On 30 Oct 2012, at 18:29, Stephen P. King wrote:

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On 10/30/2012 12:38 PM, Bruno Marchal wrote:No? If they do not have something equivalent to concepts, how canthey dream?Yes, the universal numbers can have concept.Dear Bruno,Let's start over. Please plain in detail what is a universalnumber and how it (and not ordinary numbers) have concepts or 1p.

`I will give more detail on FOAR, soon or later. But let me explains`

`quickly.`

`Fix your favorite Turing universal system. It can be a programming`

`language, a universal Turing machine, or a sigma_1 complete theory, or`

`even a computer.`

`Enumerate the programs computing functions fro N to N, (or the`

`equivalent notion according to your chosen system). let us call those`

`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 the`

`equality 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 both undefined.`

`In phi_u(B(x,y)) = phi_x(y), x is called the program, and y the data.`

`u is the computer. u i said to emulate the program (machine, ...) x on`

`the input y.`

`Comp is the thesis that I can survive with a physical digital computer`

`in place of the physical brain, as far as it emulates me close enough.`

`Comp gives a special role to computer (physical incarnation of a`

`universal number). The comp idea is that computer can supports`

`thinking and consciousness, and makes them capable of manifestation`

`relatively to other universal structure (physical universes if that`

`exists, people, etc.). This should answer your question.`

`The lobian machines are only universal numbers, having the knowledge`

`that they are universal.`

`I can prove to any patient human that he/she is Löbian (I cannot prove`

`that he/she is sound or correct, note).`

`The UDA results is that whatever you mean by physical for making comp`

`meaningful, that physicalness has to emerge entirely and only, from a`

`'competition' between all universal numbers. There is no need to go`

`out of arithmetic, and "worst", there is no possible use of going out`

`of arithmetic, once betting on comp.`

`By arithmetic I mean arithmetical truth, or the standard model of`

`arithmetic, I don't mean a theory. I mean the whole set of true`

`arithmetical propositions, or of their Gödel numbers.`

Bruno

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