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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


In article <e9150f1557624dce9513b40500d2e5b0@g8g2000vbf.googlegroups.com>, WM <mueckenh@rz.fhaugsburg.de> wrote:
> 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?
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? 



