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Topic: Set Theory: Should you believe?
Replies: 778   Last Post: Aug 8, 2006 12:02 PM

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R. Srinivasan

Posts: 252
Registered: 12/13/04
Re: Set Theory: Should you believe?
Posted: Jul 15, 2006 2:44 PM
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stephen@nomail.com wrote:
> In sci.math R. Srinivasan <sradhakr@in.ibm.com> wrote:
> > Turing machines that halt do not require infinite tapes -- so these are
> > not infinite objects. What about TM's that do not halt, but for which a
> > proof of not-halting is available? E.g. the TM goes into a simple and
> > obvious loop. I feel these are not problematic either -- they might be
> > treated as finite objects if we let them run for a certain large number
> > of steps, and then pause and look for (and find) a proof of not-halting
> > -- either via human input or via an automated proof-checker -- and then
> > return an error condition and halt. So we could treat these as finite
> > objects, provided the proof of not-halting exists. The really
> > problematic case is with Turing's proof that there must exist TM's that
> > do not halt, but for which a proof of not-halting is not available.
> > These are unavoidably infinite objects and are problematic. The logic
> > NAFL that I have proposed does not permit these and so Turing's proof
> > of their existence must use some infinitary reasoning not acceptable in
> > NAFL.

>
> How can that possibly work? Consider the following "Turing Machine"
> (written in the form of idealized C-like code)
>
> int f(int n)
> {
> while (n!=1)
> {
> if (n%2==0)
> n=n/2;
> else
> n=n*3+1;
> }
> }
>
>
> This program clearly exists. Does it halt for a given n? No
> proof is currently available that works for all n. So
> is this an "unavoidably infinite object"?
>


Well, I paraphrased NAFL in very simple terms -- there are some more
subtleties that I did not mention. The notion of provability in an NAFL
theory T is a metamathematical notion and every proposition in the
language of T is either provable or refutable or undecidable in T (this
holds in classical logic too, but not in intuitionistic logic). So the
proposition P that the above TM halts is either provable or refutable
or undecidable in T when suitably formalized in T (say, take T to be
Peano Arithmetic). In NAFL the undecidability of P in T is ruled out by
the NAFL truth definition,(the Main Postulate) and so P is either
provable or refutable in T. The fact that we do not have a proof of
either P or its negation at this point of time does not matter. The
problem is that Turing's argument would lead us to the conclusion that
there must exist TM's that do not halt, but we cannot prove it in T--
so the resulting undecidability in T of halting will violate NAFL's
Main Postulate. Indeed, the undecidability of the halting problem will
lead to non-standard models of arithmetic, which are not possible in
NAFL. So I have no option but to look for finitary principles of
reasoning (by the NAFL yardstick) that are violated in Turing's proof,
as I mentioned in my previous post.

To say that a TM "really" does not halt, but there is no way for us to
convincingly prove this fact leads to an uncomputable real number, say,
specified by a binary sequence of 0's and 1's. So you have to imagine
that this sequence "really" exists in some sense, independent of the
human mind, i.e.,it "exists" as an actual infinity despite our
inability to provide a finite rule for constructing it. This is denied
by the NAFL truth definition, which links truth for formal propositions
with the human mind via provability in axiomatic theories. Note that
this truth definition is only for formal propositions of an NAFL
theory; the notion of provabiliy itself is not formalizable in NAFL
theories (as noted above) and so the law of the excluded middle applies
in the sense that every proposition of a NAFL theory T is either
provable or refutable or undecidable in T (possibly independent of the
human mind).

Regards, RS



Date Subject Author
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Shmuel (Seymour J.) Metz
7/19/06
Read Re: Set Theory: Should you believe?
Aatu Koskensilta
7/19/06
Read Re: Set Theory: Should you believe?
Chas Brown
7/20/06
Read Re: Set Theory: Should you believe?
Shmuel (Seymour J.) Metz
7/20/06
Read Re: Set Theory: Should you believe?
Aatu Koskensilta
7/20/06
Read Re: Set Theory: Should you believe?
Lee Rudolph
7/20/06
Read Re: Set Theory: Should you believe?
Aatu Koskensilta
7/20/06
Read Re: Set Theory: Should you believe?
David Bernier
7/21/06
Read Re: Set Theory: Should you believe?
Aatu Koskensilta
7/21/06
Read Re: Set Theory: Should you believe?
George Greene
7/18/06
Read Re: Set Theory: Should you believe?
malbrain@yahoo.com
7/18/06
Read Re: Set Theory: Should you believe?
DontBother@nowhere.net
7/18/06
Read Re: Set Theory: Should you believe?
Virgil
7/19/06
Read Re: Set Theory: Should you believe?
DontBother@nowhere.net
7/19/06
Read Re: Set Theory: Should you believe?
Virgil
7/19/06
Read Re: Set Theory: Should you believe?
DontBother@nowhere.net
7/19/06
Read Re: Set Theory: Should you believe?
Virgil
7/19/06
Read Re: Set Theory: Should you believe?
DontBother@nowhere.net
7/18/06
Read Re: Set Theory: Should you believe?
malbrain@yahoo.com
7/19/06
Read Re: Set Theory: Should you believe?
DontBother@nowhere.net
7/19/06
Read Re: Set Theory: Should you believe?
Virgil
7/19/06
Read Re: Set Theory: Should you believe?
DontBother@nowhere.net
7/19/06
Read Re: Set Theory: Should you believe?
Virgil
7/19/06
Read Re: Set Theory: Should you believe?
DontBother@nowhere.net
7/19/06
Read Re: Set Theory: Should you believe?
Virgil
7/17/06
Read Re: Set Theory: Should you believe?
