Page:Encyclopædia Britannica, Ninth Edition, v. 14.djvu/812

 788 LOGIC and incognizable. Only in the union of these, a union which objectively regarded is the combination of form and matter, of potentiality and actuality, of genus and ultimate difference, sub jectively is the combination of the data of sense, imagination, and intuitive faculty of reason, is knowledge possible. And the methods by which knowledge is formed in us regarding things exhibit the same twofold nspect. Syllogism as the form of the process from generalia to the determination of attributes of the individual sub ject, induction as the method of procedure from the vaguely apprehended individuals to the generalia or principles, alike, when analysed, exhibit the conjunction of the universal and parti cular. 16. In each branch of knowledge there are involved the specific genus or class, the attributes concerning which there is to be demonstration, and the common axioms or principles. Each branch, moreover, implies special principles, ffiiai apxa i, there is no all-comprehensive science from which truths are to be deduced, and from the common maxims alone nothing can be inferred. A7ro 8ejjs involves principles, and starts therefore of necessity with what maybe called definitions. Yet definitions are at the _ same time the final result of apodictic demonstration, and the original assumptions may be pushed farther and farther back till they appear as the rrpcoTai nal fytcroi Trpordffeis which are only apprehended by vovs. From this distinction between knowledge as completed and knowledge as in process of formation, as from the distinction between sciences of the same genus as more or less general (e.g., geometry and optics), there follow the distinctions between proposi tions necessary and propositions true i-rrl rb TTOV, between proof of fact and proof of essence, between deduction and induction, between syllogism as generic form of all proof, and the special type of syllogism in which completed knowledge is expressed. We are thus enabled to reconcile what seem at first sight discrepancies in the Aristotelian doctrine, as, e.g., the insistance upon induction as furnishing the principles of reasoning (TO, KaQoKov) coupled with the attempt to show that induction too is a kind of syllogism ; the explanation of proof as involving essence, coupled with the admis sion of syllogisms of fact ; the treatment of propositions as necessary and contingent in themselves, coupled with the distinction between firiffrij/j.7] and 5o |a. In all forms of knowledge there is the twofold aspect, that which turns upon the essential connexions, and that which refers to the isolated facts wherein such connexions make their appearance. Syllogistic as formal analysis of what is common in all knowledge is one part of the all-comprehensive theory of knowledge, an integral but not a self-existing part. 1 17. The general idea of the Aristotelian analytic thus obtained does not require to be supplemented by any detailed survey of the logical system into which it is evolved, but a brief summary of the most important points and indication of the relation in which the parts stand to the whole may be of advantage. The simplest form of knowledge, that in which being as true or false is apprehended, is the judgment. The consideration of the judgment is therefore the first part of the analytical researches. Here Aristotle distinguishes more accurately than any of his prede cessors (indeed for the first time with accuracy) between subject and predicate as integral parts, symbolized by the noun and verb, and signifying the relations for us of things as appearing under the schemata of the categories. The material basis of the judgment, as one may call it, is the thing as an object of possible knowledge, i.e., the thing as individual (and therefore as involving matter and form, the particular and the general), as qualified, specifically, in time, space, quantity, and relation, and existing as one mode in the vmiversal nexus of potentiality and actuality. These metaphysical forms, and, specially, the deep-lying modes of potentiality and actuality, reflect themselves in the forms whereby subjectively knowledge is realized in us, and the resulting knowledge is con ditioned partly by them, partly by the modes in which intellect as a reality is developed in us. The proposition has necessarily a reference to them, and thus alongside of formal distinctions between universal, particular, singular, and indefinite judgments we have 1 The passages in which an apparently formal view of logical relations is ex pressed are mainly the following -.Topics, i. chap. vi. (in which the fundamental ledge is formed. Probably the relations of extent and the distinctions between necessary, contingent, and possible, which appear partly as given qualities of the judgment, partly as repre senting differences in the conditions of knowledge, partly as refer ring to differences of subjective apprehension. The essence of the judgment as the apprehension of truth or falsehood consists in its twofold aspect as affirmative and negative, the former of these in a sense prior and better known, but the latter no less necessary, and both referring to objective relations of things. The affirmative and negative character of judgments, the essential dy-n^acm of human thought, is further defined in reference to (a) the quantitative distinctions already recognized (the doctrine of logical opposition), (6) the distinctions of necessary, contingent, and possible, which are rightly regarded as real matters about which the assertion is, 2 and (c), consequent on this, the oppo sition of modal judgments. 