An Aristotelian Realist Philosophy of Mathematics

Mathematics as the Science of Quantity and Structure

Authors: Franklin, J.

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About this book

Mathematics is as much a science of the real world as biology is. It is the science of the world's quantitative aspects (such as ratio) and structural or patterned aspects (such as symmetry). The book develops a complete philosophy of mathematics that contrasts with the usual Platonist and nominalist options.

About the authors

James Franklin is Professor of Mathematics at the University of New South Wales, Australia and founder of the 'Sydney School' in the philosophy of mathematics. His books include The Science of Conjecture: Evidence and Probability Before Pascal; Corrupting the Youth: A History of Philosophy in Australia; and What Science Knows.

Reviews

“An Aristotelian Realist Philosophy of Mathematics is an interesting and challenging book. … Franklin goes through a wealth of material in philosophy, mathematics, and science to motivate and justify his position. … there will still be something for all readers to enjoy due to its large scope and variety of interesting and detailed examples.” (Alex Koo, The Mathematical Intelligencer, Vol. 38, September, 2016)

“The book is comprised of fifteen chapters plus a brief epilogue. … An Aristotelian Realist Philosophy of Mathematics contains many interesting and important discussions, in particular, the discussion of the use of inductive reasoning in mathematics … . This book is provocative and interesting reading for anyone interested in how mathematical entities are related to the physical world and how we gain knowledge of such entities.” (James Davies, Metascience, Vol. 24, 2015)

"A short review cannot do justice to the variety of problems considered and the interesting angles of attack offered by [Franklin's] realist point of view."

-David Guaspari, The New Criterion

"Most of the traditional problems in the philosophy of mathematics arise, in James Franklin's words, out of the 'oscillation between Platonism and nominalism, as if those were the only alternatives' (p. 11). In An Aristotelian Realist Philosophy of Mathematics Franklin develops a tantalizing alternative to these approaches by arguing that at least some mathematical universals exist in the physical realm and are knowable through ordinary methods of access to physical reality. By offering a third option that lies between these extreme all-or-nothing approaches and by rejecting the 'dichotomy of objects into abstract and concrete', Franklin provides potential solutions to many of these traditional problems and opens up a whole new terrain for debate in the philosophy of mathematics (p. 15). The acknowledgement of this by no means new but oft neglected Aristotelian position sheds refreshing new light on debates that have become somewhat stagnant in recent times. Furthermore, by drawing attention to the possibility of an Aristotelian alternative, Franklin opens the way for a whole host of new debates to emerge regarding the correct Aristotelian approach. The scope of the book is ambitious and the overall position defended is controversial in a number of ways. As such, it gives rise to as many new questions as it provides answers. However, this should be seen as a positive, since the many questions that arise are deeply significant and have been neglected by philosophers of mathematics for far too long."

-Max Jones, Philosophica Mathematica

"This book should be part of the personal library of any university-level student of philosophy."

-Jude P. Dougherty, Review of Metaphysics


Table of contents (17 chapters)

Table of contents (17 chapters)

Buy this book

eBook $79.99
price for USA (gross)
  • ISBN 978-1-137-40073-4
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $109.99
price for USA
  • ISBN 978-1-137-40072-7
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $99.99
price for USA
  • ISBN 978-1-349-48618-2
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.

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Bibliographic Information

Bibliographic Information
Book Title
An Aristotelian Realist Philosophy of Mathematics
Book Subtitle
Mathematics as the Science of Quantity and Structure
Authors
Copyright
2014
Publisher
Palgrave Macmillan UK
Copyright Holder
Palgrave Macmillan, a division of Macmillan Publishers Limited
eBook ISBN
978-1-137-40073-4
DOI
10.1057/9781137400734
Hardcover ISBN
978-1-137-40072-7
Softcover ISBN
978-1-349-48618-2
Edition Number
1
Number of Pages
X, 308
Topics