Develops and defends a new metaphysical and logical theory of arbitrary objects that will reinvigorate the philosophy of mathematics.

Presenting the first comprehensive, in-depth study of hyperintensionality, this book equips readers with the basic tools needed to appreciate some of current and future debates in the philosophy of language, semantics, and metaphysics. After introducing and explaining the major approaches to hyperintensionality found in the literature, the book tackles its systematic connections to normativity and offers some contributions to the current debates. The book offers undergraduate and graduate students an essential introduction to the topic, while also helping professionals in related fields get up to speed on open research-level problems.

Frans Coenen University of Liverpool, UK This volume comprises the refereed technical papers presented at AI2003, the Twenty third SGAI International Conference on the theory, practice and application of Artificial Intelligence, held in Cambridge in December 2003. The conference was organised by SGAI, the British Computer Society Specialist Group on Artificial Intelligence (previously known as SGES). The papers in this volume present new and innovative developments in the field, divided into sections on Machine Learning, Knowledge Representation and Reasoning, Knowledge Acquisition, Constraint Satisfaction, Scheduling and Natural Language Processing. This year's prize for the best refereed technical paper was won by a paper entitled An Improved Hybrid Genetic Algorithm: New Results for the Quadratic Assignment Problem by A. Misevicius (Department of Practical Informatics, Kaunas University of Technology, Lithuania). SGAI gratefully acknowledges the long-term sponsorship of Hewlett-Packard Laboratories (Bristol) for this prize, which goes back to the 1980s. This is the twentieth volume in the Research and Development series. The Application Stream papers are published as a companion volume under the title Applications and Innovations in Intelligent Systems XI. On behalf of the conference organising committee I should like to thank all those who contributed to the organisation of this year's technical programme, in particular the programme committee members, the referees and our administrator Fiona Hartree and Linsay Turbert.

In this illuminating collection, Charles Parsons surveys the contributions of philosophers and mathematicians who shaped the philosophy of mathematics over the course of the past century. Parsons begins with a discussion of the Kantian legacy in the work of L. E. J. Brouwer, David Hilbert, and Paul Bernays, shedding light on how Bernays revised his philosophy after his collaboration with Hilbert. He considers Hermann Weyl’s idea of a “vicious circle” in the foundations of mathematics, a radical claim that elicited many challenges. Turning to Kurt Gödel, whose incompleteness theorem transformed debate on the foundations of mathematics and brought mathematical logic to maturity, Parsons discusses his essay on Bertrand Russell’s mathematical logic—Gödel’s first mature philosophical statement and an avowal of his Platonistic view. Philosophy of Mathematics in the Twentieth Century insightfully treats the contributions of figures the author knew personally: W. V. Quine, Hilary Putnam, Hao Wang, and William Tait. Quine’s early work on ontology is explored, as is his nominalistic view of predication and his use of the genetic method of explanation in the late work The Roots of Reference. Parsons attempts to tease out Putnam’s views on existence and ontology, especially in relation to logic and mathematics. Wang’s contributions to subjects ranging from the concept of set, minds, and machines to the interpretation of Gödel are examined, as are Tait’s axiomatic conception of mathematics, his minimalist realism, and his thoughts on historical figures.

"The book is about the problem of vagueness. It begins by discussing some of the existing views on vagueness and then explains why they have not been thought to be satisfactory. It then outlines a new account of vagueness, based upon the general idea that vagueness is a global rather than a local phenomenon.. In other words, the vagueness of an expression or object is not an intrinsic feature of the object or an expression but a matter of how it relates to other objects and expression. The development of this idea leads to a new semantics and logic for vagueness. The semantics and logic are then applied to a number of issues, including the sorites paradox, the transparency of mental states, and personal identity. It is shown that the view allows one to hew to a much more intuitive position on these various issues"--