On 7 Apr 2017 11:22 p.m., "Bruno Marchal" <marc...@ulb.ac.be> wrote:
On 07 Apr 2017, at 14:21, David Nyman wrote: On 7 April 2017 at 11:24, Bruno Marchal <marc...@ulb.ac.be> wrote: > > On 07 Apr 2017, at 00:11, David Nyman wrote: > > > > On 6 Apr 2017 6:44 p.m., "Bruno Marchal" <marc...@ulb.ac.be> wrote: > > > On 06 Apr 2017, at 12:02, David Nyman wrote: > > > > On 6 Apr 2017 8:45 a.m., "Bruno Marchal" <marc...@ulb.ac.be> wrote: > > > On 05 Apr 2017, at 22:51, David Nyman wrote: > > > > On 5 Apr 2017 7:46 p.m., "Brent Meeker" <meeke...@verizon.net> wrote: > > > > On 4/5/2017 1:54 AM, Bruno Marchal wrote: > > > On 04 Apr 2017, at 16:47, David Nyman wrote: > > I've been thinking about the Lucas/Penrose view of the purported > limitations of computation as the basis for human thought. I know that > Bruno has given a technical refutation of this position, but I'm > insufficiently competent in the relevant areas for this to be intuitively > convincing for me. So I've been musing on a more personally intuitive > explication, perhaps along the following lines. > > The mis-step on the part of L/P, ISTM, is that they fail to distinguish > between categorically distinct 3p and 1p logics which, properly understood, > should in fact be seen as the stock-in-trade of computationalism. The > limitation they point to is inherent in incompleteness - i.e. the fact that > there are more (implied) truths than proofs within the scope of any > consistent (1p) formal system of sufficient power. L/P point out that > despite this we humans can 'see' the missing truths, despite the lack of a > formal proof, and hence it must follow that we have access to some > non-algorithmic method inaccessible to computation. What I think they're > missing here - because they're considering the *extrinsic or external* (3p) > logic to be exclusively definitive of what they mean by computation - is > the significance in this regard of the *intrinsic or internal* (1p) logic. > This is what Bruno summarises as Bp and p, or true, justified belief, in > terms of which perceptual objects are indeed directly 'seen' or > apprehended. Hence a computational subject will have access not only to > formal proof (3p) but also to direct perceptual apprehension (1p). It is > this latter which then constitutes the 'seeing' of the truth that > (literally) transcends the capabilities of the 3p system considered in > isolation. > > > I don't think so. It is not direct perceptual "seeing the truth"; it is > an inference in language and depends on language. The fallacy of L/P is > they assume you can know what machine you are and therefore you can "see" > the truth of your Godel sentence, but in fact you don't know what > algorithmic machine you are. > > > That's an interesting point also, but I'm not sure you've quite taken my > meaning. I'm specifically making use of Tarski's criterion of truth as > correspondence with the facts. When considering matters in the > first-person, the "facts" in question are in the first instance perceptual > and hence as such directly apprehended. Hence we have access to a second > means of judging truth, in this specific sense, over and above the > restrictions of any purely algorithmic procedure. In other words, we are > able directly to apprehend or "see" a correspondence *in concrete > perceptual terms* of an assertion with facts to which it purports to refer. > And indeed that's exactly how we are able to make the relevant distinction: > i.e. between working through a formal procedure, which we are equally able > to do, and at the same time grasping a directly perceptible correspondence > that eludes the restrictions of that procedure. The linguistic part comes > later in justifying our judgement (to another or for that matter to > ourselves) post hoc. > > > Yes, that is what I said, but you put it in a much more better way than > me! Consciousness is in the truth, or in its "direct perception through > sense". Note that happens in dreams too, where the cortex will build the > []p, and the stem is bringing the "p", which sometimes can be random > letting the [] in need of some imagination (dream weirdness). > > > Actually it might really have been more accurate to have said that, rather > than it being a second means, our *primary* means of judging truth is by > direct apprehension of perceptual correspondence. Algorithmic proof is > surely secondary to this. > > > It is secondary, like the brain is secondary to consciousness. > > > Yes, I think I grasp that subtlety, because of the relation between the > two logics encapsulated in Bp and p. However, I was referring here in > particular to formal analysis as actually performed within an individual > first-person perspective, being inevitability secondary to primary > apprehension within that perspective. > > > > Yes. I ask myself if you are not tempted by founding everything from the > 1p view. > Well, I was certainly much more open to this temptation when we first began our discussions (was it really 10 years ago?!). But you have persuaded me - or more accurately helped me to persuade