Towards a philosophy of real mathematics

300 Pages·2003·0.984 MB·English

by  Corfield D.

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TOWARDS A PHILOSOPHY OF REAL
MATHEMATICS
Inthisambitiousstudy,DavidCorfieldattacksthewidelyheldview
thatitisthenatureofmathematicalknowledgewhichhasshapedthe
wayinwhichmathematicsistreatedphilosophically,andclaimsthat
contingentfactorshavebroughtustothepresentthematicallylimited
discipline. Illustrating his discussion with a wealth of examples, he
setsoutavarietyofnewwaystothinkphilosophicallyaboutmathe-
matics,rangingfromanexplorationofwhethercomputersproducing
mathematicalproofsorconjecturesaredoingrealmathematics,tothe
useofanalogy,theprospectsforaBayesianconfirmationtheory,the
notionofamathematicalresearchprogramme,andthewaysinwhich
newconceptsarejustified.Hishighlyoriginalbookchallengesboth
philosophersandmathematicianstodevelopthebroadestandrichest
philosophicalresourcesforworkintheirdisciplines,andpointsclearly
tothewaysinwhichthiscanbedone.
david corfield holds a Junior Lectureship in Philosophy of
Science at the University of Oxford. He is co-editor (with Jon
Williamson) of Foundations of Bayesianism (2001), and he has pub-
lishedarticlesinjournalsincludingStudiesinHistoryandPhilosophy
ofScienceandPhilosophiaMathematica.

TOWARDS A PHILOSOPHY
OF REAL MATHEMATICS
DAVID CORFIELD
         
The Pitt Building, Trumpington Street, Cambridge, United Kingdom
  
The Edinburgh Building, Cambridge CB2 2RU, UK
40 West 20th Street, New York, NY 10011-4211, USA
477 Williamstown Road, Port Melbourne, VIC 3207, Australia
Ruiz de Alarcón 13, 28014 Madrid, Spain
Dock House, The Waterfront, Cape Town 8001, South Africa
http://www.cambridge.org
©David Corfield 2004
First published in printed format 2003
ISBN 0-511-04270-1 eBook (netLibrary)
ISBN 0-521-81722-6 hardback
FromtheeasttowesternInd,
NojewelislikeRosalind.

Contents
Preface page ix
1 Introduction: a role for histor y 1
parti human and artificial mathematicians
2 Communicating with automated theorem provers 37
3 Automated conjecture formation 57
4 The role of analogy in mathematics 80
partii plausibility, uncertainty and probability
5 Bayesianism in mathematics 103
6 Uncer tainty in mathematics and science 130
partiii the growth of mathematics
7 Lakatos’s philosophy of mathematics 151
8 Beyondthemethodologyofmathematicalresearch
programmes 175
9 The impor tance of mathematical conceptualisation 204
partiv the interpretation of mathematics
10 Higher-dimensional algebra 237
Appendix 271
Bibliography 274
Index 286
vii