On 1/6/2012 18:57, Bruno Marchal wrote:

On 05 Jan 2012, at 11:02, acw wrote:Hello everything-list, this is my first post here, but I've been reading this list for at least half a year, and I'm afraid this post will be a bit long as it contains many thoughts I've had on my mind for quite some time now.Welcome acw. It looks like you wrote an interesting post. But it is very long, as are most sentences in it. I will make some easy comments. I will come back on it later, when I have more time.

Thanks, I look forward to the full response.

A bit about me: I'm mostly self-taught in the matters concerning the topics of 'everything-list' (Multiverse hypotheses, philosophy of science, 'rationalism', theory of computation, cognitive science, AI, models of computation, logic, physics), and I greatly enjoy reading books and papers on the related subjects. My main activities center mostly around software development and a various other fields directly related to it.OK. Self-teaching is often of better quality than listening to others.

`It's fine and allows one to better study some matters, but it also may`

`lead to gaps in knowledge if one isn't aware of the gaps.`

I will give my positions/assumptions first before talking about the actual topic I mentioned in the subject. One of my positions (what I'm betting on, but cannot know) is that of computationalism, that is, that one would survive a digital substitution.OK. As you know that is my working hypothesis. As a scientist I don't know the truth. I certainly find it plausible, given our current knowledge, and my main goal is to show that it leads to testable consequences. Mainly, it reduces the mind body problem into an arithmetical pure body problem.

`Neither do I claim to know the truth, or should anyone else, if someone`

`claims to know it, they may be telling a lie, voluntarily or not. Our`

`senses aren't that reliable to claim absolute knowledge about the world`

`and even when talking about mathematical truth, the incompleteness`

`theorem applies to everyone.`

`Instead of truth, I tend to assign a theory a high confidence value, or`

`to consider it more probable than others, but the only thing that we can`

`really do beyond that is testing, falsification or verification of our`

`expectations/theories.`

`It sort of was the main goal of my post - to show that there are some`

`practical ways to test COMP that one might be able to do some day.`

There are however many details regarding this that would have to be made more precise and topic's goal is to elucidate some of these uncertainties and invite others to give their ideas on the subject. Why computationalism? Chalmers' "Absent Qualia, Fading Qualia, Dancing Qualia" thought experiment/argument shows that one can be forced to believe some seemingly absurd things about the nature of consciousness if functionalism is false (that is, if one assumes that conscious nature depends on more than just functional organization, such as some "magical" properties of matter). Taking it from functionalism to computationalism isn't very hard either, all it takes is assuming no concrete infinities are involved in the brain's implementation and the CTT(Church Turing Thesis) does the rest.OK. And if you make explicit that COMP assumes only the existence of a level, then you see that COMP, as discussed on this list, is a weaker hypothesis that all the comp discussed in the literature. That is why I refer to the generalized brain. The level can be so low that the "generalized brain" is an entire galaxy or even a multiverse quantum state. This does not make the assumption trivial, the main reversal, between Aristotle theology and Plato theology still follows.

`Too low a level and functionalism is no longer very practically`

`testable, but the consequences of COMP (reversal) would still apply if`

`it's true.`

`In my example (the experiment) from the previous post, I tried to assume`

`a reasonable (mid(atomic)/high(neurons or higher)) substitution level,`

`in that it could be tested someday. Such a mid/high-substitution level`

`allows for the mind's implementation to become substrate independent`

`(SIM), but if the new implementation isn't too exact, would the`

`continuation likely or not: it should be conscious, but would it be`

`likely to experience a continuation into a SIM after saying 'yes' to the`

`doctor? Would it be more likely to end up "amnesiac" and just choose not`

`to become a SIM?`

`I've discussed the matter of errors or inexact 'copies' in the previous`

`post and will wait for your response on that part before going into more`

`details again. In a way, I think it might be more reasonable to consider`

`the mind's implementation and the environment's implementation`

`separately (even if environment+mind are at least one (and infinity of)`

`TM in COMP) as the environment has more chance to vary and only`

`indirectly leads to conscious experience, or that it might be more of a`

`wildcard.`

While I cannot ever know if concrete infinities are involved in the mind's functioning (leaving aside various forms of observer selection from some Plentitude, such as Marchal's UD* or Arithmetical Platonia, or possibly some larger ontology, although if higher infinities do exist ontologically, I don't think there is any way for a way for a system that isn't even as powerful as an UTM (Universal Turing Machine) to be able to know if they have a access to a genuine oracle of a more powerful system; to be more specific, in the state we are now, we have finite memory), neuroscience does indicate that we (our brain) is a (partially self-modifying) neural network and that each component (neuron) of this network can be simulated digitally.That's a good evidence. But I would not say yes to a doctor if he misses the functional composition and state of the glial cells. I can imagine that my consciousness is "in" the neural network, but some deeper personality traits can be dependent of the glial cells.

