The Applicability of Mathematics as a Philosophical Problem

Mark Steiner

• Publisher: Harvard University Press
• Year: 2009
• Print ISBN:
  9780674009707
  9780674040977
• eBook ISBN:
  9780674043985
• Topic: Mathematics
• Subtopic: Mathematics General
• Index: Mathematics

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.

Table of contents

• Contents
• Acknowledgments
• Introduction
• 1. The Semantic Applicability of Mathematics: Frege’s Achievements
• 2. The Descriptive Applicability of Mathematics
• 3. Mathematics, Analogies, and Discovery in Physics
• 4. Pythagorean Analogies in Physics
• 5. Formalisms and Formalist Reasoning in Quantum Mechanics
• 6. Formalist Reasoning: The Mystery of Quantization
• Appendix A: A “Nonphysical” Derivation of Quantum Mechanics
• Appendix B: Nucleon–Pion Scattering
• Appendix C: Nonrelativistic Schroedinger Equation with Spin
• References
• Index