the context principle in wittgenstein

8/6/2019 THE CONTEXT PRINCIPLE IN WITTGENSTEIN

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MARCO ANTONIO RUFFINO

T H E C O N T E X T P R I N C I P L E A N D W I T T G E N S T E I N ' SC R I T I C I S M O F R U S S E L L ' S T H E O R Y O F T Y P E S *

ABSTRACT . In this paper, I try to uncover the role played by Wittgenstein's contextprinciple in his criticism of Russell's theory of types. There is evidence in Wittgenstein'swritings that a syntactical version of the context principle in connection wi th the theoryof symbolism functions as a good reason for his dispensing with the theory o f types.1 . INTRODUCTION

T h e a p h o r i s m 3 .3 o f t he Tracta tus h a s b e e n t h e s o u r c e o f so m e d e b a t ea b o u t t h e i n t e r p r e t a t i o n o f W i t t g e n s t e i n ' s e a r l y p h i l o so p h y :Only the proposition has sense; only in the nex us of a proposition does a nam e havemeaning. (1961, sec. 3.3)T h e m a j o r i t y o f W i t t g e n s t e i n ' s c o m m e n t a t o r s r e c o g n i se i n t hi s a p h o r i smthe in f luence o f F rege ' s con tex t p r inc ip le , wh ich i s mos t c l ea r ly s t a t eda t t h e b e g i n n i n g o f T h e F o u n d a t i on s o f A r i t h m e t i c a s o n e o f F r e g e ' sf u n d a m e n t a l m e t h o d o l o g i c a l p r i n c i p l e s :[N]ever to ask for the meaning of a wo rd in isolation, but only in the con text of aproposition. (1953, p. x)

T h e b i a s a c c o r d i n g t o w h i c h c o m m e n t a t o r s h a v e m a i n l y i n t e r p r e t e dthis cent ra l thesis in the Tracta tus i s semant i c , i . e . , i t has a lmos t a lwaysb e e n s e e n a s su g g es t in g a t h e o r y o f m e a n i n g o r o f o b j e c t - c o n s t r u c t i o n .I t is n o t m y a i m h e r e t o d e p r i v e t h is i n t e r p r e t a t i v e t e n d e n c y o f it sl eg i t imacy , bu t i t seems c lea r tha t the semant i c ques t ion i s no t amongW i t t g e n s t e i n ' s p r i m a r y m o t i v a t i o n s a t t h e v e r y b e g i n n i n g o f h is p h il o s -o p h y . I n m y o p i n i o n , i f t h e s e m a n t i c b ia s t o d a y s e e m s t o b e o n e o f t h emost a t t r ac t ive aspec t s o f the Tracta tus , t h i s i s because o f the g rea te m p h a s i s p l a c e d o n q u e s t i o n s c o n c e r n i n g l a n g u a g e in c o n t e m p o r a r yp h i l o so p h y .

W h a t I i n t e n d t o d o h e r e i s t o e l a b o r a t e t h e r o l e p l a y e d b y t h e c o n t e x tp r inc ip le in the c r i t ic i sm of Russe l l ' s t he ory o f types , a s fo rm ula ted byWi t tgens te in in h i s pre -Trac ta tu s wr i t ings . The con tex t p r inc ip le as ac e n t r a l t h e s i s o f t h e v e r y e a r l y W i t t g e n s t e i n h a s t h e n e g a t i v e r o l e o fsh o w i n g t h e d i sp e n sa b i l it y o f th e t h e o r y o f t y p es , a s f o r m u l a t e d i nSynthese 98: 401-414, 1994. 1994 Kluwer Academic Publishers. Printed in the .Netherlands.


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402 M A R C O A N T O N I O R U F F I N ORussel l ' s Principia Mathematica, as well as the p ositive role o f providingan adequate account of the mechanism o f symboli sm. The connec t ionbet we en W it tgenstein 's cr i tic ism of the theo ry of types and an a deq uatetheory of symbol i sm has a l ready been s t ressed by some comm enta tors(see, for example, Ishiguro, 1981) . What I intend to show is that thecontext pr inciple plays a fundamental role in this connect ion.

