Indefinite Extensibility in Natural Language

The Monist 96 (2):295-308 (2013)
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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.

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Laureano Luna
Universidad Nacional de Educación a Distancia (PhD)

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References found in this work

On notation for ordinal numbers.S. C. Kleene - 1938 - Journal of Symbolic Logic 3 (4):150-155.
All Things Indefinitely Extensible.Stewart Shapiro & Crispin Wright - 2006 - In Agustín Rayo & Gabriel Uzquiano (eds.), ¸ Iterayo&Uzquiano:Ag. Clarendon Press. pp. 255--304.
Context and unrestricted quantification.Michael Glanzberg - 2006 - In A. Rayo & G. Uzquiano (eds.), Absolute Generality. Oxford University Press. pp. 45--74.
What is a Truth Value And How Many Are There?Roy T. Cook - 2009 - Studia Logica 92 (2):183-201.

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