Philosophy of Mathematics: A Contemporary Introduction to the World of Proofs and Pictures (Routledge Contemporary Introductions to Philosophy) 2nd Edition by James Robert Brown (PDF)

Description

In his long-awaited new edition of Philosophy of Mathematics, James Robert Brown tackles important new as well as enduring questions in the mathematical sciences. Can pictures go beyond being merely suggestive and actually prove anything? Are mathematical results certain? Are experiments of any real value? This clear and engaging book takes a unique approach, encompassing non-standard topics such as the role of visual reasoning, the importance of notation, and the place of computers in mathematics, as well as traditional topics such as formalism, Platonism, and constructivism. The combination of topics and clarity of presentation make it suitable for beginners and experts alike. The revised and updated second edition of Philosophy of Mathematics contains more examples, suggestions for further reading, and expanded material on several topics including a novel approach to the continuum hypothesis.

User’s Reviews

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐I’ve always had trouble with the idea that mathematicians discover things, as opposed to inventing them. You see, if you discover something, the implication is that that something is, in some sense, out there. But where would mathematical entities reside, if not inside human brains and thought processes? I must say, reading this book has if not changed my mind at least made me seriously question my positions – which is really what you want from any good book. Brown’s treatment is relatively accessible, but of course you will be in for a good amount of philosophy, and some not so easily digestible math. Still, the attentive reader can get the gist of the arguments without having to follow every proof presented by the author. I am a little less convinced, though still intrigued, by Brown’s claim that pictures can – in some circumstances – do the work of formal proofs. Then again, that notion does appeal to my generally pluralistic attitude about methods of inquiry, and it does fit very well with the author’s overall contention that mathematics is – surprisingly – a lot more like the natural sciences than one might think at first. Of course, all of this leaves completely unanswered the underlying question of the ontological status of mathematical objects. Oh well, can’t get everything out of a single book.

⭐Good and thorough coverage of the major subjects with plenty of references. Clearly written with lots of examples. Highly recommended.

⭐subtract the left-wing anti-american rants and you may have an interesting book on the philosophy of mathematics. i wouldn’t know. i stopped reading after seeing brown call murray & herrnstein’s The Bell Curve “a vile book”, which, judging by the author’s comments, it is plain that he has not read.

⭐I second the objections to this book raised by the previous 1 star review. I further wish to rant about the tone of the entire book…I must be honest, I have not finished the book. I am considering not doing so. The Platonist biased is too strong for a simple introduction.In that this is pegged as an introduction the demographic is presumably those who are not familiar with the arguments for the positions philosophers of mathematics hold. In this regard I feel it is bad form to produce an introduction that is so obviously skewed. It is reassuring that the author is up front concerning his position and bias. However, when the author off handedly rejects arguments by some of the giants in the field as non-sequiturs, he is doing a diservice to his readers who are as much his students. This is bias affecting argumentation that is bad form in philosophy, as far as I am concerned.

⭐I didn’t read this book, but I’d like to share with the other customers the “review” by Thomas William Körner, a mathematician from Cambridge University (winner of the Salem Prize 1972) that I appreciate so much for his vastly erudite, instructive, and entertaining books on mathematics. In chapter 1 of his ”

⭐,” Professor Körner states: “A good example of this [that people are easily fooled by intuition and ignorance of mathematics] is given in the book [9] [J. R. Brown, “Philosophy of Mathematics]. The author cannot understand the problems involved in proving results like the intermediate value theorem and has written his book to share his lack of understanding with a wider audience.”What else can I say?

⭐I am neither an undergraduate philosophy student nor a logician so the second half of this book was lost on me.However the first half was a suprisingly entertaining and to me somewhat iconoclastic defence of Platonism in mathematics and a suprisingly informative and convincing demonstration that diagrams can be more than heuristic devices as I have been taught but can be used to create valid general proofs.

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