Virgil
Posts:
8,833
Registered:
1/6/11


Re: � 454 Equality and the axioms of natural numbers
Posted:
Mar 23, 2014 2:22 PM


In article <6e9a20e451cd47f785886e07643b0df2@googlegroups.com>, mueckenh@rz.fhaugsburg.de wrote:
> On Saturday, 22 March 2014 22:50:53 UTC+1, Virgil wrote: > > In article <6d4210aa069645dab4acd80c55d6a4cb@googlegroups.com>, > > > Why should anyone else be required by WM to do what WM himself CANNOT > > do, or at least never has done. namely successfully defend his own idiot > > assertions.
> You are right that I never defended idiot assertions.
But you certainly have made enough of them.
> > The Peano postulates are accepted by the vast majority of mathematicians > > in the world as being the skeleton of mathematical induction and that it > > is by such an induction that the wellordered set of natural numbers is > > defined. > > That has been mentioned here frequently, but it is not an argument. The fact that an idea is being widely accepted by mathematicians. certainly argues that it is widely acceptable to mathematicians.
The fact that WM's idea are being widely rejected by mathematicians. certainly argues thatthey are widely unacceptable to mathematicians.
> It is > obvous to everybody whose brain has not been perverted or deleted completely > that the Peano axioms do not define the natural numbers.
But they do define the essential properties of mathematical induction without which properties the natural numbers would be much less useful. > > In principle it is without interest whether you understand that. But this > discussion is a splendid demonstration of the fact that ridiculous but not so > obviously foolish ideas like uncountable sets and undefinable numbers can > exist in "modern mathematics".
Any sort of idea can and will exist in modern mathematics if enough modern mathematicians are sufficiently interested in it, and both uncountable sets and individually undefineable numbers are both such ideas. 