Russell Easterly
7/17/06
Read Re: Set Theory: Should you believe?
jirka@5z.com
7/17/06
Read Re: Set Theory: Should you believe?
malbrain@yahoo.com
7/17/06
Read Re: Set Theory: Should you believe?
jirka@5z.com
7/17/06
Read Re: Set Theory: Should you believe?
malbrain@yahoo.com
7/17/06
Read Re: Set Theory: Should you believe?
Patricia Shanahan
7/17/06
Read Re: Set Theory: Should you believe?
malbrain@yahoo.com
7/17/06
Read Re: Set Theory: Should you believe?
DontBother@nowhere.net
7/17/06
Read Re: Set Theory: Should you believe?
Virgil
7/18/06
Read Re: Set Theory: Should you believe?
namducnguyen
7/18/06
Read Re: Set Theory: Should you believe?
DontBother@nowhere.net
7/18/06
Read Re: Set Theory: Should you believe?
Virgil
7/19/06
Read Re: Set Theory: Should you believe?
DontBother@nowhere.net
7/19/06
Read Re: Set Theory: Should you believe?
Virgil
7/19/06
Read Re: Set Theory: Should you believe?
DontBother@nowhere.net
7/19/06
Read Re: Set Theory: Should you believe?
Virgil
7/19/06
Read Re: Set Theory: Should you believe?
DontBother@nowhere.net
7/19/06
Read Re: Set Theory: Should you believe?
Virgil
7/20/06
Read Re: Set Theory: Should you believe?
DontBother@nowhere.net
7/20/06
Read Re: Set Theory: Should you believe?
Virgil
7/20/06
Read Re: Set Theory: Should you believe?
DontBother@nowhere.net
7/18/06
Read Re: Set Theory: Should you believe?
namducnguyen
7/18/06
Read Re: Set Theory: Should you believe?
namducnguyen
7/18/06
Read Re: Set Theory: Should you believe?
DontBother@nowhere.net
7/18/06
Read Re: Set Theory: Should you believe?
Virgil
7/19/06
Read Re: Set Theory: Should you believe?
DontBother@nowhere.net
7/19/06
Read Re: Set Theory: Should you believe?
Virgil
7/19/06
Read Re: Set Theory: Should you believe?
DontBother@nowhere.net
7/19/06
Read Re: Set Theory: Should you believe?
Virgil
7/20/06
Read Re: Set Theory: Should you believe?
DontBother@nowhere.net
7/20/06
Read Re: Set Theory: Should you believe?
Virgil
7/20/06
Read Re: Set Theory: Should you believe?
DontBother@nowhere.net
7/18/06
Read Re: Set Theory: Should you believe?
namducnguyen
7/19/06
Read Re: Set Theory: Should you believe?
DontBother@nowhere.net
7/19/06
Read Re: Set Theory: Should you believe?
Virgil
7/19/06
Read Re: Set Theory: Should you believe?
DontBother@nowhere.net
7/19/06
Read Re: Set Theory: Should you believe?
Virgil
7/20/06
Read Re: Set Theory: Should you believe?
DontBother@nowhere.net
7/20/06
Read Re: Set Theory: Should you believe?
Virgil
7/20/06
Read Re: Set Theory: Should you believe?
DontBother@nowhere.net
7/20/06
Read Re: Set Theory: Should you believe?
Virgil
7/21/06
Read Re: Set Theory: Should you believe?
DontBother@nowhere.net
7/21/06
Read Re: Set Theory: Should you believe?
Virgil
7/22/06
Read Re: Set Theory: Should you believe?
DontBother@nowhere.net
7/22/06
Read Re: Set Theory: Should you believe?
Virgil
7/22/06
Read Re: Set Theory: Should you believe?
DontBother@nowhere.net
7/22/06
Read Re: Set Theory: Should you believe?
Virgil
7/23/06
Read Re: Set Theory: Should you believe?
DontBother@nowhere.net
7/23/06
Read Re: Set Theory: Should you believe?
Virgil
7/23/06
Read Re: Set Theory: Should you believe?
DontBother@nowhere.net
7/23/06
Read Re: Set Theory: Should you believe?
Virgil
7/23/06
Read Re: Set Theory: Should you believe?
DontBother@nowhere.net
7/23/06
Read Re: Set Theory: Should you believe?
Virgil
7/23/06
Read Re: Set Theory: Should you believe?
Jan Burse
7/24/06
Read Re: Set Theory: Should you believe?
Virgil
7/24/06
Read Re: Set Theory: Should you believe?
DontBother@nowhere.net
7/24/06
Read Re: Set Theory: Should you believe?
DontBother@nowhere.net
7/24/06
Read Re: Set Theory: Should you believe?
DontBother@nowhere.net
7/24/06
Read Re: Set Theory: Should you believe?
Virgil
7/18/06
Read Re: Set Theory: Should you believe?
Rupert
7/18/06
Read Re: Set Theory: Should you believe?
namducnguyen
7/19/06
Read Re: Set Theory: Should you believe?
Rupert
7/20/06
Read Re: Set Theory: Should you believe?
namducnguyen
7/20/06
Read Re: Set Theory: Should you believe?
DontBother@nowhere.net
7/20/06
Read Re: Set Theory: Should you believe?
namducnguyen
7/21/06
Read Re: Set Theory: Should you believe?
DontBother@nowhere.net
7/21/06
Read Re: Set Theory: Should you believe?
Virgil
7/22/06
Read Re: Set Theory: Should you believe?
DontBother@nowhere.net
7/22/06
Read Re: Set Theory: Should you believe?
Virgil
7/22/06
Read Re: Set Theory: Should you believe?
DontBother@nowhere.net
7/27/06
Read Re: Set Theory: Should you believe?
Rupert
7/27/06
Read Re: Set Theory: Should you believe?
DontBother@nowhere.net
7/28/06
Read Re: Set Theory: Should you believe?
Rupert
7/29/06
Read Re: Set Theory: Should you believe?
