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Topic: Cantor's absurdity, once again, why not?
Replies: 77   Last Post: Mar 19, 2013 11:02 PM

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ross.finlayson@gmail.com

Posts: 1,218
Registered: 2/15/09
Re: Cantor's absurdity, once again, why not?
Posted: Mar 14, 2013 10:02 PM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

On Mar 14, 2:47 am, david petry <david_lawrence_pe...@yahoo.com>
wrote:
> In a previous aritcle a while back, "marcus_b" wrote:
>
> ** start quote **
> In math, the great pons asinorum now is Cantor's diagonal proof.  There seem to be scads of people out there who just cannot quite get it and who yearn to achieve their rightful 15 minutes of fame by trying to shoot it down, thus thrusting themselves ahead of Cantor in the pantheon of mathematical geniuses.  Can you shed some light on the motivation here?
> ** end quote **
>
> The "cranks" who insist on pointing out the absurdity of Cantor's argument are puzzled that mathematicians "cannot quite get it".
>
> Cantor's argument relies on accepting the notion of an actual infinite, and that's problematic.  It is reasonable to accept the assertion that the purpose of mathematics is to provide a rigorous language and conceptual framework for reasoning quantitatively about real-world phenomena.  It's a good bet that mathematicians before the time of Cantor would have heartily endorsed that view.  And the actual infinite is not needed for the mathematics or the real world, as has been pointed out by many top notch mathematicians over the last century, from Poincare' to Feferman:
>
> "The actual infinite is not required for the mathematics of the physical world" (Soloman Fefermanm, in an article titled "Is Cantor Necessary?")
>
> That article also contains the following quote:
>
> "I am convinced that the platonism which underlies Cantorian set theory is utterly unsatisfactory as a philosophy of our subject, despite the apparent coherence of current set-theoretical conceptions and methods ... platonism is the medieval metaphysics of mathematics; surely we can do better" (Feferman)
>
> Some of the "cranks" are saying that yes indeed, we can do better.  We can do better by rejecting platonism and accepting falsifiability as part of the underlying philosophy of mathematics.
>
> Falsifiability is a cornerstone of scientific reasoning. When we reason about the real world, we apply falsifiability, even if sometimes we do it only subconsciously. Falsifiability is part of the natural logic we are born with.  It can be formalized in such a way that it can serve as a cornerstone of mathematical reasoning, and if we don't accept it as part of the underlying logic of our mathematics, then our mathematics is deficient as a language for reasoning about the real world.
>
> Platonism, on the other hand, is a perversion of natural logic.  It would be insane to apply platonism to reasoning about the real world.  Falsifiability and platonism are not compatible. Falsifiability would exclude Cantor from mathematics.  Just as the scientists use falsifiability as a criterion to distinguish real science from crackpot science, it can serve as a criterion to distinguish real mathematics from crackpot mathematics.
>
> Cantorian mathematics is crackpot mathematics.


I think highly of Feferman with his generally reasonable opinion, but
don't agree that infinity and a "completed" infinity isn't in or the
fabric of the cosmos.

Instead, indeed, it is even by definition so that a sound theory, of
everything, a theory of everything, wouldn't not have infinities.

Assuming logicism in physics, that there is causality else there
wouldn't be, there is a theory of physics, from my view A theory, and,
we know ZF as incomplete or inconsistent, and as not its logical
foundation.

Then physicists search high and low, literally as it were, and
figuratively, from the infinitesimal strings to the infinite multiple-
worlds interpretation, the Universe, for mathematics in physics.

And that's Infinite.

