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Nordic Wittgenstein Review 2(2013)

NikolayMilkov

The Joint PhilosophicalProgram of Russelland Wittgenstein andIts Demise

Abstract Between Apriland November 1912, BertrandRussell andLudwig Wittgenstein were engagedinajoint philosophical program. Wittgenstein’s meeting with Gottlob FregeinDecember1912 led, however, to itsdissolution – thejoint program wasabandoned. This paper outlinesthe keypointsofthat program, identifying whatRussell andWittgenstein each contributedtoit. It determines precisely those features of theircollaborativeworkthatFrege criticized. Finally, buildinguponthe evidence developed in the first twosections, it recasts, alongpreviously undeveloped lines, Wittgenstein’s logical– philosophical discoveries in the two yearsfollowing hisencounter with Frege in 1912. The paper concludeswithanoverviewofthe dramatic consequences theFrege-Wittgenstein critiquehad for Russell’s philosophical development.

1. Wittgenstein-Frege-Russell 1912-13 This paper investigates the interactionbetweenthe three founding fathersofanalyticphilosophy – Russell, Wittgenstein andFrege – during aformative period of theirphilosophical development. It sheds lightonthe joint program that Russell andWittgenstein collaborated on from ApriltillNovember 1912, as well as on its collapse afterWittgensteinvisited FregeinJena in December the same year.The key finding is that Frege’s criticism of elements of theprogram both motivated andinformed Wittgenstein’s criticism

81 NikolayMilkov BY-NC-SA of Russell’s approach to . This radical challenge culminatedinMay and Juneof1913when, facing Wittgenstein’s criticism, Russell abandoned his book project on theory of knowledge.Frege’s remarks also impelled Wittgenstein to rethink and reformulate hisown philosophical . Among othermatters, germane to this seminal development in thehistory of early analyticphilosophy is an issue, addressedin section 4.2, that hasbeen actively debated in theliterature over the past thirty years: Wittgenstein’s criticism of Russell’s multiple- theory of judgment (Griffin 1985,Hanks 2007). Rather thanexplainingthis criticism in the usual manner, i. e., on the basis of purely logical considerations,the move here is to discloseits groundinFrege’s impact on Wittgensteinataparticularhistorical moment. Theevidence adduced in this accountimplicitlydiscredits the “competitive interpretation” of the collaboration between Russell andWittgenstein, an account that casts the purported competitioninterms of who was thebetter philosopher, Russellor Wittgenstein.Nicholas Griffin andGregory Landini, for example, criticizethe allegedclaim thatinthe monthsbetween April 1912 andJune1913 Wittgensteinrepeatedly correctedmistakesofhis teacherRussell,sothat “if only Russellhad been abetter philosopher, he wouldhavebeen Wittgenstein” (Griffin 1996: 222; Landini2003/4, 2007). By with thelatterview, this essayestablishes thatwhile between April and November1912 Wittgensteinenhances Russell’s philosophicaldevelopment, this occurredonlybecausethe young studentopenedRussell to newperspectivesonRussell’s own philosophy.Moreover,the evidence makesitclearthat between January andJuneof1913what WittgensteinconfrontedRussell withweremainly changes in Wittgenstein’sthinking, which trace directly to the influence of Frege’sphilosophicallogic. Russell’s putative “defeat”inthe face of Wittgenstein’scriticism in June 1913 thus merely signaled the former’srealization that theidea of an exact philosophy, as he had initiallyconceivedit, facedviable alternatives, andhence that theprospect of systematically articulating suchaphilosophywas fraught with much more complexitythan he had anticipated.

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2. Thejoint program (April–November 1912) After the publicationofVolumeIof in 1910, BertrandRussellconcentratedhis effortsmainlyonquestions of .In“Knowledge by Acquaintance and Knowledge by Description” (1911) and TheProblems of Philosophy (written in July andAugust of 1911, andpublished in 1912), he addressed someof theepistemologicalproblemsthat hisnew logichad raised.Late in October 1911,Russell first metLudwigWittgenstein. During the Winter Term at Cambridge astrong intellectualsympathy developed between thetwo men.Russellrevealed as much in a remark that appearsinaletter dated March 15, 1912, aweekafter the term ended: “His [Wittgenstein’s]attitude justifies all Ihave hoped about my work” (Clark 1975: 172). In the spring and Fall Terms of 1912, Russell andWittgenstein collaborated intensively on what can be seen as ajoint philosophicalprogram. This was first brought to light in 1988 by the Wittgensteinbiographer Brian McGuinness,who observedthat “the twophilosophers were concerned withthe same problems” (McGuinness 1988: 159). Some years later, RayMonk made explicit in hisbiographyofRussell that“Russell andWittgenstein regarded themselves as collaborators on the same project” (Monk 1996: 286). During themonths of their mutualengagementinthis project, Russell andWittgenstein often workedtogether. It is noteworthy thatthis was the only period in his careerthat Wittgensteinever collaborated with another philosopher. While he frequently challenged Russell’sconceptions, Wittgensteinlimited himself to constructivecriticism, concentratinghis theoretical energieson developing ideas that supplementedthose of Russell. Apparently, the jointprogram featured adivision of labor. While Russell concentrated on problems of epistemology, Wittgenstein focusedmainlyonproblemsoflogic.Asweshall see, however, eachofthem also introduced ideas into the other’s field. This culminatedinOctober–November 1912, during the last weeks of their collaboration, whenRussell wrote apaper on logic –“What is Logic?” (see section 2.3, below) – and Wittgenstein authoredone on epistemology: “What is Philosophy?”,whichhereadatthe

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Moral Science Club in Cambridge on November 22.Init “philosophy was defined as all those primitive which are assumed as true withoutaproofbythe various sciences” (McGuinness1988: 144). Things changedradically afterWittgensteintraveled to Jena and metwith FregeinDecember1912. As we shall see, Frege convinced him thathis joint project with Russellwas basedon flawed assumptions and hence was fundamentallymisconceived. Thefirst sign thatthe collaborationwithRussell was at an end wasthatWittgensteinceased seeking out Russell’s forcollabo- ration. He now felt that he couldprogress more profitablyby thinkinghis waytological–philosophical discoveries of his own, withoutconsulting Russell(cf. Milkov2007: 83–4; 2012). The dissolution of the collaborative spirit between thetwo philosophers is capturedinanote by DavidPinsent from February 4, 1913. Wittgenstein, we read, dictated “his latest discoveries in the Fundamentals of Logic. […]Russell acquiescedinwhathesaid without amurmur” (Pinsent 1990: 44). Concomitant with thisbreakdownofsignificant philosophical interactionwas apalpable cooling of the personaltiesbetween Russelland Wittgenstein.InMarch 1913Russell“began to feel that Wittgensteinwas narrow and uncivilized, ‘rathertoo muchthe champion of aparty’” (McGuinness 1988: 172, Russell’sletterto Ottoline Morrell #717 6.3.19131). By May of that year they had becomesoestranged thatRussell did not bother to inform his younger colleaguethat he was composing anew book on episte- mology: TheoryofKnowledge. Theevent thatsealedthe terminationoftheirjoint programwas Wittgenstein’s devastating criticism of Russell’s Theory of Knowledge in late May 1913 (which will be discussed in section 4.2).The first positive resultofthis total breakwithRussell was Wittgenstein’s “Notes on Logic”, whichhewrote in August andSeptember of that year.Inpractical terms, theestrangement between the two