DontBother@nowhere.net
7/29/06
Read Re: Set Theory: Should you believe?
Virgil
7/29/06
Read Re: Set Theory: Should you believe?
DontBother@nowhere.net
7/29/06
Read Re: Set Theory: Should you believe?
Virgil
7/30/06
Read Re: Set Theory: Should you believe?
DontBother@nowhere.net
7/30/06
Read Re: Set Theory: Should you believe?
Virgil
7/30/06
Read Re: Set Theory: Should you believe?
DontBother@nowhere.net
7/29/06
Read Re: Set Theory: Should you believe?
Rupert
7/30/06
Read Re: Set Theory: Should you believe?
DontBother@nowhere.net
7/29/06
Read Re: Set Theory: Should you believe?
namducnguyen
7/29/06
Read Re: Set Theory: Should you believe?
DontBother@nowhere.net
7/29/06
Read Re: Set Theory: Should you believe?
Rupert
7/18/06
Read Re: Set Theory: Should you believe?
DontBother@nowhere.net
7/19/06
Read Re: Set Theory: Should you believe?
Rupert
7/19/06
Read Re: Set Theory: Should you believe?
namducnguyen
7/19/06
Read Re: Set Theory: Should you believe?
DontBother@nowhere.net
7/20/06
Read Re: Set Theory: Should you believe?
Rupert
7/20/06
Read Re: Set Theory: Should you believe?
DontBother@nowhere.net
7/20/06
Read Re: Set Theory: Should you believe?
Virgil
7/20/06
Read Re: Set Theory: Should you believe?
DontBother@nowhere.net
7/20/06
Read Re: Set Theory: Should you believe?
Virgil
7/21/06
Read Re: Set Theory: Should you believe?
DontBother@nowhere.net
7/21/06
Read Re: Set Theory: Should you believe?
Virgil
7/21/06
Read Re: Set Theory: Should you believe?
DontBother@nowhere.net
7/21/06
Read Re: Set Theory: Should you believe?
Virgil
7/22/06
Read Re: Set Theory: Should you believe?
herbzet@cox.net
7/22/06
Read Re: Set Theory: Should you believe?
DontBother@nowhere.net
7/23/06
Read Re: Set Theory: Should you believe?
herbzet@cox.net
7/23/06
Read Re: Set Theory: Should you believe?
DontBother@nowhere.net
7/22/06
Read Re: Set Theory: Should you believe?
DontBother@nowhere.net
7/22/06
Read Re: Set Theory: Should you believe?
Virgil
7/22/06
Read Re: Set Theory: Should you believe?
DontBother@nowhere.net
7/22/06
Read Re: Set Theory: Should you believe?
Virgil
7/23/06
Read Re: Set Theory: Should you believe?
DontBother@nowhere.net
7/23/06
Read Re: Set Theory: Should you believe?
Virgil
7/23/06
Read Re: Set Theory: Should you believe?
DontBother@nowhere.net
7/23/06
Read Re: Set Theory: Should you believe?
Virgil
7/24/06
Read Re: Set Theory: Should you believe?
DontBother@nowhere.net
7/22/06
Read Re: Set Theory: Should you believe?
herbzet@cox.net
7/22/06
Read Re: Set Theory: Should you believe?
DontBother@nowhere.net
7/22/06
Read Re: Set Theory: Should you believe?
Virgil
7/22/06
Read Re: Set Theory: Should you believe?
DontBother@nowhere.net
7/22/06
Read Re: Set Theory: Should you believe?
Virgil
7/23/06
Read Re: Set Theory: Should you believe?
DontBother@nowhere.net
7/23/06
Read Re: Set Theory: Should you believe?
Virgil
7/23/06
Read Re: Set Theory: Should you believe?
DontBother@nowhere.net
7/23/06
Read Re: Set Theory: Should you believe?
Virgil
7/23/06
Read Re: Set Theory: Should you believe?
DontBother@nowhere.net
7/23/06
Read Re: Set Theory: Should you believe?
Virgil
7/24/06
Read Re: Set Theory: Should you believe?
DontBother@nowhere.net
7/24/06
Read Re: Set Theory: Should you believe?
Virgil
7/23/06
Read Re: Set Theory: Should you believe?
herbzet@cox.net
7/23/06
Read Re: Set Theory: Should you believe?
herbzet@cox.net
7/23/06
Read Re: Set Theory: Should you believe?
DontBother@nowhere.net
7/23/06
Read Re: Set Theory: Should you believe?
Virgil
7/23/06
Read Re: Set Theory: Should you believe?
DontBother@nowhere.net
7/23/06
Read Re: Set Theory: Should you believe?
Virgil
7/24/06
Read Re: Set Theory: Should you believe?
DontBother@nowhere.net
7/24/06
Read Re: Set Theory: Should you believe?
Virgil
7/23/06
Read Re: Set Theory: Should you believe?
herbzet@cox.net
7/24/06
Read Re: Set Theory: Should you believe?
DontBother@nowhere.net
7/24/06
Read Re: Set Theory: Should you believe?
herbzet@cox.net
7/24/06
Read Re: Set Theory: Should you believe?
DontBother@nowhere.net
7/24/06
Read Re: Set Theory: Should you believe?
herbzet@cox.net
7/24/06
Read Re: Set Theory: Should you believe?
DontBother@nowhere.net
7/24/06
Read Re: Set Theory: Should you believe?
herbzet@cox.net
7/25/06
Read Re: Set Theory: Should you believe?
DontBother@nowhere.net
7/25/06
Read Re: Set Theory: Should you believe?
DontBother@nowhere.net
7/26/06
Read Re: Set Theory: Should you believe?
herbzet@cox.net
7/26/06
Read Re: Set Theory: Should you believe?
DontBother@nowhere.net
7/27/06
Read Re: Set Theory: Should you believe?
herbzet@cox.net
7/28/06
Read Re: Set Theory: Should you believe?
