A by-product of all this has been some cool stuff intrinsically interesting to graph theory and other areas of math. One such tangent, with a lot of help from Matt Macauley, turned into a proof of Brouwer's fan theorem (one using Goedel compatness) and then into a proof of the Heine-Borel theorem. Matt has also tidied it up into a cute prose-style paper, which can be found here.
The work on the paradoxes is scattered throughout various emails but we are hoping to pull it all together soon. Anyway, this is all a distraction from my real work...so back to a priori contingencies, etc.