myself - that this would be merely begging the question for which we seek an explanation. However, that isn't really what I meant by my comment. I was simply saying that pragmatically formal analysis is only ever performed in the framework of some 1p perspective, so it is secondary in that purely procedural sense. OK. In fact the first person is "attached" to an infinite of procedural senses, which differentiates. The "physical" is the relatively and locally more probable among the one making sense. However, on the more general point you raise, where comp has been particularly illuminating for me is the way it can provide a principled derivation of the logic of self-referential subjectivity from the basis of a purely objective, abstract ontology. In many quarters this has been thought impossible. Furthermore, this subjectivity opens up a logical space in which we can for the first time make sense of the appearance of "concrete" reality, as distinct from any of its hypothesised abstract precursors, in terms of direct perceptual apprehension. This is what permits us to understand properly a notion of intrinsic or internal, which is otherwise a genuine mystery on the basis of an entirely extrinsically-characterised physical mechanism. OK. Trouble is, when the latter is accepted more or less uncritically, as it tends to be, we can all too easily be led into the absurdities of outright denialism of the subjective on the one hand, or frank incoherence about the supposedly "intrinsic" panpsychic nature of primitive matter, on the other. It is difficult to decide which of these two polarities is the more comprehensively misleading, but either way they have tended to generate a great deal more heat than light. In the final analysis it is surely quite useless to think of "looking inside" physical objects for the locus of consciousness because matter, as reductively and exhaustively characterised by an extrinsically-specified mathematical physics, simply *cannot have any inside*. Nor genuine outside. They are more like map of the future. Electron orbital is a map shaping where electron can be found in the neighborhood of histories. As I remarked before, it is as if consciousness were concealed from the outside by a two-part public/private encryption scheme. Whereas the public part is in principle entirely extrinsically inspectable the decryption can be completed only in terms of the private perspective of *the system in question*. This then inevitably entails that decrypted messages of this kind must be inter-subjectively incommunicable despite the ultimate irony that they amount to the entirety of inter-subjectively "shareable" concrete reality. It is of course in this sense also that the brain is secondary to consciousness: i.e. that self-referential perceptual apprehension is the filter through which a concrete reality, with all its brains and bodies, is enabled in the first place to emerge (and I do mean emerge in a strong sense). That primary "grasp on reality" is what enables any subsequent abstract analysis in terms of a reductive "bottom up" physical mechanism playing the role of a locally-dominating computational mechanism (or IOW what you have termed the reversal of physics and machine psychology). OK. That is it. It would be truly remarkable if this analysis could be shown to rely on nothing more than the ontology of 0 and its successors with the combinatorics of addition and multiplication. But of course this is strictly implied by computationalism and cannot therefore be avoided, on pain of abandoning the comp hypothesis. Yes, and here comes the work of Gödel and followers. The set of solutions of just one degree 4 diophantine polynomial equation is already enough for the base level. But any other universal system will do. By making consciousness invariant for a recursive permutation at some level of the brain description, we make physics invariant for the choice of the "first" or "basic" universal system used to describe the whole things. It is just more natural to believe that 2+2 is 4 independently of us than to believe that (CAR '(A B C)) = A, like in Lisp, but arithmetic "run" all lisp program like Lisp notion of truth run all arithmetical computational relations. Then the first person points of view statistics should be based only on Löbianity, which is already machine independent. It is useless to seek to found comp on a primitive physical ontology because such an ontology need result in neither subjectivity itself nor a fortiori the entire hypothesis of a concrete "physical" reality, which can (or should) be understood to be an inter-subjective perceptual projection. It is difficult to say the least to see how either consciousness or its concomitant perceptual accompaniments might be relevant to the continuing evolution of the wave-function, or for that matter any alternative hypothetical characterisation of a fully-reducible "bottom up all the way down" primitive physics. We need math to compute the limit, or limits, and test the hypothesis. If it miss key physical apparent features, it will