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Actually there's no such thing as a completely logically consistent mathematical system.

The consistency is patchy. You can start from axioms and build systems, but you have to accept the axioms as given. They're not provable - nor are some of the processes used to build system.

According to George Lakoff, logic is founded in cognitive psychology. Certain processes 'make sense' because they use internally consistent metaphors. The process of selecting and refining those metaphors is trial and error, and not a metaphysical revelation of philosophical truth.

by ThatBritGuy (thatbritguy (at) googlemail.com) on Mon Jun 1st, 2009 at 02:58:37 PM EST
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