Thank you Bruno for your response. Honestly I don't know if I'd say yes to the doctor. It's cowardly of me, but I think I'd like to see the device work on someone else first. If they appear to be fine after the operation then I guess I'll go under the knife - and have to swallow the logical consequences whole! Your reply helps. I suppose what I feel is missing from the account is the *necessity* of qualia, because it seems to me that everything that exists, necessarily exists, and as it stands in the comp account, the necessity for there to be an interior to mathematics remains mysterious. My guess is that comp is wrong, but it may be that it is still a whole lot more right than materialism. It may be wrong in the same way that general relativity and QM are "wrong", i.e., correct, but to some limit. My next step is to read the Amoeba's Secret and see if I can start to wrap my head around the S4Grz and the []p & p - the maths is still largely a mystery to me.
However I wanted to put some less argumentative and more curious questions to you about the way you imagine the comp-driven universe to be (yes, there's no universe, I know, but I lack words: this apparent "space" we inhabit?). The question comes up in the comp account about the physical explanation for the origin of the Löbian organism the self-consistency of whose mind creates the appearance of matter (allegedly). Liz and Brent were throwing around this "if a tree falls in the forest" question on the MGA thread. The account whereby the observer arises out of the long, deep history of matter sure looks convincing. What is the status of this alternative origin story if the observer is actually grounded in Platonia? I seem to recall you talking about the idea that the observer's self consistency demands that it also find a consistent account of itself in the "material hypostases". OK, I can go with that, but something here still troubles me. We can't surely dismiss these origins as fictive any more than we can dismiss the other observers we find in our environment as fictive. How do you see the relationship between these accounts (the exterior physical and the machine psychological)? It occurs to me that in some ways the anthropic explanation of the fluky coincidences of the laws of nature resembles the machine psychology account - in that the requirements of existing as a complex self-aware machine in a sense "cause" the laws of the universe to be what they are. The need for logical consistency constrains the environment and its laws in very specific, complex ways. It's almost strange that it's taken us so long to realize just how extraordinary it is that the "laws" work, that they are capable of creating the complexity and beauty we see. Only a huge, unfathomable amount of selective work could lead to a structure like the calabi yau manifolds etc, with its staggeringly elegant capacity to generate complexity from simplicity. So... that work I describe would be the infinite computations in the UD, and just as all the complexity in the UD is surrounded by a vastly greater region of garbled junk, so the physical account relies on a similar surrounding region of incoherence. Which makes me wonder: are the two accounts just mirror images somehow? Are the garbled, dead, sterile, incoherent universes the reflection of those infinite sterile computations? Is there an observer of these dead regions? Or are the observers like fleeting Boltzmann brain or quantum fuzz in the void: incoherent, fleeting, barely aware, but just there enough? I hope I make sense... Now a second thing. Comp suggests, or predicts, Many Worlds, and says physics arises from the measure of the observer computations. But string theory suggests many physics(es!). So this is intriguing. Are we humans (and other animals in this multiverse) bound to one set of physics as it were, while perhaps other (more complex?) observers occupy a world with different laws? Because it seems we have only one of two options. Either the other possible physics are all sterile, or there is something about the types of mathematical structures that we are that keeps us bound to this particular set of observer states, not letting us "slip over" into universes with different laws? Might we not be capable of a kind of mathematical state change that would see us metamorphose, wake up in a world with different laws? Might death and birth not be such state changes? (This last suggestion no doubt getting too mystical for many whose self-appointed job it is to crush any idea that smacks of the Big Guy Upstairs who we've had so much trouble with in the past, but you're not afraid of the G-word it seems, so I ask anyway (not that survival of death has to bring God with it, but some people are sensitive about these things.)) My own pet idea at the moment is a simple rule that seems at the least strongly suggested by scientific experience to date and to me just intuitively compelling. It is simply that there are no brute facts. Or another way of saying this is that there are no "hard" ontological boundaries, no places where that which exists nakedly abuts non-existence, in the way that a brute fact is encased as it were in a boundary of nothingness beyond which one cannot travel. So far, wherever we look we find that apparently hard boundaries are illusions. Every apparently closed system turns out to be incomplete (yes Gödel again), to be contained as a special case within some more encompassing whole. I believe this is true infinitely and in all "directions". And so when people pin their hopes on string theory as a Final Explanation, I don't believe it, just as I don't believe the spatial dimensions will stop at the current count of 11. They can't, if my idea is correct, because that 11th dimension would be a hard boundary. The flower of knowledge will keep opening and opening. And so I also do not believe in the boundary of death, the ultimate brute fact. So - maybe I won't say yes to the doctor but yes to Doctor Death instead, preferring to embrace the transformation than to perpetuate the machine in its current form. On Sunday, August 10, 2014 4:01:00 AM UTC+10, Bruno Marchal wrote: > > > On 09 Aug 2014, at 05:34, Pierz wrote: > > In "The Conscious Mind", Chalmers bases his claim that materialism has > failed to provide an explanation for consciousness