Indefinite Extensibility in Natural Language
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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 nonintentional semantics, do not seem able to accountfor the indefinitely extensible productivity of natural language.