DontBother@nowhere.net
7/28/06
Read Re: Set Theory: Should you believe?
herbzet@cox.net
7/29/06
Read Re: Set Theory: Should you believe?
DontBother@nowhere.net
7/30/06
Read Re: Set Theory: Should you believe?
herbzet@cox.net
7/30/06
Read Re: Set Theory: Should you believe?
DontBother@nowhere.net
7/24/06
Read Re: Set Theory: Should you believe?
Virgil
7/24/06
Read Re: Set Theory: Should you believe?
Virgil
7/23/06
Read Re: Set Theory: Should you believe?
herbzet@cox.net
7/22/06
Read Re: Set Theory: Should you believe?
herbzet@cox.net
7/22/06
Read Re: Set Theory: Should you believe?
Virgil
7/22/06
Read Re: Set Theory: Should you believe?
herbzet@cox.net
7/20/06
Read Re: Set Theory: Should you believe?
Rupert
7/21/06
Read Re: Set Theory: Should you believe?
namducnguyen
7/21/06
Read Re: Set Theory: Should you believe?
Rupert
7/21/06
Read Re: Set Theory: Should you believe?
namducnguyen
7/22/06
Read Re: Set Theory: Should you believe?
Rupert
7/23/06
Read Re: Set Theory: Should you believe?
namducnguyen
7/24/06
Read Re: Set Theory: Should you believe?
Rupert
7/24/06
Read Re: Set Theory: Should you believe?
namducnguyen
7/24/06
Read Re: Set Theory: Should you believe?
Rupert
7/27/06
Read Re: Set Theory: Should you believe?
namducnguyen
7/27/06
Read Re: Set Theory: Should you believe?
Rupert
7/29/06
Read Re: Set Theory: Should you believe?
namducnguyen
7/29/06
Read Re: Set Theory: Should you believe?
Rupert
7/30/06
Read Re: Set Theory: Should you believe?
DontBother@nowhere.net
7/31/06
Read Re: Set Theory: Should you believe?
namducnguyen
7/21/06
Read Re: Set Theory: Should you believe?
DontBother@nowhere.net
7/21/06
Read Re: Set Theory: Should you believe?
Virgil
7/21/06
Read Re: Set Theory: Should you believe?
DontBother@nowhere.net
7/21/06
Read Re: Set Theory: Should you believe?
Virgil
7/21/06
Read Re: Set Theory: Should you believe?
Dr. David Kirkby
7/22/06
Read Re: Set Theory: Should you believe?
DontBother@nowhere.net
7/22/06
Read Re: Set Theory: Should you believe?
DontBother@nowhere.net
7/22/06
Read Re: Set Theory: Should you believe?
Virgil
7/22/06
Read Re: Set Theory: Should you believe?
DontBother@nowhere.net
7/22/06
Read Re: Set Theory: Should you believe?
Virgil
7/23/06
Read Re: Set Theory: Should you believe?
DontBother@nowhere.net
7/23/06
Read Re: Set Theory: Should you believe?
Virgil
7/23/06
Read Re: Set Theory: Should you believe?
DontBother@nowhere.net
7/23/06
Read Re: Set Theory: Should you believe?
Virgil
7/25/06
Read Re: Set Theory: Should you believe?
Rupert
7/19/06
Read Re: Set Theory: Should you believe?
DontBother@nowhere.net
7/19/06
Read Re: Set Theory: Should you believe?
Virgil
7/19/06
Read Re: Set Theory: Should you believe?
DontBother@nowhere.net
7/19/06
Read Re: Set Theory: Should you believe?
Virgil
7/19/06
Read Re: Set Theory: Should you believe?
DontBother@nowhere.net
7/19/06
Read Re: Set Theory: Should you believe?
Virgil
7/20/06
Read Re: Set Theory: Should you believe?
DontBother@nowhere.net
7/20/06
Read Re: Set Theory: Should you believe?
Virgil
7/20/06
Read Re: Set Theory: Should you believe?
DontBother@nowhere.net
7/20/06
Read Re: Set Theory: Should you believe?
Virgil
7/21/06
Read Re: Set Theory: Should you believe?
DontBother@nowhere.net
7/21/06
Read Re: Set Theory: Should you believe?
jirka@5z.com
7/22/06
Read Re: Set Theory: Should you believe?
DontBother@nowhere.net
7/22/06
Read Re: Set Theory: Should you believe?
Virgil
7/22/06
Read Re: Set Theory: Should you believe?
DontBother@nowhere.net
7/22/06
Read Re: Set Theory: Should you believe?
Virgil
7/22/06
Read Re: Set Theory: Should you believe?
DontBother@nowhere.net
7/22/06
Read Re: Set Theory: Should you believe?
Virgil
7/23/06
Read Re: Set Theory: Should you believe?
DontBother@nowhere.net
7/23/06
Read Re: Set Theory: Should you believe?
Virgil
7/23/06
Read Re: Set Theory: Should you believe?
DontBother@nowhere.net
7/23/06
Read Re: Set Theory: Should you believe?
Virgil
7/24/06
Read Re: Set Theory: Should you believe?
DontBother@nowhere.net
7/24/06
Read Re: Set Theory: Should you believe?
Virgil
7/23/06
Read Re: Set Theory: Should you believe?
jirka@5z.com
7/23/06
Read Re: Set Theory: Should you believe?
DontBother@nowhere.net
7/23/06
Read Re: Set Theory: Should you believe?
Virgil
7/23/06
Read Re: Set Theory: Should you believe?
DontBother@nowhere.net
7/23/06
Read Re: Set Theory: Should you believe?
Virgil
7/24/06
Read Re: Set Theory: Should you believe?
DontBother@nowhere.net
7/24/06
Read Re: Set Theory: Should you believe?
