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. 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. 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