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Here is a list of some books on the philosophy of Mathematics and logic founded in an article about this matter. I would like to buy one or maybe two of these or any other suggested books.

I would be very grateful if you could give me opinions about these or other books. Thank you in advance.

  • Benacerraf, Paul, and Hilary Putnam, editors (1983), Philosophy of Mathematics: selected readings,
  • Hart, W. D., editor (1997), The Philosophy of Mathematics
  • Jacquette, Dale, editor (2002), Philosophy of Mathematics: An Anthology
  • Schirm, Matthias, editor (2003), The Philosophy of Mathematics Today
  • Shapiro, Stewart (2000), Thinking About Mathematics. Oxford
  • Shapiro, Stewart, editor (2005), The Oxford Handbook of Philosophy of Mathematics and Logic
  • Beaney, Michael, editor (1997), The Frege Reader
  • Ewald, William, editor (1996), From Kant to Hilbert: a source book in the foundations of mathematics
  • Giaquinto, Marcus (2002), The Search for Certainty: a philosophical account of foundations of mathematics
  • Haaparanta, Leila, ed., The History of Modern Logic
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Everything you mention has some virtues, but if philosophy of maths (and relevant bits of logic) is your main interest, I'd start with one or both of

Shapiro's book, The Philosophy of Mathematics Today, for a good reliable introduction to the area, written for students (the level of senior undergraduate philosophers).

Also written for students, Giaquinto's The Search for Certainty: a philosophical account of foundations of mathematics is also quite excellent and very lucid.

I (used to) recommend these very warmly to students. Then, for a lot more at a notch or two up in sophistication,

Shapiro's Handbook is terrific -- mostly very accessible but very good essays on various areas of the philosophy of maths and logic written by distinguished and reliable authors.

As handbooks of this type go, Shapiro's is quite outstanding. Each of the articles has a biblio that will point you to further reading if a topic graps your interest.

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My to bets where Shapiro's Handbook and Bencerraf and Putman Philosophy of mathematics. Thank you very much for the advise. – Guillermo Jan 2 '13 at 11:55
@Guillermo You are welcome -- but if you use math.SE do get into the habit of voting up/accepting answers you like. – Peter Smith Jan 2 '13 at 12:06

Beaney's The Frege Reader (1997) is a good book, but if you are particularly interested about Frege's philosophy of mathematics I would better recommend:

Dummett's Frege Philosophy of Mathematics (1991)

Beaney's Frege Making Sense (1996)

Kenny's Frege: An introduction to the Founder of Modern Analytic Philosophy (1995)

Weiner's Frege (Past Masters) (1999)

No one has studied (and written more books on the subject) than Micheal Dummett about Frege's philosophy. His treatment of Frege's philosophy on the above book is more systematical and complex than the above authors (although I particularly do not appreciate his writing style). For a soft introduction, I would rather recommend you to pick the three other ones.

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