The book seeks to characterize reflexive conceptual structures more thoroughly and more precisely than has been done before, making explicit the structure of paradox and the clear connections to major logical results. The goal is to trace the structure of reflexivity in sentences, sets, and systems, but also as it appears in propositional attitudes, mental states, perspectives and processes. What an understanding of patterns of reflexivity offers is a deeper and de-mystified understanding of issues of semantics, free will, and the nature of consciousness.

This book is the product of a collaboration stretching the years 2007-10, whose initial fruit was a paper on "Plenum Theory" published in Nous. The work grew out of the author's conviction that standard set theory, which had evolved to meet the needs of mathematics, was not fully adequate to the less abstractly geared and rigidly determine needs of less finalized ranges of inquiry and deliberation.

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

This latest volume of "The Philosopher's Annual" presents the ten best articles published in the field during 2001. No limitations are placed on the articles' sources, subject matter or mode of treatment, providing for a diverse collection of engaging, high-caliber work that stands as a valuable sample of contemporary philosophy. This year's volume includes papers by Robert Bernasconi, Hans Halvorson, Christopher Hitchcock, Ignacio Jane, Brian Leiter, Liam Murphy and Thomas Nagel, Joel Pust, Alison Simmons, Jason Stanley and Timothy Williamson, and Crispin Wright.

"The Philosopher's Annual" attempts to select the ten best articles published in philosophy the previous year. Impossible? Yes. By attempting the impossible this collection calls attention to truly exceptional critiques from the philosophical field. This is the 22nd volume of the series, collecting outstanding work from the philosophy literature of 1999. Each year the members of the distinguished nominating board are asked to name three papers that most impressed them from the literature of the previous year. No limitations are placed on sources from which articles may be nominated, on subject matter, or on mode of treatment. The process delivers a diverse collection of engaging, high caliber work that stands as a valuable sample of contemporary work in philosophy.

Each year, "The Philosopher's Annual" presents the ten best articles published in the field of philosophy during the previous twelve months--with the absence of limits on the articles' sources, subject matter, or modes of treatment making for a very diverse collection of engaging, high-caliber work. This year's volume includes papers by Katalin Balog, Tyler Burge, Cheshire Calhoun, Sally Haslanger, Thomas Hofweber, Philip Kitcher, Charles G. Morgan, Thomas W. Pogge, James Pryor, and Elliott Sober.