1 Henceforth, letters fromRussell to Lady Ottoline Morrell, as systematised at the Harry Ransom Centre, University of Texas at Austinwillbereferred to with their numbers precededby#.Inothercases,Russell’s lettersare identified by the date they were written.

84 Nordic Wittgenstein Review 2(2013) philosophers was evident in Wittgenstein’s decisioninthe summer of 1913 to leave Cambridge forNorway – he no longer neededto collaboratewithRussell.

2.1The impact of Wittgenstein on Russell’s epistemology Elements of thejoint program appear in Russell’s paper“On the of Cause” (Russell 1912c), whichhereadatameetingof the Aristotelian Society in earlyNovember of 1912. As merely a popularversion of Russell’s highlydeveloped views on the relation betweenphilosophyand physics,however,ithardlycountsasa significantresource for understanding the Program. Be thatasit may, Russell’s criticism of thenotionofcausalityinthe paper clearly parallels Wittgenstein’s approach to the topic in Tractatus 5.136–1: onlylogic is necessary;causalitycan convey neither regularitynor . The most important document attesting to Russell and Wittgenstein’s bonafide collaborationinajoint programis“On ”(Russell 1912b),apaper thatRussell wroteinMay 1912 and deliveredthat same monthatameeting of the Philosophical SocietyofUniversityCollege,Cardiff. Russellrevised theessayin October 1912 and read it near theend of thatmonthbefore the MoralScience Club at Cambridge.2 Russell’sdeclaredaim in “On Matter”istoshow (i) that all thearguments hitherto alleged by philosophers against matterare fallacious;(ii)thatall thearguments hithertoallegedinfavor of matterare fallacious; (iii) that, although theremay perhapsbe reason to supposethatthere is matter,yet we canhave no meansof finding out anything whatever as to its intrinsicnature. (Russell 1912b: 80) The first thingthatstrikesthe readerofthese lines is their close affinity with the highly truncated style of Wittgenstein’s writings from the period 1912–16.Asregards their content, Russell’s radical skepticism reflectsWittgenstein’s impactonhis . The link betweenskepticism andWittgenstein in Russell’s thinking is borne

2 This variantofthe paper was published as Russell 1992b. In our analysis of theJoint Program below we will refertoit.

85 NikolayMilkov BY-NC-SA out by Russellhimself in aremarkfromMay 2, 1912:Wittgenstein, he confessed, “is the onlyman Ihaveevermet withareal bias for philosophicalscepticism; he is glad when it is proved that something can’t be known” (McGuinness 1988:106). Thus it is no surprise that, when Russelldelivered the revisedversion of “On Matter” in October, his feeling was that“no one except Wittgenstein understood it at all” (#608).Itisworth notingthat alongwith Wittgenstein, G. E. Moorewas also in the audience, butevenhe failed to makesense of Russell’s newideas. On the other hand, Wittgenstein thought thatRussell’s paper “OnMatter” wasthe best thinghehad done (#460) – notexcluding ThePrinciples of and Principia Mathematica. The results of Russell’snewly adopted skepticalstancecan be brieflyoutlined.Afewmonths beforehemet Wittgenstein,Russell adopted the view, which he presented in The Problems of Philosophy. It maintained that we do not directly perceive physical objects perse– we perceive sense-data; the latterare qualities andrelations, includingqualitiesand of sense-data. Nevertheless,wecan know physical objects, although only by description. This is because thesense-data with whichweare acquainted help us logically to infer thatthere arephysicalobjects. At that , Russell believedthat despite not absolutely satisfactory,this conception is much more consistentwith the factsofthe external worldthan any competing philosophy of matter, especially , according to which thereare no physical objects at all. When Russell raisedthe problem of solipsism with Wittgenstein on 23 April 1912,however, the latter breezily dismissed its significance as aphilosophical challenge, declaring thatsolipsism “doesn’t hurt, since [even if there are no otherminds,] physicsand astronomy, and allthe other sciences could still be interpreted so as to be true” (Monk1996: 260). Indeed, we can imagineaprivate world – aworld existingonlyinorder to affect oursenses – in which the laws of science arevalid. This argument impelled Russell to abandonthe view thatwecan infer matter from sense-data. Instead,hebegan regarding matterasalogicalconstruction on the

86 Nordic Wittgenstein Review 2(2013) basis of the objectsofacquaintance (Russell 1912b: 84). 3 What underlay thisradical shift in Russell’s thinking was theidea that the worldconsistsultimatelyofindependent atomic units (latercalled “logical atoms”) – sense-data. These primitive elementscould be ordered in many different,logicallyorganizednetsinwhich sense- data interrelate with one another.4 The objects of commonsense and those of the hypotheses of science couldbeseen,inthis account,asalternative constructs of these andother units. In thephilosophy of science,Russell now subscribed to the viewthat physicsmay be studied, […]asapiece of pure mathematics; thespace andmatterconcerned in this studyare variables,[5] concerning which certain hypotheses aremade;that is to say, they arenot definite entities, but merely anything having certainproperties. (Russell 1912b: 83) This statementreveals how fundamentally Russellrevised his philosophyduring hiscollaboration with Wittgenstein. He now claimed that we canabandon theproblem of thecontent of the beliefs of commonsense,contending instead thatits supposed content – thematter – andthe objects of common sense are logicallycongruent. Justhow radicalthe changewas in Russell’s positionisclear in thatRussell,who had since1898 consideredhimselfacommitted realist, saw hisrevised program as “The bankruptcy of Realism” (#423). Notsurprisingly, the newdoctrinehad consequences for Russell’sworldview.Among other things,itbroughtwith it an unsettling sense that nothing in thisworldissolidand secure.

