On 14 Feb 2014, at 05:42, meekerdb wrote:
On 2/13/2014 8:40 PM, Russell Standish wrote:
I had a look at your SANE paper, which is the main paper where you
describe
your work that you published since your thesis. I can sort of see you
saying something a bit like the above on page 11 "Now DU [sic -
should
be UD in English] is emulated platonistically by the verifiable
propositions of arithmetic. They are equivalent to sentences of the
form ``if exists n such that P(n)'' with P(n) decidable."
That is actually rather confusing. Obviously a UD executes all proofs
of all true Sigma 1 sentences, but I think what you are trying to
say that
all programs executed by the UD correspond to a proof of some true
Sigma 1 sentence. Is that obvious? I didn't get that when I read
the SANE paper
originally, only got it in context of your statements above.
How can that be? Many programs executed by the UD are non-halting,
just loops. Can they be considered to correspond to a proof?
Yes, like a failed proof. Like searching the first even prime number
bigger than 2. The search for ExP(x) when Ax~P(x), but you don't know
that. But for the probability calculus, you can limit yourself on the
finite pieces of computations, as the first person will glue the
infinities of them to experience their "consistent" infinite union.
Bruno
Brent
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