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Topic: Problem with Cantor's diagonal argument
Replies: 65   Last Post: Mar 4, 2002 1:36 PM

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Alan Stern

Posts: 108
Registered: 12/13/04
Re: Problem with Cantor's diagonal argument
Posted: Mar 4, 2002 1:36 PM
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"Harlan Messinger" <hmessinger@erols.com> wrote in message news:<a4tua8$34a32$1@ID-114100.news.dfncis.de>...
> "Virgil" <vmhjr2@attbi.com> wrote in message
> news://vmhjr2-9E34CB.16521518022002@netnews.attbi.com...

> > In article <a4revv$2cs7s$1@ID-114100.news.dfncis.de>,
> > "Harlan Messinger" <hmessinger@erols.com> wrote:
> >

> > > > It is quite possible to do large amounts of mathematics in systems
> > > > whose axioms do not include or allow a law of the excluded middle.
> > > >
> > > > And there is a school of thought that rejects anything that cannot
> > > > be done in such systems.

> > >
> > > In other words, are these people who refuse to see the difference that

> most
> > > people implicitly understand to exist between "short" and "not tall"?
> >
> > More accurately, they refuse to accept that everyone is either tall
> > or not tall without some sort of constructive proof.

>
> Why does it not suffice for them to say that that's how "not" is *defined*?


Because that *isn't* how "not" is defined in intuitionistic logic.
The notions of truth, falsity, negation, ... all have intuitionistic
definitions that are somewhat different from the classical definitions
you may be accustomed to.

Under intuitionism, saying that A is true means something like this:
There is a constructive procedure for determining whether A holds or
not, and it gives a positive result. Saying that A is false means
that there is such a constructive procedure and it gives a negative
result.

Now you can see that from this point of view, A could be neither true
nor false. In particular, if there is no constructive procedure for
determining whether A holds or not, then an intuitionist would say
that neither A nor not-A is true.

