On 5/26/2012 2:16 AM, Bruno Marchal wrote:

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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 beformalized into an axiomatic system, for example by using one axiom to assert thetruth of each independent piece of information. Thus, assuming that our reality hasﬁnite information content, there must be an axiomatic system that isisomorphic to our reality, where every true thing about reality can be proved as atheorem from the axioms of that system"Doesn't this thinking contradict Goedel's Incompleteness theorem for consistentsystems because there are true things about consistent systems that cannot be derivedfrom its axioms? RichardPresumably those true things would not be 'real'. Only provable things would be trueof reality.Provable depends on the theory. If the theory is unsound, what it proves might well befalse.And if you trust the theory, then you know that "the theory is consistent" is true, yetthe theory itself cannot prove it, so reality is larger that what you can prove in thattheory.So in any case truth is larger than the theory. Even when truth is restricted toarithmetical propositions. Notably because the statement "the theory is consistent" canbe translated into an arithmetical proposition.Bruno

`Does arithmetic have 'finite information content'? Is the axiom of succession just one or`

`is it a schema of infinitely many axioms?`

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