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Topic: Distinguishability argument x Cantor's arguments?
Replies: 15   Last Post: Jan 9, 2013 4:32 PM

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 mueckenh@rz.fh-augsburg.de Posts: 18,076 Registered: 1/29/05
Re: Distinguishability argument x Cantor's arguments?
Posted: Jan 3, 2013 9:19 AM

On 2 Jan., 22:19, Zuhair <zaljo...@gmail.com> wrote:

> On the other hand Cantor have presented many arguments all of which
> are rigorously formalized in second order logic under full semantics,
> and those arguments PROVED that there are uncountably many reals

that can be distinguished by their finite initial segments.
>
> So which one we to believe?
>
> The answer is Cantor's of course!

So let us believe that uncountably many real numbers can be
distinguished by their countably many finite initial segments, because
no infinite diagonal of a Cantor list can be defined other than by its
finite initial segments (or a finite definition).
>
> Why?

because Cantor by distinguishing real nunbers "proved" the existence
of indistinguishable "real" numbers. (He would rotate in his grave

> Because Cantor's arguments are very clear, and are formalizable in an
> exact manner, so they are quite understandable and obvious. While the
> distinguishability argument of mine is actually ambiguous and shredded
> in mystery.

No, every sensible formalization requires finite distinguishability.

> The Consideration step in that argument and the analogy of
> that with the Generalization step in that argument is really just an
> intuitive leap nothing more nothing less.
>
> This only demonstrates how common intuition fail at absolute infinity.

This demonstrates that Cantor's argument has created thousands of
matheologians who have a block in their brains.

Regards, WM