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Topic: Matheology § 223: AC and AMS
Replies: 3   Last Post: Mar 15, 2013 3:56 PM

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mueckenh@rz.fh-augsburg.de

Posts: 14,735
Registered: 1/29/05
Re: Matheology § 223: AC and AMS
Posted: Mar 15, 2013 6:59 AM
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On 15 Mrz., 11:36, Alan Smaill <sma...@SPAMinf.ed.ac.uk> wrote:
> WM <mueck...@rz.fh-augsburg.de> writes:
> > On 14 Mrz., 16:22, Alan Smaill <sma...@SPAMinf.ed.ac.uk> wrote:
> >> WM <mueck...@rz.fh-augsburg.de> writes:
> >> > On 14 Mrz., 13:59, Alan Smaill <sma...@SPAMinf.ed.ac.uk> wrote:
> >> >> WM <mueck...@rz.fh-augsburg.de> writes:
> >> >> > On 14 Mrz., 12:35, Alan Smaill <sma...@SPAMinf.ed.ac.uk> wrote:
> >> >> >> You can and do of course  reject this axiom.
>
> >> >> >> To show something is self-contradictory, however, you need to use the
> >> >> >> reasoning principles of the system you want to show is
> >> >> >> self-contradictory, not your own beliefs.

>
> >> >> > The axiom belongs to the system. It says that elements can be chosen.
> >> >> > To choose immaterial elements,  hmm, how is that accomplished in a
> >> >> > system that contains the axiom of choice?

>
> >> >> I can only repeat myself --
> >> >> where is the *logical* contradiction there, in terms of classical
> >> >> mathematics?

>
> >> > You will find it if you try to answer my question. Choosing means
> >> > defining (by a finite number of words) a chosen element (unless it is
> >> > a material object). No other possibility exists.

>
> >> Of course other possibilities exist, even in WMaths.
> >> Forget Zermelo's exposition, and look at the axiom.

>
> > That is the axiom.
>
> I'm talking about its place in a formal system, not the interpretation
> in natural languagfe that you (WM) place upon it.


In formal system choice means choice, no? What is choice? Choosing.
How can that occur according to the formal system?
>
> Do yuo see that there is a difference?
>

> >> Can you derive a contradiction using classical set theory?
>
> > Zermelo used classical set theory. He developed it.
>
> Dodging the question, as ever.


Ad hominem arguments do not help.
>
> Can *you* (WM)  derive a contradiction using classical set theory?


Of course. For instance, I showed that the real numbers in the unit
interval cannot be distinguished by more than a countable set of
labels.
>
> If so, that would put a stop to all these indoctrinated fools
> you are so concerned about.


No, it would not, because those Fools Of Matheology obviously cannot
learn that even formal choice means having a label available for every
element to be chosen.

Regards, WM




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