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Re: Matheology § 223: AC and AMS
Posted:
Mar 15, 2013 6:59 AM


On 15 Mrz., 11:36, Alan Smaill <sma...@SPAMinf.ed.ac.uk> wrote: > WM <mueck...@rz.fhaugsburg.de> writes: > > On 14 Mrz., 16:22, Alan Smaill <sma...@SPAMinf.ed.ac.uk> wrote: > >> WM <mueck...@rz.fhaugsburg.de> writes: > >> > On 14 Mrz., 13:59, Alan Smaill <sma...@SPAMinf.ed.ac.uk> wrote: > >> >> WM <mueck...@rz.fhaugsburg.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 selfcontradictory, however, you need to use the > >> >> >> reasoning principles of the system you want to show is > >> >> >> selfcontradictory, 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