3 This was the firsttime everRussell spoke about “logical constructions”. Thenew was, however, related to ideasfrom Principia Mathematica,inparticular, with the definition (in Introduction, chapter 3) of classes as “incomplete symbols”. The term itself was firstusedinF.H.Bradley’s The of Logic wherehespoke about “logical, or ideal, constructions”(Bradley 1883: 257). 4 Howexactly such nets aretobeconstructed Russell learned from Whitehead. In December 1912 the lattershowedRussell the technique of definingpoints,instants and “things” as logical constructions (Russell 1914:11).The of “logical constructing”, however, wasborn in thediscussionsofRussell with Wittgenstein some weeks earlier. 5 Thesevariablescan be replaced by thesense-data we perceive.

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Russell himself intended his paper“On Matter” to be “a model of cold passionless analysis, setting forth the most painful conclusions with utter disregard of human feelings” (24.5.12).

2.2 Russell’snew andWittgenstein’s new logic Even as Russell developed hisphilosophical position in writing and redrafting “On Matter”, Wittgensteinwas doing work in the whichexhibitsdemonstrable parallels with it. In fact, Russell’s discussionofthe problemofmatterand Wittgenstein’s of the natureoflogic “proceeded pari passu” (McGuinness 1988:160). There is concrete evidence testifying to this mutualengagement. On the versoofthe folio 1ofRussell’s project-paper “Matter,the ProblemStated” (Russell 1912/13: 96) we findnotesonlogic,someinWittgenstein’shand andone in Russell’s, most probably written beforeWittgenstein visitedFrege (before December 1912).6 It is thus undeniable that between April andNovember of 1912, Russell andWittgensteincollaborated closely. Wittgenstein’s jottings provedofconsiderable historical significance,includingastheydothe first sketchofatruth table device. 7 Thelatter schematized in atabular form thetruth- possibilities of the combinations (of the logicalconnections, or operations)oftwo propositions.Thisinnovationhad important consequences, most significantlyindemonstrating that logical operations can be represented in aradically perspicuousway by means of one symbol. Forexample,‘pvq’can be presented as follows:

6 Cf.n.8. 7It is nottobeconfused with the propositionallogic of introducedbyFrege in his Conceptual Script.The difference between them is thatwhereas the latter is “a logical analysis of the -values of aproposition,the truth-table device is the presentationof thisanalysis in tabular or matrix form” (Anellis 2004:57).

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‘ pq

TTT

FTT

TFT

FFF

’.

In otherwords, this innovation helped “to explain theself- evidence of logicalpropositions” (Wittgenstein1976:177). As we are going to seeinsection4.3,below, the truth table device proved to be afirststep toward the DoctrineofShowing thatWittgenstein introduced ayearlater. Besidesthe truth table device,inNovember 19128 Wittgenstein also originated the notion that thereisonly one logical constant. To be more specific, he determinedthat we can expresstruth- operations by employing asingle signfor the . The idea was that logical constants can be reduced to asingle logicaloperation, ‘ )( ’(cf. McGuinness1988: 161). Most significantly,Wittgenstein’s logical innovations at thistime were closely tied to the ontology Russelladvanced in “OnMatter”, which Wittgensteinthus evidentlyembraced. As remarkedabove,

8 I.e. before H. M. Sheffer, who first presented asimilar ideatothe American Mathematical SocietyonDecember 31, 1912. This shows Gregory Landini’sclaim that in the jottings Russell andWittgenstein discussed Sheffer’s stroke to be mistaken. As Landini himself notes, Russell received acopy of Sheffer’s paperonApril 15, 1913 (Landini 2007: 107 f.). (The paper itself was published in October 1913.) After Wittgenstein returned from Vienna at the very endofJanuary 1913,however, he did notworked together with Russell:hedictated his “newideas” (cf. section 2,above). Andsubsequent to the “terrific contest” between Russell andWittgensteinfrom 6.3.1913 (Monk 1996:291), tête-à-tête collaborative work between them was unthinkable.

89 NikolayMilkov BY-NC-SA in section2.1,Russell’s ontology assumed thatthe world consists of complex units, sense-data, which physicsrepresents as variables and which we can order, or compose, in manydifferentlogically organizednets: either hypothesesofscience, or “things” of common sense. We could call this Russell’sCompositionality Thesis. Apparently, Russell’sminimalistontology, withoutphysical objectsand withoutobjectsofcommonsense,went hand in hand with Wittgenstein’snovel minimalist logic, with its singlelogical constant. 9 Indeed,both maintained aparsimonious form of compositionality: Russell in ontology,Wittgenstein in logic. Corroborating this interconnectionisthe factthat Russell initially employedthe sign ‘ )( ’torefer to the interweaving of the elements of ontological complexes with which we areacquainted (Russell 1905: 169,cf. section2.3 below).Wittgenstein, on his side, used it to symbolize the only logicalconstant and, so, the inter- weaving of thelogical atoms (“atomic propositions”). Wittgenstein himself appears to have been cognizantofthe interconnection betweenRussell’s constructivist ontology and the assumption that there is only one logical constant, which he eventuallyexpressedthis way: “Wherever there is compositeness […] wealreadyhaveall thelogical constants”,and thismeans that there is a“sole logical constant” (TLP 5.47).

2.3Harmonybetween logic and ontology The foregoing points cast additional light on Russell’s motivation to addressdirectly the relatedness between logic and ontology in theJoint Program.This he did in thedaysimmediately after 13 October 1912, when he wrote “What is Logic?” (cf. section 2, above), apiece merely two pagesinlength. Itspremise is that “logic is thestudyofthe forms of complexes” (Russell 1912b: 55). 10 Logic, it declares, does not deal with judgments,somethingit

9We cansee thisfact as an example of how Russell’s “ideal of eliminativistic reconstruction” (Landini 2003/4: 118) – in this case,the elimination of physicalobjects – was also embracedbyWittgenstein in theform of eliminationoflogicalobjects. Cf. also Landini 2007. 10 An echo of this program is found in Our Knowledge,whereRussell claimed that“the first business of logic [is ...] aclassificationoflogical forms of facts” (Russell 1914: 60).

