David,

First of all, as I have already said, you seem to be well aware of the hardest part of the hard problem of consciousness. And this gives me the opportunity to try to explain what you are missing. Indeed, in this post, I will try to explain how comp does solve completely the conceptual hard problem of consciousness. (With the usual price that physics becomes a branch of machine's theology).



On 22 Feb 2010, at 15:00, David Nyman wrote:

On 22 February 2010 07:37, Bruno Marchal <marc...@ulb.ac.be> wrote:

What do you mean by "implicit" here? What is implicit is that the
subjectivity (1-p), to make sense, has to be referentially correct
relatively to the most probable histories/consistent extensions.

What I mean by implicit is "already accounted for", at least according
to the assumptions of the closed 3-p hypothesis, which of course is
what I'm questioning.

Then the incommunicable and private aspect of those knowledge and qualia is provided by the theory of knowledge and the quale logic, provided by the respective intensional variant of G and G*. The difference between G and G*
(provable and true) is reflected in those intensional variant.

Yes, but G and G*, and indeed all formally expressible logics, are
themselves closed 3-p (i.e. objective) notions - i.e. they would exist
and possess the same explanatory power in the absence of any
accompanying *qualitative* component.


I am not sure what you mean exactly by closed 3-p or even objective. But it is OK (I see it is a minor question of vocabulary).

G and G* are formal modal logics, and it happens that they describe completely (at some level) the self-referential discourse of ideally self-referentially correct machines.

We have no interest in those formal theories per se, if it were not for their semantics, including their interpretations in arithmetic, and their intensional variants.
I come back on this below.





 This is just another way of
gesturing towards the Really Hard Problem - that the qualitative
component, per se, is seemingly redundant to the account if we assume
we already have a closed, or sufficient, non-qualitative explanation.
Consequently these logics AFAICS lead to the same paradoxical
conclusions as the closed 3-p physical hypothesis - i.e. that the
references to qualitative experiences - even those references we
ourselves produce - would occur even in the absence of any such
experiences.  This would leave us in the position of doubting the
basis even of our own statements that we are conscious!


And this would be very paradoxical indeed. But you are wrong in saying that those logics lead to those paradoxes. Probably because you are wrong in saying that those logics are "closed". Those logic are tools or systems talking about *something*, provably in some correct sense. More below. I prefer to read first your whole post, so that I can avoid confusing repetitions.




I want to seriously discuss the proposition that certain behaviours
are actually contingent on qualitative experience, as distinguished
from any accompanying 3-p phenomena.  That is, for example, that my
withdrawing my hand from the fire because it hurts indispensably
requires the qualitative *experience* of pain to mediate between 1-p
and 3-p narratives.  This would of course mean in turn that the
explanatory arc from stimulus, through cognitive processing, to
response would be, without the qualitative component, in some way
demonstrably incomplete as an explanation.


Indeed. May be it would help to remember that with comp, we already know that the physical world is a 1-p construct; It is not 3-p (as amazing as this could seem for a materialist). The only 3-p is given by arithmetic/logic/computer science.




 ISTM that this would make
it impossible to ignore the implication that the context in which we
conceive 3-p processes to be situated (whether we are talking in terms
of their physical or mathematical-logical expression) would itself be
capable of taking on "personal" characteristics in apparent
interaction with such processes.

Something related to this, ISTM, is already implied in the background
to 1-p indeterminacy, observer moments, the "solipsism of the One"
etc, because all these notions implicitly contain the idea of some
general context capable of embodying and individuating "personal"
qualitative experience - given relevant 3-p-describable structure and
function.  But in order for that personhood not to be vacuous - i.e.
redundant to the supposedly primary 3-p narrative - such personal
qualitative states must be conceived as having consequences, otherwise
inexplicable, in the 3-p domain, and not merely vice-versa.  How to
incorporate such consequences in the overall account is indeed a
puzzle.


A puzzle? No more ... (see below).




Not only can't we prove it, but we couldn't, from a 3-p pov, even
predict or in any way characterise such 1-p notions, if we didn't know from a 1-p perspective that they exist (or seem to know that they seem
to exist).

This is not true I think. Already with the uda duplication experience, you can see predict the difference, for example, the apparition of first person
indeterminacy despite the determinacy in the 3d description. This is
captured by the difference between (Bp and p) and Bp, and that difference is
a consequence of incompleteness, when self-observing occurs.

I don't deny what you're saying per se, but I'm commenting on this
because it brings out, I hope, the distinction between purely formal
descriptions of 1-p notions, and actual first-personal acquaintance
with qualitative experience.

I think you are confusing a theory or a machine discourse WITH the subject matter of the theory, or the object of discourse of the machine. In that sense formal theory (sufficiently rich to talk on numbers) are already NEVER closed in your sense. Arithmetical TRUTH, which plays a key role here is NOT a formal object. Indeed it is a provably non formalizable object.



 It's the latter that I'm claiming is
non-computable from any formal premise

You are entirely right here. Both "I", and the Löbian machine agree with you.



(which, as I think we'd both
agree, is the essence of the HP).

OK. In which case you will see how that problem is solved.



