The definition of the sign places it in relation to “the thought that interprets it” and “its object,” meaning that the sign is part of a process of signification.
For this sign process, Peirce introduces the term semiosis:
By semiosis, I mean an action or influence which is, or involves, cooperation between three subjects, such as a sign, its object, and its interpretant
In other words, Peirce defines the sign process as a triadic relation between the Sign, Object, and Interpretant:
A Sign, or Representamen, is something which stands in a triadic relation to something else, its Object, such that it is capable of determining a third, called its Interpretant.
Following Peirce, the American philosopher Charles Morris introduces a fourth factor in semiosis:
The process by which something functions as a sign can be called semiosis. This process, in the tradition that comes from the Greeks, is usually considered to involve three (or four) factors: that which acts as a sign; that to which the sign refers; and the effect produced on the interpreter, because of which the sign is a sign for that interpreter. The three elements of semiosis can be respectively called the sign vehicle, the designatum, and the interpretant; the interpreter can be considered a fourth factor.
The term “designatum” in Morris’s theory has a particular meaning:
Every sign has a designatum, but not every sign refers to something that actually exists. Where that to which it refers does exist, the object of reference is a denotatum. It becomes clear that while every sign has a designatum, not every sign has a denotatum.
Some authors use the term “designatum” instead of “interpretant.” To avoid confusion, modern semiotic theory prefers to use the term “referent” instead of designatum and denotatum.
As for the interpretant, it is a mental image not of a single object but of a class of objects, that is, a concept, which is defined in logic textbooks as “a form of thought by which the objects of a given class are distinguished and generalized based on essential, distinctive features” . Concepts can correspond to a universal class of objects (e.g., star), a singular class of objects (e.g., Moon), or a null class (names behind which there is no real existing class).
The latter type includes all signs with an imaginary denotatum, such as “dragon,” “nymph,” “fairy,” etc., or what Morris calls “designatum without denotatum.”