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Philosophy of Mathematics: Selected Readings Paperback – January 27, 1984

ISBN-13: 978-0521296489 ISBN-10: 052129648X Edition: 2nd

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Product Details

  • Paperback: 612 pages
  • Publisher: Cambridge University Press; 2 edition (January 27, 1984)
  • Language: English
  • ISBN-10: 052129648X
  • ISBN-13: 978-0521296489
  • Product Dimensions: 1.5 x 6 x 8.9 inches
  • Shipping Weight: 2 pounds (View shipping rates and policies)
  • Average Customer Review: 4.4 out of 5 stars  See all reviews (5 customer reviews)
  • Amazon Best Sellers Rank: #292,906 in Books (See Top 100 in Books)

Editorial Reviews

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Includes several classic essays from the first edition, a representative selection of the most influential work of the past twenty years, a substantial introduction, and an extended bibliography. Originally published by Prentice-Hall in 1964. -- Book Description

Book Description

Includes several classic essays from the first edition, a representative selection of the most influential work of the past twenty years, a substantial introduction, and an extended bibliography. Originally published by Prentice-Hall in 1964.

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4 of 5 people found the following review helpful By Flash Sheridan on March 10, 2011
Format: Paperback
This is an excellent standard selection of classic works in the field; indeed, by now, that is something of a self-fulfilling prophecy, since inclusion in this anthology is approximately the definition of classic. The essays cover a broad range of positions, many of which (of course) I disagree with. But they're almost all well worth reading--my particular favorite is the unpopular part of Godel's Platonism, which is a useful antidote to overconfidence that these matters are settled.
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Format: Paperback
The amazing thing about the little handful of books on Mathematical Philosophy--2 by Shapiro, Frege, Russell and of course Benacerraf and Putnam's classic, is the paucity of literature in this key field!
Some will say that mathematical philosophy, or the closely related philosophy of mathematics, only began in the 1980's in earnest. But reading the "big 5" shows threads going back to antiquity. The field is far from settled, and the two aspects--the philosophy of math itself, and the closely related field of applying math and logic TO other branches of philosophy, has enough active journalized information in the mid 2014+ years to fill 50 volumes. Since thousands have been written in mainline philosophy, and even the philosophy of science as well as logic, this is not without surprise and mystery.

The good news is that an invested, energetic reader can pick up this handful of keys and be in the top percent of folks on the planet with a good foundation! This is hardly true of any other field. I'd start with Shapiro's Oxford Encylopedia, study Benacerraf and Putnam's classic collection of essays, then finish with Shapiro's deep and difficult "Thinking about" and of course Russell and Frege for historic and specialized puzzle pieces.
One "sleeper" I'd like to recommend that is not usually included in comparisons of books in this field is Steinhart: More Precisely: The Math You Need to Do Philosophy.

Eric helps with both math within philosophy (the basics) and tangentially helps with the math used as examples within the philosophy OF math. Beyond the issues of categorization, discovery, math as model vs.
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1 of 2 people found the following review helpful By Lisa P. Maguire on October 4, 2012
Format: Paperback Verified Purchase
The pro comments (that the book is definitive) as well as the con (that one needs some background in logic, math, phil to understand it) are both correct. I have a bare bones undergraduate grasp of philosophical issues & my math is inadequate, therefore I found numerous passages just in the introduction that challenged my patience, intelligence (such as it is) & will to absorb. My conclusion, however, is that the reward-to-work ratio is greater in this text than any other book I know of in contemporary philosophy. The results of the labor required has been an added measure of humility and enlightenment. In fact, I wish I could trade years I devoted to Nietzsche, Heidegger, Derrida, Foucault, Ayer, Rorty and even Wittgenstein (as pleasurable as all that was at the time) to get to this work earlier.
No sterile polemics, Benacerraf & Putnam simply highlight the questions, the positions, the conundrums, & the costs of holding the various positions in these compelling debates around mathematical truth & understanding.
This book is my vote for heavyweight champ in 20th century philosophy.
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12 of 22 people found the following review helpful By Isaac Adams on January 24, 2008
Format: Paperback
Don't try reading this book if you have little background with analytic philosophy, logic, and math. Although you're unlikely to be interested in it if you don't have that background. Some great works about the nature of mathematics are included here but make sure you have the background or it won't make sense.
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6 of 17 people found the following review helpful By Viktor Blasjo on June 29, 2009
Format: Paperback
This is a useful anthology. I shall not argue its merits or demerits, but rather submit the following thesis: the shortcomings of virtually all of these theories are traceable to their unwarranted identification of mathematics with 20th century axiomatic mathematics. Bernays asserts that since "the customary manner of doing mathematics ... consists in establishing theories detached as much as possible from the thinking subject," any contrary view is "extreme" (p. 267). "The customary manner of doing mathematics" is thus glorified: it is tacitly assumed that "the customary manner" will reign supreme for all future. Otherwise it would not be "extreme" to suggest that "the customary manner" may not be infallible. Now of course one does not infer the absolute truth of an economic theory from its successful account of one particular society. But precisely this is being done in the case of philosophy of mathematics.

Let us begin with the ever-foolish logical positivists. They define their position against Mill, who "maintained that [mathematical] propositions were inductive generalizations based on an extremely large number of instances" (Ayer, p. 317). Incidentally we later see Hempel making the exact same argument (p. 378), the positivist herd being predictable as always. But back to Ayer. The argument against Mill is that mathematical propositions are unfalsifiable: "Whatever instance we care to take, we shall always find that the situations in which a logical or mathematical principle might appear to be confuted are accounted for in such a way as to leave the principle unassailed" (p. 319). Therefore, the doctrine goes, mathematical propositions are analytic a priori, they are true "by virtue of definitions" (Hempel, p.
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