90 Nordic Wittgenstein Review 2(2013) consigns to psychology; nordoeslogic concern propositions, which can be falseand henceinRussell’sview cannotbeanything objectivebut merely formsofwords. Indeed,“true and false”, assertsRussell, “are extra-logical” (ibid.). What evidentlyinspired Russell’s paperwereideas that Wittgensteinhad formulated even prior to their collaboration. In November 1911, Wittgensteintookashis own philosophical point of departurethe position from which Mooreand Russellhimself began in 1899: 11 “there is nothinginthe world except asserted propositions whicharecomplexes of ”(McGuinness 1988: 89). In the Springand Fall Terms of 1912,Russell readily embracedWittgenstein’s (and Russell’sold) position, andhehad compelling reasons fordoing so:itharmonizedwith atendency in Russell to restoretohis philosophythe notion of complexes which he hadchampionedbetween1898and 1900, but which he had more or less repudiated between1900 and1905underthe influence of Peano and Frege.(In §3below, we will call the impact of Frege’slogic on Russellimmediately afterAugust 1900 the “first lesson” Russell received from Frege.) Theyear 1905, however, saw Russell adopting (arguably, under ’sinfluence)onceagain,anontologyof complexes. After assigning “knowledgebyacquaintance” aprimary roleinepistemology in “On Denoting”, Russell contended that complexesare among the things withwhichweare acquainted (Milkov2003: 50).This move partly restoredtohis philosophythe realistic mereology(i.e., part/whole “logic”)ofcomplex and simplesthat was an ingredient in hisphilosophyprior to August 1900. This tendency persisted. Shortly after he formulated the theory of descriptions, Russell eliminated classesfrom his logic: classes are “incomplete symbols”.There areonlypropositions and propositionalfunctions. Two yearslater, in 1907,Russell discovered that propositions produce paradoxes of theirown. In consequence, he came to maintain thatpropositions too are

11 Apparently,Moore and Russell did so underthe influence of the Brentanist school. Cf. Bell 1999.

91 NikolayMilkov BY-NC-SA incompletesymbols. To be more exact, theywereeliminated with thehelp of themultiple relation theory of judgment which claims that propositions only receive (and unity) through the judging (Stevens2005: 79). Truth-bearers arejudgments,not propositions. The signalresult of this development was thatthe ontology of complexes came to play an importantrole in Principia Mathematica, somethingclearlyattested to in thefollowingstatement from that work: … the consistsofobjects having various qualitiesand standing in various relations. Some of the objects which occur in the universe arecomplex. When an objectiscomplex, it consistsof interrelated parts. (Russell &Whitehead 1910:43) This ontology is clearly closetothat of Russellin1898–1900.Be this as it may, till 1912, Russell’srealistic mereology wasnomore than afocal tendency in hisontology.With “What is Logic?”, however,Russellrecast hismereology as aconsistent program.

3. Frege’scriticism In December 1912Wittgenstein met with FregeinJenatodebate philosophical logic, and subsequently reported that Frege “absolutelywiped the floor with [him]” (Goodstein1972: 272). What followed wasthat Russellreceived his “second lesson in logic” from Frege. Russell got his “first lessoninlogic” in 1900. Up to that time, his logic followed the relational theoryofjudgmentelaborated in Moore(1899). According to thelatter, judgments and propositions arecomposed of complexesconsistingofconcepts andrelations betweenthem. This was aprogram for part/whole “logic”,or mereology,inwhich logical implicationispossible both between terms andbetween propositions.Russell’s doctrine wasalso in conformitywith thelogic of classes, as wellaswith Boole’s algebra of thought. However, at the International Philosophy Congress in Paris,inAugust 1900,Russell learned from Peano (something the latter learnedfrom Frege) thatbesides the relations between parts and whole there is also arelationofimplicationwhichholds

92 Nordic Wittgenstein Review 2(2013) between propositions,not between individuals,and that this second relationismore fundamental.12 Otherintensionalities(unanalyzed units) which Russell introduced intohis logic after August1900 were the conceptsof “” and “denoting phrase”.Itwas in accordancewith Frege’s principle that Russell nowsubscribedtothe view thatweemployaproposition’s terms withinthe frameofthe entire proposition, not as autonomous, discrete units. 13 As forthe intensionalityofthe denoting phrase,Russellmaintained that even when singular,adenoting phrase refers to acollection, whichmay be either finiteorinfinite(Milkov 2003: 50,63).Inshort,denoting phrasesand propositions signify holistically, and do not require the availability of alltheir elements in order to have asense. While Russell did notwant to understate the importance of analysisand of relations,incorporatingintensionalities in hislogic in 1903 led himtorecognizetwo kindsofwholes: aggregatesand units. An aggregate is definiteonlywhen allits constituents are known.Units, by contrast,havenosuchrequirement; what’s more, we can know aunit when we knowmerely apartofit. The paradigm of the unit in Russell’s logic is the proposition(Russell 1903:§135; Stevens2005). F. H. Bradley correctly observed thatthis assumption contra- dicts Russell’s defenseof“strictpluralism, forwhich nothingis admissiblebeyondsingle termsand external relations”(Bradley 1910: 179). It appears that Russellwas consciousofthis inconsistency,for in alettertoBradley datedMarch 2, 1911,he implicitlyconceded Bradley’spoint:“With regard to unities,Ihave

12 Russell embracedarudimentary form of whatayearlater was called “material implication” alreadyinRussell (1899–1900). He didsounderthe continuinginfluence of Moore’s work in philosophical logic, especially of hispaper “Necessity” (Moore1900). 13 In fact, Russell accepted this position only with reservation – apoint setout by Peter Hylton whoinsisted that “Russellian propositions [of 1903]are hybrid entities. On the onehand, they are, likeFregean Gedanken,abstractentities representing or embodying the content of adeclarative sentence. On the other hand, unlike their Fregeananalogues, these abstract entities can containconcrete entities,such as people andmoments of time.” (Hylton 2005: 35) This in Russell’s 1903 position on propositions came to light in his rehabilitation of the mereological conception of propositionsafter 1905.

