On 03 Mar 2011, at 02:54, Pzomby wrote:



On Mar 2, 6:03 am, Bruno Marchal <marc...@ulb.ac.be> wrote:
On 02 Mar 2011, at 05:48, Pzomby wrote:


That is why I limit myself for the TOE to natural numbers and their
addition and multiplication.
The reason is that it is enough, by comp, and nobody (except
perhaps
some philosophers) have any problem with that.

Yes.  A couple of questions from a philosophical point of view:

Language gives meaning to the numbers as in their operations;
functions, units of measurements (kilo, meter, ounce, kelvin etc.).

I am not sure language gives meaning. Language have meaning, but I
think meaning, sense, and reference are more primary.
With the mechanist assumption, meaning sense and references will be
'explained' by what the numbers 'thinks' about that, in the manner of
computer science (which can be seen as a branch of number theory).

Not sure what you mean by “what the numbers ‘thinks’ ”.  Are you
stating that numbers have or represent some type of dispositional
property?

Yes. Not intrinsically. So you cannot say the number 456000109332897
likes the smell of coffee, but it makes sense to say that relatively
to the universal numbers u1, u2, u3, ... the number 456000109332897
likes the smell of coffee. A bit like you could say, relatively to
fortran, the number x computes this or that function.
A key point is that if a number feels something, it does not know
which number 'he' is, and strictly speaking we are confronted to many
vocabulary problems, which I simplifies for not being too much long
and boring. I shoudl say that a number like 456000109332897 might play
the local role of a body of a person which likes the smell of coffee.
But, locally, I identify person and their bodies, knowing that in
fine, the 'real physical body" will comes from a competition among all
universal numbers, or among all the corresponding computational
histories.



What of the opinion that ‘numbers’ themselves (without human
consciousness to perform operations and functions) only represent
instances of matter and forces with their dispositional properties?

Once you have addition and multiplication, you don't need humans to do
the interpretation. Indeed with addition and multiplication, you have
a natural encoding of all interpretation by all universal numbers.
The idea that matter and forces have dispositional properties is
locally true, but we have to extract matter and forces from the more
primitive relation between numbers if we take the comp hypothesis
seriously enough (that is what I argue for, at least, cf UDA, MGA,
AUDA).



If “once you have addition and multiplication, you don't need humans
to do the interpretation” and “the idea that matter and forces have
dispositional properties is locally true, but we have to extract
matter and forces from the more primitive relation between numbers”:
Then, in what describable realm does that ultimately put numbers under
the ‘comp hypothesis’?

At the ultimate ontological bottom, you need a infinite collection of abstract primary objects, having primary elementary relations so that they constitute a universal system (in the sense of Post, Church, Turing, Kleene ...).

My two favorite examples (among an infinity possible) are
1) the numbers (0, s(0), s(s(0)), ...) together with addition and multiplication. This is taught in high school, albeit their Turing universality is not easy at all to demonstrate. In that case, the numbers are put at the bottom. 2) the combinators (K, S, (K K), (K S), (S K), (S S), (K (K K)), (K (S K), ....) Combinators are either K or S or any (X Y) with X and Y being combinators. The basic basic elementary operation are the rule of Elimination and Duplication:

((K x) y) = x
(((S x) y) z) = ((x z)(y z))

It can be shown that with the numbers you can define the combinators, and with the combinators you can define the numbers. If you choose the combinators at the ontological bottom, you get the numbers by theorems, and vice versa. Both the numbers and the combinators are Turing universal, and that makes them enough to emulate the Löbian machines histories, and explain why from their points of view the physical realm is apparent, and sensible.

We could start with a quantum universal system, but then we will lose a criteria for distinguishing the quanta from the qualia (it is not just 'treachery' with respect to the (mind) body problem).

Bruno


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



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