Stathis Papaioannou wrote: > Bruno Marchal writes: > > > > Le 21-oct.-06, à 06:02, Stathis Papaioannou a écrit : > > > > > > > > > > > Bruno Marchal writes: > > > > > >>>> The UD is both massively parallel > > >>>> and massively sequential. Recall the UD generates all programs and > > >>>> executes them all together, but one step at a time. The "D" is for > > >>>> dovetailing which is a technic for emulating parallelism > > >>>> sequentially. > > >>> > > >>> Given that no actual physical hardware is needed to run it, why did > > >>> you choose the UD to generate all the computations rather than just > > >>> saying they are all run in parallel. There is enough room in Platonia > > >>> for infinite parallel virtual machines, isn't there? > > >> > > >> > > >> This is an interesting and key question. It is also a rather difficult > > >> one. To answer it we have to dig deeper on the importance and > > >> miraculous aspect of Church thesis, which makes existing a universal > > >> dovetailer, and which makes precise what a computational states is, > > >> and > > >> why we have to postulate Arithmetical Realism, and why we have to be > > >> cautious with any form of larger mathematical platonism (but such > > >> platonism is not prohibited per se). > > >> Now with comp, and Church thesis in particular, it can be shown that > > >> the computational states can be said to exist (in the same sense than > > >> numbers) and it can be defined thoroughly by the UD. If you introduced > > >> infinite machines (and I agree that it is defensible that some of such > > >> machine exists in Platonia) , either you will lose Church thesis, or > > >> you will lose the "YES DOCTOR", at least in the form I usually gave > > >> it. > > >> Your move here can be done, nevertheless, without changing the > > >> mathematical structure of the hypostases, but this asks for a non > > >> trivial generalization of comp, and of Church thesis in particular. I > > >> would not do that unless it is needed to get the physics (and then > > >> this > > >> would be a refutation of comp, or more precisely here: of Sigma_1 > > >> comp). > > > > > > The Chuch thesis concerns what can in theory be computed by a physical > > > computer with unlimited resources. > > > > > > Church thesis just assert that a universal turing machine can compute > > all computable functions from N to N. > > It relate a mathematical object with a human cognitive notion. It does > > not invoke physical machine at all. > > In a sense that is true, but a TM is still a model of what could possibly be > built > in a physical universe such as ours.

That may be true, but if it is , it is true because of the empirically-arrived-at laws of physics, not because of apriori reasoning of the CT. --~--~---------~--~----~------------~-------~--~----~ You received this message because you are subscribed to the Google Groups "Everything List" group. To post to this group, send email to everything-list@googlegroups.com To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/everything-list -~----------~----~----~----~------~----~------~--~---