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Topic:
Matheology § 163
Replies:
1
Last Post:
Nov 27, 2012 2:49 AM




Matheology § 163
Posted:
Nov 27, 2012 1:53 AM


Matheology § 163
First hidden necessary condition of Cantor's proof.  In the middle of the XX c., metamathematics announced Cantor's set theory "naive" and soon the very mention of the term "actual infinity" was banished from all metamathematical and set theoretical tractates. The ancient logical, philosophical, and mathematical problem, which during millenniums troubled outstanding minds of humankind, was "solved" according to the principle: "there is no term  there is no problem". So, today we have a situation when Cantor's theorem and its famous diagonal proof are described in every manual of axiomatic set theory, but with no word as to the "actual infinity". However, it is obvious that if the infinite sequence (1) of Cantor's proof is potential then no diagonal method will allow to construct an individual mathematical object, i.e., to complete the infinite binary sequence y*. Thus, just the actuality of the infinite sequence (1) is a necessary condition (a Trojan Horse) of Cantor's proof, and therefore the traditional, set theoretical formulation of Cantor's theorem (above) is, from the standpoint of classical mathematics, simply wrong and must be re written as follows without any contradiction with any logic. [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. 2] http://www.ccas.ru/alexzen/papers/CANTOR2003/Zenkin%20PILM2002.doc
Regards, WM



