Le 03-sept.-06, à 12:17, Stathis Papaioannou a écrit :
> Sure, the computation is the same (although I find it much harder to > imagine the computation as a pure Platonic > object than I do numbers), but its expression and implementation are > infinitely variable. With CT you can see "all the computations" as the collection of the computational states get by the Universal Dovetailer. In term of the Fi, you can related "all the computations" with the set of the trace of length z of the computation of Fx on the input y, for all z, x, y positive integers. This is not obvious at all, and can be seen as a consequence of Church thesis. As I have shown or try to show this already entails incompleteness of theories. Note that a computation of Fx(y) = t can be seen as a proof that it exists a z such that z codes a proof of Fx(y) = t . It has the shape of "ExP(x,y)", that is a sigma1 sentence. So, with CT, "All the computational states" is captured by the set of all true sigma1 sentences, and their proof (finite or infinite) gives the finite computations: the DU-accessible states. Note the DU generates also the infinite proof (thanks to God) of the *wrong* sigma1 sentence which will determine in part the first person measure on all computations. I guess I am too technical ... Bruno http://iridia.ulb.ac.be/~marchal/ --~--~---------~--~----~------------~-------~--~----~ You received this message because you are subscribed to the Google Groups "Everything List" group. To post to this group, send email to [email protected] To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/everything-list -~----------~----~----~----~------~----~------~--~---