Virgil
7/23/06
Read Re: Set Theory: Should you believe?
Aatu Koskensilta
7/23/06
Read Re: Set Theory: Should you believe?
Dr. David Kirkby
7/23/06
Read Re: Set Theory: Should you believe?
DontBother@nowhere.net
7/23/06
Read Re: Set Theory: Should you believe?
Virgil
7/23/06
Read Re: Set Theory: Should you believe?
DontBother@nowhere.net
7/23/06
Read Re: Set Theory: Should you believe?
Virgil
7/23/06
Read Re: Set Theory: Should you believe?
DontBother@nowhere.net
7/23/06
Read Re: Set Theory: Should you believe?
Virgil
7/24/06
Read Re: Set Theory: Should you believe?
DontBother@nowhere.net
7/24/06
Read Re: Set Theory: Should you believe?
Virgil
7/24/06
Read Re: Set Theory: Should you believe?
R. Srinivasan
7/24/06
Read Re: Set Theory: Should you believe?
DontBother@nowhere.net
7/24/06
Read Re: Set Theory: Should you believe?
Virgil
7/23/06
Read Re: Set Theory: Should you believe?
jirka@5z.com
7/23/06
Read Re: Set Theory: Should you believe?
DontBother@nowhere.net
7/24/06
Read Re: Set Theory: Should you believe?
Aatu Koskensilta
7/24/06
Read Re: Set Theory: Should you believe?
DontBother@nowhere.net
7/25/06
Read Re: Set Theory: Should you believe?
Gc
7/25/06
Read Re: Set Theory: Should you believe?
Aatu Koskensilta
7/25/06
Read Re: Set Theory: Should you believe?
Gc
7/25/06
Read Re: Set Theory: Should you believe?
Aatu Koskensilta
7/25/06
Read Re: Set Theory: Should you believe?
Gc
7/25/06
Read Re: Set Theory: Should you believe?
Aatu Koskensilta
7/25/06
Read Re: Set Theory: Should you believe?
Gc
7/25/06
Read Re: Set Theory: Should you believe?
Aatu Koskensilta
7/25/06
Read Re: Set Theory: Should you believe?
Gc
7/25/06
Read Re: Set Theory: Should you believe?
Aatu Koskensilta
7/25/06
Read Re: Set Theory: Should you believe?
Gc
7/25/06
Read Re: Set Theory: Should you believe?
Gc
7/25/06
Read Re: Set Theory: Should you believe?
Aatu Koskensilta
7/25/06
Read Re: Set Theory: Should you believe?
Gc
7/25/06
Read Re: Set Theory: Should you believe?
Aatu Koskensilta
7/25/06
Read Re: Set Theory: Should you believe?
Gc
7/25/06
Read Re: Set Theory: Should you believe?
Aatu Koskensilta
7/25/06
Read Re: Set Theory: Should you believe?
Gc
7/25/06
Read Re: Set Theory: Should you believe?
Aatu Koskensilta
7/25/06
Read Re: Set Theory: Should you believe?
Gc
7/25/06
Read Re: Set Theory: Should you believe?
Gc
7/25/06
Read Re: Set Theory: Should you believe?
Chris Menzel
7/25/06
Read Re: Set Theory: Should you believe?
Gc
7/26/06
Read Re: Set Theory: Should you believe?
Chris Menzel
7/26/06
Read Re: Set Theory: Should you believe?
Gc
7/28/06
Read Re: Set Theory: Should you believe?
George Greene
7/28/06
Read Re: Set Theory: Should you believe?
Aatu Koskensilta
7/25/06
Read Re: Set Theory: Should you believe?
Pierre Asselin
7/25/06
Read Re: Set Theory: Should you believe?
Dr. David Kirkby
7/26/06
Read Re: Set Theory: Should you believe?
DontBother@nowhere.net
7/26/06
Read Re: Set Theory: Should you believe?
DontBother@nowhere.net
7/26/06
Read Re: Set Theory: Should you believe?
Pierre Asselin
7/27/06
Read Re: Set Theory: Should you believe?
DontBother@nowhere.net
7/26/06
Read Re: Set Theory: Should you believe?
jirka@5z.com
7/26/06
Read Re: Set Theory: Should you believe?
Gc
7/24/06
Read Re: Set Theory: Should you believe?
Aatu Koskensilta
7/24/06
Read Re: Set Theory: Should you believe?
jirka@5z.com
7/24/06
Read Re: Set Theory: Should you believe?
Aatu Koskensilta
7/25/06
Read Re: Set Theory: Should you believe?
jirka@5z.com
7/25/06
Read Re: Set Theory: Should you believe?
Aatu Koskensilta
7/18/06
Read Re: Set Theory: Should you believe?
DontBother@nowhere.net
7/18/06
Read Re: Set Theory: Should you believe?
Virgil
7/19/06
Read Re: Set Theory: Should you believe?
DontBother@nowhere.net
7/19/06
Read Re: Set Theory: Should you believe?
Virgil
7/19/06
Read Re: Set Theory: Should you believe?
DontBother@nowhere.net
7/19/06
Read Re: Set Theory: Should you believe?
Virgil
7/20/06
Read Re: Set Theory: Should you believe?
DontBother@nowhere.net
7/20/06
Read Re: Set Theory: Should you believe?
Virgil
7/20/06
Read Re: Set Theory: Should you believe?
DontBother@nowhere.net
7/20/06
Read Re: Set Theory: Should you believe?
Virgil
7/21/06
Read Re: Set Theory: Should you believe?
DontBother@nowhere.net
7/21/06
Read Re: Set Theory: Should you believe?
Virgil
7/22/06
Read Re: Set Theory: Should you believe?
DontBother@nowhere.net
7/22/06
Read Re: Set Theory: Should you believe?
Virgil
7/22/06
Read Re: Set Theory: Should you believe?
