexorum — complex apprehension, or apprehension of complex things — as opposed to simple apprehension, apprehensio incomplexa, or in- complex orum) . IN. Reasoning is a linking-together of judgments. The rea- soning faculty compares with a middle term two extreme terms, the. identity of which it does not immediately grasp, with the result of seeing, by the aid of this comparison, whether they are identical or not. This process is also termed ratiocination. The acts of apprehension under their manifold forms, judgment and reasoning, fundamentally constitute one and the same act 1 On the various types of distinction (real, of pure reason, virtual) see General Metaphysics, n°. 49. 10 LOGIC — the apprehension or seeing that something is. They depend upon a single faculty indifferently called intelligence, understand- ing, or reason. 11. The Abstract Character of Concepts Renders Judgment and Reasoning Possible. — Every being which exists in nature is itself and no other, it is an incommunicable individuality, and it is inconceivable that one real being should be affirmed of an- other or attributed to another. Socrates is himself, he is no one else; this tree is this tree and no other. 1 How is it, then, that things are affirmed of one another in our judgments? It is because the mind has the power of looking at things without their individualizing notes : it abstracts. In consequence of this abstractive mode of apprehension, the object of the concept is universal; that is to say, it is found, or can be found, in many other individuals, and can be attributed to them in our judgments (universale in prcedicando) . . - Therefore, by means of intellectual abstraction, things can be affirmed, or, if we may so express it, are predicable, of one an- other. Thanks to this power of abstraction, our notions of beings as they are, are attributable to a whole species-, a whole genus; in other words they reproduce characteristics of classes — i. e., of genera and species. Abstraction makes reasoning possible ; for reasoning, as we shall see later, supposes a universal middle term, and universality follows abstraction — abstrahi ad quod sequitur intentio universalitatis. 1 See General Metaphysics. "Particulars are not predicated of other [objects], but other [objects are predicated] of them." Aristotle, Prior Analytics, I, 27. CHAPTER II The Matter or Material Cause of Logical Order 12. Object and Division of Chapter II. — By the matter or material cause of logical order we mean what this order consists of (id ex quo aliquid fit) the materials to be used in constitut- ing it. The elementary materials are concepts (Article I) and terms (Article II). Article I will treat of: the concept, its object, its properties (§1); the division of concepts (§2). Article II will have a parallel division. ARTICLE I. Concepts. § 1. The Concept, its Object, its Properties 13. The Concept from the Logical Point of View. — From the logical point of view (4) the concept is an element of judgment: it is adapted to the role of subject or of predicate, in a proposition, notio subjicibilis vel prcedicabilis in enitntiatione. In fact, judg- ment is the central act of the understanding: the apprehension prepares the elements of the judgment, as reasoning forms a new judgment by means of judgments already known. By logical concepts, then, we mean the object conceived which is enunciated of another and that of which it is enunciated. The connection of these two concepts, the copula, is made with the verb to be. The two concepts, the subject (id quod est sub jec turn attri- bution* vel prccdicationi) and the predicate or attribute (id quod pra-dicatur vel attribuitur ) are called the terms {termini) of the proposition ; they are in fact its extreme points or limits. 14. What Has Logic to do with the Act of Mere Apprehen- sion? — Logic is concerned with the acts of the reasoning faculty in 11 12 LOGIC so far as it can direct them towards what is true. Now we have seen that truth and error appertain to judgment, and not to mere apprehension (5). What, then, has logic to do with the study of concepts? — They concern it in so far as they furnish the matter of true judgments and occasion erroneous judgments. 15. Logical Problems Arising Out of the Act of Mere Apprehension. — The concept can have nothing to do with logic except either as subject or as predicate. I. In the last analysis, but only in the last analysis, the sub- ject of the proposition is always individual. To be sure the proposition can have as its subject — indeed often has — an abstract type, but in such a case this is the predicate of an antecedent subject. The reason of this is twofold: (a) Psychological: The first object of thought is taken from sensible experience, which is incapable of seizing anything but an individual and concrete reality. (b) Ontological: Only the individual is, rigorously, a subject. Aristotle calls itirpur-n ofola, first substance. For, on the one hand, it is not attributable to any antecedent subject. Individuality is in fact incommunicable to something else : . Socrates is Socrates, he is identified only with himself. 1 On the other hand this first substance is the subject of abstract and universal concepts which •can be attributed to it on various grounds. 2 Take the proposition: Snow melts in the sun. Snozu is an abstract subject. — But what is snow? Something white which I see falling in light flakes, and which I feel to be cold to the touch. This thing that is white to the sight, cold to the hands, and falls in light flakes, is some snow. This something which our senses perceive as white, cold, light, is a first subject; of this first subject, some snow is predicated. Snow then becomes the subject of a further predicate, the property of melting in the sun. An examination of the terms of a proposition brings us face 1 Cf. General Metaphysics, n°. 46. 2 "Of all things that are, some are such that they cannot be truly predicated of any other, as Cleon and Callias, both a singular thing and something that is subjected only to the senses, but other things can be predicated of them ; for either of these [sc. Cleon and Callias] is a man and an animate being." Aristotle, Prior Anal., I, 27. THE M \ T l ER OR MATERIAL CAUSE OF LOGICAL < iRDER 13 to face with a first term which is by its origin an individual subject (r65e n) and to which our thought refers all its predicates. The individual subject being disposed of, there remains the predicate. II. The predicate is the object of two principal considerations. (1) What does it represent, ivhat does it say about the sub- ject? — The study of the logical categories, or predicaments. (2) Hoie is it connected with the subject / in what manner must it be attributed to the subject? — The study of categoremes or predicablcs. 16. Logical Categories or Predicaments. — Obviously, it is out of the question to go in detail through all the predicates of the judgments which the human mind enunciates under an indefinite variety of forms. But Aristotle has essayed to reduce them to certain types of attribution, so as to understand what determina- tions they 'bring to the subject which experience supplies, each type of attribution (typus prcedicationis) constituting a category of homogeneous concepts. He recognized the existence of ten great kinds of predicates or attributes, the sum of which is virtually equivalent to all the range of human thought, and in one or other of which it is possible to find a place for any con- cept whatsoever. What are the ten predicaments or categories ? (1) Substance, that is, second or abstract, substance. This thing which we perceive as white, cold, light, is some snow. Some snow represents, under an abstract form the sub- stance to which our senses find attached those accidental deter- minations which are expressed by the adjectives white, cold, light. When the mind attributes an abstract substance to the concrete substance, rbfe n, perceived by the senses, it applies to that concrete substance the first category, ij ova la, n tdrl. In contradistinction to the individual subject, irpurrt ovala, prima substantia, upon which all predicates rest (15), the category of substance is called devrtpa ovala, sccunda substantia. The latter, indeed, can be the subject of attributes, but it presupposes a concrete subject to which it is referred. (2) The other nine types of attribution represent accidental determination-. 1 1 On the difference between the substantial quiddity which we take hold of by our logical predicates, see General Metaphysics, n os . S3 sq. 14 LOGIC Of these some are inherent in the subject to which the mind attributes them; two of them are absolutely inherent in the sub- ject considered, the categories of quantity (e. g., two feet long) and of quality (e.g., white, learned) ; a third belongs to the sub- ject in respect to a being or beings other than itself — the predi- cament of relation (e. g., double). Certain predicates represent something extrinsic to the sub- ject; the predicates of place (e. g., in the public street), of time (e. g., yesterday) are borrowed from measure, the one of quan- tity, the other of the duration of the subject. Action and passion are attributable to the subject because it is the principle (origin) of the former and the term, or aim, of the latter (e. g., he cuts the stone; the stone is cut). The last two categories, the meaning of which has much ex- ercised Aristotle's commentators, seem to have been felicitously interpreted by the philologist, Max Miiller, who sees in the word KeTcrOai, intransitive action, the active intransitive verb (e.g., I walk, I am afraid), in £x« v >the passive intransitive state (e. g., I am feeling well). 1 17. The Predicables. — Human thought is abstractive and uni- tive. It represents the reality of nature by means of an assem- blage of abstract notes susceptible of being universalized. How do these notes (predicates) contribute to the formation of a com- plete intelligible object (subject) ? What relation exists be- tween the subject and the predicate? In other words, by what right is the latter "predicated" of the former? There are various predicables or modes of predicability: (1) Necessary, because essential predicables .—Certain charac- teristics constitute the essence of the thing, which makes the thing what it is (quod quid est, rb ri t)v efocu), and without which it could not exist or be conceived : such are animality and reason in man. (2) Necessary, though non-essential predicables. — Other attri- butes do not constitute the substance, but necessarily result from it. In an invariable manner they interpret — develop — the con- stitutive perfection of the subject: these are called its properties (proprium, tdwv.). 1 St. Thomas, In Met, V, lect. 9. THE M \T IKK ( >K MATERIAL CAUSE OF LOGICAL ORDER 15 (3) Contingent or accidental prcdicables. — Others, again, have a contingent connection with the essence: these are called contin- gent accidents (contingit ut sint, av^t^Ko^ ), or, more briefly, accidents.* Essential predicables are subdivided: The object of the intelli- gence is not the individual essence, but the specific essence repre- sented by different abstract and universal concepts. The term species (ef5os) designates the sum of the abstract and universal notes which constitutes an essence as the human mind knows it. 2 Certain of these constitutive notes of a species are at the same time applicable to other species; these are called generic, they constitute the kind, or genus (ytvos) ; some are proper to it and differentiate it from other species of the same genus, and these form the specific difference (diaop&). Hence three distinct essential predicables ; the species and its two parts, the genus and the specific difference. Add to these three predicables property and accident, and we have altogether five predicables, or catagoremes. The properties (idiov) are the determinations which, with- out being of the essence of the thing, necessarily follow from the essence and, consequently, cannot be separated from it. A note is said to be proper to a given species when it belongs exclusively to that species, universally to all individuals of that species, and constantly to each one of them. "Proprium dicitur quod convenit soli alicui speciei, omni et semper." Thus the radical aptitude for learning letters is proper to man ; incorruptibility is proper to immaterial substances ; limitation is pre per to creatures. In this, the only rigorous acceptation, prop- erty, has the same extension as essence. When a characteristic does not combine the three conditions 1 Evidently, we must take care not to confound the (ontological) accident which is contradistinguished from the substance — whether it have contingent or necessary attachments to the substance — with the (logical) accident which is immediately contradistinguished from the essence on the one hand, and, on the other hand, from the accidents called properties. What is predicated as accidental of one subject may be predicated 'as essential of another. 2 Species in the logical acceptation here defined must not be con- founded with the same term in the sense attached to it by naturalists — that of a collection of individuals capable of indefinite reproduction among themselves. 16 LOGIC here stated, it is no longer, rigorously speaking, a property ; it is no longer co-extensive with essence. Nevertheless, though in a lesser sense, it justifies the appella- tion when it presents one or two of the three distinctive notes of property : A characteristic which belongs exclusively to a specific type, even though it do not belong either universally or con- stantly to the representatives of the species, is, in this sense, a property: thus, it is proper to man to be a physician, to be a geometrician. Similarly, a characteristic found in all the individuals of a species, and always, but not belonging to them exclusively, may be called a property : in this sense, says Porphyry, it is proper to man to be a two-legged animal. Such, too, is a characteristic which is common to all the repre- sentatives of the species and to them only, but temporarily : Thus, according to Porphyry, it would be proper to mail — to every man and to men only — to grow grey in old age. The common accidental quality, accident (o-u^e/3i;/c6s as opposed to idiov, accidens commune as opposed to proprium), may be de- fined in a negative way : the quality which is not a property in the strict sense of the word. In a positive way Porphyry defines it : An accident is a quality to the presence or absence of which the essence of the subject is indifferent (Accidens est quod adest et abest praeter subjecti corruptionem). The common accidental quality, Porphyry adds, is sometimes constant, sometimes belongs to the subject only intermittently. We may say of the animal that it sleeps ; black plumage may be attributed to the crow constantly. From this we see that care must be taken not to confound the quality, even the constant quality, with the property. The mere observation of facts does not suffice to effect the discernment of a property. This discernment, we shall see later, forms the object of scientific induction and calls for the employ- ment of experimental methods. 