The Autonomy of Mathematical Knowledge: Hilbert's Program Revisited

The Autonomy of Mathematical Knowledge: Hilbert's Program Revisited

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Curtis Franks
Cambridge University Press, 10/8/2009
EAN 9780521514378, ISBN10: 0521514371

Hardcover, 228 pages, 22.9 x 15.2 x 1.7 cm
Language: English

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.

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