Philosophy of Mathematics 2ed: Selected Readings Paperback – 27 Jan 1984
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The present collection brings together in a convenient form the seminal articles in the philosophy of mathematics by these and other major thinkers. It is a substantially revised version of the edition first published in 1964 and includes a revised bibliography. The volume will be welcomed as a major work of reference at this level in the field.
From the Back Cover
In a similar vein, we tried also to narrow the range of philosophical issues discussed in the selection ones that could most easily be recognized as concerning the philosophy of mathematics. Both of these admittedly loose principles served as guidelines only; but any attempt to observe them inevitably constrains the range of literature available for consideration.See all Product Description
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It's an excellent introduction to the debates for the beginner and a must-have reference for the graduate.
Most Helpful Customer Reviews on Amazon.com (beta)
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
No sterile polemics, Benacerraf & Putnam simply highlight the questions, the positions, the conundrums, & the costs of holding the various positions in these compelling debates around mathematical truth & understanding.
This book is my vote for heavyweight champ in 20th century philosophy.
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