... or engenders a tradition of philosophical reflection, questions will arise about the relation between divine knowledge and power and human freedom. ...

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.

John Abbruzzese has recently attempted a defense of omniscience against a series of my attacks. This affords me a welcome occasion to clarify some of the arguments, to pursue some neglected subtleties, and to re-think some important complications. In the end, however, I must insist that at least three of four crucial arguments really do show an omniscient being to be impossible. Abbruzzese sometimes misunderstands the forms of the argument themselves, and quite generally misunderstands their force.

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)

An overview of contemporary part-whole theories, with reference to both their axiomatic developments and their philosophical underpinnings.

One set of neglected problems consists of paradoxes of omniscience clearly recognizable as forms of the Liar, and these I have never seen raised at all. Other neglected problems are difficulties for omniscience posed by recent work on belief de se and essential indexicals. These have not yet been given the attention they deserve.