On 01 Nov 2012, at 21:42, Stephen P. King wrote:

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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)) andphi_x(y) are defined (number) and that they are equal, OR theyare both undefined.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 theontological level mechanism that distinguishes the u and the x andthe y from each 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 isit chosen or even defined such that there exist arithmeticstatements that can possibly be true or false?

`Nobody needs to do the choice, as the choice is irrelevant for the`

`truth. If someone choose the combinators, the proof of "1+1= 2" will`

`be very long, and a bit awkward, but the proof of KKK = K, will be`

`very short. If someone chose elementary arithmetic, the proof of 1+1=2`

`will be very short (Liz found it on FOAR), but the proof that KKK = K,`

`will be long and a bit awkward.`

`The fact is that 1+1=2, and KKK=K, are true, independently of the`

`choice of the theory, and indeed independently of the existence of the`

`theories.`

We can assume some special Realm or entity does the work of choosingthe consistent set of arithmetical statements or, as I suggest, wecan consider the totality of all possible physical worlds

`As long as you make your theory clearer, I can't understand what you`

`mean by "physical world", "possible", "totality", etc.`

as the implementers of arithmetic statements and thus their"provers". Possible physical worlds, taken as a single aggregate, isjust as timeless and non-located as the Platonic Realm and yet wedon't need any special pleading for us to believe in them. ;-)

? Bruno

My thinking here follows the reasoning of Jaakko Hintikka. Areyou familiar with it? Game theoretic semantics for Proof theory-- Onward! Stephen --You received this message because you are subscribed to the GoogleGroups "Everything List" group.To post to this group, send email to everything-list@googlegroups.com.To unsubscribe from this group, send email to everything-list+unsubscr...@googlegroups.com.For more options, visit this group at http://groups.google.com/group/everything-list?hl=en.

http://iridia.ulb.ac.be/~marchal/ -- You received this message because you are subscribed to the Google Groups "Everything List" group. To post to this group, send email to everything-list@googlegroups.com. To unsubscribe from this group, send email to everything-list+unsubscr...@googlegroups.com. For more options, visit this group at http://groups.google.com/group/everything-list?hl=en.