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 (exceptperhapssome 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).`

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 their operations.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 ‘nouns’?

`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`

`theories).`

`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`

`thesis).`

Thanks

You are welcome, Bruno

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. Bruno

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