`That might be true, although more research would have to be done to know`

`for sure how much glial cells matter. I wonder if you'd be you if you`

`lost one very minor personality trait (let's say one encoded by 5`

`neurons+their glial cells). We tend to lose a lot more during a single`

`day. A SIM would be less likely to forget due to his implementation`

`being less error-prone (and backups).`

Not only that, it also seems to be very resilient to noise and component loss, it's also very adaptable (neuroplasticity).Like everything in nature, it is highly redundant.Various research shows that the substitution level might even be higher than the neuron level, in the sense that the abstract functionality performed by the brain still stays nearly the same after more high-level substitution. An example of this view is described in the Jeff Hawkins' "On Intelligence" book and in abstracted models of the visual system where instead of neurons one can just use larger components which perform some forms of bayesian inference based on the input given. AGI research hints that the mindspace (the space of possible minds) may be much larger than we ever thought, and this is only talking about that of finite computational minds, which obviously have no concrete infinities in their implementation. I have a very hard time imagining what an infinite mind could be, how it could even think a single thought, how it could maintain unity of consciousness, or be embedded in time, hence I will assume most minds are finite and have bounded or unbounded memory.OK.We are currently memory bound due to evolution/physical limits, but an AGI(Artificial General Intelligence) living within some TM(Turing Machine) or a very robust potentially infinite universe could have unbounded memory (which is finite at any given time, but potentially growing, depending on the actual program).I don't think humans are memory bound. They use their environment to extend their memory all the time, from cave's wall to magnetic tapes. It is not different from a universal (Turing) machine using bigger and bigger portion of its tape/environment in the course of a computation.

`I only considered the internal memory storage (the brain), but if we`

`consider the entire environment (and assuming the environment isn't`

`memory bound, which seems to be the case - it's expanding at least at`

`the speed of light, however unfortunately, it doesn't seem trivial to be`

`able to take advantage of available resources past a certain limit as 2`

`very distant objects can be moving away from each other at speeds faster`

`than the speed of light), you're right. If COMP is assumed (and unusual`

`continuations), there are ways to even get around those limits.`

CTT tends to follow from the belief that 'abstract finite rules applied on abstract finite objects can be applied and they will always give the same abstract result in any possible universe', which is fairly close to some form of Platonism, however there is substantial (mathematical) evidence for CTT being true. The evidence is in the form of the equivalency of a large class of abstract machines (for more on this you can read Boolos, Burgess and Jeffrey's "Computability and Logic").That's a powerful empirical evidences indeed, especially that those abstract universal system can be very different, like number+addition+multiplication, combinators, quantum topology, billiard balls, Conway's game of life, Penrose pavements, etc. But the conceptual reason which makes me think the most that CT might be true is the closure of the set of partial computable functions for the Cantorian diagonalization procedure. Diagonalization is a killer of universality-pretension, but it fails on the universal (with respect to computability) machines. Unlike the fact that it succeeds for provability (Gödel) or definability (Tarski), or infinity (Cantor), we cannot use it to find more powerful computation system (with respect to the class of computable functions).

`That's strong evidence indeed. As a side note, I think universality`

`would be lost if one tries to go hypercomputational (formally), but it`

`also seems unlikely we'll ever be able to physically implement it (in`

`the case COMP is false), or be able to truly know that we actually have`

`a hypercomputational oracle on our hands.`

Some other interesting results are how everything that we can talk about regarding formal systems can be encoded and formalized by a TM-equivalent machine. Of course, this doesn't mean that a system is consistent, merely that we can't talk more about it than a machine could (within some system, you can of course assume stronger systems and so on). Personally I'm willing to assume PA(Peano Arithmetic) consistent and that valid sentences in it have a truth value, although I cannot /know/ that for sure, I'm only betting on it being consistent.Well, you are not alone. Virtually all mathematicians assume PA consistent, and even the consistency of stronger systems (in which you can prove the consistency of PA by "quasi elementary method". You can prove the consistency of PA from transfinite induction up to a reasonably little ordinal (epsilon_0), or you can convince yourself of the consistency of PA by appeal to the intuitive (but accepted in math) notion of arithmetical truth (which can be defined in reasonable set theory).

