A Boole Anthology: Recent and Classical Studies in the Logic of George Boole PDF
Preview A Boole Anthology: Recent and Classical Studies in the Logic of George Boole
A BOOLE ANTHOLOGY SYNTHESE LIBRARY STUDIES IN EPISTEMOLOGY, LOGIC, METHODOLOGY, AND PHILOSOPHY OF SCIENCE Managing Editor: JAAKKO HINTIKKA, Boston University Editors: DIRKVANDALEN, University ofUtrecht, TheNetherlands DONALDDAVIDSON, University ofCalifornia, Berkeley THEOA.F.KUIPERS, University ofGroningen,TheNetherlands PATRICKSUPPES, Stanford University, California JAN WOLENSKI,Jagiellonian University,Krak6w,Poland VOLUME291 A BOOLE ANTHOLOGY Recent and Classical Studies in the Logic of George Boole Editedby JAMES GASSER University0/Lausanne,Switzerland ~. " Springer-Science+Business Media, B.Y. AC.I.P.Cataloguerecord forthis book isavailable from the Library ofCongress. ISBN 978-90-481-5491-3 ISBN 978-94-015-9385-4 (eBook) DOI 10.1007/978-94-015-9385-4 Printed onacid-free paper All Rights Reserved © 2000 SpringerScience+BusinessMediaDordrecht Softcoverreprintofthehardcover1stedition2000 OriginallypublishedbyKluwerAcademicPublishersin2000 Nopartofthe material protectedbythiscopyright notice may bereproducedor utilized inanyform orbyany means,electronic ormechanical, including photocopying,recordingorbyanyinformation storage and retrieval system,withoutwritten permissionfrom thecopyrightowner. TABLEOFCONTENTS PREFACE VB ACKNOWLEDGEMENTS ix CLASSICALSTUDIES 1.BACKGROUND S.NEILt'TheLateGeorgeBoole,LL.D.,D.C.L.(1865) G.P.YOUNGIRemarksonProfessorBoole's MathematicalTheoryofthe LawsofThought(1865) 27 2. MATHEMATICAL ASPECTS L.M.LAITAITheInfluenceofBoole's SearchforaUniversalMethodin AnalysisontheCreationofHisLogic(1977) 45 T. HAILPERINI Boole's AlgebraIsn't BooleanAlgebra(1981) 61 3.PHILOSOPHICALASPECTS M.DUMMETTIReviewofBoole,Studies inLogicand Probability,andof 'CelebrationoftheCentenaryofTheLaws 0/Thought' (1959) 79 J.W.VAN EVRAI AReassessmentofGeorgeBoole's TheoryofLogic(1977) 87 J.CORCORAN andS.WOODI Boole's CriteriaforValidityandInvalidity(1980) 101 vi CONTENTS RECENT STUDIES 1.BACKGROUND T. HAILPERINI AlgebraicalLogic:LeibnizandBoole 129 M.-J.DURAND-RICHARDI LogicversusAlgebra:EnglishDebatesandBoole's Mediation 139 2.MATHEMATICALASPECTS M.PANTEKIITheMathematicalBackgroundofGeorgeBoole's Mathematical Analysis0/Logic 167 I. GRATTAN-GUINNESsIOnBoole'sAlgebraicLogicafterTheMathematical Analysis0/Logic 213 3.PHILOSOPHICALASPECTS S.NAMBIARITheInfluenceofAristotelianLogiconBoole'sPhilosophyof Logic:theReductionofHypotheticalstoCategoricals 217 B. GODART-WENDLINGITheConceptualizationofTime inBoole's Algebraic Logic 241 G.BORNETI GeorgeBooleandtheScienceofLogic 257 4.CONSEQUENCES V.PECKHAUSIWasGeorgeBooleReallythe 'Father' ofModernLogic? 271 S.RAHMAN/HughMacCollandGeorgeBooleonHypotheticals 287 N.VASSALLOI PsychologisminLogic:SomeSimilaritiesbetweenBooleand Frege 311 CONTRIBUTORS 327 INDEXOFNAMES 329 INDEXOFSUBJECTS 333 PREFACE Centuries ofstagnation in the study oflogic were followed by an explosion ofprog ress in the late nineteenth century. It was George Boole's first book on logic, pub lished in 1847 as The Mathematical Analysis of Logic, that provided the spark. Boole showed not only that algebraic formulas can be used to express logical rela tions but also that an entirely algebraic logic can be devised as a pure calculus ad mitting various interpretations. His logic was not merely developed from mathemat ics but went on to become a tool that mathematicians actually make use of. It was Boole, then, who realised Leibniz's project of creating a truly mathematical logic thatwould involve replacing verbal reasoning with asymbolic calculus. While few would deny Boole's place as a key figure inthe history of