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Topic: Matheology § 208
Replies: 5   Last Post: Feb 3, 2013 4:58 PM

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Virgil

Posts: 7,005
Registered: 1/6/11
Re: Matheology � 208
Posted: Feb 3, 2013 4:29 PM
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In article
<a5a38f23-8607-4d13-bac5-cf74ce3ab7d6@9g2000yqy.googlegroups.com>,
WM <mueckenh@rz.fh-augsburg.de> wrote:

> Matheology § 208
>
> In Consistency in Mathematics (1929), Weyl characterized the
> mathematical method as
>
> the a priori construction of the possible in opposition to the a
> posteriori description of what is actually given. {{Above all,
> mathematics has to be consistent. And there is only one criterion for
> consistency: The "model" of reality.}}
>
> The problem of identifying the limits on constructing ³the possible²
> in this sense occupied Weyl a great deal. He was particularly
> concerned with the concept of the mathematical infinite, which he
> believed to elude ³construction² in the naive set-theoretical sense.
> Again to quote a passage from Das Kontinuum:
>
> No one can describe an infinite set other than by indicating
> properties characteristic of the elements of the set.


That is effectively true for all but "small" sets.

One rarely sees sets of 100 or more members that lists all members
individually. And the difficulty in actually listing increases with the
size of the set to become effectively impossible well before actual
infiniteness.

There is not now, and almost certainly never will be an up to date and
accurate list of every living person on earth at any particular moment.

But at any fixed moment such a SET actually exists, even in WMYTHEOLOGY.

Thus WM's pseudo-set-theory" crashes and burns.
--





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