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Russell on Substitutivity and the Abandonment of Propositions IanProops UniversityofTexasatAustin Introduction In the summer of 1905 Bertrand Russell wrote to his American friend, LucyDonnelley,withthenewsthathehadjustcompleted“anarticleon GeorgeIVforMind”(Russell1994,414).Inspiteofitsmildfrivolity,such a description of “On Denoting” contains a large measure of truth. For this article’s puzzle about George IV does indeed have a claim to be considered one of its main foci. This is so partly because of the well- known role the puzzle plays in motivating the Theory of Descriptions, butalsobecauseofthelesswell-knownroleitsfull solution—something that requires resources beyond the Theory of Descriptions—plays in shapingthemetaphysicaland(especially)epistemologicalviewsRussell developsfrom1905onward.Mostnotably,inthecontextofcertainofhisother commitments,Russell’ssolutionentailsthefollowing(shortlytobeexpli- cated)epistemologicalprinciple: For comments and illuminating discussion of issues in this article, I am grateful to RayBuchanan,JoshDever,KatherineDunlop,StevenGross,IvanHeyman,CoryJuhl, KevinKlement,LouisLoeb,PauloMancosu,AdamPautz,BryanPickel,MichaelPotter, AdamRigoni,MarkSainsbury,JonShaheen,SanfordShieh,NicoleSmith,PeterSullivan, Zolta´nGendlerSzabo´,andMichaelTye.VersionsofthisarticlewerepresentedatLondon University,JohnsHopkinsUniversity,YaleUniversity,theUniversityofCalifornia,Berke- ley,andtheUniversityofSheffield.Iamgratefultotheaudiencesoneachoccasionfor theirstimulatingcommentsandquestions.Iamalsodeeplyindebtedtothreeanonymous refereesforthePhilosophicalReview,whoprovidedgenerousandilluminatingcomments onnumerousversionsofthisarticle. PhilosophicalReview,Vol.120,No.2,2011 DOI10.1215/00318108-2010-027 q2011byCornellUniversity 151 IAN PROOPS FullDisclosure:Wheneverasubject,S,isacquainted(inRussell’s technicalsenseofthatterm)withanobject,x,Sisacquaintedwith everypartofx. This substantive principle1 has a profound relevance for Russell’s con- ception of what is usually (if somewhat inaccurately) called a “logically propername.”2Anameofthissort,whichIshallsimplyterma“genuine Russellian name”—or “genuine name”—for short, is a symbol that is not“definedincontext”—as,forexample,inRussell’sopiniondescrip- tionsare—butratherhas“meaninginisolation”(compareRusselland Whitehead1990,66).SinceRussellsupposesthatweunderstandagenu- inenameonlyifweareacquaintedwithitsbearer(Marsh1956,205),Full Disclosure entails that the bearer ofagenuinename must, in acertain sense,revealitselffullytoanysubjectwhounderstandsitsname.Tracing out this and other consequences of Russell’s solution to the George IV puzzlewillbethemaingoalofthisarticle.Weshallaskwhathissolution entails,andhowfarRussellisawareofthevariouscommitmentsheincurs byadoptingit. PerhapsthemostsurprisingimplicationofRussell’ssolutioncon- cerns his conception of our cognitive relation to propositions. I shall arguethat,inthecontextofhisothercommitments,hissolutionentails thatwecannotbeacquaintedwithpropositions.Asweshallsee,Russellin all likelihood appreciated this fact, and his appreciation of it would plausiblyhavemotivatedhisadoptionoftheso-calledMultipleRelation TheoryofJudgment.Thesedevelopments,Ishallargue,deprivedhimof anypositive reason tobelieveinpropositions, andso promptedhimto deviseargumentsagainstthem.Themostpromisingofthesearguments, Ishallargue,restsonthePrincipleofSufficientReason. My aims will also be critical. I will argue that certain of Russell’s epistemologicalviewsentailthatthereexistcertaincasesoftheGeorgeIV puzzlethatresisthissolution.IwillfurtherarguethatRusselleventually 1. AcquaintanceforRussellisaformofimmediateawareness;soonecannotbesaid tobeacquaintedwithanobjectinitsentiretybyvirtueofbeingacquaintedwithoneofits parts(asonemight,forexample,intheordinarysensebesaidtobeacquaintedwithParis byvirtueofbeingacquaintedwiththeChamps-Elyse´es).Accordingly,FullDisclosureis notinthiswaytriviallytrue.NordoesRussellregardFullDisclosureastruebydefinition; for, as we shall see, he eventually comes to regard this principle as false but without changinghisconceptionofacquaintance. 