Virgil
Posts:
9,012
Registered:
1/6/11


Re: Joel David Hamkins on definable real numbers in analysis
Posted:
Jun 22, 2013 1:24 PM


In article <074182a0f2d54a58899b38b7951de168@googlegroups.com>, mueckenh@rz.fhaugsburg.de wrote:
> On Friday, 21 June 2013 21:53:31 UTC+2, Virgil wrote: > > > > The axiom of choice leads to the wellordering theorem. Zermelo proved > > > "every set can be wellordered", which is literally a lie. > > > > It is a lie to claim that Zermelo proved "every set can be wellordered". > > > Beweis, daß jede Menge wohlgeordnet werden kann. (1904) > > > > What he may have proved is that given the axioms of ZFC, THEN "every set > > can be wellordered", which is quite different. > > No. At those times people did not use nonsenseaxiom and derive other > nonsense from them  like matheologians today do without being ashamed. At > those times axioms had to be meaningful. Compare the discussion about the > "validity" or "truth" of the axiom of choice.
Without having assumed some one of the many forms of the axiom of choice, neither Zermelo, nor anyone else has ever claimed to have proven that every set can be well ordered. > > > > We know that it is > impossible to wellorder any uncountable set because > > > there are only countably many marks which can be attached to the > > > elements.
Mark Twain said it: "It ain't what you don't know that hurts you most, its what you know for sure that jest ain't so." Mark Twain
> > > What WM claims to "know" is neither evidence nor necessarily true anywhere > > It is obviously ture everywhere.
If it were so obvious, why is WM the only one claiming it here?
Mark Twain said it: "It ain't what you don't know that hurts you most, its what you know for sure that jest ain't so." 

