Philosophy of Mathematics

* What is an impredicative definition? How is this notion used by Russell to resolve Cantor's Paradox?
* What goes wrong when we try to figure out the cardinality of the set C which collects together all the members of the cardinals? How does Russell's requirement that there be no impredicative definitions resolve the problem?
* Give an account of each of the following paradoxes: Russell's, Cantor's, the Heterological, the Berry, and the Liar.