2 . W I T T G E N S T E I N , R U S S E L L , A N D T H E T H E O R Y O F T Y P E SOf the mult ipl ic i ty of quest ions involved in the phi losophical dialoguebetween Wit tgenstein and Russel l , a topic that seems to have haddecis ive importance for Wit tgenstein 's very ear ly phi losophy (and alsoa decis ive inf luence on the la ter e laborat ion of the Tractatus) is thatregarding the the ory o f types. W it tgenstein 's cr it ic isms concerning thistopic assume special re levance by involving some quest ions of the ut-most importance in the theory of the symbolism, which were cer tainlyto shape la ter the central theses of the Tractatus. The significance ofthis cr i t ic ism has been ignored or underest imated by most com-mentators because of the lack of a his tor ical examinat ion of Wit tgen-stein 's ear ly p hi losophy.Russel l sets out the version o f the theo ry of types, which is the focusof Wit tgenstein 's cr it ic ism, in Ch apter I I of the Introduct ion of PrincipiaMathem atica. I According to Russel l , when one reviews the main para-doxes, which unt i l that t ime had tormented logicians and mathemati-cians, one can perceive as their common character is t ic the presence ofself-reference on reflexivity (Russell and Whitehead, 1973, p. 63).Terms such as " t ru th" , " fa l s i ty" , " func t ion" , "proper ty" , "c lass" , e tc . ,which typical ly occur in the formulat ion of such paradoxes, include anambigui ty of meaning that , once con cealed in ordinary discourse, leadsto the em erg enc e o f wh at R ussell called "vicious-circle fallacies" (ibid. ,p . 64) . That is , the formulat ions which lead to paradoxes may be, bymeans o f som e approp riate analysis , shown to be reducible to ex-pressions of the typ e "q~(~p2)", wh ere "q02" expre sses a propo sitiona lfunct ion. They are , therefore, cases in which the funct ion is taken asan argument of i tself .The pr inciple according to which formulat ions of this kind must beforbidden in logico-mathematical discourse is es tabl ished by Russel lthrough two arguments . Firs t , the previous comprehen sion o f the total-i ty of i ts values is nec essary for the intell igibility of a func tion (p~. It


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C R I T I C I S M O F R U S S E L L ' S T H E O R Y O F T Y P E S 403fol lows that a funct ion cannot have among i ts va lues an object tha tpresupposes the funct ion i t se l f ; in o ther words , express ions of the form", ~ (~ )" a re no t we l l fo rmed , fo r in th is case we cou ld no t cons ide r thetotali ty of i ts values as intel l igible before the function i tself is intel l i-gible, thus generating a vicious circle.

Russel l ' s second argum ent is based on the explanat ion, by mea ns ofdirec t inspect ion of the correspo nding "logical in tu i t ion", of the natureof wha t co r responds to the word " func t ion" and o f wha t d i ffe ren t ia tesi t f rom the nature of individuals . This d i f ference in nature b etw eenfunct ion and individuals impl ies tha t not only express ions of the type"p( ~2 )" a re nonsens ica l , bu t a l so express ions o f the fo rm " 0( ~z )" ,when " 0~ " and " ~ " deno te any funct ions fo r which the re ex is ts anarg um en t a such tha t ' q)a" and "~a" were both meaningful ( i .e . , when

and p belong to the same logical type) . Russel l ' s approach to thenature of a funct ion is one of the most important points of th is chaptero f Principia. I t conta ins ob servat ions l ike the fo l lowing:The ques t ion as to the na tu re o f a func t ion is by no mean s an easy one . I t would seem ,however , tha t the essen t ia l charac te r i s t ic o f a func t ion i s ambiguity. (Ibid. , p . 39)and later:A fu nc t ion , in fac t , i s no t a de f in i te ob jec t , which cou ld be o r no t be a man: i t i s a mereambigu i ty aw ai t ing de te r min a t ion , a nd in o rde r tha t i t may occur s ign i f ican t ly i t mus trece ive the necessa ry de te rmina t ion , which i t obv ious ly does no t rece ive i f i t i s mere lysubs t i tu ted fo r someth ing de te rmina te in a p ropos i t ion . ( Ib id . , p . 48)The kind of ambigui ty ment ioned above is a lso an essent ia l character-ist ic of propor t io nal funct ions . Fo r R ussel l, the p roposi t ional funct iondenotes i ts va lues amb iguously ( ib id . , p . 40) ; in o the r words , ~ , forinstance, s im ultaneo usly den ote s th e values q~a, q~b, ~c, etc. , bu t no nein part icular:W e ma y r e g a r d t h e f u n c t io n i t s el f a s t h a t wh ic h a mb ig u o u s ly d e n o te s , wh i l e an u n d e t e r -mine d va lue o f the func t ion i s tha t which i s ambiguous ly deno t ed . ( Ib id . , p . 40)

The re is, of course , a go od deal o f obscur i ty in th is Russel l ian not ionof ambiguous denota t ion, as there is in the procedure of d i rec t inspec-t ion involving logical ly pr imit ive not ions . What can be emphasised,never theless , is tha t the m etho d involved in the formulat ion of thesecond argument above is the direct consideration of the proposi t ional


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404 M A R C O A N T O N I O R U F F I N O

function i tself . And this direct inspection involves regarding the func-tion as having a kind of thing-hood.Final ly , Russel l presents in Sect ion V of th is chapter the famoushierarchy of logical types for funct ions and proposi t ions . The r igorousobservance of th is h ierarchy would suff ice to avoid the emergence ofanf inomies in th e co nstruct ion of logical sys tems.

