alone left standing, and the formal doctrine of syllogism is complete.
Syllogism already defined[1] becomes through exhibition
in its valid forms clear in its principle. It is a speech-and-thought-form
(λόγος) in which certain matters being posited
something other than the matters posited necessarily results
because of them, and, though it still needs to receive a deeper
meaning when presumed truth gives way to necessary truth of
premises, the notion of the class to that of the class-concept,
collective fact to universal law, its formal claim is manifest.
“Certain matters being posited.” Subject and predicate not
already seen to be conjoined must be severally known to be in
relation with that which joins them, so that more than one
direct conjunction must be given. “Of necessity.” If what
are to be conjoined are severally in relation to a common third
it does perforce relate or conjoin them. “Something other.”
The conjunction was by hypothesis not given, and is a new
result by no means to be reached, apart from direct perception
save by use of at least two given conjunctions. “Because of
them,” therefore. Yet so long as the class-view is prominent,
there is a suggestion of a begging of the question. The class is
either constituted by enumeration of its members, and, passing
by the difficulty involved in the thought of “its” members,
is an empirical universal of fact merely, or it is grounded in the
class-concept. In the first case it is a formal scheme which helps
knowledge and the theory of knowledge not at all. We need
then to develop the alternative, and to pass from the external
aspect of all-ness to the intrinsic ground of it in the universal
καθ᾽ αὑτὸ καὶ ᾗ αὐτό, which, whatsoever the assistance it receives
from induction in some sense of the word, in the course of its
development for the individual mind, is secured against dependence
on instances by the decisive fiat or guarantee of νοῦς,
insight into the systematic nexus of things. The conception of
linkage needs to be deepened by the realization of the middle
term as the ground of nexus in a real order which is also rational.
Aristotle’s solution of the paradox of inference, viz. of the fact that in one sense to go beyond what is in the premises is fallacy, while in another sense not to go beyond them is futility, lies in his formula of implicit and explicit, potential and actual.[2] The real nexus underlying the thought-process Problem of inference. is to be articulated in the light of the voucher by intelligence as to the truth of the principles of the various departments of knowledge which we call sciences, and at the ideal limit it is possible to transform syllogism into systematic presentation, so that, differently written down, it is definition. But for human thought sense, with its accidental setting in matter itself incognizable is always with us. The activity of νοῦς is never Nous. so perfectly realized as to merge implication in intuition. Syllogism must indeed be objective, i.e. valid for any thinker, but it is also a process in the medium of individual thinking, whereby new truth is reached. A man may know that mules are sterile and that the beast before him is a mule, and yet believe her to be in foal “not viewing the several truths in connexion.”[3] The doctrine, then, that the universal premise contains the conclusion not otherwise than potentially is with Aristotle cardinal. The datum of sense is only retained through the universal.[4] It is possible to take a universal view with some at least of the particular instances left uninvestigated.[5] Recognition that the class-concept is applicable may be independent of knowledge of much that it involves. Knowledge of the implications of it does not depend on observation of all members of the class. Syllogism as formula for the exhibition of truth attained, and construction or what not as the instrumental process by which we reach the truth, have with writers since Hegel and Herbart tended to fall apart. Aristotle’s view is other. Both are syllogisms, though in different points of view. For this reason, if for no other, the conception of movement from the potential possession of knowledge to its actualization remains indispensable. Whether this is explanation or description, a problem or its solution, is of course another matter.
In the Posterior Analytics the syllogism is brought into decisive connexion with the real by being set within a system in which its function is that of material implication from principles which are primary, immediate and necessary truths. Hitherto the assumption of the Posterior Analytics. probable as true rather than as what will be conceded in debate[6] has been the main distinction of the standpoint of analytic from that of dialectic. But the true is true only in reference to a coherent system in which it is an immediate ascertainment of νοῦς, or to be deduced from a ground which is such. The ideal of science or demonstrative knowledge is to exhibit as flowing from the definitions and postulates of a science, from its special principles, by the help only of axioms or principles common to all knowledge, and these not as premises but as guiding rules, all the properties of the subject-matter, i.e. all the predicates that belong to it in its own nature. In the case of any subject-kind, its definition and its existence being avouched by νοῦς, “heavenly body” for example, the problem is, given the fact of a non-self-subsistent characteristic of it, such as the eclipse of the said body, to find a ground, a μέσον which expressed the αἴτιον, in virtue of which the adjectival concept can be exhibited as belonging to the subject-concept καθ᾽ αὑτὸ in the strictly adequate sense of the phrase in which it means also ᾗ αὐτό.[7] We are under the necessity then of revising the point of view of the syllogism of all-ness. We discard the conception of the universal as a predicate applicable to a plurality, or even to all, of the members of a group. To know merely κατὰ παντὸς is not to know, save accidentally. The exhaustive judgment, if attainable, could not be known to be exhaustive. The universal is the ground of the empirical “all” and not conversely. A formula such as the equality of the interior angles of a triangle to two right angles is only scientifically known when it is not of isosceles or scalene triangle that it is known, nor even of all the several types of triangle collectively, but as a predicate of triangle recognized as the widest class-concept of which it is true, the first stage in the progressive differentiation of figure at which it can be asserted.[8]
Three points obviously need development, the nature of definition, its connexion with the syllogism in which the middle term is cause or ground, and the way in which we have assurance of our principles.
Definition is either of the subject-kind or of the property that is grounded in it. Of the self-subsistent definition is οὐσίας τις γνωρισμός[9] by exposition of genus and differentia.[10] It is indemonstrable. It presumes the reality of its subject Definition. in a postulate of existence. It belongs to the principles of demonstration. Summa genera and groups below infimae species are indefinable. The former are susceptible of elucidation by indication of what falls under them. The latter are only describable by their accidents. There can here be no true differentia. The artificiality of the limit to the articulation of species was one of the points to which the downfall of Aristotle’s influence was largely due. Of a non-self-subsistent or attributive conception definition in its highest attainable form is a recasting of the syllogism, in which it was shown that the attribute was grounded in the substance or self-subsistent subject of which it is. Eclipse of the moon, e.g. is privation of light from the moon by the interposition of the earth between it and the sun. In the scientific syllogism the interposition of the earth is the middle term, the cause or “because” (διότι), the residue of the definition is conclusion. The difference then is in verbal expression, way of putting, inflexion.[11] If we pluck
- ↑ Prior Analytics, i. 1. 24a 18-20, Συλλογισμὸς δὲ ἑστὶ λόγος ἐν ᾦ τεθέντων τινῶν ἕτερόν τι τῶν κειμένων ἐξ ἀνάγκης σνμβαίνει τῷ ταῦτα εἶναι. The equivalent previously in Topics 100a 25 sqq.
- ↑ Prior Analytics, ii. 21; Posterior Analytics, i. 1.
- ↑ 67a 33-37, μὴ συνθεωρῶν τὸ καθ᾽ ἑκάτερον.
- ↑ 67a 39-63.
- ↑ 79a 4-5.
- ↑ 24b 10-11.
- ↑ Posterior Analytics, i. 4 καθ᾽ αὐτὸ means (1) contained in the definition of the subject; (2) having the subject contained in its definition, as being an alternative determination of the subject, crooked, e.g. is per se of line; (3) self-subsistent; (4) connected with the subject as consequent to ground. Its needs stricter determination therefore.
- ↑ 73b 26 sqq., 74a 37 sqq.
- ↑ 90b 16.
- ↑ Metaphys. Z. 12, H. 6 ground this formula metaphysically.
- ↑ 94a 12, 75b 32.