`In a way, I do wonder what exactly would it mean for PA to be`

`inconsistent, or its standard model to not exist. Not entirely sure`

`there would be any math that would be left standing, except maybe some`

`logic.`

`I'm aware of Gentzen's proof about PA's consistency by transfinite`

`induction, although I still need to do more studying to better`

`understand some of its details.`

> This shows that humans are richer Löbian machine than PA, very > plausibly. Nevertheless, with the COMP assumption, we might defend > the idea that we might not be so much stronger than PA.

`Possibly, although humans can just take a formal system and assume its`

`truth, then reason within it. It's hard to a human to claim to know for`

`sure that a system is consistent, it seems to me to be as much as a bet`

`as COMP.`

`For much stronger formal systems such as some set theories that talk of`

`higher infinities, it might even be harder to claim to know their truth`

`as they can talk about behavior of infinite processes (non-halting),`

`which is far from what we can assume.`

`Yet, I do think such stronger formal systems are very useful as far as`

`taking shortcuts about finding the behavior(such as convergence) of such`

`processes - I don't think you can ask a scientist to give up his`

`analysis or differential equations just because there's a small chance`

`of ZFC not being consistent.`

`I also tend to try to think a bit differently about the levels of truth`

`a human can know. Direct experience is truth, although not always`

`communicable - it is also the truth of the lower-level of systems that`

`support the human's existence. Mathematical truth where we reason`

`formally about some system is also truth (if a system is consistent and`

`sound, but we cannot always know), but it's non-experiential, and having`

`a wrong belief about it wouldn't make your lower-level self`

`inconsistent, although you'd be wrong if you were asserting it as truth`

`- it's a bit like how a Turing Machine which encodes a theorem prover`

`for some system can talk about what's provable (or isn't provable)`

`within it, but isn't the formal system itself. If one identifies`

`directly with the system, it's not hard to make the same mistake found`

`in some conclusions about the "Chinese Room Argument" or "China Brain`

`Argument".`

`On the other hand, I do think that PA formalizes well how we think about`

`arithmetic and it likely matches our beliefs (unless you're an`

`ultra-finitist, and thus reject the induction axiom or the natural`

`numbers, but rejection of such an axiom is rather strange, as one could`

`perform induction manually for any k steps, but then one assumes`

`eventually that there is some finite k+1 step where it fails). In that`

`way, truths about PA can be lifted and used as truths about the world`

`(in science and more), and if COMP is true, truths about computability`

`have very far-reaching consequences.`

> Also, there is no interesting theorem in math which cannot be proved > in PA, except in mathematical logic and > higher algebra (category theory).

`What about results that can be shown to have very small proofs in Second`

`Order logic, but have non-trivial (longer than we'll ever be able to`

`write) proofs in first order logic (Boolos' "A Curious Inference") or`

`that Goodstein's sequence's termination cannot be proven in PA, as well`

`as certain facts about non-primitively recursive computable total functions?`

I'm agnostic about the consistency of stronger set theories that imply higher infinities, although it is very useful to be able to talk about them, regardless of their ontological existence - they might even have useful computational consequences: such as assuming certain types of processes will converge to some specific value and so on (surely calculus/analysis is scientifically very useful), although of course, with stronger systems we risk inconsistency even more.OK. But a lot in "real analysis" is arithmetic in disguised. I heard Maccintyre saying this, and that view is also defended by Torkel Franzen in his lovely book "inexhaustibility".

`Some of it might be translatable to PA. I'll have to read the works you`

`mentioned to get a better understanding of it.`

Post-edit note: When I speak of TMs in this post, I mean any Turing-equivalent machine as by CTT. It might have been better for me to have used UM(Universal Machine) or UN(Universal Number) instead of TM, as the particular choice of universal machine implementing the computation is irrelevant, just that some UTM-equivalent machine exist and the UTM runs UD at least, or merely UD running directly as some specific Turing-equivalent machine. I've seen the terms used in this list, and I'm not always sure they are exactly the same concept, but they seemed to me (although I may be wrong when the term LUM(Lobian Universal Machine) is used, that seemed to me to be more about specific formal systems that are used to model truth that can also be generalized to persons).OK. LUMs have just a little more provability (not computability) power. In fact provability itself can model computability. In that case a theory like Robinson Arithmetic (RA, it is PA without the induction axioms) is already Turing universal. But it lacks serious introspection ability, which are present for PA and ZF (which are Löbian, they obeys Löb's theorem). More on this later, probably.

