1.

Record Nr.

UNINA9910783041003321

Autore

Tiles Mary

Titolo

Mathematics and the image of reason / / Mary Tiles

Pubbl/distr/stampa

London ; ; New York : , : Routledge, , 1991

ISBN

1-134-96771-3

1-134-96772-1

1-280-53925-9

9786610539253

0-203-02836-8

0-203-32706-3

Descrizione fisica

1 online resource (198 p.)

Collana

Philosophical issues in science

Disciplina

510/.1

Soggetti

Mathematics - Philosophy

Lingua di pubblicazione

Inglese

Formato

Materiale a stampa

Livello bibliografico

Monografia

Note generali

Description based upon print version of record.

Nota di bibliografia

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

Nota di contenuto

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

Sommario/riassunto

A thorough account of the philosophy of mathematics. In a cogent



account the author argues against the view that mathematics is solely logic.