Customer Reviews

Thinking about Mathematics: The Philosophy of Mathematics

5 star:		(4)
4 star:		(2)
3 star:		(2)
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Anybody who's interested in why mathematics might have the least bit to do with philosophy will be interested in this book. To many the philosophy of mathematics may seem too specialized and peripheral to be of much interest. But such is not the case. The philosophy of math is intricately intertwined with many of the classic epistemological questions that I have never seen satisfactory answers to. This book will force you to think about things you have never considered before. Why does mathematics 'just happen' to describe empirical studies so well if mathematics is solely logical and in the head? Or is mathematics empirical and merely charading as necessary logical truth? These questions will be brought up in the book and the different answers given from the different philisophical sides.

Some of the book is a little dense and may be skimmed. He does go into detail a bit much in some places and the non technical reader will be lost. But Shapiro usually does do a good job of summarizing complex thoughts.

This book whetted my appetite for more and I plan on continuing thinking about these things and hopefully take some classes in mathematical logic and philosophy.

In this introductory level text Prof. Shapiro has presented a thorough introduction to the philosophy of mathematics. Not only does he discuss the three most fundamental positions in the field, but he also provides insight into more recent developments. I would highly suggest this work to anyone interested in having a solid understanding of this issues at stake in the philosophy of mathematics. Along with Paul Benacerraf and Hillary Putnam's book of philosophy of mathematics readings this is a must have!

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.

I am a reader with some basic background in logic and philosophy of language. Despite this background, I find Shapiro terribly difficult to read. For example, I read the section on Kant three times and am still not sure whether I understood anything. There must be simpler ways of explaining the material he presents.

So this might be a great book for someone with a solid backgrounds in both philosophy and mathematics who wants to know more about questions at the crossroads of both fields. However, I absolutely do not recommend it as an introduction to these ideas.

An excellent book that I recommend to readers interested on mathematical philosophy who are not specialists. A nice difference with other books covering the topic is that no term is considered known so the reader does not have to be accompanied with a philosophy encyclopedia. Needless to say that concepts and ideas are clearly exposed. Congratulations to Prof. Shapiro.

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.

Shapiro does a good job of creating an overview of the philosophy of mathematics as it exists from inception to contemporary thought. The topic material is usually difficult but it is also explained as well as I've seen anywhere else.

I recommend this book to all that are interested in the philosophy of mathematics that have only a minimal background in both. It clearly explains all of the debates that exist in the philosophy of mathematics and the major schools of it. Read this book.