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Scots Philosophical AssociationUniversity of St Andrews

Leibniz's Principle of the Identity of IndiscerniblesAuthor(s): Fred ChernoffSource: The Philosophical Quarterly, Vol. 31, No. 123 (Apr., 1981), pp. 126-138Published by: Oxford University Presson behalf of the Scots Philosophical Associationand theUniversity of St. AndrewsStable URL: http://www.jstor.org/stable/2218719.

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126

LEIBNIZ'S PRINCIPLEOF THE IDENTITY OF INDISCERNIBLESBY FRED CHERNOFF

Therehave been numerousttempts odetermine hatLeibniz'sgroundsare forhis principle fthe identity f indiscernibles.n thisstudy shallquestion he assumption hat there s a single,uniquefoundation orthatprinciple.By analysing pecific rguments,nd most mportantly,y dis-tinguishingwo sortsof question hat Leibniz addresses, he supposition fa uniqueground urns ut to be spurious.We needto separate wotypesofquestion:whether odcouldhavebroughtbout statesX and Y conjointly;and whetherGod couldhave brought bout stateX or,alternatively,tateY, butnota singleworld hat containsbothX and Y.I. INTRODUCTORYLeibniz'sfinalviews on a broadrangeofquestions re presentedn theLeibniz-Clarke orrespondence.1n trying o excavate the groundof theprinciple f the identity f indiscerniblesPII], as it appears there, t isusual to restrict neself ntirely o the correspondence. ecourseto otherwritingss not generally egarded s instructive ere. The reasoncited isLeibniz's alleged inconsistencyn fundamental uestionsof metaphysics.It is heldthat, n thecorrespondence,eibnizgrants hereality fmaterial,spatio-temporalbjects in a way denied elsewheren his writings.2 hispapermay providefurther easonsforheeding his advice. For if t can beshown hat there s morethanone version fPII in the correspondence,tfollows fortiorihatthere s more hanone versionnherentntheLeibniziancorpus.The questionusuallyraised n connectionwiththeground fPII is, 'Isit presented s a necessary r as a contingent roposition?'.3 ut we mustbe verycarefulwhenformulatinghe problem n these terms. It is onlytooeasytoequivocate n necessary', articularlynconnection ithLeibniz.There rea number fcommonly mployed ensesof necessity',ndLeibnizscrupulously istinguisheseveralofthem.4Some commentatorse.g.,Res-cher,Russell,Vinci nd perhapsAdams)haveargued hatPII, in the corres-

1The original edition was edited, and Leibniz's letters were translated, by Clarke.The most recent editions are edited by H. G. Alexander and by Loemker: see list ofreferences elow.2Montgomery urth discusses this supposed inconsistency,as does Thomas Vinci.3Among hecommentatorswhopursuethisquestionare G. H. R. Parkinson,NicholasRescher,BertrandRussell and P. F. Strawson.4In his fifth etterto Clarke,as well as in his Theodicy nd On the Radical Origina-tion of Things , Leibniz distinguishesmetaphysical fromphysical necessity, logicalfrommoral necessity,and absolute fromhypotheticalnecessity.

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LEIBNIZ'S PRINCIPLE 127pondencewithClarke, s a necessary roposition,nd some e.g.,Parkinsonandperhaps trawson) aveargued hat t is contingent. omeofthosewhohold it to be contingento so becausethe set ofpremises romwhich t isdeduced includespropositionsconcerning,orexample,the nature of theDivineWill)which re notnecessaryruths.Otherse.g.,Vinci)havearguedthat,since Leibniz viewsthesepremises s necessary, II is presented s anecessary roposition.Thusevenwhen greement as beenreachedregard-ing the premises romwhichLeibniz deducesPII, therehas been discordover ts own nature.At least someof thisdisagreementestsuponan equivocation.Leibnizholds that a principleike God willsonlywhat s best' is necessaryn onesense,but not in another. He believes t to be morally ecessary; ut itsdenial is not self-contradictory,o it is not absolutely ecessary.We canelude thisproblemby altering ur nomenclature. shall make use ofthedistinction etween logical and non-logical propositions orthe pur-posesof nvestigatingheground f PII. Logical coverspropositionshatare true in virtueof our conceptualcapabilities nd limitationsthat is,those whosenegations re inconceivable). t is not possibleto conceiveofan armadillo s havingfour egswhile lso havingfewer han four egs,noris it possible o conceive f a set as havingmanymemberswhile lso beingempty.Truths f ogic nd settheory re ncluded nder herubriclogical',which orresponds,n theLeibnizian exicon, o 'absolutelynecessary'.Allotherpropositions,ncluding hose Leibnizholds to be morally but notabsolutely necessary, re non-logical.Hence some claims that PII isnecessary ssert t to be a logicaltruth,whileother uch claimsassert t tobe non-logical.II. LEIBNIZ'S THIRD LETTER AND THE LOGICAL PRINCIPLELeibnizprofesseso provide manydemonstrationso confutehefancyof those who take space to be . . . an absolutebeing . The first fthesedemonstrationss presented t L III. 5.5 He offers negativeargument,againsttheNewtonian onceptionfspace as absolute, nd a positive rgu-ment, upporting is own relational heory fspace. Thenegative rgumentis thefollowing:I saythen, hat f pacewasan absolutebeing, herewould omethinghappenforwhich t would be impossible here hould be a sufficientreason. Which s against myaxiom. And I prove t thus. Space issomethingbsolutelyuniform; nd, without he thingsplaced in it,onepointofspacedoesnotabsolutely iffernanyrespectwhatsoever

