In Quine's New Foundations
In the New Foundations approach to set theory pioneered by W.V.O. Quine, the axiom of comprehension for a given predicate takes the unrestricted form, but the predicates that may be used in the schema are themselves restricted. The predicate (C is not in C) is forbidden, because the same symbol C appears on both sides of the membership symbol (and so at different "relative types"); thus, Russell's paradox is avoided. However, by taking P(C) to be (C = C), which is allowed, we can form a set of all sets. For details, see stratification.
Read more about this topic: Axiom Schema Of Specification
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—Willard Van Orman Quine (b. 1908)
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