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Why a Little Bit Goes a Long Way: Logical Foundations of Scientifically Applicable Mathematics

Published online by Cambridge University Press:  19 June 2023

Solomon Feferman
Solomon Feferman*
Affiliation:
Stanford University
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Extract

Does science justify any part of mathematics and, if so, what part? These questions are related to the so-called indispensability arguments propounded, among others, by Quine and Putnam. The general idea of the arguments has been fonnulated (for critical assessment) by Penelope Maddy in a recent article as follows:

We have good reason to believe our best scientific theories, and mathematical entities are indispensable to those theories, so we have good reason to believe in mathematical entities. Mathematics is thus on an ontological par with natural science. Furthermore, the evidence that continns scientific theories also confirms the required mathematics, so mathematics and science are on an epistemological par as weil. (Maddy 1992, p. 78)

Type
Part XIII. Is Foundational Work in Mathematics Relevant to the Philosophy of Science?
Information
PSA: Proceedings of the Biennial Meeting of the Philosophy of Science Association , Volume 1992 , Issue 2: Volume Two: Symposia and Invited Papers 1992 , 1993 , pp. 442 - 455
Copyright
Copyright © 1993 by the Philosophy of Science Association

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Footnotes

1

Invited lecture in the Symposium, “Is foundational work in mathematics relevant to the philosophy of science?” at the meeting of the Philosophy of Science Association, Chicago, Nov. 1, 1992.

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