- Paperback: 328 pages
- Publisher: Oxford University Press; 1 edition (October 5, 2000)
- Language: English
- ISBN-10: 0192893068
- ISBN-13: 978-0192893062
- Product Dimensions: 8.2 x 0.7 x 5.2 inches
- Shipping Weight: 1.1 pounds (View shipping rates and policies)
- Average Customer Review: 18 customer reviews
- Amazon Best Sellers Rank: #188,973 in Books (See Top 100 in Books)
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Thinking about Mathematics: The Philosophy of Mathematics 1st Edition
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"Stewart Shapiro admirably provides an accessible introduction to contemporary thinking in mathematics, while avoiding caricature of the technicalities. His ease with the subject and lucid style makes this book a succinct introduction to a fascinating intellectual discipline." Times Literary Supplement
About the Author
Stewart Shapiro is Professor of Philosophy at Ohio State University at Newark and Professorial Fellow in the Department of Logic and Metaphysics at the University of St Andrews, Scotland.
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Some will say that mathematical philosophy, or the closely related philosophy of mathematics, only began in the 1980's in earnest. But reading the "big 5" shows threads going back to antiquity. The field is far from settled, and the two aspects--the philosophy of math itself, and the closely related field of applying math and logic TO other branches of philosophy, has enough active journalized information in the mid 2014+ years to fill 50 volumes. Since thousands have been written in mainline philosophy, and even the philosophy of science as well as logic, this is not without surprise and mystery.
The good news is that an invested, energetic reader can pick up this handful of keys and be in the top percent of folks on the planet with a good foundation! This is hardly true of any other field. I'd start with Shapiro's Oxford Encylopedia, study Benacerraf and Putnam's classic collection of essays, then finish with Shapiro's deep and difficult "Thinking about" and of course Russell and Frege for historic and specialized puzzle pieces.
One "sleeper" I'd like to recommend that is not usually included in comparisons of books in this field is Steinhart: More Precisely: The Math You Need to Do Philosophy.
Eric helps with both math within philosophy (the basics) and tangentially helps with the math used as examples within the philosophy OF math. Beyond the issues of categorization, discovery, math as model vs. underpinning reality ala the Matrix, there of course is the whole field of logic, induction, deduction, etc. which has thousands of volumes. The six mentioned here cover logic, but are much more specific in the broader subject area of mathematics, which now includes dynamical systems and differential equations undreamt of in the past, and bringing many new mental tools to bear, from intuition to analytic, qualitative, numeric, perturbative and of course stochastic. Here are the other links to those mentioned in this survey:
The Oxford Handbook of Philosophy of Mathematics and Logic (Oxford Handbooks)
Thinking about Mathematics: The Philosophy of Mathematics
Philosophy of Mathematics: Selected Readings
The Foundations of Arithmetic: A Logico-Mathematical Enquiry into the Concept of Number
Introduction to Mathematical Philosophy
you could have trouble understanding this book (and likely any other book
on the philosophy of mathematics). Having a mathematics education with no
real philosophy classes taken isn't enough The course in logic ( the one offered
by the philosophy department) that college mathematics majors take will not help
you very much. A dictionary of philosophy is needed when you are reading
the text. and then it's still hard to read through -- that's how it was for me! And I
thought that I could get good at the philosophy of mathematics! The book
is described by the author as a popular math philosophy book. You can start reading
this book with the intention of going through all of it and you might not complete the read.
There are more basic philosophy of mathematics books available, but not many.
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.