The Joint Philosophical Program of Russell and Wittgenstein and Its Demise

Abstract Between April and November 1912, Bertrand Russell and Ludwig Wittgenstein were engaged in a joint philosophical program. Wittgenstein’s meeting with Gottlob Frege in December 1912 led, however, to its dissolution - the joint program was abandoned. This paper outlines the key points of that program, identifying what Russell and Wittgenstein each contributed to it. It determines precisely those features of their collaborative work that Frege criticized. Finally, building upon the evidence developed in the first two sections, it recasts, along previously undeveloped lines, Wittgenstein’s logical- philosophical discoveries in the two years following his encounter with Frege in 1912. The paper concludes with an overview of the dramatic consequences the Frege-Wittgenstein critique had for Russell’s philosophical development.


Wittgenstein-Frege-Russell 1912-13
This paper investigates the interactionb etweent he three founding fatherso fa nalyticp hilosophy -Russell, Wittgenstein andF regeduring af ormative period of theirp hilosophical development.It sheds lighto nt he joint program that Russell andW ittgenstein collaborated on from Aprilt illN ovember 1912, as well as on its collapse afterW ittgensteinv isited Fregei nJ ena in December the same year.T he key finding is that Frege's criticism of elements of thep rogram both motivated andi nformed Wittgenstein's criticism of Russell's approach to philosophy.This radical challenge culminatedi nM ay and Juneo f1 913w hen, facing Wittgenstein's criticism, Russell abandoned his book project on theory of knowledge.F rege's remarks also impelled Wittgenstein to rethink and reformulate hisown philosophical ideas.
Among otherm atters, germane to this seminal development in theh istory of early analyticp hilosophy is an issue, addressedi n section 4.2, that hasbeen actively debated in theliterature over the past thirty years: Wittgenstein's criticism of Russell's multiplerelation theory of judgment (Griffin 1985(Griffin ,H anks 2007)).Rather thanexplainingthis criticism in the usual manner, i. e., on the basis of purely logical considerations,t he move here is to disclosei ts groundi nF rege's impact on Wittgensteina tap articularh istorical moment.Theevidence adduced in this accountimplicitlydiscredits the "competitive interpretation" of the collaboration between Russell andW ittgenstein, an account that casts the purported competitioninterms of who was thebetter philosopher, Russellor Wittgenstein.N icholas Griffin andG regory Landini, for example, criticizet he allegedc laim thati nt he monthsb etween April 1912 andJ une1 913 Wittgensteinr epeatedly correctedm istakeso fh is teacherR ussell,s ot hat "if only Russellh ad been ab etter philosopher, he wouldhavebeen Wittgenstein" (Griffin 1996: 222;Landini2003/4, 2007.
By contrast with thelatterview, this essayestablishes thatwhile between April and November1912 Wittgensteinenhances Russell's philosophicald evelopment, this occurredo nlyb ecauset he young studento penedR ussell to newp erspectiveso nR ussell's own philosophy.M oreover,t he evidence makesi tc leart hat between January andJ uneo f1 913w hat Wittgensteinc onfrontedR ussell withw erem ainly changes in Wittgenstein'st hinking, which trace directly to the influence of Frege'sp hilosophicall ogic.Russell's putative "defeat"i nt he face of Wittgenstein'sc riticism in June 1913 thus merely signaled the former'sr ealization that thei dea of an exact philosophy, as he had initiallyc onceivedi t, facedv iable alternatives, andh ence that thep rospect of systematically articulating suchaphilosophyw as fraught with much more complexitythan he had anticipated.
In the spring and Fall Terms of 1912, Russell andWittgenstein collaborated intensively on what can be seen as aj oint philosophicalp rogram.This was first brought to light in 1988 by the Wittgensteinbiographer Brian McGuinness,who observedthat "the twop hilosophers were concerned witht he 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 them onths of their mutuale ngagementi nt his project, Russell andW ittgenstein often workedt ogether.It is noteworthy thatt his was the only period in his careert hat Wittgensteine ver collaborated with another philosopher.While he frequently challenged Russell'sc onceptions, Wittgensteinl imited himself to constructivec riticism, concentratingh is theoretical energieso n developing ideas that supplementedthose of Russell.