3 Propositions as integral parts of knowledge turn upon the ulti mate relations of things known. The distinctions between first principles and deduced truths, out of which the theory of proof is developed, themselves rest upon those distinctions which have been already noted in treating of apodictic. Syllogism as the form by which the general and particular elements are mediated and con joined is therefore of universal application, and may be analysed formally. 4 The various modes in which syllogistic inference, pure or modal, the main types to which these modes may be reduced, their relations to one another, and the general laws implied in them are worked out in a fashion which does not admit of any brief statement. The conclusion unites the elements which in isolation appear in the premisses, and is, in a sense, the complex or organic whole unfolded in the syllogistic form. To every syllogism three things are necessary, the presence of a positive element, uni versality in one of the premisses (resting, as above shown, on the recognized property of all proof as involving a general fact), and consequence, or necessary connexion between conclusion and pre misses. Now from this third element there follow certain interest ing deductions. The necessity of consequence rests on the very nature of syllogistic thought, and if each syllogism be taken as it stands, as a simple unit, no further inquiry is needful. But the character of the premisses in themselves may be taken into account, and we then discover that syllogism proceeds continuously on the assumption that the general law of syllogistic proof is in the special case realized. It need not be in fact realized. We may have premisses in themselves false, from which a true conclusion is reached, and the falsity of the premisses only becomes apparent when they are themselves treated as conclusions of a possible syllogism, and so the regress made towards ultimate principles. Syllogistic form, in short, is the hypothetical application of the general rule of necessary connexion between ground and consequent. If A (the premisses), then B (the conclusion). Quite possibly, then, we may have, in syllogistic form, conclusions drawn from pre misses not avayKcua but only o&amp;gt;s eirl T!&amp;gt; TTOV. Science and opinion (5oa) are equally sources of propositions or premisses. If formal consequences be united with real uncertainty of matter, there arises a syllogism in character dialectical. Were the real uncertainty overlooked, the syllogism would be sophistic in charac ter. Dialectical reasoning, then, dealing with the stage beneath science, may be of service, not only for practice in distinguishing true and false, but as bringing the particulars of each branch of knowledge into closer relation with the first principles special to that branch. 5 For wherever the particular element as such, the transitory and material, is present, there room is left for opinion, and reasoning is possible, not of the particular as such, but in so far as the particular manifests an underlying universal. 6 The pro cesses of dialectic reasoning thus resemble very closely those modes by which the empirical detail, the region of given fact, is treated, viz., induction, example, use of signs and probable indications. For the univessal has always its empirical side, and the complete process of scientific proof is a final result for which the way may be prepared by treatment, according to scientific form, of the empirical fact. There are syllogisms of fact as well as syllogisms of reason or ground, and the reason or ground becomes apparent through knowledge of the fact. Occasionally indeed the fact and ground are so immediately connected that transition from one to the other may be at once effected, but generally this is not the case. Of these intermediate forms of reasoning, the only one calling for 2 On this account the modality is affirmed not to attach to the copula ; thus the opposite of &quot;it is necessary-to-be&quot; is &quot; it is not necessary -to-be,&quot; and not either &quot; it is necessary-not-to-be,&quot; or &quot; it is not-necessary-to-be.&quot;&quot; 3 There are obscurities in Aristotle s doctrine of modals, which remain even after Prantl s laborious treatment (Ges. d. Logik, i. 104-82). A careful survey is given in Rondelet, Theorie logique des propositions nwdales, 1861. The definitions of evSexP-fvov and Svvarov, which have given rise to much diversity of opinion (c/. Prantl, i. 167 sq., as against Waitz, i. 376, and Bonitz, p. 387), are excellently dealt with by Ueberweg, Logik, J 69. 4 In this sense only can we recognize the distinction between Aristotle s Technik and his idea of Apodiktik on which Lange (Logische Studien, 1880) lias laid so much stress. What underlies Aristotle s treatment must never be thrown out of account. 5 Topics, i. 2, 3-6. 6 On this distinction &amp;lt;/. Kampo, Erkenntniiitheorie d. A., pp. 202,253; Heyder, Method, d. A., p. 322.