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
Famous quotes containing the words quine and/or foundations:
“Physics investigates the essential nature of the world, and biology describes a local bump. Psychology, human psychology, describes a bump on the bump.”
—Willard Van Orman Quine (b. 1908)
“For me, it is as though at every moment the actual world had completely lost its actuality. As though there was nothing there; as though there were no foundations for anything or as though it escaped us. Only one thing, however, is vividly present: the constant tearing of the veil of appearances; the constant destruction of everything in construction. Nothing holds together, everything falls apart.”
—Eugène Ionesco (b. 1912)