2. Thelabel“logicallypropername,”althoughwidelyattributedtoRussell,occurs, tomyknowledge,nowhereinhiswritings. 152 Russell on Substitutivity and the Abandonment of Propositions cametoappreciatethisproblemandthathisappreciationofitledhim eventuallytobackawayfromFullDisclosure. Such a project will require a more sustained examination of Russell’sdiscussionoftheGeorgeIVpuzzlethanhasyetbeenattempted in the scholarly literature. I submit that this task is worth undertaking foranumberofreasons.First,commentatorshaveyettoachieveafully satisfactory understanding either of the puzzle itself or of Russell’s solutiontoit.Thiscircumstanceisowing,Ibelieve,toafailurecorrectly to identify the substitutivity principle Russell intends to be defending. Second, partly as a result of this first failing, there is a lacuna in the scholarlyliteratureonthequestionofwhatexactlyRusselliscommitted tobyhissolutiontotheGeorgeIVpuzzleandhowfarthosecommitments shape his logical atomism. Third, the identification of those commit- ments reveals Russell’s position to be more multiply buttressed than one might otherwise suppose: features of his view that are adopted for apparently remote reasons turn out to be also demanded by his solution to the puzzle, and certain points of detail in his view turn out tobemotivated,inpart,bythatsolution. Thearticledividesintoeightsectionsandaconclusion.Thefirst sectiondiscussesthecontextinwhichRussellintroducesthepuzzle.The second defends a nonstandard interpretation of the puzzle and of its solution. The third and fourth sections consider the consequences of Russell’s solutionforhisconceptionof genuine Russellian names (and forhisconceptionoftheirbearers).Thefifthsectionraisesaproblemfor Russell’ssolutiontotheGeorgeIVpuzzle,arguingthat,evenwhenitis charitablyinterpreted,thereremainrecalcitrantinstancesofthepuzzle. ThesixthsectionarguesthatoneoftheconsequencesofRussell’ssolu- tionisthatsomesentences needtobetreatedas“incompletesymbols.”It argues,further,thatinthecontextofhisotherviews,hissolutionentails thatwecannotbeacquaintedwithpropositions.Thisaspectofhisview,I shallargue,motivatesRussell’sadoptionoftheMultipleRelationTheory of Judgment. The seventh section asks what role, if any, the paradoxes playedinmotivatingthistheory.Iarguethatalthoughcertainparadoxes prompted Russell’s first experiments with the theory, they do not by themselvesexplainhiseventualfirmendorsementofit.Theeighthand final section examines Russell’s reasons for eventually coming to hold thattherearenopropositions. 153 IAN PROOPS 1. SituatingtheGeorgeIVPuzzle BeforepresentingtheGeorgeIVpuzzle,itwillbeusefultoconsiderthe contextinwhichitarises.ThepuzzleisoneofthreethatRussellsupposes must be solved by any adequate theory of the meanings of those expressionshecalls“denotingphrases.”InthePrinciplesofMathematics, first published in 1903, Russell (1996, sec. 58) identifies the denoting phrases of English with those expressions having one of the following forms:“allFs,”“anyF,”“someF,”“everyF,”“anF,”“theF.”In“OnDenot- ing”headdstheexpressions“everything,”“nothing,”and“something”to thelist.ThechallengeRussellfacesin“OnDenoting”istogiveanaccount of the meanings of these phrases that solves all three puzzles without generating any further conundrums orparadoxes. Thepuzzlesall con- cernthepropertreatmentofthephrase“theF.” Thefirstpuzzleisaversionoftheproblemofnegativeexistentials. It challengesus toexplain how astatement such as“The round square does not subsist”3 can be both significant and true.4 The puzzle arises because,fromanaivepointofview,itcanseemasthoughthissentence