Naive set theory, as practiced in the nineteenth century by Cantor, Dedekind, and Frege, consists of two basic principles: extensionality and naive comprehension. According to the latter, every condition determines a set. This is usually formalized by the schema \(\exists y \forall x\, (x \in y \leftrightarrow A(x))\) , where \(A(x)\) is any condition on \(x\) in which \(y\) doesn’t occur free. Some philosophers have argued that, since this restriction is in place to avoid paradox, in a logic weak enough to handle paradoxes, the restriction on \(A(x)\) should be lifted in order to better capture the full generality of naive comprehension. I argue that, on the contrary, lifting the restriction doesn’t do more justice to naive comprehension but is the product of a serious misunderstanding of what the principle really says.