It's one thing to say that
"self-observing occurs", and quite another to actually experience
self-observing.  But beyond this, ISTM that we must also believe that
the *experience* of self-observing entails consequences that the mere
*description* of "self-observing" would not, to avoid the paradoxes
contingent on the idea that qualitative experiences are somehow
redundant or merely "epiphenomenal".


OK.




One of the
places it leads (which ISTM some are anxious not to acknowledge)) is
the kind of brute paradox I've referred to. So what I'm asking you is how is this different from a comp perspective? Can our 3-p references
to 1-p phenomena escape paradox in the comp analysis?

Yes, because we do accept the truth of elementary arithmetic. We can study the theology of simple (and thus *intuitively* correct) Löbian machine. We *know* in that setting that the machine will be aware of an explanation gap,
etc.
Again, the price is that we have to recover physics without introducing a
3-p physical world.

I see that it is already important that comp predicts the *existence*
of an explanatory gap.

It is a part of the solution. But not the entire solution indeed.



 But what does it say about how that gap is to
be bridged:

Le me anticipate. It says that the gap cannot be bridged in any experiential way. No more than you can bridge the gap between any axiomatic theory on numbers, and the informal arithmetical truth.




i.e. about the relevance of the *experience* - as distinct
from the bare description - of the 1-p notions, to the unfolding of
the integrated 1-p + 3-p narrative?


Actually the *experiences* are so much relevant that without them, the physical world would not even exist. Of course I am NOT talking of the human experiences, but really on all the experiences of all Löbian machines.





Do you
believe that such a "closed" explanation is fundamentally unable to
account seriously for consciousness for the reasons I've cited?  Is
there any way to "re-open" it outside of comp?

Not in a way which is not already provided by comp. But unless you weaken comp so much as becoming "God", weakening comp does not provide different
clue for solving the consciousness/reality problem.
You may try, but 1500 years of materialism seems to lead only to person eliminativism. Where comp and its weakening reintroduce automatically a
knower, a feeler, a better, etc.

Can you say anything about the way in which the knower/feeler/better's
actual *experiences* (as distinct from their bare description) make a
difference to the unfolding of histories in the comp hypothesis?

Yes. The histories emerge from those experiences, and none are formal object. They are not generated by the UD, only filtered by persons. But like 'meaning' we can approximate them by infinite formal structures. Infinite structures may look locally syntactical, but they are not. Infinity is before all things a quale itself. No finite formal things can describe them. But we can have some informal intuition.


Can
it be shown that qualitative experience is per se indispensable to
giving an adequate account of persons and their histories, thus
avoiding the paradoxes which result from the assumption of the
independent sufficiency of the purely formal descriptions?


Yes. Those experiences are indispensable already in the same sense that the number 4564310089 is indispensable in arithmetic. It is there. You cannot say that number theory make sense without that number. Likewise, comp explains why the experience are there, and why we cannot eliminate them. But comp provides also a major role to those experiences. Not only they provide the logic of physics (and the whole physical realities after that), but they define what persons are, mainly the owner of those experiences. It can give a role of consciousness: relative self-speeding up of a universal machine relatively to another probable universal machine. Comp explains why the consciousness (quale) is needed in that process. See below.




In a sense, this is correct. Materialist seems to be able to use the same self-reference logic than the one used by the computationalist. But then, the point is that we are confronted to the measure problem, and the problem of the relation between 1-p and 3-p is transformed into a reduction of the physical 3-p from and only from the self-reference logic and the restriction of 3-p possibilities to the accessible state by the UD. And this works indeed. In that sense, at the propositional level, it makes sense to say that the mind-body problem is solved by comp. It remains to see how far this works. Is the comp first order logic of the hypostases compatible with the
empirically observable facts.

Keep in mind that, by the self-reference logic (or even just
self-multiplication), we *already* know why a machine comes to differentiate
quanta and qualia, and the math describes this precisely. (By the
G*\G-equivalence of Bp with Bp & p, etc). If those comp quanta are the "real" quanta remains to be assessed, and if it is case, as it seems at the propositional level (already mathematically studied) this would support this
theory of qualia.

Again, the formal differentiation of quanta and qualia, and the math
descriptions thereof, must be distinguished from any possible
consequential role of qualitative experience per se.


I explain below, but the qualitative experiences have a huge impact on reality, not on the 3-p reality (arithmetic) but on the 1-p (hopefully plural) realities (intelligible and sensible): they make them appear relatively to the persons, and they make them stable (right relative measure (to be sure this remains to be verified)).




 If we are to
take qualia seriously as part of our explanations, they must have a
role distinct from their mere description.


Absolutely so.


 If they do not, we're
faced with a situation in which the same histories are describable in
terms of "qualia" whether actual qualitative states are present or
not.


Yes, but this cannot happen.



 AFAICS this is the unavoidable crux of the HP, and I don't at
this juncture see that it is addressed by comp or indeed any other
approach I've encountered (please forgive me if this is just my
missing the point as usual).


I forgive you. It seems to me that we can understand the comp solution with just UDA, but it is far more easy with AUDA, where the complexity is reduced to the understanding of some "known" results in mathematical logic. See below.



