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Technology and Mathematics pp 345–373Cite as

What the Applicability of Mathematics Says About Its Philosophy

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Part of the book series: Philosophy of Engineering and Technology ((POET,volume 30))

Abstract

What does the existence of applied mathematics say about the philosophy of mathematics? This is the question explored in this chapter, as we take as axiomatic the existence of a successful applied mathematics, and use that axiom to examine the various claims on the nature of mathematics which have been made since the time of Pythagoras. These claims – on the status of mathematical objects and how we can obtain reliable knowledge of them – are presented here in four “schools” of the philosophy of mathematics. The perspective and claims of each school and some of its subschools are presented, along with some historical development of the school’s ideas. Each school is then examined under what we call the lens of the existence of applied mathematics: what does the existence of applied mathematics imply for the competing claims of these various schools? Although, unsurprisingly, this millennia-old debate is not resolved in the next few pages, some of the key issues are brought into sharp focus by the lens. We end with a summary and a tentative discussion of the physicist Max Tegmark’s Mathematical Universe Hypothesis.

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  1. School of Mathematics and Statistics, University of Canterbury, Christchurch, New Zealand

    Phil Wilson

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Correspondence to Phil Wilson .

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  1. Division of Philosophy, Royal Institute of Technology (KTH), Stockholm, Sweden

    Sven Ove Hansson

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Wilson, P. (2018). What the Applicability of Mathematics Says About Its Philosophy. In: Hansson, S. (eds) Technology and Mathematics. Philosophy of Engineering and Technology, vol 30. Springer, Cham. https://doi.org/10.1007/978-3-319-93779-3_15

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