Indefinite Extensibility in Natural Language

The Monist 96 (2):295-308 (2013)
Abstract
The Monist’s call for papers for this issue ended: “if formalism is true, then it must be possible in principle to mechanize meaning in a conscious thinking and language-using machine; if intentionalism is true, no such project is intelligible”. We use the Grelling-Nelson paradox to show that natural language is indefinitely extensible, which has two important consequences: it cannot be formalized and model theoretic semantics, standard for formal languages, is not suitable for it. We also point out that object-object mapping theories of semantics, the usual account for the possibility of non intentional semantics, doesn’t seem able to account for the indefinitely extensible productivity of natural language.
Keywords natural language  formalization  indefinite extensibility.  universe of discourse  semantics
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Peter Clark (1993). Sets and Indefinitely Extensible Concepts and Classes. Aristotelian Society Supplementary Volume 67:235--249.
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