Alan Stern






Date Subject Author
2/13/02
Read Problem with Cantor's diagonal argument
Henry
2/13/02
Read Re: Problem with Cantor's diagonal argument
Andy Berget
2/14/02
Read Re: Problem with Cantor's diagonal argument
Mike Oliver
2/14/02
Read Re: Problem with Cantor's diagonal argument
Doug Norris
2/14/02
Read Re: Problem with Cantor's diagonal argument
Keith Keller
2/14/02
Read Re: Problem with Cantor's diagonal argument
Dudley Brooks
2/14/02
Read Re: Problem with Cantor's diagonal argument
Mike Oliver
2/14/02
Read Re: Problem with Cantor's diagonal argument
Dudley Brooks
2/14/02
Read Re: Problem with Cantor's diagonal argument
Dave Seaman
2/14/02
Read Re: Problem with Cantor's diagonal argument
Dudley Brooks
2/14/02
Read Re: Problem with Cantor's diagonal argument
Dave Seaman
2/14/02
Read Re: Problem with Cantor's diagonal argument
Dudley Brooks
2/14/02
Read Re: Problem with Cantor's diagonal argument
Bob Kolker
2/14/02
Read Re: Problem with Cantor's diagonal argument
Dave Seaman
2/14/02
Read Re: Problem with Cantor's diagonal argument
Seth Dutter
2/14/02
Read Re: Problem with Cantor's diagonal argument
mareg@mimosa.csv.warwick.ac.uk
2/14/02
Read Re: Problem with Cantor's diagonal argument
Nico Benschop
2/14/02
Read Re: Problem with Cantor's diagonal argument
mareg@mimosa.csv.warwick.ac.uk
2/14/02
Read Re: Problem with Cantor's diagonal argument
Willondon
2/14/02
Read Re: Problem with Cantor's diagonal argument
Henry
2/14/02
Read Re: Problem with Cantor's diagonal argument
magidin@math.berkeley.edu
2/15/02
Read Re: Problem with Cantor's diagonal argument
Doug Magnoli
2/14/02
Read Re: Problem with Cantor's diagonal argument
mareg@mimosa.csv.warwick.ac.uk
2/14/02
Read Re: Problem with Cantor's diagonal argument
Dudley Brooks
2/14/02
Read Re: Problem with Cantor's diagonal argument
Nico Benschop
2/15/02
Read Re: Problem with Cantor's diagonal argument (re finite case)
Nico Benschop
2/15/02
Read cancel <3C6CD566.97EA8F20@chello.nl>
Nico Benschop
2/15/02
Read Re: Problem with Cantor's diagonal argument
Nico Benschop
2/14/02
Read Re: Problem with Cantor's diagonal argument
Dave Seaman
2/14/02
Read Re: Problem with Cantor's diagonal argument
Herman Jurjus
2/14/02
Read Re: Problem with Cantor's diagonal argument
Dave Seaman
2/15/02
Read Re: Problem with Cantor's diagonal argument
Jon and Mary Frances Miller
2/15/02
Read Re: Problem with Cantor's diagonal argument
Torkel Franzen
2/15/02
Read Re: Problem with Cantor's diagonal argument
Virgil
2/15/02
Read Re: Problem with Cantor's diagonal argument
Harlan Messinger
2/15/02
Read Re: Problem with Cantor's diagonal argument
Virgil
2/15/02
Read Re: Problem with Cantor's diagonal argument
Harlan Messinger
2/15/02
Read Re: Problem with Cantor's diagonal argument
Virgil
2/18/02
Read Re: Problem with Cantor's diagonal argument
Harlan Messinger
2/18/02
Read Re: Problem with Cantor's diagonal argument
Virgil
2/19/02
Read Re: Problem with Cantor's diagonal argument
Harlan Messinger
2/19/02
Read Re: Problem with Cantor's diagonal argument
Virgil
2/19/02
Read Re: Problem with Cantor's diagonal argument
Dudley Brooks
3/4/02
Read Re: Problem with Cantor's diagonal argument
Alexey Dejneka
3/4/02
Read Re: Problem with Cantor's diagonal argument
Torkel Franzen
3/4/02
Read Re: Problem with Cantor's diagonal argument
Alan Stern
2/16/02
Read Re: Problem with Cantor's diagonal argument
Chip Eastham
2/20/02
Read Re: Problem with Cantor's diagonal argument
SRK
2/14/02
Read Re: Problem with Cantor's diagonal argument
Dale Hurliman
2/14/02
Read Re: Problem with Cantor's diagonal argument
Randy Poe
2/14/02
Read Re: Problem with Cantor's diagonal argument
Henry
2/14/02
Read Re: Problem with Cantor's diagonal argument
Randy Poe
2/14/02
Read Re: Problem with Cantor's diagonal argument
Wade Ramey
2/14/02
Read Re: Problem with Cantor's diagonal argument
nospam@auerbachatunity.ncsu.edu
2/14/02
Read Re: Problem with Cantor's diagonal argument
Dudley Brooks
2/15/02
Read Re: Problem with Cantor's diagonal argument
Chris Menzel
2/15/02
Read Re: Problem with Cantor's diagonal argument
Dudley Brooks
2/14/02
Read Re: Problem with Cantor's diagonal argument
Phil Carmody
2/14/02
Read Re: Problem with Cantor's diagonal argument
Harlan Messinger
2/14/02
Read Re: Problem with Cantor's diagonal argument
Jim Heckman
2/15/02
Read Re: Problem with Cantor's diagonal argument
Randy Poe
2/15/02
Read Re: Problem with Cantor's diagonal argument
LarryLard
2/18/02
Read Re: Problem with Cantor's diagonal argument
Harlan Messinger
2/14/02
Read Re: Problem with Cantor's diagonal argument
George Greene
2/15/02
Read Re: Problem with Cantor's diagonal argument
Duran Castore
2/18/02
Read Re: Problem with Cantor's diagonal argument
Jonathan Hoyle

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