on a distinction between > 'logical' and 'natural' supervenience, where logical supervenience simply > means that if A supervenes on B, then B logically and necessarily entails > A. Because we can logically conceive of a (philosophical) zombie, then it > seems that consciousness cannot *logically* supervene on the physical. > There is simply nothing in the physical description that entails or even > *suggests* the arising of subjective experiences in any system, > biological or otherwise. This is a well-trodden path of argumentation that > I'm sure we're all familiar with. However, since it does appear that, > empirically, consciousness supervenes on physical processes, then this > supervenience must be "natural" rather than logical. It must arise due to > some natural law that demands it does. So far so good, though what we end > up with in Chalmers' book - "property dualism" - hardly seems like the > nourishing meal a phenomenologically inclined philosopher might have hoped > for. Bruno's version of comp seems like more nourishing fare than the the > watery gruel of property dualism, but Chalmers' formulation of logical > supervenience got me thinking again about the grit in the ointment of comp > that I've never quite been able to get comfortable with. This is only > another way of formulating an objection that I've raised before, but > perhaps it encapsulates the issue neatly. We can really only say we've > "explained" something when explicated the relationships between the higher > order explanandum and some ontologically prior basis, demonstrating how the > latter necessarily entails the former. Alternatively we might postulate > some new "brute fact", some hitherto unknown principle, law or entity which > we accept because it does such a good job of uniting disparate, previously > unexplained observations. > > Now the UDA does a good job of making the case that if we accept the > premise of comp (supervenience on computational states), then materialism > can be seen to dissolve into "machine psychology" as Bruno puts it, or to > emerge from arithmetic. But the problem here is that we can no more see > mathematical functions as necessarily entailing subjective experience as we > can see physical entities as doing so. It is perfectly possible to imagine > computations occurring in the complete absence of consciousness, and in > fact nearly everybody imagines precisely this. I would say that it is an > undeniable fact that no mathematical function can be said to* logically > entail *some correlated conscious state. Rather, we must postulate some > kind of law or principle which claims that it is just so that mathematical > functions, or certain classes thereof, co-occur with or are somehow > synonymous with, conscious experiences. In other words, we are still forced > back on a kind of natural supervenience. But the problem here is that, > whereas with matter we may be able to invoke some kind of ontological > 'magic' that "puts the fire into the equations" to quote Hawking, with pure > mathematics it is hard to see how there can be any such natural law that is > distinct from pure logic itself. > > Now when I've put this objection to Bruno in the past in slightly > different words, claiming that it is hard to see any way to reconcile the > language of mathematics with the language of qualia, Bruno has invoked > Gödel to claim that mathematics is more than mere formalism, that it > embodies a transcendent Truth > > > > Well, that's Gödel's discovery, with "transcendent is defined by > "satisfied by the model (N, +, *) but non provable by the machine concerned. > > That entails that the following logic, although being the meat-logic of > the set set of arithmetical beliefs, obeys completely different logics: > > []p > []p & p > []p & <>t > []p & <>t & p > > And more: Gödel's incompleteness split in two, three of those logics > ([]p, []p & <>t , []p & <>t & p). One part (derived from G) describes what > the machines can prove on this modality/person-point-of-view, and one > derived from G* (representable in G) describes what is true about those > modalities, including the laws that the machine cannot proves, but still > can guess or intuit, or observe ...). > > > > > > that is beyond that which can be captured in any mathematical formulation. > At least, that is the best summary I can make of my understanding of his > reply. He also claims to have discovered the 'placeholder' for qualia > within the mathematics of Löbian machines: the gap between statements which > the machine knows to be true and those which the machine knows to be true > and can prove to be so. It's a fascinating argument, but it seems at the > very least incomplete. The fact that a machine making self-referentially > correct statements will be able to assert some (true) things without being > able to prove them does not compel me in any way to believe that such a > machine will have a conscious experience of some particular phenomenal > quality. > > > But nothing can do that. You ask for too much. We *assume* comp all along, > even if in the math part, we do it only at the meta-level, to ease our > comprehension. In he math part, you can forget consciousness, and only talk > in terms of beliefs, knowledge, etc. Those are defined precisely, either > directly in arithmetic, or in terms of arithmetical notions (set of > numbers). > > > > > It may be true that correct statements about qualia are correct statements > which can't be proven, but this does not mean that statements about qualia > are statements about unprovable mathematical propositions. > > > Careful. I don't say this. > All you need is the classical (analytical) most common axioms for > knowledge, or knowability: > > (Knowable p) -> p > Knowable (p -> q) ->. [Knowable (p) -> knowable (q)] > > and for the richer introspective form: > > knowable(p) ->. knowable(knowable(p)). > > I study very special machine, who have simple correct arithmetical > beliefs. Then, applying theaetetus definition (knowing p = justifying p, > with p true) gives a logic obeying the standard theory of knowledge, and > you can use it to talk with the machine, noitably on the difference between > 3p and 1p, etc. > > > > > > I might claim that Chaitin's constant is 0.994754987543925216... and it > might just happen that I'm right, through