On 6 Apr 2017 8:28 a.m., "Bruno Marchal" <[email protected]> wrote:
On 05 Apr 2017, at 13:47, David Nyman wrote: If Darwinism may be said to have shown how the illusion of design may exist without need of a designer, we have still perhaps lacked an equivalently powerful form of explication that might show how the illusion of creativity could exist without need of invoking a creator. It has been claimed in some quarters that QM might provide such an explanation in that it purportedly allows for "something" to appear where there had previously been "nothing". This view is however open to criticism on the grounds of quibbling about the meaning of the terms employed. It occurs to me however that the thrust of the computationalist explanation, independent of its other putative merits or defects, could be seen as tending in this direction. At least, if it cannot intelligibly be shown how something could arise from nothing, it is rather less puzzling how 0 might be followed by its successors. Indeed it makes little sense to quibble about this at least as an abstract point of departure. And this very point of departure is itself little more than we need to invoke the existence of a maximally-compact intensional widget, the unfolding extension of which, when filtered through the strenuous sieve of first-personal logic, may ultimately give rise to the entire perceptual panoply of concrete creativity. This kernel of creation, in its intensional and extensional forms, is of course what Bruno refers to as the UD and its trace. One might say, aphoristically, that arithmetic might be a maximally lazy creator's way of ensuring the implicit creation of everything without explicitly invoking anything other than one simple expression. And although the creative principle is maximally compressed within this single expression there is no way of discovering its concrete consequences other than inhabiting the infinite spaces of its expansion. Perhaps one could say with only a tinge of hyperbole that this may indeed be the divine route to knowledge. I think I will exchange my bottle of grains of sand for a box with some tinges of hyperbole! I would not say that so easily that the successor relation is creative, but it can be said once we have the + and * laws. When Emil post discovered Gödel's incompleteness (10 years before Gödel) and "Church's thesis" (15 years before Church, Turing, ..), he made the "Penrose-Lucas" mistake (30 years before Lucas, 60 years before Penrose), and concluded that machines cannot think and that << the logical process is essentially creative>> But then, after explaining and defending something as a law, and which was just the first apparition of "Church's thesis", he realizes that it was a mistake, that the machine could make the same reasoning. He wrote: << the following suggestions came up: (a) The conclusion that man is not a machine is invalid. All we can say is that man cannot construct a machine which can do all the thinking he can. To illustrate this point we may note that a kind of machine-man could be constructed who would prove a similar theorem for his mental-acts" >> Note that this is still wrong, and he should have written: "...All we can say is that man cannot construct [provably] a machine which can do all the thinking ...". But the idea of the correction of main Lucas-Penrose error, was there. Like Judson Web will understand, the Gödelian argument against machine is double edged, and flip back once made precise enough. He added, using the expression "creative germ" (taken from Brouwer, I think): << (b) The creative germ, seems not to be capable of being purely presented but can be stated as consisting in constructing ever higher type>> This refer more to the fact that the machine will be able to diagonalize against any formal description of itself, making it in some sense constructively not constructive, and much later, he will invent his notion of creative set of numbers, which much later will be proved equivalent with Turing Universality. One day I can say more on this. A creative set is a recursively enumerable set whose complement is recursively not recursively enumerable: it means that for any RE set in that complement, the machine is able to find an element in the complement and not in that re set, contradicting its pretension of being RE. That gave the "Gödel's theorem in miniature" of his 1944 paper, and which is at the base of Recursion theory. So, that Post's creativity notion is more directly related to incompleteness and to the ability of the machine to know its incompleteness and to overcome it ... mechanically. It is of course highly debatable that this is "real" creativity. In fact, it leads to similar paradox than to the "mechanical" definition of free-will, and admits similar response, which would lead me a bit too far for this morning and so please add the right amount of "tinges of hyperbole" meanwhile (grin). Indeed, when indulging in hyperbole, as with so many things, "the dose maketh the poison". David Best, 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. 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. -- 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.