The very idea of a theory of types as Russel l conceives i t ra isescrucia l ques t ions ab out the nature of i ts meth od and i ts epis temologicalcharacter . What , a f ter a l l , i s i t ta lk ing about? And is i t s procedurelegit imate? As regards the theory i tself , i t gives the impression of tel l ingus someth ing new, i . e . , p resen t ing new in fo rmat ion . Bu t f rom wheredoes th is form of knowledge get i t s appearance of novel ty and, a t thesame t ime, of necessary t ru th? Russel l ' s pos i t ion wi th respect to th ispoint is to be l inked with his general ideas on epistemology of logic. Agood synthes is of Russel l ' s thought on th is topic can be found in h is'Logical Data ' of 1913. There , Russel l provides an accoun t of wha t hecal ls "acquaintance wi th logical objects" . He sees acquaintance , in aformal ised way, as a re la t ion es tabl ished between two objects , one ofwhich is the knowing subject and the o ther the object of knowledge:[E]xperien ce is a dual relat io n of subject to an ob ject , thou gh i t is not necessary to assumethat we exper ience e i ther the subjec t or the re la t ion, but only the objec t and (somet imes)the comp lex subject-experien cing-object . Assum ing that this analysis is correct , we calledthe dual relat ion in question "acquaintance". (Russell , 1979a, p. 100)Acco rding to the k ind of objec t tha t occupies the second posi t ion, in theexper ience-re la t ion we shal l have a lso di f ferent k inds of acquaintance:We then considered various kinds of acquaintance. The first classif icat ion is according tothe logical chara cter of the ob ject , name ly, according as i t is (a) part icular , (b) u niversal ,or (c) formal, i .e . purely logical . (Ibid.)The exis tence and the nature of the th ird k ind of acquaintance men-t ioned in the qu ota t ion, i .e . wi th logical objects , is the m ain preoccu pa-t ion of the text in quest ion, and i t is m ade poss ible on the bas is of twotranscendenta l argum ents prese nted by Russel l. F i rs t, for our d iscourseon terms such as "funct ion", "re la t ion", " logical form", e tc . , to beintell igible, as i t in fact is , i t is necessary that objects correspond tothese not ions wi th which we are a l ready famil iar :I t i s not a t a l l c lear what i s the r ight logica l account of " f orm " , but wh atever th is accountmay be , i t i s c lear tha t we have acquaintance (possibly in an extended sense of the w ord


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C R I T I C I S M O F R U S S E L L ' S T H E O R Y O F T Y P E S 405"acquaintance") wi th something as abstract as the pure form, since otherwise we couldnot use intelligently such a word as "relation". (Ibid., pp . 98-99)

T h e s e c o n d a r g u m e n t i s t h a t e x p e r i e n c e o f l o g i c al o b j e c t s is a n e c e s -s a r y co n d i t io n o f o u r u n d e r s t a n d i n g o f c e r t ai n s e n t e n c e s t h a t d e s c r ib es i t u a t i o n s o f w h o s e a c t u a l i ty w e s t il l h a v e n o i n f o r m a t i o n :If we are acquainted with a and with similarity and with b, we can understand thestatement "a is similar to b', even if we cannot directly compare them and "see" theirsimilarlity. But this would not be possible unless we knew how they are to be put together,i.e., unless we are acquainted with the form of a dual complex. Thus all "mentalsynthes is", as it may be called, involves acquaintance with logical form. (Ibid., p. 101)T h e c o n c l u s i o n , t h a t i n o u r l o g i c a l d i s c o u r s e l o g i c a l o b j e c t s c o r r e s p o n d -i n g to f o r m a l n o t i o n s a r e r e f e r r e d t o , i s e x t e n d e d n o t o nly - t o t e r m s f o rf o r m s o r l o g i c a l t y p e s , b u t a l s o t o l o g i c a l c o n n e c t i v e s a n d o p e r a t o r s :Besides the forms of atomic complexes, there are m any other logical objects which areinvolved in the formation of non-atomic complexes. Such word s as or , no t , a l l , some ,plainly involve logical notions; and since we can use such words intelligently, we m ustbe acquainted w ith the logical objects im~olved. (Ibid., p. 99)

W e h a v e t h u s a s k e t ch o f R u s s e l l ' s o p i n i o n s , a n d R u s s e ll s h o u l d b ec o n s i d e r e d t h e m a i n i n t e r l o c u t o r o f W i t t g e n s t e i n ' s f ir st w o r k s , t h e' N o t e s o n L o g i c ' o f 19 13 a n d t h e ' N o t e s D i c t a t e d t o G . E . M o o r e i nN o r w a y ' o f 1 9 1 4. 2 B u t w e f in d W i t t g e n s t e i n a l r e a d y v o i c i n g h is f ir stc r it i ca l o b s e r v a t i o n r e g a r d i n g t h e t h e o r y o f t y p e s i n h i s l e t t e r t o R u s s e l lo f 1 6 J a n u a r y 1 9 1 3 , s o m e m o n t h s b e f o r e ' N o t e s o n L o g i c ' w a s w r i t t e n .T h e r e , w e r e a d :And further: every theory of types must be rende red superfluous by a proper theory ofsymbolism . . . . What I am most certain is not however the correctness of my presentway of analysis, but of the fact that all theory of types must be done away with by atheo13J of symbolism showing that what seem to be different kind s of things are symbolisedby dif ferent kinds of symbols which cannot possibly be substituted in one anothe r's place.(Wittgenstein, 1974, pp. 19-20)W h a t W i t tg e n s t ei n h e r e c o m m u n i c a t e s t o R u s s e ll c a n n o t b e s e e n , f r o ma s y s t e m a t i c p o i n t o f v i e w , a s a s s u m i n g t h e f o r m o f a w e l l - a r t i c u l a t e do b j e c t i o n . I t w o u l d b e p r e f e r a b l e t o d e s c r i b e i t a s a m a n i f e s t a t i o n o f ac e r t a i n d i s c o n t e n t w i t h t h e f a c t t h a t w i t h R u s s e l l ' s t h e o r y o f t y ~ e s o n eh a d t o i m a g i n e a f ie ld o f o b j e c t s o r l o g i c a l p r i m i t i v e i d e a s r e f e r r e d t oby log ic .

