Semiotic Elements and Classes of Signs - Semiotic Elements - Sign Relation

Sign Relation

Signhood is a way of being in relation, not a way of being in itself. Anything is a sign — not as itself, but in some relation or other. The role of sign is constituted as one role among three: object, sign, and interpretant sign. It is an irreducible triadic relation; the roles are distinct even when the things that fill them are not. The roles are but three: a sign of an object leads to interpretants, which, as signs, lead to further interpretants. In various relations, the same thing may be sign or semiotic object. The question of what a sign is depends on the concept of a sign relation, which depends on the concept of a triadic relation. This, in turn, depends on the concept of a relation itself. Peirce depended on mathematical ideas about the reducibility of relations — dyadic, triadic, tetradic, and so forth. According to Peirce's Reduction Thesis, (a) triads are necessary because genuinely triadic relations cannot be completely analyzed in terms of monadic and dyadic predicates, and (b) triads are sufficient because there are no genuinely tetradic or larger polyadic relations—all higher-arity n-adic relations can be analyzed in terms of triadic and lower-arity relations and are reducible to them. Peirce and others, notably Robert Burch (1991) and Joachim Hereth Correia and Reinhard Pöschel (2006), have offered proofs of the Reduction Thesis. According to Peirce, a genuinely monadic predicate characteristically expresses quality. A genuinely dyadic predicate — reaction or resistance. A genuinely triadic predicate — representation or mediation. Thus Peirce's theory of relations underpins his philosophical theory of three basic categories (see below).

Extension × intension = information. Two traditional approaches to sign relation, necessary though insufficient, are the way of extension (a sign's objects, also called breadth, denotation, or application) and the way of intension (the objects' characteristics, qualities, attributes referenced by the sign, also called depth, comprehension, significance, or connotation). Peirce adds a third, the way of information, including change of information, in order to integrate the other two approaches into a unified whole. For example, because of the equation above, if a term's total amount of information stays the same, then the more that the term 'intends' or signifies about objects, the fewer are the objects to which the term 'extends' or applies. A proposition's comprehension consists in its implications.

Determination. A sign depends on its object in such a way as to represent its object — the object enables and, in a sense, determines the sign. A physically causal sense of this stands out especially when a sign consists in an indicative reaction. The interpretant depends likewise on both the sign and the object — the object determines the sign to determine the interpretant. But this determination is not a succession of dyadic events, like a row of toppling dominoes; sign determination is triadic. For example, an interpretant does not merely represent something which represented an object; instead an interpretant represents something as a sign representing an object. It is an informational kind of determination, a rendering of something more determinately representative. Peirce used the word "determine" not in strictly deterministic sense, but in a sense of "specializes", bestimmt, involving variation in measure, like an influence. Peirce came to define sign, object, and interpretant by their (triadic) mode of determination, not by the idea of representation, since that is part of what is being defined. The object determines the sign to determine another sign — the interpretant — to be related to the object as the sign is related to the object, hence the interpretant, fulfilling its function as sign of the object, determines a further interpretant sign. The process is logically structured to perpetuate itself, and is definitive of sign, object, and interpretant in general. In semiosis, every sign is an interpretant in a chain stretching both fore and aft. The relation of informational or logical determination which constrains object, sign, and interpretant is more general than the special cases of causal or physical determination. In general terms, any information about one of the items in the sign relation tells you something about the others, although the actual amount of this information may be nil in some species of sign relations.