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
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
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
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,
Numbers alone may symbolize some fundamental describable matter and
forces but a complete and coherent TOE should include elevated human
consciousness beyond the primitive which in itself requires a
relatively sophisticated language to give meaning to the numbers and
Hmm... You can use numbers to symbolize things, by coding, addresses,
etc. But numbers constitutes a reality per se, more or less captured
(incompletely) by some theories (language, axioms, proof
technics, ...). In this context, that might be important.
Then, you are inferring, that ‘numbers’ can be and perhaps are
Why not. '24 is even', or '24 is the address of my uncle', etc. 24 is
a noun there.
If so, then numbers would be human mental objects that have properties
of both functions and relations.
Again, you don't need humans for that.
Universal numbers exists (provably so in even very little arithmetical
And assuming comp, it is (not so easy) to show that humans mental
state are relative computational states, which means relative numbers
(relative to universal numbers).
If you fix a universal number, each number can play the role of a
partial computable function: x(y) === phi_x(y), with phi_i an
enumeration of all partial computable function (which exists by Church
You are welcome,
Would not any TOE describing the universe appears to require human
sophisticated language using referent nouns, (and conjunctions,
adjectives and verbs etc.) to give meaning to the numbers and their
functions and operations?
With the mechanist assumption, humans and their language will be
described by machine operations, which will corresponds to a
collection of numbers relations (definable with addition and
multiplication). This is not obvious and relies in great part of the
progress of mathematical logic.
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