93 NikolayMilkov BY-NC-SA nothing short to say.The is difficult […] &Ido not pretend to have solvedall its problems.” (Bradley 1999: 145) As we noted in §2.3,aggregatesgradually came to assume an ever greater importance at theexpense of unitsinRussell’s work after1905. This development culminated in theJoint Program, whichsaw unitsvirtually eliminated.And it was thenthatRussell got his second lesson in intensionalityinlogic – from Frege again but thistimevia Wittgenstein. Before exploring this, it shouldbesaid that the only place where Wittgensteinexplicitly acknowledges what he took from his meeting with Frege in December 1912isinafragment published both in his PhilosophicalRemarks and Philosophical Grammar.Hence it is that fragment that serveshereasthe starting pointfor the analysis of the Joint Program’sdemise. Fregecriticized Russell’s andWittgenstein’s move to identifycomplexeswithfacts,pointing out that a“complexisnot likeafact. For Ican, for example,say of acomplexthat it movesfrom oneplace to another,but not of a fact”(Wittgenstein 1964:301, Wittgenstein1974: 199).Frege also questioned Wittgensteinabout whetherifanobjectwereapartofa fact aboutit, the fact wouldbelarger than theobject. Frege obviously held that whereas “a complex is aspatialobject, composed of spatialobjects” (ibid.: 302; 200), afactisnot. At first sight it is surprisingthatFrege spokeabout facts at all. Usually,herestrictedfacts to the realmofsense(or thought), so they didnot play asignificant role in hisontology (Dummett1981: 177). It seems that Fregestarted to thinkabout factsmore intensively only after hismeeting withWittgenstein in December 1912. What especially struck Fregeasmistaken was the idea that when we understand propositionswegraspspatial complexes. He argued, instead,thatinsuchcases, we understand one thing that is not spatial, namely the sense of the proposition that we grasp, which can be eithertrueorfalse.Itreally differs from thespatial complex,which is segmented. We findanecho of these considerations in Frege’s paper “”(1918/19)where he defined “fact” as “athought that is true” (Frege 1918/19:368). It deserves noticethatthis was the only placeinFrege’s corpuswhere he discussed facts.

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4. Wittgenstein’s transformation Wittgensteindid nottake long to assimilate Frege’s insight, process which McGuinness describes thus: At the time [Wittgenstein] thought theremark[of Frege on propositions andcomplexes]silly, butlater he came to see thepoint of it. It wasinfactanattack on thewhole notion of explaining the meaning of propositions by saying thatthere were complexes corresponding to them. (McGuinness1988: 164) However,between Frege andWittgenstein significant differences remained.Above all, Fregecontinued to consignfacts to the realm of sense (thought). Wittgenstein, on theother hand,claimed that whereasaproposition’s sense is the possible fact we grasp whenwe understand it (Wittgenstein1914: 112),and which can be true or false, its meaning,bycontrast,“is the[real]factwhichactually corresponds to it”(ibid.: 94).Inaword, Wittgenstein persisted in being arealist in logic. In this respect, at least, he remained true to Russelland to theJoint Program. Wittgenstein’s taking up Frege’s pointwas followedbyaseries of discoveries Wittgensteinmadeinthe next twentymonths.

4.1 Truth-making The upshot of theanalyses describedinthe preceding section is thatFrege urged Wittgensteintoconceive truth as a correspondence of propositions to singular objects of theexternal world such as facts.Facts, for their part, eitherexist or are merely possible. This meansthat every correctly constructed proposition, i.e. everyproposition with sense,either does or does not correspond to afactinthe real world,which is itsmeaning.14 This,bythe way, was apositionthatRussell opposed in the period of 1907–12.Ifweaccept it, Russell objected,wemust also accept theexistenceofcounterfeit objects,such as “Charles I’s death in hisbed”.This conceptioncontradictedRussell’s“robust sense of ” andhesharply repudiated it. He concluded that

14 “The Bedeutung of aproposition is the factthat corresponds to it” (Wittgenstein 1914: 112).

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“no judgment consistsinarelationtoasingleobject” (Russell 1910a: 120). Instead, Russell embraced theview that both the judgment and the proposition arerelations between the judging subject andthe different particular objectsofthe judgment or proposition, with which thesubject forms acomplex. This was his famous multiple relationtheoryofjudgmentwealreadyspoke about in section 2.3.15 By contrast, in 1913 Wittgensteinhad come to advocate the view that propositions correspond to those facts which are the meanings of theproposition. In this way he introducedanimportant refinement to the conventionalcorrespondencetheoryoftruth,the theoryRussell defendedafter1907.Wittgensteinnow heldthat world makes some of the possible worlds of the sentences we use true, or “real”.Thiswas nothingless than the theoryoftruth-making, whichWittgensteinlaunched in “Notes on Logic” (Wittgenstein 1913: 95). He would later speak of truth-making in the Tractatus (5.101). Russell embraced the theory of truth-making only in “The Philosophy of Logical ” (Russell 1918a: 182ff.). Significantly, this newly adopted theoryoftruth was consistent with the truth table device that Wittgensteininitially sketched in his jottings on logic of November1912, albeitwithsomemodify- cations. He now conceivedofthe truth table as schematizing possible meanings or grounds – not just the truth-possibilities – of propositions in thesense of facts thatmake propositions true or false. Incidentally,Wittgenstein’stransitionfromtruth-possibilitiesto truth-groundsexplains afact to which McGuinness first called attention. After November 1912,Wittgenstein did notdiscuss the truth tabledevice. Neither in the “NotesonLogic” nor in the

15 Russell, not always being careful about the terminology he employed, sometimes, for example, in The Problems of Philosophy,also defined truth as “some formofcorrespondence between beliefand fact” (Russell 1912a: 190).

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Notebooks 1914–1916 is there anytraceofit. It does subsequently showup, however, in the Tractatus (4.31, 4.442,and 5.101).16 What likely explains Wittgenstein’s silence on thetruth table device is that afterthe changeinhis outlook followinghis encounter with Frege in December1912, he began thinkingabout how this innovation might serve roles quite different fromthose it had played duringhis collaborationwith Russell. Indeed,as reintroduced in the Tractatus the truthtabledevice servesanew function.While in 1912 it was apurely symbolicfigurethathelpsto grasp the truth-dependence of thepropositions, in the Tractatus (5.101) it referredtothe real world. Thus if initially the truth table schematically identified only truth-possibilities, by the timeofthe Tractatus it identifiedtruth-grounds,ortruth-makers.

4.2 Criticismofthe multiple relation theory of judgment In May and June1913, when Russellshowed Wittgenstein the first partsofTheoryofKnowledge,Wittgensteinhad theopportunityto criticizeRussell’s multiple relation theoryofjudgment directly.In light of the analysis in the preceding sections,itisreasonable to conclude that thegist of Wittgenstein’s criticism was addressed againsttakingthe ontologyofcomplexesasfundamental in logic. Indeed, Wittgenstein was in effect to argue thatRussell’s theory wasbuilt on the ontology of complexes, according to which,for example, “‘C’s belief that A hates B’isacomplex in which belief combines A and B and C and hatredinto onewhole”(Russell 1911:169). In fact, in “The Philosophy of LogicalAtomism” (1918)Russell himself suggested an interpretation in thisdirection. He statedthat whatWittgenstein showed him in 1913 was that we cannot make a geometricallyarticulated mapofabeliefsince we cannotpresent a belief in Euclidean space.Thisisthe casebecause in propositions suchas“Othellobelievesthat Desdemona lovesCassio” the subordinateverb(“loves”)doesnot function as averbwhen the

16 Brian McGuinness commented on this factinthisway: “These jottings [on logic] are a valuable reminder of how little we knowabout the genesis of the Tractatus and how misleading thefragmentary preliminary workwehave can be”(McGuinness 1988:162).