Apparently, the jointp rogram featured ad ivision of labor.While Russell concentrated on problems of epistemology, Wittgenstein focusedmainlyonproblemsoflogic.Asweshall see, however, eacho ft hem 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?",w hichh er eada tt he Moral Science Club in Cambridge on November 22.I ni t "philosophy was defined as all those primitive propositions which are assumed as true withoutaproofb yt he various sciences" (McGuinness1988: 144).
Things changedradically afterWittgensteintraveled to Jena and metw ith Fregei nD ecember1 912.As we shall see, Frege convinced him thath is joint project with Russellw as basedo n flawed assumptions and hence was fundamentallymisconceived.
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).T he first positive resulto ft his total breakw ithR ussell was Wittgenstein's "Notes on Logic", whichh ew rote in August andS eptember of that year.I np ractical terms, thee strangement between the two

2.1The impact of Wittgenstein on Russell's epistemology
Elements of thej oint program appear in Russell's paper" On the Notion of Cause" (Russell 1912c), whichh er eada tameetingo f the Aristotelian Society in earlyN ovember of 1912.As merely a popularversion of Russell's highlydeveloped views on the relation betweenp hilosophya nd physics,h owever,i th ardlyc ountsa sa significantr esource for understanding the Program.Be thata si t may, Russell's criticism of then otiono fc ausalityi nt he paper clearly parallels Wittgenstein's approach to the topic in Tractatus 5.136-1: onlyl ogic is necessary;c ausalityc an convey neither regularitynor principle.
The most important document attesting to Russell and Wittgenstein's bonaf ide collaborationi naj oint programi s" On Matter" ( Russell 1912b),ap aper thatR ussell wrotei nM ay 1912 and deliveredt hat same montha tameeting of the Philosophical Societyo fU niversityC ollege,C ardiff.Russellr evised thee ssayi n October 1912 and read it near thee nd of thatm onthb efore the MoralScience Club at Cambridge. 2ussell'sdeclaredaim in "On Matter"istoshow (i) that all thea rguments hitherto alleged by philosophers against matterare fallacious;(ii)thatall thearguments hithertoallegedinfavor of mattera re fallacious; (iii) that, although therem ay perhapsb e reason to supposet hatt here is matter,y et we canh ave no meanso f finding out anything whatever as to its intrinsicnature.(Russell 1912b: 80) The first thingt hats trikest he readero ft hese lines is their close affinity with the highly truncated style of Wittgenstein's writings from the period 1912-16.out by Russellhimself in aremarkfromMay 2, 1912:Wittgenstein, he confessed, "is the onlyman Ihavee vermet withareal bias for philosophicalscepticism; he is glad when it is proved that something can't be known" (McGuinness 1988:1 06).Thus it is no surprise that, when Russelld elivered the revisedv ersion of "On Matter" in October, his feeling was that" no one except Wittgenstein understood it at all" (#608).I ti sw orth notingt hat alongw ith Wittgenstein, G. E. Moorew as also in the audience, bute venh e failed to makes ense of Russell's newi deas.On the other hand, Wittgenstein thought thatRussell's paper "OnMatter" wasthe best thingh eh ad done (#460) -note xcluding TheP rinciples of Mathematics and Principia Mathematica.
The results of Russell'sn ewly adopted skepticals tancec an 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 persewe perceive sense-data; the lattera re qualities andr elations, includingqualitiesa nd relations of sense-data.Nevertheless,wecan know physical objects, although only by description.This is because thes ense-data with whichw ea re acquainted help us logically to infer thatthere arephysicalobjects.At that time, Russell believedt hat despite not being absolutely satisfactory,t his conception is much more consistentw ith the factso ft he external worldthan any competing philosophy of matter, especially solipsism, according to which thereare no physical objects at all.
