New Essays on Leibniz Reception: In Science and Philosophy of Science 1800-2000 PDF
Preview New Essays on Leibniz Reception: In Science and Philosophy of Science 1800-2000
Publications des Archives Henri Poincaré Publications of the Henri Poincaré Archives Textes et Travaux, Approches Philosophiques en Logique, Mathématiques et Physique autour de 1900 Texts, Studies and Philosophical Insights in Logic, Mathematics and Physics around 1900 Éditeur/Editor: Gerhard Heinzmann, Nancy, France New Essays on Leibniz Reception In S cience and Philosophy of Science 1800–2000 Ralf Krömer Yannick Chin-Drian Editors Editors Ralf Krömer Yannick Chin-Drian Departement Mathematik Archives Poincaré Universität Siegen Université de Lorraine Siegen Nancy Germany France ISBN 978-3-0346-0503-8 ISBN 978-3-0346-0504-5 (eBook) DOI 10.1007/978-3-0346-0504-5 Springer Basel Heidelberg New York Dordrecht London Library of Congress Control Number: 2012934367 © Springer Basel AG 2012 This work is subject to copyright. 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Violations are liable to prosecution under the respective Copyright Law. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. While the advice and information in this book are believed to be true and accurate at the date of publication, neither the authors nor the editors nor the publisher can accept any legal responsibility for any errors or omissions that may be made. The publisher makes no warranty, express or implied, with respect to the the material contained herein. Printedonacid-freepaper Springer is part of Springer Science+Business Media (www.springer.com) Contents R.KrömerandY.Chin-Drian Introduction .......................................................... vii P.Séguin TheIdeaofNumberfromGausstoCantor. TheLeibnizianHeritageanditsSurpassing .............................. 1 V.Peckhaus TheReceptionofLeibniz’sLogicin19thCentury GermanPhilosophy ................................................... 13 F.Willmann Leibniz’sMetaphysicsasanEpistemologicalObstacleto theMathematizationofNature:TheViewof aLate19thCenturyNeo-Kantian,KurdLasswitz ......................... 25 E.Luciano PeanoandHisSchoolBetweenLeibnizandCouturat: TheInfluenceinMathematicsandinInternationalLanguage .............. 41 A.-F.Schmid Couturat’sReceptionofLeibniz ........................................ 65 N.Griffin RussellandLeibnizontheClassificationofPropositions .................. 85 J.Seidengart Cassirer,Reader,Publisher,andInterpreterof Leibniz’sPhilosophy .................................................. 129 V.DeRisi LeibnizonRelativity.TheDebatebetweenHansReichenbach andDietrichMahnkeonLeibniz’sTheoryofMotionandTime ............ 143 v vi Contents D.Rabouin InterpretationsofLeibniz’sMathesisUniversalisat theBeginningoftheXXthCentury ..................................... 187 E.Scholz LeibnizianTracesinH.Weyl’sPhilosophiederMathematik undNaturwissenschaft ................................................. 203 G.Crocco Gödel,Leibnizand“Russell’sMathematicalLogic” ...................... 217 H.Breger Chaitin,LeibnizandComplexity ........................................ 257 Abbreviations .............................................................. 267 AuthorIndex .............................................................. 269 SubjectIndex .............................................................. 