`I'm currently reading some of Boolos' books on the matter, when I'm done`

`I plan on re-reading AUDA. Looking forward to your elaboration on it as`

`well.`

The assumptions so far: Mind, COMP, CTT, Cons(PA).Well, as I explain COMP, it contains the mind, CT and cons(PA) assumption. In fact it assumes even more: it assumes that PA is not just consistent, but arithmetically sound. But all mathematicians assumes this (consciously or not).The 'Mind' assumption is just that I have a 1p (first person) internal view, or consciousness. It had to be stated as if you only assume a 3p(third person) world, there is no reason to believe that the 1p view exists. To someone else that only considers that ONLY the 3p view exists (let's say, some physical reality for the sake of the argument, or 'materialism'), explaining the existence of 1p seems impossible, so they eliminate it away with Occam's razor by saying that all this 1p view talk is the person being defective/delusional "by design"(not in the sense of "Intelligent Design", just due to how it happened to evolve) and there's no such thing as 1p. The major problem with that is the 3p world is only inferred to exist using the 1p view, so belief in a mind is natural, but then so is the inference of the 3p world. At least it seems to be that using 1p and by induction to get to 3p and then to notice that there doesn't seem to be a reason for 1p to exist from the 3p view and thus to conclude that 1p doesn't exist would make the reasoner's beliefs inconsistent.To believe that 1p are delusional is self-defeating. The 1p have been methodologically eliminated by the Aristotelian, but this has led to the reification of nature, and the abandon of the fundamental human science to political authorities, and to making of the mind-body problem, and then its hide under the rug. But her-and-now-consciousness or 1p views are our only certainties. The rest is (3p)- theories/conjectures/postulates.

`I agree with most of that, but I'm not entirely about the politics part.`

`In another way though, I do wonder how can someone claim to have no`

`phenomenology and then claim that it only seems they have a 1p view,`

`because the 3p view says that that must be the case. In another way, it`

`may be that one trusts the 3p view more than the 1p view, which is`

`strange because the 3p view only exists because the 1p view is able to`

`reason about it (in COMP, both exist of course (as computation and`

`arithmetical truth about it), but it also says that one should care`

`about 1p as much as they care about 3p).`

From these assumptions one can use Marchal's UDA (Universal Dovetailer Argument) and MGA(Movie Graph Argument) to notice that if we are conscious and we have a digital substitution level then any notion of "physical" reality loses its meaning/explanatory power, and that physics is just local relative numerical phenomenology, or just a shared 1p reality, you also get a plentitude for free (in UD*, in AR) and 1p indeterminacy similar to that of MWI(Many Worlds Interpretation), and also confirming observed facts(QM).Good :)Why a plentitude and which plentitude? A long time ago, I used to often think "Why these specific physical circumstances?" or the more general "Why these physical laws/universal law?" Eventually I came to read Tegmark's Ultimate Ensemble/Mathematical Universe Hypothesis - if the universe can be described/contained in a consistent mathematical object, why then not just assume that it is one. If you assume this, Occam's Razor or its formalized versions (such as Solomonff Induction) will say that your hypothesis is rather complex.OK. That's the main motor of the everything-list.Assuming all possible (consistent mathematical) structures is the simplest possible hypothesis. The problem with this is that this 'whole' might be a bit too large or inconsistent in itself (like Russell's Paradox), and like I've said before, there is no way for us finite humans to know an oracle when we see it. If we're a bit more modest, we can use the only mathematical notion that we know to be truly universal - computation as by CTT.OK. The main problem also is in the self-localization in the possible math structure. Comp entails a first person indeterminacy which distribute us in the mathematical reality, and what we perceive might NOT be a purely mathematical structure, but something "supervening" on it from the inside view. This is a point missed by people like Chalmers, Tegmark, Schmidhuber, etc.

`What does 'what we perceive might NOT be a purely mathematical`

`structure' mean? Qualia? Or the undefinable truth?`

`Maybe in a less related way, we could imagine partially`

`non-computational physics (even without assuming any 'jump') where`

`appearances are some seemingly non-computational structure being`

`computed in the limit - such as computable reals, this would make`

`digital physics false in its naive formulation, but true in the sense`

`that there always existed a TM that computed those states (even though`

`it may run very deep).`

The first papers I've read that described used computation (CTT) to describe a plentitude were Schmidhuber's "Algorithmic Theories of Everything", which describes the Universal Dovetailer (and assumes COMP), the program that can run all possible programs(in the limit), and by CTT which shows the existence of an universal TM, it describes a computational plentitude. Unfortunately it bugged me a bit that he avoided using some Platonia or some form of AR(Arithmetic Realism) to put the UD in and just used some "Great Programmer" that runs the program in some magical undefined land. If anything this land only seems to grant 'existence' and nothing more - my Occam's Razor sense was tingling a bit.OK. It misses also the first person indeterminacy. he did not seems to have accepted here when discussing on the list.