from notherpointofspace. Now from ence t follows,supposingspace to be somethingn itself, esidesthe order of bodies amongthemselves,)hat tis impossible here houldbe a reason,whyGod,preservinghe same situations f bodies amongthemselves,houldhave placed them n space after ne certainparticularmanner, nd5I followthe conventionalreferencenotation: 'LIII. 5' is paragraphfiveofLeibniz'sthird etter.



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128 FRED CHERNOFFnot otherwise;why every thingwas not placed the quite contraryway,for nstance, y changing ast intoWest.The negative rgumentmakesexplicituse ofthe principle f sufficient

reason[PSR]. The argument an be restated s follows:(N1) Space is absolute, nNewton's ense.(N2) Space is homogeneous:ny twopointsofempty pace are thesame in every espect.(N3) The universes orderedn some determinate ay.(N4) Thepresent rder fthe universes distinct romomecontraryorder, .g.,the order hat wouldexist fEast were nsteadWest.(N5) There s no sufficienteasonwhyGodorders he universenthewaythatHe does and not n someotherway.(N6) Something appensforwhich here s no sufficienteason..'.(N7) If space is absolute, henPSR is false.The firsttep sthehypothesisobe considered.Thesecond tep spresentedas a tenetofboththeories,nd is notquestioned yClarke, ince t is indeeda consequenceof Newton's doctrinethat Euclidean geometrydescribesphysical pace. The third tepis theworthy bservationhat theuniverseexistsand is arranged n some particularway. (N4) is a consequenceof(N1), since (N1) impliesthat there are absolute directions f East andWest. (N5) is impliedby (N4), givenLeibniz's conception f sufficient

reason . According o this conception, will,even God's will,cannot actwithout sufficienteason beyond he mere willto act ). (N6) is a validgeneralizationf (N5), giventhe existential ssumption, ontainedn (N3),that there s a world. The hebdomad s completed y (N7), whichfollowsfromN1) and (N6) byconditionalization.The objectionClarkeraises to thisargument oncerns eibniz'suse, in(N5), of sufficienteason . Leibnizsays that there s a sufficienteasonwhythings houldbe so, and nototherwise L II. 1). Clarkereplies, Butthis ufficienteason soft-timesoother,han hemerewill fGod (C II. 1).Leibnizabhors hisexception o God'sperfectlyationalnature, ndretortsthatClarke grantsme this mportant rinciple. . But he grants t onlyin words, nd in realitydenies t (L III. 2). Fromhereensuesa debateoverthenatureof God'swill. But we can conclude, t thispoint, hatthevalidity f thenegative rgumentt L III. 5 hinges ponthe Divineapplic-abilityofPSR, thatis, uponwhetherGod's will to act can itself onstitutea reason forhis acting.The positive rgument,ubjoined o thenegativeone,is the following:But ifspace is nothing lse,but thatorder rrelation; nd is nothingat all without odies,butthepossibilityfplacing hem; henthosetwo states,the one such as it now is, the other upposedto be thequite contraryway,wouldnot at all differ rom ne another.Their

6The identityof a point of Newtonian space is independentof any matter it maycontain. (Cf.Newton's Principia, scholiumto definition , sects. II-LV, in Alexander.)Therefore ny axes and directions can be definedsolely in terms ofpoints of absolutespace.