97 NikolayMilkov BY-NC-SA judgment happens to be false, as in this example. 17 Russell concluded that “youcannot getinspace anyoccurrencewhichis logicallyofthe same formasbelief” (Russell 1918a: 225). He was explicitthat “the discovery of this fact is duetoMr. Wittgenstein” (ibid.: 226). In asense, Russell was right – we cannotmake amap of a belief. Still, this interpretationshowsthat he failedtograspthe full force of Wittgenstein’s argument with allits consequences.Itisnot just of beliefs that we cannot make maps; we cannot make maps of any fact whatsoever. This is because maps arearticulated in space and so cannotcommunicate facts. Facts can be “modelled”, not mapped (cf.section4.3 below).Wecan map only complexes. More specifically, Wittgenstein showed Russell’s multiple relationtheory of judgment to be invalid in light of acorollary of his own (Wittgenstein’s)position, afterDecember1912, on the status of complexes. What we judge, asserted Wittgenstein,are propositions’senseswhichare singular objects; we do notjudge complexes. OneofWittgenstein’s elliptical pronouncementsonthe subject supports this readingofhis new doctrine: “When we sayA judgesthat etc., thenwehavetomention a whole proposition whichA judges” (Wittgenstein 1913:94, my italics). It does notsuffice merely to enumerate theelements of thejudgment, as themultiple relationtheory prescribes. Wittgensteinconcluded that “theproper theory of judgmentmust make it impossible to judgenonsense [suchas] ‘this table penholders thebooks’” (ibid.: 95). The latter phrase is not aproposition with sense but aheap (concatenation) of words. We hold thatthis interpretationofWittgenstein’s critique of Russell’s multiplerelationtheoryofjudgment is much simplerand has greater explanatory powerthanthe competing ones. For example, it comfortablyexplainsthe “directionalproblem” of Russell’s theory thatGriffin (1985) sees as the main pointattacked by Wittgenstein. According to Griffin, Russell’s theoryofjudgment

17 In fact, here Russell harksback to his argument against the correspondencetheory of truth from 1910 which, he claimed, is incorrectsince when theproposition happens to be false, it must correspondtocases of nonsense such as “the present King of France” (Russell 1910a).

98 Nordic Wittgenstein Review 2(2013) lacks the resources to distinguishbetween “Cassio loves Desdemona” and “Desdemonaloves Cassio”;italsofails to exclude cases where instead by averb, the elements of arelation are connected by asubstantive, as it is in the aforementioned example “This tablepenholders thebooks”.Ifweaccept that judgments signify facts, however, then all these difficulties instantly disappear; all constituents of thejudgment come in their proper places andare unambiguously directed. Thesame is true of the interpretationpresentedinHanks (2007). According to it, in May1913 Wittgensteindrew to Russell’s attentionthat thecontent of judgment is something that must be true or false.This something, we would like to add, is nothing but the sense of the judgmentthat afactmakes true, or false.

4.3 ThePicture Theory and theDoctrine of Showing: criticism of thetheory of types In aletter to Russelldated December26, 1912, Wittgenstein dropped acrypticremarkabouthis encounter with Frege: Ihad along discussion with Frege aboutour TheoryofSymbolismof which, Ithink,heroughly understoodthe general outline. He saidhe wouldthink thematterover. Thecomplex-problem is now clearer to me and Ihopevery much that Imay solveit. (Wittgenstein 1995: 21) Having considered the complex-problemin§§4.1–2, we turn here to the theory of symbolism that Russelland Wittgenstein worked on together in 1912, and to itstransformationafter December 1912. Recallthat Frege’s main idea was to advance aconcept-script thatwouldserve as a“perspicuousrepresentation ofthe formsof thought” (Frege1881: 89). This wastobesomethinglikeavisual instrument (similar to amicroscope) with the help of which we would immediately grasp the logic of propositions. Hence,itcomes as no surprise that what Wittgenstein primarily wished to discuss with him in December 1912was thetheory of symbolism – all the more so giventhatWittgenstein felt he was making significant progressinthis direction (cf. section2.2). During the courseof discussion, WittgensteinlikelyshowedFrege,among other things,

99 NikolayMilkov BY-NC-SA his newly invented truth tabledevice, because till then it hadbeen his major achievement in thisareaofresearch. As we observed,byearly 1913 Wittgensteinunderstood facts andpropositions eachassingularobjects. By thesummerof1913, he realized that “the meaning of aproposition is the fact which actually corresponds to it”(Wittgenstein 1913:94). Working out these insightsWittgensteinhad in effect adumbratedthe picture theory of language,according to which propositionsare facts which picture facts.18 On this view, sentences arepictures, or facts, that do not map factsbut rather model them. Wittgenstein’s “Noteson Logic” articulates this idea as follows:“in ‘aRb’ it is not the complex that symbolizesbut the fact thatthe symbol‘a’ stands in a certain relationtothe symbol ‘b’. […] Thus factsare symbolizedby facts” (Wittgenstein1913:96, cf. TLP3.1432). Armedwith this conception, in December1913Wittgenstein visited Frege again, and thistime“he wiped the floorwithFrege” (Goodstein1972: 272). Apparently, what most impressedFrege, so thathedid not challenge theargument straightaway, was Witt- genstein’s newlydevised picturetheory, which introduced the conception that factssymbolizefacts. Thestory, however,doesnot end here.Wittgenstein’ssecond discussion with Frege evidentlymade him confident that he should continuedown thepath he had taken on hisown, completely independent of Russell. IndeedbyApril 1914, he concluded that his picture theory made the theoryoftypes impossible. Wittgenstein foundthat we cannot say what atypeissince the character of the type is shown by thesigns themselves: [The Theory of Types] tries to saysomethingabout thetypes, when you canonlytalkabout the symbols. But what yousay about the symbols is notthatthis symbolhas that type,whichwould be nonsense for [the]same reason: but yousimply say: This is thesymbol, to prevent misunderstanding.E.g., in ‘aRb’,‘R’ is not asymbol, but that ‘R’isbetween one name andanother symbolises. Here we have not

18 On this point we agree with Thomas Ricketts (2002: 227) that the picture theory (Rickettscalled it “”) was introducedbyWittgenstein in 1913.Toremindthe reader, the picturetheory of language wasexplicitly formulated in September 1914 (Wittgenstein 1979: 7).

