Cf: Semiotics, Semiosis, Sign Relations • Comment 1
I opened a topic on Sign Relations in the Logic stream of
Category Theory Zulipchat to work on Peirce's theory of
triadic sign relations in a category-theoretic framework.
I had been reading Peirce for a decade or more before I found a math-strength
definition of signs and sign relations. A lot of the literature on semiotics
takes almost any aperçu Peirce penned about signs as a “definition” but barely
a handful of those descriptions are consequential enough to support significant
theory. For my part, the definition of a sign relation coming closest to the
mark is one Peirce gave in the process of defining logic itself. Two variants
of that definition are linked and copied below.
C.S. Peirce • On the Definition of Logic
Selections from C.S. Peirce, “Carnegie Application” (1902)
No. 12. On the Definition of Logic
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. (NEM 4, 20–21).
No. 12. On the Definition of Logic [Earlier Draft]
Logic is formal semiotic. A sign is something, A, which brings something, B, its interpretant sign, determined or
created by it, into the same sort of correspondence (or a lower implied sort) with something, C, its object, as that in
which itself stands to C. This definition no more involves any reference to human thought than does the definition of a
line as the place within which a particle lies during a lapse of time. It is from this definition that I deduce the
principles of logic by mathematical reasoning, and by mathematical reasoning that, I aver, will support criticism of
Weierstrassian severity, and that is perfectly evident. The word “formal” in the definition is also defined. (NEM 4, 54).
Charles S. Peirce (1902),
“Parts of Carnegie Application” (L 75), published in Carolyn Eisele (ed., 1976),
“The New Elements of Mathematics by Charles S. Peirce”, vol. 4, pp. 13–73.
Online ( https://arisbe.sitehost.iu.edu/menu/library/bycsp/L75/l75.htm