On Jan 27, 5:55 am, Bruno Marchal <marc...@ulb.ac.be> wrote:
> On 26 Jan 2012, at 07:19, Pierz wrote:
> > As I continue to ponder the UDA, I keep coming back to a niggling
> > doubt that an arithmetical ontology can ever really give a
> > satisfactory explanation of qualia.
> Of course the comp warning here is a bit "diabolical". Comp predicts
> that consciousness and qualia can't satisfy completely the self-
> observing machine. More below.
> > It seems to me that imputing
> > qualia to calculations (indeed consciousness at all, thought that may
> > be the same thing) adds something that is not given by, or derivable
> > from, any mathematical axiom. Surely this is illegitimate from a
> > mathematical point of view. Every  mathematical statement can only be
> > made in terms of numbers and operators, so to talk about *qualities*
> > arising out of numbers is not mathematics so much as numerology or
> > qabbala.
> No, it is modal logic,

A nice term for speculation! Mind you, that's OK. Where would we be
without speculation? But the term 'modal logic' might be used for
numerology too - it *might* be the case that a 4 in one's birthdate
does signify a practical soul.

>although model theory does that too. It is
> basically the *magic* of computer science.

Magic, but not numerology then.

> relatively to a universal
> number, a number can denote infinite things,

I think you're saying that a number can be part of an infinite number
of sets, calculations etc, which is true, but what it denotes is
always purely a matter of logical numerical relationships, unless it
denotes something beyond mathematics itself, such as when I count
oranges. I am saying that to denote qualia, the numbers must be
denoting 'oranges' (or maybe the colour orange as an experience),
things outside of pure logic, not mathematical entities.

> like the program
> factorial denotes the set {(0,0),(1,1),(2,2),(3,6),(4,24),(5,120), ...}.
> Nobody can define consciousness and qualia, but many can agree on
> statements about them, and in that way we can even communicate or
> study what machine can say about any predicate verifying those
> properties.

> > Here of course is where people start to invoke the wonderfully protean
> > notion of ‘emergent properties’. Perhaps qualia emerge when a
> > calculation becomes deep enough.Perhaps consciousness emerges from a
> > complicated enough arrangement of neurons.
> Consciousness, as bet in a reality emerges as theorems in arithmetic.

Sorry, I cannot parse that sentence. It doesn't seem grammatical.

> They emerge like the prime numbers emerges.

'They'? The theorems? You mean consciousness is a bet on an
arithmetical theorem?

>They follow logically,
> from any non logical axioms defining a universal machine. UDA
> justifies why it has to so, and AUDA shows how to make this
> verifiable, with the definitions of knowledge on which most people
> already agree.
> > But I’ll venture an axiom
> > of my own here: no properties can emerge from a complex system that
> > are not present in primitive form in the parts of that system.
> I agree with that in the logical sense. that is why I don't need more
> than arithmetic for the universal realm.
> > There
> > is nothing mystical about emergent properties. When the emergent
> > property of ‘pumping blood’ arises out of collections of heart cells,
> > that property is a logical extension of the properties of the parts -
> > physical properties such as elasticity, electrical conductivity,
> > volume and so on that belong to the individual cells. But nobody
> > invoking ‘emergent properties’ to explain consciousness in the brain
> > has yet explained how consciousness arises as a natural extension of
> > the known properties of brain cells  - or indeed of matter at all.
> Because the notion of matter prevent the progress. What arithmetic
> explains is why universal numbers can develop a many-dream-world
> interpretation of arithmetic justifying their local predictive
> theories. Then for consciousness, we can explain why the predictive
> theories can't address the question, for consciousness is related to
> the big picture behind the observable surface. Numbers too find truth
> that they can't relate to any numbers, or numbers relations.
> > In the same way, I can’t see how qualia can emerge from arithmetic,
> > unless the rudiments of qualia are present in the natural numbers or
> > the operations of addition and mutiplication.
> Rudiment of qualia would explains qualia away. They are intrinsically
> more complex. A qualia needs two universal numbers (the hero and the
> local environment(s) which executes the hero

Once executed, he's not a hero any more, he's a martyr :)

> (in the computer science
> sense,

oh, right ;)

> or in the UD). It needs the "hero" to refers automatically to
> high level representation of itself and the environment, etc. Then the
> qualia will be defined (and shown to exist) as truth felt as directly
> available, and locally invariants, yet non communicable, and applying
> to a person without description (the 1-person). "Feeling" being
> something like "known as true in all my locally directly accessible
> environments".
> > And yet it seems to me
> > they can’t be, because the only properties that belong to arithmetic
> > are those leant to them by the axioms that define them.
> Not at all. Arithmetical truth is far bigger than anything you can
> derive from any (effective) theory. Theories are not PI_1 complete,
> Arithmetical truth is PI_n complete for each n. It is very big.