273 Introduction RalfKrömerand YannickChin-Drian ThereisnodoubtthateversinceLeibniz’sthinkingbecameknown,itinfluencedmanyre- searchstudiesinthefoundationsandphilosophyoflogic,mathematicsandexactsciences. Alongwithhisgeneralepistomologicalandmetaphysicalapproach,thereisanumberof moreparticularconcepts,problemsandideaswhichoccupiedLeibnizandlatermotivated muchworkinthesefields:theconceptsofcontinuum,space,identity,number,theinfinite andtheinfinitelysmall,andthedevelopmentofsuchconstructsasauniversallanguage, ananalysissitus,acalculusoflogicandsoon.TheLeibnizianinfluencehasactuallybeen sogreatandvariedthatagreatpartofitisstilltobeuncoveredbyhistoriansofscience andphilosophy,andithasbeensoimportantforthedevelopmentofmodernscienceand philosophy that it merits being studied much closer than it has been so far. While the existing secondaryliterature on Leibniz’swork could be said to be as vast as this work itself, only part of it concerns the Leibnizian influence, and relatively few works con- cernthe Leibnizianinfluencein science andphilosophyof science in the 19thand20th centuriesinparticular. It was for this reason that an international meeting entitled “Leibniz reception in thesciencesandphilosophyofscience1850–1950”wasorganizedin April2008bythe “Laboratoired’HistoiredesSciencesetdePhilosophie(LHSP)-ArchivesHenriPoincaré” (UMR7117CNRS)atNancy/France.Thebasicideaofthemeetingwastobringtogether twofieldsofresearchinthehistoryofphilosophyandofscience: Leibnizresearch,and relatedresearchonhistoryof science andits philosophyinthe 19thand20thcenturies. OuraimwastocharacterizeLeibniz’sthoughtasitappearsintheworksofsomeauthors fromthelatterperiod,andinthiswaytobetterunderstandLeibniz’sinfluenceoncontem- poraryscienceandphilosophy,butalsotoinspectthisreceptioncritically,inparticularto confrontitwiththeactualstateofLeibnizresearchandpublicationofnumerouseditions ofhiswork. Theresultofthiseffortisthepresentvolume. Asthetitlesuggests,oursisnotthefirstcollectionofessaysonLeibnizreception. Besides many isolated studies scattered around the literature,1 another volume was de- voted to such studiesin 1986 [Heinekamp1986]. We are convincedthat 25 years after 1Seetheonline-bibliographyofthewritingsonLeibnizavailableat http://www.leibniz-bibliographie.deforreferences. vii viii R.KrömerandY.Chin-Drian this volume, it is a good time for a new collection of such essays to appear. In the re- mainderofthisintroduction,weshallpointouttherelationsbetweenthepresentvolume and the 1986volumewheneverthereis occasionto doso. A first observationis thatin 1986therewere27contributionstocoverthewholeperiod1716–1986,andtherewasno restrictionconcerningthetopicscovered,whereasourvolumeisrestrictedtotheperiod 1800–2000andtoreceptioninthefieldsoflogic,mathematicsandphilosophyofscience – a set of restrictions under which only a handful of contributions to the 1986 volume wouldfall. (Ourdecisiontoconcentratepreciselyonthisperiodandthesefieldsactually wasmotivatedbyourfeelingthattheywereunderrepresentedintheexistingliterature.) Asarule,incaseswheretheLeibnizreceptionbysomeauthororsomeschoolhasbeen studiedbefore,thestudiespresentedherecovernewparticularaspectsandquestionsnot inthescopeofexistingstudies,ortheyusenewmaterialnotknownorevaluatedbefore, ortheyarejustmoredetailedthanexistingstudies. On the other hand, this is not (andactually, is notmeant to be) a definitivestudy, nothinglikea“handbookonLeibnizreception”. Achoicewasmadefromthetotalityof questionsrelevanttoLeibnizreception,evenintherestrictedsenseexplainedabove,and themajorcriterionforthischoicewasaverynon-objectiveone,namelythewillingnessof thecontactedauthorstocontribute,whichinturnisatleastpartlyrelatedtotheaccident of knowing one of the editors. We are nevertheless convinced that the product of our collectiveeffortconstitutesanimportantstepforwardinthestudyofLeibniz’sinfluence onscienceanditsphilosophy. Letusnowpasstoadescriptionofthecontributionscontainedinthisvolume.2 We organizedthechaptersroughlyinchronologicalorderwithrespecttotheauthorswhose Leibniz reception is studied. By this structure, we hope to help the reader to read this book as a partial history of Leibniz’s influence, and to follow up lines of development. Orderings of a more thematical kind would have been possible; we hope that the thor- oughlypreparedauthorandsubjectindexeswillhelpthereadertoaccesstheworkfrom particularthematicalperspectives.Everychapterisfollowedbyitsownlistofreferences (sothatthereisnogeneralbibliography;seehowevertheendofthisintroductionforsome additionalreferences). Inthefirstchapter,PhilippeSéguinstudiesinaparticularwaytowhatdegreeLeib- nizianviewpointsplayedaroleinthedevelopmentoftheideaofnumberinthethinking of some 19th century German mathematicians: Gauss, Jacobi, Kummer and Dedekind. ThehistorySéguinpresentsisratheraculturalthanaconceptualhistory3,amethodology healreadyemployedinhisthesis(supervisedbyImreToth)[Séguin1996]. SéguinshowsthatGermanmathematicsinthe19thcenturysawaphenomenonthat todaycouldseemsurprisingto us: the notionofnumberwasornamentedwith somuch prestigethatitbecamemorethanasimpleconcept,andcertainGermanmathematicians allemands made of it what Séguin calls an “idea”. Hidden behind this ennoblementis the multiple and diffuse presence of Leibniz’s philosophical thinking, notably across a discipline which was the great German science from 1750 towards the end of the 19th 2Thefollowingpresentationisbasedonabstractsprovidedinmostcasesbytheauthors. 3Forthelatter,see[Ferreiros2007]and[Boniface2007],forinstance. Introduction ix century: philology. This discipline considereditself as the science of the humanmind. ButtheLeibnizianlegacyhasalsobeenharvestedandexceededbytheformidablevigor ofGermanidealismwhichisnothostiletotheconceptionofnumberasatruecreationof themindratherthanasimpledefinition. InChapter2,VolkerPeckhausstudiesthereceptionofLeibniz’slogicin19thcen- turyGermanphilosophy.Althoughthereisgoodevidencethatmodernmathematicallogic wascreatedinthesecondhalfofthe19thcenturyindependentlyofLeibniziananticipa- tions,itbecamequiteearlyacommonplacefortheproponentsofthenewlogicthatmany oftheirideashadbeeningeniouslyanticipatedbyLeibniz. Thesourcesoftheseinsights were importantpublicationsin German philosophy. The central role of Johann Eduard Erdmann’seditionofLeibniz’sphilosophicalworks(1839/40)andAdolfTrendelenburg’s paperon Leibniz’ssketch of a generalcharacteristic (1856)must be recognized. These worksconveyedLeibniz’sconsiderationsonlogicalcalculiandhisideasaboutsemiotics. Chapter3byFrançoiseWillmannisonKurdLasswitz(1848–1910),theauthorofa historyofatomism(GeschichtederAtomistikvomMittelalterbisNewton).Tothishistory publishedin 1890, critical thinkingis central. Lasswitz tries to retrace, in the labyrinth ofuncountableatomistictheoriesandtheirdifferentmotives,thelongwaytowardscon- questofthe“thinkingtools”thatallowedaccesstomodernscience.Apartisanofacinetic atomism, Lasswitz sets himself the task to show that the perfection of the corpuscular theorywasachievedbyHuygens. Thepassagetoadynamicaltheoryofmatter,asitcan be found in Leibniz’s writings, is a setback for Lasswitz. He sees it as subject to two major epistemologicalobstacles, anthropomorphicrepresentationson the one hand, the metaphysicaland theologicalinterest on the other hand; according to him, these obsta- cleshinderedLeibnizfrommakingfulluseofthemathematicaltoolswhichwereathis disposal. Chapters4to7areconnectedbyagreatercommontheme,namelybywhatcouldbe calledthe“Leibnizrenaissance”attheturnofthe19thtothe20thcentury. InChapter4, ErikaLucianostudiestheLeibnizreceptionbyGiuseppePeanoandhisschool. Shefirst analyzesthesourcesandthesecondaryliteratureconsultedbyPeanoduringhisstudieson Leibniz;reconstructionofthisinformationhasbeenpossibleduetotherecentdiscovery ofPeano’spersonallibrary. Next,sheexaminesthesecondeditionoftheFormulairede mathématiques(1898–1899),where for the first time excerptaof Leibniz’s manuscripts onlogicandarithmeticwerepublished;sheconsidersinparticularPeano’smarginaliaand theadditionsandcorrectionsduetohisteamofcollaborators. Finally,shedescribesthe receptioninItalyofLeibnizstudiesbyG.Vacca,G.Vailati,A.NatucciandL.Couturat, membersof Peano’s School, on the basis of their correspondenceand of contemporary Italianperiodicals. This leads directly to the Leibniz reception by Couturathimself, studied by Anne