RE: The seven step-Mathematical preliminaries

[Jesse Mazer]

> Date: Tue, 9 Jun 2009 12:54:16 -0700
> From: meeke...@dslextreme.com
> To: everything-list@googlegroups.com
> Subject: Re: The seven step-Mathematical preliminaries
> 

> You don't justify definitions.  How would you justify Peano's axioms as being 
> the "right" ones?  You are just confirming my point that you are begging the 
> question by assuming there is a set called "the natural numbers" that exists 
> independently of it's definition and it satisfies Peano's axioms. 
What do you mean by "exists" in this context? What would it mean to have a 
well-defined, non-contradictory definition of some mathematical objects, and 
yet for those mathematical objects not to "exist"? 

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