The main notions of set theory -- including cardinals, ordinals, and transfinite induction -- are fundamental to all mathematics. This advanced undergraduate- and graduate-level text offers a thorough exploration that extends from the history of set theory and its paradoxes to connections with symbolic and mathematical logic. Advanced topics include relations and functions, equipollence, and more. 1971 edition.

THE PHILOSOPHY which I advocate is generally regarded as a species of realism, and accused of inconsistency because of the elements in it which seem contrary to that doctrine. For my part, I do not regard the issue between realists and their opponents as a funda- mental one; I could alter my view on this issue without changing my mind as to any of the doctrines upon which I wish to lay stress. I hold that logic is what is fundamental (...) in philosophy, and that schools should be characterized rather by their logic than by their metaphysic. My own logic is atomic, and it is this aspect upon which I should wish to lay stress. Therefore I prefer to describe my philosophy as "logical atomism," rather than as "realism," whether with or without some prefixed adjective. (shrink)