Mathematics and the image of reason / Mary Tiles.

Format:

Book

Author/Creator:

Tiles, Mary.

Series:

Philosophical issues in science.

Philosophical issues in science

Language:

English

Subjects (All):

Frege, Gottlob, 1848-1925.

Frege, Gottlob.

Russell, Bertrand, 1872-1970.

Russell, Bertrand.

Hilbert, David, 1862-1943.

Hilbert, David.

Mathematics--Philosophy.

Mathematics.

Physical Description:

1 online resource (198 p.)

Edition:

1st ed.

Place of Publication:

London ; New York : Routledge, 1991.

Language Note:

English

Summary:

A thorough account of the philosophy of mathematics. In a cogent account the author argues against the view that mathematics is solely logic.

Contents:

Cover; MATHEMATICS AND THEIMAGE OF REASON; Title Page; Copyright Page; Table of Contents; Acknowledgements; Introduction; 1 AXIOMATIZATION, RIGOUR AND REASON; Rigour and Proof; Deserting Euclidean Standards; The Return to Euclidean Standards; 2 FREGE: ARITHMETIC AS LOGIC; Calculation and Reasoning; Numbers and the Nature of Arithmetical Truths; Numbers as Objects; The Natural Numbers; Word Games?; 3 RUSSELL: MATHEMATICS AS LOGIC; Geometry and Relational Structures; Paradoxes and Logical Types; Empiricism, Logical Positivism and the Sterility of Reason

4 HILBERT: MATHEMATICS AS A FORMULA-GAME?Formalism and Hilbert's Programme; Geometrical Rigour; Forging the Formal Chains of Reason; Successes and Failures; Logic and its Limitations; Appendix - Recursive Functions; 5 IDEAL ELEMENTS AND RATIONAL IDEALS; Formulae, Symbols and Forms; Ideal Elements and Ideals; Geometry: Diagrams and Rigour; Pragmatism, Axiomatization and Ideals; Logic and the Objects of Mathematical Knowledge; Lack of Closure and the Power of Reason; Glossary of Symbols; Further Reading; Bibliography; Index

Notes:

Description based upon print version of record.

Includes bibliographical references (p. 178-183) and index.

ISBN:

1-134-96771-3

1-134-96772-1

1-280-53925-9

9786610539253

0-203-02836-8

0-203-32706-3

9780203028360

OCLC:

826853497