When Russell raisedthe problem of solipsism with Wittgenstein on 23 April 1912,h owever, the latter breezily dismissed its significance as ap hilosophical challenge, declaring thats olipsism "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" (Monk1 996: 260).Indeed, we can imagineap rivate world -aw orld existingo nlyi no rder to affect ours enses -in which the laws of science arevalid.This argument impelled Russell to abandont he view thatw ec an infer matter from sense-data.Instead,h eb egan regarding mattera salogicalc onstruction on the basis of the objectso fa cquaintance (Russell 1912b: 84). 3 What underlay thisradical shift in Russell's thinking was theidea that the worldc onsistsu ltimatelyo fi ndependent atomic units (laterc alled "logical atoms") -sense-data.These primitive elementsc ould be ordered in many different,l ogicallyo rganizedn etsi nw hich sensedata interrelate with one another. 4The objects of commons ense and those of the hypotheses of science couldb es een,i nt his account,asalternative constructs of these andother units.
In thep hilosophy of science,R ussell now subscribed to the viewthat physicsmay be studied, […]asapiece of pure mathematics; thespace andm atterc oncerned in this studya re variables, [5] concerning which certain hypotheses arem ade;t hat is to say, they aren ot definite entities, but merely anything having certainproperties.(Russell 1912b: 83) This statementr eveals how fundamentally Russellr evised his philosophyd uring hisc ollaboration with Wittgenstein.He now claimed that we cana bandon thep roblem of thec ontent of the beliefs of commons ense,c ontending instead thati ts supposed content -them atter -andt he objects of common sense are logicallycongruent.
Nots urprisingly, the newd octrineh ad consequences for Russell'sw orldview.A mong other things,i tb roughtw ith it an unsettling sense that nothing in thisw orldi ss olida nd secure.
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).
Wittgenstein's jottings provedo fc onsiderable historical significance,i ncludinga st heyd ot he first sketcho fatruth table device. 7Thel atter schematized in at abular form thet ruthpossibilities of the combinations (of the logicalc onnections, or operations)o ft wo propositions.T hisi nnovationh ad important consequences, most significantlyi nd emonstrating that logical operations can be represented in ar adically perspicuousw ay by means of one symbol.Fore xample,' pvq 'c an be presented as follows: 6 Cf.n.8. 7It is nottobeconfused with the propositionallogic of truths introducedbyFrege in his Conceptual Script.T he difference between them is thatw hereas the latter is "a logical analysis of the truth-values of ap roposition,t he truth-table device is the presentationo f thisanalysis in tabular or matrix form" (Anellis 2004:57  In otherw ords, this innovation helped "to explain thes elfevidence of logicalp ropositions" (Wittgenstein1 976:1 77).As we are going to seeinsection4.3,below, the truth table device proved to be afirststep toward the DoctrineofShowing thatWittgenstein introduced ayearlater.
Besidest he truth table device,i nN ovember 1912 8 Wittgenstein also originated the notion that thereisonly one logical constant.To be more specific, he determinedt hat we can expresst ruthoperations by employing as ingle signf or the logical connective.The idea was that logical constants can be reduced to as ingle logicaloperation, ' ) ( ' (cf. McGuinness1988: 161).
Most significantly,Wittgenstein's logical innovations at thistime were closely tied to the ontology Russelladvanced in "OnMatter", which Wittgensteint hus evidentlye mbraced.As remarkeda bove, in section2 .1,Russell's ontology assumed thatt he world consists of complex units, sense-data, which physicsr epresents as variables and which we can order, or compose, in manyd ifferentl ogically organizedn ets: either hypotheseso fs cience, or "things" of common sense.We could call this Russell'sC ompositionality Thesis.Apparently, Russell'sm inimalisto ntology, withoutp hysical objectsa nd withouto bjectso fc ommons ense,w ent hand in hand with Wittgenstein'sn ovel minimalist logic, with its singlel ogical constant. 9Indeed,b oth maintained ap arsimonious form of compositionality: Russell in ontology,Wittgenstein in logic.
