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.
Just arithmetical realism without which CT has no meaning at all. 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.
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?

Actually the most you go deep in fundamental physics, the more you  
need deep results in number theory. The most amazing example is the  
evaluation of the mass of the photon in string theory. You get that  
the mass of the photon is given by two terms. The first one can be  
evaluated into -1/12, the second one get evaluated into  
1+2+3+4+5+6+7+ ...
Again an infinity, but lucklily enough number theorist knew that on  
the complex plane there is a sense to say, like Ramanujan found by  
himself in India, that the infinite sum 1+2+3+4+5+6+7+ ... is actually  
equal to -1/12, which gives zero for the mass of the photon, as  
expected.
1+2+3+4+5+6+7+ ... is zeta(-1) which analytical definition is defined  
on -1 and equal to -1/12.


Bruno




http://iridia.ulb.ac.be/~marchal/




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