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Topic: § 524 Are finite cardinal numbers natural numbers?
Replies: 54   Last Post: Jul 22, 2014 10:45 AM

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 mueckenh@rz.fh-augsburg.de Posts: 18,076 Registered: 1/29/05
§ 524 Are finite cardinal numbers natural numbers?
Posted: Jul 8, 2014 5:49 AM

Cantor has shown how the natural numbers can be defined as cardinal numbers of sets.
First Zermelo and later v. Neumann have shown how the natural numbers can be defined as ordinal numbers of sets.
Zero, the most unnatural number though, has been raped and mutilated to become a "natural" number, only in order to justify the unsound idea that a finite initial segment of the ordered set of natural numbers has a cardinal number surpassing all its elements and to deceive mathematicians with the lie that this is a natural state and therefore cannot be different in |{1, 2, 3, ... }| = aleph_0.
The Löwenheim-Skolem argument has been perverted by defineing what "the system thinks". The countability of all really real numbers has been dampened by imaginating undefinable "real numbers". The impossibility of well-ordering uncountable sets has been overridden by "proving" that the impossible is possible.
But all these desperate attempts to keep set theory free of contrsdictions have been without success. Some set theorists have recognized that contradictions nevertheless are unavoidable and now are claiming that finite cardinal numbers are not natural numbers.

Now mathematics is completely decoupled and isolated from its asserted "basis".
That's the best inconsistency proof of set theory, isn't it?

Regards, WM