On 03 Mar 2011, at 19:44, Pzomby wrote:
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
addition and multiplication.
The reason is that it is enough, by comp, and nobody (except
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
I am not sure language gives meaning. Language have meaning,
think meaning, sense, and reference are more primary.
With the mechanist assumption, meaning sense and references
'explained' by what the numbers 'thinks' about that, in the
computer science (which can be seen as a branch of number
Not sure what you mean by “what the numbers ‘thinks’ ”. Are you
stating that numbers have or represent some type of dispositional
Yes. Not intrinsically. So you cannot say the number
likes the smell of coffee, but it makes sense to say that
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
vocabulary problems, which I simplifies for not being too much long
and boring. I shoudl say that a number like 456000109332897 might
the local role of a body of a person which likes the smell of
But, locally, I identify person and their bodies, knowing that in
fine, the 'real physical body" will comes from a competition among
universal numbers, or among all the corresponding computational
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
Once you have addition and multiplication, you don't need humans to
the interpretation. Indeed with addition and multiplication, you
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
primitive relation between numbers if we take the comp hypothesis
seriously enough (that is what I argue for, at least, cf UDA, MGA,
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
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
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
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).
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 were existing *in* something, they would not constitute an
You can take sets in place of numbers, and then the numbers exists
*in* models of set theories. or you can take the combinators, and the
number will be special combinators. But then you will ask "and where
the sets are living?", or "Were the combinators are living?". In
particular, the notion of sets is more demanding than he notion of
But it is a category error to ask oneself *where* are the numbers. To
be somewhere has no meaning for a number. Their properties are more
like "to be even", "to be prime", "to be the Gödel number of a piece
of a computation", etc. You can define them by first order formula,
for example "x is even" is given by the formula Ey(x = s(s(0)) * y).
numbers are not a part of matter, forces and human consciousness where
do they exist?
I answered this above. The question "where" does not apply to numbers,
like the question "what does that smell" does not apply to light.
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’.
Numbers can manifest themselves in many ways, and certainly the quanta
are among their most wonderful manifestations. I mean the quantum
quanta! But QM is a wave theory, and waves have a long standing
relationship with number (and music), since at least Pythagorus. But
waves, and quantum quanta are more complex than numbers. Your mind
needs to make sense of them before making sense of the waves and their
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.
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.
Somehow. The fundamentality arrow is roughly like this: NUMBERS =>
UNIVERSAL CONSCIOUSNESS => PHYSICAL LAWS => BIOLOGICAL CONSCIOUSNESS.
A bit like in Neoplatonism.
Now, numbers can be replaced by combinators, fortran programs, lambda
expressions, diophantine polynomials, ... anything (Post-Turing-
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.
I think that is the case and this in a sufficiently precise way as to
be refuted, or not, by nature. I would never have dared to explain
this if QM, without collapse, did not fit so nicely with this
(informally and formally).
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