Semiotic elements and classes of signs

Logician, mathematician, philosopher, and scientist Charles Sanders Peirce (1839–1914) began writing on semeiotic, semiotics, or the theory of sign relations in the 1860s, around the time that he devised his system of three categories. He eventually defined semiosis as an "action, or influence, which is, or involves, a cooperation of three subjects, such as a sign, its object, and its interpretant, this tri-relative influence not being in any way resolvable into actions between pairs" (Houser 1998, 411). This specific type of triadic relation is fundamental to Peirce's understanding of "logic as formal semiotic". By "logic" he meant philosophical logic. He eventually divided (philosophical) logic, or formal semiotic, into (1) speculative grammar, or stechiology, on the elements of semiosis (sign, object, interpretant), how signs can signify and, in relation to that, what kinds of signs, objects, and interpretants there are, how signs combine, and how some signs embody or incorporate others; (2) logical critic, or logic proper, on the modes of inference; and (3) speculative rhetoric, or methodeutic, the philosophical theory of inquiry, including his form of pragmatism. His speculative grammar, or stechiology, is this article's subject.