On What There is—Infinitesimals and the Nature of Numbers

Inquiry: An Interdisciplinary Journal of Philosophy 58 (1):57-79 (2015)
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Abstract

This essay will be divided into three parts. In the first part, we discuss the case of infintesimals seen as a bridge between the discrete and the continuous. This leads in the second part to a discussion of the nature of numbers. In the last part, we follow up with some observations on the obvious applicability of mathematics

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10.1080/0020174x.2015.978535

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reprint Fenstad, Jens (2018) "On What There Is—Infinitesimals and the Nature of Numbers". In Fenstad, Jens Erik, Structures and Algorithms: Mathematics and the Nature of Knowledge, pp. : Springer Verlag (2018)

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References found in this work

On Computable Numbers, with an Application to the Entscheidungsproblem.Alan Turing - 1936 - Proceedings of the London Mathematical Society 42 (1):230-265.
The nature of mathematical knowledge.Philip Kitcher - 1983 - Oxford: Oxford University Press.
From Frege to Gödel.Jean Van Heijenoort (ed.) - 1967 - Cambridge,: Harvard University Press.
Representation and Invariance of Scientific Structures.Patrick Suppes - 2002 - CSLI Publications (distributed by Chicago University Press).
The unreasonable effectiveness of mathematics in the natural sciences.Eugene Wigner - 1960 - Communications in Pure and Applied Mathematics 13:1-14.

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