How to use this book Introduction: Terminology and Axioms Part I: Ancients and Medievals Introductory overview I.1. Pythagoreans I.2. Parmenides and Zeno’s Paradoxes I.3. Plato I.4. Aristotle Part II: Moderns Introductory overview II.1. The Rationalists II.2. The Empiricists II.3. Kant Part III: 19th and Early 20th Centuries Introductory overview III.1. Mill III.2. Cantor III.3. Logicism III.4. Formalism III.5. Intuitionism III.6. Conventionalism III.7. Wittgenstein III.8. Gödel’s Theorem III.9. Gödel’s Platonism Part IV: Contemporary Views Introductory overview IV.1. The Problem IV.2. The Indispensability Argument IV.3. Benacerraf’s Number Puzzle and Structuralism IV.4. Modalism IV.5. Fictionalism. IV.6. Apriorism IV.7. Naturalism. IV.8. Plenitudinous Platonism V.9. Challenges to Mathematical Apriorism Bibliography Index
An introduction to the philosophy of mathematics, using a collection of historical sources with an informed eye to contemporary debates.
Russell Marcus is Assistant Professor in the Department of Philosophy at Hamilton College, New York, USA. Mark McEvoy is Associate Professor of Philosophy at Hofstra University, USA.
This is a reader-friendly, broad collection of original works on
the philosophy of mathematics, ranging from Pythagoras to other
contemporary authors. The subjects are organized chronologically,
rather than thematically. Each chapter starts with a valuable
introductory overview; this puts the original works of the chapter
into context, suggests aspects of information to explore, and
offers recommendations for further reading. Part 1
(“Ancients”—Pythagoras, Plato and Aristotle) and part 2
(“Moderns”—Descartes, Leibniz, Locke, Kant, etc.) are primarily
meant for undergraduate and beginning graduate students. The later
parts of the work will be of interest to advanced graduate students
and researchers. These include part 3 (“Nineteenth and Early
Twentieth Centuries”) and part 4 (“Contemporary Views”), which
comprise more than two-thirds of the volume. Particularly
refreshing is the fact that the book explores classic authors like
Cantor and Gödel. However, the book also surveys the contemporary
school of “experimental mathematics” and the ideas of its
proponents—Doron Zeilberger (Rutgers Univ.) and Jonathan Borwein
(The Univ. of Newcastle, Australia). This branch of mathematics did
not exist as recently as 25 years ago. As a result, it is a
milestone for experimental mathematics to be discussed in this
volume.
*CHOICE*
[This book] brings together an impressive collection of primary
sources from ancient and modern philosophy of mathematics ... It is
aimed primarily at undergraduates and early graduate students,
however it can serve as an invaluable sourcebook for working
researchers as well.
*Zentralblatt MATH*
This rich historical collection is an invaluable resource. The
greats are represented from Pythagorus to Putnam. Classic issues
and even current ones, such as fictionalism and naturalism, are
included. Plato famously insisted that no one gets into his academy
who is ignorant of geometry. Today we should insist that no one
gets out of the academy who is ignorant of the philosophy of
mathematics. This book will greatly help in that regard.
*James Robert Brown, Professor of Philosophy, University of
Toronto, Canada and author of 'Philosophy of Mathematics: A
Contemporary Introduction to the World of Proofs and Pictures'*
A highly-accessible introduction to the philosophy of mathematics.
This well-curated reader includes engaging introductory essays for
each chapter that will help students tackle some challenging
material. It is a welcome addition to the pedagogical
literature.
*Dr. Lisa Warenski, The City College of New York, USA*
This is a unique anthology of texts in the philosophy of
mathematics, thematically grouped, with informative introductory
overviews.
*Mathematical Reviews*
 |
Ask a Question About this Product More... |
|