`If one takes 3p as primary and 1p as non-existing (I don't know what his`

`view is on this), I can see how it's easy to reach that conclusion. If`

`1p is accepted, just arithmetic is sufficiently rich.`

Some time after that I've read Egan's "Permutation City" novel, which seem to informally do what Marchal does with his UDA+MGA, although not in a formal rigorous way, but enough to give a strong intuition for it, but I think it still keeps assuming only a finite, bounded universe, given the novel's conclusion (or merely it being one of those improbable observations that nevertheless exist, or a "white rabbit") - would it be an assumption of PA being inconsistent such as in his "Luminous" and "Dark Integers" short stories - it's still something which I have trouble imagining: if there is an abstract structure (supported by arithmetic modulo some number) of finite size k which is consistent, why cannot a structure of size k+1 exist - it's my belief in mathematical induction (induction schema) that makes this hard to imagine.OKI think conscious/self-aware beings which are embedded in time (probably a requirement for consciousness) are likely to come to such inductive beliefs by themselves if they think hard enough, although I don't think that having such a high-level belief affects low-level consciousness - for example, there are ultrafinitists which don't believe in natural numbers beyond some unspecified finite limit (I don't know how they justify their beliefs, but I think it has to do with assuming a finite material reality).I guess so. In this list, such an ultrafinitist physicalism has been defended, contra comp, by Thorgny Tolerus, if I remember well.

`I'll see about looking up his posts. I've talked with one ultrafinitist`

`in the past, but I still have a terribly hard time understanding how one`

`can use it to talk about ontology. It seems sufficient if you only want`

`to talk about finite-state machines, but much harder to talk about math,`

`physics or philosophy in it. In another way, I feel that it would only`

`be acceptable if one could show PA inconsistent ( Vladimir Voevodsky`

`seemed to contemplate such a view in:`

`http://video.ias.edu/voevodsky-80th ), but then, what could replace it?`

The way I see it: certain mathematical (or computational) structures will contain within themselves observers like us (or even us), and those structures can be seen as having states which are temporally related(a naive example: f:N->N, u:N->N, f(0)=U0, f(n)=u(f(n-1)), where U0 is some initial state, U is some computable function calculating the next state given some previous state, usually giving a greater complexity to the output; note that I'm not claiming this to be the case for us, if you want it to apply better to us, instead of the function 'u', you may think of it as a class of functions that support you, selected at random from a countably infinite set. Although I do expect the criticism that an /uniform/ probability cannot be defined on such a set).They do exist, but are not always sigma-additive, which does not prevent the use of some probability calculus.

I'd be interested to read a paper on this.

Some time after reading Egan's works, I've read Russell Standish's "Theory of Nothing" book which discusses some of these ideas in more detail, but gives more importance to the observer, with the Anthropic Principle and his derivation of the laws of QM as being observational laws. Not that long after, I've read Marchal's UDA+MGA/AUDA and some of his other papers. I was very impressed by the argument - it seemed to provide exactly what was missing from Schmidhuber's idea - the notion that the observer cannot be magically attached to some program running an universe: if computationalism is true (and a person has a 1p view), then the observer is only attached to whatever infinite ensemble of programs which happen to contain the 'body' of his mind (1p indeterminacy), not one particular piece of (virtual) matter.Good.It seemed to me like a (relatively more) formalized version of the ideas presented in "Permutation City" (which I think came before Tegmark, Schmidhuber or Marchal's works, although I would love to be corrected if I'm wrong about this).I published the whole thing in 1988 (the Toulouse paper, but I present it orally in many places in the seventies). Also in 1991 (in artificial life proceedings). Egan's permutation city is 1994.

`I was under the impression that Tegmark was one of the first that`

`thought that idea, but I suppose it just means that no well-known`

`authors had published it at that time. I find it a bit strange that your`

`idea(UDA+MGA) has remained so little well-known, despite that there has`

`been a lot of talk about computationalism and functionalism in general.`

`I can see why it wouldn't be that popular because it shows some forms of`

`materialism false, but then, isn't that also Tegmark's assumption that`

`matter is just math anyway?`

Another very interesting idea that Marchal has seems to be of consciousness/observation as arithmetical truth (or similar universal system capable of representing computation), it gives you whole worlds contained in timeless arithmetic, and it also gives you the 1p view. My only problems so far with it are that there were some parts of the AUDA which I either didn't understand too well (and might need to read more logic books then re-read AUDA again) or which I failed to interpret correctly within the proper context. There is a possibility that some of my questions that I will ask are due to my current incomplete understanding of the AUDA. After understanding some of the consequences of the UDA, I was fearing that the 1p reality of a conscious observers might be too jumpy (too many "afterlives" due to many consistent continuations outside of the current computations that support us) or even worse, border on white noise, thus you get very frequent zombie-like consciousness - this might even be worse if we allow a continuum to exist (such as sets of cardinality aleph_1 or more, if Continuum Hypothesis is to be assumed true).That's what I call the (first person) white rabbit problem. Too many parallel realities, and a possible inflation of predictions. But that's what make the comp hyp eventually testable. QM has also first person white rabbits, despite the Feynman formulation almost explains how they go away. Comp has to succeed similarly, and AUDA shows indeed why that is possible.

