Le 25-mai-06, à 09:04, Kim Jones a écrit :
> what would an "unreasonable machine" be like? You seem to be implying > they exist, also that they can prove things about their possible > neighborhoods and or histories. (?) They are degrees. The worst "unreasonableness" of a (platonist or classical or even intuitionist) machine is when she believes some plain falsity (like p & ~p, or 0 = 1). The false implies all propositions, so that such machine believes everything, including everything about their maximal consistent extensions or histories (which does not exist). Those machines are just inconsistent. Then you have machines which, although they are consistent, are not self-referentially correct. They are unsound, and does also believe some falsity, but here the falsity is irrefutable. Like consistent machine asserting they are inconsistent, or, curiously enough (it is a consequence of the second incompleteness theorem), consistent machine asserting they are consistent. Although it is true that they are consistent they cannot assert it without becoming either inconsistent, or, if they assert it in some special cautious way, they become different machine (and in that case they remain consistent and also get some new provability power). But again here we anticipate. I hope I will make clear that with Church thesis the notion of computability will appear as absolute and universal, and then we will see that the notion of provability is relative and never universal, although some universal pattern can appear there too (like the logic G and G*, etc.). I guess we will come back on this, but we have to do a transfinite ascension before :) 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 -~----------~----~----~----~------~----~------~--~---