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LEIBNIZ'S PRINCIPLE 129differenceherefores onlyto be found n ourchimericaluppositionof thereality fspace in itself.But in truth he one wouldexactlybe the same thing s the other, heybeingabsolutely ndiscernible;and consequentlyhere s no room to enquireafter reasonof thepreferencef the one to the other.This argument iffers rom he negativeone in two important espects.First, t is independent f the interpretationf PSR. Its validity s un-affected y whether r not we choose to interpret sufficienteason toincludeGod's merewillto act. PSR is used to showonlythat no conflictwiththerelational heory rises. And no conflict riseson eitherLeibniz'sor Clarke's nterpretationf PSR. Secondly, hisargument ses PII. Thepositive rgumentan be recast s follows.(P1) Space is relational.(P2) The stateof theuniverse s it is now (SN) and the state thequitecontrary ay (SC) are indiscernible.(P3) If two states are indiscernible,hen one is identicalwith theother PII).(P4) SN = SC.(P5) It is notthecasethatGodproduces hestateSN totheexclusionofSC... (P6) We cannot nfer he denialofPSR (as we could n thenegativeargument)..(P7) It is not the case that the relational heorymplies he denialofPSR.The negativeand positive arguments ombineto yieldLeibniz's con-clusionn thefollowing ay. Let A' = 'Space is absolute', nd R' = 'Spaceis relational'.(01) PSR Axiom(02) A -+ r PSR (N7)..(03) A (01), (02), MT(04) -(R+ PSR) (P7)(05) A v R Assumption..(06) R (03), (04), (05)Although his is a plausiblerepresentationf the text, the argument sredundant.Giventhetruth f 05), we can do without04), theconclusionofthe positive rgument.Leibniz often xpresseshis belief n (05). So itis perhapsbecause (05) is not a truth f ogic,nor s anywhere rovenbyLeibniz,that he includes 04) in theoverallargument.But this s not be-yondquestion. (04), i.e.,thepositive rgument,maybe included or hetor-ical purposes, o lend additionalweight o whathas alreadybeenproven.

Or perhaps t is included o showthatwe neednot seek further isjunctsin (05). In any case, Leibniz's firm elief n (05) is clear from uch state-ments s If space and timewereanythingbsolute, hat is, iftheywereany thingelse besidesa certainorderof things . . (L IV. 16).The positive rguments at least intended o show that the relationaltheorydoes not suffer rom he same defect s Leibniz attributes o the



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130 FRED CHERNOFFNewtonian heory.The conclusion,which paraphrased s (P7), does notactuallyfollow romP1)-(P6). It requires ualification. he positive rgu-ment does not prove that the relationaltheory s consistentwithPSR.Leibnizhas shown hat the absolute heory onflicts ithPSR, in a specificway. The positive argument evealsonlythat the relational heorydoesnot conflictwithPSR in thatparticularway. It is stillpossible hat theremaybe someotherpointof tensionbetween hem. But eventhisqualifiedconclusion erves Leibniz's purpose, f that purpose s to demonstratehesuperiority,t leastin thisrespect, fLeibniz'stheory ver tsrival.Let us return o the analysisof the positive rgument.The feature fthe argumenthat most nterests s is (P3), that s,PII. Its use is evidentin the sentence,But in truth he one wouldexactlybe the samething stheother,heybeing bsolutelyndiscernible'.n order o determine hetherornotPII here s a logicalprinciple,et us examine he role t plays n theargument.The proofbeginsbyhypothesizingpace to be relational. Fromthis t follows hat the spaces SN and SC are orders, hat s, setsofrela-tions. Let us simplifyhe analysis by considering ant's example of auniverse omprisedfa singlehand. Supposethis oneobject s a lefthand.Space wouldthenconsist ftherelations l,r2, 3, . . constitutingheset{rl, 2,r3,. .}, which shallcall U. NowchangeEast intoWestandconsidera universe onsistingf a righthand. Let us call thesetofspatialrelationsof thisuniverseU'.As Kant observed, he pointsof a lefthand are relatedto one anotherjust as thecorrespondingointsofa righthand are related o one another.For everyri n U (or U') there s an rjsuchthatri= r,and rj s a memberof U' (or U). Therefore, y the axiom of extensionality, = U'. Thisjustifieshequalified onclusion fthepositive rgument.God can nomorepreferU to theexclusion f U' thanHe can prefer to theexclusion fA.Thus the relational heorydoes not violatePSR in the way the absolutetheorydoes. Indeed, there s no roomto enquireafter reason of thepreferencef theoneto theother , incethere s no one in addition o theother.That PII is here a logical principle an be seen by recognizinghatLeibnizmustdeny hat tispossible vento conceive hat SN = SC. Leibnizoften sesthe factthat the relational heorymplies hatspace is somethingideal, n order o contrasttwith heabsolute heory. n thepositive rgu-mentLeibnizpostulates hat the materialworld s thesame n both SN andSC, except forthe spatial relations mongmaterialpoints. Leibniz hereuses PII to arguethat two ideal entities pointsof spatial relations) reidentical.But if t is possible o conceive wo deal entities s distinct,hensurely heyare distinct. So ifthepositive rguments valid,wemustcon-struePII as denyinghepossibilityfconceivinghem o be distinct.ThusPII, as it is employed ere, s an exampleof what havetermed logicalprinciple .77Note that the question addressed by Leibniz and Clarke here is not 'Could Godproduce a possible worldcontainingboth SN and SC?'. It is rather,Could God produce



