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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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Conclusion

Conclusion

Chapter:
(p.205) C Conclusion
Source:
A Subject With No Object
Author(s):

John P. Burgess (Contributor Webpage)

Gideon Rosen (Contributor Webpage)

Publisher:
Oxford University Press
DOI:10.1093/0198250126.003.0008

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

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