logic, there are many who do not consider hirna truly great thinker on a level with, say, Frege. As Donald Gillies has put it, Boole's research programme 'led to important, but not revolutionary advances';' A similarly cautious appraisal is made by Michael Dum mett ina review that first appeared intheJournal ofSymbolic Logic and is reprinted inthis volume (pp. 79-85).Other authors expressing negative opinions have showed less concern for fairness and accuracy. Until recently, the prevailing view was that since Boole had not had the advantage of reading the Begriffsschrift he therefore amounted to Iittle more than apre-modern curiosity. After a long period of finding faultwith Boole whereverpossibleandcomparing hirnunfavourably with other early modern logicians, a new attitude developed following studies by Hailperin, Laita, Van Evra and others. The 'reassessment' brought about by these authors led to abundant newresearch that hasconfirmed Boole's importance and perhaps even true greatness. It is no accident that the adjective 'Boolean' is now in everyday use, at least byanyone whohasever usedacomputersearch programme. Nor is it an accident that interest in Boole's work has probably never been greater than it is today. Two new editions of The Mathematical AnaLysis ofLogic have appeared in the past five years:"in addition, Boole's Selected Manuscripts on Logicand lts PhiLosophy, whichhad never been published, appeared in 1997.3There hasalso been a resurgence of interest inthe manbehind the adjective, George Boole hirnself, especially since the publication in 1985 of Desmond MacHale's full-length biography."As articles on Boole continue to proliferate, the present anthology con stitutes anattempt tocapture some ofthe 'buzzabout Boole'. The idea of the present collection arose during the planning ofa conference or ganised by the Swiss Society for Logic and Philosophy of Science. One of the soci ety's more active members, Gerard Bornet,sent me a note in the mid-1990s which 1 = quote in full: '1847 + 150 1997.Why not a meeting?'.(I was weil acquainted with Gerard's research on Boole, but it did come as a surprise that he would adopt the language ofequations in his own communications!) It was not long before our soci ety decided to prepare a major international conference to mark the 1997 sesquicen tenary ofthe 1847 publication of Boole's The Mathematical Analysis ofLogic.The meeting took place at Lausanne on 26-27 September 1997. Generous financial sup- viii PREFACE port from the Swiss National Science Foundation, the Swiss Academy of Sciences, and the University of Lausanne made it possible to invite the leading specialists in the field,almost allof whom were able to accept. As the conference programme be gantotakeshape andtheprestige oftheinvitedspeakers began tosink in,the idea of an ordinary volume of proceedings seemed inadequate. At the suggestion of my friend and teacher John Corcoran, I undertook instead toprepare ananthology,com bining under one cover the recent work presented at theconference and c1assictexts frequently referred to.From Ivor Grattan-Guinness I laterlearned of theexistence of little-known but useful studies by Samuel Neil and G.P. Young published in 1865, the year of Boole's death, whieh had never been reprinted. Hence this anthology, hence its two major divisions. The 'Classical Studies' have been previously pub lished; the 'RecentStudies',based on papers presented attheconference, have not. The 'ClassicalStudies' have been re-set for this volume but an attempt has been made to remain faithful to the original presentation of each, so far as was consistent withthe Kluwerstyle adopted for thevolume asa whole.Theodore Hailperin'sc1as sie 'Boole's Algebra Isn't Boolean Algebra' is reprinted here with the author's cor rections.At the suggestion of an anonymous referee, the 'Recent Studies' have been grouped together under thefour headings that appear inthetable ofcontents: 'Back ground', 'Mathematical Aspects', 'Philosophical Aspects', and 'Consequences'. These subject categories, like those inthe 'Classieal Studies', give only an approxi mate indieation ofcontent. Institute ofAppliedMathematics, University ofLausanne J.G. IGillies,Donald,ed.1992.Revolutionsinmathemaues.Oxford:Clarendon Press,p.267. 