User blog comment:LittlePeng9/Higher order set theory/@comment-1605058-20141017183223

Unfortunatelly, I think oodles are inconsistent as defined so far - first of all, there are oodles which contain themselves: consider, for example, the oodle of all oodles. It's an oodle, so it must contain itself. But there are also oodles not containing themselves - for example, empty oodle. Because of that, it's quite meaningful to ask which oodles contain themselves and which don't. These two give partition of all oodles into two oodles - first one contains all the oodles which contain themselves and the second contains all oodles which do not contain themselves. But does the latter contain itself?

(oodles actually create a perfect setting for naive set theory, which, unfortunatelly, is inconsistent)