canbemeaningfulonlyifitintroducesasubjectofpredication,andyet,if itistrue,nosuchsubjectsubsists.Russellsolvesthepuzzlebyrejectingthe underlying assumption that this statement is of subject-predicate form. Instead, the Theory of Descriptions treats this statement and its fellowsasnegatedexistentialgeneralizations.Thestatementistakento mean“Thereisnouniqueroundsquare”—thatis,“, ’x [;y (round y &squarey $ y ¼x)]”—andsoistreatedasunproblematicallytrue. Thesecondpuzzlearisesfromthefactthatsentencescontaining improper definite descriptions—“The present King of France is bald,” for example—can seem to generate counterexamples to the law of ex- cludedmiddle.Itgainspurchase,ifitdoes,onlybecauseittakesseriously 3. Here“subsist”means“havebeing”ratherthan“havetemporalbeing”or“exist.” 4. Thisversionofthepuzzleisprominentintheparagraphof“OnDenoting”in whichRussellpresentsitssolution(seetheparagraphnumbered“(3)”inRussell1956, 48).Butwhenthepuzzleisfirst presentedin“OnDenoting”(45),itisformulatedina mannermorefaithfultothehistoricalpositionofRussell’sopponentinthiscontext, AlexiusMeinong.Atthisearlierpoint,Russellpresentshistargetasbeingtheviewthatthe likesoftheroundsquareandthepresentKingofFrance,althoughtheydonotsubsist,are nonetheless to be “admitted” as objects (45, 47). Russell appears to be picking up on Meinong’sviewthattheroundsquareandthepresentKingofFrancehaveabsistence (Aussersein)(thatis,thepropertyofbeinganobject)eveniftheylacksubsistence(Sein) (the property of being). (I am indebted to Jon Shaheen for help in understanding Meinong’sview.) 154 Russell on Substitutivity and the Abandonment of Propositions atraditionalformulationofthatlawinwhichnegationistakentoattach toapredicate,namely,“A isB orA isnotB.”Soformulated,thelawcan appear to face a counterexample because neither the sentence “The present King of France is bald” nor the sentence “The present King of Franceisnotbald”seemstoexpressatruth.Russellsolvesthepuzzleby maintaining that, because descriptions introduce distinctions of scope, the traditional formulation of the law of excluded middle is incorrect. Theproblemwiththetraditionalformulationisthatitforcesthedescrip- tionin“ThepresentKingofFranceisnotbald”tohavewidescopewith respecttonegation.Thecorrectformulationwouldberather:“EitherP oritisnotthecasethatP,”whichpermitsthenegationsigntohavewide scopewithrespecttothedescription. 2. FormulatingtheGeorgeIVPuzzle—andInterpretingItsSolution These puzzles are familiar and their interpretation relatively uncontro- versial.TheGeorgeIVpuzzle,bycontrast,ishardertoformulate,andthe detailsofitspresentationandsolutionhave—inmyview—notyetbeen adequatelynaileddown.Thepresentsectionisdevotedtoarguingfora nonstandardinterpretationofthepuzzle. Russell(1956,47–48)introducesthepuzzleasfollows: Ifaisidenticalwithb,whateveristrueoftheoneistrueoftheother,and eithermaybesubstitutedfortheotherinanypropositionwithoutaltering thetruthorfalsehoodofthatproposition.NowGeorgeIVwishedtoknow whetherScottwastheauthorofWaverley;andinfactScottwastheauthor ofWaverley.HencewemaysubstituteScott fortheauthorof ‘Waverley’,and therebyprovethatGeorgeIVwishedtoknowwhetherScottwasScott.Yet an interest in the law of identity can hardly be attributed to the first gentlemanofEurope. Inordertoanalyzethepuzzle,itwillbeconvenienttohavereferenceto thefollowingformalstatementoftheargumentitdiscusses. ArgumentA P1. ScottistheauthorofWaverley. P2. GeorgeIVwishedtoknowwhetherScottwastheauthorof Waverley. C. GeorgeIVwishedtoknowwhetherScottwasScott. 