Logic, Inductive and Deductive

by William Minto

Discoverings of t' other are.

Since, then, everything that comes within our consciousness comes as a change or transition from something else, it results that our knowledge is counter-relative. It is in the clash or conflict of impressions that knowledge emerges: every item of knowledge has its illuminating foil, by which it is revealed, over against which it is defined. Every positive in thought has its contrapositive.

So much for the element of difference. But this is not the whole of the inter-relativity. The Hegelians rightly lay stress on the common likeness that connects the opposed items of knowledge.

"Thought is not only distinction; it is, at the same time, relation.[¹] If it marks off one thing from another, it, at the same time, connects one thing with another. Nor can either of these functions of thought be separated from the other: as Aristotle himself said, the knowledge of opposites is one. A thing which has nothing to distinguish it is unthinkable, but equally unthinkable is a thing which is so separated from all other things as to have no community with them. If then the law of contradiction be taken as asserting the self-identity of things or thoughts in a sense that excludes their community—in other words, if it be not taken as limited by another law which asserts the relativity of the things or thoughts distinguished—it involves a false abstraction.... If, then, the world, as an intelligible world, is a world of distinction, differentiation, individuality, it is equally true that in it as an intelligible world there are no absolute separations or oppositions, no antagonisms which cannot be reconciled."[²]

In the penultimate sentence of this quotation Dr. Caird differentiates his theory against a Logical counter-theory of the Law of Identity, and in the last sentence against an Ethical counter-theory: but the point here is that he insists on the relation of likeness among opposites. Every impression felt is felt as a change or transition from something else: but it is a variation of the same impression—the something else, the contrapositive, is not entirely different. Change itself is felt as the opposite of sameness, difference of likeness, and likeness of difference. We do not differentiate our impression against the whole world, as it were, but against something nearly akin to it—upon some common ground. The positive and the contrapositive are of the same kind.

Let us surprise ourselves in the act of thinking and we shall find that our thoughts obey this law. We take note, say, of the colour of the book before us: we differentiate it against some other colour actually before us in our field of vision or imagined in our minds. Let us think of the blackboard as black: the blackness is defined against the whiteness of the figures chalked or chalkable upon it, or against the colour of the adjacent wall. Let us think of a man as a soldier; the opposite in our minds is not the colour of his hair, or his height, or his birthplace, or his nationality, but some other profession—soldier, sailor, tinker, tailor. It is always by means of some contrapositive that we make the object of our thoughts definite; it is not necessarily always the same opposite, but against whatever opposite it is, they are always homogeneous. One colour is contradistinguished from another colour, one shade from another shade: colour may be contradistinguished from shape, but it is within the common genus of sensible qualities.

A curious confirmation of this law of our thinking has been pointed out by Mr. Carl Abel.[³] In Egyptian hieroglyphics, the oldest extant language, we find, he says, a large number of symbols with two meanings, the one the exact opposite of the other. Thus the same symbol represents strong and weak; above—below; with—without; for—against. This is what the Hegelians mean by the reconciliation of antagonisms in higher unities. They do not mean that black is white, but only that black and white have something in common—they are both colours.

I have said that this law of Homogeneous Counter-relativity has not been recognised by logicians. This, however, is only to say that it has not been explicitly formulated and named, as not being required for Syllogism; a law so all-pervading could not escape recognition, tacit or express. And accordingly we find that it is practically assumed in Definition: it is really the basis of definition per genus et differentiam. When we wish to have a definite conception of anything, to apprehend what it is, we place it in some genus and distinguish it from species of the same. In fact our law might be called the Law of Specification: in obeying the logical law of what we ought to do with a view to clear thinking, we are only doing with exactness and conscious method what we all do and cannot help doing with more or less definiteness in our ordinary thinking.

It is thus seen that logicians conform to this law when they are not occupied with the narrow considerations proper to Syllogism. And another unconscious recognition of it may be found in most logical text-books. Theoretically the not-A of the Law of Contradiction—(A is not not-A)—is an infinite term. It stands for everything but A. This is all that needs to be assumed for Conversion and Syllogism. But take the examples given of the Formal Obverse or Permutation, "All men are fallible". Most authorities would give as the Formal Obverse of this, "No men are infallible". But, strictly speaking, "infallible" is of more limited and definite signification than not-fallible. Not-fallible, other than fallible, is brown, black, chair, table, and every other nameable thing except fallible. Thus in Obversion and Conversion by Contraposition, the homogeneity of the negative term is tacitly assumed; it is assumed that A and not-A are of the same kind.