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LEIBNIZ' S PRINCIPLE 131III. LEIBNIZ'S FOURTHLETTER AND THE TWO PRINCIPLESThe positive nd negative rgumentsre attackedby Clarke at C II. 2and C III. 5. He deniesthatPSR appliesto Divinedecrees.He maintainsthat a reversal f the orderof three ndiscernibleodiesconstitutes realchange, ven f pace s only he mere rder fbodies . Likewise,f heearthwere nsteadplacedwhere ome distant tar s, twouldoccupy genuinelydifferentlace. And Clarkeclaimsthat these cannotbe accountedforbythe relational heory.Leibniz'sreplyat L IV. 1-6 makes mportant se ofPII. We can distinguishhreearguments.Two, at L IV. 1-4,attempt oprovePII, and one, at L IV 6, uses PII as a premise. The fourthetterbeginsas follows:1. In thingsabsolutely ndifferent,hereis no [foundation or]

choice;and consequently o election,norwill;sincechoice mustbefounded n somereason, rprinciple.2. A merewill without nymotive, s a fiction, otonly contrarytoGod'sperfection,ut alsochimericalndcontradictory;nconsistentwiththe definitionf thewill,and sufficientlyonfutedn myThe-odicy.3. 'Tis a thing ndifferent,o place threebodies, equal and perfectlyalike, in any orderwhatsoever; and consequently they will never beplacedin anyorder, yhim who doesnothingwithoutwisdom.Butthen he beingthe authorofthings, o suchthingswillbe producedbyhimat all; and consequentlyhere re no suchthings n nature.4. There is no such thingas two individuals ndiscernibleromeach other.The firstrgument, hich eeksto provePII, can be restated s follows:(M1) A will,by definition,equires motive n order o act.(M2) There an be nomotive o order everal ndiscerniblendividualsin someway,rather han n some other.(M3) Thewill ofGod,thoughDivine, s nevertheless will..'.(M4) God does not order ndiscerniblendividuals o be ordered nanyway... (M5) God doesnotproduce ndiscerniblendividuals.(M6) God is the creator f all nature..'.(M7) No indiscerniblendividuals xist n nature.A seconddeduction fPII canbe abstracted rom IV. 3-4,whenwereplace(M1)-(M3) bove by:(M1') 'Tis a thing indifferent o place two or more indiscernibleindividualsn anyorderwhatsoever.(M2') Wisdomcould not move God to order several indiscernibleindividuals n someway,rather han in some other.(M3') Goddoesnothingwithoutwisdom.(M4)-(M7)follow s in the above argument.a possible world containingeither SN or SC?', that is, 'Could He produce one, to theexclusion of the other?'. And secondly, t is here assumed that PII governs aggregatesbased on simple substances in the same way that it governssimple substances. Thosewho deny this assumption face the formidable task of explaining how the aggregatescould be subject to different ules ofidentity.



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132 FRED CHERNOFFThe versionof PII deducedhereis clearlya non-logical rinciple. ttellsus nothing bout logic,nor about what it is possibleto conceive. Ittellsus only hat, n the actualworld,weshallnever ncounterwo ndiscern-