divine inspiration, but Chaitin's > constant is not a quale of mine. Bruno can point to this space in his > formalism to say "that's where the qualia fit", but there is a similar leap > of faith involved to actually put them there as we make when attributing > qualia to emergence from neurology. > > > It is the same as attributing consciousness to any other one person than > oneself. You need just to accept the axiomatic definition beliefs, > knwoledge, etc. It fits, like we fits between us right now, despite this > never prove anything. But this we know, we assume comp, and neither in the > UDA, nor in the AUDA, we pretend having provided a proof that comp is true, > or that the classical theory of knowledge is true. the nice thing is that > we show them empirically refutable, as their restriction to the sigma_1 UD > must give the logic of the observable. And unfortunately it fits, so > *classical* comp is confirmed (not proved), and not yet refuted. > > > > > Gödel's theorem might show that mathematics is more than mere formalism, > but it does not allow us to make the leap to mathematics being more than > abstract relationships between numbers. There will always be some true, > unprovable statement in any set of axioms, but this statement will still be > about numbers, not about feelings. > > > But then with comp, your own statement should be seen as a statement about > some (very) complex number. All statements in physics are also just > statement about numbers and numbers relations. > > I guess you are not aware of the crucial distinction between extensional > mathematics, and intensional mathematics, which take into account the body > of the sentences/machines making sentences, with notion of (self) reference. > > > > > > If we start to say mathematics is more than that, we are making a > metaphysical, and indeed mystical claim, and I believe we have also > expanded mathematics to become something else, something that we can no > longer truly claim to be maths as that is usually understood. > > > Indeed. I do not hide this. It is a key point. Comp entails it belongs to > arithmetic, up to a theological act of faith; when saying "yes" to the > doctor. You put your life in a number on that occasion. That is why I > insist it is theology. Then in AUDA, we get what was needed: machine > looking inward *are* confronted with many sort and types of non justifiable > (by them) truth, about them. > > > > > Now of course the "gap" between the maths and the qualia (I don't like the > obfuscating and often confused language of Craig's posts, but I think > "Gödel of the gaps" is a pretty good turn of phrase, if indeed he is > pointing to the same thing as me) is actually imported into comp with the > initial assumption of qualia supervening on computational states. That > postulate is of course unexplained, mystifying and, when taken to its > logical end as Bruno has done, mystical. > > > But you do it when you bet on comp and say "yes" to the doctor. Then with > Gödel we get that a machine can guess a reality (<>t, by Gödel completeness > theorem it is equivalent, with model playing the role of reality), and > justifies, as we do, that if that reality exists, it can't be proved: <>t > -> ~[]<>t. > We can also define the mystic part of the machine by all the intensional > variant (see above) of G* minus G. > > > > But when all is said and done, we're still left with it as a "brute fact", > if anything more naked than it was at the beginning of the argument. More > naked because it is even less clear how we are going to get a natural law > to bridge the gap between the putative ontological basis of consciousness > and consciousness itself when that basis is pure mathematics. > > > Pure arithmetic. Even pure sigma_1 arithmetic (the UD*). We get it because > the comp act of faith, connect consciousness, or its invariance, to > computer science theoretical notions. > > It is a fact that computer science is embedded faithfully in the > arithmetical truth. No theories at all unifies that. > > > > > After all, what is mathematics? If it includes all consciousness, is > inseparable from it, if it encompasses love, pain, the smell of rain, and > everything else it is possible to experience, then we are really talking > about the mind as a whole, and the claim of a reduction to arithmetic > starts to look at the very least misleading. Arithmetic is just the sugar > coating that gives the rationalist a better chance of swallowing the > psychedelic pill. > > > > Mathematics does not include consciousness. It is that once a number is > Turing universal, or sigma_1 complete, its view of arithmetic is provably > beyond mathematics. > > Mathematics (we need only arithmetic) is only the 3p view "outer view", > but theaetetus applied to provability leads to first person view much > richer than arithmetic. > > Understanding comp is understanding that we are, even just for arithmetic, > confronted with the Unknown. It leads to coming back to the scientific > attitude in theology, and perhaps the human sciences and affairs. > > I just derive consequences for an assumption, which link consciousness and > first person to 3p number-object that we can put on a disk for awhile, and > I have never hide the theological aspect of it. In fact, it is part of comp > to admit it is a theology. We can just hope for it, or fear it, and perhaps > refute it, thanks to the level of rigor and precision it permits. > > Bruno > > > > > > > -- > You received this message because you are subscribed to the Google Groups > "Everything List" group. > To unsubscribe from this group and stop receiving emails from it, send an > email to everything-li...@googlegroups.com <javascript:>. > To post to this group, send email to everyth...@googlegroups.com > <javascript:>. > Visit this group at http://groups.google.com/group/everything-list. > For more options, visit https://groups.google.com/d/optout. > > > http://iridia.ulb.ac.be/~marchal/ > > > > -- You received this message because you are subscribed to the Google Groups "Everything List" group. To unsubscribe from this group and stop receiving emails from it, send an email to everything-list+unsubscr...@googlegroups.com. To post to this group, send email to everything-list@googlegroups.com. 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