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said:thissymbolisnot of thistypebut of that,but only: This symbolises andnot that. (Wittgenstein1914:109) Wittgensteinformulated theDoctrine of Showing this way: “logicalso-called propositions shew [the] logical properties of language” (Ibid.:108). This discovery had atransformative impact uponWittgenstein’sphilosophy,changing it in ways thatRussell nevercompletely understood.19

5. Theeffects of the Frege-Wittgenstein critiqueonRussell Russell had great hopes withthe Joint Project. “[He] aspired to nothing less than arevolutioninthe aims and methods of philosophy, atransformation of thewhole discipline” (Monk 1996: 282). Hisfeeling was that there is “a whole newscience to be created” (# 628, 09.11.1912). The reintroduction of newintensionalitiesinlogic had dramatic effectsupon his philosophicaldevelopment. In short,itpersuaded Russell that theproject for anew, “scientific” philosophy that he also called “analyticphilosophy” cannotberealizedinthe form in which he initiallyenvisaged it. Here is the story toldinRussell’s words: [Wittgenstein’scriticism] wasanevent of first-rate importance in my life, andaffected everything Ihavedone since. Isaw he wasright,and Isaw that Icouldnot hope ever againtodofundamental work in philosophy.Myimpulse wasshattered,like awave dashed to pieces against abreakwater. Wittgensteinpersuaded me that what wanted doinginlogicwas toodifficult forme. So therewas no really vital satisfaction of my philosophical impulse in thatwork, andphilosophy lost its hold on me.That wasdue to Wittgenstein morethan to the war.Whatthe war hasdoneistogivemeanew andlessdifficult ambition, whichseemstobequite as good as theold one.20 (Russell 1968:57) Some interpreters try to downplay this avowal. For Gregory Landini, forexample,theseremarks are to be read against the background of “Russell’s personal andemotional turmoil over

19 For the effects of Wittgenstein’s discussionwithFregeonFrege’sphilosophysee Milkov (1999). 20 Letter to Lady Ottoline Morrell #1,123 from 4.3.1916.

101 NikolayMilkov BY-NC-SA failed relationships with Ottoline[Morrell]and his wife Alys” (Landini2003/4: 104).Incontrast,wetake it at itsface-. Russell’shopes withthe Joint Program were connectedwith the introductionofanew, “scientific” method in philosophy. In short, the idea was to treat problemsofthe external worldand of other mindswithlogical means, and more precisely,withthe help of ideas of Russell’s analyticlogic of relations that is based on the ontology of simple and complex.Mostgenerally, this was a program foraradical (reductiveand constructive) analysis of any subject-matter in philosophy. 21 This explains Russell’s profound disappointment when he was confronted with thefactthat this program could not be carriedout in its full forminall areas. To be more exact,after Wittgenstein’s criticism,Russellsaw that “analysis is not enough”, and this for the secondtime. In our interpretation, however, whatreally happenedwas not that the impossibilityofradically wasdemon- strated. Rather, Russellrealizedthat his programfor exact philosophy has alternativesand is notassimple as he initially believed.22

References Anellis,I., 2004.“The Genesis of theTruth TableDevice”. Russell: theJournal of Studies 24: 55–70. Bell,D., 1999.“TheRevolution of Moore andRussell: AVery British Coup?” In: A. O’Hear,ed., 1999. German Philosophy Since Kant. Cambridge: Cambridge University Press, pp.193–208.

21 And not only in it; Russell often made statements which showthathebelieved to follow themethod of analysis also whendiscussing problems of public or personal interest. 22Afirstversion of thispaper was presented at theKirchberg (Austria) International Wittgenstein Symposiumin2002,asecond at the Lunch Time Colloquium at the Center for Philosophy of Science, University of Pittsburgh, andatthe Bertrand Russell Society Session at the Central Division Meeting of theAPA in Chicago in 2006. In 2009 Iread it at aFinnish–German Workshop in Paderborn. Thefinal version of the paper was prepared at McMaster University, Ontario, where Ialso had the opportunity to check some of thedocuments in The Bertrand Russell Archives. In March 2012 Ipresented it at McMaster, as well as at SUNY at Buffalo. Kenneth Blackwell and NicholasGriffinwere mosthelpfulbyimproving the whole format of the paper.

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Bradley, F. H., 1883. The PrinciplesofLogic,2vols.Oxford: OxfordUniversity Press. Bradley, F. H., 1914. EssaysinTruthand Reality.Oxford: ClarendonPress. Bradley, F. H., 1999. Selected Correspondence, January1905–June1924,ed. C. A. Keene. Bristol:Thoemmes Press. Clark,R.W., 1975. TheLife of BertrandRussell. London: Jonathan Cape and Weidenfeld &Nicolson. Dummett, M.,1981. TheInterpretationofFrege’s Philosophy.London: Duckworth. Frege,G., 1881. “Onthe ScientificJustification of aConceptualNotation”. In: G. Frege, Conceptual Notation and RelatedArticles,trans.T.W. Bynum.Oxford:Clarendon Press, 1972, pp.83–9. Frege, G., 1918/19. “Thoughts”. In: G. Frege, Collected Papers.Oxford: Blackwell,1984, pp.351–72. Goodstein, R. L. 1972. “Wittgenstein’sPhilosophy of Mathematics”. In: A. Ambroseand M. Lazerowitz, eds. 1972. : .London: Allen &Unwin, pp. 271–86. Griffin, N., 1985. “Russell’s Multiple Relation Theory of Judgment”. PhilosophicalStudies 47,pp. 213–47. Griffin, N., 1996.“Hager, P. J., Continuity andChange in the Development of Russell’s Philosophy”. AustralasianJournalofPhilosophy 74,pp. 221–2. Hager, P., 1987.“Russell’s and Zeno’s ArrowParadox”. Russell: theJournal of BertrandRussell Studies 7, pp.3–10. Hanks, P., 2007.“HowWittgenstein Defeated Russell’s MultipleRelation Theory of Judgment”. Synthese 154, pp.121–46. Hylton,P., 2005. Propositions, Functions,and Analysis.Oxford: Clarendon Press. Landini,G., 2003/4.“Wittgenstein’sTractarianApprenticeship”. Russell: the Journal of BertrandRussell Studies 23,pp. 101–30. Landini,G., 2007. Wittgenstein’s Apprenticeship with Russell.Cambridge: Cambridge University Press. McGuinness, B. F., 1988. Wittgenstein,ALife,vol.1,YoungLudwig,1889– 1921. London:PenguinBooks. Milkov, N., 1999. “The Latest Frege”. Prima Philosophia 12, pp.41–8. Milkov,N., 2003. AHundredYears of EnglishPhilosophy,Dordrecht:Kluwer (Philosophical Studies Series, vol. 94). Milkov, N., 2007. “Russell, Wittgenstein,and the Project for‘Analytic Philosophy’”. Contributions of the Austrian Ludwig Wittgenstein Society 15, pp. 153–5. Milkov, N., 2012. “The Construction of the Logical World:Frege and Wittgenstein on Fixing BoundariesofHuman Thought”.In: E. Nemeth et al., eds. 2012. Crossing Borders: Thinking (Across) Boundaries. Vienna: UniversityofVienna, pp. 151–61. Monk, R.,1996. BertrandRussell: The Spirit of Solitude.London: Jonathan Cape.

