Originally Posted by Hektore

Axioms are important because where you start has a great impact on where you end up. If you want an example read up on Non-Euclidian geometry. Now, I wouldn't go so far as to say certain kinds of logic (a "kind of logic" being defined by it's particular set of axioms) are right or wrong, but certain sets of axioms are more or less useful for certain things.

Many times different axioms are the root cause of an argument, logical inconsistency or the assignment of different truth values to the same statement, if you will (If only people would realize this more often...). The trouble in any kind of debate setting (particularly one where folks are evaluating the existence of god/s) is getting people to see their own axioms as assumptions and recognizing that questioning of axioms is a very fruitful approach to debate and resolving the issue at hand, if it can be resolved at all.