The Autonomy of Mathematical Knowledge
Hilbert's Program Revisited

This study reconstructs, analyses and re-evaluates the programme of influential mathematical thinker David Hilbert, presenting it in a different light.

Curtis Franks (Author)

9780521514378, Cambridge University Press

Hardback, published 8 October 2009

228 pages
23.5 x 15.8 x 1.7 cm, 0.5 kg

'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

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.

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.

Subject Areas: Philosophy of mathematics [PBB], Philosophy [HP]