
Re: Joel David Hamkins on definable real numbers in analysis
Posted:
Jun 23, 2013 12:39 PM


On Sunday, June 23, 2013 9:25:35 AM UTC7, muec...@rz.fhaugsburg.de wrote: > On Sunday, 23 June 2013 18:10:30 UTC+2, Zeit Geist wrote: > > > > > First, no one can just wellorder the real numbers. > > > > > > Correct. But Zermelo has "proved" that someone *can*. And Fraenkle has been sceptical about that, because, although there have been great efforts, nobody "up to now" has accomplished it. >
"Can" in the proper system. In ZF + AD, there is no wellordering of the reals.
> > > The fact is that given certain assumptions about the real numbers, then one can show that a well ordering of them is logical necessity. > > > > In fact it is a logical necessity, even without any assumptions. Attempts only would fail if there were unnameable numbers, i.e. numbers that cannot be identified and distingusihed from each other with finite amount of information. But that case is not existing. >
A logical necessity without any extra assumption than from pure logic? What?
> > > We already Know that you reject the axioms of ZFC, > > > > Not even that. I reject only the erroneous interpretation of the axiom of infinity. For every set A there exists the set {A} is obviously true (when constraints of reality are neglected). >
Since AoI is part of ZFC, you reject ZFC.
> > > Is Euclidean Geometry the absolute truth? > > > > In Euclidean space Euclidean geometry is the absolute truth. >
That's a nice tautology.
You claim the real numbers can't be wellordered because of "real world" conditions. Do you believe Euclidean Geometry is true in the "real world"?
> > Regards, WM
ZG

