PHL246H1 Lecture Notes - Lecture 1: If And Only If, Augustus De Morgan, Begriffsschrift
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Extensive notation {margaret thatcher, tony blair, albert einstein} Intensive notation {x: x is a car in london} A = b iff (for any x) (x a iff x b) For any condition c, there exists a set a such that(for any x)(x belongs a iff x satis es. Every set is a subset of itself, the empty set is a subset of every set. In general, any set with n members has 2^n subsets. Russell"s set r = {x:x not belongs to x} The assumption that r exists generates an inconsistency, we can prove both that r is a member of itself and that it is not. What we have seen is that this implicit circularity is not only worrisome but vicious in the sense that it generates contradictions. Axiom of extensionality + axiom of comprehension. Sets are de ned their members(extensionality) and there is a set for any characterizable plurality of things(comprehension)
