Chapter

Strategies in the Literature

John P. Burgess and Gideon Rosen

in A Subject With No Object

Published in print December 1999 | ISBN: 9780198250128
Published online November 2003 | e-ISBN: 9780191597138 | DOI: http://dx.doi.org/10.1093/0198250126.003.0007
 Strategies in the Literature

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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

Chapter.  6351 words. 

Subjects: Philosophy of Mathematics and Logic

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