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.
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