On 22 Dec 2013, at 21:00, meekerdb wrote:
On 12/22/2013 5:14 AM, Bruno Marchal wrote:
On 22 Dec 2013, at 01:00, Edgar Owen wrote:
Hi John,
First thanks for the complement on my post!
To address your points. Of course we do have some knowledge of
reality. We have to have to be able to function within it which we
most certainly do to varying degrees of competence. That is proof
we do have sufficient knowledge of reality to function within it.
Yes, computations include logic as well as math.
Computations is only a very tiny part of arithmetic and thus of
math. Logic is something else, despite many i-rich interrelation
with computation and computability theory.
Computability can be represented in term of a very special case of
provability, and provability can be represented as a very special
case of computability, but those notion are very different and non
isomorphic.
But computable means halting and returning a value.
That means "total" computable. But we know that the price of
universality is that some program might not stop on some input, and so
we will say that a computer computes even when it does not stop. In
particular, the universal dovetailing can be considered as a "non
stopping computation". After all that universal dovetailing machine is
doing something, OK?
In terms of measure aren't there infinitely more non-terminating
programs than terminating?
Both are enumerable, although not recursively enumerable. But the
measure is not on programs, but on the (possibly non terminating)
computations as viewed from the first person (relatively to its actual
states). This forces us to dovetail on infinite streams, and makes
such computations non enumerable, and the constraints provided by the
intensional nuances (notably the "material one (p sigma_1 + "& p" or
"& Dt" or both) suggests the existence of a quantum measure (and a
quantization).
Keep in mind that, as absurd it could seem to be, the UD does dovetail
on "you" (3p) embedded in a reality or emulating a computation which
iterate infinitely the WM-duplication. That explains quickly why your
maximally complete consistent extension will be 3p non enumerable.
Bruno
Brent
Proof and mathematical theories are never universal. For
computability, we do have universality (that's why universal
purpose computer exists).
Bruno
http://iridia.ulb.ac.be/~marchal/
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