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Infinity and Continuum in the Alternative Set Theory

Trlifajová, Kateřina (2021) Infinity and Continuum in the Alternative Set Theory. [Preprint]

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Abstract

Alternative set theory was created by the Czech mathematician Petr Vopěnka in 1979 as an alternative to Cantor's set theory. Vopěnka criticised Cantor's approach for its loss of correspondence with the real world. Alternative set theory can be partially axiomatised and regarded as a nonstandard theory of natural numbers. However, its intention is much wider. It attempts to retain a correspondence between mathematical notions and phenomena of the natural world. Through infinity, Vopěnka grasps the phenomena of vagueness. Infinite sets are defined as sets containing proper semisets, i.e. vague parts of sets limited by the horizon. The new interpretation extends the field of applicability of mathematics and simultaneously indicates its limits. Compared to strict finitism and other attempts at a reduction of the infinite to the finite Vopenka's theory reverses the process: he models the finite in the infinite.


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Item Type: Preprint
Creators:
CreatorsEmailORCID
Trlifajová, Kateřinakaterina.trlifajova@fit.cvut.cz0000-0002-4997-6608
Keywords: Infinity, continuum, horizon, vagueness, idealization, feasible numbers, non-standard model, phenomenology
Subjects: Specific Sciences > Mathematics > Foundations
General Issues > History of Philosophy of Science
Specific Sciences > Mathematics
General Issues > Models and Idealization
Depositing User: Dr. Katerina Trlifajova
Date Deposited: 15 Dec 2021 20:32
Last Modified: 15 Dec 2021 20:32
Item ID: 20028
DOI or Unique Handle: 10.1007/s13194-021-00429-7
Subjects: Specific Sciences > Mathematics > Foundations
General Issues > History of Philosophy of Science
Specific Sciences > Mathematics
General Issues > Models and Idealization
Date: 13 December 2021
URI: http://philsci-archive.pitt.edu/id/eprint/20028

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