ible individuals. Furthermore,everalpremises equired n the deductionsare not absolutelynecessary ruths f logic. To see thiswe shouldrecallthat Leibniz assiduously ffirmshat God is free o actualizeany possibleworld. It is not absolutelynecessary hat God actualize our own, bestpossibleworld. He choosesthisworldonlybecause He is whollyrationalandmorally erfect.Thus neitherM3)nor M3') is a truth f ogic althoughthey remorally ecessary).Nor s (M6)a truth f ogic. So bothargumentscontainnon-logical ropositions s premises. Since PII is here deducedfromnon-logical remises, eibniz seems o think t a non-logical rinciple.AtL IV. 6 Leibniz uses PII in thefollowingrgument:To supposetwothings ndiscernible,s to supposethe samethingunder wo names. And thereforeo supposethatthe universe ouldhavehad at firstnother osition f time nd place,than that whichit actuallyhad; andyetthat all thepartsof theuniverse houldhavehadthe same situation mong hemselves,s that which hey ctuallyhad; sucha supposition, say,is an impossible iction.We may ask whether he non-logical ersion f PII deducedabove is theversionemployedhere. In order to answerthis, let us distinguishwoquestions hat are addressedby Leibniz and Clarke:(Q1) Could the entirematerialworldhave occupiedsomeregionofspace other han that which t in factoccupies?(Q2) Could the entirematerialworldbe moved from ne regionofspaceto someother?For the purposesof our inquiry nto the groundofPII, the mostsalientdifferenceetween hese two questions an be stated n termsofLeibniz'snotion of possibleworlds . (Q1) asks about two statesthat, if distinct,mustcomprise artsofseparatepossibleworlds. (Q2), on the otherhand,asks about two statesthat,even ifdistinct,might onstitute artsof thesamepossibleworld.Thesetwoquestions reexamples f two moregeneral ypesofquestion.Leibniz's notionof compossibility ppliesto a set ofstates f and only fthere s somepossibleworldwhichncludes hem.We can then characterizethetworelevant ypesofquestion hus:(Q1') Are the noncompossible,fdistinct, tates X and Y distinct?(Q2') Are thecompossibleeven fdistinct) tatesX and Y distinct?It is byrecognizingheexistence f thesetwo typesof question and thatLeibniz undertakeso answer xamplesof bothtypes)thatwe can bestseethe differentersions fPII thatappear n thecorrespondence.The argumentt L IV. 6 considers he questionof whether herecouldbe two specific, istinct tates. They are: the materialworldhavingacertain osition t the time ofcreation, nd thematerialworld, eing tself



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LEIBNIZ S PRINCIPLE 133thesame,buthaving omeotherposition t thetimeof creation.Thusit is(Q1) that is at issue. If thetwostatesare distinct, hentheyare membersofdifferentossibleworlds sinceany possibleworldhas, by definition,tmost one creation tate). We cannot hen nterpretheversion f PII usedat L IV. 6 as thenon-logicalnededuced tL IV. 1-4.8Thatprincipleellsusonlywhat we shall orshallnotfindn the actualworld. t cannot elate tatesofdiverse ossibleworlds o oneanother.But thepresent uestion onsiderstherelationshipetween wostates hat, fdistinct,re members fdifferentpossibleworlds. In orderto answerthis broaderquestion,Leibnizwouldhave to make use of a principle elating tatesof distinct ossibleworlds.And indeedthat is preciselywhathe appearsto offer,n the argument tL IV. 6. He presents conceptualprinciple hat deniesthe possibility fdistinguishing,ven in thought, he one state from he other: to supposetwo things . . is to suppose . . . . Therefore,he argument t L IV. 6bothrequires, nd infactmakes use of,the ogicalversion f PII.Leibniz's fourthetter ontainsone furtherrgument hat interestinglyemploys II. It occurs t L IV. 13.To say thatGod can cause thewholeuniverse o move forwardna right ine, or in any other ine, withoutmakingotherwise nyalteration n it; is anotherchimerical upposition.For, two statesindiscerniblerom ach other, re the same state; and consequently,

'tisa changewithout nychange. Besides, here s neither hyme orreason n t. But Goddoesnothingwithout eason; nd tis mpossiblethere houldbe anyhere.9It appearsthat (Q2) rather han(Q1) is addressedhere. Leibniz s consider-ing the possibility f a singlepossibleworld, he actual world,containingtwo states. Theyare: theuniverse ccupying omespatialregion, nd theuniverse,materiallyunchanged,occupying ome otherspatial region, tsome othertime. The non-logical ersionof PII is sufficiento generateLeibniz'snegative nswer o (Q2). Let us thenassumefor hemomenthatthenon-logical ersion fPII is intended ere. We can detect woargumentsin thispassage:(R1) The state of the materialuniverse, efore t is movedalong astraight ine, is indiscerniblerom ts state after t has beenmovedalonga straightine.(R2) Two states ndiscerniblerom ach other reidentical PII]... (R3) Thetwostatesareidentical... (R4) God does notmove the materialuniverse longa straightine.

8It mightbe objected that what is really at issue here is not (Q1), since we shouldinterpret IV. 6 as consideringwhetherthe universecould have had atfirst differentposition, giventhat it now occupies its present position. It is thena question ofwhetherthe world could be moved, in which case (Q2) is at stake. Thus Leibniz can use thenon-logicalPII, deduced at L IV. 1-4. But this interpretation s not the one closest tothe text. Leibniz asks if the universe could have at first nother position . . . thanthat whichit actually had . He thus contrasts two (possibly distinct) nitial positions.OIwish only to offer ome suggestionsfor nterpreting his very dense passage. Itmay well be impossibleto divine Leibniz's actual intentions.



