firstname.lastname@example.org (Matthew P. Wiener) says...
>> The fact that we can nevertheless >>reason with larger cardinals might show that something strange happened >>in our evolution, but that's a side issue. > >No, it's not a side issue. It's the central issue: my claim is that this >"something strange" is a probability 0 event for TM minds formed by evolution >in a world with no physical correlates
Where do you get that conclusion? Why do you believe that there is a 0-1 law involved?
>I claim that we are more complicated than an evolved real world TM mind >could ever be with probability 1, no more, no less.
Again, why do you think the probability must be either 0 or 1? Assuming that it is possible for DNA to encode a TM mind, surely a TM mind that is capable of reasoning about ZFC is a finite number of mutations away from a TM mind that is capable of reasoning about Peano arithmetic. Therefore, even if we assume that there is *no* advantage to having a smarter mind, there is a nonzero probability of it developing anyway. Perhaps eventually a nonadvantageous mutation would disappear, but the Earth has only been around for a few billion years. The probability is definitely nonzero that the right combination of mutations could appear and persist for 4 billion years.