I am finishing up reading Penelopy Maddy's [2007] "Second Philosophy". I really enjoy her flavor of naturalism. Like Quine, she justifies parts of mathematics because of its application. Unlike Quine, she also justifies the rest of mathematics because it is unreasonable to separate mathematics into philosophically justified and unjustified pieces.

However, to really understand the book, I would like to read some good responses to it. Do you know any strong anti-Second Philosophy responses? Bonus points if they are article (instead of book) length and readable by a mathematician.

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    Any chance I can persuade you to make this a bit more specific (maybe provide a relevant cite summarizing her views, or even a few claims you're interested in finding responses to) -- and perhaps you could discuss what you have found already? – Joseph Weissman Aug 21 '11 at 18:59
  • @Joseph I don't have a good citation to summarize her views, but I guess the answer provides one. I am also a bit afraid to try summarizing it myself, since her arguments are pretty subtle at times, so I feel like I would break them. I will look at my notebook though, and maybe ask more specific questions I had from when I was reading the text! – Artem Kaznatcheev Aug 26 '11 at 0:14

Because it is such a recent work, I doubt you're going to find a lot of literature beyond book reviews.

If you have access to an academic library, I suggest that you do a search in the Philosopher's Index, which will help you find any reviews or articles published in the major journals.

The only review I've found online is this (largely positive) one from the NDPR.

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