W h a t w e f i n d i n t h e ' N o t e s o n L o g i c ' o n t h i s t o p i c i s a l s o , a c c o r d i n g


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406 M A R C O A N T O N I O R U F F I I N Oto this interpretatio n, an ech o of this rejection, bu t one w hich is sti llnot completely ar t iculated:I t is easy to suppose that "individual", "part icular", "co mp lex" etc. , are primit ive ideasof logic. Russel l , e .g. , says "individual" and "matrix" are "primit ive ideas". This errorpresumably is to be explained by the fact that , by employment of variables instead ofthe gen erality-sign, it comes to see m as if logic dealt with things which have been depriv edof all properties except thing-hood, and with propositions deprived of all propertiesexce pt comp lexity. (Wittgenstein, 1979a, p. 107)

As w e can see, W it tgenstein here at t r ibutes the so urce of this miscon-cept ion to the fact that Russel l was also making use of var iables outs idea quantificational context, which creates the i l lusion that one is dealingwi th someth ing wi thout any o ther proper ty than th ing-hood. Here ,Wit tgenstein rejects Russel l ' s view, but without explaining why. Rath er ,what W it tgenstein prop oses is an explanat ion of the or igin of the necess-i ty of assuming the real i ty of logical objects , but without providingreasons why this is a false step. Further evidence that, at the t ime ofwri t ing the 'Notes on Logic ' , Wit tgenstein himself had not yet reachedcomplete clar i ty on this topic is provided by his comment in his le t terto Russel l of 17 October 1913:Types ha ve got a good deal clearer to me on the journey . (Wittgenstein, 1974, p. 29)

I f this object ion does not y et seem comp letely art iculated, the oppo-si t ion between the recognit ion of a f ie ld of logical objects as whatconfers significance on logical discourse and Wittgenstein's conceptionof phi losophy (already present in the 'Notes on Logic ' ) is neverthelessquite clear:Philosophy gives no picture of reality.Philosophy is the do ctrine o f the logical form of scientific propositions (not on ly ot:prim itive prop osition s). (Wittg enste in, 1979a, p. 106)

To recognise the exis tence of logical objects would also imply theacceptance of a logical real i ty whose descr ipt ion ( t rue or fa lse) wouldbe the task of phi losophy, which contradicts what Wit tgenstein says inthe f i rs t sentence above. On the other hand, i t would also be to gobe yo nd the pro per task of phi losophy, i .e ., the descr ipt ion of the logicalforms of empir ical language (proposi t ions of science or s imply thesymbolic notat ion for such proposi t ions) - which is expressed in thesecond sentence above. This reveals the confl ic t between Russel l ' s ap-


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C R I T I C I S M O F R U S S E L L ' S T H E O R Y O F T Y P E S 407proach o f the "logical expe r ience " pres ented in 'Logical D ata ' and thepr imary purposes of the logico-analyt ica l phi losophy of Wit tgenste in .Logic as such must be res t r ic ted to formal analys is of language and,hence , to a theory of symbol ism; and i t s inves tigat ion m ust be com-ple te ly independent of the exis tence of any kind of ' logical fac ts ' .

