On 11/1/2012 11:39 AM, Bruno Marchal wrote:

Enumerate the programs computing functions fro N to N, (or theequivalent notion according to your chosen system). let us callthose functions: phi_0, phi_1, phi_2, ... (the phi_i)Let B be a fixed bijection from N x N to N. So B(x,y) is a number.The number u is universal if phi_u(B(x,y)) = phi_x(y). And theequality means really that either both phi_u(B(x,y)) and phi_x(y)are defined (number) and that they are equal, OR they are bothundefined.In phi_u(B(x,y)) = phi_x(y), x is called the program, and y thedata. u is the computer. u i said to emulate the program (machine,...) x on the input y.OK, but this does not answer my question. What is the ontologicallevel mechanism that distinguishes the u and the x and the y fromeach other?The one you have chosen above. But let continue to use elementaryarithmetic, as everyone learn it in school. So the answer is:elementary arithmetic.

Dear Bruno,'

`If there is no entity to chose the elementary arithmetic, how is it`

`chosen or even defined such that there exist arithmetic statements that`

`can possibly be true or false? We can assume some special Realm or`

`entity does the work of choosing the consistent set of arithmetical`

`statements or, as I suggest, we can consider the totality of all`

`possible physical worlds as the implementers of arithmetic statements`

`and thus their "provers". Possible physical worlds, taken as a single`

`aggregate, is just as timeless and non-located as the Platonic Realm and`

`yet we don't need any special pleading for us to believe in them. ;-)`

`My thinking here follows the reasoning of Jaakko Hintikka. Are you`

`familiar with it? Game theoretic semantics for Proof theory`

`<http://www.hf.uio.no/ifikk/forskning/publikasjoner/tidsskrifter/njpl/vol4no2/gamesem.pdf>`

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