The Autonomy of Mathematical Knowledge: Hilbert's Program Revisited

by Curtis Franks

Overview

Most scholars think of David Hilbert's program as the most demanding and ideologically motivated attempt to provide a foundation for mathematics, and because they see technical obstacles in the way of realizing the program's goals, they regard it as a failure. Against this view, Curtis Franks argues that Hilbert's deepest and most central insight was that mathematical techniques and practices do not need grounding in any philosophical principles. He weaves together an original historical account, philosophical analysis, and his own development of the meta-mathematics of weak systems of arithmetic to show that the true philosophical significance of Hilbert's program is that it makes the autonomy of mathematics evident. The result is a vision of the early history of modern logic that highlights the rich interaction between its conceptual problems and technical development.

Product Details

ISBN-13:	9780521183895
Publisher:	Cambridge University Press
Publication date:	12/16/2010
Pages:	228
Product dimensions:	5.90(w) x 8.90(h) x 0.50(d)

Table of Contents

Preface; 1. A new science; 2. David Hilbert's naturalism; 3. Arithmetization; 4. Intensionality; 5. Interpreting G2 for Q; 6. Autonomy in context; Bibliography; Index.

Editorial Reviews

"Franks' book is remarkable for the clarity of the prose and the originality of the arguments. It is a beautiful introduction to Hilbert's thought on the nature of mathematics and a natural extension of his work."
Jeffrey Barrett, University of California, Irvine


"...Curtis Franks argues that Hilbert's deepest and most central insight was that mathematical techniques and practices do not need grounding in any philosophical principles. He weaves together an original historical account, philosophical analysis, and his own development of the meta-mathematics of weak systems of arithmetic to show that the true philosophical significance of Hilbert's program is that it makes the autonomy of mathematics evident."
—Mathematical Reviews


"...Overall, the author offers an historical approach to the topic with a twist to it. A sophisticated reader interested in connections between philosophy, mathematics, and logic would gather interesting points of views from this book... Recommended..."
—S. L. Sullivan , Catawba College, CHOICE


"This short but inspiring book questions the received view of Hilbert’s contribution to the foundations of mathematics, and offers a newly clarified position within the philosophical attitude known as naturalism, especially of the (fiercely) anti-foundationalist persuasion. ... this is without a doubt one of the most thoughtful as well as one of the most beautifully written books on the philosophy of mathematics to have been published in recent memory."
—Juliette Kennedy, Bulletin of Symbolic Logic

From the Publisher