Understanding and ad hoc Explanation: A Case of Russell’s Reducibility Axiom

Authors

  • Vitaly Valentinovich Tselishchev Institute of Philosophy and Law of the Siberian Branch of the Russian Academy of Sciences, Novosibirsk, Russia
  • Aleksander Valerievich Khlebalin Institute of Philosophy and Law of the Siberian Branch of the Russian Academy of Sciences, Novosibirsk, Russia https://orcid.org/0000-0002-3536-3974

DOI:

https://doi.org/10.25206/2542-0488-2022-7-2-102-107

Keywords:

branched type theory, axiom of reducibility, explanatory scheme, understanding, intensionality of mathematics

Abstract

The article examines the common interpretation of the axiom of reducibility in Principia Mathematica according to which the axiom cannot be considered as logical, which casts doubt on the success of the program of logicism. In particular, the ad hoc character attributed to the reducibility axiom is refuted and its explanatory role in substantiating Russell’s uniform approach to resolving set-theoretic and semantic paradoxes is affirmed. The key emphasis in the explanatory nature of the axiom of reducibility is placed on the intensional interpretation of mathematical discourse.

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Author Biographies

Vitaly Valentinovich Tselishchev, Institute of Philosophy and Law of the Siberian Branch of the Russian Academy of Sciences, Novosibirsk, Russia

Doctor of Philosophical Sciences, Professor, Scientific Director of Philosophy and Law Institute, Siberian Branch of the Russian Academy of Sciences, Novosibirsk.

Aleksander Valerievich Khlebalin, Institute of Philosophy and Law of the Siberian Branch of the Russian Academy of Sciences, Novosibirsk, Russia

Candidate of Philosophical Sciences, Deputy Director for Research of Philosophy and Law Institute, Siberian Branch of the Russian Academy of Sciences, Novosibirsk.

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Published

2022-05-26

How to Cite

Tselishchev В. В., & Khlebalin А. В. (2022). Understanding and ad hoc Explanation: A Case of Russell’s Reducibility Axiom. Omsk Scientific Bulletin. Series Society. History. Modernity, 7(2), 102–107. https://doi.org/10.25206/2542-0488-2022-7-2-102-107

Issue

Vol. 7 No. 2 (2022)

Section

Philosophy

Categories

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