18. Comprehension and Extension of Concepts. — There are relations of subordination between various predicables. To under- stand these it is necessary to establish two logical properties of abstract concepts : their comprehension and their extension. The comprehension of an idea is its content, the sum of the characteristics or notes which analysis can find in it. Take the THE MATTER OR MATERIAL C UJSEOP LOGIC VL ORDER 17 abstract idea of man. When we consider what this idea repre- sents, we find in it different characteristics taken by abstraction from the individuals. The extension of an idea is its rang* oi applicability, the sum of the subjects to which the abstract idea is applied or can be applied, extends or can extend. We thus consider the abstract and universal concept as a whole, whether metaphysical or logical. Man is a metaphysical whole, which comprises corporeality, life, sensibility, reason, as so many metaphysical parts. 1 The idea of man is attributable to all men, past, present, future, or merely possible : it forms a logical whole of which men. taken distributive^-, are the logical parts. The Latin words totus and omnis correspond to the two mem- bers of this distinction. An idea is more or less comprehensive accordingly as it em- braces more or fewer notes. It has greater or less extension ac- cordingly as it applies to a greater or smaller number of subjects. These two properties of the idea are in inverse ratio to each other: the greater the comprehension of an idea, the less its ex- tension, and vice versa. When we compare two or more ideas in the twofold respect of their extension and their comprehension, certain relations are seen to arise between them. 19. Relations of Subordination among- Ideas in Respect of Their Extension. — There are degrees in the universality of con- cepts; those referable to the same category thus form a logical scale. On the lowest step we find the individual substance, which is not attributable to any subject, and to which all predicates are attributed, Next above comes the species, which is asserted of the indi- viduals. Then the genus, which is asserted of the subordinate species and the individuals. The genera (kinds) may in their turn be manifold: nearest, or immediate, genus; or subordinate genera: highest, or most gen- eral genus. Porphyry has drawn up a Table showing the essential pred- icates of substance and their mutual subordination. i Sec General Metaph., no. 48. 18 LOGIC Most general genus . . . Substance Difference . Animate Subordinate genus . . Difference . Corporeal . . . Subordinate genus Body Living: Difference . With feeling . . Subordinate genus ..... Animal Incorporeal Inanimate Without feelinp- Difference . Rational . . . Subordinate genus .... Man Irrational Individuals Some man Some horse Hypostases Socrates Bucephalus Singulars That man That horse \l \ r fER OR MATER] UL CAUSE OJ LOGK Ai.< IRDER 19 20. Comparison of Ideas in Respect of Their Comprehension. Relations of Identity and Opposition. Two ideas are identical or different accordingly as they have the same or a different con- tent (the ideas of man and rational animal; of man and animal i. ( >f nun-identical ideas some are compatible (liquid and sweet) ; others, incompati'ble (liquid and solid). Opposition, or incompatibility, between two idea- is produced in four ways: it is contradictory, privative, contrary, relative. 1 i The opposition is contradictor}- when the two terms have nothing in common; for one of the terms is being, and the other is the negative of being. Two ideas, in short, are contradictory when one is neither more nor less than the negation of the other i ti'hitc and not white, just and not just, etc. ). Privation is the negation of a perfection in a subject which is naturally fitted to possess it (negatio alicujus forma? in subjecto apto nato habere illam) ; thus blindness is the privation of sight, death is the privation of life. Privation is not merely synonymous with negation or absence; a mineral has no sight, but is not deprived of it. I Contraries form the two extreme points of a series of elements which are joined in the same genus. Suppose, e. g., that the degrees of light are mentally arranged in a series, the two extreme terms of the series, white and black, are two contraries. •There is the opposition of contrariety between things which can- not coexist in the same subject. Health and sickness, justice and injustice, courage and' timidity, are contraries. ! "i Relative opposition, or relation, is that between two terms either of which needs the other to explain it. Ex.: the ideas of father and son. of double and half, of knowledge and the object known. s; 2. Classification of Concepts 21. Principal Heads of the Classification of Concepts. — Con- cepts, or ideas, are divided: ( 1) in respect of the object which the intelligence abstracts from the things to be known; (2) in respect of their manner of representing the thing known; (3) in respect of their origin or their formation. Certain members of these divisions might be placed indif- ferently under any of several heads. 20 LOGIC 22. In Respect of the Object Abstracted by the Intelligence. ideas are divided (1) into transcendental, generic, specific, singular ideas. This classification is based on the degrees of abstraction of the intellectual cognition. The idea which represents all the determinations of the object, including- those which make it an individuality, is singular. Ex. : the ideas of Caesar, of Napoleon, etc. The idea which represents the thing- in a more indeterminate manner, offering to the mind. only those notes which belong in common to individuals of the same species, or to several species of the same genus, is either specific or generic, as the case may be, but in either case is universal. When the idea is still more indeterminate, and the intelligence represents things by means of certain characteristics common to all being in nature, the idea is called transcendental, ''because it transcends every genus, every category" ; the extension of this idea goes beyond all the categories. We distinguish six transcendental notions: being (ens), thing, one, something, true, good. 1 Remark: When several individual things are considered as forming one whole, the idea which represents them is called collective; such, e.g., is the idea of a people, an army. The collective idea must never be confounded with the universal. (2) Into adequate and inadequate ideas. The former make known to us all the characteristics which belong to the object — all those, at least, which are within the natural range of the in- telligence. The latter does not attain this degree of complete- ness. The inadequate idea is confused, indeterminate, indistinct ; or it is clear, determinate, distinct. The confused idea shows us the object by means of notes which are insufficient to let us distinguish it from every other object, as when I conceive of a fish as a creature that swims. The clear and distinct idea may include certain notes which are common to several objects, but it contains some which belong exclusively to the object to be known, and which therefore distinguish it from every other 1 See General Metaph., n° 39. MATTER OR MATERIAL CAUSE OF LOGN \JLORDER -.'1 object; e.g., when I define the fish as the living creature which breathes only through gills. (3) Into complex and simple. The idea is complex when it embraces several parts each of which by itself can be a predicate, as the idea just man. The ideas just and man are simple. 23. In Respect of the Manner of Representing Their Object, idea- are principally divided into concrete and ahstraet, positive and negative, proper and analogical idea-. i 1 i No concrete idea exists, hut by this name we Improperly jiate an idea the object of which is conceived in union with mcrete subject, as the idea- white, animal. In opposition to this, an idea is said to he abstract when it sents a note apart from any concrete subject; e. g., the ideas of whiteness, of animalitv. In reality the "concrete" idea grows out of an abstractive act; the "abstract" idea comes of a second abstraction, and is re- flexively abstract. (2) The positive idea represents a thing by means of notes which really belong to it; as the ideas of light, of life. The negative idea makes an object known to us by eliminating from the thought notes which the object excludes; as the ideas of darkness, of death. i 3) The positive idea is proper when it grasps a property, i. e., a quality which is distinctive of a being, such as it is positively. The analogical idea is that which we form of a being in itself inaccessible to the intelligence: to know it, we compare it with another being of which we know the properties positively. E. g., the Divine life is known to us by analogy with created life; the presence of spirits by analogy with the presence of bodies in space. 24. In Respect of Their Origin or Their Formation, cogni- tions are immediate or mediate. They are immediate or intuitive when the object to be known self united with the intelligence or, at least, itself begets in the intelligence the representation of what it is. When the cognition of the object is dependent upon that of another object, the cognition is called mediate. This is proper or analogical accordingly as the object which serves as inter- mediary is or is not of the same nature as the object to be km iwn. 22 LOGIC Mediate cognition is sometimes called ''abstractive," as op- posed to ''intuitive'' cognition. ARTICLE II. " Terms. § 1. The Term, its Objects and Properties 25. The Object of the Term. — Terms are vocal signs which express objects as they are conceived by the intelligence ; they are not the expression of subjective concepts as such, or of things as they are in nature, but of things as the intelligence conceives them; in a word, they designate known objects. "It is through the medium of intellectual conception", says St. Thomas, "that words are related to the representation of things." (Voces referuntur ad res significandas mediante conceptione in- tellectus). 1 The word sun, e. g., does not signify the idea of the sun, but the sun itself. And yet that word does not directly designate the sun as it is in nature. For it was long supposed that the sun was a disc moving around our planet ; now this is not the true sun, but only the sun as humanity imagined it before the discoveries of Galileo and Copernicus. It belongs to psychology to study the nature and functions of language. 26. The Ten Parts of Speech. — As the objects of our thoughts can be divided into ten categories, it seems natural to find an analogous division in the terms which correspond to our con- cepts. Grammarians do, as a matter of fact, distinguish ten parts in speech, just as Aristotle had distinguished ten categories of thoughts in connection with ten kinds of things known. There is, however, no adequate correspondence between the categories and the parts of speech. The first subject of all logical attributions is what the senses perceive in its concrete reality, and which at the outset presents itself to the thought in complete indeterminateness, — this some- thing, hoc aliquid, this, that. 1 Summa'Theol.j I, q. 13, a. 1. THE M \T I IK ( IE M \TI R] ^.L CAUSE OF LOGICAL ( >RDEB Formal determinations which the mind conceives in an abstract manner, and which the terms of language express, gradually fill up this first indeterminateness. The chief are expressed by the substantive, the adjective, and the attributive verb, which con- stitute the essential elements of language. i 1 i The first determination is the essence, or the very sub- stance, of the subject, designated by the noun, or substantive. The substantive designates any object which is a substance or any quality considered as if it were a substance (man, horse, height, whiteness). In its first acceptation the noun is abstract and, therefore, common. Further determinations have individualized its signification and made proper nouns out of it. (2) Two categories represent determinations inherent in the subject: some are qualitative; others, quantitative; these are adjectives. (3) The attributive verb represents action or passion in operation. As for the verb to be, it either designates the act of existing (I am) or plays a merely copulative part, uniting subject and predicate, in which latter character it is implied in every attri- butive verb — e. g., I work == I am working. It is interesting to note that the results of linguistics agree with the study of logical concepts : just as the predicates of judgments are abstract, so the roots, or primitive forms, of language express abstract ideas. § 2. Classification of Terms 27. Classification of Terms. — The classification of concepts is applied to terms. Let us note a few properties of the latter. (1) Terms are common or singular. Common terms are transcendental or merely general universal, and these arc generic or specific. Generic and specific terms are univocal; transcendental terms are analogical. This distinction is based on another classification of terms. (2) Terms are univocal when with a common name they 24 LOGIC designate things to which an essentially identical definition cor- responds. E. g., the noun animal is applied to a man and an. ox in an identical sense, either of the two being an animate sub- stance endowed with feeling. Equivocal terms designate with a common name diverse things the concepts of which are different. E. g. the noun dog is ap- plied to an animal and a constellation. Analogical terms designate with the same name things the corresponding concepts of which are partly the same and partly different. Thus, when we say of bodies and of spirits that they occupy a portion of space, the words occupy space have not an identical sense in the two cases, but an analogical sense. Analogy is expressed by metaphor. (3) Terms, like concepts, are simple or complex. (4) They are concrete or abstract. The word white is a con- crete term ; the word zvhitenesSj an abstract term. (5) Terms are positive or negative: e.g., death, immortality. —A positive term may convey a negative idea; a negative term, a positive idea. (6) Terms are direct or reflex: e. g., substance, man, are direct terms ; genus, species are reflex. (7) Categorematic terms have a complete sense in themselves, and can by themselves play the part of subject or attribute (e. g., man) ; syncategorematic terms have a complete sense only through their union with another term (e.g., none, all). CHAPTEE III Form \i. ( )ai se of I .ogk u ( >rder. 28. Preliminary Note.— The orderly arrangement of science is accomplished in a progressive way. First, the predicate is formally connected with the subject: an >f judgment. Then, being brought together and combined, the judgments produce more complex judgments: reasoning. Lastly, several reasonings relating to the same object con- tribute to the formation of a logical system: organization of science. Chapter 111 will consist of three articles corresponding to the three stages of logical order. Article I, devoted to the study of the judgment and the proposi- tion, will be divided into three sections: § 1. Meaning of the judgment and the proposition. ^ •.'