FrançoiseSchmidinChapter5. The objectiveofSchmid’scontributionis to showhow Couturatconstructed his interpretationof Leibniz, throughhis philosophicalprinciples, his preferencefor the algebra of logic, and his conceptionof the history of philosophy. Amonghiswritings,hisbookandhisarticleonLeibnizaswellashiseditionoftheunpub- lishedmanuscriptscopiedinHanoverremainkeyreferencesinthehistoryofphilosophy. However,hisinterpretationofLeibnizmoreprofoundlyengageshisownphilosophyand x R.KrömerandY.Chin-Drian allows us to understand how the former was a semi-failure for him. On the one hand, althoughhisbookonLeibnizwaswidelyknownandadmired,itsmainthesisthatlogic is the heartof the system was not followed. Yet, Couturathopedhis bookwould carry weightincontemporarydebatesaboutlogicandthephilosophyofmathematics. Onthe otherhand,his“rationalism”hamperedhiminhisownstudiesonlogictothepointthat he progressivelylost interest in keeping up with Russell’s ongoingwork on symbolism andrefiningtheprecisionofthedetailindemonstration. Thissituation,atthesametime theoreticaland biographical, had consequencesin the history of this discipline because Couturathad completedtwo substantial workson these same questions, which are now lost. Here, Schmid reviews the criticisms made of Couturat’s reading of Leibniz, and rendersanaccountofhisinterpretationbyhypothesisingontheusehemakesoflogic’s relationstootherdisciplinesinLeibniz’swork. Chapter 6 by Nicholas Griffin is on the historical backgroundand the contents of Russell’sbookonLeibniz.Griffin’smainconcernwastoconsiderthewaysinwhichRus- sell’sstudyofLeibnizaffectedtwopositionsRusselltookupeitherimmediatelybeforeor atthetimehestartedhisworkonLeibniz,namely,hisviewthatdecompositionalanalysis wasthe propermethodforphilosophyandhisrejectionof theneo-Hegeliandoctrineof internal relations. These views were central to Russell’s rejection of the neo-Hegelian philosophyhe had previously held and they paved the way for the major philosophical advanceshemadeinthenextfewyears. EvenifGriffinstressesthatRussellgotneither oftheseviewsfromLeibniz,hesuggeststhatRussell’sstudyofLeibnizwasnotonlyan event of major importance in Leibniz scholarship but of the greatest importance to the developmentofhisownphilosophyaswell. Griffinaddressestwomainthemes: theimpactofthecontainmentprincipleonthe possibility of contingentand/or synthetic propositions and the status of relations as in- ternal or external. The former was of immense concern to Leibniz and is discussed in detail in Russell’s book. The latter was not discussed by Leibniz, who seems to have simplyacceptedwithoutdisputethatallrelationswerewhatRussellwouldsubsequently callinternal,butitwasofenormousimportancetoRussell. Chapter7 by Jean Seidengartison Cassirer’s reading,publishingandinterpreting ofLeibniz’sphilosophy.4 SeidengarttakesashisstartingpointCassirer’spresentationof Leibniz’sphilosophywhich,accordingto LouisCouturat’scriticism, madeofLeibniza sortof“pre-Kantian”. WhileCouturatcouldn’tyethaveaclearideaofCassirer’sphilo- sophicalintentwhenhewrotehisreview,SeidengartmakesanefforttoshowthatCassirer ratheraimedatcorrectingKantianismwith the helpofLeibnizianphilosophemes. Cas- sirereventookupsomanybasicelementsofLeibniz’stheoryofknowledgeinthebuild- ing of his own philosophy,includingthe philosophyof symbolicalforms, that one can, accordingtoSeidengart,considerCassirer’sNeo-KantianismasacomebackofLeibniz’s thinkinginthedomainofphilosophyofscience,paradoxicalasthismightseem. Cassirer 4TheimportanceofLeibniztotheMarburgschoolandtoCassirerinparticularhasbeenstressedandanalyzed before, tothepoint that [Holzhey 1986]suggested that onecould even speak about a“Neo-Leibnizianism” insteadofa“Neo-Kantianism” inthiscase(p.289). ButwhileHolzheydiscussesCassireronlyshortly, the moreextensivestudy[Ranea1986]islargelycomplementarytotheonebySeidengartpresentedhere.
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