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

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