Corroborating this interconnectioni st he factt hat Russell initially employedt he sign ' ) ( 't or efer to the interweaving of the elements of ontological complexes with which we area cquainted (Russell 1905: 169,cf.section2.3below).Wittgenstein, on his side, used it to symbolize the only logicalc onstant and, so, the interweaving of thelogical atoms ("atomic propositions").
Wittgenstein himself appears to have been cognizanto ft he interconnection betweenR ussell's constructivist ontology and the assumption that there is only one logical constant, which he eventuallye xpressedt his way: "Wherever there is compositeness […] wea lreadyh avea ll thel ogical constants",a nd thism eans 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 addressd irectly the relatedness between logic and ontology in theJ oint Program.T his he did in thed aysi mmediately after 13 October 1912, when he wrote "What is Logic?" (cf.section 2, above), apiece merely two pagesinlength.Itspremise is that "logic is thes tudyo ft he forms of complexes" (Russell 1912b: 55). 10  Logic, it declares, does not deal with judgments,s omethingi t 9 We cans ee thisf act as an example of how Russell's "ideal of eliminativistic reconstruction" (Landini 2003/4: 118) -in this case,the elimination of physicalobjectswas also embracedb yW ittgenstein in thef orm of eliminationo fl ogicalo bjects.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).
What evidentlyi nspired Russell's paperw erei deas that Wittgensteinh ad formulated even prior to their collaboration.In November 1911, Wittgensteint ooka sh is own philosophical point of departuret he position from which Moorea nd Russellh imself began in 1899:11 "there is nothingi nt he world except asserted propositions whicha r ec omplexes of concepts" ( McGuinness 1988: 89).In the Springa nd Fall Terms of 1912,R ussell readily embracedW ittgenstein's (and Russell'so ld) position, andh eh ad compelling reasons ford oing so:i th armonizedw ith atendency in Russell to restoretohis philosophythe notion of complexes which he hadc hampionedb etween1 898a nd 1900, but which he had more or less repudiated between1 900 and1 905u ndert he 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.) They ear 1905, however, saw Russell adopting (arguably, under Alexius Meinong'si nfluence)o ncea gain,a no ntologyo f complexes.After assigning "knowledgebyacquaintance" aprimary rolei ne pistemology in "On Denoting", Russell contended that complexesa re among the things withw hichw ea re acquainted (Milkov2003: 50).This move partly restoredtoh is philosophythe realistic mereology( i.e., part/whole "logic")o fc omplex and simplest hat was an ingredient in hisp hilosophyp rior to August 1900.
This tendency persisted.Shortly after he formulated the theory of descriptions, Russell eliminated classesfrom his logic: classes are "incomplete symbols".T here areo nlyp ropositions and propositionalf unctions.Two yearsl ater, in 1907,R ussell discovered that propositions produce paradoxes of theiro wn.In consequence, he came to maintain thatp ropositions too are incompletes ymbols.To be more exact, theyw eree liminated with theh elp of them ultiple relation theory of judgment which claims that propositions only receive meaning (and unity) through the judging mind (Stevens2 005: 79).Truth-bearers arej udgments,n ot propositions.
The signalr esult of this development was thatt he ontology of complexes came to play an importantr ole in Principia Mathematica, somethingc learlya ttested to in thef ollowings tatement from that work: … the universe consistso fo bjects having various qualitiesa nd standing in various relations.Some of the objects which occur in the universe arec omplex.When an objecti sc omplex, it consistso f interrelated parts.(Russell &Whitehead 1910:43) This ontology is clearly closet ot hat of Russelli n1 898-1900.B e this as it may, till 1912, Russell'sr ealistic mereology wasn om ore than af ocal tendency in hiso ntology.W ith "What is Logic?", however,Russellrecast hismereology as aconsistent program.
