Books on the philosophy of mathematics and logic

Question

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

Answer 1

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.

Answer 2

I've been working through Benacerraf and Putnam. As the title suggests, it is a selection of readings, seemingly with the intent of giving an impression of what was happening in mathematical philosophy during the early 1900s (the book itself is from 1964).

Some observations are now obvious to us, such as Hilbert's idea of viewing logical formulas purely abstractly. In these cases it is interesting to see the sources of these ideas and to be reminded that they were once nonobvious.

Some I haven't been able to make sense of, such as Goodman's nominalism, which appears to me to be far removed from our modern understanding of sets. Again, very valuable in reminding us that our modern understanding of sets was once nonobvious.

What has frustrated me the most is when important context is missing. The book is simply a series of writings of mathematical philosophers, and there are occasions where key notation or ideas which were in common use at the time (such as $\varepsilon$ notation) aren't explained.

Answer 3

You might want to add to your list: Lectures on the Philosophy of Mathematics by Joel David Hamkins