Perhaps a sort of thing which allows axioms to be submitted and organized hierarchically, and then some mechanism to vote on the axioms (yea or nea) so that level of agreement can be assessed. Discussion could fork off of each axiom submitted so that qualifications and whatnot can be discussed. Based on the level of agreement, the axioms could then be organized on another page according to the level of agreement.
Bad idea in my opinion. I've seen plenty of mantras tossed about in this forum where the poster feels it qualifies as an axiom, and the general groupthink in this forum would probably allow it to be qualified as an axiom, thus lending credence to an argument only by virtue of the biased thinking present herein.
It would be akin to a board full of Global Warming deniers setting up and voting on a set of axioms which seemingly demonstrate that Global Warming is not an issue.
I agree, but the purpose isn't to agree on the truth of the matter, but to find fruitful topics for discussion (I think that's what OP is getting at, anyways). The best topics to discuss might be ones which have equal amounts of agreement and disagreement; avoiding topics which are skewed either way might help avoid the groupthink problem.