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Rating: Summary: Excellent introduction to the philosophy of mathematics Review: I finished my Maths degree in 1975, so many of the more recent developments (references are made right up to 1997) were not always comprehensible to me, but I still got enjoyment out of dipping through this book.If these 2 examples don't spark any interest for you in the discussion that followed, then this book is not for you : Kant : The concept expressed by the English word 'triangle' contains the concept of being 'three-angled'. Does it also contain the concept of 'three-sided'? The German word for 'triangle' is 'Dreieck', or 'three-cornered'. Presumably, that concept includes 'three-angled', but, again, does it include 'three-sided'? Formalism : Consider the equation 0=0. If you print this out, you cannot say that the equation says that the leftmost hunk of ink shaped like an oval is identical to the rightmost hunk of ink also shaped like an oval. Clearly, those are two different hunks of ink.
Rating: Summary: 5 Stars for Stain on Tie! Review: I found this book gave an excellent and amazingly evenhanded overview of the history and contemporary state of PhiMath. Since any discussion of the Philosphy of Science usually takes only 5 minutes before getting into PhiMath, this book will also interest PhiSci-ers as well. The presentation was clear without being simplistic and without any waste. As an electrical engineer with a strong interest in PhiSci this book was the best general intro to the subject I've come across. I especially liked the large coffee stain on the author's tie on the front cover.
Rating: Summary: Incredibly clear Review: The title of my review doesn't imply that it's bad for a philosopher, but I'm mostly a student of math (so I can't speak for philosophers). Anyway, this book does seem mostly designed for people who know a bit about set theory and logic. I would also think that in any discussion of the philosophy of math, one also needs to have some understanding of mathematics as a whole (i.e. to be able to hold a semi-intelligent conversation on mathematical topics). If you have this background, then this book seems to cover (what I presume to be) the basics of the philosophy of mathematics in such a way that little background in philosophy is required. I highly recommend it.
Rating: Summary: Incredibly clear Review: This is the best introduction to the philosophy of mathematics I've come across. The concepts presented are clear, up to date, and presented with a minimum of formulas and symbols. The author has an easy going style that will just pull you into this fascinating topic.
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