Date: Feb 3, 2013 4:58 PM
Author: fom
Subject: Re: Matheology § 208
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.