The applicability of mathematics as a scientific and a logical problem

Philosophia Mathematica 18 (2):144-165 (2010)
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Abstract

This paper explores how to explain the applicability of classical mathematics to the physical world in a radically naturalistic and nominalistic philosophy of mathematics. The applicability claim is first formulated as an ordinary scientific assertion about natural regularity in a class of natural phenomena and then turned into a logical problem by some scientific simplification and abstraction. I argue that there are some genuine logical puzzles regarding applicability and no current philosophy of mathematics has resolved these puzzles. Then I introduce a plan for resolving the logical puzzles of applicability

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10.1093/philmat/nkp014

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Feng Ye
Capital Normal University, Beijing, China

Citations of this work

Philosophy of mathematics: Making a fresh start.Carlo Cellucci - 2013 - Studies in History and Philosophy of Science Part A 44 (1):32-42.
Foundations as truths which organize mathematics.Colin Mclarty - 2013 - Review of Symbolic Logic 6 (1):76-86.

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References found in this work

Science Without Numbers: A Defence of Nominalism.Hartry H. Field - 1980 - Princeton, NJ, USA: Princeton University Press.
Naturalism in mathematics.Penelope Maddy - 1997 - New York: Oxford University Press.
Constructibility and mathematical existence.Charles S. Chihara - 1990 - New York: Oxford University Press.

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