Hi David,

Le 02-sept.-07, à 17:00, David Nyman a écrit : > > On 02/09/07, Bruno Marchal <[EMAIL PROTECTED]> wrote: > >> You could have chosen a better moment because next week I have exams >> and will not be in my office, but the week after I will try to explain >> this. It is necessary to get the UDA, and even more for the AUDA (the >> lobian interview). > > Hi Bruno > > Given your current commitments, I'll continue my reading, and also > thinking about the various issues recently posted. Let's continue the > dialogue the week after the exams. No problem. I hope you don't mind if I give little exercises from time to time. My goal is not to teach logic on the list but only to explain the minimal amount so that I can explain better some result, so that people are not mislead by the vocabulary. It is just OK to ask me for answesr if only for the benefits of the others. It is obvious that comp makes sense only through some COMPuter science ... > > BTW, I've also been intermittently reading Schopenhauer (and Bryan > Magee's book on him) and ISTM that maybe comp is a way to approach the > Kant-Schopenhauer noumenon, at least in the sense that what is below > our substitution level is indiscernible, and hence in that way > inescapably 'noumenal', for us (i.e. it's constitutive of us, but > never an object of our knowledge). It is bit more complex, in the sense that it is not just because those sublevel substitution are indiscernible, but also because we have to bet on a substitution level at the start: so, eventually, the theological part is more related to the G/G* distinction than to the unknowability of what happens below the subtitution level, but again we are anticipating ... Of course those points are related. > Is this in any way similar to what > you mean by machine 'theology', in the sense that its theology (or > noumenon) is equivalent to a machine's beliefs about its ontology > (i.e. its constitutive or 'substitution' level), but that these > beliefs can never be formulated as proofs about its epistemic (or > 'phenomenal') world? It is related. Actually I am not yet sure about the best way to define this 'machine theology'. But the simplest way is to define the theology of machine M by the difference between TRUTH ABOUT the machine M, and what the machine M can prove about herself, once she bets on some substitution level (and once she bets on comp, also). This is a non normative definition of theology. Nobody pretends to know truth about us. But it is a fact that rich lobian machine can *prove* everything about simpler machine theology (at the propositional level). > If so, the content of such a belief would then > be what Wittgenstein, taking his lead from Schopenhauer, claimed > (though he stressed its primacy) that we couldn't make intelligible > statements about (i.e. the mystery *that* the world is); but the > notion of substitution level in comp would in fact give us a way of > speaking about it in a relative way. Yes, again this is related. In "CONSCIENCE ET MECANISME" I make that relation explicit. I take as axiom what I did call the WITTGENSTEIN principle: such content is an x such that, well not only we cannot prove x, but the truth of x entails the non-provability of x. That is, we have both: ~Bx, and x -> ~Bx with "B" meaning "provable by M", in the language of the (ideally correct) machine M. Note that any falsity, like "0 = 1" satisfies the first formula trivially: ~B'0=1' is true for an ideally correct machine. But that very fact is a truth which, by the second incompleteness result, cannot be given by the machine. So x = consistency (x = ~B'0=1') statisfies the second formula: ~B"0=1' -> ~B(~B'0=1'), or ~Bf -> ~B(~Bf). OK? To sum up: theology of machine M = truth about M minus provability by M about M. (Tell me if this makes some sense for you, or nothing, but again we are anticipating). best, Bruno http://iridia.ulb.ac.be/~marchal/ --~--~---------~--~----~------------~-------~--~----~ You received this message because you are subscribed to the Google Groups "Everything List" group. To post to this group, send email to [EMAIL PROTECTED] To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/everything-list?hl=en -~----------~----~----~----~------~----~------~--~---