The three basic (metaphysical) axioms according to Objectivists are Existence, Identity and Consciousness. Anyhow, as far as I can tell, all you're saying is t

The three basic (metaphysical) axioms according to Objectivists are Existence, Identity and Consciousness. Anyhow, as far as I can tell, all you're saying is that either (1) Cantor's argument is invalid within ZF(C) or (2) you find ZF(C) objectionable on the grounds that it conflicts with the basis of your metaphysics. That's fine — I don't care whether it does or not — but mathematics has no opinion on the matter. You're free to choose a set of mathematical axioms which you don't find objectionable and go about doing your math in that universe. If you want to claim Cantor's argument is invalid then you need to tell me what axioms you're taking as the foundation for your mathematics. It is valid in ZF(C) and I'm 99% sure it's valid in plain ZF. Which of the axioms of ZF do you find objectionable and what would you replace them with? Assuming you're trying to engage sincerely, I'd ask you to be precise. This means listing whatever foundations of mathematics you don't find objectionable and talking about how they differ from ZF(C). If you're unfamiliar with it, I'd read up on proof theory: http://en.wikipedia.org/wiki/Proof_theory http://en.wikipedia.org/wiki/Proof_theory