DontBother@nowhere.net
7/22/06
Read Re: Set Theory: Should you believe?
Virgil
7/22/06
Read Re: Set Theory: Should you believe?
DontBother@nowhere.net
7/22/06
Read Re: Set Theory: Should you believe?
Patricia Shanahan
7/23/06
Read Re: Set Theory: Should you believe?
DontBother@nowhere.net
7/23/06
Read Re: Set Theory: Should you believe?
Virgil
7/23/06
Read Re: Set Theory: Should you believe?
DontBother@nowhere.net
7/23/06
Read Re: Set Theory: Should you believe?
Virgil
7/23/06
Read Re: Set Theory: Should you believe?
DontBother@nowhere.net
7/23/06
Read Re: Set Theory: Should you believe?
Virgil
7/24/06
Read Re: Set Theory: Should you believe?
DontBother@nowhere.net
7/24/06
Read Re: Set Theory: Should you believe?
Virgil
7/22/06
Read Re: Set Theory: Should you believe?
Virgil
7/23/06
Read Re: Set Theory: Should you believe?
DontBother@nowhere.net
7/23/06
Read Re: Set Theory: Should you believe?
Virgil
7/23/06
Read Re: Set Theory: Should you believe?
DontBother@nowhere.net
7/23/06
Read Re: Set Theory: Should you believe?
Virgil
7/24/06
Read Re: Set Theory: Should you believe?
DontBother@nowhere.net
7/24/06
Read Re: Set Theory: Should you believe?
Virgil
7/18/06
Read Re: Set Theory: Should you believe?
Aatu Koskensilta
7/18/06
Read Re: Set Theory: Should you believe?
DontBother@nowhere.net
7/19/06
Read Re: Set Theory: Should you believe?
David Bernier
7/19/06
Read Re: Set Theory: Should you believe?
Aatu Koskensilta
7/22/06
Read Re: Set Theory: Should you believe?
Keith Ramsay
7/22/06
Read Re: Set Theory: Should you believe?
David Bernier
7/22/06
Read Re: Set Theory: Should you believe?
Virgil
8/3/06
Read Re: Set Theory: Should you believe?
Rupert
7/17/06
Read Re: Set Theory: Should you believe?
Toni Lassila
7/14/06
Read Re: Set Theory: Should you believe?
Phil Carmody
7/14/06
Read Re: Set Theory: Should you believe?
Stephen Montgomery-Smith
7/20/06
Read Re: Set Theory: Should you believe?
Y. T.
7/13/06
Read Re: Set Theory: Should you believe?
Peter Webb
7/13/06
Read Re: Set Theory: Should you believe?
Gerry Myerson
7/13/06
Read Re: Set Theory: Should you believe?
Stephen Montgomery-Smith
7/14/06
Read Re: Set Theory: Should you believe?
Kevin Karn
7/14/06
Read Re: Set Theory: Should you believe?
Gene Ward Smith
7/15/06
Read Re: Set Theory: Should you believe?
Stephen Montgomery-Smith
7/15/06
Read Re: Set Theory: Should you believe?
Stephen Montgomery-Smith
7/15/06
Read Re: Set Theory: Should you believe?
Gene Ward Smith
7/15/06
Read Re: Set Theory: Should you believe?
Hatto von Aquitanien
7/15/06
Read Re: Set Theory: Should you believe?
Stephen Montgomery-Smith
7/15/06
Read Re: Set Theory: Should you believe?
Barb Knox
7/15/06
Read Re: Set Theory: Should you believe?
Daryl McCullough
7/15/06
Read Re: Set Theory: Should you believe?
Peter Webb
7/15/06
Read Re: Set Theory: Should you believe?
Chas Brown
7/15/06
Read Re: Set Theory: Should you believe?
T.H. Ray
7/15/06
Read Re: Set Theory: Should you believe?
DontBother@nowhere.net
7/15/06
Read Re: Set Theory: Should you believe?
Lee Rudolph
7/17/06
Read Re: Set Theory: Should you believe?
James Dolan
7/14/06
Read Re: Set Theory: Should you believe?
Peter Webb
7/17/06
Read Re: Set Theory: Should you believe?
Rupert
7/13/06
Read Re: Set Theory: Should you believe?
Russell Easterly
7/13/06
Read Re: Set Theory: Should you believe?
Gene Ward Smith
7/13/06
Read Re: Set Theory: Should you believe?
stephen@nomail.com
7/13/06
Read Re: Set Theory: Should you believe?
Virgil
7/13/06
Read Re: Set Theory: Should you believe?
Hatto von Aquitanien
7/13/06
Read Re: Set Theory: Should you believe?
Stephen Montgomery-Smith
7/13/06
Read Re: Set Theory: Should you believe?
Gene Ward Smith
7/13/06
Read Re: Set Theory: Should you believe?
Hatto von Aquitanien
7/13/06
Read Re: Set Theory: Should you believe?
Stephen Montgomery-Smith
7/14/06
Read Re: Set Theory: Should you believe?
Hatto von Aquitanien
7/13/06
Read Re: Set Theory: Should you believe?
lDontBother@nowhere.net
7/13/06
Read Re: Set Theory: Should you believe?
Hatto von Aquitanien
7/13/06
Read Re: Set Theory: Should you believe?
DontBother@nowhere.net
7/15/06
Read Re: Set Theory: Should you believe?
John Jones
7/15/06
Read Re: Set Theory: Should you believe?
Virgil
7/13/06
Read Re: Set Theory: Should you believe?
Kevin Karn
7/13/06
Read Re: Set Theory: Should you believe?
Russell Easterly
7/13/06
Read Re: Set Theory: Should you believe?
Kevin Karn
8/4/06
Read Re: Set Theory: Should you believe?
seand602
7/13/06
Read Re: Set Theory: Should you believe?
