The problem of the foundations of mathematics and the roots of logical anti-exceptionalism

Authors

DOI:

https://doi.org/10.51359/2357-9986.2020.248949

Keywords:

logical anti-exceptionalism, foundations of mathematics, Lázslo Kálmar, mathematical empiricism

Abstract

The so-called foundational crisis started by the discovery of the set-theoretic paradoxes in naive set theory, as well as by the discovery of Gödel’s incom-pleteness theorems, was responsible for a series of reactions over the way we understand mathematical knowledge. Among the common views, the most popular ones try to construct mathematical knowledge on a priori elements, such as the notion of proof, or even ideas of “primordial intuitions”, as de-fended by some intuitionists. The purpose of the present paper is to introdu-ce opposite views to the traditional aprioristic ones as a way to trace the his-torical roots of the so-called anti-exceptionalism about logic. In order to do so, the paper presents Lázslo Kalmár’s ideas over his mathematical empiricism as a way to contrast two types of anti-exceptionalism, namely pre- and post-Quine. The problem of mathematical foundations is explored as a demarcati-on criterion between these positions.

Author Biography

Sanderson Molick, Universidade Federal do Rio Grande do Norte; Ruhr-Universität Bochum

PhD candidate in Philosophy at the Federal University of Rio Grande do Norte/UFRN and the Ruhr-Universität Bochum/RUB

References

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[Molick, 2020] Molick, S. (2020). Logical theory revision through data un-derdetermination: an anti-exceptionalist exercise. A publicar em Principia: aninternational journal of epistemology.

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[Szabó, 2018] Szabó, M. (2018). Kalmár’s argument against the plausibilityof Church’s thesis. History and Philosophy of Logic, 39(2):140–157.

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Published

2020-11-27

Issue

Vol. 47 No. 2 (2020): Filosofia da Lógica

Section

Número Especial sobre Filosofia da Lógica

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