At 9:52 -0700 5/07/2002, Wei Dai wrote: >On Fri, Jul 05, 2002 at 12:05:02PM +0200, Bruno Marchal wrote: >> But from the point of view of the *conscious* observer there is >> an intrinsical ignorance (for sound machine) about *which* histories >> he/it/she/they participate, and the uda thougth experiment shows that in >> some sense we belong to all, but we differentiate along consistent >>many path. >> We face a measure problem. Actually we face two measure problems, due to >> the 1/3 distinction. > >Here is something basic in your ideas which I've never understood. What >does "conscious observer" have to do with "sound machine"? I understand >that an observer can be considered as a machine, but how can an observer >be sound or not sound? Soundness as far as I understand it applies to an >axiomatic theory, that is, the theory is sound if you can't deduce "false" >from its axioms. Now if you have a machine that enumerates theorems of an >axiomatic theory, maybe you can say that it's sound if the theory itself >is sound. But obviously an observer is not a theorem producing machine, so >what does it mean for an observer to be a sound machine?
If you cannot deduce false from a theory, the theory is said consistent. Soundness is a more general semantical notion which implies consistency, but the reverse does not hold in general. Ah! I see you corrected yourself so I will not insist. The relation between "conscious observer" and "sound observer" is based on the fact that (motivated by the uda which shows that a UTM which introspect itself should find the "physical laws") I purposefully limit myself in interviewing sound UTM. By comp, conscious observer are machine, and it is just more in line with the comp hyp to ask sound UTM. Of course those UTM are seen as producing arithmetical propositions (theorems). I suppose those machine are capable of proving enough theorems in arithmetic. Those machines are extended UTM. In fact in my thesis I just say that I interrogate LOBIAN machine, which have just the sufficient amount introspective and provability capacities to be able to describe the emerging "physical laws" in their language (this gives the Z logics ...). The idea that Godel's theorem applies to machine has been used by J.R. Lucas and Roger Penrose, for arguing that we are not machine. This is well know and everybody knows the argument is wrong. Even Penrose corrects it in his second book. Godel's incompleteness theorem for (proving) machines just say that a machine cannot prove to be any "particular" machine. A machine cannot knows its own program code (but can bet on it). Search perhaps the list archive for "benaceraff" which is the first guy who has undertand this point. Or, please, insist for better explanation from me! In a nutshell, just remember that I limit my machine's interviews to machines which beliefs (= propositions they just print out!) are sound and closed for usual rules of formal arithmetic. With comp it applies to us, *as far* as we are sound, in our "3-person scientific" communcations. More psychological logics will be account for by the intensional (modal) variants of the provability logic. I will probably say a little more in my answer of your other post later. Bruno