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Strict finitism, feasibility, and the sorites
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Dean, Walter (2018) Strict finitism, feasibility, and the sorites. Review of Symbolic Logic, 11 (2). pp. 295-346. doi:10.1017/S1755020318000163 ISSN 1755-0211.
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Official URL: https://doi.org/10.1017/S1755020318000163
Abstract
This paper 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 seman- tics 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 non-classical 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 et al. 1971) to vagueness in the nonstandard setting are also explored.
| Item Type: | Journal Article | ||||||
|---|---|---|---|---|---|---|---|
| Subjects: | B Philosophy. Psychology. Religion > BC Logic Q Science > QA Mathematics |
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| Divisions: | Faculty of Social Sciences > Philosophy | ||||||
| Library of Congress Subject Headings (LCSH): | Logic, Symbolic and mathematical, Mathematics -- Philosophy, Computational complexity | ||||||
| Journal or Publication Title: | Review of Symbolic Logic | ||||||
| Publisher: | Cambridge University Press | ||||||
| ISSN: | 1755-0211 | ||||||
| Official Date: | June 2018 | ||||||
| Dates: |
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| Volume: | 11 | ||||||
| Number: | 2 | ||||||
| Page Range: | pp. 295-346 | ||||||
| DOI: | 10.1017/S1755020318000163 | ||||||
| Status: | Peer Reviewed | ||||||
| Publication Status: | Published | ||||||
| Access rights to Published version: | Restricted or Subscription Access | ||||||
| Date of first compliant deposit: | 12 June 2018 | ||||||
| Date of first compliant Open Access: | 12 June 2018 | ||||||
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