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Topic: § 454 Equality and the axioms of natural numbers
Replies: 30   Last Post: Mar 23, 2014 2:41 PM

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 Virgil Posts: 8,833 Registered: 1/6/11
Re: � 454 Equality and the axioms of natural numbers
Posted: Mar 23, 2014 2:08 PM

mueckenh@rz.fh-augsburg.de wrote:

> On Saturday, 22 March 2014 22:38:51 UTC+1, Virgil wrote:

> > Since "x" and "y" and "f(x) and "f(y)" are merely names, x = y if and
> > only if "x" and "y" are merely different names for the same thing,
> > and f(x) = f(y) if and only if "f(x)" and "f(y)" are merely different
> > names for the same thing.
> >
> > What part of the above does WM not understand?

>
> If there are only names, how can someone claim that the Peano axioms define
> the natural numbers?

I did not say that there were only names, but that we can only refer to
things by their names. We can also refer to things by physically
pointing at them if both we and they are all physically present within
sight of each other, but that does not happen here.

> And how can a man equipped with a healthy brain accept
> that?

How can a man equipped with a healthy brain reject that?
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