Giuseppe Peano between Mathematics and Logic: Proceeding of the International Conference in honour of Giuseppe Peano on the 150th anniversary of his ... Mathematico Torino

204 Pages·2010·3.09 MB·English

by  Fulvia Skof

Giuseppe Peano between Mathematics and Logic
GiuseppePeano(1858–1932)in1928–DepartmentofMathematicsG.Peano,
UniversityofTorino
Fulvia Skof
Editor
Giuseppe Peano between
Mathematics and Logic
Proceeding of the International Conference in honour
of Giuseppe Peano on the 150th anniversary
of his birth and the centennial of the Formulario
Mathematico, Turin (Italy), October 2–3, 2008
123
Editor
FulviaSkof
DepartmentofMathematics“G.Peano”
UniversityofTorino,Italy
Thepublication ofthisbookhasbeenmadepossiblebythefinancialsupportoftheAccademiadelle
ScienzeofTorino,DepartmentofMathematicsoftheTorinoUniversityandCompagniadiSanPaolo.
ISBN 978-88-470-1835-8 e-ISBN 978-88-470-1836-5
DOI 10.1007/978-88-470-1836-5
SpringerMilanDordrechtHeidelbergLondonNewYork
LibraryofCongressControlNumber:2010938967
©Springer-VerlagItalia2011
Thisworkissubjecttocopyright.Allrightsarereserved,whetherthewholeorpartofthematerialis
concerned,specificallytherightsoftranslation,reprinting,reuseofillustrations,recitation,broadcasting,
reproductiononmicrofilmorinanyotherway,andstorageindatabanks.Duplicationofthispublication
orpartsthereofispermittedonlyundertheprovisionsoftheGermanCopyrightLawofSeptember9,
1965,initscurrentversion,andpermissionforusemustalwaysbeobtainedfromSpringer.Violations
areliabletoprosecutionundertheGermanCopyrightLaw.
Theuseofgeneral descriptive names, registered names, trademarks, etc. inthis publication does not
imply,evenintheabsenceofaspecificstatement,thatsuchnamesareexemptfromtherelevantprotective
lawsandregulationsandthereforefreeforgeneraluse.
Thepublisherandtheauthorsacceptnolegalresponsibilityforanydamagecausedbyimproperuseof
theinstructionsandprogramscontainedinthisbookandtheCD.Althoughthesoftwarehasbeentested
withextremecare,errorsinthesoftwarecannotbeexcluded.
Coverdesign:SimonaColombo,Milano
Typesetting:le-texpublishingservicesGmbH,Leipzig,Germany
Printingandbinding:GrafichePorpora,Segrate(MI)
Printedonacid-freepaper
Springer-VerlagItaliaS.r.l,ViaDecembrio28,I-20137Milano
SpringerispartofSpringerScience+BusinessMedia(www.springer.com)
Preface
GiuseppePeanowasoneofthegreatestfiguresin modernmathematicsandlogic,
andwithoutadoubtthemostimportantItalianmathematicallogician,esteemedby
BertrandRussellaswellasRudolfCarnapandKurtGödel.Borninasmallvillage
near Cuneo, in southernPiedmont,in August1858– on the eve of Italian unity–
he studied in Turin, where he would then rapidly advance through the successive
levelsofhisacademiccareer:hereceivedhishabilitationinInfinitesimalCalculus
in1884,becameaprofessorattheMilitaryAcademyin1889,enteredtheUniversity
of Torino in 1890and was a full professorof InfinitesimalCalculus from1895to
1931,andwasalsoafullprofessorofComplementaryMathematicsuntilhisdeathin
April1932.Asearlyas1891hewasamemberofTurin’sAccademiadelleScienze,
andin1905becameamemberoftheAccademiaNazionaledeiLinceiaswell.
On the occasion of the one hundred fiftieth anniversary of Peano’s birth, and
a centuryafterthe publicationof the fiftheditionofthe FormularioMathematico,
a grandioseattemptto systematise mathematicsin symbolic form,the Accademia
