Bruno Marchal wrote:

> 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,

Huh ? Physics studies matter, energy, time and space. Those
are its topics. Physics may not have a single neat definition of
matter, but
that does not mean physicsts are a lot to know what it is.
Arguably, the whole of economics is a definition of "money",
Likewise for physics and matter.

> and  I would say experimentally vague since the birth of experimental
> quantum philosophy (EPR, Bell, Shimoni, Feynman, Deutsch, Bennett ...).

Huh???? Electrons and photons are still matter...what *do* you mean ?

(BTW, Deutsch uses the Johnsonian "if it kicks back" appraoch
to reality).

> The big problem with the notion of *primary* matter =  how to relate
> "1-experiences" with "3-experiments".

The mind-body prolbem boild down to qualia, and
the problem of qualia and physics boils down to
the problem of qualia and mathematical description

Consciousness is a problem for all forms of materialism and physicalism
to some
extent, but it is possible to discern where the problem is particularly
There is no great problem with the idea that matter considered as a
bare substrate can
have mental properities. Any inability to have mental proeprties would
itslef be a property and
therefore be inconsistent with the bareness of a bare substrate. The
"subjectity" of
consciouss states, often treated as "inherent" boils down to a problem
of communicating
one's qualia -- how one feesl, how things seem. Thus it is not truly
inherent but
depends on the means of communication being used. Feelings and seemings
can be more readily
communicated in artistic, poetice language, and least readily in
scientifi technical
language. Since the harder, more technical a science is, the more
mathematical it is,
the communication problem is at its most acute in a purely mathematical
Thus the problem with physicalism is not its posit of matter (as a bare
but its other posit, that all properties are phycial. Since physics is
that amounts to the claim that all properties are mathematical (or at
least mathematically
describable). In making the transition from a physicalist world-view to
a mathematical
one, the concept of a material substrate is abandoned (although it was
never a problem
for consciousness) and the posit of mathematical properties becomes,
which is a problem
for consciousness becomes extreme.

> The naïve idea of attaching consciousness to physical activity leads to
> fatal difficulties.

Do you mean the Maudlin/Olympia/Movie argument ? But that is
very much phsyical activity as opposed to physical passivity.
If you are the kind of physicalist who thinks
counterfactuals and potentials are part of the total
physical situation, the Maudlin argument has little

> >> 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.

Of course. I start from the assumption
that I exist, since I do.

I don't start from the assumtion that numbers
exist supernaturally , floating around in Plato's

> > 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).

The question then is whether numbers have any role at all,
if they have no epistemological role.

> >> 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.

If that is all it means, it cannot possibly support an argument
whose conclusion is that something really exists.

The conclusion of a deductive argument has to be implicit in its

> >> 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?

It's true here, in the non-Platonic world.

We don't need the Platonic World to *make* it true. It fulfils
no epistemological role.

> >>> 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).

Of course, *standard* computationalism doesn't by itself allow
you to attach cognition/consciousness to anything abstract.

> 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.

I dare say *algorithms* can be defined Platonically.
Computations can be multiply replicated at different points
in space and time (or not at all) so they are not Platonic.

> 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.

Then nothing actually existing can possible "emerge".

> >> 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)".

Which still isn't helpful, since different
schools of mathematical philosophy put different
interpretations on the mathematical sense of "exists".

Some take it to mean "can be defined wtihout contraciction",
some "can be finitely constructed" and so on.

> 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.

The point remains that existence cannot emerge
out of truth.

> >> 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).
> Honestly why?

Logic. Something has to exist before it has any particular properties.

> I presuppose some amount of arithmetic.

Presume its existence or just its truth ?
Back to the usual ambiguity.

> 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*.

Then nothing can appear *from* it.

> > 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 that *does* entail existence ?

In any case, you do switch between epistemology (realism-qua-truth) and
 ontology (realism-qua-existence), as these quotes  from

BM: 'Arithmetical Realism (AR). This is the assumption that
arithmetical proposition, like
''1+1=2,'' or Goldbach conjecture, or the inexistence of a
bigger prime, or the statement
that some digital machine will stop, or any Boolean formula bearing on
numbers, are
true independently of me, you, humanity, the physical universe (if that
exists), etc. '

PJ: That's an epistemological claim then....

BM: 'It is
a version of Platonism limited at least to arithmetical truth'.

PJ: Is it ? But Platonism is an ontological thesis. As a standard
reference work has it: "The philosophy of Plato, or an
approach to philosophy resembling his. For  example, someone who
asserts that numbers exist  independently of the
things they number could be called a Platonist."

BM: 'It should not be confused
with the much stronger Pythagorean form of AR, AR+, which asserts that
only natural
numbers exist together with their nameable relations: all the rest
being derivative from
those relations.

If Pythagoreanism is stronger than Platonism in insisting that
everything is
derivable from (existing) natural numbers, is Platonism weaker than
in insisting that everything is derivable from existing numbers of all
natural or not? Is Platonism not being taken as a claim about existence
here, not just a claim about truth ?

BM: "A machine will be
said an Arithmetical Platonist if the machine believes enough
arithmetical truth (including some scheme of induction axiom)."

PJ: Switching back to an epistemological definition of "platonism"

BM:'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
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).'

PJ: Another use of Realism as a thesis about existence.

PJ: And if the pain-feeling "you" exists eternally, how do
ever *not* feel pain ? There is an ontological gulf
between tokens and types, between the temporal
and the eternal, which has been leaped over  at a bound here.

> And I don't believe that mathematical objects, or even *any* 3-object,
> are capable of having experiences (which by definition are *never*
> illusory).

In which case it is hard to see how your argument could work at all.

> Only subject or person can have experiences, and subject and persons
> emerges from infinities of (sigma_1) relation between numbers.

What can "emerge" from relationships between mathematical
structures except more mathematical structures ?

"And then a miracle occurs"

> The UD
> generates those relations and assigns some weight to all of them.

"Weight" of course being just another number -- not actual

> > 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":

It seems to me that materialism can survive the Maudlin/Olympia
with only a slight adjustment; phenomenal states supervene
on the total physical state, not just on the active physical state.

> 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.

You have a mathematical proof that phenomenality emerges from
mathematics ??? (And that's *phenomenality*, not uncertainty
or undecidability).

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