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Re: Matheology § 208
Posted:
Feb 3, 2013 4:58 PM
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On 2/3/2013 3:29 PM, Virgil wrote:
> 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.
And, I have published papers on my bookshelf in which mathematicians
consider that limitation just as seriously as others have considered
infinity to be a monolithic epistemic limitation.
For you, the received paradigm seems easily accepted, although I
do not think you have fully considered it. That is perfectly
fine. You certainly do have a talent when you are not being
quite so argumentative. Being somewhat slow, I have enjoyed
many of your examples.
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