That Russel l ' s theory of types funct ions as a paradigm of how, inWit tgenste in 's opinion, one should not proceed in logic is somethingwe can infer f rom above, together wi th the fo l lowing remarks f romNotebooks 1914-1916:If syntactical rules for functions can be set up at all, then the whole theory of th ings ,propert ies, etc. , is superfluous. I t is also too obvious that this theory isn ' t what is inques t ion e i ther in the Grundgese tze or in Principia Mathernatica. Once more: loNc musttake care of i tself . (Wittgenstein, I979, p. 2e, remark of 22 Aug. 19t4)It mus t in a certain sense be imp ossible for us to go wrong in logic. This is already part lyexpressed by saying: Logic must take care of i tself . This is an extremely profound andimpo r tant ins ight . ( Ib id . , rema rk of 2 Sept . 1914)That logic should "take care of i t se l f" here expresses the phi losophicaldem and tha t log ic shou ld no t be made poss ib le by recourse to somekind of reali ty (be i t empirical , psychical , or even logical) . The impossi-bi l i ty of er ror in logic which Wit tgenste in ment ions here is not due toa special kind o f r igour in its pro ced ure or to the exactnes s of :itsmethod , bu t r a the r to the nature of its task. Logic should deal only wi ththe description of syntactica l ru les for the use o f symbols :In phi losophy there are no deduct ions ; it is purely descriptive. (Wittgenstein, 1979a, p.106)And here i t i s impossible to go wrong. But such a k ind of descr ip t iveact iv i ty cannot , for Wit tgenste in , re ly on any kind of exper ience . Whatthe symbol ism presents to us , i .e . i t s pr imit ive const i tuents (Bausteine)and the form of their art iculation in sentences, should suffice for thisdescriptive activity:I f the exis tence of the subjec t -predica te sentence does not show everything needful , thenit could surely only be shewn by the existence of some part icular fact of that form, Andacquaintance with such a fact cannot be essential for logic. (Wittgenstein, 1979, p. 3e,remark of 4 Sept. 1914)

But why have I made th is d igress ion through Wit tgenste in 's concep-t ion of the legi t imate task of phi losophy ? A nd what i s the re levance o fth is aspect of W it tgenste in 's thought to the main que st ion a t hand -


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408 M A R C O A N T O N I O R U F F I N Othe role played by the context principle in the refutation of Russell'stheory of types? Because I am trying to defend the following point ofview: the reason for Wittgenstein's rejection of Russellian theory oftypes is not motivated by the detection of formal errors of any kind init, but rather has deep motivations in his conception of logic (and henceof philosophy). Wittgenstein not only rejected the misleading focus ofRussell's theory, but also showed how an adequate theory should beconstructed, i.e., limited to the symbolism.3 The construction of a'correct' theory of types is intimately connected with an adequate an-swer to the question about what really symbolises, and it is here thatthe context principle plays a decisive role. In other words, the contextprinciple does not motivate the very early Wittgenstein's criticism ofthe theory of types, but it is essential in showing its dispensability. Asfar as I know, this point has not been made in previous discussions ofthe role of the context principle in Wittgenstein's philosophy.

3 . T H E C O N T E X T P R I N C I P L E A N D T H E T H E O R Y O F S Y M B O L I S MWittgenstein's alternative to the theory of types is most clearly formu-lated in his 'Notes Dictated to G. E. Moore in Norway', of April, 1914.We may say that here Wittgenstein had finally reached the clarity hesought both in his correspondence with Russell and in his 'Notes onLogic' regarding the theory of types, and also that the essential featuresof his thought on this matter had assumed their definitive form. Amonga multiplicity of topics dealt with, we find the following observation:Therefore a THEORY of types is impossible. It tries to say something about the types,when you can only talk about the symbols. But what you say about the symbol s notthat this symbolhas that type, which would be nonsense for [the] same reason: hut yousay simply:This is the symbol, to prevent a misunderstanding. (Wittgenstein, 1979a, p.109)The first sentence of the quotation clearly reinforces the difference inWittgenstein's perspective regarding the theory of types. But the secondsentence reveals something new: what a correct theory of types shouldbe like, i.e., an elucidation of what is really symbolising in a certainsymbol. Hence, an elucidation of what transforms a 'dead' sign in a'living' symbol. (It is true that the idea that what really symbolises is theoccurrence of a sign combined with other signs had already appeared in


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C R I T I C I S M O F R U S S E L L ' S T H E O R Y O F T Y P E S 409the 'Notes on Logic ' , but , there , i t i s s t i l l not in connect ion wi th thecr it ic ism of the theory of types .)The mos t genera l fo rmula t ion o f an answer to the ques t ion abou twha t symbol ises can be found be low:Wh at symbol izes in &~ is that ch s tands to the le f t o f a p roper name and obv ious ly th isi s n o t s o i n - p . W h a t i s c o m mo n to a l l p r o p o s i t i o n s in wh ic h t h e n a me o f a p r o p e r ty ( t ospeak loose ly ) occurs i s tha t th i s name s tands to the le f t o f a name- form, ( W i t tg e n s t e in ,1979b, p, 116)And fu r the r :~b cann o t poss ib ly s tand to the le f t o f (o r in any o ther re la t ion to ) the symbol o f ap r o p e r ty . For the sy mb ol o f a prop erty , e.g., O/x is that q~ stands to the left of a nam ef o r m . . . . ( I b id .; my e mp h a s i s , e x c e p t f o r " th a t " )W e can see f rom bo th quo ta t ions tha t w ha t symbol i ses fo r Wi t tgens te inare the signs "4~" or " ~ " in a certain posi tion in relation to neighbour ingsigns ( those of a d i f ferent logical type) . In o th er wo rds , w hat symbot isesis the perceptible sign plus its relative position in propositional signs.Posi t ion here is unders tood as some kind of re la t ion (spat ia l or tempo-ra l, according to the nature of the s ign employ ed) that the s ign main-ta ins wi th o ther s igns which are members of the complete proposi t ionalsign. In my opinion, this is not more than the context principle in aspecial for mu lation which I shall call syntactic, 4 i .e . , only in the articu-lated context of perceptible signs .forming a propo sition al sign does asimple sign acquire symbolic nature. We can find a clear indicationabout th is point in the fo l lowing passage:T h e r e a s o n wh y , e . g . , i t s e e ms a s i f "P l a to S o c r a t e s " mig h t h a v e a me a n in g , w h i l e"Ab r a c a d a b r a S o c r a t e s " w i l l n e v e r b e s u s p e c t e d t o h a v e o n e , i s b e c a u s e we k n o w th a t"P l a to " h a s o n e , a n d d o n o t o b s e r v e t h a t i n o r d e r t h a t t h e wh o le p h r a s e s h o u ld h a v eone , wha t i s necessa ry i s no t t h a t "P l a to " s h o u ld h a v e o n e , b u t t h a t t h e f a c t that " P l a t o "is to the le f t o f a name shou ld . ( Ib id . )"Pla to" as such is merely a percept ib le s ign, but the .fact tha t "P la to"occurs to the lef t of another name is what has meaning.