155 IAN PROOPS The puzzle arises because, in argument A, a patently invalid substitu- tional inference seems to be licensed by a substitutivity principle that, according to the purveyor of the puzzle,has overwhelmingplausibility. Letuscallthisprinciple,whoseproperformulationwilloccupyusshortly, “SP.” Russell’s first task, whatever else he might do in his discussion of George IV’s curiosity, is to show that argument A is not in fact a counterexampletoSP. HowshouldSPbeformulated?Standardly,itistakentobeaprin- ciplegoverningthesubstitutionofonelinguisticexpressionforanother (see,forexample,L.Linsky1966,673;Soames2003,119).WhileLeonard LinskyventuresnodeterminateformulationofSP,ScottSoamesformu- latesitaswhathecalls“thelawofsubstitutivityofidentity”(“SI”): SI:Whenaandbaresingularreferringexpressions,andthesen- tencea5bistrue,aandbrefertothesamething,andsosub- stitutionofonefortheotherinanytruesentencewillalwaysyield atruesentence. (Hereandhereafterboldfaceisusedasadeviceofquasi-quotation.) Principle SI is expressly concerned with the substitution of certain linguistic items within others. In contrast, I take SP to concern thesubstitutionofpropositionalconstituents,whicharenot,ingeneral, linguisticinnature,withinnonlinguisticRussellianpropositions.5Iwould therefore formulate it as the following generalization of a salva veritate principle(“SV,”for“Saving(truth-)Value”): SV:Thesubstitutionofidenticalpropositionalconstituentswithin apropositionpreservesthatproposition’struth-value.6 Bya“propositionalconstituent”Imeananythingthatisa“term”inRus- sell’stechnicalsenseof“term”derivingfromThePrinciplesofMathematics (hereafterabbreviatedas“Principles”butcitedas“Russell1996”).Aterm, inthissense,isanyobjectthatisonedefinitething,asopposedtoaplural orintrinsicallyindefiniteobject(Russell1996,sec.47;comparesec.58, 5. Sincesomepropositionsareaboutlinguisticitems,“nonlinguistic”propositions maycontainsomelinguisticconstituents.Thepointisthatnotall oftheirconstituents maybelinguistic—inotherwords:propositionsarenotsentences. 6. ThepossibilityofconceivingofSPinthiswaywasfirstsuggestedtomebyMichael Potter(inconversation).TheargumentsIpresentforthisinterpretationare,however, myown. 156 Russell on Substitutivity and the Abandonment of Propositions footnote“*”).7Whatmattersmostforourpurposesisthatpropositional constituents are not in general linguistic items—though, because some propositionsareaboutlinguisticitems,incertaininstancestheymaybe. In the present section I will explain how the Theory of Descrip- tionssolvesthepuzzle.Itdoesso,Iwillargue,byshowingthatSP,when construedasSV,isnot—inspiteofappearancestothecontrary—falsi- fiedbythemanifestinvalidityofargumentA.Iwillthendiscussthemore standardaccountofthesemattersofferedbyLinskyandSoames.Against thisstandardreading,Iwillcontendthatthetextualevidencesupports theinterpretivethesisthatSPisSVratherthanSI. InordertoseehowtheTheoryofDescriptionssolvestheGeorge IVpuzzle,itwillbehelpfultosetthepuzzleoutasanargumentforthe falsehoodofSV.So,tothatend,considerthefollowingpairofsentences: [A] GeorgeIVwantedtoknowwhetherScottwastheauthorof Waverley. [B] GeorgeIVwantedtoknowwhetherScottwasScott. Theargumentwouldrunasfollows: Premise1 ScottandtheauthorofWaverley areidenticals. Premise 2 The proposition expressed by [B] results from the proposition expressed by [A] by the substitution of ScottfortheauthorofWaverley. Premise3 [A]istrueand[B]isfalse. Therefore: SVisfalse. Russell’s solution involves rejecting this argument’s second premise on thegroundthatthephrase“theauthorofWaverley”contributesnoprop- ositionalconstituenttothepropositioninwhoselinguisticexpressionit occurs. Accordingly,the proposition expressed by [B]cannot, after all, be taken to result from the substitution of the man, Scott, for a prop- ositionalconstituentdesignatedbythephrase“theauthorofWaverley”in [A]. From this it follows that the proposition expressed by [B] is notobtainedfromtheoneexpressedby[A]bythesubstitutionofiden- ticals. The invalidity of argument A is thus shown not to constitute a counterexampletoSVafterall.8 7. AtthisstageRussellviewedthedenotationof“aman”asanindefiniteobject (Russell1996,sec.58,footnote“*”). 