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C. S. Peirce What is a Triad? Quoted from CP 1

  1. 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.

Peirce: CP 1.472 Cross-Ref:††

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I am not sure grammatical acuity is possible

A note to the Peirce list

Seems to me that in a triad you are acknowledging that it is a unity and that everything in it is subsumed to the point that such things as subject and object are if there at all blurred. The object of a triad might be seen as an expression, an action  or both, following the Pragmatic Maxim — the entire consideration. So you might have a sign which is sort of a subject and an index which is sort of a colander through which to strain your thoughts and when they reach the symbol stage they have morphed into the object which was not there until now as it were. I am not sure grammatical acuity is possible in this context. But then again what do I know.

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