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Topic: Go Deep Blue!
Replies: 334   Last Post: Aug 22, 1997 11:23 AM

 Messages: [ Previous | Next ]
 Matthew P Wiener Posts: 513 Registered: 12/8/04
Re: 0-1 Laws (was Re: Go Deep Blue! (on Lucas)
Posted: Jun 3, 1997 5:09 PM

In article <5mve2i\$gjn\$1@news.fas.harvard.edu>, kubo@abel (Tal Kubo) writes:
>Matthew P Wiener <weemba@sagi.wistar.upenn.edu> wrote:

>>Note that very little of PA is actually needed for the relevant analysis,
>>and in fact, one simply needs the finite number of 0-1 related stuff used,
>>which isn't that much.

>Only for toy theories with toy models, like first order graph theory.
>Not for 0-1 laws applicable to PA and beyond (if any exist, that is).

No, they would be relatively simple.

>>>other than the ability to implement 0-1 arguments and Goedel's theorem.

>>Only the end of the argument. The choice of initial theory was made for
>>physical reasons. Hence the name, "physical mathematics".

>But your argument isn't sensitive to that choice.

Of course not. We *know* we are beyond that choice already, so we must
have evolved that far anyway, and then the argument kicks in.

> What part of the
>Goedelian 0-1 argument goes wrong if we choose a lower starting point?

Ultimately it breaks down when the Goedelian argument itself can't be done.

>>> So start the argument at a weaker subsystem of PM that
>>>shares these properties, PA perhaps, and prove that we don't even get as
>>>high as PM. To get around this you'd have to give some handwaving about
>>>not all types of evolution being created equal for 0-1 purposes, which
>>>defeats the purpose of the argument (to appeal to the supposed robustness
>>>of 0-1 laws).

>>No, no handwaving. Just plain old natural selection. A superior mental job
>>of handling the real world is supposed to translate into a superior physical
>>job of handling the real world. So sub-PM-minds are pressured to up to PM.

>That doesn't deal with the objection.

Yes it does.

> How does your Goedelian argument
>allow for any upward mobility at all, once a certain threshold is
>crossed which is below PM?

The Goedelian 0-1 argument has no say on the upward mobility, period. The
0-1 aspect cannot in any way restrain natural selection. It can only be
applied to the part without physical correlate.
--
-Matthew P Wiener (weemba@sagi.wistar.upenn.edu)

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