Russell got his "first lessoni nl ogic" in 1900.Up to that time, his logic followed the relational theoryo fj udgmente laborated in Moore(1899).According to thelatter, judgments and propositions arec omposed of complexesc onsistingo fc oncepts andr elations betweent hem.This was ap rogram for part/whole "logic",o r mereology,i nw hich logical implicationi sp ossible both between terms andb etween propositions.R ussell's doctrine wasa lso in conformitywith thelogic of classes, as wellaswith Boole's algebra of thought.However, at the International Philosophy Congress in Paris,i nA ugust 1900,R ussell learned from Peano (something the latter learnedf rom Frege) thatb esides the relations between parts and whole there is also ar elationo fi mplicationw hichh olds between propositions,n ot between individuals,a nd that this second relationismore fundamental. 12 Otheri ntensionalities( unanalyzed units) which Russell introduced intoh is logic after August1 900 were the conceptso f " proposition" and "denoting phrase".I tw as in accordancew ith Frege's context principle that Russell nows ubscribedt ot he view thatweemployaproposition's terms withinthe frameofthe entire proposition, not as autonomous, discrete units. 13As fort he intensionalityo ft he denoting phrase,R ussellm aintained that even when singular,adenoting phrase refers to ac ollection, whichm ay 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 notw ant to understate the importance of analysisa nd of relations,i ncorporatingi ntensionalities in hisl ogic in 1903 led himt or ecognizet wo kindso fw holes: aggregatesa nd units.An aggregate is definiteo nlyw hen alli ts constituents are known.Units, by contrast,havenosuchrequirement; what's more, we can know au nit when we knowm erely ap arto fi t.The paradigm of the unit in Russell's logic is the proposition ( Russell 1903: §135;Stevens2005).
Before exploring this, it shouldb es aid that the only place where Wittgensteine xplicitly acknowledges what he took from his meeting with Frege in December 1912i si nafragment published both in his PhilosophicalRemarks and Philosophical Grammar.H ence it is that fragment that servesh erea st he starting pointf or the analysis of the Joint Program'sd emise.Fregec riticized Russell's andWittgenstein's move to identifycomplexeswithfacts,pointing out that a"complexisnot likeafact.For Ican, for example,say of ac omplext hat it movesf rom onep lace to another,b ut not of a fact" ( Wittgenstein 1964:3 01, Wittgenstein1 974: 199).F rege also questioned Wittgensteinabout whetherifanobjectwereapartofa fact abouti t, the fact wouldb el arger than theo bject.Frege obviously held that whereas "a complex is as patialo bject, composed of spatialobjects" (ibid.: 302; 200), afactisnot.
At first sight it is surprisingt hatF rege spokea bout facts at all.Usually,h er estrictedf acts to the realmo fs ense( or thought), so they didnot play asignificant role in hisontology (Dummett1981: 177).It seems that Freges tarted to thinka bout factsm ore intensively only after hism eeting withW ittgenstein in December 1912.What especially struck Fregea sm istaken was the idea that when we understand propositionsw eg rasps patial complexes.He argued, instead,t hati ns uchc ases, we understand one thing that is not spatial, namely the sense of the proposition that we grasp, which can be eithert rueo rf alse.I tr eally differs from thes patial complex,w hich is segmented.We finda ne cho of these considerations in Frege's paper "Thoughts"( 1918/19)w here he defined "fact" as "at hought that is true" (Frege 1918/19:3 68).It deserves noticethatthis was the only placeinFrege's corpuswhere he discussed facts.However,b etween Frege andW ittgenstein significant differences remained.Above all, Fregecontinued to consignfacts to the realm of sense (thought).Wittgenstein, on theo ther hand,c laimed that whereasaproposition's sense is the possible fact we grasp whenwe understand it (Wittgenstein1 914: 112),a nd which can be true or false, its meaning,b yc o ntrast," is the[ real]f actw hicha ctually corresponds to it"( ibid.: 94).I naword, Wittgenstein persisted in being ar ealist in logic.In this respect, at least, he remained true to Russelland to theJoint Program.

