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Topic: Matheology § 223: AC and AMS
Replies: 102   Last Post: Apr 18, 2013 12:26 AM

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 fom Posts: 1,968 Registered: 12/4/12
Re: Matheology § 223: AC and AMS
Posted: Mar 17, 2013 2:49 AM
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On 3/16/2013 1:25 PM, WM wrote:
> On 16 Mrz., 18:17, fom <fomJ...@nyms.net> wrote:
>
> An additional remark:
>

>> No. Zermelo's AC requires that one name can be written
>> with certainty.

>
> This statement is not Zermelo's original statement. It can be proven
> to hold, iff it was possible to choose, in practice, one element from
> every subset of T. If this was do-able.

Well, the critical investigation of the
statement during the twentieth century
resulted in taking it as an axiom.

Its provability is not the criterion
by which it is to be understood.

>
> There have been many mathematicians criticizing Zermelo's axiom
> (Borel, Peano, Poincaré and others). Zermelo discusses a lot of
> objections in another 1908 paper. And the most amazing fact is, that
> at that time none of the arguments aims at the fact, that there are
> only countably many choices possible by theoretical reasons.
>
> Zermelo agrees that the AC is not provable. He did not know, at that
> time, that it is disprovable by theoretical mathematics.

Disprovable by belief, perhaps.

If you insist that this is problematic,
then provide some standard by which
others can understand the semantics of
your proof methods and the mechanism
by which the nominal subjects of your
statements refer.

You can ignore all of modern metamathematics.

Simply explain how others are to interpret
your words so that others can understand
how your beliefs could constitute truths.

As for my statement, you are correct.
My assertion concerning the axiom of choice
is informed by the nature of proven equivalent
formulations relative to personal
deliberations about the model theory
of set theory.

And, for the record, to me a 'mark' in
the sense that your finitism accepts
is meaningless syntax.

In contrast, Cantor's topological insight
in relation to Leibniz' philosophical
insight is explanatory. And, in the
middle are a few systematic philosophies
that you pretend to with your words
but violate with your statements.

Even children who cannot yet express
themselves make marks with crayons.

Date Subject Author
3/14/13 Alan Smaill
3/14/13 mueckenh@rz.fh-augsburg.de
3/14/13 Virgil
3/14/13 fom
3/14/13 mueckenh@rz.fh-augsburg.de
3/14/13 fom
3/14/13 mueckenh@rz.fh-augsburg.de
3/14/13 fom
3/15/13 mueckenh@rz.fh-augsburg.de
3/15/13 fom
3/15/13 mueckenh@rz.fh-augsburg.de
3/15/13 Virgil
3/15/13 fom
3/16/13 mueckenh@rz.fh-augsburg.de
3/16/13 fom
3/16/13 mueckenh@rz.fh-augsburg.de
3/16/13 fom
3/16/13 mueckenh@rz.fh-augsburg.de
3/16/13 Virgil
3/17/13 fom
3/17/13 Virgil
3/16/13 mueckenh@rz.fh-augsburg.de
3/16/13 Virgil
3/17/13 fom
3/17/13 mueckenh@rz.fh-augsburg.de
3/17/13 Virgil
3/17/13 mueckenh@rz.fh-augsburg.de
3/17/13 Virgil
3/18/13 fom
3/18/13 mueckenh@rz.fh-augsburg.de
3/18/13 fom
3/18/13 mueckenh@rz.fh-augsburg.de
3/18/13 fom
3/18/13 Virgil
3/18/13 mueckenh@rz.fh-augsburg.de
3/18/13 fom
3/18/13 mueckenh@rz.fh-augsburg.de
3/18/13 fom
3/19/13 mueckenh@rz.fh-augsburg.de
3/19/13 fom
3/19/13 fom
3/19/13 mueckenh@rz.fh-augsburg.de
3/19/13 fom
3/19/13 Virgil
3/19/13 fom
3/19/13 Virgil
3/19/13 Virgil
4/17/13 Virgil
3/18/13 Virgil
3/18/13 Virgil
3/18/13 fom
3/18/13 fom
3/18/13 mueckenh@rz.fh-augsburg.de
3/18/13 fom
3/18/13 Virgil
3/19/13 fom
3/18/13 Virgil
3/18/13 fom
3/18/13 fom
3/18/13 mueckenh@rz.fh-augsburg.de
3/18/13 fom
3/18/13 mueckenh@rz.fh-augsburg.de
3/18/13 Virgil
3/18/13 fom
3/18/13 fom
3/18/13 mueckenh@rz.fh-augsburg.de
3/18/13 Virgil
3/19/13 mueckenh@rz.fh-augsburg.de
3/19/13 Virgil
3/19/13 mueckenh@rz.fh-augsburg.de
3/19/13 Virgil
3/18/13 fom
3/19/13 mueckenh@rz.fh-augsburg.de
3/19/13 Virgil
3/19/13 fom
4/17/13 Virgil
4/18/13 fom
3/18/13 Virgil
3/18/13 mueckenh@rz.fh-augsburg.de
3/18/13 Virgil
3/18/13 Virgil
3/18/13 Virgil
3/17/13 Ralf Bader
3/16/13 Virgil
3/16/13 Virgil
3/17/13 fom
3/15/13 fom
3/16/13 mueckenh@rz.fh-augsburg.de
3/16/13 Virgil
3/15/13 Virgil
3/15/13 mueckenh@rz.fh-augsburg.de
3/15/13 Virgil
3/15/13 fom
3/15/13 fom
3/15/13 Virgil
3/15/13 fom
3/16/13 Virgil
3/14/13 Virgil
3/14/13 Virgil
3/16/13 mueckenh@rz.fh-augsburg.de
3/16/13 Virgil
3/17/13 fom

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