. Judgments and propositions. Relations between judgments and propositions. ARTICLE I. Judgment and Proposition. § I. Meaning of Judgment and of Proposition 29. The Judgment and the Proposition. — The proposition is the expression of the judgment and consists in enunciating (asserting) one thing of another. "Propositio est oratio enuncia- tiva", dv6((>apuis, says Aristotle. All speech signifies something — "omnis oratio est significa- tiva." (pdais, RMAL CAUSE OF LOGIC \I. I IRDER 27 verb; composite, or complex, propositions include ninny simple propositiorfs joined together. Simple propositions are in their turn divided according to their metier, their form, their quantity, their quality. I. Classification of Simple Propositions 32. First Classification of Propositions: According to Their Matter. — By matter is meant the terms in their mutual relation, hut previous to the effective enunciation which the judgment formulates. Seme propositions are in necessary nuttier; others ; in contin- gent matter. A proposition is said to be in necessary matter when the con- nection between the two terms absolutely cannot be other thaw it is, and is revealed to the intelligence by mere analysis of the terms and independently of all experience; as 2+2=4. A proposition is said to be in contingent matter when the con- nection between the two terms is such as it is, only uppn certain conditions realized in contingent existences and cannot, therefore, be enunciated without experience; e. g., that water freezes at 0° centigrade. The judgment in contingent matter with which logic is cerned presents, then, a necessity* but a contingent necessity, whilst the necessity of the judgment in necessary matter is abso- lute. 1 fence judgment in necessary matter must not be con- founded with necessary judgment. The necessary proposition is knowable by itself, "propositio per se nota"; the contingent proposition, on the contrary, is knowable dependently upon something other than the mere terms of the proposition, "propositio per aliud nota." 33. Two Kinds of Judgments in Necessary Matter. — I. First bud: The connection is necessary because the subject, consid- ered in it-, osential elements, is either the same term as the pred- icate (identical judgment I, as: a square is an equilateral rectangle ; l The particular judgment in contingent matter does nol directly belong to the domain of science. Scicntid non est de singularibus. 28 LOGIC 2=1—1 ; or includes the predicate, the latter being in this case part of the essence of the subject, as : a square is a rectangle; man is intelligent. In both cases the comparison of the two terms of the judgment reveals to the mind the necessity of their connec- tion. II. Second kind: The connection between the two terms of the judgment is necessary when the predicate necessarily presup- poses the subject and, consequently, is not definable without bring- ing the essence of the subject into evidence. This case is where the predicate is a property (in the rigorous- acceptation) of the subject. The definition of the predicate (simple or disjunctive), put side by side with the essential notion of the subject, brings out the necessary connection of the two terms. (a) Example of a simple predicate: A prime number is one out of which it is impossibLe to form several groups each containing the same number of objects. ! This definition does not mention as a component part the num- ber 5. But if we place the definition on one side, and on the other side the result of breaking up the number 5 into two groups of two units each and one of one unit, it will then appear that the definition of a prime number necessarily applies to the number 5. That is, a prime number is not the definition of the number 5, but to be prime is one of its properties. (b) Example of a disjunctive predicate: Every number is either even or odd. The attribute even is not essential to number ; it is not even a necessary property. Neither is the attribute odd of the essence of number or a property of it. The alternative even or odd forms no part of the definition of number, but it is a necessary conse- quence of that definition. Given that unity is not a number, but the principle of numbers, every number is or is not divisible by 2, is even or odd. The Scholastics, following Aristotle, called the two kinds of necessary propositions which we have just been studying, duo modi dicendi per se, propositiones per se (two ways of saying by 1 A prime number is usually denned as one which is divisible only by i t - elf and unity. I't IRMAL CAUSE OF LOGICAL ORDER themselves, propositions by themselves), 3 Ka.6" afod, and op to thorn modi dicendi per accidens, propositiones per accidens, Kara (TVfxPe^rjKds. It must be added that the necessity of the connection becomes apparent sometimes immediately, sometimes in a mediate way after more i r less laborious analysis. This is an entirely subjec- tive affair which nowise affects the nature of the connection. 34. Synonymous Designations of the Foregoing. — Propositions in necessary matter are also called metaphysical and absolute, he- cause their objed is metaphysically necessary, independent of the conditions inherent in contingent existences, ruder the- ignations they are opposed to conditional or physical pr ti( ms. The former are called pure rational to indicate that reason is of itself capable of apperceiving their truth; whilst the knowledge of the latter, the experimental, empiric propositions, is subject to a verification of fact. Lastly, since Kant, the former a"re called a priori; the latter, a posteriori; the former, analytic; the latter, synthetic. It is im- portant to note care full\ that these expressions are given in the Kantian philosophy a special signification which precludes their identification with the expressions used by the Scholastics. Between the judgments in necessary and in contingent matter of the Scholastics and the analytic and synthetic judgments of Kant there are fundamental differences which it belongs to cri- terii »logy to establish. 35. Second Classification of Propositions : According to Their Form. — /•"<r L< JGICAL ORDER 31 36. Logical Value of the Predicate of a Simple Proposition. — The comprehension and extension of the predicate are a func- tion of the form of the proposition, [n an affirmative proposition they are in Inverse ratio to what they arc in a negative. (1) In an affirmative proposition the predicate is taken in all of its comprehension, although this may be less than that of the subject; but only in a part of its extension. All the notes of the predicate, taken together or separately, apply to the subject; hut ibject need no1 represent, and consequently does not, so far as the enunciation goes, represent more than a portion of the objects within the extension of the predicate. E. g., when I say, log is a vertebrate'*, I mean to assert that the dog has all the properties included in the idea vertebrate, collectively < r distrib- utively; but nut that there are no other vertebrates hut the dog. Then- is, however, this reservation to be made: that in essential ■definitions, the thing defined and its definition have the same ex- tension and the same comprehension. I 2 i In a negative proposition, on the contrary, the predicate is taken in its whole extension, but only in an indeterminate -part of it-, comprehension. E. g., when I say, "The mollusc is not a vertebrate", I mean to say that the mollusc is not any one of the vertebrate-, because it does not include all the attributes of the vertebrates; but that does not prevent its having some of the properties which belong to the vertebrates. I exclude all the subject- to which the idea i i vertebrate applies, but I need not therefore exclude all ' e notes which that idea comprehends. 37. Third Classification of Propositions: According to Their Quantity. — A proposition is universal, singular (or particular), indefinite. i 1) The universal proposition asserts that an attribute belongs to (/// the subjects of an idea or to none of them. As: All men are mortal ; No man fatally misses his destiny. i 2 i The singular proposition enunciates an attribute of one in- dividual. When the subject represents a determinate group of individuals, it is collective: in the logical point of view it is of the same nature as the singular subject. We also call all those prop- ositions particular the subject of which is not universal, whether it include many individuals of the same species or only one. As: Some men are learned ; the Belgian people is active. 32 LOGIC (3) The indefinite proposition expresses the agreement or non- agreement of a predicate and a subject without expressly saying whether the subject is taken in all its extension or only in part of it. As: They have been unjust in this matter. The universal proposition is more important than the particular. The former, indeed, contains the latter in its extension; to know the former is virtually to know the latter ; but the converse is not true. 38. Fourth Division of Propositions: According to Their Quality. — Propositions are true or false accordingly as the con- nection which they assert is or is not in agreement with that which is. 1 II. Classification of Composite Propositions 39. Classification of Complex Propositions. — Rigorously speak- ing, a composite, or better, a complex, proposition is an enuncia- tion which includes several simple propositions. The authors of Port-Royal enumerate six types of proposition in which the complexity is manifest, and four in which it is more or less latent. We will define them and establish the conditions of truth in each. I. The first six are the copulative, disjunctive, conditional, causal, relative and discrctive. (1) The copulative proposition is that which includes many subjects and many attributes joined by an affirmative or negative conjunction, and or nor: This proposition is true only if its parts are true. (2) Disjunctive propositions state an incompatibility at the same time as an alternative, as : Every free action is morally good or bad. The condition of. truth in these propositions is that the two parts of the disjunction should be mutually opposed and should admit of no middle term. (3) Conditional propositions consist of two parts connected by if; the first, which contains the condition, is called the antecedent; 1 Many authors call that quality which we have called the form of a proposition. In respect to the quality, they say, propositions are affirma- tive or negative. — A question of mere words, of very slight importance. |( )KM \l. I UJSE < IF LOGIC \I. < >RDER 33 the second, the consequent. E. g.\ It the soul is spiritual (ante- cedent), it is immortal (consequent). For the truth of these propositions we have to consider only the truth of the consequence: the falsity of both parts does not hinder the proposition, as a conditional proposition, from being true. !•'.. g. : If the soul of animals were spiritual, it would be immortal. (4) The causal proposition contains two propositions joined by some word indicating a cause — because, etc. Reduplicative propositions also belong to this class. E. g. : Evil, as such, is not the object of the will. For the truth of these propositions it is not enough that the two parts should be true; one part must also be the real cause of the other. (5) Relative propositions express a connection. E. g. : As the life so is the death. Their truth depends on the correctness of the connection. (6) . idversative, or discretive, propositions include several different judgments separated by some such particle as but, yet, nevertheless, etc. E. g. : Not on riches, but on virtue, depend" happiness. The truth of these propositions depends on the truth of their parts and of the opposition between them. II. Four types of apparently simple, but really complex, propo- sitions. (1) Exclusive propositions which assert that an attribute be- longs to but one subject, as: God alone is to be loved for Himself. (2) Exceptive propositions affirm an attribute of a subject, but with the exception of some subdivisions of that subject. E. g. : Excess is possible in all the virtues except in the love of Cod. (3) Comparative propositions say not only that a thing is so, but that it is more so or less so than some other thing. E. g. : Wisdom is more valuable than fortune. (3) Inceptive, or desitive, propositions assert that a thing has commenced or ceased to be so. E. g. : The independence of Bel- gium dates from 1830. Each of these four propositions really includes two judgments ; it is not true unless the two parts are true. 84 LOGIC § 3. Relations Betzveen Propositions 40. Relations Between Propositions. — Various kinds of rela- tions between propositions are to be distinguished : their equiva- lence, convertibility, subordination, opposition. 41. Equivalence of Several Propositions. — Propositions are called equivalent when they differ only in expression, and in reality are identical as to sense and logical value. E. g. : Every man is just; there is no man who is not just. 42. Convertibility of Propositions. — Conversion consists in transposing the two terms of a proposition so that the new propositions so obtained shall also be true if the original is true. (1) The universal negative is convertible, for both the terms are universal. E. g. : No mineral is capable of vital functions ; no being capable of vital functions is a mineral. (2) The particular affirmative proposition is convertible, for here, also, the two terms are of the same extension. E. g. : Some sentient beings are endowed with reason; some beings endowed with reason are sentient. In these two cases the convertibility is evident: the two terms are purely and simply interchangeable. These are in fact the only cases of interchangeability. (3) It must be noted, first of all, that singular propositions .are never susceptible of any but an apparent conversion, since .a determinate individual term, representing in the last analysis a first substance, cannot serve to express a formal predicable idea. E. g., whether I say, "Peter is a learned man," or, "A learned man is Peter," the same Peter, in spite of the inversion, will still be the subject. (4) The universal affirmative is susceptible of conversion, in the sense that the predicate can take the place of the subject and vice versa, but on condition that the subject turned into a predi- cate is modified by some mark of particularity with a restrictive sense. The conversion effected on these conditions is said to be imperfect. E. g. : All men are sentient ; certain beings endowed with feeling are men. There must still be an exception in the essential definition, where the idea defined is equal to the definition. FORMAL ( U SK OF LOGICAL ORDER 35 This "imperfect" conversion is no true conversion, for this consists in the simple mutual substitution of the two terms. The addition of a sign of particularity which renders the conver- sion imperfect alters its nature. 43. Relations of Opposition and Subordination. — These rela- tions between propositions may be produced in four different ways : propositions are contradictory, contrary, sub-contrary, or subaltern. The first two are relations of opposition properly so called. (1) Judgments so opposed to each other as to exclude any intermediate judgment are said to be contradictory. They differ both in form and in quantity. E. g. : Every man is white ; some man is not white. 