On Mar 3, 2:07 am, Bruno Marchal <marc...@ulb.ac.be> wrote:
> 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



I believe, I somewhat follow (in general) what you are stating, but
the question remains as to the realm that the primitive or fundamental
numbers exist in, if, in fact, they are at an ontological bottom.  If
numbers are not a part of matter, forces and human consciousness where
do they exist?  Perhaps it could be considered that quanta and qualia,
along with their obvious properties, have, and exude and perhaps
metaphorically contain the property of ‘number’.  I think “number” is
a property of a ‘set’.

My brief opinion(s):

As well as numbers having dispositional and computational properties,
numbers remain symbolic or representative of their own dispositional,
relational and computational characteristics or attributes.  A TOE
will describe in detail what numbers, mathematics and languages
represent (or what the computations represent).  An accurate
description of the induction of universals (what numbers represent)
into particulars (matter, personhood etc.) would be a result.

‘Numbers’ (along with comp) appear to…like languages, words,
mathematical symbols and notations….have a trait of ‘being’
representational of forces and matter.

If universal numbers along with their dispositions and relations are
at the ontological bottom, then the process, (maybe evolvement or
induction) to matter, forces, body and mind, consciousness and
personhood should be describable in a coherent way.

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