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.
The book is clear despite its often technical subject matter, and the main theses are well argued for. It's packed with interesting examples from physics—particularly quantum mechanics…[and] is a valuable addition to the philosophy of science and philosophy of mathematics literature. It presents a rigorous and detailed presentation of a puzzle that I believe is crying out for attention.
If mathematics is about finding solutions to well-defined problems, then philosophy is about finding problems in what previously we thought were well-established solutions. Mark Steiner's The Applicability of Mathematics as a Philosophical Problem mirrors both sides of this statement, admitting that mathematics is the key to solving problems in the physical sciences, but also asserting that this very applicability of mathematics to physics constitutes a problem...Steiner's challenge to naturalism is accessible, powerful, and well worth pondering.
- 224 pages
- 5-1/16 x 7-15/16 inches
- Harvard University Press
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