[Ivoirians]

It doesn't matter if someone thinks Cantor "breaks the rules", or the square root of -1 "doesn't exist." The (majority of) mathematicians who take those as true have created a wealth of rigorous, interesting, and worthwhile results built on top of these concepts. I vehemently believe mathematics is more "abstract thought experiments" than "discoveries of universal truth".

[cubefox]

I doubt that any results which rested on the assumption of Hume's Principle are worthwhile. Indeed, set theory seems to have been useless for most mathematicians except those who are interested in "foundations", since it is mostly ignored.