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Philosophy of Mathematics
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This study guide will recommend sources that provide an introduction to the major issues in the philosophy of mathematics, and the historically important views on these issues. Some familiarity with mathematics is a prerequisite for thinking about these issues. The book What is Mathematics?, by Richard Courant and Herbert Robbins, is a brilliant exposition of the topics and methods of modern mathematics. The book is intended for laymen, but none of the essence of the mathematics has been omitted; it is not a simple book, but it is rewarding.
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The Philosophy of Mathematics Today gives a panorama of the best current work in this lively field, through twenty essays specially written for this collection by leading figures. The topics include indeterminacy, logical consequence, mathematical methodology, abstraction, and both Hilbert's and Frege's foundational programmes. The collection will be an important source for research in the philosophy of mathematics for years to come. Contributors Paul Benacerraf, George Boolos, John P. Burgess, Charles S. Chihara, Michael Detlefsen, Michael Dummett, Hartry Field, Kit Fine, Bob Hale, Richard G. Heck, Jnr., Geoffrey Hellman, Penelope Maddy, Karl-Georg Niebergall, Charles D. Parsons, Michael D. Resnik, Matthias Schirn, Stewart Shapiro, Peter Simons, W.W. Tait, Crispin Wright.
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Philosophy of mathematics is an active discipline of inquiry and the resulting subject matter. As a branch of philosophy, it addresses questions about the character of mathematics, the conduct of mathematical inquiry, and the role of mathematical objects in describing empirical phenomena. As a form of philosophical inquiry, it examines the record of mathematical inquiry and poses questions regarding its aims, its conduct, and its results. Although the questions are diverse and never-ending, a number of recurrent themes can be recognized:
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The Philosophy of Mathematics Workshop traditionally meets most quarters on Mondays at 3:00 PM in the Philosophy Common Room (Dodd 399). It has not met during the 2006-07. Officially this is a graduate course, but most attendees are not enrolled -- participants are mostly faculty and graduate students from graduate programs in Philosophy or Linguistics within driving distance of UCLA, and others who are visiting the area. All faculty and graduate students are welcome. Topics vary from quarter to quarter, and sometimes during the quarter. Sometimes a departmental colloquium speaker is enticed into leading a workshop discussion, and sometimes speakers from elsewhere come and talk.
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"For breadth of coverage, Jacquette's anthology of recent work in philosophy of mathematics has few if any rivals. Many of Jacquette's selections are important for understanding current debates, and he provides helpful introductory discussions. This collection will very likely become a standard resource for students and teachers of this field." Sanford Shieh, Wesleyan University
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This course focuses on points of contact between philosophy and the arts. The course examines and attempts to develop theories of artistic representation, of expression in art and elsewhere, of the nature of metaphor and its role in art criticism, and of the nature of art. These matters are approached via works in the various arts and the writings of philosophers.
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Philosophy of Mathematics