On 10/15/2013 7:49 AM, Bruno Marchal wrote:
On 15 Oct 2013, at 12:45, Richard Ruquist wrote:
Bruno: On the contrary: I assume only that my brain (or generalized brain) is
computable, then I show that basically all the rest is not. In everything, or just in
arithmetic, the computable is rare and exceptional.
Richard: Wow. This contradicts everything I have ever though Bruno was claiming. How
does anything exist if it is not computed by "the" or "a" machine?
We assume the arithmetical truth. In particular we assume that all closed formula
written in the language of arithmetic (and thus using logical symbol + the symbol 0, s
(+1), + and *) are all either true or false, independently of us.
From this we cannot prove that matter exists, or not, but we can prove that the average
universal numbers will (correctly) believe in matter (but it will not know that it is
That's not at all clear to me. A universal number encodes proofs - is that what you mean
by it believes something? But how is this something identified at 'matter'?
So, if you have no problem in believing propositions like "there is no biggest prime
number" are true independently of me and you, and the universe, then you can understand
that the proposition asserting the existence of (infinitely many) computations in which
you believe reading my current post, is also true independently of us.
The appearance of matter emerges from the FPI that the machines cannot avoid in the
Arithmetical truth escapes largely the computable arithmetical truth (by Gödel).
And I thought the generalized brain did the computations,
Only the computations associated to your mind.
not that it was only computed. How does Bruno show that "all the rest" which presumably
includes energy and matter is not computed. Bruno is constantly confusing me.
I guess you missed the step seven of the UDA, and are perhaps not aware that
arithmetical truth is incredibly big, *much* bigger than what any computer can generate
Then my, or your, mind is associated to *all* computations going through your actual
state of mind,
That sounds like an uncomputable totality.
and below your substitution level there are infinitely many such computations. They all
exist in arithmetic, and the FPI glues them, in a non computable way, in possible long
and deep physical histories.
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