Cambridge University Press (2009)

Authors
Curtis Franks
University of Notre Dame
Abstract
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.
Keywords Mathematics Philosophy
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Reprint years 2010
Call number QA8.4.F695 2009
ISBN(s) 0521183898   9780521514378   9780511642098
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Labyrinth of Continua†.Patrick Reeder - 2018 - Philosophia Mathematica 26 (1):1-39.
Cut as Consequence.Curtis Franks - 2010 - History and Philosophy of Logic 31 (4):349-379.
Finitistic Arithmetic and Classical Logic.Mihai Ganea - 2014 - Philosophia Mathematica 22 (2):167-197.
The Gödelian Inferences.Curtis Franks - 2009 - History and Philosophy of Logic 30 (3):241-256.

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