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fom
Posts:
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Registered:
12/4/12


Re: Matheology § 208
Posted:
Feb 3, 2013 4:58 PM


On 2/3/2013 3:29 PM, Virgil wrote: > In article > <a5a38f2386074d13bac5cf74ce3ab7d6@9g2000yqy.googlegroups.com>, > WM <mueckenh@rz.fhaugsburg.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 settheoretical 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.



