Oooh, I really like this. Brilliant idea. It would take some time to get the wording right, but the end result would be worth it.
I'm going to add to this in an extremely geeky way below the fold...
There is, however, one axiom, called the "axiom of choice", that is up for some debate. It cannot be proved from the other axioms; you either take it as an axiom or you reject its validity. In its simplest form, it says that if you present me with a whole bunch of sets, I can pick one element from each. Simple, right? How can anyone disagree with such a harmless thing? Well, it directly leads to the following result, called The Banach-Tarski paradox: we can take a ball of any size, cut it into 5 pieces, and re-assemble the pieces to get two balls, both of equal size to the first. Despite this (and other) paradoxes, the axiom of choice is good in so many ways that the vast majority of mathematicians believe it.
You can probably see where I'm going with this -- the axiom of choice in mathematics seems to me to be intimately related with the right to privacy in politics. (The axiom of choice is conveniently named for this discussion, as the right to privacy is roughly equivalent to a woman's right to choose.) We have a large group of people (the majority, in fact) that believe it exists and a smaller group that believes it doesn't. So why not make it an axiom? It's good in so many ways.