In article <email@example.com>, firstname.lastname@example.org wrote:
> On 19 Jun., 12:05, fom <fomJ...@nyms.net> wrote: > > On 6/19/2013 4:11 AM, david petry wrote: > > > > > > > > > > > > > On Tuesday, June 18, 2013 7:26:58 PM UTC-7, fom wrote: > > > > >> Joel David Hamkins answer to the question in > > >> this link seems relevant to some of the discussions > > >> that have been in various threads recently > > > > >>http://mathoverflow.net/questions/44102/is-the-analysis-as-taught-in-... > > > > > That link includes the following quote: > > > > > "...the concept of definability is a second-order concept, that only > > > makes sense from an outside-the-universe perspective" > > > > > I think Mueckenheim would tell us that the phrase "an > > > outside-the-universe perspective" would only make sense to a > > > math-theologian. > > > > > Is he not right? > > > > WM will be right in his own mind. > > Look: Zermelo has "proved" that the real numbers can be well-ordered.
That proof requires certain assumptions, not all of which need be true.
> > With suitable axioms I could "prove" that all reals can be written with four > letters of the Latin alphabet.
All one need to do is assume one's conslusions, a technique WM has far too often relied on. --