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

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Virgil

Posts: 9,012
Registered: 1/6/11
Re: Matheology � 223: AC and AMS
Posted: Mar 15, 2013 3:56 PM
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In article
<e9150f15-5762-4dce-9513-b40500d2e5b0@g8g2000vbf.googlegroups.com>,
WM <mueckenh@rz.fh-augsburg.de> wrote:

> 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?


In a formal system "choice" means on of the many formal statements of
the axion of choice, such as Zorn's Lemma, for example.
> >
> > 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.


Then why do you use them so often?
> >
> > 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.


Perhaps to your own satisfaction but not to that of anyone else.
WM's "proofs" are all like that, they satisfy no one other than WM.
> >
> > 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.


Those whom WM calls the "fools of matheology" have produced well over
90% of the mathematics now extant, and WM appears to have produced none
at all.

So who is the fool?
--





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