The Philosophy of Mathematics: An Introductory Essay

by Stephan Körner

Concise, accessible sketches of the views of Plato, Aristotle, Leibniz, and Kant highlight this study of the general structure and foundation of pure and applied mathematics. Author Stephan Körner dedicates two chapters apiece — one expository and one critical — to each of the three main modern schools of thought on mathematical the formalists, the logicists, and the intuitionists. After critically examining the propositions and theories of each philosophy, Körner presents a new position concerning the relation between mathematical theories, empirical data, and philosophical presuppositions. 
The Review of Metaphysics praised this volume as "a lucid and stimulating essay which combines accuracy and sophistication with a minimum of technical language." Compact but comprehensive, this nontechnical introduction will appeal to professionals, students, and other readers interested in the intersection of philosophical problems with pure and applied mathematics.

Genres: Philosophy, Mathematics, Science, Nonfiction

198 pages, Paperback

First published January 1, 1960

About the author

Stephan Körner was a British philosopher, who specialised in the work of Kant, the study of concepts, and in the philosophy of mathematics. Born to a Jewish family in Czechoslovakia, he left the country to avoid certain death at the hands of the Nazis after the German occupation in 1939, and came to the United Kingdom as a refugee, where he began his study of philosophy; by 1952 he was a professor of philosophy at the University of Bristol, taking up a second professorship at Yale in 1970. He was married to Edith Körner, and was the father of the mathematician Thomas Körner and the biochemist, writer and translator (née) Ann M. Körner.

Reviews

[AC · Rating 5 out of 5]

Contains an elegant discussion of Russell's paradox and of the failed attempt (known as 'Logicism') to derive mathematics from logic.

[Adam · Rating 3 out of 5]

A relatively clear survey of the major historical views in the philosophy of mathematics. The end, however, delivers the author's own attempt at answering the major questions, which is unclear and develops a formalism that seems not particularly interesting or helpful.

[Rick Sam · Rating 3 out of 5]

I picked up this book in an old book-store. Although, I did not understand every single detail, but I enjoyed learning the groups within Philosophy of Mathematics. It will give you an outline in Philosophy of Mathematics. I learnt some new terms as Finitism, Transfinitism and Methodological Finitism.

Maybe if you're interested to knowing what's Philosophy of Mathematics is about, you might want to read this. Otherwise, it would be boring.

[Erickson · Rating 5 out of 5]

Too difficult for me to understand at the moment. Most likely due to lack of understanding on the schools of thought namely intuitionism, logicism, formalism, etc. Will read this again after I know more about the pertinent issues.