Somehow we need to be able to entertain
a "non-formal" component in the histories to accommodate this issue,
or else conclude that we don't recognise any distinction of role
between formal description and actuality.


Very well said.
We need indeed to entertain such a non formal component, and may be even many of them.

So here is the solution (in AUDA, I may try later to explain this with just UDA, but it is more confusing, given the highly counter-intuitive frame).

Actually, there are many non formal components. Let us consider the first three (primary) 'hypostases" or 'machine-points-of view':

p    (meaning p is true: this will appear to be NON FORMAL)
Bp (meaning "I can prove p", asserted by the machine: this will appear to be FORMAL) Bp & p (Meaning "I can prove p, and it is the case that p": this will appear to be NON FORMAL).

It may looks like a paradox. The logic of (Bp & p) is, at the propositional level, entirely captured by the formal system S4Grz. Yet, what is captured, is not a formal object, and it cannot be made formal. It describes the necessary formal logic of knowledge, but knowledge itself is NOT a formal, nor formalizable, notion. Yoou can define Bp in the lngauge of the machine, but you cannot even just define Bp & p in the language of the machine (this would lead to "0 = 1", by using the diagonalization lemma of Gödel).

It is hard, I think, to be clearer than that. S4Grz is an incredible logic capturing the formal structure of a concept which is NOT formalizable at all, nor even nameable, except by a reference to truth, which is itself not formalizable.

Now, we can restrict 'p' on the sigma_1 true sentences (which correspond to the accessible state of the machine), and the logic of observability will be captured by the following logic and their interplay:

Bp & p (again)
Bp & Dt (the logic of the measure 1 on the consistent extension: it can be made formal, and corresponds roughly to Ploitinus intelligible matter). Bp & Dt & p (the logic of sensible matter, physical sensation: it cannot been made formal).

How can we understand those non formal things? Because we are ourselves, from our first person point of view, non formal things. We are not our body, nor our Gödel number, still less our indentity cart number, and trough introspection, perhaps on the Ramana Maharsi koan "Who am I", we can have some glimpse of how much "we" are really different from any possible description.

Of course G* proves that all the hypostases are equivalent in the sense that they access (trivially for the CORRECT machine) the same set of arithmetical true propositions, but, the machine CANNOT know that, cannot believe that, cannot feel that, and this G* can also prove. That is why those non formal components, which are the on-bject of study of the hypostases in which "& p" appears, plays a so big role in the definition of both sensible person and sensible realities.

So what I think you may be missing, is that a formal theory (or a machine) can refer correctly (without knowing that!) to informal notions, and those informal notions can and does play a role in the very apparition of the coupling consciousness/realities.

This appears, but less clearly, already in UDA. The non formal components is bring up at the start, in both Church thesis, which refers to arithmetical truth, and in the "you" who accepts, or not, the proposition of the doctor. But UDA does not explain consciousness. It explains only that linking the non formal notion of consciousness to a formal object (the computations) entails the reversal physics/ machine-theology/psychology. AUDA, eliminates somehow the indexical reference to "you", and replace it by a universal (Löbian) machine. But then the incompleteness phenomena, shows that the logic of consciousness (or first person) will be different of the logic of what you link the consciousness too. This appears in UDA at step 7, where you see that the physical machine (brain) is eventually provided by a measure on 1-person notions, which cannot be formalizable at all, and bear on infinities of computations.

It remains only one mystery: the informal notion of number theoretical truth. But this again, accepting the truth (non formal) of elementary arithmetical proposition, provides an explanation why, we will never been able to solve that mystery. So comp solves the consciousness reality problem as far as it is possible to solve it. This can also be tackled formally, and it can be shown that the whole of physics (assuming comp) is eventually PI_2 complete IN arithmetical truth (that is, with Arithmetical truth as oracle). This is far beyond any effective complete theory. Even "God" (arithmetical truth) cannot answer all physical questions!

Now, given that most Löban machine are as clever as you and me, you may still believe that there is a paradox. After all, when studying the theology of a correct machine, we know that Bp and Bp & p are equivalent. But the key point is that no machine can know this about herself, so its qualia will obey a different logic from its quanta. We just don't know our own truth notion, we cannot even name it. That is why we can only lift the theology of the correct machine on ourselves through an act of faith (like betting on a substitution level). But it remains a theology, which is of course not "close" syntactically. It points on three informal things God (truth), the universal soul (Bp & p) and the sensible matter (Bp & Dt & p). from this emerge the fabric of reality, in a sufficiently precise way as to be tested.

I think you are confusing simply a theory and what a theory is about. It is very rare that a theory captures the thing it talks about. It capture tiny aspects of it. The comp theory is conceptually complete by referring to those (mathematically necessarily INFORMAL) notions, in both UDA and AUDA.

I hope this help. I think your confusion is simple, but we use the distinction theory/model in a very complex setting, where simple confusion can easily be obscured by the complexity of the subject. I tend to believe that almost all errors in philosophy or theology comes either from a confusion between the hypostases, or from between theories and their intended semantics.

Did this helped?

Bruno


http://iridia.ulb.ac.be/~marchal/



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