I do appreciate Gödel's theorem and its proof that there are true,
unprovable statements within any given arithmetic, so you are correct.
But my error is one of technical terminology I think. Surely there are
statements that can be made within a certain arithmetic and others
that can't. For instance, within Peano arithmetic it does not make
sense to ask about the truth value of statements involving i (the
imaginary number). Then there are limits to what can be called a
mathematical statement - ie one involving the truth and falsity of
purely logical relations. So I can't, in any arithmetic or system of
mathematics, ask if the number 20 is nice or not. Or if the prime
numbers are pink or blue. Arithmetical truth may be as vast as you
like, but my point is that it is still *arithmetical*, and qualities
don't come into it. It is the set of sentences that can be made about
numbers and those sentences are limited in their symbols. So Gödel
doesn't help you here I don't think.

> > Indeed
> > arithmetic *is* exactly those axioms and nothing more.
> Gödel's incompleteness theorem refutes this.
> > Matter may in
> > principle contain untold, undiscovered mysterious properties which I
> > suppose might include the rudiments of consciousness. Yet mathematics
> > is only what it is defined to be. Certainly it contains many mysteries
> > emergent properties, but all these properties arise logically from its
> > axioms and thus cannot include qualia.
> It is here that you are wrong. Even if we limit ourselves to
> arithmetical truth, it extends terribly what machines can justify.

Terribly perhaps, but still not beyond the arithmetical, by

> > I call the idea that it can numerology because numerology also
> > ascribes qualities to numbers. A ‘2’ in one’s birthdate indicates
> > creativity (or something), a ‘4’ material ambition and so on. Because
> > the emergent properties of numbers can indeed be deeply amazing and
> > wonderful - Mandelbrot sets and so on - there is a natural human
> > tendency to mystify them, to project properties of the imagination
> > into them.
> No. Some bet on mechanism to justify the non sensicalness of the
> notion of zombie, or the hope that he or his children might travel on
> mars in 4 minutes, or just empirically by the absence of relevant non
> Turing-emulability of biological phenomenon.
> Unlike putting consciousness in matter (an unknown into an unknown),
> comp explains consciousness with intuitively related concept, like
> self-reference, non definability theorem, perceptible incompleteness,
> etc.
> And if you look at the Mandelbrot set, a little bit everywhere, you
> can hardly miss the unreasonable resemblances with nature, from
> lightening to embryogenesis given evidence that its rational part
> might be a compact universal dovetailer, or creative set (in Post
> sense).

Well I certainly don't dispute the central significance mathematics
must play in any complete scientific or philosophical world view. I
suppose the question is whether that mathematics is ontologically
primary or not.
> > But if these qualities really do inhere in numbers and are
> > not put there purely by our projection, then numbers must be more than
> > their definitions. We must posit the numbers as something that
> > projects out of a supraordinate reality that is not purely
> > mathematical - ie, not merely composed of the axioms that define an
> > arithmetic.
> Like arithmetical truth. I think acw explained already.

Are you saying arithmetical truth is not purely mathematical?

> > This then can no longer be described as a mathematical
> > ontology, but rather a kind of numerical mysticism.
> It is what you get in the case where brain are natural machines.
> > And because
> > something extrinsic to the axioms has been added, it opens the way for
> > all kinds of other unicorns and fairies that can never be proved from
> > the maths alone. This is unprovability not of the mathematical
> > variety, but more of the variety that cries out for Mr Occam’s shaving
> > apparatus.
> No government can prevent numbers from dreaming. Although they might
> try <sigh>.
> You can't apply Occam on dreams.
> They exist epistemologically once you have enough finite things.

Well, I'm not trying to prevent anyone from dreaming! I'm arguing
whether or not maths can include dreams.

> Feel free to suggest a non-comp theory. Note that even just the
> showing of *one* such theory is everything but easy. Somehow you have
> to study computability, and UDA, to construct a non Turing emulable
> entity, whose experience is not recoverable in any first person sense.
> Better to test comp on nature, so as to have a chance at least to get
> an evidence against comp, or against the classical theory of knowledge.

Hehe. I suppose you have some idea that I can't do that! As noted in
 prior post in this thread, these are my attempts to understand, as
completely as I can, this interesting philosophy. I admit I like your
theory better than materialism. I am trying to discover if I like it
enough ('like' in the sense that it satisfies my intellectual
intuition and my logic sufficiently) to entertain it seriously over my
current admission of nearly total ignorance as to what the world 'is'.
I don't need to posit an alternative to make that enquiry, and to do
so by questioning whatever in the theory seems weak (even if it proves
in the end to be my understanding that is the weakness).
> Bruno
> http://iridia.ulb.ac.be/~marchal/

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