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Introduction

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Strict Finitism and the Logic of Mathematical Applications

Part of the book series: Synthese Library ((SYLI,volume 355))

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Abstract

This chapter will first introduce my general philosophical position, which is radical naturalism and nominalism. Then, I will explain how the problem of applicability of mathematics can be naturalized, that is, formulated as a problem about some natural regularity in a class of natural phenomena (i.e., the phenomena involving human brains and their physical interactions with other physical entities in human environments in mathematical practices). Applicability becomes a logical problem after we abstract away psychological, physiological, physical, and many other details. I will argue that there are some genuine logical puzzles regarding applicability, due to the gap between infinity in mathematics and the finitude of the physical things to which we apply mathematics. No current philosophy of mathematics, neither Platonism nor nominalism, has resolved these logical puzzles. Finally, a strategy for resolving some of the puzzles and explaining applicability is introduced. I will also discuss how this solution is a naturalistic solution and how it supports nominalism.

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Notes

  1. 1.

    I will ignore the subtle differences between ‘Platonism’ and ‘realism’ (or between ‘nominalism’ and ‘anti-realism’) in the literature, since my position is straight nominalism and anti-realism.

  2. 2.

    Maddy [22] has another kind of naturalistic description of logic. It is not based on naturalized reference and truth and is not radical naturalism in my sense.

  3. 3.

    I would like to thank a referee for raising this question and the question discussed in the next paragraph.

  4. 4.

    I want to thank several referees for raising some of the questions discussed here.

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Authors and Affiliations

  1. Department of Philosophy, Peking University, 100871, Beijing, P. R. China

    Prof. Feng Ye

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  1. Prof. Feng Ye
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Correspondence to Feng Ye .

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Ye, F. (2011). Introduction. In: Strict Finitism and the Logic of Mathematical Applications. Synthese Library, vol 355. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-1347-5_1

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