Gene Ward Smith
7/13/06
Read Re: Set Theory: Should you believe?
Gerry Myerson
7/13/06
Read Re: Set Theory: Should you believe?
Gene Ward Smith
7/13/06
Read Re: Set Theory: Should you believe?
R. Srinivasan
7/13/06
Read Re: Set Theory: Should you believe?
lDontBother@nowhere.net
7/13/06
Read Re: Set Theory: Should you believe?
Aatu Koskensilta
7/13/06
Read Re: Set Theory: Should you believe?
DontBother@nowhere.net
7/13/06
Read Re: Set Theory: Should you believe?
Aatu Koskensilta
7/14/06
Read Re: Set Theory: Should you believe?
Shmuel (Seymour J.) Metz
7/14/06
Read Re: Set Theory: Should you believe?
DontBother@nowhere.net
7/14/06
Read Re: Set Theory: Should you believe?
Virgil
7/15/06
Read Re: Set Theory: Should you believe?
DontBother@nowhere.net
7/15/06
Read Re: Set Theory: Should you believe?
Virgil
7/15/06
Read Re: Set Theory: Should you believe?
DontBother@nowhere.net
7/15/06
Read Re: Set Theory: Should you believe?
Virgil
7/16/06
Read Re: Set Theory: Should you believe?
DontBother@nowhere.net
7/13/06
Read Re: Set Theory: Should you believe?
Peter Webb
7/13/06
Read Re: Set Theory: Should you believe?
Gene Ward Smith
7/13/06
Read Re: Set Theory: Should you believe?
Gerry Myerson
7/13/06
Read Re: Set Theory: Should you believe?
Gene Ward Smith
7/14/06
Read Re: Set Theory: Should you believe?
R. Srinivasan
7/14/06
Read Re: Set Theory: Should you believe?
R. Srinivasan
7/14/06
Read Re: Set Theory: Should you believe?
Soap_Dude
7/16/06
Read Re: Set Theory: Should you believe?
R. Srinivasan
7/16/06
Read Re: Set Theory: Should you believe?
Gerry Myerson
7/17/06
Read Re: Set Theory: Should you believe?
Rupert
7/13/06
Read Re: Set Theory: Should you believe?
Daryl McCullough
7/13/06
Read Re: Set Theory: Should you believe?
tez_h@nospam.yahoo.com
7/13/06
Read Re: Set Theory: Should you believe?
Gerry Myerson
7/13/06
Read Re: Set Theory: Should you believe?
DontBother@nowhere.net
7/14/06
Read Re: Set Theory: Should you believe?
Lee Rudolph
7/15/06
Read Re: Set Theory: Should you believe?
George Greene
7/15/06
Read Re: Set Theory: Should you believe?
David Petry
7/14/06
Read Re: Set Theory: Should you believe?
George Greene
7/15/06
Read Re: Set Theory: Should you believe?
Andrew Bettilyon
7/16/06
Read Re: Set Theory: Should you believe?
George Greene
7/17/06
Read Re: Set Theory: Should you believe?
Andrew Bettilyon
7/16/06
Read Re: Set Theory: Should you believe?
bogus address
7/16/06
Read Alternative Trigonometry: [Was: Re: Set Theory: Should you believe?]
Patricia Shanahan
7/16/06
Read Re: Alternative Trigonometry: [Was: Re: Set Theory: Should you believe?]
Patricia Shanahan
7/17/06
Read Re: Alternative Trigonometry: [Was: Re: Set Theory: Should you believe?]
Andrew Bettilyon
7/13/06
Read Re: Set Theory: Should you believe?
George Greene
7/13/06
Read Re: Set Theory: Should you believe?
Gene Ward Smith
7/13/06
Read Re: Set Theory: Should you believe?
Gerry Myerson
7/13/06
Read Re: Set Theory: Should you believe?
DontBother@nowhere.net
7/13/06
Read Re: Set Theory: Should you believe?
Gene Ward Smith
7/14/06
Read Re: Set Theory: Should you believe?
DontBother@nowhere.net
7/14/06
Read Re: Set Theory: Should you believe?
Gene Ward Smith
7/14/06
Read Re: Set Theory: Should you believe?
Hatto von Aquitanien
7/14/06
Read Re: Set Theory: Should you believe?
DontBother@nowhere.net
7/14/06
Read Re: Set Theory: Should you believe?
Ralf Bader
7/14/06
Read Re: Set Theory: Should you believe?
DontBother@nowhere.net
7/14/06
Read Re: Set Theory: Should you believe?
Virgil
7/15/06
Read Re: Set Theory: Should you believe?
DontBother@nowhere.net
7/15/06
Read Re: Set Theory: Should you believe?
Virgil
7/15/06
Read Re: Set Theory: Should you believe?
DontBother@nowhere.net
7/16/06
Read Re: Set Theory: Should you believe?
Virgil
7/16/06
Read Re: Set Theory: Should you believe?
DontBother@nowhere.net
7/18/06
Read Re: Set Theory: Should you believe?
Rupert
7/19/06
Read Re: Set Theory: Should you believe?
DontBother@nowhere.net
7/19/06
Read Re: Set Theory: Should you believe?
Dave L. Renfro
7/19/06
Read Re: Set Theory: Should you believe?
DontBother@nowhere.net
7/19/06
Read Re: Set Theory: Should you believe?
Virgil
7/20/06
Read Re: Set Theory: Should you believe?
Dave L. Renfro
7/20/06
Read Re: Set Theory: Should you believe?
Dave L. Renfro
7/20/06
Read Re: Set Theory: Should you believe?
DontBother@nowhere.net
7/20/06
Read Re: Set Theory: Should you believe?
DontBother@nowhere.net
7/20/06
Read Re: Set Theory: Should you believe?
Virgil
7/20/06
Read Re: Set Theory: Should you believe?
