The Difference That Makes A Difference That Peirce Makes : 10

Re: Peirce List Discussion • Jon Alan Schmidt

As I am realizing more and more in recent years, analyzing and classifying signs as a substitute for analyzing and classifying objects is the first slip of a slide into nominalism, namely, the idea that the essence or reality of objects is contained in the signs we use to describe them.

The operative phrase in what I wrote is “as a substitute for”.  We always have the task of classifying signs and classifying objects but the problems arise when your favorite ism thinks that half the work will do double duty.  It hardly ever does.

Dyadic forms of correspondence between syntactic structures and objective functions are always nice when you can get them and it’s always worth taking advantage of them when they occur.  It would make things a whole lot simpler if the forms of signs always mirrored the forms of their objects.  That is one of the attractions of Fregean compositionality and Russell’s isomorphism theory and it’s one of the reasons programming language designers keep to the realm of context-free languages for as long as they can.  Taking the Chomsky–Schützenberger Hierarchy as our first rough guide to the complexity of formal languages and the competencies demanded of their processors, we run into a critical point at the threshold between context-free and context-sensitive languages where the mirror of language breaks and the triadic nature of genuine symbols can no longer be avoided.

This entry was posted in Automata, C.S. Peirce, Category Theory, Chomsky, Complementarity, Formal Languages, Inquiry, Laws of Form, Logic, Logic of Relatives, Logical Graphs, Mathematics, Peirce, Philosophy, Physics, Pragmatism, Quantum Mechanics, Relation Theory, Relativity, Science, Scientific Method, Semiotics, Spencer Brown and tagged , , , , , , , , , , , , , , , , , , , , , , . Bookmark the permalink.

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