This is an exploration of a cluster of related logical results. Taken together these seem to have something philosophically important to teach us: something about knowledge and truth and something about the logical impossibility of totalities of knowledge and truth. The book includes explorations of new forms of the ancient and venerable paradox of the :Liar, applications and extensions of Kaplan and Montague's paradox of the Knower, generalizations of Godel's work on incompleteness, and new uses of Cantorian diagonalization. Throughout, the (...) concern is with metaphysical and epistemological implications of these results: what such results may have to teach us about knowledge, truth, and possibility. (shrink)

A Cantorian argument that there is no set of all truths. There is, for the same reason, no possible world as a maximal set of propositions. And omniscience is logically impossible.

An exchange between Patrick Grim and Alvin Plantinga regarding Cantorian arguments against the possibility of an omniscient being.