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Polomnožiny a matematika možného

100%
Holeček M.
Filosofický časopis (Philosophical Journal)
|
2016
|
vol. 64
|
issue 4
601-618
EN
Alternative set theory (AST), or the theory of semisets, the spiritual father of whom is the well-known mathematician Petr Vopěnka, has never received wide recognition and at the present time is subject to neglect. In spite of this, however, it is a conception which is notable for its absolute straightforwardness and for the fundamentally different way in which it mathematises the concept of indeterminacy: the mathematisation of the infinite can be interpreted as an absolutely fundamental mathematisation of the indeterminate. A key role is played by an undetermined grouping – so called semisets. In this article, examples of semisets are discussed in detail and it is shown that semisets should be understood consistently as potentially infinite sets in the spirit of Aristotelian potential infinity. In other words, as sets contain in them a permanent possibility of creating or discovering more and more objects belonging to the given grouping.
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Nieskończoność w matematyce. Zmagania z potrzebnym, acz kłopotliwym pojęciem

86%
Murawski R.
Zagadnienia Filozoficzne w Nauce
|
2014
|
issue 55
5-42
PL
Infinity has appeared in mathematics since the very beginning. Moreover the mathematical concept of infinity was and is connected with philosophical and theological concepts. The aim of the paper is to show how mathematicians struggled with this concept and how they tried to bring it under control.
3

Skończone/nieskończone jako problem filozoficzny

86%
Łagosz M.
Edukacja Filozoficzna
|
2017
|
issue 63
37-58
EN
In this paper, I consider the problem of the spatial and temporary infinity of the Universe. I give an ontological interpretation of the mathematical definition (Bolzano-Dedekind definition) of infinity. I consider the problem of the infinitesimal too.
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