Hal Finney wrote:
I have gone back to Tegmark's paper, which is discussed informally
at http://www.hep.upenn.edu/~max/toe.html and linked from
http://arXiv.org/abs/gr-qc/9704009.
I see that Russell is right, and that Tegmark does identify mathematical
structures with formal systems. His
I'm not so sure that I do perceive positive integers directly. But
regardless of that, I remain convinced that all properties of them
that I can perceive can be written as a piece of ASCII text.
The description doesn't need to be axiomatic, mind you. As I have
mentioned, the Schmidhuber
At 19:08 -0400 29/09/2002, Wei Dai wrote:
On Thu, Sep 26, 2002 at 12:46:29PM +0200, Bruno Marchal wrote:
I would say the difference between animals and humans is that humans
make drawings on the walls ..., and generally doesn't take their body
as a limitation of their memory.
It's possible
On Tue, Sep 24, 2002 at 12:18:36PM +0200, Bruno Marchal wrote:
You are right. But this is a reason for not considering classical *second*
order logic as logic. Higher order logic remains logic when some
constructive assumption are made, like working in intuitionist logic.
A second order
At 21:36 -0400 21/09/2002, [EMAIL PROTECTED] wrote:
For those of you who are familiar with Max Tegmark's TOE, could someone tell
me whether Georg Cantor's Absolute Infinity, Absolute Maximum or Absolute
Infinite Collections represent mathematical structures and, therefore have
physical
At 22:26 -0700 21/09/2002, Brent Meeker wrote:
I don't see how this follows. If you have a set of axioms, and
rules of inference, then (per Godel) there are undecidable
propositions. One of these may be added as an axiom and the
system will still be consistent. This will allow you to prove
At 2:19 -0400 22/09/2002, Wei Dai wrote:
This needs to be qualified a bit. Mathematical objects are more than the
formal (i.e., deductive) consequences of their axioms. However, an axiom
system can capture a mathematical structure, if it's second-order, and you
consider the semantic consequences
At 11:34 -0700 23/09/2002, Hal Finney wrote:
I have gone back to Tegmark's paper, which is discussed informally
at http://www.hep.upenn.edu/~max/toe.html and linked from
http://arXiv.org/abs/gr-qc/9704009.
I see that Russell is right, and that Tegmark does identify mathematical
structures with
Russell Standish writes:
[Hal Finney writes;]
So I disagree with Russell on this point; I'd say that Tegmark's
mathematical structures are more than axiom systems and therefore
Tegmark's TOE is different from Schmidhuber's.
If you are so sure of this, then please provide a description of
I have gone back to Tegmark's paper, which is discussed informally
at http://www.hep.upenn.edu/~max/toe.html and linked from
http://arXiv.org/abs/gr-qc/9704009.
I see that Russell is right, and that Tegmark does identify mathematical
structures with formal systems. His chart at the first link
On Monday, September 23, 2002, at 11:34 AM, Hal Finney wrote:
I have gone back to Tegmark's paper, which is discussed informally
at http://www.hep.upenn.edu/~max/toe.html and linked from
http://arXiv.org/abs/gr-qc/9704009.
I see that Russell is right, and that Tegmark does identify
]; [EMAIL PROTECTED]
Sent: Saturday, September 21, 2002 7:18 PM
Subject: Re: Tegmark's TOE Cantor's Absolute Infinity
Dave Raub asks:
For those of you who are familiar with Max Tegmark's TOE, could someone
tell
me whether Georg Cantor's Absolute Infinity, Absolute Maximum or
Absolute
On 21-Sep-02, Wei Dai wrote:
On Sat, Sep 21, 2002 at 10:26:45PM -0700, Brent Meeker wrote:
I don't see how this follows. If you have a set of axioms,
and rules of inference, then (per Godel) there are
undecidable propositions. One of these may be added as an
axiom and the system will still
On Sat, Sep 21, 2002 at 11:50:20PM -0700, Brent Meeker wrote:
I was not aware that 2nd-order logic precluded independent
propositions. Is this true whatever the axioms and rules of
inference?
It depends on the axioms, and the semantic rules (not rules of inference
which is a deductive
Osher Doctorow wrote:
From: Osher Doctorow [EMAIL PROTECTED], Sat. Sept. 21, 2002 11:38PM
Hal,
Well said. I really have to have more patience for questioners, but
mathematics and logic are such wonderful fields in my opinion that we need
to treasure them rather than throw them out
For those of you who are familiar with Max Tegmark's TOE, could someone tell
me whether Georg Cantor's Absolute Infinity, Absolute Maximum or Absolute
Infinite Collections represent mathematical structures and, therefore have
physical existence.
Thanks again for the help!!
Dave Raub
For those of you who are familiar with Max Tegmark's TOE, could someone tell
me whether Georg Cantor's Absolute Infinity, Absolute Maximum or Absolute
Infinite Collections represent mathematical structures and, therefore have
physical existence.
Thanks again for the help!!
Dave Raub
For those of you who are familiar with Max Tegmark's TOE, could someone tell
me whether Georg Cantor's Absolute Infinity, Absolute Maximum or Absolute
Infinite Collections represent mathematical structures and, therefore have
physical existence.
Thanks again for the help!!
Dave Raub
Dave Raub asks:
For those of you who are familiar with Max Tegmark's TOE, could someone tell
me whether Georg Cantor's Absolute Infinity, Absolute Maximum or Absolute
Infinite Collections represent mathematical structures and, therefore have
physical existence.
I don't know the answer to
On Sat, Sep 21, 2002 at 09:20:26PM -0400, [EMAIL PROTECTED] wrote:
For those of you who are familiar with Max Tegmark's TOE, could someone tell
me whether Georg Cantor's Absolute Infinity, Absolute Maximum or Absolute
Infinite Collections represent mathematical structures and, therefore
On 21-Sep-02, Hal Finney wrote:
...
However we know that, by Godel's theorem, any axiomatization
of a mathematical structure of at least moderate complexity
is in some sense incomplete. There are true theorems of that
mathematical structure which cannot be proven by those
axioms. This is
Subject: Tegmark's TOE Cantor's Absolute Infinity
For those of you who are familiar with Max Tegmark's TOE, could someone
tell
me whether Georg Cantor's Absolute Infinity, Absolute Maximum or
Absolute
Infinite Collections represent mathematical structures and, therefore
have
physical
On Sat, Sep 21, 2002 at 10:26:45PM -0700, Brent Meeker wrote:
I don't see how this follows. If you have a set of axioms, and
rules of inference, then (per Godel) there are undecidable
propositions. One of these may be added as an axiom and the
system will still be consistent. This will
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