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:

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Turns from exposition to evaluation of nominalist interpretations, first considering the revolutionary claim that the nominalist theories are superior to current mathematically formulated ones. We argue that this is not so by any recognizably scientific standards of theory evaluation, part of our argument being that Occam's razor, as understood by nominalists, is not really such a scientific standard. We next consider the hermeneutic claim that the interpretations reveal something like deep structures or logical forms underlying surface structures or grammatical forms, and show that current mathematically formulated theories do not really involve ontological commitments to abstract entities after all. We argue that these claims are implausible as empirical linguistics, and philosophically irrelevant even if true. Finally we suggest a different kind of value the nominalist interpretations may have, as partial indicators of what aspects of our scientific theories are the products of convention.

Keywords: deep structure; hermeneutic nominalism; revolutionary nominalism; Occam's razor; ontological commitment; surface structure

Chapter.  16281 words. 

Subjects: Philosophy of Mathematics and Logic

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