On 22 Sep, 15:10, Bruno Marchal <marc...@ulb.ac.be> wrote:
> On 22 Sep 2009, at 10:50, Flammarion wrote:
>
> > No he doesn't. His arguments have to assume Platonism as
> > well as CTM.
>
> CTM needs Church thesis (to define the C of CTM). This requires
> Arithmetical Realism, that is the belief that classical logic can be
> applied in the number realm. (and there is an intuitionist variant
> which works as well).
Classical logic doesn't give you an immaterial UD
> I make clear Arithmetical realism to avoid lengthy discussion with
> exotic philososophies of mathematics, like utltrafinitism, abusive
> formalism, etc.
A justification of the assimption that numbers exist immaterially
is just what is needed.
> I prefer to reserve Platonism for the deeper (neo)platonist idea that
> what we see and measure is the border, shadow or projection of
> something else. And that is part of the *consequences* of UDA1-8.
"Platonism" is often used just to mean that numbers exist
immaterially.,
e.g by Penrose.
> I have never met any defenders of CTM who is not an arithmetical
> realist, which is not so astonishing, given that the mere acquaintance
> with the idea of programming a computer, and reasoning on computers
> relies on this very usual and common notion, more or less taught in
> school.
If realism means bivalence, that is probably true. The
problem is using bivalence to smuggle in Platonism.
> Then the seven first step of UDA relies on CTM. Actually only the
> seventh requires Church Thesis.
>
> And it is at the eigth steps, the ancien preamble which can be read
> independently, which 'reminds us' that linking consciousness to
> physical activity (physical supervenience thesis) is just
> epistemologically incompatible with the CTM idea, unless you
> (re)define the physical as the border of the universal machine first
> person (plural) indeterminacies.
That CTM and phsycialism are incopatible is a philsophical
arguemnt, not a mathematical proof, and it has counter-arguments,
eg. Colin Klein's response to Maudlin's Olympia.
> This is mathematically definable, and its makes the comp theory
> testable. Comp is just a weaker and preciser version than Putnam
> functionalism. The existence of the level is itself a non constructive
> existence, which necessitates the realism.
>
> You did not answer my question: can you doubt about the existence of
> primary matter?
Yes. Can you doubt the actual existence of numbers?
> Would you be so astonished if the physicists themselves would resume
> the unification of forces by a relation among natural numbers?
>
> I could have use the combinators. I made a try on the list. No need to
> be sanguine on the positive integers. I could have use real numbers +
> a trigonometric function. To be realist about them consists in
> believing that their digital computations stop or does not stop
> independently of any consideration.
> You introduce confusion by using the term "Platonism" here. I know
> that mathematicians use sometimes Platonism in that sense (of
> accepting classical logic, and the truth of mathematical statements,
> including the non constructive one), but in the present context it
> hides the main facts which is that MGA makes it necessary to redefine
> the notion of matter. Observable Matter becomes an invariant for a
> digital notion of universal machine's observation.
>
> After the seventh thread, we will come back on the eight step. I
> suggest you follow that, and tell us where you object.
>
> You have said nothing about the seventh first steps, which does not
> invoke the materiality issue. Any problem there?
"Instead of linking [the pain I feel] at space-time (x,t) to [a
machine state] at space-time (x,t), we are obliged to associate [the
pain I feel at space-time (x,t)] to a type or a sheaf of computations
(existing forever in the arithmetical Platonia which is accepted as
existing independently of our selves with arithmetical realism). "
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