Stanford Encyclopedia of Philosophy (2008)

Authors
Mark Colyvan
University of Sydney
Abstract
One of the most intriguing features of mathematics is its applicability to empirical science. Every branch of science draws upon large and often diverse portions of mathematics, from the use of Hilbert spaces in quantum mechanics to the use of differential geometry in general relativity. It's not just the physical sciences that avail themselves of the services of mathematics either. Biology, for instance, makes extensive use of difference equations and statistics. The roles mathematics plays in these theories is also varied. Not only does mathematics help with empirical predictions, it allows elegant and economical statement of many theories. Indeed, so important is the language of mathematics to science, that it is hard to imagine how theories such as quantum mechanics and general relativity could even be stated without employing a substantial amount of mathematics.
Keywords mathematics   indispensability   platonism   toread
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References found in this work BETA

Science Without Numbers: A Defence of Nominalism.Hartry H. Field - 1980 - Princeton, NJ, USA: Princeton University Press.
Word and Object.Willard Van Orman Quine - 1960 - Les Etudes Philosophiques 17 (2):278-279.
Mathematical Truth.Paul Benacerraf - 1973 - Journal of Philosophy 70 (19):661-679.
What Numbers Could Not Be.Paul Benacerraf - 1965 - Philosophical Review 74 (1):47-73.

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Citations of this work BETA

The Intrinsic Structure of Quantum Mechanics.Eddy Keming Chen - 2019 - In Essays on the Metaphysics of Quantum Mechanics. New Brunswick, NJ: PhD dissertation, Rutgers University. pp. Chapter 1.
Neo-Positivist Metaphysics.Alyssa Ney - 2012 - Philosophical Studies 160 (1):53-78.
Indispensability and Explanation.Sorin Bangu - 2013 - British Journal for the Philosophy of Science 64 (2):255-277.

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