The Autonomy of Mathematical Knowledge: Hilbert's Program Revisited

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Cambridge University Press, Oct 8, 2009 - Mathematics - 213 pages
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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Contents

A new science Qp_
1
David Hilberts naturalism
29
Arithmetization
61
Intensionality
105
Interpreting Godels second incompleteness theorem for Q
139
Autonomy in context
169
References
200
Index
209
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About the author (2009)

Curtis Franks is Assistant Professor in the Department of Philosophy, The University of Notre Dame.

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