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, subjectively 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 aspect. Syllogism as the form of the process from generalia to the determination of attributes of the individual subject, 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 particular.
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, (
Greek characters); there is no all-comprehensive science from which truths are to be deduced, and from the common maxims alone nothing can be inferred. (Greek characters) 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 (Greek characters) which are only apprehended by (Greek characters). 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 propositions necessary and propositions true (Greek characters), 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 ((Greek characters)) coupled with the attempt to show that induction too is a kind of syllogism; the explanation of proof as involving essence, coupled with the admission of syllogisms of fact; the treatment of propositions as necessary and contingent in themselves, coupled with the distinction between (Greek characters) and (Greek characters). 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 predecessors (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 universal 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 conditioned 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 the distinctions between necessary, contingent, and possible, which appear partly as given qualities of the judgment, partly as representing differences in the conditions of knowledge, partly as referring 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 (Greek characters) of human thought, is further defined in reference to (a) the quantitative distinctions already recognized (the doctrine of logical opposition), (b) 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 opposition of modal judgments.[3]
Propositions as integral parts of knowledge turn upon the ultimate 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 conjoined 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, universality 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 premisses. Now from this third element there follow certain interesting 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 premisses not (Greek characters) but only (Greek characters). Science and opinion ((Greek characters)) 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 character. 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 processes 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 universal 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
1 The passages in which an apparently formal view of logical relations is expressed are mainly the following: – Topics, i. chap. vi. (in which the fundamental logical forms of definition, genus, property, and accident are explained by refereace to the coincidence of the spheres of subject and predicate in a proposition); Anal. Post., i. chap. 26 ((Greek characters)); Anal. Post., ii. 3 ((Greek characters)); Rhetoric, i. 2, § 19. The general treatment of syllogism in Anal. Pr., i. 4, as apparently resting on the principle of subsumption or logical substitution, has no precise bearing. But the use of the term (Greek characters) by Aristotle is not to be regarded as identical with its use by later logicians, and it is not rashly to be assumed that in Aristotle's view the only logical relation is that between genus and species. The distinction between extent and intent, on which later writers have laid stress, is never suffered in Aristotle to become a distinction in kind; the two elements, extent and content ((Greek characters) and (Greek characters)), are always involved, and the difference is only in the process by which our knowledge is formed. Probably the relations of extent and content would never have been severed from one another had it not been for the error, almost a necessary failing in the attempt to treat formal logic systematically, of regarding notions and judgments as completely formed and defined products apart from the reasoning in which they appear (see, for a diametrically opposed view, Hamilton, Lectures on Logic, ii. p. 266).
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, Théorie logique des propositions modales, 1861. The definitions of (Greek characters) and (Greek characters), which have given rise to much diversity of opinion (cf. Prantl, i. 167 sq., as against Waitz, i. 376, and Bonitz, p. 387), are excellently dealt with by Ueberweg, Logik, § 69.
- ↑ 1
- ↑ On this account the modality is affirmed not to attach to the copula; thus the opposite of "it is necessary-to-be" is "it is not necessary to-be," and not either "it is necessary-not-to-be," or "it is not-necessary-to-be."
- ↑ 3
- ↑ In this sense only can we recognize the distinction between Aristotle's Technik and his idea of Apodiktik on which Lange (Logische Studien, 1880) has laid so much stress. What underlies Aristotle's treatment must never be thrown out of account.
- ↑ Topics, i. 2, §§ 3-6.
- ↑ On this distinction cf. Kampe, Erkenntnisstheorie d. A., pp. 252,253; Heyder, Method. d. A., p. 322.
