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
From: Osher Doctorow [EMAIL PROTECTED], Sat. Sept. 21, 2002 10:39PM
I've glanced over one of Tegmark's papers and it didn't impress me much, but
maybe you've seen something that I didn't.
As for your question (have you ever been accused of being over-specific?),
the best thing for a person not f
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
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