Bruno Marchal writes:

> >> 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. Of course the model is still 
> > valid irrespective
> > of the existence of a physical machine or indeed a physical universe, 
> > but if you
> > abandon the idea of a physical universe there is no need to constrain 
> > yourself to
> > models based on one.
> I am not sure why you say the TM model is based on what we can build in 
> the physical universe.
> Both with comp and without, the physical universe is a priori far 
> richer than a UTM.
> The UTM of Turing relies explicitly on an analysis of human capacity 
> for computations.
> Post universal systems are based on analysis of mathematician 
> psychology.

The word "machine" implies something that can be physically built, even though 
that definition is stretched a bit when we talk about idealised machines. 
compass and ruler proofs are based on what can be done with a physical compass 
and ruler, even though they are still valid if all the compasses and rulers are 
in a big fire, and even though they strictly rely on idealised lines and 
points. If there is 
no physical universe, then there is no basis for favouring one mathematical 
model (of 
geometry, of computation) over all the other theoretically possible ones, 
except that
it *seems* we are living in such a universe. If we go beyond the apparent to 
true reality 
why not say that the requisite computations are "just there" rather than 
invoking a TM?

> > So I suppose the two questions I have (which you partly
> > answer below) are, having arrived at step 8 of the UDA could you go 
> > back and
> > say that the UD is not really necessary but all the required 
> > computations exist
> > eternally without any generating mechanism or program (after all, you 
> > make this
> > assumption for the UD itself), or alternatively, could you have 
> > started with step
> > 8 and eliminate the need for the UD in the argument at all?
> This is the way I proceed in "Conscience and Mechanism". I begin, by 
> using the movie graph argument MGA,  to show that consciousness cannot 
> be attached to physical activities, and then I use the UD to explain 
> that the comp-physics get the form of a measure on all computations.
> In my Lille thesis I do the opposite because the UDA is simpler than 
> the MGA. It is not so important.
> UD is needed to justify and to make mathematically precise the ontic 
> 3-observer moments. They correspond to its (the UD) accessible states.

But any other mathematical model of computation, even if impossible in the real 
such as infinite parallel computers, would do just as well?

> >>> It seems that this is the computer you
> >>> have in mind to run the UD.
> >>
> >> Only for providing a decor for a story. This assumption is eliminated
> >> when we arrive (step eight of UDA-8) at the conclusion that universal
> >> digital machine cannot distinguish any "reality" from an arithmetical
> >> one.
> >>
> >>
> >>> That's OK and the argument works (assuming
> >>> comp etc.), but in Platonia you have access to hypercomputers of the
> >>> best
> >>> and fastest kind.
> >>
> >> Fastness is relative in Platonia. Universal machine can always been
> >> sped up on almost all their inputs (There is a theorem by Blum and
> >> Marquez to that effect). Then indeed there are the "angels" and
> >> hierachies of "non-comp" machine. A vast category of "angels" can be
> >> shown to have the same hypostases (so we cannot tested by empirical
> >> means if we are such angels). Then they are entities very closed to 
> >> the
> >> "one", having stronger hypostases, i.e. you need to add axioms to G 
> >> and
> >> G* (or V, V* with explicit comp) to get them.
> >
> > Of course I was joking when I said "best and fastest". In Platonia 
> > there is
> > no actual time and everything is as fast and as perfect as you want it.
> OK. But of course there exist notion of relative time: a fast Fourier 
> transform is faster than a slow Fourier transform, even in Platonia. Of 
> course this can be said in term of number of steps in computations (no 
> need to invoke time).

OK, I understand that point.

Stathis Papaioannou
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