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Matheology § 237
Posted:
Apr 5, 2013 1:39 AM


Matheology § 237
The Cantor's set theory is a Trojan Horse of the mathematicsXX: on the one hand, it is a natural, visual, universal language to describe mathematical objects, their properties and relations, originating from the famous Euler's "logical circles", and just therefore this language was accepted by all mathematicians with a natural enthusiasm. However, on the other hand, together with the language, Cantor's transfinite conceptions and constructions (like the actualization of all infinite sets, a distinguishing of infinite sets by the number of their elements (i.e., their cardinalities), the hierarchy of ordinal and cardinal transfinite numbers, continuum hypothesis, etc.) went into the mathematicsXX. Just the Cantor's actualization of infinite sets generated a lot of settheoretical paradoxes and, ultimately, the Third Great Crisis in foundations of mathematics in the beginning of the XX c. The theme itself of the present conference shows that the problem of the actual infinity is not closed and the Third Great Crisis in foundations of mathematics goes on hitherto.
[A.A. Zenkin: "Scientific Intuition of Genii Against Mytho'Logic' of Cantor?s Transfinite Paradise" Procs. of the International Symposium on ?Philosophical Insights into Logic and Mathematics,? Nancy, France, 2002, p. 1] http://www.ccas.ru/alexzen/papers/CANTOR2003/Zenkin%20PILM2002.doc
Regards, WM



