The autonomy of mathematical knowledge : Hilbert's program revisited / Curtis Franks.

Format:

Book

Author/Creator:

Franks, Curtis, author.

Language:

English

Subjects (All):

Hilbert, David, 1862-1943.

Mathematics--Philosophy.

Physical Description:

1 online resource (xiii, 213 pages) : digital, PDF file(s).

Edition:

1st ed.

Place of Publication:

Cambridge : Cambridge University Press, 2009.

Language Note:

English

Summary:

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.

Contents:

A new science

David Hilbert's naturalism

Arithmetization

Intensionality

Intrepreting Gödel's secind incompleteness theorem for Q

Autonomy in context.

Notes:

Title from publisher's bibliographic system (viewed on 05 Oct 2015).

Includes bibliographical references (p. 200-208) and index.

ISBN:

1-107-19014-2

0-521-18389-8

1-282-38641-7

0-511-64081-1

9786612386411

0-511-64149-4

0-511-63905-8

0-511-63798-5

0-511-64013-7

OCLC:

609846195