The Applicability of Mathematics as a Philosophical Problem

The Applicability of Mathematics as a Philosophical Problem

4.14 (14 ratings by Goodreads)
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Description

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.
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Product details

  • Paperback | 224 pages
  • 129 x 202 x 15.49mm | 231g
  • Cambridge, Mass, United States
  • English
  • Revised ed.
  • 6 line illustrations, 2 tables
  • 0674009703
  • 9780674009707
  • 1,467,010

Table of contents

The semantic applicability of mathematics - Frege's achievements; the descriptive applicability of mathematics; mathematics, analogies and discovery in physics; Pythagorean analogies in physics; formalisms and formalist reasoning in quantum mechanics; formalist reasoning - the mystery of quantization; appendix - a "nonphysical" derivation of quantum mechanics; appendix - nucleon-pion scattering; appendix -nonrelativistic Schroedinger equation with spin.
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Review quote

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. -- Mark Colyvan * Mind * 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. -- William A. Dembski * Books & Culture *
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About Mark Steiner

Mark Steiner is Professor of Philosophy at the Hebrew University of Jerusalem.
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Rating details

14 ratings
4.14 out of 5 stars
5 36% (5)
4 43% (6)
3 21% (3)
2 0% (0)
1 0% (0)
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