In article <5mphjj$tmv$1@news.fas.harvard.edu>, kubo@abel (Tal Kubo) writes: >Matthew P Wiener <weemba@sagi.wistar.upenn.edu> wrote:
>>>>The original theory can thus talk about the theory that >>>>consists of the evolved probability 1 statements. >>>>These are consistent and definable in the original TM-mind. >>Define them collectively as the probability 1 sentences in the omega limit.
>Tarski's theorem says this is impossible. A theory can't define >it's own true sentences in any particular model,
Right! That's what I'm doing.
> such as the one >that a hypothetical 0-1 law would produce under some given evolution.
As I said in long hand before, one gets (in a uniform way) the consistency of any finite fragment of the starting theory. If your prefer the Tarskian contradiction instead, be my guest.
>>>>So by the Goedel theorem, it's just the original system!
>>Not _the_ Goedel's theorem, correct, but the obvious variants.
>Ah, the OBVIOUS variants. That's reassuring.
Well, you came up with one yourself, above.
>Let's assume, although we've established that both are impossible,
Dream on.
>that (a) there's a 0-1 law, and (b) the "omega limit" is definable in >the original. What is the OBVIOUS variant of Goedel's theorem that >applies, and how does it show that "it's just the original system"?
In the finite models I was talking about, it refers to lengths of proofs. I believe I have mentioned this before. -- -Matthew P Wiener (weemba@sagi.wistar.upenn.edu)
