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 ensemble
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
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
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 that we will never be able to access more
At 12:51 -0400 25/09/2002, Wei Dai wrote:
>If we can take the set of all deductive consequences of some axioms and
>call it a theory, then why can't we also take the set of their semantic
>consequences and call it a theory? In what sense is the latter more
>"technical" than the former? It's true
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 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 w
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 consequen
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 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 e
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
>
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 ab
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 descri
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
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 conc
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
lt;[EMAIL PROTECTED]>
To: <[EMAIL PROTECTED]>; <[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
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
D]>
Cc: <[EMAIL PROTECTED]>
Sent: Saturday, September 21, 2002 6:59 PM
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,
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
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, therefo
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
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
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