In article <firstname.lastname@example.org>, kubo@abel (Tal Kubo) writes: >Matthew P Wiener <email@example.com> 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.
>>>another problem: your argument used nothing about the initial theory >>>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 (firstname.lastname@example.org)