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STRICT FINITISM, FEASIBILITY, AND THE SORITES

Published online by Cambridge University Press:  30 July 2018

WALTER DEAN
WALTER DEAN*
Affiliation:
Department of Philosophy, University of Warwick
*
*DEPARTMENT OF PHILOSOPHY UNIVERSITY OF WARWICK COVENTRY CV4 7AL, UK E-mail: [email protected]
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Abstract

This article bears on four topics: observational predicates and phenomenal properties, vagueness, strict finitism as a philosophy of mathematics, and the analysis of feasible computability. It is argued that reactions to strict finitism point towards a semantics for vague predicates in the form of nonstandard models of weak arithmetical theories of the sort originally introduced to characterize the notion of feasibility as understood in computational complexity theory. The approach described eschews the use of nonclassical logic and related devices like degrees of truth or supervaluation. Like epistemic approaches to vagueness, it may thus be smoothly integrated with the use of classical model theory as widely employed in natural language semantics. But unlike epistemicism, the described approach fails to imply either the existence of sharp boundaries or the failure of tolerance for soritical predicates. Applications of measurement theory (in the sense of Krantz, Luce, Suppes, & Tversky (1971)) to vagueness in the nonstandard setting are also explored.

Keywords

03B5203H1503D15Strict finitismultrafinitismvaguenesssorites paradoxnonstandard modelsbounded arithmeticsemisetsYessenin-VolpinDummett
Type
Research Article
Information
The Review of Symbolic Logic , Volume 11 , Issue 2 , June 2018 , pp. 295 - 346
Copyright
Copyright © Association for Symbolic Logic 2018 

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