Reason's Nearest Kin: Philosophies of Arithmetic from Kant to Carnap [Hardcover]

Michael Potter (Author)

Book Description

Publication Date: June 1, 2000 | ISBN-10: 019825041X | ISBN-13: 978-0198250418

This is a critical examination of the astonishing progress made in the philosophical study of the properties of the natural numbers from the 1880s to the 1930s. Reassessing the brilliant innovations of Frege, Russell, Wittgenstein, and others, which transformed philosophy as well as our understanding of mathematics, Michael Potter places arithmetic at the interface between experience, language, thought, and the world.

Editorial Reviews

Review

`both stimulating and insightful' MIND, Vol.110, No.439

`Another virtue of the book is its careful attention to the interaction of technical and philosophical issues. Adept in mathematics, Potter nicely brings out the mathematical content of various philosophical positions. His chapter on the Tractatus is particularly admirable in this respect; it must be one of the best discussions available of the philosophy of mathematics developed in that work' MIND, Vol.110, No.439

`refreshingly different from much of the recent work in the field' MIND, Vol.110, No.439

`There is much of value in the book, not just for those interested in the philosophy of mathematics.' Michael Potter, TLS

`an instructive and absorbing history of a critical fifty-year period in the philosophy of mathematics' Michael Potter, TLS

About the Author

Michael Potter is a Fellow of Fitzwilliam College, Cambridge, and University Lecturer in Philosophy, having previously been Lecturer in Mathematics.

Product Details

• Hardcover: 320 pages
• Publisher: Oxford University Press, USA (June 1, 2000)
• Language: English
• ISBN-10: 019825041X
• ISBN-13: 978-0198250418
• Product Dimensions: 9.3 x 6 x 1 inches
• Shipping Weight: 1.4 pounds (View shipping rates and policies)
• Average Customer Review: 3.0 out of 5 stars  See all reviews (1 customer review)
• Amazon Best Sellers Rank: #4,249,908 in Books (See Top 100 in Books)

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13 of 18 people found the following review helpful:

3.0 out of 5 stars Mainly suited for professional philosophers, November 26, 2004

By 

Marvin J. Greenberg (Berkeley, CA USA) - See all my reviews
(REAL NAME)   

This review is from: Reason's Nearest Kin: Philosophies of Arithmetic from Kant to Carnap (Paperback)

After the great enjoyment and education I obtained from Potter's excellent new book SET THEORY and its PHILOSOPHY, I immediately bought a copy of this treatise, subtitled PHILOSOPHIES OF ARITHMETIC from KANT to CARNAP.

I am a mathematician, not a professional philosopher. I am very interested in the philosophical ideas that motivate, generate, justify or refute parts of mathematics. Yet, after reading this dedicated effort by Potter to explain and criticize the thinking of Kant, Frege, Wittgenstein and Carnap regarding the nature of arithmetic truths, I came away, regarding those four, agreeing even more with Gauss' disparagement of "the say-nothing word-wisdom of the metaphysicians" (letter to Taurinus in 1824). At least Potter in his Conclusion section, announces frankly that "all the accounts we have considered have turned out to be flawed."

Fortunately, the chapter on Dedekind reviewed what I had already enjoyed about his work in Potter's set theory book. The chapters on Hilbert and Gödel were outstanding, though much too brief. Potter's discussion of his version of Gödel's second incompleteness theorem, with a discussion of outer consistency and inner consistency and their formal equivalence in case the proof function is "well-presented" was especially fascinating. I wish he had supplied a reference or two (e.g., to Sol Feferman's work) for the technical details he skipped in his argument .

Just as he wrote a much better philosophy of set theory book the second time, I think Michael Potter is certainly capable of writing a much better philosophy of arithmetic book the second time, provided he focuses only on the seriously mathematical work in that subject, such as that by Hilbert, Gödel, Gentzen, Kleene, Tarski, Feferman, Matiyasevich, Davis and other more recent mathematical workers in the logic of arithmetic.

My advice to mathematicians is to avoid this book except for the chapters on Hilbert and Gödel. Mathematicians really don't worry, as Frege did, about whether or not Julius Caesar was a number.