You raised the following point:
- One important usage of a sign is as an element of a language,
especially a formal one, i.e. with a formal grammar.
For context you cited a standard definition of a formal language with a formal grammar (Aho and Ullman 1972).
Viewed from the standpoint of pragmatic semiotics, where a sign relation is a structure of the form we are starting out on pretty much the same page, since I’m always thinking of a sign as an element of a sign domain and I’m mainly interested in cases where the sign domain is a formal language with a formal grammar along the lines defined above.
That brings us to your question, “What is the grammar of Peirce’s language?”, which I will take up next time.
- Barwise, J. (1977), “An Introduction to First-Order Logic”, pp. 5–46 in Barwise, J. (1977, ed.), Handbook of Mathematical Logic, Elsevier (North Holland), Amsterdam.
- Eisele, C. (1982), “Mathematical Methodology in the Thought of Charles S. Peirce”, Historia Mathematica 9, pp. 333–341. Online. PDF.