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-universities-in-fact-the-analysis-of-definable-numbe/44129#44129 > > 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. With regard to your question, WM rejects the first-order formal axiomatics of number theory despite its similarities with many of his statements. He also insists on the basic fundamental nature of classical induction. But this is a second-order expression of induction. It is doubtful that he can make the needed formal distinctions.
You are correct that the link would not be convincing to WM. But, there are others who participate in his threads who would find Hamkins' remarks of interest, and, there are others, such as Herc, who post similar objections to infinitary set theory on the same basis that might find this perspective informative.
I did not bring attention to Hamkins' remarks as an appeal to authority. That only works when the authorities are respected and treated with deference. That is not the case here.