Logical Form in Principia Mathematica and English

Russell: The Journal of Bertrand Russell Studies 31 (1) (2011)
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Abstract

The theory of descriptions, presented informally in "On Denoting" and more formally in Principia Mathematica, has been endorsed by many linguists and philosophers of language as a contribution to natural-language semantics. However, the syntax of Principia’s formal language is far from ideal as a tool for the analysis of natural language. Stephen Neale has proposed a reconstruction of the theory of descriptions in a language of restricted quantification that gives a better approximation of the syntax of English (and, arguably, of other natural languages). This has led to resistance from some Russell scholars who object to the identification of descriptions with quantifiers at the level of logical form in this new language on the grounds that the identification fails to respect the Russellian conception of descriptions as incomplete symbols. I defend Neale’s reconstruction of the theory and argue that he has preserved everything essential to the theory, including the notion of an incomplete symbol. However, I then go on to argue, contrary to Neale and his objectors as well as Russell himself, that the doctrine of incomplete symbols is a superfluous and undesirable element of the theory that is best jettisoned from the theory.

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Author's Profile

Graham Stevens
University of Manchester

Citations of this work

Principia mathematica.A. D. Irvine - 2008 - Stanford Encyclopedia of Philosophy.

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References found in this work

On Denoting.Bertrand Russell - 1905 - Mind 14 (56):479-493.
The foundations of arithmetic.Gottlob Frege - 1884/1950 - Evanston, Ill.,: Northwestern University Press.
On Denoting.Bertrand Russell - 2005 - Mind 114 (456):873 - 887.
Generalized quantifiers and natural language.John Barwise & Robin Cooper - 1981 - Linguistics and Philosophy 4 (2):159--219.

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