As soon as someone creates a set of axioms to go by, that person sets him or herself against the exception - the experience. There will be a violation that has to be either tolerated or eliminated, either of which does violence to someone's experience. There are almost always exceptions to the rule.
For example, infinity is taken for granted. Never mind if the idea makes sense. It's the same with the existence of the point, the zero-dimensional. Abstraction does not always make sense. And extension of ideas beyond the experiential runs the risk of creating paradox. --MathPoet 19:19, 22 August 2007 (UTC)