This book is a defense of modal realism; the thesis that our world is but one of a plurality of worlds, and that the individuals that inhabit our world are only a few out of all the inhabitants of all the worlds. Lewis argues that the philosophical utility of modal realism is a good reason for believing that it is true.

This study provides a unified theory of properties, relations, and propositions (PRPs). Two conceptions of PRPs have emerged in the history of philosophy. The author explores both of these traditional conceptions and shows how they can be captured by a single theory.

This book, one of the first full-length studies of the modalities to emerge from the debate to which Saul Kripke, David Lewis, Ruth Marcus, and others are contributing, is an exploration and defense of the notion of modality de re, the idea that objects have both essential and accidental properties. Plantinga develops his argument by means of the notion of possible worlds and ranges over such key problems as the nature of essence, transworld identity, negative existential propositions, and the existence (...) of unactual objects in other possible worlds. He also applies his logical theories to the elucidation of two problems in the philosophy of religion: the problem of evil and the ontological argument. (shrink)

Set theory is concerned with the foundations of mathematics. In the original formulations, there were paradoxes concerning the idea of the "set of all sets." Current standard theory avoids these paradoxes by restricting the way sets may be formed by other sets specifically to disallow the possibility of forming the set of all sets. In the 1930s, Quine proposed a different form of set theory in which the set of all sets-- the universal set-- is allowed, but other restrictions are (...) placed on these axioms. Since then, the steady interest expressed in these non-standard set theories has been boosted by their relevance to computer science. This text concentrates heavily on Quine's New Foundations, reflecting the author's belief that it provides the richest and most mysterious of the various systems dealing with set theories with a universal set. The result is a work that provides a useful introduction for those new to this topic, and a valuable reference for those already involved in the area. (shrink)

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)

This paper discusses the principle of recombination for possible worlds. It argues that arguments against unrestricted recombination offered by Forrest and Armstrong and by David Lewis fail, but a related argument is a challenge, and recommends that we accept an unrestricted principle of recombination and the conclusion that possible worlds form a proper class.

First-order logic. The origin of modern foundational studies. Frege's system and the paradoxes. The teory of types. Zermelo-Fraenkel set theory. Hilbert's program and Godel's incompleteness theorems. The foundational systems of W.V. Quine. Categorical algebra.