Table Of ContentA 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
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OriginallypublishedbyKluwerAcademicPublishersin2000
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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.
