History of Logic

Aristotle would assign to Socrates the elaboration of two log ical f unctions :—general definition and inductive method. Rightly, if we add that he gives no theory of either, and that his practical use of the latter depends for its value on selection. It is rather in virtue of his general faith in the possibility of construction, which he still does not undertake, and because of his consequent insistence on the elucidation of general concepts, which in common with some of his contemporaries, he may have thought of as endued with a certain objectivity, that he induces the contro versies of what are called the Socratic schools as to the nature of predication. These result in the formulation of a new dialectic or logic of Plato. Manifestly Socrates' use of certain forms of argu mentation, like their abuse by the sophists, tended to evoke their logical analysis. The use and abuse, confronted one with the other, could not but evoke it.

Plato.

Plato's logic supplies a theory of universals in the doc trine of ideas. Upon this it bases a theory of predication. And it sets forth a dialectic with a twofold movement, towards differ entiation and integration severally, which amounts to a formu lation of inference. The more fully analysed movement, that which proceeds downward from less determinate to more deter minate universals, is named Division. Its associations, accord ingly, are to the modern ear almost inevitably those of a doctrine of classification only. Aristotle, however, treats it as a dialectical rival to syllogism, and it influenced Galilei and Bacon in their views of inference of ter the Renaissance. If we add to this logic of "idea," judgment and inference, a doctrine of categories in the modern sense of the word which makes the Theaetetus, in which it first occurs, a forerunner of Kant's Critique of Pure Reason, we have clearly a very significant contribution to logic.

(a) Of the idea we may say that whatever else it is, it is opposed to that of which it is the idea as its intelligible formula or law, the truth or validity of the phenomenon from the point of view of nexus or system. The thing of sense in its relative isolation is unstable. It is and is not. What gives stability is the insensible principle or principles which it holds, as it were, in solution. These are the ideas, and their mode of being is natu rally quite other than that of the sensible phenomena which they order. The formula for an indefinite number of particular things in particular places at particular times, and all of them presentable in sensuous imagery of a given time and place, is not itself pre sentable in sensuous imagery side by side with the individual members of the group it orders. The law, e.g., of the equality of

the radii of a circle cannot be exhibited to sense, even if equal radii may be so exhibited. It is the wealth of illustration with which Plato expresses his meaning, and the range of application which he gives the idea—to the class-concepts of natural groups objectively regarded, to categories, to aesthetic and ethical ideals, to the concrete aims of the craftsman as well as to scientific laws—that have obscured his doctrine, viz., that wherever there is law, there is an idea.

(b) The paradox of the one in the many is none, if the idea may be regarded as supplying a principle of nexus or organiza tion to an indefinite multiplicity of particulars. But the principle of difference must be carried into the field of ideas. Not only sense is a principle of difference. The ideas are many. The multi plicity in unity must be established within thought itself. Other wise the objection stands : man is man, and good is good, but to say that man is good is clearly to say the thing that is not. Plato replies with the doctrine of the interpenetration of ideas, obvi ously not of all with all, but of some with some, the formula of identity in difference with thought itself. Nor can the oppo nent fairly refuse to admit it, if he affirms the participation of the identical with being, and denies the participation of differ ence with being, or affirms it with not-being. The Sophistes shows among other things that an identity-philosophy breaks down into a dualism of thought and expression, when it applies the predicate of unity to the real, just as the absolute pluralism on the other hand collapses into unity if it affirms or admits any form of rela tion whatsoever. Identity and difference are all-pervasive cate gories, and the speech-form and the corresponding thought-form involve both. For the proposition and judgment involve subject and predicate and exhibit what a modern writer calls "identity of reference with diversity of characterization." Plato proceeds to explain by his principle of difference both privative and nega tive predicates, and also the possibility of false predication. It is obvious that without the principle of difference, error is inexpli cable. Even Plato, however, perhaps scarcely shows that with it, and nothing else but it, error is explained.