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

 Messages: [ Previous | Next ]
 Virgil Posts: 3,521 Registered: 12/6/04
Re: Problem with Cantor's diagonal argument
Posted: Feb 15, 2002 7:08 PM

In article <a4k5a2\$tlnc\$1@ID-114100.news.dfncis.de>,
"Harlan Messinger" <hmessinger@erols.com> wrote:

> "Virgil" <vmhjr2@attbi.com> wrote in message
> news://vmhjr2-35D8AB.16133915022002@netnews.attbi.com...

> > Jon Miller <jonathanemiller@home.com> writes:
> >

> > > There are even (intelligent) people who (claim that they) are unable
> > > to believe in infinite sets at all. To them, Cantor's argument
> > > makes no sense.

> >
> > Why is that? Cantor's argument does not presuppose the existence
> > of any infinite set.
> >

> > > There are people who deny the law of the excluded middle. To them,
> proving
> > > that not-A is false does not prove that A is true.
> >
> > There are people who will deny that (P or (not P)) is necessarily
> > true, but those same people will insist that (P and (not P)) is
> > necessarily false. It is the second form which is relevant to
> > Cantor's proof, not the first.

>
> I don't get it. In symbolic logic, isn't "not" *defined* such that (P or
> (not P)) is necessarily true and (P and (not P)) is necessarily false?
>

For most people, yes, but there are those that insist that the
falseness of P is insufficient to guarantee the truth of not P and
vice versa. They deny what is generally known as the law of the
excluded middle, and say that there may be something in the middle,
"between" P and not P.

Date Subject Author
2/13/02 Henry
2/13/02 Andy Berget
2/14/02 Mike Oliver
2/14/02 Doug Norris
2/14/02 Keith Keller
2/14/02 Dudley Brooks
2/14/02 Mike Oliver
2/14/02 Dudley Brooks
2/14/02 Dave Seaman
2/14/02 Dudley Brooks
2/14/02 Dave Seaman
2/14/02 Dudley Brooks
2/14/02 Bob Kolker
2/14/02 Dave Seaman
2/14/02 Seth Dutter
2/14/02 mareg@mimosa.csv.warwick.ac.uk
2/14/02 Nico Benschop
2/14/02 mareg@mimosa.csv.warwick.ac.uk
2/14/02 Willondon
2/14/02 Henry
2/14/02 magidin@math.berkeley.edu
2/15/02 Doug Magnoli
2/14/02 mareg@mimosa.csv.warwick.ac.uk
2/14/02 Dudley Brooks
2/14/02 Nico Benschop
2/15/02 Nico Benschop
2/15/02 Nico Benschop
2/15/02 Nico Benschop
2/14/02 Dave Seaman
2/14/02 Herman Jurjus
2/14/02 Dave Seaman
2/15/02 Jon and Mary Frances Miller
2/15/02 Torkel Franzen
2/15/02 Virgil
2/15/02 Harlan Messinger
2/15/02 Virgil
2/15/02 Harlan Messinger
2/15/02 Virgil
2/18/02 Harlan Messinger
2/18/02 Virgil
2/19/02 Harlan Messinger
2/19/02 Virgil
2/19/02 Dudley Brooks
3/4/02 Alexey Dejneka
3/4/02 Torkel Franzen
3/4/02 Alan Stern
2/16/02 Chip Eastham
2/20/02 SRK
2/14/02 Dale Hurliman
2/14/02 Randy Poe
2/14/02 Henry
2/14/02 Randy Poe
2/14/02 nospam@auerbachatunity.ncsu.edu
2/14/02 Dudley Brooks
2/15/02 Chris Menzel
2/15/02 Dudley Brooks
2/14/02 Phil Carmody
2/14/02 Harlan Messinger
2/14/02 Jim Heckman
2/15/02 Randy Poe
2/15/02 LarryLard
2/18/02 Harlan Messinger
2/14/02 George Greene
2/15/02 Duran Castore
2/18/02 Jonathan Hoyle