One of Peirce’s clearest and most complete definitions of a sign is one he gives in the context of providing a definition for logic, and so it is informative to view it in that setting.
Logic will here be defined as formal semiotic. A definition of a sign will be given which no more refers to human thought than does the definition of a line as the place which a particle occupies, part by part, during a lapse of time. Namely, a sign is something, A, which brings something, B, its interpretant sign determined or created by it, into the same sort of correspondence with something, C, its object, as that in which itself stands to C. It is from this definition, together with a definition of “formal”, that I deduce mathematically the principles of logic. I also make a historical review of all the definitions and conceptions of logic, and show, not merely that my definition is no novelty, but that my non-psychological conception of logic has virtually been quite generally held, though not generally recognized. (C.S. Peirce, NEM 4, 20–21).
In the general discussion of diverse theories of signs, the question frequently arises whether signhood is an absolute, essential, indelible, or ontological property of a thing, or whether it is a relational, interpretive, and mutable role a thing can be said to have only within a particular context of relationships.
Peirce’s definition of a sign defines it in relation to its object and its interpretant sign, and thus defines signhood in relative terms, by means of a predicate with three places. In this definition, signhood is a role in a triadic relation, a role a thing bears or plays in a given context of relationships — it is not an absolute, non-relative property of a thing-in-itself, a status it maintains independently of all relationships to other things.
Some of the terms Peirce uses in his definition of a sign may need to be elaborated for the contemporary reader.
- Correspondence. From the way Peirce uses this term throughout his work it is clear he means what he elsewhere calls a “triple correspondence”, in short, just another way of referring to the whole triadic sign relation itself. In particular, his use of this term should not be taken to imply a dyadic correspondence, as in the varieties of “mirror image” correspondence between realities and representations bandied about in contemporary controversies about “correspondence theories of truth”.
- Determination. Peirce’s concept of determination is broader in several ways than the sense of the word referring to strictly deterministic causal-temporal processes. First, and especially in this context, he uses a more general concept of determination, what is known as formal or informational determination, as we use in geometry when we say “two points determine a line”, rather than the more special cases of causal or temporal determinisms. Second, he characteristically allows for the broader concept of determination in measure, that is, an order of determinism admitting a full spectrum of more and less determined relationships.
- Non-psychological. Peirce’s “non-psychological conception of logic” must be distinguished from any variety of anti-psychologism. He was quite interested in matters of psychology and had much of import to say about them. But logic and psychology operate on different planes of study even when they happen to view the same data, as logic is a normative science where psychology is a descriptive science. Thus they have distinct aims, methods, and rationales.
- Charles S. Peirce (1902), “Parts of Carnegie Application” (L 75), in Carolyn Eisele (ed., 1976), The New Elements of Mathematics by Charles S. Peirce, vol. 4, 13–73. Online.