be tempting to add oracles, or to believe we are failed by daemons (or malevolent descendant). It is about the same if we find serious discrepancies, ... all this can help to measure a sort of degree of non-computationalism, like if the divine could invite itself to the lower plane after all. But there is no sign of this, except for the random oracle, and that is a good sign, as it makes us more free, I think. But strictly speaking, the limit can reserve surprises, especially near death, or just in sleep. We know few things. Science has not yet reawaken. Taboos persist. They do, they do. But I must make haste before the witching hour to a crossroads, there to bury a toad. Yours in hope of reawakening. David Bruno David > Note that this can be done, but is technically much more difficult. You > would need to formalize "provability" in something like Heyting Arithmetic > (PA without excluded middle). Albert Visser has studied this, but it is > more difficult (no truth table in intuitionist logic, so the propositional > basic logic is already more complex). You will need some formula like > ([](~~[]A -> []A) -> [][]A). in Intuitionist logic ~~A does not imply A. > > An interesting question would be in this context: can we get all this from > S4Grz. I think we should, but that is an open problem, like the > intuitionist Church thesis, or close constructive principle. > > I understand your motivation for this. I prefer to stay in the classical > framework mainly for pedagogical reason: the basic logics are better known. > > > > > > > > This is a bit like the egg and the chicken. p does precede logically []p > (the representational or algorithmic). Yet the senses are useful only if we > can re-enact the experience. You can see "p" as the fact (like the true > fact that it rains, blurred with some representation of that fact), and []p > as the building of a theory with the axiom "it rains", which needs to be > represented in some way that the entity can re-enact the experience that it > rains when needed, like when looking for an umbrella in a room without > windows (so that you need to remember that it rains all along). > > p comes first, and like Everett you can identify it with the first > perceptual judgment (to be sure that will need more basic "theory" already > in the brain, so we might add nuances on the perceptual p, (but here the > theories are trivial, like accepting that the needle is on 4 when it is on > 4) in between the truth of p and the truth of the perceptual experience. > Then []p is more for a long term memory, building into the subject his/her > conception/theory predicting/anticipating/extrapolating/explaining the > probable neighborhood. > > So, as far as reality/truth/the-one is concerned, p is more primary. But > concerning the subject I would say that both p and []p are needed, and both > []p and []p & p are needed to, and collaborate together though some > (arithmetical) corpus callosum. Going from []p & p to p is quite an > out-of-body experience! > > > > It can only be subsequent to apprehension of primary facts (which exhaust > in effect our grasp on concrete inter-subjective reality) that we are able > to deploy algorithmic methods. These latter are applicable not to the > concrete perceptual world directly but rather to its formally abstracted > "view from nowhere" idealisation. > > > Hmm.. the "[]" is really the body/brain. It is the local representation of > you in the languages of, say, nucleus and electromagnetic interaction > (chemistry). Some would say that it is the "p" which is in the view of > nowhere. It is delicate because it depends from which mode we tackle the > distinction. Eventally we know that G* knows that there is no difference: > all the points of view points on the same reality (the sigma1 truth) > > > In that case, perhaps p is the view from everywhere. > > > p is the view from all points of view, but that is seen only from the > "divine intellect" view. I would say here that it is the view from > everywhere, when see from the view of nowhere. But I guess we get closer > and closer to "1004". Of course, subtle philosophy requires eventually to > add nuances in the formal apparatus. > > > > But again, my reference was to the actual practice of algorithmic > reasoning which I'm contending leads to the L/P mis-step because of the > implicit assumption that its application is entirely restricted to the 3p > view from nowhere. > > > ... up to invoking their feeling that they know their own correctness, or > that mechanism asks for knowing which machine we are. But this cannot be > known by machine. Of course would Penrose be able to prove that he is a > correct entity, then his proof on non-mechanism would be correct. But he > has not done that, and indeed, it is hard to imagine how that would be > possible. self-correctness requires some faith in a reality. His proof > relies on an intuition. But his idea that machine cannot have a similar > intuition relies on the fact that for simple machine like PA we can be > confident that []p = []p & p. PA cannot know this, but