Mathematical Method • Discussion 7

Re: Ontolog ForumAlex Shkotin

Dear Alex,

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 L is a structure of the form L \subseteq O \times S \times I, we are starting out on pretty much the same page, since I’m always thinking of a sign s as an element of a sign domain S and I’m mainly interested in cases where the sign domain S 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.  OnlinePDF.


cc: CyberneticsOntolog • Peirce List (1) (2) (3)Structural ModelingSystems Science

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