On 6 Apr 2017 6:44 p.m., "Bruno Marchal" <[email protected]> wrote:
On 06 Apr 2017, at 12:02, David Nyman wrote: On 6 Apr 2017 8:45 a.m., "Bruno Marchal" <[email protected]> wrote: On 05 Apr 2017, at 22:51, David Nyman wrote: On 5 Apr 2017 7:46 p.m., "Brent Meeker" <[email protected]> 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. 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. 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. 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. It's just that I have insufficient command of the technicalities to satisfy my intuition purely by this means. Hence my "grandmother" versions. Thank you as ever for your helpful responses. 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 [email protected]. To post to this group, send email to [email protected]. 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. 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