I just read this very insightfull online commentary by Robert Brown from Duke University:
No fooling, and this is, sadly, not a joke. I wish I were fooling. If nothing else, I've learned that as soon as one discovers in a debate of any sort that your opponent/partner has different Prime Axioms ... the wisest thing to do is immediately terminate the discussion, back away slowly (possibly with one hand on your wallet and another on a small but powerful handgun), and go do something useful, like doing a crossword puzzle, or taking a nice long nap, or playing World of Warcraft until your mouse-hand is sore.
At least those things will improve your mind and are unlikely to get you beheaded, burned at the stake, pilloried, broken on the wheel, enslaved, or just plain beaten up and left for dead - all of which have happened at one time or another to the loser of what should have been an open-minded and fair philophical debate between holders of different axioms. Including repeatedly, religious axioms, where the ``debates'' were, for example, known as crusades.
The damnedest thing is, of course, that I can no more prove my axioms than they can prove theirs, and hence both our conclusions are in some deep sense equally irrational. Maybe the laws of physics have changed over time in a way that (precisely) cannot be detected now. Formulated this way, how can I prove otherwise by any experiment or experience, by definition?