Epistemology Lesson II

December 26, 2006 § Leave a comment

Consider the statement “Given logic L and factual premeses F, there exists a deductive proof P[i] for every true theorem D[i].”

This is not a claim of consistency. It is a claim of completeness. In fact it is probably a claim of inconsistency in disguise.

If logic L has the machinery to represent ordinary arithmetic, for example, this completeness claim asserts that either the given facts F are mutually inconsistent or that logic L is itself inconsistent.

When someone makes a claim of this form thinking that what he is insisting on is consistency, what he is in fact probably insisting on is inconsistency.


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