Bruno Marchal wrote:
> Le 11-juil.-06, ˆ 21:06, 1Z a Žcrit :
> > And mathematical MWI *would* be in the same happy position *if*
> > it could find a justification for MWI or classical measure.
> See my work and this list for some path toward it.
> > To have material existence is to have non-zero measure,
> > and vice-versa.
> So, in the space {0,1}* (that is: the space of functions from N to
> {0,1}, or the space of infinite sequence of "0" and "1") together with
> some reasonable topology)  the set of random sequences, just because it
> has non-zero measure, has a material existence ?!?!?!.

I mean that is what material exists regardless of any mathematical

> Well, why not, if that is your definition. I understand better why you
> say you could introduce "matter" in Platonia. Plato would have disagree
> in the sense that "matter" is the shadow of the ideal intelligible
> reality.

What is material exists. Whether Platonia exists
is another matter. It is for Platonism to justify itslef
in terms of the concrete reality we find oursleves in,
not for concrete reality to be justify itself in terms
of Platonia.

>  Note the "intelligible", which will be developped by Plotinus
> (notably), taking then "ontology" in "my" sense (or Jesse one, or as I
> and Jesse are suspecting: the common current one).

The "intelligible" is a quasi-empiricist mathematical epistemology.
Mathematicians are supposed by Platonists to be able to "perceive"
truth with some extra organ.

> > Platonists about mathematical objects claim that the theorems of our
> > mathematical theories - sentences like '3 is prime' (a theorem of
> > arithmetic) and 'There are infinitely many transfinite cardinal
> > numbers' (a theorem of set theory) - are literally true and that
> > the only plausible view of such sentences is that they are ABOUT
> I agree, (although in some context it helps to consider mathematical
> objects like numbers and strings, turing machine's computation as
> concrete, to better appreciate the non concreteness of "variables and
> functions", but this should not be relevant here).

What are you agreeing with? That Platoism is an ontological
claim ?

> > Some do. In any case, if numbers don't exist at all -- even
> > platonically --
> I am just saying that the truth value of the sentence "there is a prime
> number" does not depend on me ...

Then your AR is non-ontological, and does
not justify the claim that we are in Platonia,
since it doesn't justify the claim that Platonia exists.

> I don't understand what you mean by "numbers don't exist at all".

Well, I've never seen one.

> Numbers exists in Platonia in the sense that the classical proposition
> "4356667654090987890111 is prime or 4356667654090987890111 is not
> prime" is true there.

It's true here. why bring Platonia into it ?

> > they they cannot even produce the mere appearance of a physical world,
> > as Bruno requires.
> Why?

What doesn't exist at all cannot underpin the existence of anything --
even of an illusion.

> With Church thesis all computations, as defined in computer
> science (not in physics), exists in Platonia, exactly in the same sense
> that for the prime numbers above.

That is a most unhelpful remark. All you said above is
that true mathematical sentences have truth-values
independent of you. You have now started treating
that as a claim about existence. It is as if
your are using "is true" and "exists" as synonyms.

> And I do provide evidence that "rational unitary transform" could be
> the mathematical computations winning the measure-battle in Platonia.

Huh???? How can you have a battle without time ?

> This would explain not only the existence of computations with
> self-aware observers, but also they relative stability.@
> But MUCH more can be said, from Solovay theorem (justifying the modal
> logics G and G* for the provable and non provable by a machine/entity
> self-referential truth) I get not only an arithmetical quantization
> justifying the quanta, I get a larger theory divided into sharable and
> non sharable measurement results. This means I get one mathematical
> structure explaining not only the appearance of a physical world (the
> quanta),

You have to explain how a mathematical structure can appear
at all, before you can explain how it can appear quantal (or whatever).

> but explaining why such quanta are accompanied by non
> communicable personal truth (like the qualia experienced by the
> physicist at the moment where he look at the needle of his/her
> measuring apparatus). In *that* precise sense, the comp-physics is in
> advance on the "materialist hypo based physics".

Materialism does not imply everything should be communicable.

> Now when you say in another post:
> > I cant address your anti-materialism arguments directly since
> > you idn't state them, only alluding to them.
> I think you have a memory problem. See my URL for my papers. Search in
> Science-direct Elsevier for my last one.

That's an allusion, too.

> > Insamuch as you claim that COMP is your only
> > assumption, CT and AR are *not* assumed explicitly.
> I defined in this list comp by "yes doctor"+ CT + AR.

So it is 3 assumptions bundled into one?

>In my Brussel's
> thesis  "conscience et mŽcanisme" I call it digital mechanism. CT is
> explicitly assumed for giving a univocal sense to the words
> computations or digital machine, and AR is made explicit for clarity.
> That comp entails immateriality (in the sense that the observable must
> be justified by computer science exclusively) is just a result (not
> obvious at all).

I'll say. Every computer I have seen has been material.

> > Brains are material. Computers are material.
> Ah. If you say so. Perhaps you are right,  but then they are actual
> material realities, not emulable at all by any turing machine.

I didn't say that. I am not (remotely) defining
materiality in terms of emulability.

>  It is up
> to you to find the mistake in the UDA, if you still believe that comp
> does not entail the reversal between physics and number theory (large
> sense like in the book of Manin on Number Theory).

The problem is the slide from

"mathematical statements are objectivley true"
"mathematical objects exist Platonically"
"mathematical objects are capable of having experiences (however

> > Comp is about the behaviour of the brain as a material system.
> This is the naturalist preconception of comp.

It is "computationalism" as understood in philosophy and cognitive
science, yes.

> If you want it is comp
> before I get the proof that comp entails immateriality. But perhaps you
> agree now, giving that you gave us an immaerial definition of matter:
> measure ­ 0

Huh ?

> . (But elsewhere you gave another: casually capable of
> interacting with you: so I am not sure).
> >> Why should I prove my assumptions?
> >
> > You could at least state them.
> I do it in all paper on this subject, and I have done it at nauseam in
> this list. It is computationalism: the doctrine according to which
> there is a level of substitution such that I survive a digital graft
> made correctly at that level. (+ CT + AR for giving univocal sense to
> word like "number" and (discrete) computation").  Just go there:
> SANE2004MARCHALAbstract.html

> (I recall having already given to you this reference).
> Bruno

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