Regards,

Ross Finlayson


Date Subject Author
3/14/13
Read Cantor's absurdity, once again, why not?
David Petry
3/14/13
Read Re: Cantor's absurdity, once again, why not?
fom
3/14/13
Read Re: Cantor's absurdity, once again, why not?
David Petry
3/14/13
Read Re: Cantor's absurdity, once again, why not?
fom
3/14/13
Read Re: Cantor's absurdity, once again, why not?
David Petry
3/14/13
Read Re: Cantor's absurdity, once again, why not?
fom
3/17/13
Read Re: Cantor's absurdity, once again, why not?
Shmuel (Seymour J.) Metz
3/17/13
Read Re: Cantor's absurdity, once again, why not?
ross.finlayson@gmail.com
3/18/13
Read Re: Cantor's absurdity, once again, why not?
fom
3/18/13
Read Re: Cantor's absurdity, once again, why not?
Shmuel (Seymour J.) Metz
3/19/13
Read Re: Cantor's absurdity, once again, why not?
fom
3/14/13
Read Re: Cantor's absurdity, once again, why not?
Virgil
3/14/13
Read Re: Cantor's absurdity, once again, why not?
mueckenh@rz.fh-augsburg.de
3/14/13
Read Re: Cantor's absurdity, once again, why not?
Virgil
3/14/13
Read Re: Cantor's absurdity, once again, why not?
mueckenh@rz.fh-augsburg.de
3/14/13
Read Re: Cantor's absurdity, once again, why not?
fom
3/14/13
Read Re: Cantor's absurdity, once again, why not?
mueckenh@rz.fh-augsburg.de
3/14/13
Read Re: Cantor's absurdity, once again, why not?
fom
3/14/13
Read Re: Cantor's absurdity, once again, why not?
Virgil
3/14/13
Read Re: Cantor's absurdity, once again, why not?
Virgil
3/14/13
Read Re: Cantor's absurdity, once again, why not?
Virgil
3/14/13
Read Re: Cantor's absurdity, once again, why not?
mueckenh@rz.fh-augsburg.de
3/14/13
Read Re: Cantor's absurdity, once again, why not?
harold james
3/14/13
Read Re: Cantor's absurdity, once again, why not?
Virgil
3/14/13
Read Re: Cantor's absurdity, once again, why not?
fom
3/14/13
Read Re: Cantor's absurdity, once again, why not?
mueckenh@rz.fh-augsburg.de
3/14/13
Read Re: Cantor's absurdity, once again, why not?
Virgil
3/14/13
Read Re: Cantor's absurdity, once again, why not?
fom
3/14/13
Read Re: Cantor's absurdity, once again, why not?
Jesse F. Hughes
3/14/13
Read Re: Cantor's absurdity, once again, why not?
fom
3/14/13
Read Re: Cantor's absurdity, once again, why not?
mueckenh@rz.fh-augsburg.de
3/14/13
Read Re: Cantor's absurdity, once again, why not?
fom
3/14/13
Read Re: Cantor's absurdity, once again, why not?
David Petry
3/15/13
Read Re: Cantor's absurdity, once again, why not?
mueckenh@rz.fh-augsburg.de
3/15/13
Read Re: Cantor's absurdity, once again, why not?
Virgil
3/15/13
Read Re: Cantor's absurdity, once again, why not?
mueckenh@rz.fh-augsburg.de
3/15/13
Read Re: Cantor's absurdity, once again, why not?
Virgil
3/15/13
Read Re: Cantor's absurdity, once again, why not?
fom
3/16/13
Read Re: Cantor's absurdity, once again, why not?
mueckenh@rz.fh-augsburg.de
3/16/13
Read Re: Cantor's absurdity, once again, why not?
FredJeffries@gmail.com
3/16/13
Read Re: Cantor's absurdity, once again, why not?
mueckenh@rz.fh-augsburg.de
3/16/13
Read Re: Cantor's absurdity, once again, why not?
Virgil
3/16/13
Read Re: Cantor's absurdity, once again, why not?
fom
3/16/13
Read Re: Cantor's absurdity, once again, why not?
mueckenh@rz.fh-augsburg.de
3/16/13
Read Re: Cantor's absurdity, once again, why not?
Virgil
3/16/13
Read Re: Cantor's absurdity, once again, why not?
mueckenh@rz.fh-augsburg.de
3/16/13
Read Re: Cantor's absurdity, once again, why not?
Virgil
3/17/13
Read Re: Cantor's absurdity, once again, why not?
fom
3/19/13
Read Re: Cantor's absurdity, once again, why not?
mueckenh@rz.fh-augsburg.de
3/19/13
Read Re: Cantor's absurdity, once again, why not?
fom
3/19/13
Read Re: Cantor's absurdity, once again, why not?
mueckenh@rz.fh-augsburg.de
3/19/13
Read Re: Cantor's absurdity, once again, why not?
Virgil
3/19/13
Read Re: Cantor's absurdity, once again, why not?
fom
3/19/13
Read Re: Cantor's absurdity, once again, why not?
fom
3/19/13
Read Re: Cantor's absurdity, once again, why not?
fom
3/19/13
Read Re: Cantor's absurdity, once again, why not?
fom
3/19/13
Read Re: Cantor's absurdity, once again, why not?
fom
3/19/13
Read Re: Cantor's absurdity, once again, why not?
fom
3/19/13
Read Re: Cantor's absurdity, once again, why not?
Virgil
3/16/13
Read Re: WM's absurdity, once again, why not?
Virgil
3/17/13
Read Re: Cantor's absurdity, once again, why not?
fom
3/14/13
Read Re: Cantor's absurdity, once again, why not?
Virgil
3/14/13
Read Re: Cantor's absurdity, once again, why not?
Jesse F. Hughes
3/15/13
Read Re: Cantor's absurdity, once again, why not?
mueckenh@rz.fh-augsburg.de
3/15/13
Read Re: Cantor's absurdity, once again, why not?
Virgil
3/14/13
Read Re: Cantor's absurdity, once again, why not?
David Petry
3/14/13
Read Re: Cantor's absurdity, once again, why not?
Jesse F. Hughes
3/14/13
Read Re: Cantor's absurdity, once again, why not?
David Petry
3/14/13
Read Re: Cantor's absurdity, once again, why not?
Jesse F. Hughes
3/15/13
Read Re: Cantor's absurdity, once again, why not?
David Petry
3/15/13
Read Re: Cantor's absurdity, once again, why not?
Jesse F. Hughes
3/15/13
Read Re: Cantor's absurdity, once again, why not?
David Petry
3/15/13
Read Re: Cantor's absurdity, once again, why not?
Virgil
3/15/13
Read Re: Cantor's absurdity, once again, why not?
fom
3/15/13
Read Re: Cantor's absurdity, once again, why not?
fom
3/15/13
Read Re: Cantor's absurdity, once again, why not?
fom
3/15/13
Read Re: Cantor's absurdity, once again, why not?
Jesse F. Hughes
3/14/13
Read Re: Cantor's absurdity, once again, why not?
ross.finlayson@gmail.com

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