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A Subject With No ObjectStrategies for Nominalistic Interpretation of Mathematics$
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John P. Burgess and Gideon Rosen

Print publication date: 1999

Print ISBN-13: 9780198250128

Published to Oxford Scholarship Online: November 2003

DOI: 10.1093/0198250126.001.0001

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Strategies in the Literature

Strategies in the Literature

Chapter:
(p.190) B Strategies in the Literature
Source:
A Subject With No Object
Author(s):

John P. Burgess (Contributor Webpage)

Gideon Rosen (Contributor Webpage)

Publisher:
Oxford University Press
DOI:10.1093/0198250126.003.0007

Relates the ideal types of strategies presented in earlier chapters to actual proposals in the literature. We begin with the geometric strategy of Harty Field, and claim that our version better reveals what is really going on than do his own claims about mathematically formulated theories always being conservative extensions of corresponding nominalistic theories. We also consider strategies using modal logic, as found in the works of Charles Chihara and Geoffrey Hellman, emphasizing that one must distinguish metaphysical necessity and possibility from logical necessity and possibility, and use all the resources of cross‐comparison provided by ordinary language, in order to make these strategies work. A potpourri of further strategies is briefly examined.

Keywords:   Charles Chihara, conservative extension, Harty Field, Geoffrey Hellman, logical necessity, logical possibility, metaphysical necessity, metaphysical possibility, modal logic, necessity, possibility

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