§5. Triads

471. We come now to the triad. What is a triad? It is a three. But three what? If we say it is three subjects, we take at the outset an incomplete view of it. Let us see where we are, remembering that logic is to be our guide in this inquiry. The monad has no features but its suchness, which in logic is embodied in the signification of the verb. As such it is developed in the lowest of the three chief forms of which logic treats, the term, the proposition, and the syllogism. The dyad introduced a radically new sort of element, the subject, which first shows itself in the proposition. The dyad is the metaphysical correlative of the proposition, as the monad is of the term. Propositions are not all strictly and merely dyadic, although dyadism is their prominent feature. But strictly dyadic propositions have two subjects. One of these is active, or existentially prior, in its relation to the dyad, while the other is passive, or existentially posterior. A gambler stakes his whole fortune at an even game. What is the probability that he will gain the first risk? One half. What is the probability that he will gain the second risk? One fourth; for if he loses the first play, there will be no second. It is one alternative of the prior event which divides into two in the posterior event. So if A kills B, A first does something calculated to kill B, and then this subdivides into the case in which he does kill B and the case in which he does not. It is not B that does something calculated to make A kill him; or if he does, then he is an active agent and the dyad is a different one. Thus, there are in the dyad two subjects of different character, though in special cases the difference may disappear. These two subjects are the units of the dyad. Each is a one, though a dyadic one. Now the triad in like manner has not for its principal element merely a certain unanalyzable quality sui generis. It makes [to be sure] a certain feeling in us. [But] the formal rule governing the triad is that it remains equally true for all six permutations of A, B, C; and further, if D is in the same relation at once to A and B and to A and C, it is in the same relation to B and C; etc.

472. Each of the three subjects introduces a dyad into the triad, and so does each pair of subjects. The distinctive character or quality of the triad is a monadic element. The formal law of the triad is essentially triadic. It is in that, that the threeness inheres.

473. Every triad is either monadically degenerate, dyadically degenerate, or genuine. A monadically degenerate triad is one which results from the essence of three monads, its subjects. A dyadically degenerate triad is one which results from dyads. A genuine triad is one which cannot be resolved in any such way. That orange color is intermediate between red and yellow is a monoidally degenerate triad. So that one given quality is a compound of two others. So [that] red and green resemble violet more than they resemble each other. That red is a determination of color and scarlet of red involves a monadically degenerate triad and belongs to the class of essential triads; yet it is properly a dyadically degenerate triad where the component dyads are essential dyads. It is thus essential, but only indirectly essential. So that oranges and lemons smell alike, though it is properly only a dyad, yet may be considered as a triad, the common quality of smell being the third subject. That a citric taste and a perfume of a cologne water kind coexist in the lemon can only be regarded as a triad and not as a dyad. That A is father of B and B father of C is a genuinely dyadic degenerate triad. That A is as far north of B as B is east of C is a triad formed of two dyads of one kind and a dyad of another kind — (I mean the similarity of the other two, but this is accidental). This is an almost, but not quite, genuine triad. A is mother of B and B is wife of C. Here the two component dyads are more independent of one another. This is a purer case of the dyadic degenerate triad.

474. In considering the genuine triad, it is well to notice first that the last fact supposed involves the fact that A is mother-in-law of C, which is no triad, but a dyad. Indeed, every triad, as above remarked, involves a dyad; but it is the peculiarity of the dyadic triad that this dyad only differs from the triad in the lack of particularization of the mediating subject. So, reversing the process, every dyad by a particularization evolves a dyadic triad. Thus, A murders B is a generalization of A shoots that bullet, and the bullet fatally wounds B. This is true even in regard to the dyad, A winks, which evolves the triad, A experiences a nervous irritation and the nervous irritation causes winking of the eyelid. Such an evolution may be called an explication of the dyad. So the monad colored is explicated in the monadic dyad, red is colored, and red is explicated in scarlet is red. A triad may be explicated into a triadic tetrad. Thus, A gives B to C becomes A makes the covenant D with C and the covenant D gives B to C.

475. But if we compare the monad implicated in a genuine dyad, as red is in "this thing is red,« with that dyad, we see that the latter is more than any mere explication of red. It is the truth of what Kant called a synthetic (that is, genuinely dyadic) judgment. It involves existence, while red or any mere explication of red is but a possibility. Even in »something is red,« which leaves wholly indeterminate what it is that is red, and consequently does not really explicate red, at all, existence is just as positive as in, »this is red.« Now let us consider the triad, A makes a contract with C. To say that A signs the document D and C signs the document D, no matter what the contents of that document, does not make a contract. The contract lies in the intent. And what is the intent? It is that certain conditional rules shall govern the conduct of A and of C. There is no positive fact in this; it is only conditional and intentional. Still less, if possible, is it any mere monadic quality. It has reference to conditions of experience, involving existence, involving dyadic fact. It may be said that it is a psychical fact. This is in so far true, that a psychical fact is involved; but there is no intent unless something be intended; and that which is intended cannot be covered by any facts; it goes beyond anything that can ever be done or have happened, because it extends over the whole breadth of a general condition; and a complete list of the possible cases is absurd. From its very nature, no matter how far specification has gone, it can be carried further; and the general condition covers all that incompletable possibility.