>>>>You're forgetting one of my basic assumptions: *no* such sentence is >>>>beneficial, since it lacks a physical correlate to be beneficial with.
>I just thought of something else that, in my opinion, tends to weaken >your argument.
Very good. I know of several things that would weaken my argument.
> You claim that a race of TM-minds would experience no >evolutionary pressures to develop reasoning power above and beyond >perhaps PA, because there is no physical advantage to higher-powered >mathematics. However, if there is a survival advantage for one TM to >be able to make predictions about another TM, then I don't think that >you can set an a priori limit on what reasoning power is physically >relevant.
Such predictions sound non-recursive, and thus are not relevant. Of related genre, and probably relevant, is Goedelian speedup. -- -Matthew P Wiener (email@example.com)