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.

Kurt Gödel, mathematician and logician, was one of the most influential thinkers of the twentieth century. Gödel fled Nazi Germany, fearing for his Jewish wife and fed up with Nazi interference in the affairs of the mathematics institute at the University of Göttingen. In 1933 he settled at the Institute for Advanced Study in Princeton, where he joined the group of world-famous mathematicians who made up its original faculty. His 1940 book, better known by its short title, The Consistency of (...) the Continuum Hypothesis, is a classic of modern mathematics. The continuum hypothesis, introduced by mathematician George Cantor in 1877, states that there is no set of numbers between the integers and real numbers. It was later included as the first of mathematician David Hilbert's twenty-three unsolved math problems, famously delivered as a manifesto to the field of mathematics at the International Congress of Mathematicians in Paris in 1900. In The Consistency of the Continuum Hypothesis Gödel set forth his proof for this problem. In 1999, Time magazine ranked him higher than fellow scientists Edwin Hubble, Enrico Fermi, John Maynard Keynes, James Watson, Francis Crick, and Jonas Salk. He is most renowned for his proof in 1931 of the 'incompleteness theorem,' in which he demonstrated that there are problems that cannot be solved by any set of rules or procedures. His proof wrought fruitful havoc in mathematics, logic, and beyond. (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.

This is the first of a three-volume collection of David Lewis's most recent papers in all the areas to which he has made significant contributions. The purpose of this collection (and the two volumes to follow) is to disseminate even more widely the work of a preeminent and influential late twentieth-century philosopher. The papers are now offered in a readily accessible format. This first volume is devoted to Lewis's work on philosophical logic from the last twenty-five years. The topics covered (...) include: deploying the methods of formal semantics from artificial formalised languages to natural languages, model-theoretic investigations of intensional logic, contradiction, relevance, the differences between analog and digital representation, and questions arising from the construction of ambitious formalised philosophical systems. The volume will serve as an important reference tool for all philosophers and their students. (shrink)

is the second-order theory of the part-whole relation. It can express such hypotheses about the size of Reality as that there are inaccessibly many atoms. Take a non-empty class to have exactly its non-empty subclasses as parts; hence, its singleton subclasses as atomic parts. Then standard set theory becomes the theory of the member-singleton function—better, the theory of all singleton functions—within the framework of megethology. Given inaccessibly many atoms and a specification of which atoms are urelements, a singleton function exists, (...) unique up to isomorphism. (This article is partly abridged from my Parts of Classes, partly a sequel.). (shrink)

This book discusses a range of important issues in current philosophical work on the nature of possible worlds. Areas investigated include the theories of the nature of possible worlds, general questions about metaphysical analysis and questions about the direction of dependence between what is necessary or possible and what could be.