Le 11-juil.-06, 21:06, 1Z a crit :
> 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 ?!?!?!.
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. 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).
> 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
> ABSTRACT OBJECTS
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).
> 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 ...
I don't understand what you mean by "numbers don't exist at all".
Numbers exists in Platonia in the sense that the classical proposition
"4356667654090987890111 is prime or 4356667654090987890111 is not
prime" is true there.
> they they cannot even produce the mere appearance of a physical world,
> as Bruno requires.
Why? 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.
And I do provide evidence that "rational unitary transform" could be
the mathematical computations winning the measure-battle in Platonia.
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), 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".
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.
> 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. In my Brussel's
thesis "conscience et mcanisme" 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).
> 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. 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).
> Comp is about the behaviour of the brain as a material system.
This is the naturalist preconception of comp. 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. (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:
http://iridia.ulb.ac.be/~marchal/publications/
SANE2004MARCHALAbstract.html
(I recall having already given to you this reference).
Bruno
http://iridia.ulb.ac.be/~marchal/
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