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/



--
You received this message because you are subscribed to the Google Groups 
"Everything List" group.
To post to this group, send email to everything-list@googlegroups.com.
To unsubscribe from this group, send email to 
everything-list+unsubscr...@googlegroups.com.
For more options, visit this group at 
http://groups.google.com/group/everything-list?hl=en.

Reply via email to