Truth-making
The upshot of thea nalyses describedi nt he preceding section is thatF rege urged Wittgensteint oc onceive truth as a correspondence of propositions to singular objects of thee xternal world such as facts.F acts, for their part, eithere xist or are merely possible.This meanst hat every correctly constructed proposition, i.e. everyp roposition with sense,e ither does or does not correspond to afactinthe real world,which is itsmeaning. 14 This,b yt he way, was ap ositiont hatR ussell opposed in the period of 1907-12.I fw ea ccept it, Russell objected,w em ust also accept thee xistenceo fc ounterfeit objects,s uch as "Charles I's death in hisb ed".T h is conceptionc ontradictedR ussell's" robust sense of reality" andh es harply repudiated it.He concluded that 14 "The Bedeutung of ap roposition is the factt hat corresponds to it" (Wittgenstein 1914: 112).

Bereitgestellt von | provisional account
Unangemeldet | 37.201.158.136Heruntergeladen am | 20.08.13 09:08 "no judgment consistsi nar elationt oas ingleo bject" (Russell 1910a: 120).Instead, Russell embraced thev iew that both the judgment and the proposition arer elations between the judging subject andt he different particular objectso ft he judgment or proposition, with which thes ubject forms acomplex.This was his famous multiple relationt heoryo fj udgmentw ea lreadys poke about in section 2.3. 15y contrast, in 1913 Wittgensteinh ad come to advocate the view that propositions correspond to those facts which are the meanings of theproposition.
In this way he introduceda ni mportant refinement to the conventionalc orrespondencet heoryo ft ruth,t he theoryR ussell defendeda fter1 907.W ittgensteinn ow heldt hat the real world makes some of the possible worlds of the sentences we use true, or "real".T hisw as nothingl ess than the theoryo ft ruth-making, whichW ittgensteinl aunched 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 Atomism" (Russell 1918a: 182ff.).
Significantly, this newly adopted theoryo ft ruth was consistent with the truth table device that Wittgensteininitially sketched in his jottings on logic of November1 912, albeitw iths omem odifycations.He now conceivedo ft he truth table as schematizing possible meanings or grounds -not just the truth-possibilities -of propositions in thes ense of facts thatm ake propositions true or false.
Incidentally,W ittgenstein'st ransitionf romt ruth-possibilitiest o truth-groundse xplains af act to which McGuinness first called attention.After November 1912,W ittgenstein did notd iscuss the truth tabled evice.Neither in the "Noteso nL ogic" nor in the  showup,however,in the Tractatus (4.31,4.442,and 5.101). 16 What likely explains Wittgenstein's silence on thet ruth table device is that aftert he changei nh is outlook followingh is encounter with Frege in December1 912, he began thinkinga bout how this innovation might serve roles quite different fromt hose it had played duringh is collaborationw ith Russell.Indeed,a s reintroduced in the Tractatus the trutht abled evice servesanew function.While in 1912 it was apurely symbolicfigurethathelpsto grasp the truth-dependence of thep ropositions, in the Tractatus (5.101) it referredt ot he real world.Thus if initially the truth table schematically identified only truth-possibilities, by the timeo ft he Tractatus it identifiedtruth-grounds,ortruth-makers.

