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On 20 Aug, 00:43, Bruno Marchal <marc...@ulb.ac.be> wrote: > On 19 Aug 2009, at 22:59, Flammarion wrote: > > > > > > > On 19 Aug, 15:20, Bruno Marchal <marc...@ulb.ac.be> wrote: > >> On 19 Aug 2009, at 10:36, Flammarion wrote: > > >>> On 19 Aug, 01:29, David Nyman <david.ny...@gmail.com> wrote: > > >>>> Bruno's position is that only one of the above can be true (i.e. > >>>> CTM > >>>> and PM are incompatible) as shown by UDA-8 (MGA/Olympia). I've > >>>> also > >>>> argued this, in a somewhat different form. Peter's position I > >>>> think > >>>> is that 1) and 2) are both false (or in any case that CTM and PM > >>>> are > >>>> compatible). Hence the validity of UDA-8 - in its strongest form - > >>>> seems central to the current dispute, since it is essentially this > >>>> argument that motivates the appeal to arithmetical realism, the > >>>> topic > >>>> currently generating so much heat. UDA-8 sets out to be provable > >>>> or > >>>> disprovable on purely logical grounds. > > >>>> I for one am unclear on what > >>>> basis it could be attacked as invalid. Can anyone show strong > >>>> grounds > >>>> for this? > > >>> Of course, no argument can validly come to a metaphysical > >>> conclusion-- > >>> in this > >>> case, that matter does not exist --without making a single > >>> metaphysical assumption. > > >> I completely agree with that point, but I don't see the relevance. > >> Comp, alias CTM, > > > CTM does not have Platonism tacked on as a sub-hypothesis > > > Classical Digital mechanism, or Classical Computationalism, or just > > comp, is the conjunction of the following three sub-hypotheses: > > > 1) The yes doctor hypothesis: It is the assumption, in cognitive > > science, that it exists a level of description of my parts (whatever I > > consider myself to be[2]) such that I would not be aware of any > > experiential change in the case where a functionally correct digital > > substitution is done of my parts at that level. We call that level the > > substitution level. More simply said it is the act of faith of those > > willing to say yes to their doctor for an artificial brain or an > > artificial body graft made from some description at some level. We > > will see such a level is unknowable. Note that some amount of folk or > > grand-mother psychology has been implicitly used under the > > granting > > of the notion of (self) awareness[3]. > > > 2) Church Thesis. A modern version is that all digital universal > > machines are equivalent with respect to the class of functions (from > > the natural numbers to the natural numbers) they can compute[4]. It > > can be shown that this entails such machines compute the same > > functions, but also they can compute them in similar ways, i.e. > > following similar algorithm. So, the thesis says, making abstraction > > of computation time, all digital universal machine can simulate each > > other exactly (I will say emulate each other). > > > 3) Arithmetical Realism (AR). This is the assumption that > > arithmetical proposition, like 1+1=2, or Goldbach conjecture, > > or the > > inexistence of a bigger prime, or the statement that some digital > > machine will stop, or any Boolean formula bearing on numbers, are true > > independently of me, you, humanity, the physical universe (if that > > exists), etc. It is a version of Platonism limited at least to > > arithmetical truth. It should not be confused with the much stronger > > Pythagorean form of AR, AR+, which asserts that only natural numbers > > exist together with their nameable relations: all the rest being > > derivative from those relations. > > Thanks for quoting my sane2004 definition of comp, and showing that > indeed platonism is not part of it. "It is a version of Platonism" > Just arithmetical realism without which CT has no meaning at all. The CT thesis requires some mathematical claims to be true. it doesn't require numbers to actually exist > This > should be made clear in the seventh step series thread. > > You told us that you are OK with AR some post ago, but now I have no > more clue at all about what do you assume or not. I may well have subscribed to some truth claims > Get the feeling you have change your mind on AR. You believe that a > proposition like the statement that there is no biggest prime number > has something to do with physics. In which physical theory you prove > that statement, and how? Its truth is not a physical truth. The existence or non-existence asserted is not any kind of real existence > Actually the most you go deep in fundamental physics, the more you > need deep results in number theory. I am not denying nay truths, only the interpretation of backwards-E as actual existence --~--~---------~--~----~------------~-------~--~----~ 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 -~----------~----~----~----~------~----~------~--~---