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Moore,G.E.1899. “The NatureofJudgment”. In: Moore 1986, pp. 59–80. Moore,G.E.1900.“Necessity”. In:Moore 1986,pp. 81–100. Moore,G.E.1986. TheEarly Essays,ed. T. Regan, 1986. Philadelphia: TempleUniversityPress. Pears,D., 1979.“The Relation betweenWittgenstein’s PictureTheory of Propositions andRussell’s Theories of Judgement”. In: C. G. Luckhardt,ed. 1979. Wittgenstein:Sources and Perspectives.Ithaca(NY): Cornell University Press, pp. 190–212. Pinsent, D., 1990. APortrait of Wittgenstein as aYoung Man,ed. G. H. von Wright. Oxford:Blackwell. Ricketts, Thomas.2002. “Wittgensteinagainst Frege andRussell”. In: E. Reck, ed., 2002. From Frege to Wittgenstein: PerspectivesonEarly Analytic Philosophy.Oxford: University Press, pp.227–51. Russell,B., 1899/1900. “The Principles of Mathematics.Draft of 1988–1900”.In: TheCollectedPapers of BertrandRussell,vol.3,ed. by G. H. Moore. London: Routledge, 1993, pp.15–180. Russell, B.,1903. ThePrinciplesofMathematics.2nd ed. London:Allen& Unwin,1937. Russell, B.,1905. “On Fundamentals”. In:B.Russell, FoundationsofLogic. 1903–05,A.Urquhart,ed., TheCollected PapersofBertrand Russell,vol. 4. London:Routledge, 1994, pp.359–413. Russell,B., 1910. “Onthe NatureofTruthand Falsehood”. In:Russell 1992, pp. 115–24. Russell,B., 1911. “Onthe Relations of Universals andParticulars”. In: Russell 1992,pp. 162–82. Russell, B.,1912a. TheProblems of Philosophy.London: Thornton Butterworth. Russell, B.,1912b. “OnMatter”. In:Russell 1992, pp.77–95. Russell, B.,1912c. “WhatisLogic?” In:Russell 1992,pp.54–56. Russell, B.,1912d. “On the Notion of Cause”. In:Russell 1918b,pp.180– 208. Russell,B., 1912/13. “Nine Short Manuscripts on Matter”. In:Russell 1992, pp. 96–111. Russell, B.,1914a. Our Knowledge of the External World.London: Allen & Unwin,1993. Russell, B.,1914b. “The RelationofSense-Data to Physics”. In: Russell 1918b, pp.145–79. Russell, B.,1918a. “The Philosophy of LogicalAtomism”. In: B. Russell, Logicand Knowledge,ed. R. C. Marsh. London: Allen&Unwin, 1956, pp. 175–281. Russell, B.,1918b. Mysticism andLogic.London: Allen&Unwin. Russell,B., 1968. TheAutobiography of BertrandRussell,3vol., vol. 2. London: Allen &Unwin.

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Russell, B.,1992. Logical and Philosophical Papers, 1909–13. J. G. Slater, ed.,The CollectedPapers of Bertrand Russell,vol.6.London: Routledge. Russell,B.and Whitehead, A. N.,1910. Principia Mathematica,3vols.,2nd ed., 1st vol. Cambridge: Cambridge University Press,1925. Sheffer,H.M., 1913. “A of Five Independent Postulatesfor Boolean Algebras,with ApplicationtoLogical Constants”, Transactions of the American Mathematical Society 14,pp. 481–8. Simons, P., 1985. “The Old ProblemofComplexand Fact”. Teoria 5, pp. 205–25. Stevens,G., 2005. The Russellian Origins of AnalyticPhilosophy: BertrandRussell and theUnity of Proposition.London: Routledge. Wittgenstein, L., 1913. “Notes on Logic”. In:Wittgenstein 1979,pp. 93–107. Wittgenstein, L., 1914.“NotesDictatedtoG.E.Moore in Norway”. In: Wittgenstein 1979, pp.108–119. Wittgenstein,L., 1922. Tractatus Logico-Philosophicus. Trans. C.K. Ogdenand F.P. Ramsey.London:KeganPaul, Trench, Trubner. Wittgenstein,L., 1964. PhilosophicalRemarks.Ed. R. Rhees, trans.R. Hargreaves and R. White.Oxford: Blackwell. Wittgenstein,L., 1974. Philosophical Grammar.Ed. R. Rhees,trans.A.Kenny. Oxford: Blackwell. Wittgenstein, L., 1976. Wittgenstein’s Lecturesonthe Foundations of Mathematics. Ed. C. Diamond. Hassocks:Harvester Press. Wittgenstein, L., 1979. Notebooks 1914–1916.2nd ed., ed.G.H.von Wright andG.E.M.Anscombe, trans.G.E.M.Anscombe. Oxford:Blackwell. Wittgenstein, L., 1995. CambridgeLetters: Correspondence with Russell, Moore, Ramsey andSraffa. Ed.B.F.McGuinnessand G. H. vonWright. Oxford: Blackwell.

Biographical note NikolayMilkovisAssociate Professor(Privatdozent)atthe University of Paderborn, Germany. Hispublicationsinclude thebooks KaleidoscopicMind: an Essay in Post-WittgensteinianPhilosophy (1992) and A Hundred Years of EnglishPhilosophy (2003).Milkovhas authored papers in SouthwestPhilosophyReview,the BritishJournal for the History of Philosophy, Studies in History and PhilosophyofScience, Essays in Philosophy, Axiomathes,the Internet Encyclopaedia of Philosophy,and Grazer Philosophical Studies.

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