Paul Halmos remarked in his automathography that a good way to learn a lot of mathematics is by reading the first chapters of many mathematics books. Wouldn't it be nice, though, if there was a single book that eliminated the overlapping material such an exercise would entail, included frequent cross-references between topics, and sought to show the connections between various branches of mathematics...and all this between the covers of one volume for around a hundred bucks?
Eric Schechter has written such a book, "The Handbook of Analysis and Its Foundations", Academic Press, 1997.
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This seems like a great text. I just looked at some of the reviews on Amazon. Perhaps the conceptual emphasis would make this an appropriate text for graduate students in philosophy who need exposure to these topics. Such a text might be used to introduce philosophy students to modeling perspectives other than the logical frameworks that are usually taught in philosophy departments. Not that there is anything wrong with logical frameworks, but I'm inclined to think that their emphasis on language can lock one into a certain mindset. Sometimes a shift in perspective is just what the doctor ordered. Then again, I might be way off on this.
I agree that there is a lopsided emphasis on language in philosophy.
Computer scientists tend to be more flexible about formal methods--promiscuous, even. And I have a soft spot for people with loose morals. But the price paid in this instance is that there is typically less interest in foundations and a premium placed on positive results, no matter how hair-brained.
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