- Paperback: 315 pages
- Publisher: OUP Oxford; New Ed edition (13 Jun 2002)
- Language English
- ISBN-10: 0199252610
- ISBN-13: 978-0199252619
- Product Dimensions: 23.5 x 16.1 x 1.7 cm
- Amazon Bestsellers Rank: 1,023,817 in Books (See Top 100 in Books)
- See Complete Table of Contents
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This is an excellent book: informative, suggestive, and a genuine pleasure to read. (William Demopoulos, British Journal for the Philosophy of Science )
William Demopoulos, British Journal for the Philosophy of Science
"This is an excellent book: informative, suggestive, and a genuine pleasure to read."
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First Sentence
Our problem, I have said, is to reconcile the necessity of arithmetic with its applicability. Read the first page
Front Cover | Copyright | Table of Contents | Excerpt | Index | Back Cover
Our problem, I have said, is to reconcile the necessity of arithmetic with its applicability. Read the first page
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Front Cover | Copyright | Table of Contents | Excerpt | Index | Back Cover
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1 review
13 of 18 people found the following review helpful
Mainly suited for professional philosophers
27 Nov 2004
Format: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.
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.
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