1 (2) Judgments which differ only in form, and have the same universal quantity, are so opposed to each other as not to exclude any intermediate judgment, and are called contraries. E. g., every man is just; no man is just — two extremes between which a third judgment may be slipped in: Some man is not just. (3) Propositions which differ only in form, and have the same particular quantity, are sub-contrary. E. g. : Some man is just; some man is not just. (4) Propositions which have the same form, and differ only in quantity, are subaltern. E.g.: Every man is just; some man is just. — No man is just; some man is not just. Logicians have adopted the convention of designating by the letters A, E, I, O, the four kinds of propositions as distinguished by quantity and form. A designates a universal affirmative proposition. E designates a universal negative proposition. I designates a particular affirmative proposition. O designates a particular negative proposition. The following scheme exhibits the contradictory and contrary modes of opposition. 2 1 Perili erm., c. VI. 2 "A universal affirmative (proposition) and a universal negative are contrary, as Every man is just, No man is just: for a universal nega- tion indeed not only does away with a universal affirmation, but also in- dicates the extreme distance, inasmuch as it denies all that the affirmative asserts: this is of the essence of contrariety, and therefore the particular 3C LOGIC o Every man is CONTRADICTORIES One man is not just just I One man is just CONTRADICTORIES E No man is just. 44. Rules on the Truth or Falsity of Opposed Propositions. — (1) Contradictories are never either both true or both false, seeing that one is the negation pure and simple of the other. The truth of the one, then, carries with it the falsity of the other; and vice versa, the falsity of the one implies the truth of the other: If it is true that every man is just, it cannot be true that one man is not just. (2) Contraries cannot both be true, but they can both be false.. Contraries cannot both be true ; otherwise contradictories- would be true at the same time. Suppose the proposition, "Every man is just," to be true ; the contradictory, "One man is not just,"' is false. If it is false to say that one man — even a single indi- vidual — is not just, much more is it false to say that every man is not just, or — which comes to the same thing — that no man is just. The proposition, "No man is just," is the contrary of the proposition, "Every man is just." But the falsity of a proposition does not imply the truth of the contrary. It may be false that all men are just without its being true that no man is just; there may be some just men, even though not all are just. (3) By a rule opposed to that of contraries, sub-contraries may both be true. E.g.: Some man is just; some man is not just. Justice may be an attribute of one portion of mankind and not of the other. But sub-contradictories cannot both be false, or both of two- contradictories would be false. Let the proposition, "Some man is just," be false; the contradictory, "No man is just," is there- affirmative and the particular negative are in the nature of a mean be- tween the contraries. ... In contradictories the negation does no- more than remove the affirmative." St. Thomas, In Periherm., Lect. XI. FORMAL CAUSE OP LOGK KL OR »ER 37 fore true. .Much more, then, is it true that some man is not just, which is the sub-contrary. 45. Rules Concerning- the Truth or Falsity of Subaltern Propositions. The particular propositions I, O, are subordinate to universals A, E, respectively. The truth of universal propositions implies that of their sub- alterns; Inn the truth of subalterns di es hot carry with it that of their universals. The falsity of particulars implies the falsity of universals; but the falsity of universals duos not carry with it the falsity of part iculars. ' 46. Immediate Inferences. — We shall presently sec that, in a reasoning properly so called, the conclusion springs from the comparison of three different terms, and that this comparison is made in two propositions, the two premises of the reasoning. It is sometimes permissible to draw at once a sort of conclusion from the enunciation of a single proposition: this is called an immediate inference. The conversion, opposition, and subordination of propositions give 1 ccasion to inferences of this kind. The rules given above sufficiently show how these inferences are justified. ARTICLE IT. Reason i \<; 47. Preliminary Remarks. Object of Article II. — Chapter III of this treatise has for its object the formation <>i the logical order. 1 With regard to modal propositions, the contradiction betwee' 1 affirmation and negation does not fall upon the attribute of the proposi- tion, hut upon the verb. The most ordinary ca^es of opposition between modal propositions arc set forth in the following scheme: This must he so. CONTRADICTORIES This 1Uc( ' n,,t ' )C s o — q It is possible that this ■V/>, is not so. It is not impossible 'o'//. that this is so — This s may be so. CONTRADICTORIES This cannot be so. 38 LOGIC In a former article we saw how concepts perform their func- tions in a judgment, and terms in a proposition. We next classi- fied judgments, then set them side by side and compared them. Judgments in their turn form the elements of a more complex order. Known judgments lead to a new judgment, through a discursive process called reasoning. This process, when expressed in words or writing, is called syllogism. Hence these two paragraphs : Reasoning and syllogism (§1). The various forms of these two (§ 2). § 1. Reasoning and syllogism 48. Reasoning. — The aim of all intellectual processes is the knowledge of truth. Certain truths are known immediately ; others, mediately, by means of those known immediately. The former, as generating the latter, are called principles; the latter are consequences, or conclusions. To proceed from principles to conclusions is to reason. A conclusion is a proposition, and, as such asserts a predicate of a subject. When the predicate manifestly' belongs to the sub- ject, the proposition is evident. 1 This evidence is immediate when the objective connection between the predicate and the subject of a judgment is immediately apparent to the intelli- gence ; also immediate is the corresponding certitude. But in most cases the evidence of the judgment is brought to light only by the employment of one or more intermediaries, or middle terms — common terms of comparison between subject and predi- cate. In such cases the evidence is mediate, or by reasoning. as is the corresponding certitude. The kind of evidence is the evidence proper to conclusions. The necessity of this discursive proceeding arises from the disproportion between the complexity of intelligible things and the inadequacy of the intelligence which is called upon to know them. 2 1 See Criteriology. 2 "The discourse of reason always begins in the understanding and ends in the thing understood ; for we reason by proceeding from certain F( IRMAL C U'SH i >F l.( >GIC \l. I IRDJ R 39 The power of reasoning urges a perfection which the metaphysicians call mixed, i. e., marked by imperfection. h is a perfection to be able to reason, i. e., to reach the knowl- edge of truths which otherwise would remain unknown. It is an imperfection to be obliged to reason, i. e., to reach the truth only by winding and difficult paths. 49. The Syllogism. Terminology. — Reasoning, then, con- sists in comparing the subject and predicate of a not evident judgment, which is to be the conclusion, with a middle term to see whether, objectively, the one implies the other or excludes it. Its complete and typical expression is the syllogism. "The syllog- ism", says Aristotle, "is a discourse in which, certain thing; being laid down, another thing follows necessarily, simply be- cause those things are laid down." 1 When the reasoning faculty declares that the predicate agrees objectively with the subject, the conclusion is affirmative; when it sees that one of the two terms agrees with the middle term while the other does not, the conclusion is negative. The two terms of the conclusion are called extreme terms, or extremes, in opposition to the middle term (mcdiits terminus) with which they are both compared. The predicate is called the great extreme; the subject, the small extreme. The two propositions from which the conclusion is drawn are called premises 1 prcemittuntur conchisioni) ; together they form the antecedent. The premises are those things which, according to Aristotle, once laid down or supposed, draw the conclusion after them. The consequent is the conclusion. The proposition first in order to be enunciated is often called the major; the second, the minor. But more exactly, the proposition in which the great extreme is put with the middle term is called the major (Major, propositio) ; that in which the small extreme is compared with the middle term, the minor (Minor, assumpta). understood things; and the discourse of reason is complete when we arrive at the understanding of what was previously unknown. Our reasoning, therefore, proceeds from some precedent understanding." Summa Theol., 2 a 2*, q. 8, a. 1, ad 2. 1 Prior Anal, I. 1. 40 LOGIC The premises and the conclusion, the antecedent and the con- sequent, constitute the matter of the syllogism. The form lies in the bond between the antecedent and the consequent ; it is con- densed in the particle therefore, which expresses the consequence (consequcntia, consecutio) of the syllogism. To study the nature of reasoning is to investigate what causes that "certain things being laid down, another thing must necessarily follow simply because those things are laid down." 50. Nature and Logical Basis of the Syllogism. — Take for example this syllogism : The triangle which has two equal sides has two equal angles. This triangle has two equal sides. There- fore it has two equal angles. To reason is to place within the extension of an abstract type some ■determinate subject, with the result of concluding thai a note which belongs to the abstract type as such is attributable to this determinate subject. The major is a necessary proposition: it asserts that -the pred- icate of the conclusion (the property of having two equal angles) is necessarily associated with an abstract middle term (a triangle which has two equal sides). Being abstract, this middle term is not actually universal, but it can be universalized; by an ulterior act of reflection it can be at- tributed to one, or to several, or to all the inferiors of a species or of a genus. The reasoning faculty, on enunciating the minor, sees that the middle term extends to the subject of the minor — it sees that this triangle has two equal sides. Then, provided that the major and the minor. are taken in at one glance, it will be seen that the predicate of the conclusion has two angles equal, necessarily belonging to the middle term, tri- angle with two sides equal, belongs to the subject of the conclu- sion which is within the extension of the middle term ; therefore the necessary connection between the subject of the conclusion and its predicate becomes obvious. The syllogism is essentially a process of univcrsalization. The principle on which it is founded may be thus enunciated : The note which necessarily applies to an abstract subject — the middle term ■ — applies to the subjects of the extension of the middle term. ' Obviously, the connection established bv reasoning; between !•'< >KM \l. CAUSE < >T L( )GIC \L ( >RDER | I tin- extremes and the middle term belongs at once t" the compre- hension and to tin- extension of the terms. In the major, one of the extremes— the predicate of the con sion — is, by reference to its comprehension, connected with the middle term: Whatever things arc the same as a third thing arc the same as one another. In the minor, the same middle term is considered with refer- ence to it- extension and in this point of view is connected widi the other extreme, the subject of die conclusion. Whatever is affirmed or denied of a subject taken in the abstract must he affirmed or denied of <'// its inferiors and each one of them, in one word, affirmed or denied universally. The syllogism considered above lead- to an affirmative conclu- sion. The same analyses may be applied to syllogisms with nega- tive ci inclusions. 1 51. What Kind of Necessity Attaches to the Principles of the Syllogism? — The law which serves as a fulcrum for reasoning is sometime- metaphysical, or absolute (see example given under 50) ; sometimes physical, or natural, and therefore dependent on conditions to be determined by experience (as: Water attain- it- maximum density at 4° centigrade). Tn the former case the predicate in the conclusion expresses the essence, total or partial, of the middle term, or a property which is a corollary of that essence, and the necessity of applying this 'predicate to the subject of the conclusion is absolute. In the latter case the quality is attributed to the middle term in virtue of a law established by experience, and the attribution of predicate to subject in the conclusion is hypothetic ally necessary. These law- of experience are established by induction, as will be later. 52. Logical First Principles. — We have seen that the syllogism derives its demonstrative force from a necessary proposition. Whence does this proposition derive it- logical value? From a previous reasoning. We cannot go on from one process of rea- soning to another indefinitely. 2 i Sec ( riteriology, n°. 58: Stuart Mill'- objections against the value of the syllogism. - Criteriology, 52-54. 42 LOGIC Otherwise we should be obliged to say that no -conclusion is cer- tain. There must be propositions on which the reasonings are supported, and which themselves need no demonstration. These are called logical principles: they are the enunciation of a relation* between primary notions. There are two kinds of principles : (1) generative principles of the sciences; (2) directive principles, or axioms. 53. Figures and Modes of the Syllogism. — The various forms- of the syllogism, according to the relation of the middle term with the extremes, are called by Aristotle -figures (o-xyv-*™)'- 1st Figure: The middle term is subject in the major and attri- bute in the minor. 2nd Figure : The middle term is attribute in both premises. 3d Figure: The middle term is subject in both premises. The syllogisms possible in these figures, regard being had to* the quantity (universal or particular) of the propositions and their form (affirmative or negative) have been called the modes of the syllogism. Counting all the possible modes of the syllogism, independently of their logical value, we find a total of 256 forms. Of these 21 are conclusive ; and 5 of these 24 are useless without being vicious. Hence we have 19 valid and useful modes of the syllogism. 54. Rules of the Syllogism.