Philosophy of Mathematics: Selected Readings
Book Summary Information
Editor: Paul BenacerrafEditor: Hilary Putnam
Edition: Paperback
Audio: English (Original Language); English (Unknown); English (Published)
Published: 1984-01-27
ISBN: 052129648X
Number of pages: 612
Publisher: Cambridge University Press
Book Reviews of Philosophy of Mathematics: Selected Readings
Book Review: Indespensable compilation of the great papers.
Summary: 5 Stars
I checked the first edition of this book out from the library when composing my senior thesis, and enjoyed it so much that I continued to read it long after I was finished, finally buying a copy of the second edition for myself. The first edition was an outstanding compilation of the most influential papers on the subject, hand-picked by two of the giants of modern philosophy. The second edition is, by and large, an improvement on the first, with more relevant selections added and less relevant selections removed (I would have liked to see "Logic Without Ontology" retained in the new edition, but it can be obtained elsewhere). A great benefit of this volume is that it is the only volume, as far as I know, still in print which contains the important essays on intuitionism by Brouwer and Heyting (the series edited by the two on the foundations of mathematics is, sadly, out of print). The inclusion of these essays is not only helpful for historical interest, but also keeps with the book's spirit of presenting the full spectrum of mathematical philosophy.
One of the difficulties with presenting the philosophy of mathematics in a popular or summarized form is that, as with most analytic philosophy, it isn't possible to obtain any kind of understanding of the subject by partitioning it into schools of thought. Each author is unique. Because of this, it is much better to try to use a volume such as this one from the outset, rather than starting with an egregiously oversimplified account such as Korner's "The Philosophy of Mathematics: An Introductory Essay" (the book typically used to introduce the subject). So, not only would this make a superb text on the subject for a seminar, but it is also my first resort when I need a reference.
Summary of Philosophy of Mathematics: Selected Readings
The twentieth century has witnessed an unprecedented 'crisis in the foundations of mathematics', featuring a world-famous paradox (Russell's Paradox), a challenge to 'classical' mathematics from a world-famous mathematician (the 'mathematical intuitionism' of Brouwer), a new foundational school (Hilbert's Formalism), and the profound incompleteness results of Kurt G?del. In the same period, the cross-fertilization of mathematics and philosophy resulted in a new sort of 'mathematical philosophy', associated most notably (but in different ways) with Bertrand Russell, W. V. Quine, and G?del himself, and which remains at the focus of Anglo-Saxon philosophical discussion. The present collection brings together in a convenient form the seminal articles in the philosophy of mathematics by these and other major thinkers. It is a substantially revised version of the edition first published in 1964 and includes a revised bibliography. The volume will be welcomed as a major work of reference at this level in the field.Philosophy Books
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