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134 FRED CHERNOFFAndsecondly:(S1) There s no reasonforGodto movethematerial niverse longa straightine.

(SI') It is impossible hat God shouldhave a reasonto move thematerial niverse longa straightine.(S2) Goddoesnothingwithout eason..'.(S3) God does not movethe materialworldalonga straightine.I assumed for he moment hat Leibniz ntends non-logical II in thispassage. But there re at least twoconsiderationshatmilitate gainst hisview,and suggest hat he intends logicalprinciple.First,PII entersntothe secondargument fanywhere n the justificationor he first remise.The non-logical II tellsus that God does not producetwo indiscernibleindividualsnthisworld. But if we do not nvoke he ogicalPII, then t ispossible hatthe twostates theuniverse efore t is moved longa straightline and as it is aftert is moved)are indiscerniblenthought,ndyetdiffersolonumero. Onlythe logicalPII removes hispossibility.) n this caseGodproducesneither tate,sincetheyare indiscernible.10ut it is obviousthatGod produced t least one ofthetwo states, incethe materialworldwas in factcreated. It mustthenbe deniedthatthere re eventwo statesfromwhich God chooses. And thiscan be accomplished nly by recourseto thelogicalPII.The secondpointarisesfrom hefactthatthetwo arguments, hichhave paraphrased s (R1)-(R4) and (S1)-(S3), are conjoined n a specificway by Leibniz. The first rgumentmakes clearuse of PII, two statesindiscerniblerom ach other, re the same state . This appearsto be thelogicalversion, or hefollowingeason. The secondargumentmakesrefer-ence to PSR. The non-logical ersion fPII is a consequence fPSR, andthus s not ndependentf t. Leibnizconjoins he twoarguments ith heterm besides',whichproperlyntroduces n independentdea. The onlyway to interprethe secondargument,whichuses PSR, as independentfthefirstrguments to interprethe firstrguments employinghe ogicalPII.Eitherofthesetwo considerationss, in itself, arfrom onclusive roofthatL IV. 13 containsonlythe logicalPII. It is even possiblethat bothversions fPII are nvolvedhere. We sawthatboth re at work nL IV. 1-6.So perhaps he logicalPII is employedn (R2) ofthe firstrgumentR1)-(R4), and thenon-logicaln the second rgumentS1)-(S3).IV. LEIBNIZ'S FIFTH LETTER AND THE NON-LoGICAL PRINCIPLELeibniz presents numberof arguments hat employPII. We haveseen that the validityof someof theserequires he logicalformulation fPII, whilethe validityof othersdoes not. Leibniz profferseductions f

lOLeibni firmly ndorses thisview, e.g., at L IV. 3.



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LEIBNIZ S PRINCIPLE 135PII, buttheyproveonlythenon-logical ersion. A cardinal uleofhistoricalinterpretationemands hatwe attribute onsistency, herever ossible, ogreat philosophers.Devotion to this imperative uggests hat we trytointerpret II as an unambiguous rinciple.Sincethe ogicalversion ntailsthenon-logical ersion, emight onjecturehat Leibniz ntends heformer.That principlewillrender alid all of theargumentshatemployPII as apremise.But Leibniz'sdeductions fPII proveonly henon-logical ersion.So thispious suggestionntails that his attempted eductions fPII fail.It does,however, ave thegratifyingonsolationhat what s therededucedis not nconsistent ith he logicalPII. But this consolation, nd with tthepossibilityf nterpretingII as a univocalprinciple, anisheswhenweexamineLeibniz'sfifthetter,wherehe repeatedly isavows he ogicalPII.Leibnizprovides nother eduction f PII at L V. 21:I infer rom hat principle PSR], amongotherconsequences, hatthere re not in naturetworeal,absolutebeings, ndiscernibleromeach other;because f therewere,God and naturewouldact withoutreason, n orderinghe one otherwise hantheother; nd thatthere-foreGod does notproduce wopiecesofmatterperfectlyqual andalike.This argumentproves that no indiscerniblendividuals exist in nature.Like the proofs n the fourthetter, t demonstratesnlythe non-logicalPII. Leibnizgoes on to consider n objectionraisedby Clarke, nd thenpresents hefollowing erspicuous enial of the logicalPII:This supposition ftwoindiscernibles,uchas twopiecesof matterperfectlylike,seems ndeedto be possible n abstract erms;but itis notconsistent ith heorder fthings, orwith hedivinewisdom,bywhichnothings admittedwithout eason.The logicalPII is deniedwith qual force t L V. 25:When denythat there retwodropsof waterperfectlylike,orany twootherbodies ndiscerniblerom ach other; don't say, tis