— Besides the special rules of each of the figures, logicians have been wont to formulate eight rules applicable to the syllogism in general, expressing the nature of the reasoning. First Rule. — Terminus esto triplex: medius, major que mi- norque. — The syllogism must have three terms, neither more nor fewer. To reason is in fact to compare two terms with one and the same third, so as to see what logical relation exists between the two terms so compared. This rule may be violated by defect, in using only two terms, or by excess, in using more than three. (1) A syllogism with tzuo terms is, e. g., where one of the premises is tautological. E. g. : Every effect has a cause. But the universe is an effect. Therefore the universe has a cause. This first rule is violated by the form of sophism called petitio- principii, which resolves the question by the question (begging the question). i i IRM \1 I \i si. "I I I iGK \l. < IRD] \< 13 (2) A syllogism contains more than three terms when one term is equivocal and is taken in different acceptation-. E.g.,: The operations of thought have the brain as organ. An opera- tion which has the brain as organ is material. Therefore the operations of thought are material. In this syllogism the middle term, has the brain as organ, is equivocal. Second Rule. — Latins hoc (terminus extremes) quam prce- missce conclusio non vnlt, or: AZquc ac pneinissa? extendat con- clusio voces. — The extremes must be the same in the conclusion as in the premises. The conclusion expresses the results of the comparison made in the premises. It cannot go beyond that ; otherwise it would pass from the terms compared in the premises to other terms,. and thus would violate the first rule, the essential condition of reasoning. Third Rule. — Ant semel out iterum medius generaliter esto. • — The middle term must be taken as universal in one premise at least. The analysis of the process of reasoning (50) has made this third rule intelligible. If the middle term were taken twice in a restricted sense, that part of its extension which it represents might possibly be different in the two cases, and there would be four terms in the syllogism (first rule). E.g.: Every metal is heavy. This substance is heavy. Therefore this substance is a metal. The middle term, heavy, is not universal in either of the premises. This very common sophism is characterized by the adage : Ab uno disce omnes. Fourth Rule. — Nequaquam medium capiat conclusio fas est. — The middle term may not enter into the conclusion. It is for the conclusion to apply to the two extremes the result of the comparison made in the premises between them and the middle term. To introduce the middle term into the conclusion, then, would be to miss the aim of the reasoning. Fifth Rule. — Amine afh'rmantes nequeunl generate negatem. — Two affirmative premises cannot beget a negative conclusion. If two ideas agree with one and the same third idea, the other rules of the syllogism being observed, they cannot but agree with' 44 LOGIC each other ; and the identity affirmed in the premises cannot be denied in the conclusion. . Sixth Rule. — Utraquc si prcemissa neget, nil inde sequetur. — With two negative premises no conclusion is possible. Two extremes both excluded from one middle term cannot t>e connected with each other on account of this exclusion. But on the other hand, it is possible that two terms excluded from one given middle term may be comparable with another middle term with which both must be coupled, or else one coupled and the other separated. The use of this other middle term would .give a conclusion. The fact, then, that two extremes are excluded from a given middle term warrants no assertion as to the relation of the ex- tremes. Seventh Rule. — Pejorem sequitur semper conclusio partem. — The conclusion should follow the premise of lower rank. This formula has a double application : (1) // one of the premises is negative, the conclusion must be negative. If, of two ideas A and B, A agrees with a third idea, C, while B does not, it is impossible to conclude therefrom that A agrees with B. (2) // one of the premises is particular, the conclusion cannot be universal. As the premises cannot both be negative (sixth rule), only two •cases are to be considered : (a) Both the premises are affirmative. (b) One is affirmative; the other, negative. In case (a) both the predicates are particular; one of the two subjects is by hypothesis particular: there is, then, only one universal term in the premises. As this must be the middle term (third rule), neither of the extremes is universal in the premises and, consequently, cannot be so in the conclusion. So that the conclusion, since it necessarily has a particular subject, is par- ticular. In case (b) the premises include two universal terms: the predicate of the negative premise and the subject of the proposi- tion which, by hypothesis, is universal. But the conclusion is negative, so that its predicate is universal. This term, which is the predicate in the conclusion, is not the F( IRMAL C UJSE I IF LOGICAL I >RDER 1-5 middle term (fourth rule). The second universal term of the premises is therefore the middle term. Hence the extreme which becomes the subject of the conclusion is particular in the premises, and, consequently, in the conclusion. Therefore the conclusion is particular. For example : Every man is corporeal. But A is not cor- poreal. Therefore A is not a man. The result would he the same if one proposition were both uni- versal and negative, as: No man is spiritual. But A is a man. Therefore A is not spiritual. — Or: But B is spiritual. Therefore B is not a man. When one premise is particular, then, the conclusion must be particular. Eighth Rule. — Xi! sequitur (/(■minis ex particularibus iinqitani. — -No conclusion follows from two particular premises. As both the premises cannot be negative (sixth rule), the only possible cases are : (a) Both premises are affirmative. (b) One is affirmative; the other, negative. In case (a) all the terms are particular: the two predicates, because the propositions are affirmative; the two subjects, by hypothesis. The middle term, therefore, is not once taken uni- versally. The third rule is violated. Xo conclusion. Example: Some men are rich. Some men are ignorant. Therefore some rich men are ignorant. If this syllogism were valid, it might he proved in the -aim- way that some rich men are poor, which exposes the sophism. In case (b) the premises contain only one universal term, the predicate of the negative premiss. But the conclusion being neg- ative, its predicate is universal; being so in the conclusion, it must also be universal in the premises. Consequently, the middle term, which cannot he identical with the predicate of the conclusion (fourth rule), is twice particular in the premises. ( )nce more, the third rule is violated. No conclusion. Example : Some men are learned. But some men are not virtuous. Therefore some learned men arc not virtuous. The inconsequence is manifest. 55. Range of the Rules of the Syllogism. Logic and Truth. — The rules just given relate only to logical deduction. But 46 LOGIC logical connection between antecedent and consequent is one thing; the truth of the consequent is another. The necessary connection between the things laid down and the thing which springs from them does not affect the truth or falsity of the premises containing the former. Two general laws govern the truth and the falsity of conclu- sions : (1) If the premises are true, so will be the conclusion: ,Ex vero non sequitur nisi verum. The conclusion, indeed, confines itself to affirming relations seen in the premises ; if they have been recognized in the premises, there can be no error in ex- pressing them in the conclusion. Corollary: As true premises cannot lead to a false conclu- sion, we may fairly refute a doctrine or a theory by arguing from the falsity of its consequences. Atheism, for example, is refuted by its consequences. (2) If the premises are false, or if one of them is 'false, the conclusion will generally be false; but it may be true. Ex falso sequitur quidlibet. Examples given by Aristotle : "Every man is a mineral. Every mineral is an animal. Therefore every man is an animal." — "Every mineral is an animal. No horse is an animal. Therefore no horse is a mineral." — "Every horse is an animal. N'o man is an animal. Therefore no man is a horse." From a false principle one may arrive at an exact result, either because the principle is a mixture of true and false, and it has been used only in so far as it is true; or because the errors pro- ceeding from the principle have ended by compensating one an- other. Corollary: Since a false antecedent may have a true conse- quent, a doctrine or theory cannot be rigorously established by showing that this or that one of its consequences is true. Newton, for example, had deduced from his theory of emissions many consequences in respect to the nature of light which were after- wards verified by experiment ; nevertheless, the theory itself was disproved. For an argument drawn from the consequences of a theory to be conclusive, it must be demonstrable that the theory leads to none but true consequences. FORMAL I A.USE OF LOGICAL ORDER 17 § 2. Syllogisms 56. Preliminary remarks. — Syllogisms may be classified either by their form or by their matter. The form of a syllogism is its structure, abstracting from the truth or falsity of the premises themselves; the matter consists of the propositions, which may be true or false. In the following two articles we shall successively take the two points of view of form and of truth. Scientific induction does not essentially differ from the syl- logism. Hence the analogy and the example, which logicians connect with induction, may also be reduced to the syllogistic process. It follows that all forms of reasoning properly so called are but variants of the syllogism. Such will be the gen- eral conclusion to be drawn from this article. I. Syllogisms Considered with Reference to Their Form 57. Classification of Syllogisms by Form. — Considered with reference to its form, the syllogism is : categorical; hypothetical (or conditional) ; conjunctive ; disjunctive. The latter two may be reduced to the hypothetical syllogism. The exclusive syllog- ism and the dilemma, which are complex, more properly belong, the former to the categorical type, the latter to the hypothetical. 58. Varieties of the Categorical Syllogism. — The categorical syllogism has for its premises two categorical propositions. It will be useful to note some of its possible structural modifica- tions. Such are the forms of reasoning called epicheireme, poly- syllogism and sorites, enthymeme. (1) The epicheireme (erl and x «/»<2 , to take in hand) now 1 designates a syllogism one or both premises of which is immediately accompanied by the proof. The poly syllogism is a series of syllogisms in which the con- clusion of each serves as premise for the next. In practice the polysyllogism is condensed, under the form of 1 In Aristotle epicheireme means an attempt at demonstration as opposed to a demonstration properly so called. 48 LOGIC sorites (cQpos, heap), into a series of propositions where the predicate of the first becomes the subject of the second, and so on, in such a way that the predicate of the last in the series may be coupled with the first subject. Example : The human soul forms abstract thoughts ; a being capable of abstract thoughts is spiritual ; a spiritual being is by nature imperishable ; a being naturally imperishable cannot be annihilated ; a spiritual being that cannot be annihilated will live with an immortal life; therefore the human soul is immortal. 1 59. Nature and Rules of the Conditional Syllogism. — The conditional syllogism is that which has a conditional proposition for its major. E.g.: If the soul is simple, it is imperishable;. but the human soul is simple ; therefore it is imperishable. In the major there is only the assertion of a necessary connec- tion between the condition (simplicity of the soul) and the con- ditioned (incorruptibility). As soon as this connection is accepted as necessajy, the rest reduces to an ordinary reasoning the antecedent of which forms the minor and the consequent conclusion. The whole interest of the conditional syllogism, then, is in the major, which is equivalent to an absolute affirmative proposition. The proposition, "If the soul is simple, it is imperishable," is equivalent to, "Every simple thing is imperishable." Now a uni- versal affirmative is not convertible (42). From this observation we deduce the rules of the conditional syllogism : (1) Affirm the condition, or antecedent, and you must affirm the conditioned proposition, or consequent. E. g. : If you are from Brussels, you are a Belgian. But you are from Brussels. There- fore you are a Belgian. (2) Deny the conditioned proposition, or consequent, and you must deny the condition, or antecedent. E. g. : If you are from 1 The enthymem* is commonly reckoned among the more or less disguised forms of the syllogism, as though it consisted merely in leaving one of the premises to be understood, not expressed. This is too sec- ondary a circumstance to justify giving the enthymeme a place of its own among the forms of syllogism. As a matter of fact Aristotle understood by enthymcvie a syllogism the conclusion of which is only more or less probable. I I IRMAL CAUSE I »!•' LOGICAL I >RDER 49 Brussels, you are a Belgian. But you arc not a Belgian. There- fore you are not from Brussels. But the inverse is not true. Remarks: (1) Nevertheless, the matter of the conditional proposition may possibly be such that the truth of the consequent carries with it the truth of the antecedent. E. g. : If a figure is a circle, it has equal radii. i .' ) The conjunction if does not always mean, in the thought of one who uses it, a connection of necessary dependence between the antecedent and the consequent ; it frequently indicates only a partial or a contingent connection, and in that case expresses a presumption rather than a rigorous inference. E. g. : If this man were sorely tried by misfortune, he would return to a better state of mind. 60. Conjunctive and Disjunctive Syllogisms. — The conjunc- tive syllogism is that which has a conjunctive proposition for its major. This proposition alleges an incompatibility between two cases, one of which is affirmed in order to eliminate the other. E. g. : You could not have been in Brussels and in Paris at the same time. You were in Brussels. Therefore you could not have been in Paris. — This syllogism may be reduced to the conditional type, and follows the laws of that type. The disjunctive syllogism has for its major a disjunctive prop- osition, which not merely alleges an incompatibility, but implies an alternative admitting no middle term. Hence the disjunctive syllogism is governed by the following two rules : (1) The disjunction laid down in the major must be complete. i 2 i When the minor affirms one of the members of the dis- junction, the remaining member or members must be denied in the conclusion, and vice versa. Example : Every free act is morally good or bad. Now such or such an act (e.g., an oath) is not morally bad; therefore it is morally good. . . . Or. it is bad ; therefore it is not good. . . . Or, it is good ; therefore it is not bad. . . . Or, it is not good ; therefore it is bad. 61. Exclusive Syllogism. — This type has both premises exclu- sive. E. g. : Only a spiritual being is free. Man alone is spiritual. Therefore he alone is free. 50 LCGIC This syllogism may be broken up into two others, one affirma- tive, the other negative : A spiritual being is free. Man is spirit- ual. Therefore he is free. — A free being is spiritual. Beings other than man are not spiritual. Therefore they are not free. 62. Dilemma. — The dilemma is the combination of a disjunc- tive proposition, serving as major, with two or more conditional propositions forming a minor. First, partial conclusions exclude the members of the disjunction one after another; then it is' con- cluded in a general manner that the disjunctive proposition taken as a whole is inadmissible. This method of arguing is lively and cogent. An alternative is presented to one's opponent : he is left the choice between two positions ; then it is proved that in either case he is wrong. The validity of the dilemma requires a punctual observance of the rules of the disjunctive and of the conditional syllogisms. First rule: The disjunction of the major admits of no inter- mediary proposition, but must be complete. Second rule: Each of the two conditional syllogisms which together form the minor of the dilemma must be conclusive, and must lead to the same conclusion. Example (from Pere Felix) : "If we supposed that Jesus Christ, in spite of His own assertions, is not God, we should be led to one of these two insulting conclusions : that He is a madman ; or that He is an impostor. Now, supposing Jesus Christ to be insane, how can we reconcile with insanity the lofty wisdom manifested in His life and doctrine? Supposing Him an impostor, how make His humility and abnegation agree with such ambitious designs? Both these hypotheses, therefore, are equally inadmissible : Jesus Christ is the Christ, the Son of the living God." 1 It is easy to show that the syllogisms are fundamentally re- ducible to the categorical syllogism. 