no machine can know > this about themselves. Charitably, Penrose proves in this case, that he is > not PA. But of course we knew that beforehand. > > > > > but G* knows that the subject, and in any of its mode, is unable to grasp > the G* truth, making it trapped in the illusion (of life, physics, ...). > That illusion is "important" to survive on the terrestrial plane. Now in > that plane "important" is a difficult matter by itself (the meaning of life > question). > > > > > > Hence it is in the last analysis hardly surprising that this secondary > abstraction > > > It is the little ego. We might need to get rid of it to get enlightenment, > but what is enlightenment for if we cannot come back and help the others, > and this needs the little ego, and its body/brain/machine so that it can > manifest its knowledge/consciousness with respect to its peers. > Nobody needs a body, but everyone needs a body to manifest itself to > anything else which is not her/him. > > Now what I just said, applies to itself. The "[]p" would grasp noting if > it was not accompanied by its semantic p. Somehow, the meaning would get > trivial at the deterministic level. Why did Deep Blue win? Because of this > boolean net configuration and the laws of NAND? Why did Adolph killed all > the kids? Because Adolph got a quantum body following the quantum laws, > etc. That lack of meaning is lifted to all level of 3p description, but the > "truth" of the elementary relation lift the meaning of the higher level > description. For the sigma_1 we get the "enlightenment: "p <-> []p", a > sigma_1 proposition is true (nobody knows what that really means) if and > only if the machine can prove (syntactical procedure, arithmetical > relation). the machine does not fall in the blaphesm, because despite she > knows she is sigma1 complete (Universal, in the sense of Church, Turing), > that is: she knows p -> []p (for p sigma1-arithmetical, shape "it-exists x > (s(x) + s(x) = s(s(x))), she does not know []p -> p, even for p sigma1. > Indeed she does not know that [](0=1) -> (0=1), because that would be > knowing ~(0=1), by propositional calculus, and she would proves its own > consistency. That can be shown to be true and knowable, but still not > communicable, because the "[]p" has no name/description for "[]p & p". It > leads to the idea that in the ideally correct machine the corpus callosum > should be a one way road, which I think is not the case, or some hemisphere > lies, leading to self-conspiracy theories ... Well, I stop here. > > > > fails to bridge the gap to all the truths primarily accessible in terms of > direct perceptual correspondence. > > > > It fails, and the part of us which bridge the gap stay mute, or become > inconsistent. > > Scientific theology is the part of science which study the part of truth > which extends science. With computationalism it is computer's science minus > computer's computer science. > > From the non experiential to the non memorizable, ... to the not > describable, to the non justifiable, to the infeasible, to the feasible, > eventually to the feasible respecting the deadline. > > Even for simple machine, the full theology is quite "out of science", but > there is a non trivial core common to all arithmetically correct machine. > Propositional theology, or meta-theology, is decidable. It is platonist > only by accepting that a sigma1 sentence is either true, or false, which is > equivalent with saying that a program stop or does not stop. > > The amazing thing with computationalism, and thanks to incompleteness, is > that the proposition that truth extends science is part of that common core > of provable "scientific" statement, in the conditional form, like <>t -> > ~[]<>t. If I am consistent (if that belongs to truth) then I can't > prove/justify/communicate-rationally that I am consistent. Of course, in > the arithmetical interpretation of [], this is the second incompleteness > theorem. > > Hoping not boring you too much with the technicalities, but it is the > interest of computationalism that the study is a part of mathematics. > > > No indeed, I appreciate the rigour that you add. I always read with > interest and do my best to understand. > > > Thanks for telling me. > > > It's just that I have insufficient command of the technicalities to > satisfy my intuition purely by this means. > > > It is useful when we are on the highly counter-intuitive fringe of > computationalism. To develop an intuition there is like to develop a taste > for the bizarre. The best introduction is probably "Alice in Wonderland". > As Liz said: we must train ourself to believe at least five impossible > things before breakfast! > > > > > Hence my "grandmother" versions. Thank you as ever for your helpful > responses. > > > You are welcome. I thank you for giving me the opportunity to try to > handle interesting subtle points in the available formalism. > > Computationalism is the diplomate which invites the mystics and the > rationalists at the same table. Not always easy those days. But when we > look at the antic