Drexel dragonThe Math ForumDonate to the Math Forum



Search All of the Math Forum:

Views expressed in these public forums are not endorsed by Drexel University or The Math Forum.


Math Forum » Discussions » sci.math.* » sci.math.independent

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

Advanced Search

Back to Topic List Back to Topic List Jump to Tree View Jump to Tree View   Messages: [ Previous | Next ]
mueckenh@rz.fh-augsburg.de

Posts: 13,473
Registered: 1/29/05
Matheology § 237
Posted: Apr 5, 2013 1:39 AM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

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]
http://www.ccas.ru/alexzen/papers/CANTOR-2003/Zenkin%20PILM2002.doc

Regards, WM



Point your RSS reader here for a feed of the latest messages in this topic.

[Privacy Policy] [Terms of Use]

© Drexel University 1994-2014. All Rights Reserved.
The Math Forum is a research and educational enterprise of the Drexel University School of Education.