1 The dilemma must not be confounded with reasoning "by suc- cessive parts", which consists in enumerating all the species of a genus, to take them up afterwards one by one and finally enunciate of all the conclusion which is valid for each of the parts. FORMAL CAUSE < >F L< »G1( \l. ( IRDER 51 II. Syllogisms Considered with Reference ro T] Matter. 63. Preliminary Remarks. — Syllogisms arc divided, in respect to their matter, according to the relations of their propositions with the truth. Now, judgments are certain, probable, or erroneous; and syllogisms, accordingly, are demonstrative, prob- erroneous. I 1 i The judgment is certain when the mind firmly adheres to what it knows to be the truth: a syllogism which leads to certi- tude is a demonstration. I 2 I So long as the mind remains between two opposite judg- ment- without definitely adhering to either of the two, it is in suspense, — it doubts. When it inclines to one side or the other, but without adopting either side absolutely to the exclusion of the other, it has an opinion: the syllogism is probable when it begets an opinion, and its probability is in the direct ratio of the strength of the motives which induce the partial adherence of the mind. : 3 i The contrary of truth, the disagreement of the judgments with the thing known, is error: syllogisms which lead to error are called sophistical. We proceed to examine in order demonstrations, probable arguments, and those sophisms which are chiefly worthy of our attention. Different Kinds of Demonstration. 64. I. Primary Division. — A demonstration is a reasoning which proceeds logically from certain premises to a certain con- clusion. And in a more perfect >ense, it is a syllogism which fur- thermore produces true knowledge, i. e., makes us "know the cause of the thing, know that that cause is really the cause of the thing, and that, consequently, the thing could not be other- wise than we know it." 1 There is a primary distinction between the demonstration which i Aristotle. Posterior Anal.. I, :.'. 52 LOGIC produces a certain conclusion and that which produces a strictly scientific conclusion. 65. Conditions of a Strictly Scientific Conclusion.— Examin- ing into the nature of the scientific demonstration, Aristotle de- termines its properties as follows : The premises of the determinate syllogism must be true, pri- mary, immediate, better knotwi than the conclusion, anterior to it, and the cause or reason of its truth. (1) True: Although false premises may sometimes be followed by a true conclusion (57), falsity as such is never the origin of a truth. The aim of the demonstration being to bring a true con- clusion out of the premises, a good demonstration must proceed from true premises, the natural source of truth. (2) Primary — themselves incapable of demonstration — in the sense that all the demonstrations of a science should form a single chain, the first link of which is formed out of premises that cannot be demonstrated. Hence, in relation to those which follow them, these primary premises are : (3) Immediate, i. e., evident without need of demonstration. (4) The cause or reason 1 of the conclusion, not only in the logical order of our knowledge, but in the ontological order. (5) Anterior to the conclusion, since the premises must con- tain the cause or reason of the conclusion. This anteriority may be only a priority of nature. (6) Better knozvn than the conclusion, the aim of reasoning being to effect a passage from what is better known to what is less, or not at all, known. Observe that this Aristotelean theory refers to the ontological order. In our subjective point of view the sensible fact precedes the abstract quiddity which we separate from it ; the particular leads to the universal. But in reality nature is prior to its sensible manifestations, the law is the reason why the fact is, and is necessary to its explanation. 66. Proof of Fact and Causal Demonstration. — Correspond- ing to the fundamental distinction between the syllogism with a certain conclusion and the strictly scientific demonstration is the Aristotelean division of the proof of fact and the causal demon- stration. 1 On this distinction see General Metaphysics, n°. 165. n IRM \l I MM- ( IF L( >GIC \l. I IRDER The demonstration Srt, demonstratio quia, or quod (quia meaning not because, but that), is ///r proof that something t'j. \>- >rding to Cajetan, this proof bears both on the copulative md upon the existence, especially on the latter. 3 The causal demonstration Si6ti, demons/ratio propter quid, brings into evidence the immediate anise of the thing demon- strated, the proper reason, &px*t oUeia, for which it is. Thi why it is strictly scientific. \ demonstration which gives an extrinsic or a general reason for the connection of the predicate with the subject is not a demonstration 8i6n. but is ranked among proofs of fact. 67. II. Demonstrations a Priori, a Posteriori. — This distinc- tion, which, with modern logicians, takes the place of the preced- ing, is less rigorous, hut has a foundation in the nature of things. A demonstration is a priori or a posteriori accordingly as the middle term is in reality anterior or posterior to the predicate of the conclusion ; it proceeds from the cause or the reason (a causa vel ratioite quae in se est prior — a priori) to the effect or result ( (/GIC \l. ORDER 71. I. Arguments from Analogy: i I i The Enthymeme.— The enthymeme, says Aristotle, is "a syllogism drawn from certain resemblances or certain marks." — The "marks" here meant, it must be understood, arc not the natural properties of the subject. Such reasonings arc very frequent in ordinary life. E. g. : Mosl men act from self-interest. Therefore, in this case, Peter acted from self-interest. 72. I 2 ) Analogical Induction or Analogy. — Scientific induc- tion, with which we shall deal later on, disengages from among the many various accidents of a substance a natural property, and concludes with certainty that this property is the foundation of a general law. Analogy is a reasoning of the same nature as induction, hut it- conclusion is only probable. We employ analogical induction, or analogy, when, having recognized in two objects or phenomena certain characteristics which are really common, we infer that one or more other, here- tofore unknown, characteristics of these object- or phenomena must likewise be the same. 1 73. (3) The Example. — Induction, whether scientific or ana- logical, moves from the fact to its sufficient natural reason, to its law and. by consequence, to the universality of its applications. Example moves in a conjectural way from one particular case to another particular case. i I ) Probable hypothe-es and conclusion- drawn from the theory of probabilities. 2 74. II. Arguments from Authority. — In many circumstances of practical life men allow themselves to be guided by others, and they obey arguments from authority. The affirmation of an authority may bear upon a fact or upon a doctrine; in either case its logical value is probability. It is certain that a legitimate tendency inclines us to place reliance in a general way on the exactitude and sincerity of our fellow-men. Nevertheless, confidence in the statement of another cannot ' Analogy is abused in the sciences either by exaggerating resem- blances to suit one's purpose, ignoring differences, or by taking a metaphor for a resemblance. 2 See 95. 56 LOGIC reasonably be absolute. A man who had never before lacked prudence and circumspection in his observation of external facts might, in this one instance, have acted inconsiderately. An habitually sincere man may have lied in this case. In each particular case the argument from authority has its value; but no human testimony justifies absolute certainty. In a doctrinal affirmation, St. Thomas does not hesitate to de- clare, the argument from authority is the weakest of all : "Locus ab auctoritate, quae fundatur super ratione htimana, est infirmis- simus." This declaration is a crushing answer for those superficial minds who would make Scholasticism an abdication of the per- sonal reason in favor of authority. Erroneous and Sophistical Arguments. 75. False Reasoning. — Error proceeds from the basis or from the form: from the basis when we take for true and certain premises which are erroneous or doubtful; from the form- when, consciously or unconsciously, we draw from the premises a con- clusion which does not logically flow from them. In the former case the false reasoning is called an erroneous argument ; in the latter case it is called a paralogism or a soph- ism. The paralogism is a false reasoning of which we ourselves are the dupes ; the sophism, hr the current acceptation, implies the intention of deceiving. 76. False Reasonings or Sophisms. — With Mill we may divide sophisms into two classes : (1) Sophisms of simple inspection, or a priori sophisms. These are prejudices, that is, maxims generally accepted without argument, which, therefore, no one doubts, and which, neverthe- less, are erroneous or at least equivocal. Example : To lay down as a principle that the logical order must correspond with the ontological^-"ideas with things". This preconceived dogma is one of the supports of Pantheism. — To repudiate a priori one or more means of knozving and then to pronounce absolutely unknowable whatever eludes the one means - of knowing- which has been arbitrarily set aside. This prejudice I I iRM VL CAUS] i >i LI »GTC \l. I IRDER enables Rationalism to deny all revelation.— To affirm without v v thai man is entitled to unbounded liberty. i 2 i Sophisms in reasoning properly so called, or sophisms of infer, Of these some are sophisms of induction; others, of deduction. comprising sophisms in terms and in form. 77. False Reasonings Properly So Called. — I. Sophisms of Induction. — Under this head arc included all sophisms which arise in inductive reasoning, whether they affect the preliminaries (sophisms of obsecration) or the inductive reasoning itself (sophisms of interpretation, or of inductive inference). (1 ) SopJiisms of observation. — Patient and honest observation is the starting-point of all inductive research. Too often, how- ever, eagerness to reach a conclusion drives the investigator into assertions which go beyond the bounds of his observation. (a) We see zvhat we wish to see, instead of seeing what is. Example: Haeckel's primary monerons and Huxley's famous Bathybius. ( /' i We do not see what we wish not to see. Example: The biological theories which would demonstrate the identity of the animal and the vegetable cell. (2). Sophisms of interpretation. — Those which consist in wrongly interpreting observed facts. The observation is com- plete, but the meaning attributed to it is added by a suggestion arising from the eagerness to form a complete system. Example : To conclude from the fact that forms of energy may be expressed in terms of mechanical energy to the thesis that all corporeal energies — including those developed in nervous tissue, and accompanied by sensation, passion, spontaneous move- ment, or by thought and volition — are nothing but mechanical energies. (3) Sophisms of inductive inference, or of induction. — The example is illegitimately employed when we pass from one ob- served case to another without first taking care to connect both of them by means of induction with a natural cause. Ab uno disce omues. The analogy is abused in the same way. 3 1 Certain sophisms of induction may be classified indifferently in ■several of the groups of hasty generalizations. 58 LOGIC 78. II. Sophisms of Deduction. — (1) Sophisms of terms. — These are connected with the signification of words which are changed, distorted out of their true sense, or taken in several different senses. The principal ones are : (a) Equivocation, or ambiguity of terms. This consists in employing a word in a double sense in reasoning, or taking an ill-defined word in two different acceptations. Example : The use of the terms, liberty, equality, solidarity, evolution, rational- ism, liberalism, socialism, etc. — Equivocation introduces a fourth term into the reasoning. (b) Passing from the collective to the separate sense (fallacia compositionis). This sophism consists in affirming of things col- lectively what is true only of those same things taken separately. As when Christ says, in the Gospel : "The blind see ; the lame walk upright ; the deaf hear" ; this can only be true taking these things individually, not comprehensively. (c) Passing from the separate to the. collective sense (fallacia divisionis) . This consists, on the contrary, in taking the collec- tive sense. E. g., if we should argue : Five is o.ne number ; but two and three make five ; therefore two and three make one number. (2) Sophisms of inference or of "deduction." — (A) The petitio principii is when we begin by supposing the very thing which is in question. This sophism is committed when we take for granted: (a) the very thing that has to be established; (b) the whole, when a part of it remains to be proved; (c) a part of what has to be proved as a whole; (d) each one of the parts of the whole that has to be established; (F Li IGIC \l. < »RDER 61 82. Definitions of Words and Definitions of Things.— i L) The verbal definition explains the signification, etymological or conventional, of a word. Its purpose is to make our ideas clear and avoid equivocation. (2) The real definition says what a thing is. The real defini- tion is essential, natural, or descriptive. (a) Essential definition. — To know in a perfect manner what a thing is, is to know its intimate nature, its essence. Xow the individual essence, by reason of which this individual subject is what it is, distinct from other individuals, is unknowable to man. 1 We know only by classes. i /> ) Accidental definition. — Wither do we immediately attain the generic or specific essence. On observing the qualities of be- ings, we do not even know, at first, whether they are natural or accidental; the designation is often only a description, improperly called a descriptive 'definition. It is accidental when it designates a thing by means of acces- si iry notes the whole sum of which belongs to this thing alone. (c) Natural definition. — When, through induction, the mind comes to discern in the thing one or more necessary qualities, it defines the thing by its properties: this is natural definition. The definitions used in chemistry, mineralogy, botany, zoology, etc.. are descriptive, accidental, or at most natural. The essential definition, then, is an ideal, which is but rarely attained. And yet, it alone is rigorously scientific or philosophic. How do we form it? 83. Processes of Definition. Synthesis. Combined Analysis and Synthesis. — Some sciences are rational, others, exact or ex- perimental sciences, accordingly as their principles are rational or supplied by induction. The process of definition in the rational sciences is synthetic; in the experimental sciences it is first analytic and then synthetic. (1) Rational sciences.