For Wit tgenste in , what p lays the ro le of a theory of types is merelyshowing, for a symbol , the re la t ion that i t s percept ib le par t has to thepercep t ib le pa r t o f the o the r symbols o f the p ropos i t iona l symbol (e .g . ,be ing to the lef t of a name, or between two names, or to the r ight ofa re la t ion, e tc . ) . The wh ole theory o f types is , hence , red uce d to ta lk ingabo ut the character is tic posi t ions of cer ta in symb ols in the proposi t ional


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410 M A R C O A N T O N I O R U F F I N Ocon tex t . In o the r words , t a lk ing abou t the pos i t ions tha t a ce r ta ins y m b o l c a n o c c u p y in a c o m p le t e p r o p o s i t i o n a l s y m b o l w i th o u t f o r m in gn o n s e n s e . I n t h i s s e n s e , t e r m s s u c h a s " th in g " , " p r o p e r ty " , " r e l a t i o n " ,e tc . , a l l r e fe r to spec i f ic pos i t ions tha t these symbols may occupy . Bu tthese pos i t ions a re a l ready a cons t i tu t ive pa r t o f the sym bol . In o the rwords , i t i s imposs ib le to p ick a ce r ta in symbol and then to go on tota lk abou t i t s fo rm al p roper t ie s , because , in o rde r to iden t i fy a g ivens y m b o l , w e m u s t h a v e already speci f ied p rec i se ly those fo rmal p roper -t ies . So , agains t asser t ions such as ' symbols l ike th is are of such andsuch log ica l type ' , Wi t tgens te in poses the ob jec t ion :This you can ' t say because in o rder to say i t you mus t f i r s t know what the symbol i s : andin knowing this you see the type and therefore also [the] type of [what is] symbolized.I.e. in knowingwhatsymbolizes,you know all that is to be known; you can't say anythingabout the symbol. (Ibid., p. 110)

Le t u s t a k e a s a n e x a m p le t h e p r o p o s i t i on " a R b " , a n d l e t u s c o n s id e rthe poss ib il i ty o f say ing som eth ing ab ou t the log ical type o f "R " . F i r s t ,w e s h o u ld m a k e c l e a r w h a t t h e s y m b o l i s h e r e : t h e o c c u r r e n c e o f t h es ig n " R" b e tw e e n tw o o th e r s ( " a " a n d " b " ) i n t h e p r o p o s i t i o n a l s i g n .I f we no w w an t to a sse r t tha t th i s symbol i s a b ina ry re la t ion (an d'b ina ry re la t ion ' he re means s imply a k ind o f s ign tha t can occur be -tw e e n tw o n a m e s ) , t h i s i n f o r m a t io n h a s a l r e a d y b e e n e x p r e s s e d i nspec i fy ing wh a t i t is tha t sym bol i ses . I t i s a conseque nce o f th i s fac ttha t the a sse r t ion tha t th i s symbol i s a b ina ry re la t ion i s someth ingabso lu te ly t r iv ia l and tau to log ica l , because the correct description ofwhat symbolises a lready embodies th is in formation. This is , in my opin-io n , w h a t W i t tg e n s te in m e a n s i n t h e f o l l o w in g r e m a r k s :E . g . , in " a R b " , " R " i s no t a symbol , bu t tha t " R " is b e t w e e n o n e n a m e a n d a n o t h e rs y mb o l i z e s . He r e we h a v e no t sa id th is symbol i s no t o f th is type bu t o f tha t , bu t on ly :This symbolizes and not tha t. (Ibid., p. 109)An d , the t r iv ia l i ty o f t a lk abou t log ica l type i s the po in t o f the fo l lowingr e m a r k :E v e n i f t h e r e were propos i t io ns o f [ the] fo rm "M is a th ing" they would be super f luous( tau to logous) because wha t th is t r ie s to say i s someth ing which i s a l ready seen w h e n y o usee "M ". ( Ib id . , p . 110)W e m a y s e e h e r e h o w th e f a m o u s d o c t r i n e o f w h a t c a n b e s a id a n d o fwha t can be shown i s a na tu ra l consequence o f a co r rec t answer to theq u e s t i o n o f w h a t s y m b o l is e s . W e n e e d t o m a k e t h e d i s ti n c ti o n b e tw e e n