`Using the quasi-quantum logics? Or some RSSA-like assumption? I may get`

`back to this after re-reading AUDA (once I think I've read enough logic`

`books).`

However, since I am writing this right now, you can guess that my reality is fairly stable and non(observably)-jumpy ;) It seemed to contradict comp a bit, but then I made another assumption (which I find hard to believe in, but one must reason): the substitution level could be too low and thus we're tied to this particular set of computations in that most of our measure is here, and other continuations are just rare.That's a possibility indeed. Most probably, if comp gives exactly QM, our subst-level is given by the Heisenberg uncertainty relations. Basically the quantum state up to Heisenberg intervals.This seemed be bad news for the one getting a full brain transplant as it might make their reality jumpier, but on the other hand, the one getting the brain transplant will still act like a normal human would,Not sure.

`'Not sure' in the sense that the transplant is impossible or that`

`behavior will be wrong if taken at a higher subst level (such as neuron)?`

thus I cannot ascribe it any part-zombie status (only due to the potentially jumpy nature), they would, like I would, write up their email, observe the world and conclude that they are not jumpy. What I ended up settling with is that one has to assume some sort of relative self-referential measure, that is, one will (most probably) observe the world that is consistent with one's mind's structure and current state.Exactly, and this leads to AUDA, where everything (including physics) is based on self-reference.It was my impression that AUDA attempts to do that, but I will need to re-read it after I study more logic.OK. Good books are Boolos 1979 and Boolos 1993. Also, Smorynski 1985.

`I'm currently half-way through "Computability and Logic"(1974,2007) and`

`I've non-sequential parts of "Logic, Logic, and Logic"(1998). I plan on`

`starting on "The Logic of Provability"(1993) after being done with`

`"Computability and Logic". As for Smorynski's, is that "Self-reference`

`and modal logic"? I might read it if I can find it, although it seems to`

`be out-of-print and used copies of it seem to be quite expensive.`

However, if comp is true, I don't think jumpiness can be eliminated, merely made more rare by virtue of what the observer is and how he is embedded in the world. UDA+MGA+AUDA implies universes could be regarded to be 1p-plural observations which are the shadow on an infinity of "3p" ensembles of computations, thus have the appearance of objective 3p.More rare in the normal worlds. Which leads to the comp immortality (with the quantum immortality as a special case).

`Can true cul-de-sac's even exist? It doesn't seem to me, at least`

`intuitively. I've also seen a "no cul-de-sac" theorem mentioned on this`

`list, but I have yet to find exactly what post describes it.`

To summarize my view on: COMP as shown in the UDA+MGA+AUDA, despite its limitation to 'merely computations' seems to me to be an incredibly rich plentitude, even richer than Tegmark's MUH(Mathematical Universe Hypothesis), due to the proper attention given to 1p.OK.It may seem smaller because you can say "eh, it's just arithmetic", but in a way, for a finite observer, they cannot easily believe in knowing that something is beyond COMP, and yet in COMP, the 1p observer isn't even tied to any particular structure, but to an infinite ensemble of computations, and the observer's next moment is always selected within this ensemble.Which happens to be very rich and to possess a highly non trivial structure.In another way, it seems to me that COMP is a much stronger claim than MUH, despite being smaller.OK.(MUH being mostly: restrict modal realism to mathematical realism: my structure admits a consistent mathematical description, thus by Occam, all possible consistent descriptions exist. It does beg the question of the consistency of the multiverse can be considered a consistent object which can be part of 'all' the consistent universes or not, creating a problem similar to Russel's Paradox. This might be solvable by assuming less (such as COMP), or using some privileged meta-logical level to talk about theories (sort of like one does in meta-mathematics).OK.

OK.

I stop here to read the rest when I have more time. Oh, I will answer some questions at the end.[big snip, to comment later]

`Thanks for replying. I was worried my post was too big and few people`

`will bother reading it due to size. I hope to read your opinion on the`

`viability of the experiment I presented in my original post.`

To Bruno Marchal: Do you plan on ever publishing your thesis in english? My french is a bit rusty and it would take a rather long time to walk through it, however I did read the SANE and CC&Q papers, as well as a few others.I think that SANE is enough, although some people pushes me to submit to some more public journal. It is not yet clear if physicist or logician will understand. Physicists asks the good questions but don't have the logical tools. Logicians have the right tools, but are not really interested in the applied question. By tradition modern logicians despise their philosophical origin. Some personal contingent problems slow me down, too. Don't want to bore you with this.