— By means of ordinary observation we abstract from reality as perceived by the senses certain very sim- ple notions (decomposition) which we then combine into more and more complex objects (synthesis). Each of the notes put into the synthesis is more universal than the object of the syn- 1 See Psychology. 62 LOGIC thesis, but their totality is 'more limited than each of them by itself: synthesis progressively limits its object, and makes its definition (opos 6pt.o-iJ.6s). Example : Three is the first uneven number. Each of the attri- butes belongs to other numbers; but their combination limits their attribution to the number three : they define it. As the comprehension of the concept increases, so its extension diminishes. Synthesis, then, is a direct process of definition. We shall see later on that it is at the same time an indirect process of elimination — of division. The attribute uneven is opposed to the attribute even; it ex- cludes the number two. The attribute first excludes all the num- bers except two and three. So then, the combination, first, un- even excludes all the numbers except three. The definition, first, uneven number, fits the defined object, three, and no other object — it is adequate. (2) The experimental sciences end their work with a syn- thesis ; but they begin with an analysis. To arrive at a definition of life, we begin by observing the various beings which are called living, and look for something in them to justify a common attribute. When we eliminate in thought that which distinguishes some of the various vital acts from the rest (nutrition; cognitions; appetitive acts, whether sensual or intellectual), we find in them a common characteristic: they are immanent. 1 Immanent ac- tivity is the definition of life. Division — elimination of distinctive notes — has brought us to definition. And definition will bring back again the division from which the analysis began. Vital immanence is, in fact, found with specific differences in nutrition, in sensations, and in appetitive acts whether sensual or super-sensual. Science descends again from genus to species, from simple to composite. This alternation of analysis and synthesis, moreover, will be prolonged. Side by side with the forms of immanent activity there are forms of transitive activity; the mind abstracts their common characteristic, activity ; this is the generic element, im- 1 See Psychology. Fi IRMAL CAUSE OF L( >GIC \l. I >R1 > G3 manence is a distinctive note. And the two notes combined Eorm the definition of life, the combination of a notion of kind with a notii 'li of difference. Thus, through all these species, analysis pursues a genus which is wider and wider, then a type more and more simple, until it arrives at elements not to be analyzed, by means of which those first definitions arc formed which arc the generating principles of the sciences. This shows how important is the part played by definition in science. In the experimental or exact sciences, as well a> in the rational sciences, to define is to break a thing up and take hold of its simplest determinations, so as to again identify it with these elements (synthesis). The least comprehensive — and therefore most extensive — determination is the generic clement of the definition ; that which complements the generic elements — which delimits the concept, and hence is peculiar to, and specific of. the thing defined — is called the specific difference. Science, however, is in the end always the same: it makes effects known by their causes, consequences by their principles. 84. Rules of Definition. — These relate to the twofold function of definition. I. First point of view: The definition must furnish the first principles of the science. Hence the following rules : (1) The definition must proceed from an object antecedent to the thing defined. Consequently : (a) Correlative terms (as health and sickness), being simul- taneous, cannot be used to define each other. '(&) Different members of a division are not defined by one another. (c) A thing is not defined by itself or by that to which it is antecedent. (2) The genus used in the definition must be the nearest genus. II. Second point of viezv: The definition should help to clear- ness of ideas. It must be clearer than the thing to be defined. Consequently, it must: (a) Not repeat the name of the thing to be defined. (b) Avoid metaphorical, ambiguous, and obscure terms. (c) Be concise and adequate. 64 LOGIC 85. II. Division Inseparable from Definition. — The processes of definition and division go hand-in-hand and complete each other. The definition says what a thing is, identifies it with the simplest components of its essence (genus and specific difference). The division shows to what special forms the generic element of the thing defined applies. The genus is the foundation, or reason, of the division. (1) In the exact sciences the reasoning faculty sets out from generic notions, follows the progress of their specialization, and at every stage marks a new division or subdivision of the genus into subordinate species. In the example given in 83 (1) the number is first specialized as uneven, then it is individualized by the exclusion of all other uneven numbers which is involved in the attribute first. (2) In the positive sciences the reasoning faculty at first fol- lows the inverse process, the analytic: here division brings us to definition. We observe distinct activities in vegetable, animal, and human substances ; nevertheless, at the basis of these activi- ties, there is a common activity : immanent activity, or life. The two different forms of activity— 'the transitive and the immanent — in their turn cover a common idea — a higher genus — activity. Step by step the mind passes from species to genera, from the members of the division to the reason of their separability. Nevertheless, when the common principle is disengaged, the mind turns back to the subjects analyzed to comprehend syntheti- cally the formal divisions of the genus into its species. Definition and division, then, are indissolubly joined together. In the exact sciences the definition precedes, the division follows. In the experimental sciences a first superficial division leads to the essential difinition ; the latter in its turn becomes the formal reason of the specific differences observed in the first instance. 86. Rules of Division. — Like definition, division plays a two- fold part : one, fundamental, in the scientific order ; the other,, secondary, in the pasdagogic order. I. From the first point of view the rules of division are : It must be complete; rationally progressive ; if possible, positive. II. In a second point of view, the division is made for the FORMAL CAUSE OF Li IGICAL ORDER 65 orderly arrangement and clarification of concepts. For this pur- pose il must In- complete, clear, and methodical. ' § 2. Method and Methods 87. Method. — Diversity of Scientific Methods. — Method (ntdoSos) means road; a scientific method is the road which leads to a science. It varies with the nature of the various sciences to which it leads: synthetic or analytic accordingly. Still, it may he said that the scientific method is on the whole a mixed one, analytico-syn- thetic- This section will treat of the respective methods of (I) the abstract sciences, (II) the experimental, (III) philosophy. 88. I. The Synthetic Method. — An exact, or deductive science — such as arithmetic or geometry — sets out from certain princi- ples in necessary matter and combines them to deduce new rela- tions and to form the definitions of the object with which the science concerns itself. It passes from the simple to the com- plex, from the more general to the less general. This is the syn- thetic method. The synthesis which directly forms a definition at the same time effects the division of the defined object and governs all rational demonstrations. Let us suppose, e. g., these theorems established: (1) that the sum of the angles comprising all the space below a straight line is equal to two right angles ; (2) that the interior alternate angles are equal ; that a straight line can always be drawn parallel to a given straight line. — The combination of these three propositions under the guidance of the principle of identity gives rise to a new relation: the identity of the three angles of a triangle with two right angles. 89. II. Method of the Positive Sciences. Its Object.— The positive or experimental sciences begin from concrete facts and end by formulating laws. They go from the complex to the sim- ple, from the particular to the general — the analytical method. i The authors of Port Royal point out that it is "equally a defect to make too few and too many divisions; the one does not sufficiently en- lighten the mind, the other dissipates it too much.*' 2 The analytico-synthetic are the constructive methods of science. Nothing will be said here of the methods of teaching, the didactic methods. See Higher Course, vol. I. 66 LOGIC Though the happenings of nature are variable, the most super- ficial observation shows that this variability is dominated by cer- tain constant and general laws : to determine the laws of these happenings and the nature of things known by experience is the object of the sciences of observation. They begin from the ob- servation of complex and variable facts in order to separate from them the simple element and the permanent law: this procesS'Of de-composition (analysis), considered as a whole, is called induc- tion. Hence the expresion, inductive sciences, as opposed to the deductive, or rational, sciences. 90. Stages of the Inductive Process. — To perform an induc- tion is to ascend from effects to their cause, to determine the properties, and, through them, the nature of the cause, in order to understand the law of its action. Induction comprises four stages : (1) The observation of certain facts which are presented to the senses. E. g., the chemist observes, a certain number of times, in dissimilar circumstances, that different absolute quan- tities of hydrogen (H) and of chlorin (CI) have combined to form a definite body (HC1). (2) The hypothesis. — The investigator supposes that the ob- served phenomenon is inexplicable by constantly recurring fortu- itous coincidences, and that it must have a sufficient reason in the nature of reacting bodies. A scientific hypothesis is the provisional explanation of certain observed facts. x (3) The verification of the hypothesis, which is the heart of the inductive process, is effected sometimes by simple observa- tion, sometimes, in a decisive manner, by experiment. (a) By observation. The author of an hypothesis imagines the results that should follow if it were verified and found to operate in nature. (b) By experiment. The observer is not merely a witness of the course of events in nature, but himself influences those events. By artificial means he varies, according to the aim which he has in view, the agents which operate in a complex phenomenon. (4) The deduction. — The property of the bodies CI and H. to 1 See the thorough study of hypothesis in the Higher Course. M IRM \l. I \l SI ( IF LI >GIC \l. ' IRDE R combine in the definite proportions of l and 35.5, once recognized, the reasoning faculty goes further and from its verified observation draws a general conclusion: thenceforward, every time II and CI arc mixed in the proportions of 1 and 35.5, and exposed to the action of the sun's rays, hydrochloric acid will be formed, and 22 calories per molecule-gramme will be liberated. The consideration of these several stages raises various ques- tions: I 1 ) the observation of facts and their -verification by ex- periment belongs to the description of the methods of induction; (2) the generalization of the observed fact raises the question of the basis of induction; (3) as to deduction, or the last stage of induction, we shall note the relations between deduction and induction. 91. Inductive Methods. — Following Mill's terminology, these are the methods of agreement, of difference, of concomitant -vari- ations, of remainders, and the composite method. The first three are the principal ones. (1 ) Method of agreement: When the phenomenon, the nature of which is to he determined, has occurred in several different cases, and these different cases have a single circumstance in common, this common circumstance is probably the sufficient rea- son of the phenomenon. (2) Method of difference: Two cases are observed: in one the phenomenon occurs, in the other, it does not; all the circum- stances of the two cases are identical except one, which is present in the first case and absent in the second. It may be inferred that tins one circumstance is the whole or partial sufficient reason of the observed phenomenon. ( ."> ) Method of remainders, a composite method, produced by a modification of the methods of agreement and of difference: When the part known to result from certain antecedents, already determinerl by previous inductions, is eliminated from the phenomenon, then what is left of the phenomenon is caused by tlie remaining antecedents. | I ) Method of concomitant variations: When the degrees of variation of a phenomenon correspond with the degrees of varia- tion of a given antecedent, it is to lie presumed thai there is beteewn the two a relation of causality, immediate or mediate. This method, Mill" observes, is particularly demanded when in 68 LOGIC all the cases the preceding methods are inapplicable, as happens when the cause of the phenomenon cannot be completely isolated. (5) The composite method is the cumulative employment of all the preceding. 92. The Object of Induction. — The experiments which deter- mine the law of a chemical combination reach the formal cause of the body, since they reveal the properties springing from that formal cause. These same experiments also determine the material cause of chemical compounds, because they determine the proportional quantities of the components. They may also regard the final cause of the combinations, or the tendencies, in pursuance of which the combinations are formed. Nevertheless, whatever cause in particular may be sought by these researches, they have one object: to determine a property and, by means of it, the specific nature of a being, and, conse- quently, the laiv of its action. We may say, then, that the object of inductive researches is sometimes the discovery of causes (proof of fact, on.), some- times — and more profoundly — the discovery of natural laws and the definition of the types of nature (demonstration, Sioti). The. nature of the being is revealed by its properties ; on them its laws are based. Note that inductive conclusions pass through different degrees of generalization. 