Maxime Bôcher's concept of complementary philosophy of mathematics

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Jerzy Dadaczyński

Abstract

The main purpose of the present paper is to demonstrate that as early as 1904 pre-eminent American mathematician Maxime Bôcher was an adherent to the presently relevant argument of reasonableness, or even necessity of parallel development of two philosophical methods of reflection on mathematics, so that its essence could be more fully comprehended. The goal of the research gives rise to the question: what two types of philosophical deliberation on mathematics were proposed by Bôcher?

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References

Bôcher, M., 1904. The fundamental conceptions and methods of mathematics. Bulletin of the American Mathematical Society [Online], 11(3), pp.115–135. Available at: [visited on 3 July 2020].

Bôcher, M., 1907. Introduction to Higher Algebra [Online]. Ed. By E.P.R. Duval. New York: The Macmillan Company. Available at: [visited on 3 July 2020].

Dadaczyński, J., 2015. Tendencje w podstawach matematyki na początku XX wieku według Maxime Bôchera [Trends in the Foundations of Mathematics in the Early 20th Century According to Maxime Bôcher]. Archiwum Historii Filozofii i Myśli Społecznej [Online], (60), pp.189–204. Available at: [visited on 3 July 2020].

Hadamard, J., 1945. Psychology of Invention in the Mathematical Field. Princeton, N.J.: Princeton University Press.

Hilbert, D., 1900. Über den Zahlbegriff. Jahresbericht der Deutschen Mathematiker-Vereinigung [Online], 8, pp.180–184. Available at: [visited on 3 July 2020].

Hilbert, D., 1905. Über die Grundlagen der Logik und der Arithmetik. In: A. Krazer, ed. Verhandlungen des 3. Internationalen Mathematiker-Kongresses: in Heidelberg vom 8. bis 13. August 1904 [Online]. Leipzig: Teubner, pp.174–185. Available at: https://doi.org/10.11588/HEIDOK.00016037 [visited on 3 July 2020].

Koetsier, T., 1991. Lakatos’ Philosophy of Mathematics: A Historical Approach. Amsterdam: North-Holland.

Lakatos, I., 1963. Proofs and Refutations. The British Journal for the Philosophy of Science, XIV(53-56), pp.1–25, 120–139, 221–245, 296–342.

Lakatos, I., 1976. Proofs and Refutations: The Logic of Mathematical Discovery. Ed. by J. Worrall and E. Zahar. Cambridge: Cambridge University Press.

Poincaré, H., 1904. La valeur de la science, Bibliothèque de Philosophie Scientifique. Paris: Ernest Flammarion.

Tymoczko, T., 1986. Introduction. In: T. Tymoczko, ed. New Directions in the Philosophy of Mathematics: An Anthology. Boston; Basel; Stuttgart: Birkhäuser, pp.xiii–xvii.