Hardback : £59.15
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.
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.
Preface; 1. A new science; 2. David Hilbert's naturalism; 3. Arithmetization; 4. Intensionality; 5. Interpreting G2 for Q; 6. Autonomy in context; Bibliography; Index.
This study reconstructs, analyses and re-evaluates the programme of influential mathematical thinker David Hilbert, presenting it in a different light.
Review of the hardback: 'Franks' book is remarkable for the clarity
of the prose and the originality of the arguments. It is a
beautiful introduction to Hilbert's thought on the nature of
mathematics and a natural extension of his work.' Jeffrey Barrett,
University of California, Irvine
'This short but inspiring book questions the received view of
Hilbert's contribution to the foundations of mathematics, and
offers a newly clarified position within the philosophical attitude
known as naturalism, especially of the (fiercely)
anti-foundationalist persuasion … this is without a doubt one of
the most thoughtful as well as one of the most beautifully written
books on the philosophy of mathematics to have been published in
recent memory.' Juliette Kennedy, Bulletin of Symbolic Logic
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