The Applicability of Mathematics as a Philosophical Problem

by Mark Steiner

This book analyzes the different ways mathematics is applicable in the physical sciences, and presents a startling thesis--the success of mathematical physics appears to assign the human mind a special place in the cosmos. Mark Steiner distinguishes among the semantic problems that arise from the use of mathematics in logical deduction; the metaphysical problems that arise from the alleged gap between mathematical objects and the physical world; the descriptive problems that arise from the use of mathematics to describe nature; and the epistemological problems that arise from the use of mathematics to discover those very descriptions. The epistemological problems lead to the thesis about the mind. It is frequently claimed that the universe is indifferent to human goals and values, and therefore, Locke and Peirce, for example, doubted science's ability to discover the laws governing the humanly unobservable. Steiner argues that, on the contrary, these laws were discovered, using manmade mathematical analogies, resulting in an anthropocentric picture of the universe as "user friendly" to human cognition--a challenge to the entrenched dogma of naturalism.

Genres: Philosophy

224 pages, Hardcover

First published November 20, 1998

About the author

Mark Steiner, emeritus professor of philosophy at Hebrew University of Jerusalem, died of complications related to COVID-19.

Professor Steiner was known for his work in the philosophy of mathematics, Wittgenstein, and philosophy of science, authoring The Applicability of Mathematics as a Philosophical Problem and Mathematical Knowledge, and many articles.

Professor Steiner worked at Hebrew University of Jerusalem since 1977. Prior to that, he was a assistant professor of philosophy at Columbia University. He earned his Ph.D. from Princeton University in 1972.

Reviews

[Kevin Gibbons · Rating 3 out of 5]

This book serves as an excellent digest of some interesting historical advances in physics, and presents some interesting philosophical discussion of them. However, the book does a better job of raising questions than of answering them. The author's idiosyncratic use of received philosophical terms such as `naturalism' make the arguments somewhat hard to follow. Further, too much time is spent going into the details of examples, when more needs to be said about what relevance the examples bear to the arguments. Still, a very thought provoking book.

[Matthew Adelstein · Rating 5 out of 5]

Overall not quite sure what I think about the book's thesis, but it's interesting and well argued.

[Alexandre Guay · Rating 4 out of 5]

Steiner (à la suite de Wigner) formule la question de l'applicabilité des mathématiques comme une énigme philosophique. Sans amener de réponse plausible à cette question, la lecture de ce livre pousse le lecteur à se poser des questions, ce qui est déjà beaucoup.