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Topic: Matheology § 237
Replies: 1   Last Post: Apr 5, 2013 4:19 AM

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Posts: 18,076
Registered: 1/29/05
Matheology § 237
Posted: Apr 5, 2013 1:39 AM
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Matheology § 237

The Cantor's set theory is a Trojan Horse of the mathematics-XX: 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 mathematics-XX. Just the Cantor's actualization of infinite sets
generated a lot of set-theoretical 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]

Regards, WM

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