Bruno Marchal wrote: > > > On 24 Aug 2012, at 12:04, benjayk wrote: > >> But this avoides my point that we can't imagine that levels, context >> and >> ambiguity don't exist, and this is why computational emulation does >> not mean >> that the emulation can substitute the original. > > But here you do a confusion level as I think Jason tries pointing on. > > A similar one to the one made by Searle in the Chinese Room. > > As emulator (computing machine) Robinson Arithmetic can simulate > exactly Peano Arithmetic, even as a prover. So for example Robinson > arithmetic can prove that Peano arithmetic proves the consistency of > Robinson Arithmetic. > But you cannot conclude from that that Robinson Arithmetic can prove > its own consistency. That would contradict Gödel II. When PA uses the > induction axiom, RA might just say "huh", and apply it for the sake of > the emulation without any inner conviction. I agree, so I don't see how I confused the levels. It seems to me you have just stated that Robinson indeed can not substitue Peano Arithmetic, because RAs emulation of PA makes only sense with respect to PA (in cases were PA does a proof that RA can't do). That is, it *needs* PA to make sense, and so we can't ultimately substitute one with the other (just in some relative way, if we are using the result in the right way). It is like the word "apple" cannot really substitute a picture of an apple in general (still less an actual apple), even though in many context we can indeed use the word "apple" instead of using a picture of an apple because we don't want to by shown how it looks, but just know that we talk about apples - but we still need an actual apple or at least a picture to make sense of it.
Bruno Marchal wrote: > > With Church thesis computing is an absolute notion, and all universal > machine computes the same functions, and can compute them in the same > manner as all other machines so that the notion of emulation (of > processes) is also absolute. OK, but Chruch turing thesis is not proven and I don't consider it true, necessarily. I don't consider it false either, I believe it is just a question of what level we think about computation. Also, computation is just absolute relative to other computations, not with respect to other levels and not even with respect to instantion of computations through other computations. Because here instantiation and description of the computation matter - IIIIIIIII+II=IIIIIIIIIII and 9+2=11 describe the same computation, yet they are different for practical purposes (because of a different instantiation) and are not even the same computation if we take a sufficiently long computation to describe what is actually going on (so the computations take instantiation into account in their emulation). Bruno Marchal wrote: > > It is not a big deal, it just mean that my ability to emulate einstein > (cf Hofstadter) does not make me into Einstein. It only makes me able > to converse with Einstein. Apart from the question of whether brains can be emulated at all (due to possible entaglement with their own emulation, I think I will write a post about this later), that is still not necessarily the case. It is only the case if you know how to make sense of the emulation. And I don't see that we can assume that this takes less than being einstein. benjayk -- View this message in context: http://old.nabble.com/Simple-proof-that-our-intelligence-transcends-that-of-computers-tp34330236p34347848.html Sent from the Everything List mailing list archive at Nabble.com. -- You received this message because you are subscribed to the Google Groups "Everything List" group. To post to this group, send email to everything-list@googlegroups.com. To unsubscribe from this group, send email to everything-list+unsubscr...@googlegroups.com. For more options, visit this group at http://groups.google.com/group/everything-list?hl=en.
