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:
“Confusion of sign and object is original sin coeval with the word.”
—Willard Van Orman Quine (b. 1908)
“The objects of a financier are, then, to secure an ample revenue; to impose it with judgment and equality; to employ it economically; and, when necessity obliges him to make use of credit, to secure its foundations in that instance, and for ever, by the clearness and candour of his proceedings, the exactness of his calculations, and the solidity of his funds.”
—Edmund Burke (1729–1797)