Mathematical Method • Discussion 7

Re: Ontolog ForumAlex Shkotin

Dear Alex,

You raised the following point:

AS:
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.

References

  • 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.

Resources

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

This entry was posted in Abstraction, C.S. Peirce, Essentialism, Hypostatic Abstraction, Logic, Mathematics, Metaphysics, Method, Nominalism, Ockham, Ockham's Razor, Peirce, Pragmatic Maxim, Pragmatism, Realism, Semiotics, Theory and tagged , , , , , , , , , , , , , , , , . Bookmark the permalink.

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