On 11/2/2012 12:55 PM, Bruno Marchal wrote:

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On 01 Nov 2012, at 21:42, Stephen P. King wrote: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 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 arithmetic statementsthat can possibly be true or false?Nobody needs to do the choice, as the choice is irrelevant for thetruth. If someone choose the combinators, the proof of "1+1= 2" willbe very long, and a bit awkward, but the proof of KKK = K, will bevery short. If someone chose elementary arithmetic, the proof of 1+1=2will 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 thechoice of the theory, and indeed independently of the existence of thetheories.

Dear Bruno,

`No, that cannot be the case since statements do not even exist if`

`the framework or theory that defines them does not exist, therefore`

`there is not 'truth' for a non-exitence entity.`

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 worldsAs long as you make your theory clearer, I can't understand what youmean by "physical world", "possible", "totality", etc.

`I use the same definitions as other people use. I am not claiming a`

`private language and/or set of definitions, even if I have tried to`

`refine the usual definition more sharply than usual.`

Physical world: http://oxforddictionaries.com/definition/english/physical?q=Physical "adjective 1) relating to the body as opposed to the mind: /a range of physical and mental challenges/

`2) relating to things perceived through the senses as opposed to the`

`mind; tangible or concrete:`

the physical world 3) relating to physics or the operation of natural forces generally: /physical laws/" http://en.wikipedia.org/wiki/Possible_world

`"Those theorists who use the concept of possible worlds consider the`

`actual world to be one of the many possible worlds. For each distinct`

`way the world could have been, there is said to be a distinct possible`

`world; the actual world is the one we in fact live in. Among such`

`theorists there is disagreement about the nature of possible worlds;`

`their precise ontological status is disputed, and especially the`

`difference, if any, in ontological status between the actual world and`

`all the other possible worlds."`

Totality: http://www.merriam-webster.com/dictionary/totality *

`1:*an aggregate amount*:*sum`

`<http://www.merriam-webster.com/dictionary/sum>,whole`

`<http://www.merriam-webster.com/dictionary/whole>`

2

`/a/*:*the quality or state of beingtotal`

`<http://www.merriam-webster.com/dictionary/total>*:*wholeness`

`<http://www.merriam-webster.com/dictionary/wholeness>`

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. ;-)?

`I refuse to believe that you cannot make sense of what I wrote. Can`

`you understand that I find your interpretation of Plato's Realm of`

`Ideals to be incorrect? You seem to have read one book or taken one`

`lecture on the subject and not read any more philosophical discussion of`

`the ideas involved. I have asked you repeatedly to merely read Bertrand`

`Russell's small book on philosophy - with is available on-line here`

`http://www.ditext.com/russell/russell.html, but you seem unwilling to do`

`that. Why?`

BrunoMy thinking here follows the reasoning of Jaakko Hintikka. Areyou familiar with it? Game theoretic semantics for Proof theory<http://www.hf.uio.no/ifikk/forskning/publikasjoner/tidsskrifter/njpl/vol4no2/gamesem.pdf>--

`How about considering that there are alternatives to your idea of`

`timeless Truths? Jaakko Hintikka does a nice job exploring one of those`

`alternatives!`

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