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Science without Numbers$
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Hartry Field

Print publication date: 2016

Print ISBN-13: 9780198777915

Published to Oxford Scholarship Online: December 2016

DOI: 10.1093/acprof:oso/9780198777915.001.0001

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Why the Utility of Mathematical Entities is Unlike the Utility of Theoretical Entities

Why the Utility of Mathematical Entities is Unlike the Utility of Theoretical Entities

Chapter:
(p.7) 1 Why the Utility of Mathematical Entities is Unlike the Utility of Theoretical Entities
Source:
Science without Numbers
Author(s):

Hartry Field

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780198777915.003.0001

Argues for the legitimacy of using mathematics to draw nominalistic conclusions (ones statable without reference to mathematical entities) from nominalistic premises, without assuming that the mathematics used in this way is true. Instead we assume that mathematics is conservative: any inference from nominalistic premises to a nominalistic conclusion that can be made with the help of mathematics could be made without it. (In mathematics, conservativeness is only slightly stronger than consistency: the exact relation between the two is discussed in an appendix.) The role of conservativeness marks a fundamental difference between the use of mathematical entities and the use of the theoretical entities of science. The utility of theoretical entities in science is due solely to their theoretical indispensability. Mathematical entities appear to be theoretically indispensable too, but later chapters will argue to the contrary.

Keywords:   conservativeness, consistency, mathematical entities, nominalistic statement, theoretical indispensability

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