8. Itisworthnotingthatoneviewofthesemanticsofdefinitedescriptionsthatis rejected in“OnDenoting”would also resolve thepuzzle.This isRussell’sview inthe 157 IAN PROOPS TheTheoryofDescriptionsexplainswhythephrase“theauthor ofWaverley”contributesnopropositionalconstituenttotheproposition expressed by [A]. This theory maintains that all definite descriptions are“incompletesymbols,”meaningtherebythattheyhavenomeaning in isolation but are merely defined in context (compare Russell and Whitehead1990,66).Thetheory,whenfullydeveloped,comprisestwo contextual definitions, which show us how to eliminate descriptions fromthecontexts“TheFisG”and“TheFsubsists”—or,strictlyspeaking, fromscope-disambiguatedcounterpartsofthesecontexts.Glossingover the (in other contexts important) detail of scope, we may state these definitionsasfollows: TheF isG ¼ ’x [;y (Fy $ y ¼x)&Gx] Df. TheF subsists ¼ ’x [;y (Fy $ y ¼x)] Df. Russelltakesthesedefinitionstoshowthatthemeaningfulnessof the expression “The F” does not consist in its contributing a proposi- tionalconstituenttothepropositionsinwhoseverbalexpressionitoccurs. Rather,itsbeingameaningfulexpressionconsistsonlyinitscontributing systematically(inthewayshownbythesedefinitions)tothedetermination ofthepropositionexpressedbythesentenceinwhichitoccurs. It is important to note that Russell regarded the provision of a theory according to which the phrase “the author of Waverley” has no meaninginisolationasconstitutingafull solutiontothisinstanceofthe puzzle. His supplementary remarks about the permissibility of substi- tutionswhenthedefinitedescriptiontobereplacedhas“primaryoccur- rence,”althoughtheyguardagainstapossiblemisunderstanding,arenot essentialtothestatedpuzzle’ssolution.(Thesepointswillbeelaborated uponlater.) By combining the Theory of Descriptions with the description theory of ordinary names (and mass terms), Russell’s solution may be extendedtocasesofapparentsubstitutionfailureinwhichtheexpression tobereplacedisanordinarypropername(oramassterm),ratherthana description.From1903onward,Russellcomestotreatordinaryproper names of “mythical personages” such as “Apollo” as disguised definite PrinciplesofMathematics accordingtowhichadefinitedescriptionexpressesadenoting concept.Accordingtothistheory,thepropositionexpressedby[B]doesnotresultfrom theoneexpressedby[A]bythesubstitutionofidenticalssincewhatScottreplacesisnot anauthorbutadenotingconcept.Russell,however,rejectsthePrinciples’theoryforother reasons,amongthemthenotoriouslyobscure“Gray’sElegyArgument.” 158 Russell on Substitutivity and the Abandonment of Propositions descriptions.9Atthistimehetakesasimilarviewofnamesof“interesting persons,”presumablybecausethesenamesoccurinthedictionarywhere their meaning is given by a definite description (Russell 1994, 285). In 1904, he extends this account to terms for mythological stuffs, for example, “nectar” and “ambrosia” (Russell 1973a, 100). It is less clear exactly when he first comes to view ordinary names of (so to speak) uninterestingpersonsandnonmythologicalmaterialobjectsastruncat- ed definite descriptions; but a commitment to doing so is clearly already presentin“OnDenoting”;fortherehedeniesthatwehaveacquaintance withmaterialthingsorwithotherminds(Russell1956,56).Ifwecannot beacquaintedwiththesethings,wecannotnamethem.Butifwecannot name them, their apparent names (for example, “Venus,” “Balfour”) must be disguised definite descriptions for they clearly have meaning of some kind inasmuch as they allow us to say true things by uttering the sentences in which they occur. I take it, therefore, that as early as 1905 Russell is likely to have been aware of the applicability of his solutionto the George IV puzzle (in its extended form) to cases ofthe puzzle generated by nonintersubstitutable but apparently coreferring ordinarypropernames. Letustakestock.WehaveseenthatRussell’ssolutiontotheinitial