" Kurt Gödel, who was able to prove in 1940 that given any axiomatic system that can produce arithmetic, we have to choose between completeness and coherence. Completeness means that the truth value of every statement in the system is determinable—that is that all statements can be assigned the appropriate truth value (usually true or false, for us). Coherence means that there are no contradictory statements, which is to say no paradoxes, within the system. We can have one or the other, but except in very special cases that have little applicability, we cannot have both. "

― James A. Lindsay , Dot, Dot, Dot: Infinity Plus God Equals Folly