Georga Cantora filozofia nieskończoności

Piotr Markiewicz

Published: 2018-10-101

No. 10 (2004)

Georg Cantor’s Philosophy of Infinity

Piotr Markiewicz

Abstract

The article treats of Georg Cantor’s idea of nonformal philosophy of infinity. The main argument here is that the knowledge of controversy around the non-axiomatic definition of infinity allows for a better insight into formal procedures in the set theory. Cantorian philosophy of infinity is expressed by three heuristic principles: (1) the actual infinity principle, whereby each mathematically applicable potential infinity (a variable finite number, incomplete domain) assumes the existence of actual infinity (the variability extent is constant, defined for the variables); (2) the principle of finitism - the notion of infinity requires its finitisation if it is to be matematicised. This can be achieved by (a) introducing an ontically uniform status for all permissible mathematical sets, (b) determining that all such sets have a numerical (arithmetical) profile; (3) the principle of absolute infinity, whereby there exist such magnitudes that are not sets i.e. they are not mathematically permissible entities and do not have a full numerical profile. However, they can appear in proofs formulated indirectly as certain objects. They delimit the extent to which the notion of infinity can be matematicised.

Keywords:

Cantor, infinity, set theory

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Markiewicz, P. (2018). Georg Cantor’s Philosophy of Infinity. Humanities and Natural Sciences, (10), 51–68. Retrieved from https://czasopisma.uwm.edu.pl/index.php/hip/article/view/1525

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