Three Doctrines of the Nature of Mathematics (Some Comments of a Knowledge Theorist)

Ryszard Wójcicki

doi:10.18778/0138-0680.46.1.2.02

Three Doctrines of the Nature of Mathematics (Some Comments of a Knowledge Theorist)

Authors

Ryszard Wójcicki IFIS PAN Author

DOI:

https://doi.org/10.18778/0138-0680.46.1.2.02

Keywords:

mathematics, formalism, realism, intuitionism, truth

Abstract

In this note I am reflecting on interrelations between three concepts of truth: (1) that employed by Hilbert arguing his formalist view on the nature of mathematics, (2) Freges idea of truth supported by mathematical intuition, and (3) known as Aristotelian correspondence idea of truth concerning any propositions not merely mathematical.

References

[1] S. Feferman, Logic, mathematics and conceptual structuralism, [in:] The Metaphysics of Logic (P. Rush, ed.), Cambridge University Press (2014), pp. 72–92.

[2] G. Frege, Philosophical and Mathematical Correspondence, ed. G. Gabriel, H. Hermes, F. Kambartel, C. Thiel, and A. Veraart. Abr. B. McGuinness and trans. H. Kaal. Chicago: University of Chicago Press, 1980, pp. 39–40.

[3] F. Klein, Vergleichende Betrachtungen ber neuere geometrische Forschungen, Verlag von Andreas Deichert, Erlangen, 1872.

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Published

2017-06-30

Issue

Vol. 46 No. 1/2 (2017)

Section

Research Article

License

This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

How to Cite

Wójcicki, Ryszard. 2017. “Three Doctrines of the Nature of Mathematics (Some Comments of a Knowledge Theorist)”. Bulletin of the Section of Logic 46 (1/2): 11–19. https://doi.org/10.18778/0138-0680.46.1.2.02.