weemba@sagi.wistar.upenn.edu (Matthew P. Wiener) says...
>>Anyway, while I agree that there is no evolutionary advantage to >>knowing about transfinite ordinals, it seems quite plausible that the >>kind of mental abilities that allow primitive people to successfully >>stalk game and avoid predators would also, as a side-effect allow >>those same people to think about sets and ordinals (when they find >>time for it). And I don't see how it makes a difference whether those >>mental abilities are coded as Turing machines or neural patterns. > >The side effect argument is no escape from Goedelian limitations.
Well, I still don't understand what Goedelian limitations has to do with anything. The way I see Goedel coming into your argument seems completely redundant: You want to show that the limit theory, C is no more powerful than the initial theory, A. It is sufficient to note that, by assumption, A already contains all physically relevant mathematics, and that therefore there is no evolutionary pressure for change. If you argue that C will be equal to A, then you don't Goedel to show that C is no more powerful than A.
>The master TM mind program cannot "voluntarily" code for things beyond what >the master TM mind program is incapable of generating.
I don't know what "the master TM mind program" refers to.
>A black monolith, or even a copy of Jech SET THEORY, is capable of >inserting large cardinal thoughts into a suitable >physical-mathematics-capable TM mind, whose own >consistency strength is no more than PRA. > >My claim is that evolution would most probably not do so, though, and >thus whatever our own general purpose reasoners upstairs consist of that >have successfully specialized to higher mathematics, it is not TMs.
Well, I don't see what either 0-1 laws *or* Goedel's theorems have to do with the conclusion that evolution would not lead to minds that are capable of doing set theory. And I also don't see how it matters whether or not our minds are TM minds. It seems to me that unless you assume that humans are a wildly unlikely freak occurrence, then it must be the case that our minds are the *simplest* minds that are capable of surviving and thriving in whatever primitive environment we evolved in. Although it is conceivable that there could be a mind that was capable of doing all physically relevant mathematics (and no more), it must be the case that such a mind would be *more* complicated to evolve than the ones we actually have. I think that's very plausible; it's often *easier* to implement a general-purpose tool than it is to implement many special-purpose tools.