Criticismofthe multiple relation theory of judgment
In May and June1913, when Russells howed Wittgenstein the first partso fTheoryo fK nowledge,W ittgensteinh ad theo pportunityt o criticizeR ussell's multiple relation theoryo fj udgment directly.I n light of the analysis in the preceding sections,i ti sr easonable to conclude that theg ist of Wittgenstein's criticism was addressed againstt akingt he ontologyo fc omplexesa sf undamental in logic.Indeed, Wittgenstein was in effect to argue thatR ussell's theory wasb uilt on the ontology of complexes, according to which,f or example, "'C's belief that A hates B'i sacomplex in which belief combines A and B and C and hatredi nto onew hole" ( Russell 1911:169).
In fact, in "The Philosophy of LogicalAtomism" (1918)Russell himself suggested an interpretation in thisd irection.He statedt hat whatWittgenstein showed him in 1913 was that we cannot make a geometricallya rticulated mapo fabeliefs ince we cannotp resent a belief in Euclidean space.T hisi st he caseb ecause in propositions sucha s" Othellob elievest hat Desdemona lovesC assio" the subordinatev erb( " loves")d oesn ot function as av erbw hen the 16 Brian McGuinness commented on this factint hisway: "These jottings [on logic] are a valuable reminder of how little we knowa bout the genesis of the Tractatus and how misleading thefragmentary preliminary workwehave can be" (McGuinness 1988:162).
In as ense, Russell was right -we cannotm ake am ap 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 area rticulated in space and so cannotc ommunicate facts.Facts can be "modelled", not mapped (cf.section4.3below).Wecan map only complexes.
We hold thatt his interpretationo fW ittgenstein's critique of Russell's multipler elationt heoryo fj udgment is much simplera nd has greater explanatory powert hant he competing ones.For example, it comfortablye xplainst he "directionalp roblem" of Russell's theory thatG riffin (1985) sees as the main pointa ttacked by Wittgenstein.According to Griffin, Russell's theoryofjudgment lacks the resources to distinguishb etween "Cassio loves Desdemona" and "Desdemonal oves Cassio";i ta lsof ails to exclude cases where instead by averb, the elements of arelation are connected by as ubstantive, as it is in the aforementioned example "This tablep enholders theb ooks".I fw ea ccept that judgments signify facts, however, then all these difficulties instantly disappear; all constituents of thejudgment come in their proper places andare unambiguously directed.
Thes ame is true of the interpretationp resentedi nH anks (2007).According to it, in May1913 Wittgensteindrew to Russell's attentiont hat thec ontent of judgment is something that must be true or false.T his something, we would like to add, is nothing but the sense of the judgmentthat afactmakes true, or false.

ThePicture Theory and theDoctrine of Showing: criticism of thetheory of types
In al etter to Russelld ated December2 6, 1912, Wittgenstein dropped acrypticremarkabouthis encounter with Frege: Ihad along discussion with Frege aboutour TheoryofSymbolismof which, It hink,h er oughly understoodt he general outline.He saidh e wouldt hink them attero ver.Thec omplex-problem is now clearer to me and Ihopevery much that Imay solveit.(Wittgenstein 1995: 21) Having considered the complex-problemi n § §4 .1-2,we turn here to the theory of symbolism that Russella nd Wittgenstein worked on together in 1912, and to itst ransformationa fter December 1912.
Recallt hat Frege's main idea was to advance ac oncept-script thatw oulds erve as a" perspicuousr epresentation oft he formso f thought" (Frege1 881: 89).This wast ob es omethingl ikeavisual instrument (similar to am icroscope) 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 1912w as thetheory of symbolism -all the more so givent hatW ittgenstein felt he was making significant progressi nt his direction (cf.section2 .2).During the courseo f discussion, Wittgensteinl ikelys howedF rege,a mong other things, his newly invented truth tabled evice, because till then it hadb een his major achievement in thisareaofresearch.
As we observed,b ye arly 1913 Wittgensteinu nderstood facts andp ropositions eacha ssingularo bjects.By thes ummero f1 913, he realized that "the meaning of ap roposition is the fact which actually corresponds to it" ( Wittgenstein 1913:9 4).Working out these insightsW ittgensteinh ad in effect adumbratedt he picture theory of language,according to which propositionsare facts which picture facts. 18On this view, sentences arep ictures, 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).
