TWO:On the other hand, a theory of reasoning based on the relations of concepts, instead of on the relations of judgments, necessarily leaves out of account the whole doctrine of hypothetical and disjunctive propositions, together with that of the syllogisms based on them; since the elements of which they are composed are themselves propositions. And this inevitable omission is the more remarkable because alterna381tive and, to a less extent, hypothetical arguments form the staple of Aristotles own dialectic; while categorical reasoning never occurs in it at all. His constant method is to enumerate all possible views of a subject, and examine them one after the other, rejecting those which are untenable, and resting content with the remainder. In other words, he reaches his positive conclusions through a series of negative premises representing a process of gradual elimination. The First Analytics is itself an admirable instance of his favourite method. Every possible combination of terms is discussed, and the valid moods are sifted out from a much greater number of illegitimate syllogisms. The dialectic of Socrates and Plato followed the same procedure. It was essentially experimentala method of trial, elimination, and selection. On going back still further, we find that when there is any reasoning at all in Homer, it is conducted after the same fashion. Hector, in his soliloquy before the Scaean Gate, imagines three alternative courses, together exhausting the possibilities of the situation. He may either retreat within the walls, or offer terms of peace to Achilles, or fight. The first two alternatives being rejected, nothing remains but the third. This is the most elaborate example; but on many other occasions Homers actors are represented as hesitating between two courses, and finally deciding on one of them.Finally, while the attempt to attain extreme accuracy of definition was leading to the destruction of all thought and all reality within the Socratic school, the dialectic method had been taken up and parodied in a very coarse style by a class of persons called Eristics. These men had, to some extent, usurped the place of the elder Sophists as paid instructors of youth; but their only accomplishment was to upset every possible assertion by a series of verbal juggles. One of their favourite paradoxes was to deny the reality of falsehood on the Parmenidean principle that nothing cannot exist. Plato satirises their method in the Euthydmus, and makes a much more serious attempt to meet it in the Sophist; two Dialogues which seem to have been composed not far from one another.156 The Sophist effects a considerable simplification in the ideal theory by resolving negation into difference, and altogether omitting the notions of unity and plurality,perhaps as a result of the investiga265tions contained in the Parmenides, another dialogue belonging to the same group, where the couple referred to are analysed with great minuteness, and are shown to be infected with numerous self-contradictions. The remaining five ideas of Existence, Sameness, Difference, Rest, and Motion, are allowed to stand; but the fact of their inseparable connexion is brought out with great force and clearness. The enquiry is one of considerable interest, including, as it does, the earliest known analysis of predication, and forming an indispensable link in the transition from Platonic to Aristotelian logicthat is to say, from the theory of definition and classification to the theory of syllogism.
