On 10/31/2012 12:22 PM, Bruno Marchal wrote:
On 30 Oct 2012, at 18:29, Stephen P. King wrote:
On 10/30/2012 12:38 PM, Bruno Marchal wrote:
No? If they do not have something equivalent to concepts, how can
Yes, the universal numbers can have concept.
Let's start over. Please plain in detail what is a universal
number 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
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.
That 'fixing" occurs at our level only. We are free (relatively) to
fix our axiomatic objects from the wide variety that have been proven to
exist within the Mathematical universe of concepts or, if we are clever,
we can invent new concepts and work with them; but we cannot do things
in our logic that are self-contradictory unless we make sure that the
contradictions are not allowed to be pathological.
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.
OK, but this does not answer my question. What is the ontological
level mechanism that distinguishes the u and the x and the y from each
other? What I am trying to explain to you that ontological level objects
cannot have any logical mechanism that requires temporarily unless you
are assuming some form of Becoming as an ontological primitive.
Platonism, as far as I know, disallows this.
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.
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