Øystein Linnebo*. Philosophy of Mathematics

Philosophy of Mathematics by Øystein Linnebo is published in the Princeton Foundations of Contemporary Philosophy series, a series under the editorship of Scott Soames. It is a survey of some of the central questions, theories, and problems in the philosophy of mathematics. It is intended for graduate students and advanced undergraduate students in philosophy, as well as mathematicians and those interested in the foundations of mathematics. The book consists of twelve chapters, which together with the short introduction and back matter span 203 pages. Chapter One gives a very brief outline on the views of Plato and Kant on the philosophy of mathematics. This brief presentation of Kant’s view would have to be the most challenging part of the book for non-philosophers. Linnebo mentions in the introduction that space considerations led to some topics, including pre-Fregean philosophy of mathematics being given only the briefest treatment, and others not treated at all. Of the subjects not considered at all, Linnebo lists `Wittgenstein on mathematics, explanation in mathematical practice, the philosophy of mathematical practice, the use of experimental and nontraditional methods in mathematics, and new developments such as homotopy type theory’ (pp. 2–3).