Abstracts for 2008

See abstracts for 2008, 2007, 2006, 2005, 2004, 2003, 2002, 2001, 2000, 1999, 1998, 1997, 1996, 1995, 1994, 1993, 1992, 1991, 1990, 1989, 1988, 1987, 1986, pre-1986.

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Brown, J. (2008). Philosophy of Mathematics: a contemporary introduction to the world of proofs and pictures. 2nd edition. New York: Routledge.

In his long-awaited new edition of Philosophy of Mathematics James Robert Brown tackles important new as well as enduring questions in the mathematical sciences. Can pictures go beyond being merely suggestive and actually prove anything? Are mathematical results certain? Are experiments of any real value? This clear and engaging book takes a unique approach, encompassing nonstandard topics such as the role of visual reasoning, the importance of notation, and the place of computers in mathematics, as well as traditional topics such as formalism, Platonism, and constructivism. The combination of topics and clarity of presentation make it suitable for beginners and experts alike. The revised and updated second edition of Philosophy of Mathematics contains more examples, suggestions for further reading, and expanded material on several topics including a novel approach to the continuum hypothesis.

Mancosu, P. (2008).Explanation in Mathematics. In E. N. Salta (Ed.), Stanford Encyclopedia of Philosophy, (Summer 2008 Edition). <http://plato.stanford.edu/archives/sum2008/entries/mathematics-explanation/>.

The philosophical analysis of mathematical explanation concerns itself with two different, although connected, areas of investigation. The first area addresses the problem of whether mathematics can play an explanatory role in the natural and social sciences. The second deals with the problem of whether mathematical explanations occur within mathematics itself. Accordingly, this entry surveys the contributions to both areas, it shows their relevance to the history of philosophy and science, it articulates their connection, and points to the philosophical pay-offs to be expected by deepening our understanding of the topic.

Tennant, N., Guest Editor. (2008). Special Issue: Carnap and Some Contemporaries.Philosophia Mathematica. 16(1).

This Special Issue contains five contributions, all of them dealing either with Carnap's influence on debates in the philosophy ofmathematics, or with the thought of important contemporaries of Carnap - sympathizers such as Scholz and Weyl, and critics such as Godel and Kreisel. The contributions were originally solicited in service of the theme 'The legacy of Logical Positivism for the philosophy of mathematics'. As is often the case with joint enterprises among independent scholars, however, divergences in focus and problems resulted in a somewhat loosely related set of essays.

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See abstracts for 2008, 2007, 2006, 2005, 2004, 2003, 2002, 2001, 2000, 1999, 1998, 1997, 1996, 1995, 1994, 1993, 1992, 1991, 1990, 1989, 1988, 1987, 1986, pre-1986.