The Incomplete Universe

Book excerpt: The central claim of this powerful philosophical exploration is that within any logic we have, there can be no coherent notion of all truth or of total knowledge. Grim examines a series of logical paradoxes and related formal results to reveal their implications for contemporary epistemology, metaphysics, and the philosophy of religion. He reaches the provocative conclusion that, if the universe is thought of in terms of its truths, it is essentially open and incomplete. The Incomplete Universe includes detailed work on the liar paradox and recent attempts at solution, Kaplan and Montague's paradox of the knower, the Gödel theorems and related incompleteness phenomena, and new forms of Cantorian argument. The emphasis throughout is philosophical rather than formal, with an eye to connection's with possible worlds, the notion of omniscience, and the opening lines of the Tractatus: "The world is all that is the case. "