Closely akin to the function of comparison is that of judging, predicating, or subsuming. In fact, these elementary intellectual functions run into each other so, that it is often only a question of practical convenience whether we shall call a given mental operation by the name of one or of the other. Comparisons result in groups of like things; and presently (through discrimination and abstraction) in conceptions of the respects in which the likenesses obtain. The groups are genera or classes, the respects are characters or attributes. The attributes again may be compared, forming genera of higher orders, and their characters singled out; so that we have a new sort of series, that of predication, or of kind including kind. Thus horses are quadrupeds, quadrupeds animals, animals machines, machines liable to wear out, etc. In such a series as this the several couplings of terms may have been made out originally at widely different times and under different circumstances. But memory may bring them together afterwards; and whenever it does so, our faculty of apprehending serial increase makes us conscious of them as a single system of successive terms united by the same relation.[539]
Now whenever we become thus conscious, we may become aware of an additional relation which is of the highest intellectual importance, inasmuch as upon it the whole structure of logic is reared. The principle of mediate predication or subsumption is only the axiom of skipped intermediaries applied to a series of successive predications. It expresses the fact that any earlier term in the series stands to any later term in the same relation in which it stands to any intermediate term; in other words, that whatever has an attribute has all the attributes of that attribute; or more briefly still, that whatever is of a kind is of that kind's kind. A little explanation of this statement will bring out all that it involves.
We learned in the chapter on Reasoning what our great motive is for abstracting attributes and predicating them. It is that our varying practical purposes require us to lay hold of different angles of the reality at different times. But for these we should be satisfied to 'see it whole,' and always alike. The purpose, however, makes one aspect essential; so, to avoid dispersion of the attention, we treat the reality as if for the time being it were nothing but that aspect, and we let its supernumerary determinations go. In short, we substitute the aspect for the whole real thing. For our purpose the aspect can be substituted for the whole, and the two treated as the same; and the word is (which couples the whole with its aspect or attribute in the categoric judgment) expresses (among other things) the identifying operation performed. The predication-series a is b, b is c, c is d,... closely resembles for certain practical purposes the equation-series a = b, b = c, c = d, etc.
But what is our purpose in predicating? Ultimately, it may be anything we please; but proximately and immediately, it is always the gratification of a certain curiosity as to whether the object in hand is or is not of a kind connected with that ultimate purpose. Usually the connection is not obvious, and we only find that the object S is of a kind connected with P, after first finding that it is of a kind M, which itself is connected with P. Thus, to fix our ideas by an example, we have a curiosity (our ultimate purpose being conquest over nature) as to how Sirius may move. It is not obvious whether Sirius is a kind of thing which moves in the line of sight or not. When, however, we find it to be a kind of thing in whose spectrum the hydrogen-line is shifted, and when we reflect that that kind of thing is a kind of thing which moves in the line of sight; we conclude that Sirius does so move. Whatever Sirius's attribute is, Sirius is; its adjective's adjective can supersede its own adjective in our thinking, and this with no loss to our knowledge, so long as we stick to the definite purpose in view.
Now please note that this elimination of intermediary kinds and transfer of is's along the line, results from our insight into the very meaning of the word is, and into the constitution of any series of terms connected by that relation. It has naught to do with what any particular thing is or is not; but, whatever any given thing may be, we see that it also is whatever that is, indefinitely. To grasp in one view a succession of is's is to apprehend this relation between the terms which they connect; just as to grasp a list of successive equals is to apprehend their mutual equality throughout. The principle of mediate subsumption thus expresses relations of ideal objects as such. It can be discovered by a mind left at leisure with any set of meanings (however originally obtained), of which some are predicable of others. The moment we string them in a serial line, that moment we see that we can drop intermediaries, treat remote terms just like near ones, and put a genus in the place of a species. This shows that the principle of mediate subsumption has nothing to do with the particular order of our experiences, or with the outer coexistences and sequences of terms. Were it a mere outgrowth of habit and association, we should be forced to regard it as having no universal validity; for every hour of the day we meet things which we consider to be of this kind or of that, but later learn that they have none of the kind's properties, that they do not belong to the kind's kind. Instead, however, of correcting the principle by these cases, we correct the cases by the principle. We say that if the thing we named an M has not M's properties, then we were either mistaken in calling it an M, or mistaken about M's properties; or else that it is no longer M, but has changed. But we never say that it is an M without M's properties; for by conceiving a thing as of the kind M I mean that it shall have M's properties, be of M's kind, even though I should never be able to find in the real world anything which is an M. The principle emanates from my perception of what a lot of successive is's mean. This perception can no more be confirmed by one set, or weakened by another set, of outer facts, than the perception that black is not white can be confirmed by the fact that snow never blackens, or weakened by the fact that photographer's paper blackens as soon as you lay it in the sun.
