Page:Encyclopædia Britannica, Ninth Edition, v. 14.djvu/814

 790 LOGIC lies mainly in the matter, not in the form, of the process. For there are numerous hints in Aristotle respecting scientiiic procedure, 1 and, if we consider what is peculiar to modern views, we shall find that it consists mainly in the increased fulness and complexity of our fundamental scientific notions, a fulness and complexity resulting from long-continued scientific research. Our modern logic of induc tion has profited mainly by the general advance of scientific method, and tends to increase as these methods, by constant contact with facts become more refined and accurate. The additional cautious or limitations which we now introduce into our statement of the principles of inductive research concern not so much the form of inductive proof as the character and modes of obtaining evidence which is to satisfy the canons or rules of proof. Such limitations become apparent only through actual scientific progress, not by analysis of the form of scientific proof. 18. To Aristotle, as has been above said, proof is essentially syllo gistic or deductive in character. Not every syllogism is an apodic- tic proof, but all proof is syllogistic. For proof or adequate knowledge is reference of effects to their causes, and the cause is the general element, rb KaBoXov, which forms the middle term in apodic- tic proof. Now proof by means of the cause or reason implies the existence of the cause ; the inquiry why a thing is is useless unless we know or assume that the thing is. If it exists, then the cause or reason of its so existing is that which gives it a definite character or position ; it is, in technical phraseology, the form of the thing. Bat the form of the thing, regarded apart from the material, acci dental element essential to its concrete existence, is that which we express in a definition. Proof and definition are thus most closely connected. The terminus to which proof tends, not realized in all cases of proof but certainly in the most perfect, is the definition, and, besides, if we closely examine proof, and find that ultimately we can force back the chain of middle terms up to certain ultimate, primary universals, disclosed by vovs, and that the nature of these primary universals is stated in their definition, we see further that definition is connected with proof as the terminus from which proof starts. The exposition of definition is thus the crowning portion of Aristotle s theory of apodictic method. 2 In it we have brought into close, though not explicit, relation, the fundamental notions on which his logic rests, the notions of the essence, universal, genus and specific difference. Definition, as concerned with that which is involved in demonstration, the ground or reason, is in cases where the reason and consequent are separable the sum of the demon stration ; it is the compressed statement of the connexion between a subject and the attribute demonstrated of it, i.e., in a syllogism of the first figure, the major term. 3 Frequently a definition merely states the demonstrated attribute in relation to its subject, without indicating the rational link. 4 Such definitions, however, are de fective, just as the conclusion of a syllogism, if taken per se, is defective. 5 A genuine definition is the statement of the essence, which iu mediated notions is the cause or middle term of the demon stration, in immediate notions is directly assumed. 6 A merely nominal definition or explanation of what a name signifies is but a preparatory stadium in the progress towards real, genetic definition. Definition, then, like demonstration, rests on the essential or rational ground, the notion of the thing. The rational ground or notion has its empirical aspect ; it determines a class, and thus, just as in demonstration we may have forms of reasoning based primarily on the empirical details, so in framing definitions we may proceed from the empirical class, and may formulate rules for defining which bear special reference to the genus or body of individuals. In such procedure there is always involved the general idea of the essence or notion as the determining universal, and without this general idea the subsidiary methods, induction and division, do not yield scientific definition. To frame a definition, then, i.e., to discover the elements whose combination as an essential unity makes up the notion of the things defined, we select the predicates belonging to the things in question, 1 See, for example, the discussions in Topics, i. 17-18; ii. 10-11, on similarity ; in the Post. Ana/., i. 13, on deductive and inductive methods; in Pout. Ana!. , ii. 13, on the formation of definition; and in Post. Anal., ii. 12, 1-1-18, on the relation of cause and effect. - It does not seem necessary here to consider in detail the peculiarities of apodictic as these are laid out in the first book of the Post. Anal., nor to deal with the doubts raised regarding definition and proof in the first chapters of the second book. _ The substance of these difficult chapters can be readily summarized. If lennition be taken as a finished result, it seems to stand in no relation to proof, and indeed it is hard to discover how it comes about at all. For definition sup poses that which is implied in proof, the existence of the thing defined, and. pi oof coincide. All this follows, however, from an abstract separation of the form or essence of the thing defined from the concrete nature of the thing. The (sscnce is not to be taken apart ; the definition does not pre-exist as a given fact Ihe essence is the reason of the fact, and is only discoverable when there is the recognized distinction of fact and reason of the fact. We must consider definition tific i e nmed m e nnel ^ S Involved in and resulting from the genesis of scien- 3 arroSeift; Oe crei Sta^e povcra, Anal. Post., i. S, p. 75b 31 4 &amp;lt;ruju.7repa&amp;lt;rjuia