93. Logical Foundation of Induction. — The problem is usually stated as follows : Induction passes from the fact to the law,. from some observed cases to all observable cases. Why is this process legitimate? Because the concurrence of a large number of variable elements and forces in one harmonious and persistent combination (the fact established by observation and experi- ment) demands its sufficient reason. Now this sufficient reason can only be a natural inclination of the bodies in which the har- monious and stable combinations take place. This thesis has been demonstrated in Criteriology, n°. 63. 94. The Induction and the Syllogism. — The scientific 1 induc- tion does not differ from the syllogism. By means of the induc- 1 We are not concerned here with the complete induction, which is not scientific. See Hisher Course. Im IRM \l- C \l'SE OF LOGICAL ORDER 69 tive method, indeed, the cause of the observed phenomenon is made manifest. The inductive methods reduce to those of agree- ment and of difference, both of which are applications of the conditional syllogism. Furthermore, when, by means of induc- tive methods, it has been established that the presumed cause of the phenomenon is its true cause (demonstration on), it is shown that this cause is not indifferent, but is naturally deter- mined to the manifestation of a certain property, to act in con- formity with a law. And this demonstration, again, is expressible in syllogisms. 95. Statistics. Their Relation to Induction. — Scientific in- duction concludes with certainty to the existence of a definite law of nature. Xow we are often brought face to face with facts evidently governed by laws, the intricacy of which the mind does not fathom. We then have recourse, provisionally, to the registration of these facts and their coincidences. This con- stitutes the object of statistics. Statistics are an inventory of numerous facts in which their relative frequency and their coincidences are noted with the view of discovering indications of natural causes. It is beyond doubt that there must be a sufficient cause, in the very nature of things, for this constant recurrence of events, but we do not know, or eren guess, with what natural properties this law is connected. 1 Just as soon as the observer guesses, out of all this heap of facts, what invariable conditions (method of agreement), which are also exclusive (method of difference) and correlative in point of intensity (method of con- comitant variations), are antecedent to the event to be explained, so soon will he enter upon a science. A scientific hypothesis will have emerged. The verification of the hypothesis will be the work of induction. ] There are cases where the facts show neither the regularity nor the constancy- which indicate a law, e.g., A homogeneous die, with one of the numbers from 1 to 6 on each of its faces, is thrown. In 12 throws, the numbers 3 and .5 have each turned up three times; the 2 and the 4, twice; the 1 and the f> only once. The probability of contingent events may be submitted to calculation and affords opportunity for interesting applica- tion-. For the theory of probabilities and its logical value. Bernouflli's theorem, and Poisson's law of higher numbers, see Higher Course, vol. I. pp. 352 sqq 70 LOGIC 96. III. The Analytico-Synthetic Method. Conclusion. — Two scientific methods are commonly distinguished : that of the exact sciences, synthesis; that of the sciences of observation, analysis. Synthesis is indeed the basis of the first of these groups of sciences, and analysis of the second ; but neither character- belongs exclusively to either group. The axioms which lie at the basis of the exact sciences in- evitably rest upon certain elementary observations. The results obtained by analysis and induction in the positive sciences prepare the material for synthetic deductions. All science, in fact, aims at the knowledge of things by their causes. The demonstration propter quid alone is rigorously scientific. Even the particular sciences, which have nature for their object (e.g., mechanics, optics, chemistry), endeavor to link their con- clusions with mathematics and metaphysies. Finally, then, the only scientific method is inductivo-deductive and analy 'tic o -synthetic. 1 97. The Method of Philosophy. — The same analytico-'synthetic method rules in philosophical speculation. As philosophy is the science of being in general — of all being — it embraces both the ideal and the empirical order. It passes through both analytically, in order thereafter to explain both synthetically. In this sense we define it, with Aristotle, as "the knowledge of things by their most profound reasons", or as "the profound knowledge of the universal order." In each of its parts (physics, mathematics, metaphysics) philosophy uses the analytico-synthetic method. (1) The physics of the ancients is nowadays divided into cosmology and psychology. By the aid of the physical, chemical, and mineralogical sciences, cosmology leaches the general induc- tive conclusions that corporeal substance is composed of matter and form, and exerts certain proper and characteristic activities. By means of these principles philosophy explains synthetically both the movement of corporeal nature, and the diversity, as well as the constancy of the laws which govern it. 1 After these notions of general methodology, it would be in place, in special methodology, to determine the method proper to each science. On this subject we recommend De la mcthode dans les sciences, by vari- ous professors, Paris, Alcan, 1909. IRM \l. i \l'SK I >!• Li IG1C \1. < >RDER 71 In psychology, facts warrant the inductive conclusion that the first sjubjecl of human life is a material compound informed by an immaterial soul. This conclusion, the principle of synthetic psychology, enables us better to understand the proper object of human reason, the complexity of psychological life and the interdependence of its divers manifestations. (2) The philosophy of mathematics is, in fact and of right, bound up with mathematical sciences. The mathematicians have never separated their theorems from the axioms whence they are deduced. Certain rudimentary observations suggest the axioms, the principles of the syntheses which form the sciences of number and of quantity, and lead on to the most abstract speculations of pure geometry. (3) The various parts of the philosophical sciences lead to indefinable objects: physics, to substance composed of potential- ity and act. of matter and form — to movements produced in a passive subject by an efficient cause determined by an intrinsic end, mathematics, to the one, to the discreet, to addition, to num- ber, etc., or to continuous quantity, as the line, the surface, etc.; criteriology. to the true; ethics, to the moral eml, to moral good; lastly, logic, to the being of reason, to the orderly arrangement of the objects of the reasoning faculty. The first philosophy, or metaphysics, takes for its object these indefinable entities and their relations, and these are the point of departure of the general synthesis which constitutes, in the formal and strict sense, rational wisdom, or philosophy. The ideal of philosophy would be the power to explain the universe, its elements and its laws, judging it, as it were, from above, by means of a synthetic knowledge, as perfect as our nature can attain, of the First Cause Who has created the world by an act of His almighty power, and continually governs it by His providential wisdom: the "synthetic return.'* or study of the world in its First Cause is the summit of philosophy. 1 i Thu- we see how the circular demonstration differs from the vicious circle. CHAPTER IV Final Cause of Logical Order. Conclusion 98. Logic in the Service of the Knowledge of Truth. — The order, or. internal systematization of the judgments and reason- ings which constitute a science, is the intrinsic aim of logic. But logical order, as such, does not ensure the attainment of truth, the final aim of the human mind. This is why the ulti- mate aim — extrinsic, it is true — of the logician is the certain knowledge of truth, which alone deserves the name of science. 99. Definition of Science. — Science may be defined : A group- ing of evident and certain, necessary and universal, systematically organised propositions, which are drawn immediately oj medi- ately from the nature of the subject, and give the intrinsic reason of its properties and of the laws of its action. The propositions of a science must be : (1) Objectively evident, i. e., manifestly true. (2) Certain. An object of faith is, by definition, formally in- evident; it is not, as such, an object of science. Scientific certi- tude is the outcome of systematic thought. (3) Necessary and universal. To gather particular facts is not the work of science ; at most it is preparatory to it. The man of science seeks to know zvhat things are independently of their contingent and variable circumstances — what is the law of their action. "There is no science but the universal", is Aristotle's favorite theme. (4) Systematic, organised. Science is a unified whole. The unity of science, considered formally, consists in this : that its first definitions lay down the principles from which, by synthesis, all the following propositions are deduced. These generating prin- ciples are based upon' the formal object of the particular science. That object is, if not the essence, at least a natural property, of a real subject. Consequently, the intimate reason of the unity of the science is the essence, the nature, to ri eo-n, of its object. This unity is the ideal of a perfect science. TABLE OF CONTENTS INTRODUCTION No. 1. Definition of logic 2. Materials of logical order 3. Formal cause of logical order 4. Difference between psychology and logic 5. Final cause of logical order 6. Difference between logic and metaphysics 7. Logic may be regarded as a practical science or as an art 8. Divisions of logic Page 3 3 3 4 4 5 6 7 CHAPTER I Efficient Cause of Logical Order 9. Origin and nature of the operations of the reasoning faculty . S 10. Multiplicity of the operations of the reasoning faculty. Their fundamental identity 8 11. The abstract character of concepts renders judgment and reasoning possible 10 CHAPTER II The Matter or Material Cause of Logical Order 12. Object and division of Chapter IT 11 ART. I. CONCEPTS § 1. The concept, its abject and properties 13. The concept in its logical aspect 14. By what right does logic concern itself with acts of mere appre- hension 15. Logical problems raised by the act of mere apprehension 16. Logical categories or predicaments .... 17. The predicables 18. Comprehension and extension of concepts 73 11 n 12 13 14 16 74 LOGIC No. Page 19. Relations of subordination between ideas in respect of their ex- tension . . . .... . 1? 20. Comparison of ideas in respect of their comprehension. Relation of identity and opposition 19 8 2. Division of concepts 21. Principal heads of classification of concepts . . . . 19 22. Classification of ideas in respect of the object abstracted by the intellect 20 23. Classification of ideas in respect of their way of representing the object 21 24. Classification of cognitions in respect of their origin or their formation . . ' . . . 21 ART. II. TERMS. 8 1. The term, its object and properties 25. Object of the term 22 26. The ten parts of speech ......... 22 8 2. Classification of terms 27. Classification of terms . . . . . . . . . 23 CHAPTER III The Formal Cause of Logical Order 28. Preliminary note .......... 25 ART. I. JUDGMENT AND PROPOSITION § 1. Notion of the judgment and the proposition 29. The judgment and the proposition 25 30. Function of judgments and propositions in the intellectual life . 26 § 2. Judgments and propositions 31. General classification of propositions 26 I. CLASSIFICATION OF SIMPLE PROPOSITIONS 32. First division of propositions : In respect of their matter 33. Two kinds of judgments in necessary matter 34. Synonymous designations of the foregoing 35. Second division of propositions : In respect of their form 36. Logical value of the predicate of a simple proposition 37. Third division of propositions: In respect of their quantity 38. Fourth division of propositions : In respect of their quality 27 27 29 29 30 31 32 CON! ENTS Mb II. CLASSIFICATION 01 COMPLEX PROPOS] 39. Classification of complex propositions .... ;< 3. Relations betoveen propositions 40. Relations between propositions .... 41. Equivalence of several propositions 12. Convertibility of propositions 4:5. Relations of opposition and subordination •li. Rules relating to the truth or falsity of opposed propo 45. Rules relating to the truth or falsity of subordinate propositions 46. Immediate inferences ....... ART. II. REASONING 47. Preliminary remarks. Object of Art. IT § 1. Reasoning ami the syllogism 48. Reasoning ....... 49. The syllogism. Terminology 50 .Nature and logical basis of the syllogism 51. Of what order is the necessity of the principles of the syllogism? 52. Logical first principles 53. Figures and modes of the syllogism 54. Rules of the syllogism 55. Range of the rules of the syllogism. Logic and truth 75 34 34 34 35 36 157 37 § 2. Syllogisms 56. Preliminary remarks 37 38 39 40 41 41 42 42 45 47 I. SYLLOGISMS CONSIDERED AS TO THEIR FORM 57. Division of syllogisms in regard to their form 58. Variety of the categorical syllogism 59. Nature and rules of the conditional syllogism 60. The conjunctive and the disjunctive syllogism 61. The exclusive syllogism 62. The dilemma 47 47 48 49 49 50 II. SYLLOGISMS CONSIDERED AS TO THEIR MATTER 63. Preliminary remarks 51 76 LOGIC DIFFERENT KINDS OF DEMONSTRATION No. 64. I. Primary Division 65. Conditions of a scientific demonstration 66. Proof of fact and causal demonstration 67. II. Demonstrations a priori and a posteriori 68. III. Circular or retrogressive demonstration 69. IV. Other accidental forms of demonstration Page 51 52 52 53 53 54 PROBABLE ARGUMENTS 70. Probable arguments 71. I. Arguments from analogy: (l) The enthymeme 72. (2) The analogical induction,, or analogy 73. (3) The example 74. II. Arguments from authority .... 54 55 55 55 55 ERRONEOUS AND SOPHISTICAL ARGUMENTS 75. False reasoning . . . 76. False reasonings or sophisms . 77. False reasonings properly so called 78. II. Sophisms of deduction I. Sophisms of induction 56 56 57 58 ART. III. SCIENTIFIC SYSTEMATISATION Preliminary Remarks 79. Science is a system . 80. Scientific systematisation 59 60 § 1. Scientific processes 81. I. Definition. Its function . 82. Definitions of words and of things 83. Processes of definition. Synthesis. combined 84. Rules of definition 85. II. Division inseparable from definition 86. Rules of division Analysis and synthesis 60 61 61 63 64 64 8 2. Method and methods 87. Method. Variety of scientific methods . 88. I. The synthetic method .... 89. II. Method of the positive sciences. Its object 90 Stages of the inductive process 91. Inductive methods 65 65 65 66 CONTENTS 77 Xo. 92. Object of induction 93. Logical foundation of induction 94. The induction and the syllogism 95. Statistics. Their relation to induction . 96. Analytico-synthetic method. Conclusion 97. The method of philosophy Page 68 68 68 69 70 70 CHAPTER IV The Final Cause of Logical Order C( INCLUSION 9S. Logic in the service of science and of truth 99. Definition of science . . . 72 7;> THE MANHATTANVILLE PRESS 110 WEST ELEVENTH STREET NEW YORK CITY THE MEANY PRINTING COMPANY, N. Y. SEP 13 1912 '