The abstract scheme of successive predications, extended indefinitely, with all the possibilities of substitution which it involves, is thus an immutable system of truth which flows from the very structure and form of our thinking. If any real terms ever do fit into such a scheme, they will obey its laws; whether they do is a question as to nature's facts, the answer to which can only be empirically ascertained. Formal logic is the name of the Science which traces in skeleton form all the remote relations of terms connected by successive is's with each other, and enumerates their possibilities of mutual substitution. To our principle of mediate subsumption she has given various formulations, of which the best is perhaps this broad expression, that the same can be substituted for the same in any mental operation.[540]
The ordinary logical series contains but three terms—"Socrates, man, mortal." But we also have 'Sorites'—Socrates, man, animal, machine, run down, mortal, etc.—and it violates psychology to represent these as syllogisms with terms suppressed. The ground of there being any logic at all is our power to grasp any series as a whole, and the more terms it holds the better. This synthetic consciousness of an uniform direction of advance through a multiplicity of terms is, apparently, what the brutes and lower men cannot accomplish, and what gives to us our extraordinary power of ratiocinative thought. The mind which can grasp a string of is's as a whole—the objects linked by them may be ideal or real, physical, mental, or symbolic, indifferently—can also apply to it the principle of skipped intermediaries. The logic-list is thus in its origin and essential nature just like those graded classificatory lists which we erewhile described. The 'rational proposition' which lies at the basis of all reasoning, the dictum de omni et nullo in all the various forms in which it may be expressed, the fundamental law of thought, is thus only the result of the function of comparison in a mind which has come by some lucky variation to apprehend a series of more than two terms at once.[541] So far, then, both Systematic Classification and Logic are seen to be incidental results of the mere capacity for discerning difference and likeness, which capacity is a thing with which the order of experience, properly so styled, has absolutely nothing to do.
But how comes it (it may next be asked) when systematic classifications have so little ultimate theoretic importance—for the conceiving of things according to their mere degrees of resemblance always yields to other modes of conceiving when these can be obtained—that the logical relations among things should form such a mighty engine for dealing with the facts of life?
Chapter XXII already gave the reason (see p. 335, above). This world might be a world in which all things differed, and in which what properties there were were ultimate and had no farther predicates. In such a world there would be as many kinds as there were separate things. We could never subsume a new thing under an old kind; or if we could, no consequences would follow. Or, again, this might be a world in which innumerable things were of a kind, but in which no concrete thing remained of the same kind long, but all objects were in a flux. Here again, though we could subsume and infer, our logic would be of no practical use to us, for the subjects of our propositions would have changed whilst we were talking. In such worlds, logical relations would obtain, and be known (doubtless) as they are now, but they would form a merely theoretic scheme and be of no use for the conduct of life. But our world is no such world. It is a very peculiar world, and plays right into logic's hands. Some of the things, at least, which it contains are of the same kind as other things; some of them remain always of the kind of which they once were; and some of the properties of them cohere indissolubly and are always found together. Which things these latter things are we learn by experience in the strict sense of the word, and the results of the experience are embodied in 'empirical propositions.' Whenever such a thing is met with by us now, our sagacity notes it to be of a certain kind; our learning immediately recalls that kind's kind, and then that kind's kind, and so on; so that a moment's thinking may make us aware that the thing is of a kind so remote that we could never have directly perceived the connection. The flight to this last kind over the heads of the intermediaries is the essential feature of the intellectual operation here. Evidently it is a pure outcome of our sense for apprehending serial increase; and, unlike the several propositions themselves which make up the series (and which may all be empirical), it has nothing to do with the time- and space-order in which the things have been experienced.