Another Sort Of Mathematics
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Another Sort of Mathematics
Years ago, James V. Schall wrote Another Sort of Learning, a book listing those things you should read but probably were never required to read. It is not a curriculum, except maybe one “for life.” This book you have in your hands is something of a mathematical tribute to Schall’s basic idea and is aptly titled Another Sort of Mathematics. Like Schall’s book, it is not a curriculum. It is, however, a list of some things from mathematics you should experience but probably were never required to experience. The theorems and proofs in this book represent, in a small way, some of the best that has been said within the discipline of mathematics. There is something unique in the human soul that can only be satisfied by wondering about mathematics. And that means, regardless of your background, this book is for you. Reclaim your mathematical inheritance. Embrace the mathematician within you. Choose to wonder.
New Waves in Philosophy of Mathematics
Thirteen promising young researchers write on what they take to be the right philosophical account of mathematics and discuss where the philosophy of mathematics ought to be going. New trends are revealed, such as an increasing attention to mathematical practice, a reassessment of the canon, and inspiration from philosophical logic.
Platonism, Naturalism, and Mathematical Knowledge
This study addresses a central theme in current philosophy: Platonism vs Naturalism and provides accounts of both approaches to mathematics, crucially discussing Quine, Maddy, Kitcher, Lakoff, Colyvan, and many others. Beginning with accounts of both approaches, Brown defends Platonism by arguing that only a Platonistic approach can account for concept acquisition in a number of special cases in the sciences. He also argues for a particular view of applied mathematics, a view that supports Platonism against Naturalist alternatives. Not only does this engaging book present the Platonist-Naturalist debate over mathematics in a comprehensive fashion, but it also sheds considerable light on non-mathematical aspects of a dispute that is central to contemporary philosophy.