Virgil
Posts:
7,011
Registered:
1/6/11


Re: Matheology � 223: AC and AMS
Posted:
Mar 15, 2013 8:28 PM


In article <wNednaCf1baoKN7MnZ2dnUVZ_hSdnZ2d@giganews.com>, fom <fomJUNK@nyms.net> wrote:
> On 3/15/2013 3:01 PM, Virgil wrote: > > In article > > <c4fcdc6876bb4df0a2f573d117d0b98c@m4g2000vbo.googlegroups.com>, > > WM <mueckenh@rz.fhaugsburg.de> wrote: > > > >> On 14 Mrz., 23:54, fom <fomJ...@nyms.net> wrote: > >>> On 3/14/2013 5:47 PM, WM wrote: > >>> > >>>> On 14 Mrz., 23:16, fom <fomJ...@nyms.net> wrote: > >>> > >>>>> "... an element of T is not a set..." > >>> > >>>> Let T = {{a}, {b,c}, {c,d,e,f}} > >>>> then T has three elements, each of which is a set. That is common use > >>>> in modern set theory and has been used 100 years ago in the same sense > >>>> by Zermelo. > >>> > >>> I am well aware of modern usage. > >> > >> Zermelo used it already 100 years ago. > >>> > >>> Unless my translation is in error, Zermelo's > >>> 1908 supports urelements. > >> > >> Zermelo says (in your translation on p. 210, 3rd line): If T is a set > >> whose elements M, N, R, ... all are sets different from the null > >> set, ... > > > > That, even if accurate, in no way refutes that Zermelo allowed sets to > > contain urelements. In fact, it supports urelements, as otherwise > > there would be no reason to specify that those elements all are sets. > > It is not accurate. That is where Zermelo is explaining the > "general principle of choice". The beginning of the paper in > which the domain description is given is on page 201.
In other words, WM is quote mining again: isolating quotes from their contexts in such a way as to misled readers of those quotes or their original meanings. > > For WM's claim (snipped) to be accurate, ZF would have a > global choice function. > > If it did, I would never have run across the difficulties > I had as an undergraduate, and, I would probably have > a career in mathematics as a consequence. > > So I "know" it to be inaccurate: "proof by reality". > > Less subjectively, if it did, no one would speak > of models in which the axiom of choice fails. 