delle Scienze of Torino and the University of Torino (in particular,the Faculty of
Mathematical,PhysicalandNaturalSciencesandtheDepartmentofMathematics),
togetherwiththeItalianSocietyfortheHistoryofMathematics,createdacommit-
teeforthecelebrationofthisdualoccasion,thepresidencyofwhichwasentrusted
toProf.ClaraSilviaRoero.Amongthemanyinitiativesorganisedbythecommittee,
oneofthemostimportantwithrespecttosciencewastheinternationalconference
entitled “Giuseppe Peano between Mathematics and Logic”, which took place on
2–3 October 2008 under the auspices of the President of the Republic and with
thesponsorshipoftheAccademiaNazionaledeiLinceiandtheIstitutoLombardo
AccademiadiScienze, Letteree Arti.The conferenceprovidedanexaminationof
the variousaspects of Peano’s work, presentedby the greatest scholarsfrom Italy
andabroad.Thispresentvolumecontainsthepapersthatdevelopedoutofthepre-
sentationsgivenduringtheconference.
TheconferencewasmadepossiblebyfundingcontributedbytheRegionofPied-
mont,theCompagniadiSanPaoloandtheCassadiRisparmiodiCuneo,aswellas
the AccademiadelleScienzeofTorino– underthepresidencyofAngeloRaffaele
Meo – which hosted the conference in the “Sala dei Mappamondi”.We are most
v
vi Preface
gratefultotheseinstitutions.ParticularthanksgotoProf.Roero,thenpresidentof
theItalianSocietyfortheHistoryofMathematics,forherefficientandindefatiga-
ble organisationalwork,and for hervaluablecollaborationwith Prof.Fulvia Skof
incollectingandeditingthepapersthatappearhere.
Turin,September2010 AccademiadelleScienze
List of Contributors
GiampietroAllasia
DepartmentofMathematics“G.Peano”,UniversityofTorino,Italy
e-mail:[email protected]
EttoreCasari
ScuolaNormaleSuperioreofPisa,Italy
e-mail:[email protected]
PaoloFreguglia
DepartmentofPureandAppliedMathematics,UniversityofL’Aquila,Italy
e-mail:[email protected]
IvorGrattan-Guinness
UniversityofMiddlesex,UK
e-mail:[email protected]
GabrieleLolli
ScuolaNormaleSuperioreofPisa,Italy
e-mail:[email protected]
ElenaAnneMarchisotto
DepartmentofMathematics,CaliforniaStateUniversityofNorthridge,USA
e-mail:[email protected]
JeanMawhin
Institutderechercheenmathématiqueetphysique(IRMP)
UniversitéCatholiquedeLouvain-la-Neuve,Belgium
e-mail:[email protected]
ClaraSilviaRoero
DepartmentofMathematics“G.Peano”,UniversityofTorino,Italy
e-mail:[email protected]
FulviaSkof
EmeritusProfessoroftheUniversityofTorino,Italy
e-mail:[email protected]
vii

Contents
1 GiuseppePeanoandMathematicalAnalysisinItaly::::::::::::::: 1
F.Skof
2 SomeContributionsofPeanotoAnalysisintheLightoftheWork
ofBelgianMathematicians :::::::::::::::::::::::::::::::::::: 13
J.Mawhin
3 Peano,hisSchooland... NumericalAnalysis :::::::::::::::::::: 29
G.Allasia
4 PeanoandtheFoundationsofArithmetic:::::::::::::::::::::::: 47
G.Lolli
5 GeometricCalculusandGeometryFoundationsinPeano :::::::::: 69
P.Freguglia
6 TheFormulariobetweenMathematicsandHistory:::::::::::::::: 83
C.S.Roero
7 GiuseppePeano:aRevolutionaryinSymbolicLogic? ::::::::::::: 135
I.Grattan-Guinness
8 AttheOriginsofMetalogic:::::::::::::::::::::::::::::::::::: 143
E.Casari
9 FoundationsofGeometryintheSchoolofPeano:::::::::::::::::: 157
E.A.Marchisotto
References.........................................................171
IndexofNames ....................................................187
ListofIllustrations .................................................193
ix