The Autonomy of Mathematical Knowledge : Hilbert's Program Revisited

The Autonomy of Mathematical Knowledge presents the philosophical ideas underlying David Hilbert's foundational program in a new light. Hilbert's program is traditionally regarded as a failure, but Curtis Franks weaves together an original historical account with philosophical analysis to show both its validity and its philosophical significance.

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.