which may be used to concrete and hold on to the suggestion, so that the latter may be handled on its own account. Until thus detached and refixed there are things suggested, but hardly a suggestion; things meant, but hardly a meaning; things ideated, but hardly an idea. And the suggested thing until detached is still too literal, too tied up with other things, to be further developed or to be successfully used as a method of experimentation in new directions so as to bring to light new traits.
As data are signs which indicate other existences, so meanings are signs which imply other meanings.[8] I am doubtful, for example, whether this is a man or not; that is, I am doubtful as to some given traits when they are taken as signs or evidences, but I am inclined to the hypothesis of a man. Having such a tentative or conceptual object in mind, I am enabled to explore economically and effectively, instead of at random, what is present, provided I can elaborate the implications of the term "man." To develop its implications is all one with telling its meaning in connection with other meanings. Being a man means, for example, speaking when spoken to—another meaning which need have been no part of "man" as originally suggested. This meaning of "answering questions" will then suggest a procedure which the term "man" in its first meaning did not possess; it is an implication or implied meaning which puts me in a new and possibly more fruitful relation to the thing. (The process of developing implications is usually termed "discourse" or ratiocination.) Now, be it noted, replying to questions is no part of the definition of man; it would not be now an implication of Plato or of the Russian Czar for me. In other words, there is something in the actual situation which suggests inquiring as well as man; and it is the interaction between these two suggestions which is fruitful. There is consequently no mystery about the fruitfulness of deduction—though this fruitfulness has been urged as though it offered an insuperable objection to instrumentalism. On the contrary, instrumentalism is the only theory to which deduction is not a mystery. If a variety of wheels and cams and rods which have been invented with reference to doing a given task are put together, one expects from the assembled parts a result which could not have been got from any one of them separately or from all of them together in a heap. Because they are independent and unlike structures, working on one another, something new happens. The same is true of terms in relation to one another. When these are brought to bear upon one another, something new, something quite unexpected happens, quite as when one tries an acid with which he is not familiar upon a rock with which he is unfamiliar—that is, unfamiliar in such a conjunction, in spite of intimate acquaintance elsewhere. A definition may fix a certain modicum of meaning in the abstract, as we say; it is a specification of a minimum which gives the point of departure in every interaction of a term with other terms. But nothing follows from the definition by itself or in isolation. It is explicit (boringly so) and has no implications. But bring it in connection with another term with which it has not previously interacted and it may behave in the most delightful or in the most disgustingly disappointing way. The necessity for independent terms is made obvious in the modern theory of axioms. It escapes attention in much of the contemporary logic of transitive and non-transitive, symmetrical and non-symmetrical relations, because the terms are so loaded that there are no propositions at all, but only discriminations of orders of terms. The terms which figure in the discussions, in other words, are correlatives—"brother," "parent," "up," "to the right of," "like," "greater," "after." Such terms are not logical terms; they are halves of such terms as "brother-other-offspring-of-the-same-parents"; "parent-child"; "up-down"; "right-left"; "thing-similar-to-another-thing"; "greater-less"; "after-before." They express positions in a determined situation; they are relatives, not relations. They lack implications, being explicit. But a man who is a brother and also a rival in love, and a poorer man than his rival brother, expresses an interaction of different terms from which something might happen: terms with implications, terms constituting a proposition, which a correlative term never does—till brought into conjunction with a term of which it is not a relative. To have called a thing "up" or "brother" is to have already solved its import in some situation. It is dead till set to work in some other situation.
Experience shows, moreover, that certain qualities of things are much more fruitful and much more controllable than others when taken as meanings to be used in drawing conclusions. The term must be of a nature to develop a method of behavior by which to test whether it is the meaning of the situation. Since it is desirable to have a stock of meanings on hand which are so connected that we can move readily from one to another in any direction, the stock is effective in just the degree in which it has been worked into a system—a comprehensive and orderly arrangement. Hence, while all meanings are derived from things which antedate suggestion—or thinking or "consciousness"—not all qualities are equally fitted to be meanings of a wide efficiency, and it is a work of art to select the proper qualities for doing the work. This corresponds to the working over of raw material into an effective tool. A spade or a watchspring is made out of antecedent material, but does not pre-exist as a ready-made tool; and, the more delicate and complicated the work which it has to do, the more art intervenes. These summary remarks will have to pass muster as indicating what a more extensive treatment of a mathematical system of terms would show. Man began by working such qualities as hate and love and fear and beauty into the meanings by which to interpret and control the perplexities of life. When they demonstrated their inefficacy, he had recourse to such qualities as heavy and light, wet and dry, making them into natural essences or explanatory and regulatory meanings. That Greek mediaeval science did not get very far on these lines is a commonplace. Scientific progress and practical control as systematic and deliberate matters date from the century of Galileo, when qualities which lend themselves to mathematical treatment were seized upon. "The most promising of these ideal systems at first were of course the richer ones, the sentimental ones. The baldest and least promising ones were the mathematical ones; but the history of the latter's application is a history of steadily advancing successes, while that of the sentimentally richer ones is one of relative sterility and failure."[9]
There is no problem of why and how the plow fits, or applies to, the garden, or the watchspring to time-keeping. They were made for those respective purposes; the question is how well they do their work, and how they can be reshaped to do it better. Yet they were made out of physical material; men used ready limbs or roots of trees with which to plow before they used metal. We do not measure the worth or reality of the tool by its closeness to its natural prototype, but by its efficiency in doing its work—which connotes a great deal of intervening art. The theory proposed for mathematical distinctions and relations is precisely analogous. They are not the creations of mind except in the sense in which a telephone is a creation of mind. They fit nature because they are derived from natural conditions. Things naturally bulge, so to speak, and naturally alter. To seize upon these qualities, to develop them into keys for discovering the meanings of brute, isolated events, and to accomplish this effectively, to develop and order them till they become economical tools (and tools upon tools) for making an unknown and uncertain situation into a known and certain one, is the recorded triumph of human intelligence. The terms and propositions of mathematics are not fictions; they are not called into being by that particular act of mind in which they are used. No more is a self-binding reaper a figment, nor is it called momentarily into being by the man who wants to harvest his grain. But both alike are works of art, constructed for a purpose in doing the things which have to be done.
We may say of terms what Santayana so happily said of expression: "Expression is a misleading term which suggests that something previously known is imitated or rendered; whereas the expression is itself an original fact, the values of which are then referred to the thing expressed, much as the honors of a Chinese mandarin are attributed retroactively to his parents." The natural history of imputation of virtue should prove to the philosopher a profitable theme. Even in its most superstitious forms (perhaps more obviously in them than elsewhere) it testifies to the sense of a service to be performed and to a demand for application. The superstition lies in making the application to antecedents and to ancestors, where it is but a shroud, instead of to descendants, where it is a generating factor.
Every reflection leaves behind it a double effect. Its immediate outcome is (as I tried to show earlier) the direct reorganization of a situation, a reorganization which confers upon its contents new increments of intrinsic meaning. Its indirect and intellectual