greeks, we can see that it all started by that form of > open-mindness, in between the 1p mysticism/experience and the > 3p-description-reasoning/sharing-understanding. > > Bruno > > > > David > > > Bruno > > > > > David > > > A remark on entheogen: > > I think that with cannabis, you blur the "p" in "[]p & p", and > with salvia you blur the "[]p" in "[]p & p". (with the surprise that you > still remain as a sort of conscious person). > > Oops I have to go. Before I fall in the machine's blasphem ... More on > this later most probably. > > Bruno > > > > > David > > > > Brent > > > > Exact. And going a little further, that is what the Gödel-Löbian machine > already says (or say out of time and space). > > > > > If the foregoing makes sense, it may also give a useful clue in the debate > over intuitionism versus Platonism in mathematics. Indeed, perceptual > mathematics (as we might term it) - i.e. the mathematics we derive from the > study of the relations obtaining between objects in our perceptual reality > - may well be "considered to be purely the result of the constructive > mental activity of humans" (Wikipedia). However, under computationalism, > this very 'perceptual mathematics' can itself be shown to be the > consequence of a deeper, underlying Platonist mathematics (if we may so > term the bare assumption of the sufficiency of arithmetic for computation > and its implications). > > Is this intelligible? > > > I have no critics. Your point is done by the machine through a theorem of > Grzegorczyk on one par: the fact that S4Grz, like S4, formalises > Intutionistic logic, and of Boolos and Goldblatt on another par: the fact > that the formula Grz *has to* be added to S4 to get the arithmetical > completeness of the "[]p & p". Note that this makes the intuitionist into a > temporal logic, and attach duration to consciousness, like with Bergson and > Brouwer himself. > > Eventually it is amazing and counter-intuitive, because it ascribes > consciousness to all universal numbers, probably the same before they get > the differentiation along the infinitely many computations supporting them. > Needless to say that such consciousness is in a highly dissociated state at > the start, a bit like after consuming some salvia perhaps (!). > > Your analysis can be extended on the intelligible and sensible > (neo)Platonist theory of matter, but with p restricted to the sigma_1 > sentences (which describe in arithmetic the universal dovetailing), with or > without the adding of "<>t", which typically transform the notion of > "belief []p" or "knowledge []p & p" into notion of "probabilities". > > In summary > > p (truth, god, the one) > []p (rational belief) > []p & p (knowledge, intuitionist subject) > []p & <>t (probability, quantum logic) > []p & <>t & p (intuitionist probability, quale logic). > > The quanta themselves appear to be qualia. In fact a quanta is a sharable > qualia by two universal number when supported by a same universal number. > That can be used to show that the "many worlds" of the physicists (Everett > theory) confirms Computationalism and protect it from solipsism. The > physical is indeed first person PLURAL, and its sharableness comes from the > linearity of the tensor product. At each instant we all enter the same > replication machinery. The Z logics justifies the linearity and > reversibility, but not clearly enough to extract the unitarity and use > Gleason to make the measure unique. But this is for the next generation, > hopefully (as many seem to prefer the obscurantist statu quo alas). > > Bruno > > > > > David > > -- > 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. > Visit this group at https://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. > Visit this group at https://groups.google.com/group/everything-list. > For more options, visit https://groups.google.com/d/optout. > > > > -- > 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. > Visit this group at https://groups.google.com/group/everything-list. > For more options, visit https://groups.google.com/d/optout. > > > > -- > 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. > Visit this group at https://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. > Visit this group at https://groups.google.com/group/everything-list. > For more options, visit https://groups.google.com/d/optout. > > > > -- > 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. > Visit this group at https://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. > Visit this group at https://groups.google.com/group/everything-list. > For more options, visit https://groups.google.com/d/optout. > > > > -- > 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. > Visit this group at https://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. > Visit this group at https://groups.google.com/group/everything-list. > For more options, visit https://groups.google.com/d/optout. > -- You received this message because you are subscribed to the Google Groups "Everything List" group. 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