`If it's sufficient, I'll just have to read the right books to better`

`understand AUDA, as it is now, I understood some parts, but also had`

`trouble connecting some ideas in the AUDA.`

Maybe I should write a book. There is, on my url, a long version of the thesis in french: "conscience et mécanisme", with all details, but then it is 700 pages long, and even there, non-logician does not grasp the logic. It is a pity but such kind of work reveals the abyssal gap between logicians and physicists, and the Penrose misunderstanding of Gödel's theorem has frightened the physicists to even take any look further. To defend the thesis it took me more time to explain elementary logic and computer science than philosophy of mind.

`A book would surely appeal to a larger audience, but a paper which only`

`mentions the required reading could also be enough, although in the`

`latter case fewer people would be willing to spend the time to`

`understand it.`

I really hope to better understand AUDA in the future, especially the parts about the self-referential machine.I can explain online if you ask the questions.

`I'll ask if I still don't understand it after I finish reading Boolos'`

`books.`

If one takes seriously the idea of (undefinable) truth, it might indeed lead to ascribing some form of consciousness to Peano Arithmetic and other such formal systems which happen to be consistent.OK, nice. Note that arithmetical truth is not consciousness. It is "bigger". Consciousness of a machine will be a conjunctive link between the machine and arithmetical truth. (Bp & p). You might take a look on the Plotinus paper, which redoes AUDA in the form of an arithmetical interpretation of Plotinus. It was an accepted paper at the CiE 2009. I will perhaps submit a paper at the next CiE.

What is just 'p', then?

`I've read the Plotinus paper not that long ago, although I did miss some`

`details in its second part, just like with AUDA, will re-read it again`

`once I'm a bit more confident in my modal logic.`

The only problems with this are questions about the nature of its consciousness, it seems utterly unknowable, I'm not sure it's even possible find an answer to this using methods one could use for finding the answer to 'what qualia' would you experience if you added some new sense to your (or a copies') brain (or emulation) and thus your consciousness, or gradual structural changes to attain some particular desired form of consciousness (this assumes a digital mechanist substitution and that self-modifiability is possible). I'm not even sure if one can assign such consciousness to PA without it being embedded in some form of time, and if it would have some form of consciousness, I would expect it to be very different from ours.In all my current publication, I talk like if consciousness needs some form of "time" (not necessarily physical, it could be the natural numbers order). I have usually followed Brouwer for the intuition that consciousness and time are deeply related, but I am less sure now. Since I have smoked salvia divinorum, I have begun to doubt the necessity of that association. It looks like we can be conscious, and somehow be completely out of time. Of course I do not recommend smoking salvia. Yet, if it is legal for you to do so, it is an interesting experience of consciousness. Just be responsible. Note that a lot of people reacts to salvia like they react to the comp reversal: they don't want to know.

`It seems that at least for now, some drugs are one of the very few ways`

`one can get unusual 1p experiences (dreams would be another easily`

`accessible way).`

`I have a hard time imagining what a 'timeless' 1p experience would be,`

`but maybe one day I'll find out. The strange thing about such an`

`experience is that it has a start and an end, so it can't really be`

`timeless, or can it?`

`As for not wanting to know? Is that just fear of the unknown or`

`preferring ignorance about certain things that scare them?`

In a way, I can see how PA could contain truth to which either our consciousness supervenes or merely /is/, but what it would be like for PA to be consciousness itself?I think you should more clearly distinguish PA from arithmetical truth. PA is a little (Löbian) theory. Arithmetical truth (even from a pure 3p view) is a non computably enumerable set of truth. It is beyond all machines. The link between consciousness and truth makes consciousness inherit its ineffability or non definability (like for knowledge). To be like PA might be like to be a just born baby, or to be like you after a strong amnesia, perhaps like after a hit of strong salvia, when you don't remember anything, not even what time or space is. But I hardly understand myself what I say here. Salvia is very amazing with that respect.

`Instead of PA, should have I said 'standard interpretation of`

`arithmetic', or its standard model?`

At least I have trouble imagining the continuity or nature of that consciousness, but I'm even more curious how PA would get to find out more about itself, self-referentially.This should not be too much difficult. PA has deep (even maximal in some sense) introspective abilities. Remember that the notion of proof, definable in or by PA, does use a notion of time, through the steps of a proof. PA can assert statements on the length of proofs, compare them, etc.

