Le 12-juil.-06, à 18:06, 1Z a écrit :
>
> I mean that is what material exists regardless of any mathematical
> justification.
So this is your main hypothesis: what is material exist.
Now my problem is that a term like "material" is very vague in physics,
and I would say experimentally vague since the birth of experimental
quantum philosophy (EPR, Bell, Shimoni, Feynman, Deutsch, Bennett ...).
The big problem with the notion of *primary* matter = how to relate
"1-experiences" with "3-experiments".
The naïve idea of attaching consciousness to physical activity leads to
fatal difficulties.
>
>> 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.
It depends of the assumptions you start from.
> The "intelligible" is a quasi-empiricist mathematical epistemology.
> Mathematicians are supposed by Platonists to be able to "perceive"
> mathematical
> truth with some extra organ.
That is naïve platonism. Already condemned by Plato himself and most of
his followers. Read Plotinus for more on this (especially Ennead V).
>
>> I don't understand what you mean by "numbers don't exist at all".
>
> Well, I've never seen one.
Again that would be a critics of naïve Platonism. As I have said:
"number n exists in Platonia" means just that the proposition "number n
exists" is true. For example I believe that the equation
x^2 - 61y^2 = 1 admits integers solutions independently of any things
related to me.
>
>> 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 ?
I don't understand what you mean by "4356667654090987890111 is prime or
not" is true here.
Is it false or meaningless on the moon?
is it false or meaningless beyond the solar system?
is it false or meaningless beyond the Milky Way?
>
>>> 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.
I do agree with you. But, once we assume comp, we can attach
consciousness to sheaf of computational histories (abstract
computations which can be defined precisely from the Fi and the Wi:
more in the diagonalization posts).
Those computations are entirely defined by infinite sets of true
relations among numbers. You could perhaps wait I define the "Kleene
predicate" in the diagonalization posts. or read the beautiful work of
Matiazevitch on the diophantine equations. A set of numbers is RE, i.e.
is a Wi set, if and only if it is given by the zero of a diophantine
polynomial.
In *all* situation, when I say a number exists, or when I say a
sequence of numbers exists, I only mean that the proposition expressing
that existence is true independently of me or you.
>
>> 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.
You did not read carefully what I have said. I am just using "exists"
as a quantifier (in first or second order logic). Exists n P(n) = truth
of "exists n P(n)".
I believe that there is an infinity of twin primes ... or not,
independently of the fact that mathematicians on this planet or
elsewhere will solve, or not, that (currently open) problem.
>
>> 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 ?
By using varieties of theoretical computer science notion of
convergence. If you want, I am using the integers themselves for
measuring complexity of computations. The UDA shows that if you are in
the comp state S, then your "consistent extensions" are defined by a
measure on all computations going through that state S. It is a static
well defined mathematical set. A type of computation wins the
measure-battle if it has a reasonable measure.
>
>> This would explain not only the existence of computations with
>> self-aware observers, but also they relative stability.-AT_SYMBOL-
>> 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).
Honestly why? I presuppose some amount of arithmetic. As an
arithmetical platonist I suppose those existential proposition are
true. Comma. I don't believe math truth are related to time or space.
The number 2, or any math structure, does not *appear*.
> The problem is the slide from
>
> "mathematical statements are objectivley true"
> to
> "mathematical objects exist Platonically"
> to
> "mathematical objects are capable of having experiences (however
> illusory)"/
OK. I hope that what I say above has solved that problem. I recall
again. Note that I don't even pretend that mathematical statements are
objectively true (I am quite neutral about this). I say only this:
Arithmetical statements are objectively true.
I have never slipped into:
mathematical objects (numbers) exist Platonically" EXCEPT in the sense
that some existential arithmetical proposition is objectively true.
And I don't believe that mathematical objects, or even *any* 3-object,
are capable of having experiences (which by definition are *never*
illusory).
Only subject or person can have experiences, and subject and persons
emerges from infinities of (sigma_1) relation between numbers. The UD
generates those relations and assigns some weight to all of them.
> It is "computationalism" as understood in philosophy and cognitive
> science, yes.
I am using computationalism in the standard sense, except that I make
it more precise than usual, given that I extract counter-intuitive (for
Aristotelians) results from it.
I just show that comp, even taken at first with his materialist
background assumption, leads to the falsity of "weak materialism": the
idea that there is something genuinely stuffy at the origin of the
computations. Comp entails that the appearance of that genuine stuff
emerges from the independent truth of some formula in arithmetic. I
could even put them in polynomial form.
Bruno
http://iridia.ulb.ac.be/~marchal/
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Received on Fri Jul 14 2006 - 06:23:19 PDT