On the Nature and Meaning of Number

Year 2018, Volume: 8 Issue: 1, 61 - 77, 21.07.2018

Ayşe Kökcü

https://doi.org/10.18491/beytulhikme.446390

Abstract

This article is about the
understanding of the definition of the number concept and its content in
the context of arithmeticisation of analysis and discussions on the
basis of mathematics in the nineteenth century. The issue will be
addressed historically first and then the proposals for solutions by
mathematicians such as Dedekind, Cantor, Peano, as well as by Frege, a
logician, will be examined. The discussions on the foundations of
arithmetic in the 1870s gained intensity. For mathematics to be a
consistent and reliable science free from contradictions, the concept of
number, the cornerstone of arithmetic, had to be precisely defined. In
this article, the answer to the question of what the concept of number
is and what its meaning is will be discussed.

Keywords

The concept of number, foundations of arithmetic, philosophy of mathematics, Dedekind, Frege

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