On the Nature and Meaning of Number

Year 2018, , 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

References

• Boyer, C. B. (2015). Matematiğin Tarihi. Ankara: Doruk Yayınları.
• Burton, D. M. (2017).Matematik Tarihi. Ankara: Nobel Yayıncılık.
• Cantor, G. (1872). Ueber die Ausdehnung eines Satzes der lehre den trigonometrischen Reihen. Mathematische Annalen, 5 (1), 123-132.
• Cantor, G. (1885) Ueber verschiedene Theoreme aus der Theorie der Punctmengen in einem n-fach ausgedehnten stetigen Raume Gn: Zweite Mittheilung. Acta Mathematica, 7, 105-124.
• Dedekind, R. (1901). Essays on the Theory of Numbers. (Trans. W. W. Beman). Chicago: The Open Court.
• Everdell, W. R. (2012). İlk Modernler. (Çev. H. Kocaoluk). İstanbul: Yapı Kredi Yayınları.
• Frege, G. (2014). Aritmetiğin Temelleri: Sayı Kavramı Üzerine Mantıksal Matematiksel Bir İnceleme. (Çev. B. Gözkan). İstanbul: Yapı Kredi Yayınları.
• Frege, G. (1979). Posthumous Writings. (Trans. P. Longand & R. White). Oxford: Basil Blackwell.
• Frege, G. (1969). Begriffsschrift: A Formula Language, Modeled upon that of Arithmetic for Pure Thought. From Frege to Gödel. (Ed. J. van Heijenoort). Massachusetts: Harvard University Press.
• Joyce, D. E. (2005) . Notes on Richard Dedekind’s Was sind und was sollen die Zahlen? Clark University, https://mathcs.clarku.edu/~djoyce/numbers/dedekind.pdf.
• Katz, V. J. (1993). A History of Mathematics. New York: Harper Collins.
• Stewart, I. (2017). Matematiğin Kısa Tarihi. (Çev. S. Sevinç). İstanbul: Alfa Yayınları.
• Yıldırım, C. (2016). Matematiksel Düşünme. İstanbul: Remzi Kitabevi.