On 20 Aug, 00:43, Bruno Marchal <marc....domain.name.hidden> wrote:
> On 19 Aug 2009, at 22:59, Flammarion wrote:
>
>
>
>
>
> > On 19 Aug, 15:20, Bruno Marchal <marc....domain.name.hidden> wrote:
> >> On 19 Aug 2009, at 10:36, Flammarion wrote:
>
> >>> On 19 Aug, 01:29, David Nyman <david.ny....domain.name.hidden> 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
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Received on Fri Aug 21 2009 - 00:54:56 PDT