C.S. Peirce worked on logic and semiotics (this latter term he translated from the Greek), frequently linking the two. He argued that signs are the vehicles for thought as well as the articulation of logical forms. Peirce differs from Saussure in an important way. Peirce’s semiotics is based not on the word-as-sign but on the proposition as that which hallows comprehension and intelligibility. It is therefore a theory of the production of meaning and not a theory of language.
(i) A sign, for Peirce, is what represents something for someone. This is a sign-function:
Sign A denotes a fact or object B to a reader C. A sign always has these three aspects, it is never an isolated entity. A sign is an example of Firstness, its object—of Secondness, and the interpretant (the mediating element) of Thirdness. The First is therefore a quality, a feeling or possibility. The Second is an individual who interacts with the environment and who may actualise the possibility. The Third is a general term, a rule or law that represents the determinate quality of a regularity or principle. The interpretant is the indispensable element needed to link the sign with its particular object. That is, the presence of C is necessary for A to stand for, or represent B. Without C the connection between the sign A and the object-referent B is incomplete. Here Peirce is suggesting the role of the reader as the medium that produces meaning in her/his act of interpretation. But a sign may also indicate something else. Thus the sign “STOP” may indicate an intersection, a main road, or a dead end. The interpretant may thus extend (or abuse) the sign to make it mean something else. This is the “unlimited semiosis” of Peirce.
(ii) Peirce’s semiotics adopted many such triadic structures. Peirce classifies sign types under three types. The icon is a sign, which is in one, or more respects the same as its object (e.g.:a portrait, where the qualities of the sign are assumed to be the same as the qualities of the object represented). An index is a sign physically linked to or affected by its object. For example, take a weather-cock or a sun-dial. A cry of “HELP!,” or a knock at the door, smoke indicative of a fire, are also examples of signs that function as indices. The index evidently has a “dynamical” relationship with the object. The symbol is a conventional sign used in ship speech and writing. Its relation to its object is of “imputed” character. Also, no symbol can be a sign without being interpreted. Peirce later modified and reified this triadic structure of the sign (see below):
1. QUALISIGN SINSIGN LEGISIGN
(A quality which is a sign) (an event which is a sign) (a conventional sign)
2. ICON INDEX SYMBOL
(a sign which denotes a sign which is affected a conventional sign)
the quality of its object by its object)
3. RHEME DICENT ARGUMENT
(represents a possible object, (a sign which denotes (a sign of a law)
a qualitative possibility) the actual existence of the object)