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Friday, Apr 25, 2014
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Bubba  
November 28, 2008 9:19am
 
Mike

Most mathematical systems are based on assumptions, called axiom, which are in some sense assumed to be true statements, and then other statements in that system are proven from the axioms using logic. Therefore, each set of independent axioms place you in a new logical system (which is governed by the basic laws of logic). Notice I said that the axioms are assumed to be true. If you don't assume them to be true, then there is no reason for you to agree with my logical system.

You may say to me "What about the constructivist point of view". They tend to not like the axiomatic view, but even they start with the basic axioms of set theory, which assume that there are really objects to put into a set. What if I disagree that we (or anything else) is really here, then I fall outside of every logical system.
     
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