Thes tory, however,d oesn ot end here.W ittgenstein'ss econd discussion with Frege evidentlymade him confident that he should continued own thep ath he had taken on hiso wn, completely independent of Russell.Indeedb yA pril 1914, he concluded that his picture theory made the theoryo ft ypes impossible.Wittgenstein foundt hat we cannot say what at ypei ss ince the character of the type is shown by thesigns themselves: [The Theory of Types] tries to says omethinga bout thet ypes, when you cano nlyt alka bout the symbols.But what yous ay about the symbols is nott hatt his symbolh as that type,w hichw ould 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'i sb etween one name anda nother symbolises.Here we have not said:t hiss ymboli sn ot of thist ypeb ut of that,b ut only: This symbolises andnot that.(Wittgenstein1914:109) Wittgensteinf ormulated theD octrine of Showing this way: "logicals o -called propositions shew [the] logical properties of language" (Ibid.:108).This discovery had at ransformative impact uponW ittgenstein'sp hilosophy,c hanging it in ways thatR ussell nevercompletely understood. 19

Theeffects of the Frege-Wittgenstein critiqueonRussell
Russell had great hopes witht he Joint Project."[He] aspired to nothing less than ar evolutioni nt he aims and methods of philosophy, atransformation of thewhole discipline" (Monk 1996: 282).Hisf eeling was that there is "a whole news cience to be created" (# 628, 09.11.1912).
The reintroduction of newintensionalitiesinlogic had dramatic effectsu pon his philosophicald evelopment.In short,i tp ersuaded Russell that thep roject for an ew, "scientific" philosophy that he also called "analyticp hilosophy" cannotb er ealizedi nt he form in which he initiallye nvisaged it.Here is the story toldi nR ussell's words: [Wittgenstein'sc riticism] wasa ne vent of first-rate importance in my life, andaffected everything Ihavedone since.Isaw he wasright,and Is aw that Ic ouldn ot hope ever againt od of undamental work in philosophy.M yi mpulse wass hattered,l ike aw ave dashed to pieces against ab reakwater.Wittgensteinp ersuaded me that what wanted doingi nl ogicw as tood ifficult form e. So therew as no really vital satisfaction of my philosophical impulse in thatwork, andphilosophy lost its hold on me.T hat wasd ue to Wittgenstein moret han to the war.W hatt he war hasd onei st og ivem ean ew andl essd ifficult ambition, whichs eemst ob eq uite as good as theo ld one. 20 (Russell 1968:57) Some interpreters try to downplay this avowal.For Gregory Landini, fore xample,t heser emarks are to be read against the background of "Russell's personal ande motional turmoil over 19 For the effects of Wittgenstein's discussionw ithF regeo nF rege'sp hilosophys ee Milkov (1999). 20 failed relationships with Ottoline[ Morrell]a nd his wife Alys" (Landini2003/4: 104).Incontrast,wetake it at itsface-value.
Russell'shopes withthe Joint Program were connectedwith the introductionofanew, "scientific" method in philosophy.In short, the idea was to treat problemso ft he external worlda nd of other mindsw ithl ogical means, and more precisely,w itht he help of ideas of Russell's analyticl ogic of relations that is based on the ontology of simple and complex.M ostg enerally, this was a program foraradical (reductivea nd constructive) analysis of any subject-matter in philosophy. 21This explains Russell's profound disappointment when he was confronted with thef actt hat 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, whatr eally happenedw as not that the impossibilityo fr adically analytic philosophy wasd emonstrated.Rather, Russellr ealizedt hat his programf or exact philosophy has alternativesa nd is nota ss imple as he initially believed. 22 This ambiguity in Russell's 1903 position on propositions came to light in his rehabilitation of the mereological conception of propositionsafter 1905.