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.
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