I know not whether Mr. Spencer would subscribe to this or not;—nor do I care, for there are mysteries which press more for solution than the meaning of this vague writer's words. But to me such an explanation of our difference-judgment is absolutely unintelligible. We now find black and white different, the explanation says, because we have always have so found them. But why should we always have so found them? Why should difference have popped into our heads so invariably with the thought of them? There must have been either a subjective or an objective reason. The subjective reason can only be that our minds were so constructed that a sense of difference was the only sort of conscious transition possible between black and white; the objective reason can only be that difference was always there, with these colors, outside the mind as an objective fact. The subjective reason explains outer frequency by inward structure, not inward structure by outer frequency; and so surrenders the experience-theory. The objective reason simply says that if an outer difference is there the mind must needs know it—which is no explanation at all, but a mere appeal to the fact that somehow the mind does know what is there.
The only clear thing to do is to give up the sham of a pretended explanation, and to fall back on the fact that the sense of difference has arisen, in some natural manner doubtless, but in a manner which we do not understand. It was by the back-stairs way, at all events; and, from the very first, happened to be the only mode of reaction by which consciousness could feel the transition from one term to another of what (in consequence of this very reaction) we now call a contrasted pair.
In noticing the differences and resemblances of things, and their degrees, the mind feels its own activity, and has given the name of comparison thereto. It need not compare its materials, but if once roused to do so, it can compare them with but one result, and this a fixed consequence of the nature of the materials themselves. Difference and resemblance are thus relations between ideal objects, or conceptions as such. To learn whether black and white differ, I need not consult the world of experience at all; the mere ideas suffice. What I mean by black differs from what I mean by white, whether such colors exist extra mentem meam or not. If they ever do so exist, they will differ. White things may blacken, but the black of them will differ from the white of them, so long as I mean anything definite by these three words.[537]
I shall now in what follows call all propositions which express time- and space-relations empirical propositions; and I shall give the name of rational propositions to all propositions which express the results of a comparison. The latter denomination is in a sense arbitrary, for resemblance and difference are not usually held to be the only rational relations between things. I will next proceed to show, however, how many other rational relations commonly supposed distinct can be resolved into these, so that my definition of rational propositions will end, I trust, by proving less arbitrary than it now appears to be.
SERIES OF EVEN DIFFERENCE AND MEDIATE COMPARISON.
In Chapter XII we saw that the mind can at successive moments mean the same, and that it gradually comes into possession of a stock of permanent and fixed meanings, ideal objects, or conceptions, some of which are universal qualities, like the black and white of our example, and some, individual things. We now see that not only are the objects permanent mental possessions, but the results of their comparison are permanent too. The objects and their differences together form an immutable system. The same objects, compared in the same way, always give the same results; if the result be not the same, then the objects are not those originally meant.
This last principle, which we may call the axiom of constant result, holds good throughout all our mental operations, not only when we compare, but when we add, divide, class, or infer a given matter in any conceivable way. Its most general expression would be "the Same operated on in the same way gives the Same." In mathematics it takes the form of "equals added to, or subtracted from, equals give equals," and the like. We shall meet with it again.
The next thing which we observe is that the operation of comparing may be repeated on its own results; in other words, that we can think of the various resemblances and differences which we find and compare them with each other, making differences and resemblances of a higher order. The mind thus becomes aware of sets of similar differences, and forms series of terms with the same kind and amount of difference between them, terms which, as they succeed each other, maintain a constant direction of serial increase. This sense of constant direction in a series of operations we saw in Chapter XIII (p. 490) to be a cardinal mental fact. "A differs from B differs from C differs from D, etc.," makes a series only when the differences are in the same direction. In any such difference-series all terms differ in just the same way from their predecessors. The numbers 1, 2, 3, 4, 5,... the notes of the chromatic scale in music, are familiar examples. As soon as the mind grasps such a series as a whole, it perceives that two terms taken far apart differ more than two terms taken near together, and that any one term differs more from a remote than from a near successor, and this no matter what the terms may be, or what the sort of difference may be, provided it is always the same sort.