2In FromKant/(J Hilben:Asourcebookinthefoundationsofmathematics, edited by W.B. Ewald. Vol.I,pp.451-509 (Oxford:Clarendon Press, 1996),and as a monograph (Bristol:Thoemmes Press, 1998). 3Grattan-Guinness, Ivor,and Gerard Bornet,eds. 1997.GeorgeBoote:Selected manuscripts on logic anditsphilosophy,Basel:Birkhäuser. 4MacHale, Desmond.1985.GeorgeBoole:Hislifeandwork.Dublin:BoolePress. ACKNOWLEDGEMENTS Throughout the preparation of this volume, I have enjoyed the support of my col leagues inthe InstituteofApplied Mathematicsof the UniversityofLausanne, whom I thank for their interest, encouragement, and helpful suggestions. I am particularly indebted toHenri Volkenand MarekBlaszczyk, It is with sincere pleasure that I thank Nathalie Janz, Evelyne Thommen and Helmut Linneweber-Lammerskitten fortheir help with the Boole 1997conference. Gerard Bornetdeserves warm thanks for suggesting the conference,as does John Corcoran for suggesting the anthology and for helping me in too many ways to be mentioned here. Appreciation must be expressed to Jolanda Voogd and Rudolf Rijgersberg of Kluwer Academic Publishers for expert professional advice and patience with a per nickety editor. I am deeply grateful to the contributors for their confidence and support. They met my various requests cheerfully and conscientiously, and showed considerable forbearance and understandingasthe projectseemed toeternalise. Special thanks are due to Ivor Grattan-Guinness, who spared no effort to obtain complete and legible copiesofthe Neil and Young studies,and toMariaPanteki and Shahid Rahman, who were particularlyeagertohelp inevery way that they could. My greatest debt is to my wife Susan and son Mare, true Booleans both, who were happy to tolerate the uninterpretable in the firm belief that everything would make sense intheend. Iam grateful forpermission toreproducecopyrighted materialsas folIows: John Corcoran and Susan Wood: 'Boole's Criteria for Validity and Invalidity' (Notre Dame Journal of Formal Logic, vol. 21, no 4,October 1980, pp.609-638); copyright © 1980 The Notre DameJournal of Formal Logic;reproduced here by kind permission ofThe Notre Dame Journal ofFormalLogicandJohnCorcoran. Michael Dummett: Review of George Boole, Studies in Logicand Probability. ed. R. Rhees, London and La Salle, IIIinois, 1952, and of 'Celebration of the Centenary of The Laws of Thought byGeorge Boole',Proceedings of theRoyal lrisbAcademy, vol.57, section A, no 6, 1955(Journal ofSymbolicLogic, vol. 24, no 3. September 1959, pp. 203-209); copyright © 1959 The Association for Symbolic Logic; reproduced here by kind permission ofThe Asso ciation forSymbolicLogic and Michael Dummen. Allrights reserved.This reproduction isby special permission forthispublication only. Theodore Hailperin:'Boole'sAlgebra Isn'tBoolean Algebra' (Mathematics Magazine,vol. 54, no 4, September 1981, pp. 172-184); copyright © 1981 The Mathematical Association of America;reproducedherebykind permissionofThe MathematicalAssociationofAmericaand TheodoreHailperin. SidneyHarris:Boolecartoon;copyright© 1999Sidney Harris;reproducedhere bykind permis sionofSidneyHarris.
The list of books you might like