puzzleaboutGeorgeIV—thatis,thepuzzleabouthowSVistobesaved fromcounterexample—makesnoappealtoscopedistinctions.Hissolu- tion’stwoessentialelementsare:(a)theidea,securedbytheTheoryof Descriptions,thatdefinitedescriptionshavenomeaninginisolation,and (b)thedescriptiontheoryofordinarynames.Eachoftheseelementsis, ofcourse,opentochallenge,andindeed(b)isnowadaysalmostuniver- sallytakentohavebeenrefutedbySaulKripke’sargumentsinhisNaming andNecessity(1980).Nonetheless,inviewofthespecialplaceoccupiedby “OnDenoting”asoneofthefoundingdocumentsofanalyticphilosophy, itseemsworthaskinghowwellRussell’ssolutionfaresonitsownterms— thatis,granting(a)and(b)forthesakeofargument—andseeingwhatit entailsforhisphilosophy.Wewillturntothesequestionsshortly,butfirst itwillbenecessarytodefendourinterpretationofSPasSVratherthanSI. Perhapsthemostobviousconsiderationinfavorofthisinterpre- tation is that SV possesses a degree of obviousness that SI lacks. This 9. SeeRussell’sunpublishedessay,writtenin1903,“OntheMeaningandDenota- tionofPhrases”(Russell1994,285–96).Andforausefuldiscussionofthedevelopment ofthedescriptiontheoryofnames(fromwhichthisarticlehasbenefited),seeKaplan 2005,especially987–89. 159 IAN PROOPS mattersfortworeasons.First,ifthepuzzleistohaverealforce,oneshould not be able to solve it simply by denying SP. Russell, after all, takes the TheoryofDescriptionstoprovidethekeytothepuzzle’sresolution.And yet, on the standard interpretation, it is hard to say why he should not rather just take apparent failures of substitutivity to refute SP. (Some commentators who are apt to read SP as SI are, accordingly, inclined nottoseeapuzzlehereatall,simplybecausetheytakeSItobeobviously false.See,forexample,Sainsbury1979,107.)Second,andrelatedly,Rus- selltakesSPtohaveadegreeofobviousnessequaltothatofaparticular logicalprinciple,namely,theindiscernibilityofidenticals.Thatmuchis evidentfromthefactthat,intheparagraphthatservestointroducethe puzzle(Russell1956,47–48,quotedabove),herunsthetwoprinciples togetherandseemstosuggestthattheformerismerelyareformulation, or perhaps a corollary, of the latter. The principles are close cousins— especially so in an early Russellian setting—but they are not identical. Nonetheless, the fact that Russell seems to regard them as closely con- nectedsuggeststhatSPshouldbereadashavingtheevidenceofalawof logic.PrincipleSI,Icontend,lackssuchevidence,whileSVpossessesit. A more subtle consideration counting in favor of our reading concerns its ability to accommodate an otherwise problematic feature of the passage in which the solution is presented. This passage, which forconvenienceweshallcall“passageA,”runsasfollows: ThepuzzleaboutGeorgeIV’scuriosityisnowseentohaveaverysimple solution. Theproposition‘ScottwastheauthorofWaverley,’whichwas writtenoutinitsunabbreviatedforminthepreviousparagraph,doesnot containanyconstituent‘theauthorofWaverley’forwhichwecouldsub- stitute‘Scott.’(Russell1956,51–52) A prima facie problem for the standard reading is that the sen- tence“ScottwastheauthorofWaverley”plainlydoes containthelinguistic constituent: “the author of Waverley.” On the standard reading, then, Russell is, on the face of it, denying the obvious. This is not a problem forourreadingsincewetakeRusselltobesayingthatthenonlinguistic proposition expressed by the sentence “Scott was the author of Waverley”10containsnopropositionalconstituentcorrespondingtothe words“theauthorofWaverley.” 10. LeonardLinsky(1966,674)contendsthatthepassagejustquotedcontainsa slip.Thesentenceintowhichtheword“Scott”wouldbesubstitutedinargumentAisnot “ScottwastheauthorofWaverley”but“GeorgeIVwishedtoknowwhetherScottwasthe 160

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Introduction. In the summer of 1905 Bertrand Russell wrote to his American friend, . generating any further conundrums or paradoxes. The puzzles
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