`Very interesting way to consider time. What about those unreachable`

`truths (due to incompleteness theorem, or that it might take an infinite`

`amount of "steps" to reach them)? In a way those would be p, but not`

`Bp&p, if I understand your terminology right, so would that mean that PA`

`would never be 'conscious' of the unreachable truths? What if they seem`

`verifiable (such as tests keep confirming them, but we can never know`

`for sure because the number of steps to confirm all of them would be`

`infinite; would COMP be one such example, or something like a variant of`

`Riemann's hypothesis (of course, if one assumes a stronger formal`

`system, they might be able to assert more truth, but they increase their`

`risk of becoming inconsistent))?`

It seems rather hard to fathom, especially given that PA's set of truth sentences is infinite and I find the notion of infinite and unchanging mind rather troublesome (seems rather much like a certain theological idea of ``God'''s mind, for certain definitions of theology),Again, PA is a little formal machine. It can, like all machine, only scratch the surface of arithmetical truth. In the arithmetical interpretation of Plotinus, Arithmetical truth plays the role of "God" (or the ONE), and I have no clue if that God is conscious or not. It is not a Löbian entity.

`I think I understand my error here (as with my response to the previous`

`part): I should not consider PA equivalent with arithmetical truth or`

`the standard model of arithmetic. Regarding the not a Lobian entity`

`part? Is that because it is already 'complete' and thus it need not talk`

`about the provability of its sentences?`

On another note, what about non-standard models?

but I like the idea of PA having the potential to be conscious (of course, any history of ours is unchangeable in Platonia, but from the 1p there is always indeterminacy and consciousness and continuity).In a sense, you might be PA yourself, except that you are more full of supplementary contingent memories. You might get the consciousness of PA in dreams, or in slow (non REM) sleep every night. It might even be the consciousness of RA (PA without the induction axioms), that is the consciousness common to all (Turing) universal entities. I am not sure. Open and hard problem.

`I can follow proofs in made in PA, and I suppose most people should be`

`able to.`

`I'm not entirely sure what PA's consciousness be like, probably because`

`anything that I can talk about has to be in my memories, and (non REM)`

`sleep doesn't seem to give me any memories (unlike REM sleep dreams`

`which can be quite memorable).`

Offtopic: Does anyone have a complete downloadable archive of this mailing list, besides the web-accessible google groups or nabble one? Google groups seems to badly group posts together and generates some duplicates for older posts.I agree. Google groups are not practical. The first old archive were very nice (Escribe); but like with all software, archiving get worst with time. nabble is already better, and I don't know if there are other one. Note also that the everything list, maintained by Wei Dai, is a list lasting since a long time, so that the total archive must be rather huge. Thanks to Wei Dai to maintain the list, despite the ASSA people (Hal Finney, Wei Dai in some post, Schmidhuber, ...) seems to have quit after losing the argument with the RSSA people. Well, to be sure Russell Standish still use ASSA, it seems to me, and I have always defended the idea that ASSA is indeed not completely non sensical, although it concerns more the geography than the physics, in the comp frame.

`If someone from those early times still has the posts, it might be nice`

`if they decided to post an archive (such as a mailer spool). For large`

`Usenet groups, it's not unusual for people to have personal archives,`

`even from 1980's and earlier.`

`I had no idea that was the reason I don't seem them post anymore(when I`

`was looking at older posts, I saw they used to post here).`

`As for losing the "RSSA vs ASSA" debate, what was the conclusive`

`argument that tilts the favor toward RSSA (if it's too long, linking to`

`the thread will do)? In my personal opinion, I used to initially`

`consider ASSA as generally true, because assuming continuity of`

`consciousness is a stronger hypothesis, despite being 'felt' from the`

`inside, but then I realized that if I'm assuming consciousness/mind, I`

`might as well assume continuity as well (from the perspective of the`

`observer), otherwise I can't reason about my future expectations.`

I will give you some references in case you want pursue the study of AUDA. Like some books by Smullyan, Boolos, Franzen. The Davis book "undecidability", now published by Dover is the bible. It has the basic original paper by Gödel, Church, Turing, Rosser, and Emil Post (the deepest guy, imo). Emil Post has anticipated in the 1920s the whole thing, from Church thesis, Gödel to the ontological reversal. To be sure, he changed his mind on that last one after a discussion with Turing, who was naturalist.

`Sure, I welcome names of good books on the topic, although I'll have to`

`finish my current backlog for now.`

More comments next week. Bruno http://iridia.ulb.ac.be/~marchal/

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