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. In terms of measure aren't there
infinitely more non-terminating programs than terminating?
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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