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C R I T I C IS M O F R U S S E L L ' S T H E O R Y O F TY P ES 411saying and showing because nothing can be said in respect to formalpropert ies of symbols that is not a l ready contained in the explanat ionof what w e are ta lking a bout . In an ideal notat ion, such consti tut iveaspects of the symbol are already clear in the choice of the kinds ofs igns employed and in their possible posi t ions, in such a way that a l lta lk of logical forms becomes superf luous, because i t merely ref lectsthat which is a l ready clear in the notat ion.

An impor tan t fea ture of the theory of types so conce ived i s tha t ,once i t is der ived from an ad equ ate theo ry of the sym bolism, the logicaltypes considered here are essent ia l ly complementary. Complementar i tyhere means only tha t the de te rmina t ion of a type of symbol a l readyimplies , in a cer tain manner , the determinat ion of the type (or types)of sym bol (or symbols) that , tog ether w ith the form er, form s a proposi-tion:Th e ty pe o f a symbol o f a relation is partly fkxed by [the] type of [a] symbol of [a] thing,since a symbol of [the] latter type must occur in it . (Ibid., p. 111)This becom es c lear when one cons iders tha t in "0 a" , for example , onecannot say tha t "0" occurs to the le f t o f "a" without i t a lso beingimplicit that "a" occurs to the r igh t o f "6" . The complementar i tybetw een logical types is thus a natural conse quen ce o f the w ay in whichWittgenstein conceives the the ory o f types, i .e . as a theory of symbolismbased on the context pr inciple , and means s imply that , in the par t i t ionof the symbol of a comple te propos i t ion , complementary symbols a reobta ined .

In Russel l ' s theory, to the contrary , i t seems that this idea of com ple-mentar i ty is somewhat problematic . For , as we have seen, Russel la l lows himself to consider the nature of a funct ion in i tself , by directspeculat ion on the " logical intui t ion" corresponding to the term "func-t ion" . I t follows that the thesis according to which "fun ct ion" and"individual" seem to denote complementary logical types is due to apro per ty of the a rrangem ent of logical objects corresponding to theseterms.

A second remarkab le fea ture of Wi t tgens te in ' s theory of symbol i smis that self-reference or self-predication is not only an error, but is alsoactually impossible. F or, if we write "(q~(q~))", ev en if we are usingthe same let ter for funct ion and argument , the const i tuted symbols arein fact different, since what symbolises is not only the sign but also thefact that "q ' occurs a t the lef t of a name (or , i f "~" symbolises a


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412 M A R C O A N T O N I O R U F F I N Ofunct ion of second-order , the fact that "9" occurs a t the lef t of a f i rs t -order funct ion symbol) . As Wit tgenste in said la ter in the Tractatus,what is common to both funct ions in the express ion above is only theletter q~, whichby itself signifies nothing, (1961, sec. 3,333)(A s t ronger consequence of th is reasoning is that i t excludes , in anatural way, not only sel f -predicat ion as shown above, but a lso anypredicat ion of the form $(q~) for fi rs t- or higher-order funct ions . Thisstronger result is not, at f irst sight, achievable in Russell 's account.)The diff icul ty caused b y self-predication ar ises, therefore , merely f roman imperfect ion in our notat ion. In an ideal notat ion, di f ferent typesof symbo ls (with differen t syntactical rules) hav e differen t kinds of signs(as is the case with Frege 's notat ion in the Begriffsschrift and in theGrundgesetze der Arithmetik , al though there are , o f course , many othe raspects of Frege 's notat ion that W it tgenste in reg arded as involvingfundamental logical mistakes). This eliminates the possibil i ty of theemergence of paradoxes whose common source i s , a s we saw, se l f -reference or se l f -predicat ion.

4. CONCLUSIONThe quest ion concerning the theory of types involved in the Wit tgen-s te in-Russel l d ia logue in the pre-Tracmtus writ ings seems to have hada much deeper inf luence on the ideas of the Tractatus than is normallyrecognised. In order to show the dispensabi l i ty of the theory of types .Wit tgenste in develop s a theory of what changes a s ign into a sym bol ,and this theory is based on w hat I have cal led the syntact ical formulat ionof the context pr inciple . This important role of the context pr incipleseems to have escaped mos t o f Wi t tgens te in ' s comm enta tors .

