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.


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