The Incomplete Universe

Patrick Grim is Associate Professor in the Department of Philosophy at the State University of New York at Stony Brook.

Introduction - some philosphical fragments. Part 1 Apparent lessons of the liar: totality, truth and the liar; possible worlds; the divine liar; possible ways out; truth-value gaps, many-valued logics, and strengthened liars; the propositional response; accepting inconsistency; the appeal to hierarchy; barwise and etchemendy; conclusion. Part 2 Truth, omniscience, and the paradox of the knower: the paradox of the knower; the argument; the power of the paradox; possible ways out; propositions and the strengthened knower; redundancy theories and operators; hierarchy; conclusion. Part 3 Epistemic incompleteness: some ideal knowers and the standard Godel result; beyond standard systems; expressive incompleteness; a cantorian generalization of Godel's incompleteness theorem; conclusion. Part 4 Classes and quantification - the cantorian argument: there is no set of all truths; extensions and applications; alternative set theories - a possible way out?; the problem without power sets; the appeal to quantification; a self-reflective problem for the central thesis?; conclusion. Part 5 Concluding notes: philosophical fragments; within any logic we have ...; some twilight speculations.