N O T E S* I would l ike to than k Michael Wrigley (UN ICA MP ) and G ot t f r ied Gabr ie l (Universi t~ i tKonstanz) as wel l as an anonymous journal referee for the i r va luable comments on aprevious vers ion of th is paper .1 A deta i led account of the evolut ion of Russel l 's opinions concerning the theory of typesis given in Cocchiarel la (1980, 1989) and Consuegra (1989); the ontological implicationsof Russell ' s logical doctr ines is the main topic of Quine (1966).2 F or a reconst ruct ion of the Wit tgens te in-R ussel l d ia logue dur ing the per iod of the pre-


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C R I T I C IS M O F R U S S E L L ' S T H E O R Y O F T Y P E S 4 13Tractatus writings, see McGuinness (1972, 1974), Btackwell (t981), Hacker (1986, pp.1-27), and Ishiguro (1981).3 For this reason, Wit tgenstein 's general at t i tude towards the theory of types may seemcontradictory at first sight. Wittgenstein does indeed reject the possibility of a theory oftypes in the Russellian style, but recognises the legitimacy of a theory o f types restrictedto the different kinds of symbols. Th e con tradiction is , therefore, merely apparent .4 He re I am using the term 'syntactic' not in the m ode rn sense o f linguistics, i .e. asopposed to 'semantics ' , but rather in the same sense that Wit tgenstein uses in theTractatus (3.33) o f the "logische Syntax" as a general descriptive theory conce rning logicalpropert ies of occurrences of symbols. 'Syntact ic ' seems to me an adequate term tocharacterise a style of investigation that gives priority to formal features of linguisticexpressions and logical relations between sentences containing these expressions as rel-evant data for the formulation and solution of philosophical questions.

R E F E R E N C E SBlackwell, K.: 1981, 'The Early Wittgenstein and the Middle RusseIl ' , in Block (1981),

pp. 1-31.Block, I. (ed.): 1981, Perspectives on The Philosophy of Wittgenstein, MIT Press, C am-

bridge.Cocchiarel la, N. : 1980, 'T he D evelo pm ent of the Theory of Logical Types and the N otion

of a Logical Subject in Russel l 's Early P hi losophy' , Synthese 45, 71-116.Cocchiarel la, N. : 1989, 'Russel l 's Theory of Logical Types and the Ato mist ic Hierarchyof Sentences ' , in C. Savage and A. Anderson (eds.) , Rereading Russell, MinnesotaStudies in the Philosophy o f Science, Vol. XII , Universi ty of Minnesota Press, M innea-polis, pp. 41-62.

Cons uegra, F .: 1989, 'Russell 's Th eory of Typ es, 1901-1910: Its Com plex Origin in theUnpublished Manuscripts ' , History and Philosophy of Logic 10, 131-64.

Frege, G.: 1953, The Foundations of Arithmetic, 2nd ed., trans. J. L. Austin, Blackwell,Oxford (originally published in 1884).

Hacker , P. : 1986, Insight and Illusion, rev. ed. , Clarendon Press, Oxtord.Ishiguro, H.: 1981, 'Wittgenstein and the Theory of Types', in Block (1981), pp. 43-59.McGuinness, B. : 1972, 'Bertra nd Russell and Ludwig Wit tgenstein 's Notes on Logic ' ,Revue Internationale de Phifosophie 26, 444-60.McGuinness, B. : 1974, 'Th e Grundgedanke of the Tractatus', in G. Vessey (ed.), Under-standing W ittgenstein, Macmil lan, London, pp. 49-61.Quine, W . V.: 1966, 'Russel l 's Ontological Dev elopm ent ' , The Journal of PhilosophyLXIII , 657-67.Russell , B.: 1984, 'Logical Da ta', in Russell , Theory o f Knowledge: The 1913 Manuscript,

Vol. 7, The Collected Papers of Bertrand Russel l , ed. by E. Eames, Allen & Unwin,London, pp. 97-102.Russel l , B. , and A. Whitehead: I973, Principia Muthematica, repr . , VoL I , Cambridge

University Press, London (repr. of 1910 original).Wittgenstein, L.: 1961, Traemtus Logico-Philosophicus, trans. D. Pears and B, McGuin-ness, Routledge and Kegan Paul , London.


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4 14 M A R C O A N T O N I O R U F F I N OWittgenstein, L.: 1974, Letters to Russell, Keynes and Moore, ed. G. H. yon Wright ,

Blackwell, Oxford.Wittgenstein, L.: 1979, Notebooks 1914-1916, 2nd ed. , ed. G. H. yon Wright and G. E.M. Anscombe, t rans, G. E. M, Anscombe, Blackwell , Oxford.

Wittgenstein, L.: 1979a, 'Notes on Logic', in Wittgenstein (1979), pp. 93-104 (originallywritten in 1913).

Wit tgenstein, L. : 1979b, 'Notes Dictated to G. E. Moore in Norway' , in Wit tgenstein(1979), pp. 108-1 9 (o riginally writte n in 1914).

Department of Phi losophyUniversi ty of Cal ifornia405 Hilgard AvenueLos Angeles, CA 90024-1451U . S . A .

the context principle in wittgenstein

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