On 02 Mar 2012, at 06:18, meekerdb wrote (two month agao):
On 3/1/2012 7:37 PM, Richard Ruquist wrote:
Excerpt: "Any system with finite information content that is
consistent can be formalized into an axiomatic system, for example
by using one axiom to assert the truth of each independent piece of
information. Thus, assuming that our reality has finite information
content, there must be an axiomatic system that is
isomorphic to our reality, where every true thing about reality can
be proved as a theorem from the axioms of that system"
Doesn't this thinking contradict Goedel's Incompleteness theorem
for consistent systems because there are true things about
consistent systems that cannot be derived from its axioms? Richard
Presumably those true things would not be 'real'. Only provable
things would be true of reality.
Provable depends on the theory. If the theory is unsound, what it
proves might well be false.
And if you trust the theory, then you know that "the theory is
consistent" is true, yet the theory itself cannot prove it, so reality
is larger that what you can prove in that theory.
So in any case truth is larger than the theory. Even when truth is
restricted to arithmetical propositions. Notably because the statement
"the theory is consistent" can be translated into an arithmetical
proposition.
Bruno
http://iridia.ulb.ac.be/~marchal/
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