TI aTroSei fetos, ibid. 5 De Awtma, ii. _&amp;gt;, p. 413a, 13 sq. 6 o Se riav afiitj-iav opicrjubs fle cris eorl Toi! ri evnv avawoS but also attaching to other species of the same genus. The com bination of such predicates which is not found in any other species, which is, therefore, reciprocable with the essence or form of the species, is its definition. The definition, therefore, contains the genus and the specific attribute (or combination of attributes). Of these elements, the genus is the least important; the truly essential factor is the specific difference, and, in order that our definition should be ultimate, we must follow out the line of specific differ ence by which a genus may be divided until we reach a final, irre ducible characteristic or group of characteristics, constituting a lowest species (or natural kind, if one were to employ a term made current by J. S. Mill). The systematic following out of the specific differences is logical division ; the critical comparison of points of similarity in species of the same genus, so as to obtain a higher generality, has no special title accorded to it, but it resembles the Socratic and Platonic induction (irwayosy-f))- Division proceeds on the oppositions actually found in nature ; and, though, doubtless, the division by dichotomy has formal advantages, it has not, as a process of real cognition, any supreme value. The negative as such is the inconceivable, and presents nothing for cognition. 7 And division is not dependent on exhaustive knowledge; it is not neces sary that, in order to recognize A as distinct from B, we should know the whole universe of possible objects of cognition. A and B may be recognized as identical or distinct in essence, even though they at the same time possess distinct or identical acciden tal marks. Knowledge, in other words, turns upon the essential, not upon the numerical universal. 8 It is only needful, then, that in the systematic process of indicating the elements of definition, all must be included that concern the essence, that the order must be strictly from determining to determined (or from more abstract or general to more concrete or special), and finally that the enumer ation be complete. The final division or species reached is the notion of the thing, and its expression is the definition. 19. The analytical researches thus manifest themselves as a real theory of knowledge and as forming an integral part of the Aristotelian system. Logical relations are throughout conditioned by the characteristics of the Aristotelian metaphysical conception, and the distinction of the formal or technical from the real in cognition has no place in them. No point is more frequently insisted on by Aristotle than the impossibility of deducing any scientific principles or results from the fundamental axiom of thought, the Jaw of non-contradiction. In the Aristotelian system this axiom appears simply as the generalized expression for the peculiar characteristic of thought, its potentiality of truth or falsehood. Such potentiality accompanies thought throughout, and is the mark of its subjective character, but the actuality of thought i.s something quite distinct, and is only realized through the various processes whereby the world of fact is apprehended. Beyond a doubt knowledge has a general aspect ; and there is thus possible a general theory of knowledge, but this is not to be regarded as merely a development from the fundamental axiom of thought. It is the general statement of what constitutes actual cognition, and thus refers on the one hand to the ultimate properties of that which is to be known, on the other hand to the qualities of knowledge as a subjective, though not the less real, fact. For to Aristotle subjective has not the sense which it may be said to have assumed in modern logic, mainly through the Kantian analysis. The activity of thought which realizes itself in the consciousness of the individual is not a mere formal process of apprehension, mirroring or depicting reality that is totally distinct from it. It is a reality, one aspect or phase of the total sum of things, and its development is a real process correlative with the development inherent in things as a whole. At the same time it is impossible to overlook the difficulties which attach to the Aristotelian conception, and the consequent obscurities or perplexities in his logical researches. To remain always true to the fundamental conception of thought as one factor or phase in things, to trace its forms in such a mode- as never to lose sight of its essential correlation to the development of reality, is in itself the hardest task for any thinker, and presupposes a more completed metaphysic than is to be found in Aristotle. Some of these difficulties may be briefly noted, as they form the turning points of certain later doctrines. The judgment or proposition is taken as the initial, the simplest phase of the activity of thought, and so as having the simplest relation to things. But the distinctions of things which are subjectively seized.in the judgment are too much regarded as given facts, and Aristotle is thus involved in a difficulty respecting the import, the truth or falsity, of the judgment. The presence of this difficulty is specially discernible when he attempts to deal with the temporal reference in the judgment, with the doctrine of opposition, and with the nature of modality. Thus, ho notes that the verb, the essential part of the predicate, has a 7 Just as the ovofj.a dopta-rov is said to have no significance save as the sum mary of a proposition, while a negative proposition has significance only in regard, to the corresponding positive. 8 The reference is to a theory advanced by Spensippus; sec Prantl, i. 85. Aristotle here touches on a logical problem whicn has troubled many logicians. It is the same difficulty that arises when the question of plurality of causes is considered.