absolutelympossibleo suppose hem ....Leibnizhererepudiates commitmento the logicalPII. He does notdenythepossibility rconceivabilityf ndiscernibleodiesthatdifferolonumero, s he must n the arguments f the third etter. He denies hereonlythe actualityof indiscernible odies. This position s taken also atL V. 27: The parts of time or place, consideredn themselves, re idealthings; nd thereforeheyperfectlyesemble ne another ike twoabstractunits. But it is notso with wo concrete nes,orwithtworealtimes, rtwospacesfilled p,that s,truly ctual.Leibnizagainaffirmshepossibilityf ndividuals hat are ndiscernible,etdiffern number. It is significanthat the denials of the logicalPII areaccompanied y other rgumentshatemployPII as a premise.But theseargumentsequire nly heweaker, on-logical ersion. For example,Leib-nizis attemptingo subvert hedoctrinesfatomsand ofvacua. The views



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136 FRED CHERNOFFhe opposesassertthat atomsand vacua in factexist. Thus theyare (Q2')type questions, ather han (Ql') type questions,n thattheyrefer o theexistence of several states withina singlepossibleworld. The positionadvocatedby Leibniz on these ssuescan thereforee advancedby meansofthenon-logical II forthe samereason as thatforwhich hisprinciplewas able to providehimwithhisanswer o (Q2).In hisattackupontheexistence fatoms,he admits hat t is abstractlypossibleto conceiveof severalpiecesof matter s numerically iverse ndyet qualitatively ndiscernible. This is evident, .g., in the last passagecited.) The theory e is combatingmaintains hatatomsexist nthe actualworld, otas mere bstract ossibilities. he questiontanswers,s we havenoted, s an exampleofa (Q2') typequestion. Leibnizcan thereforedmitthebarepossibility fatoms,or the consistencyfthe concept tom,with-outundercuttingnypartofhiscounter-argument.imilarly, isargumentsagainsttheexistence fvacua do notrequire he logicalPII. He is able topresenthem sing nlyPSR and tsconsequences.Themost ft-propoundedargument gainstthe existenceof vacua states,roughly, hat any regionof space assumedto be void ofmatter ould,withoutdetracting rom heperfectionfanyothermatter, ave beenfilledwithmatter y God.l It isimpossible ora void to confer oodnesson the universe or on anything),but it is possibleforsomethingwhichfills he void to confer oodness. Itis thereforeetter o create hatregionfilledwithmatter han to create tempty.Since Goddoesonlywhat s best,He doesnot create vacuum.Leibnizopposesa finite niversewith ssentiallyhesameargument. fthe universe s finite,hen t couldhave been arger.Morematter an confermoregoodness.So iftheuniverse ad been arger,t couldhave beenbetter.If it couldhave beenbetter,hen t is not thebestthat s possible.But Godacts onlyforthe best. Thereforeheuniverse s not finite. n bothargu-ments hepremise hat God acts forthe best is employed.This is not anabsolutetruth f ogic,but rather morally ecessary, on-logical roposi-tion. Thus the conclusions fbothargumentshouldbe non-logical.ThisaccordspreciselywithLeibniz'sposition nthematter.

Absolutelypeaking, t appears that God can make the materialuniverse initen extension; utthecontraryppearsmore greeableto his wisdom L V. 30,my talics).Leibniz doesnotregard hepropositionsorwhichhe argues, n his attackson the finite niverse, nd atoms,as logicaltruths.He does not need toconfine is premises o logical truths. ITe is then at liberty o use non-logicalpremises uchas the weakerversion f PII. It is perhapsdue to hisrecognitionf thisfact that we find in the fifthetter that Leibnizusesonlythenon-logical II and disavowsthe logicalPII. He needsonlytheweaker,essdubitable rinciple. o heendorsest. He disclaims hestrongerllArguments ike this occur at L II. 2, L III. 9, L IV. 22-3,L IV P.S. and L V. 43.



