On 06 Jan 2010, at 03:34, Brent Meeker wrote:
Nick Prince wrote:
Hi Brent
Perhaps Bruno could give some clarification here. Just prior to his
conclusion on the sane paper I quoted from was this:
"So if we keep comp at this stage, we are forced to relate the inner
experience only to
the type of computation involved. The reason is that only those types
are univocally related to
all their possible counterfactuals. This entails that, from a first
person point of view, not only
the physical cannot be distinguished from the virtual, but the
virtual
can no more be
distinguished from the arithmetical. Now DU is emulated
platonistically by the verifiable
propositions of arithmetic. They are equivalent to sentences of the
form ‘‘it exists n such that
P(n)’’ with P(n) decidable. Their truth entails their provability,
and
they are known under the
name of Sigma1 sentence.
If comp is correct, the appearance of physics must be recovered from
some point of
views emerging from those propositions.
Why only the atomic sentences? Why not all true sentences? How is
"appearance" recovered?
The atomic propositions p, q, r of the modal logic (G) are interpreted
by the Sigma_1 sentences of Arithmetic (with shape ExP(x), P
decidable). Dovetailing on their (infinitely many) proofs can be shown
equivalent with a universal dovetailing (and thus truly universal with
Church thesis). Limiting the arithmetical interpretation on that tiny
Sigma_1 complete part is the way to interview the *computationalist"
machine.
The formula "p -> Bp" characterizes such Sigma_1 arithmetical formula,
provably so, by the Löbian machine.
So G + p -> Bp is used in the final.
Indeed, taking into account
the seven steps once
more, we arrive at the conclusion that the physical atomic (in the
Boolean logician sense)
invariant proposition must be given by a probability measure on those
propositions.
But what gives the probability measure? Is it just the relative
frequency of occurrence of the atomic sentences in the UD output up
to a given step?
The 'measure one' will have a logic related to the logic of Bp & Dt
(and variants). The measure itself may follow, or not.
Incompleteness; being self-discoverable, provides a geometry on the
common ignorance of all universal machines, from which the 'physical
laws" should emerge.
Hmm... I guess you miss something in the MGA, or with computational
supervenience. Computational supervenience is really "step 7", but in
front of arithmetical realism, which contains UD* in some way.
Not easy stuff ...
Bruno
http://iridia.ulb.ac.be/~marchal/
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