DontBother@nowhere.net
7/24/06
Read Re: Set Theory: Should you believe?
Rupert
7/24/06
Read Re: Set Theory: Should you believe?
DontBother@nowhere.net
7/14/06
Read Re: Set Theory: Should you believe?
George Greene
7/14/06
Read Re: Set Theory: Should you believe?
George Greene
7/14/06
Read Re: Set Theory: Should you believe?
George Greene
7/14/06
Read Re: Set Theory: Should you believe?
Rupert
7/14/06
Read Re: Set Theory: Should NW behave?
George Greene
7/14/06
Read Re: Set Theory: Should you believe?
T.H. Ray
7/12/06
Read Re: Set Theory: Should you believe?
Gonçalo Rodrigues
7/12/06
Read Re: Set Theory: Should you believe?
Gene Ward Smith
7/12/06
Read Re: Set Theory: Should you believe?
David Petry
7/12/06
Read Re: Set Theory: Should you believe?
Gene Ward Smith
7/13/06
Read Re: Set Theory: Should you believe?
Richard Herring
7/13/06
Read Re: Set Theory: Should you believe?
Gene Ward Smith
7/13/06
Read Re: Set Theory: Should you believe?
Gerry Myerson
7/13/06
Read Re: Set Theory: Should you believe?
Gene Ward Smith
7/14/06
Read Re: Set Theory: Should you believe?
Gerry Myerson
7/14/06
Read Re: Set Theory: Should you believe?
Gene Ward Smith
7/14/06
Read Re: Set Theory: Should you believe?
Gerry Myerson
7/14/06
Read Re: Set Theory: Should you believe?
Lee Rudolph
7/14/06
Read Re: Set Theory: Should you believe?
Stephen Montgomery-Smith
7/14/06
Read Re: Set Theory: Should you believe?
Gene Ward Smith
7/13/06
Read Re: Set Theory: Should you believe?
Stephen Montgomery-Smith
7/13/06
Read Re: Set Theory: Should you believe?
Gene Ward Smith
7/13/06
Read Re: Set Theory: Should you believe?
kunzmilan@atlas.cz
7/13/06
Read Re: Set Theory: Should you believe?
guenther.vonKnakspott@gmx.de
7/13/06
Read Re: Set Theory: Should you believe?
Hatto von Aquitanien
7/13/06
Read Re: Set Theory: Should you believe?
Dr. David Kirkby
7/13/06
Read Re: Set Theory: Should you believe?
Hatto von Aquitanien
7/14/06
Read Re: Set Theory: Should you believe?
David C. Ullrich
7/14/06
Read Re: Set Theory: Should you believe?
David C. Ullrich
7/14/06
Read Re: Set Theory: Should you believe?
Peter Webb
7/14/06
Read Re: Set Theory: Should you believe?
jirka@5z.com
7/14/06
Read Re: Set Theory: Should you believe?
Hatto von Aquitanien
7/13/06
Read Re: Set Theory: Should you believe?
guenther.vonKnakspott@gmx.de
7/13/06
Read Re: Set Theory: Should you believe?
Hatto von Aquitanien
7/13/06
Read Re: Set Theory: Should you believe?
guenther.vonKnakspott@gmx.de
7/14/06
Read Re: Set Theory: Should you believe?
David C. Ullrich
7/13/06
Read Re: Set Theory: Should you believe?
Dave L. Renfro
7/13/06
Read Re: Set Theory: Should you believe?
Stephen Montgomery-Smith
7/13/06
Read Re: Set Theory: Should you believe?
Gene Ward Smith
7/13/06
Read Re: Set Theory: Should you believe?
Stephen Montgomery-Smith
7/13/06
Read Re: Set Theory: Should you believe?
Gene Ward Smith
7/13/06
Read Re: Set Theory: Should you believe?
Brian Chandler
7/13/06
Read Re: Set Theory: Should you believe?
Chas Brown
7/13/06
Read Re: Set Theory: Should you believe?
DontBother@nowhere.net
7/14/06
Read Re: Set Theory: Should you believe?
guenther.vonKnakspott@gmx.de
7/14/06
Read Re: Set Theory: Should you believe?
DontBother@nowhere.net
7/14/06
Read Re: Set Theory: Should you believe?
Chas Brown
7/14/06
Read Re: Set Theory: Should you believe?
Ben Rudiak-Gould
7/14/06
Read Re: Set Theory: Should you believe?
guenther.vonKnakspott@gmx.de
7/14/06
Read Re: Set Theory: Should you believe?
Stephen Montgomery-Smith
7/14/06
Read Re: Set Theory: Should you believe?
stephen@nomail.com
7/14/06
Read Re: Set Theory: Should you believe?
Stephen Montgomery-Smith
7/14/06
Read Re: Set Theory: Should you believe?
Gene Ward Smith
7/14/06
Read Re: Set Theory: Should you believe?
Hatto von Aquitanien
7/14/06
Read Re: Set Theory: Should you believe?
Dave L. Renfro
7/14/06
Read Re: Set Theory: Should you believe?
DontBother@nowhere.net
7/14/06
Read Re: Set Theory: Should you believe?
Stephen Montgomery-Smith
7/14/06
Read Re: Set Theory: Should you believe?
Hatto von Aquitanien
7/14/06
Read Re: Set Theory: Should you believe?
Stephen Montgomery-Smith
7/14/06
Read Re: Set Theory: Should you believe?
Hatto von Aquitanien
7/14/06
Read Re: Set Theory: Should you believe?
Stephen Montgomery-Smith
7/14/06
Read Re: Set Theory: Should you believe?
Stephen Montgomery-Smith
7/14/06
Read Re: Set Theory: Should you believe?
Chas Brown
7/13/06
Read Re: Set Theory: Should you believe?
Hatto von Aquitanien
8/3/06
Read Re: Set Theory: Should you believe?
Anonymous

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