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LEIBNIZ'S PRINCIPLE 137principle,ince t smorevulnerableo criticism,nddoesnot,forhispresentpurposes, ieldresults eyond hoseobtainablefrom he weakerprinciple.l2V. CONCLUSIONThere sno single nterpretationfPII thathas thesimultaneous irtuesofrenderingalidall oftheargumentsnwhichPII occurs, nd ofremainingconsistent ithLeibniz'srepeated emarks,n the fifthetter, ntheconceiv-abilityof indiscerniblendividuals. Leibniz employs wo logicallydistinctversions fPII. The third etter ontains rguments,t L III. 5 and L III. 6,demonstratinghat supposedalternative laces and timesof creation re,on the relational heory,ndiscerniblerom ne another nd thereforeden-tical. The alternatives re noncompossible,ftheyare distinct.Thus thequestions t stake are oftype Q1'). Thenon-logical II cannotrelate uchstatesto one another, nd hencecannot be used to manufactureeibniz'sconclusions t L III. 5 and L III. 6. The fourthetter ppearsto use boththe logicaland non-logical ersion f PII. And in the fifthetterLeibnizuses thenon-logical II, whilehe rejectsthe logicalPII. Any attempt ointerpret II, as it appears n the correspondence ithClarke, s a uniqueprinciple hat accordswith all of Leibniz'srelevant emarkss doomedtofailure.Thetypeof nterpretatione have ruledoutmaybe termed Athenian ,afterCastafieda.An Athenian nterpretationresumes hatthework ofaphilosopherprang ully eveloped romtsauthor, s opposed oa Darwinianinterpretation,hich llowsthat changesmay occurwhenconflictingiewsbattlewith ne another ordomination,nd thefitterurvive.The situationwehave encounteredn thecorrespondenceociferouslyemands Darwinianapproach. The third etter ontains nlythelogicalPII. The fourthetterappearsto containboth,whileonlythenon-logical ersion s proven.Andthefifthetter sesonlythenon-logical ersion,while xplicitly enyinghelogicalversion.The Darwinian tandpoint ermits s to supposethatLeibniz ntendedonlyone version fPII. As his deaswere hallenged yNewton ndClarke,he scrutinized is positionmoreclosely, nd as the debate came to focuson somewhatdifferentssues,the need fora broaderprinciple iminished.For theseand otherreasonsPII is transfiguredrom logical nto a non-logicalprinciple.The struggle etween he two competing ersions f PIIappears oculminaten thefourthetter.Andthenon-logicalersionmergesvictorious n the fifthetter. In a discussion fa differentssue,Castaniedastatesthat The Darwinianapproach s particularly ecessaryn the case

a2Itmightbe argued that the shiftfrom he logical to the non-logicalPII could beexplained away by appeal to the distinction between two entities' sharing all theirpropertiesand theirsharingonly their non-relational roperties. But there appears tobe no evidence in the correspondence hat Leibniz viewed this as the basis of the shiftin his use of PII. And in earlierpapers (such as First Truths , Loemker I, pp. 411-7)he seems to endorse both the relational and non-relationalapplications of PII.



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138 FRED CHERNOFFof Leibniz .13The foregoingesults ubstantiate his claim. In consideringtheground f PII I have suggested hatan Atheniannterpretationfthatprinciple, otonlyas it appearsthroughoutheworks fLeibniz,but evenas it appears n hislastphilosophicalorrespondence,s notpossible.Yale University

REFERENCESRobert M. Adams, Leibniz's Theory of Contingency , Rice UniversityStudies, 63(1977), 1-41.H. G. Alexander (ed.), The Leibniz-ClarkeCorrespondenceNew York, 1970).Hector-Neri Castafieda, Leibniz's Concepts and their Coincidence Salva Veritate ,Nois, 8 (1974), 381-98.Samuel Clarke (tr. & ed.), A Collectionof Papers whichpassed between he ate LearnedMr Leibniz and Dr Clarke in theyears 1715 and 1716 relatingto thePrinciples ofNatural Philosophyand Religion (London, 1717).MontgomeryFurth, Monadology , Philosophical Review,76 (1967), 169-200.Hid6 Ishiguro,Leibniz's Philosophy ofLogic and Language (London, 1972).Leroy Loemker, GottfriedWilhelmLeibniz, Philosophical Papers and Letters Chicago,1956), 2 Vols.G. H. R. Parkinson,Logic and Reality n Leibniz's Metaphysics Oxford,1965).Nicholas Rescher, The PhilosophyofLeibniz (Englewood Cliffs, 967).BertrandRussell, A CriticalExposition ofthePhilosophyofLeibniz (Cambridge,1900).P. F. Strawson, ndividuals (London, 1965).Thomas Vinci, What is the Groundfor the Principle of the Identity of Indiscerniblesin Leibniz's CorrespondencewithClarke? ,JournaloftheHistoryofPhilosophy,12(1974), 195-201.

10p. cit.,p. 383.

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