It occurs to me that the arguments that have been advanced against membership can be strengthened to a mathematical proof that the usual notion of membership as a 2-valued binary relation is an inconsistent notion. That is, Theorem. Membership does not exist. Proof. Clearly the universe exists, or we're in serious trouble. But if membership also exists then the Cantor-Russell argument leads to a contradiction. QED My real point here is that the Cantor-Russell argument doesn't *really* prove there is no universal set, or no 2-valued membership relation, or that some sets we can name are not in the universe, or that the universe we exist in must be different from the one in which mathematical objects exist, or that we are arguing with an unreliable logic. What it proves is the sentence "false." Anything powerful enough to prove false is a theorem of the universe dual to ours. Such a theorem is a gedanken wavefunction. To bring it into our universe it has to collapse to a Gedankeneigenfunction of the operator by which we observe it, that is, our logic. When you are young and unobserved you are just some gedanken wavefunction. When you become observed, whether for the purpose of influencing future generations or getting tenure, you collapse to one of the schools of thought constituting the Gedankeneigenfunctions of the observation operator, whether set theorist, or category theorist, or intuitionist, etc. That is, you have to take a stand or risk failure to communicate. I have tried to communicate without taking a stand. I may have underestimated the disadvantages of not collapsing to a Gedankeneigenfunction. There's a lot to be said in favor of collapse. Vaughan Pratt