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. But it has been proved that the real numbers in fact cannot be well-ordered. That is as certain as that you cannot get a 13 with two dice.
Therefore such "proofs" like that of Zermelo or Hamkins are not worth the paper they are written on.
With suitable axioms I could "prove" that all reals can be written with four letters of the Latin alphabet. I would only need the axiom "All real numbers can be written with four letters of the Latin alphabet". And I had to refuse accepting objections of sober minds because they don't understand that I am "working" in my axiom system. I could use even for letter words like cran or rank.
How can it be that rather intelligent people dare to discuss that mess in public?