hillel y. - logical syntax and semantics (1954)

8/3/2019 Hillel Y. - Logical Syntax and Semantics (1954)

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Logical Syn tax and SemanticsYehoshua Bx-HillelLanguage, Vol. 30, No. 2. (Apr. - Jun., 1954), pp. 230-237.

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MGICAL SYNTAX AND SEMANTICS

Hebrew Uniuersity, JerusalemThough considerations of meaning in linguistics can be replwed, up to a

point, by rigorous STRUCTURAL procedures, i.e. procedures involving solely thekinds and order of the elements of the language under investigation, they cannotbe replaced by DISTRIBUTIONAL procedures, despite the claim recently made byHarris.' Distributional procedures may be suficient to establish the rules bywhich all longer expressions (especially sentences) can be constructed out of theelements, but they are inadequate for the establishment of certain other rulesthat would mirror the so-called logical properties and relations of sentences andother expressions.

I t is worth while to quote a t this point what the logician Rudolf Carnap hadto say on this topic some twenty years ago:=

By the logical syntax of a language, we mean the formal theory of thelinguistic forms of that lanaage-the systematic statement of the formalrules which govern it together with the development of the consequenceswhich follow from these rules.A theory, a rule, a definition, or the like is to be called formal when noreference is made in it either to the meaning of the symbols (for example,the words) or to the sense of the expressions (e.g. the sentences), but simplyand solely to the kinds and order of the symbols from which the expressionsare coustmcted.The prevalent opinion is that syntax and logic, in spite of some pointsof contact between them, are fundamentally theories of a very differenttype. The syntax of a language is supposed to lay down rules according towhich the linguistic structures (e-g. the wnbnces) are to be built up from theelements (such as words or park of words). The chief task of logic, on theother hand, is supposed to be that of formulating rules according to whichjudgments may be inferred from other judgments; in other words atcordingto which conclusions may be drawn from premksea.But the development of logic during the past ten years has shown clearlythat it can only be studied with any degree of accuracy when i t is based,not on judgments (thoughts, or the content of thoughts) but rather onlinguistic expressions, of which sentences are the most important, becauseonly for them is it possible to lay down sharply defined rules. And actually,in practice, every logician since Aristotle, in laying down sharply definedrules, has dealt mainly with sentences. But even those modern logiciam

Zellig S. Harria, Methods in slructural LinguQliea 8 fn. 7 (Chicago, 1951).The work on which the preeent paper is based waa done while the author waa employed

by the Research Laboratory of Electronics, Mmsitchusetts Institute of Technology. Itwas aupported in part by the Air Materiel Command, the Signal Corpa, and the Office ofNaval Research, and in part by the Rockefeller Foundation.

The author is grateful to the Editor of LANDUA ~ E ,ho read an earlier draft of this paperand suggested many changea and deletiom, thereby improving its cogency and reducingthe number of it8 errora.

2 Rudolf Carnap, Ths logicul s$mtaz of t a np a g e 1-2 (New York and London, 1937). TheGerman original, Die logkache Syntax der Sprache, waa published in Vienna. in 1934.


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LOGICAL SYNTAX AND SEMANTICS 231who agree with u s in our opinion th a t logic is concerned with sentences, areyet for the most part convinced that logic is equally concerned with therelations of mean ing between sentences. T he y consider th a t, in contrastwith the rules of sy ntax , th e rulea of logic ar e non-formal. In th e followingpages, in opposition to th is stand po int, th e view t ha t logic, too, is concernedwith the formal treatment of sentences will be presented and developed.We shall see that the logical characteristics of sentences (for instance,whether a, sentence is analytic, synthetic, or contradictory; whether it isa n existential sentence or no t; a nd so on) a nd th e logical relations betweenthem (for instance, whether two sentences contradict one another or arecompatible with one another; whether one is logically deducible from theother or no t; an d so on) are solely depend ent upon the syntactica1 struc tureof th e sentences. I n this w ay, logic will become a pa rt of sy nta x, providedthat the Iat ter is conceived in a sufficiently wide sense and formulatedwith exactitude. The difference between syntactica1 rules in the narrowersense a n d t h e logical rules of ded uctio n is only th e &Rerenee between for-mation rules an d transformation rules, bo th of w hich are completely for-muIable in syntactica1 terms. T hu s we are justified in designating as 'logicalsyn tax ' t h e system which comprises the rules of formation an d trans-formation.Wh at C arnap in 1934 called 'the prevalent opinion' continues to be prevalentamon g con tem pora ry linguists. Th e establishment of t he 'statem ents w hichenable anyone t o synthesize or predict utterances in the language' (Methods372)is still regarded as th e sole aim of descrip tive linguistics, 'as the term has come

to be used' (id. 5);Fries's recent book The structure of EngZglksh (New York, 1952)has the subt i tle An introductionh he construction of English sentences. I t is th erules of formation which have caug ht th e exclusive atten tion of th e structu rallinguist ;3 the rules of transfo rma tion continue t o be relegated-with one nota bleexception, to be mentioned presently-to th e limbo of a n extra-ling uistic logic.This un fo rtu na te disregard of Ca rnap 's conception of a LOGICAL SYNTAX isnot entirely th e linguists' fa ult . Ca rnap himself and th e logicians who followedhis lead were too preoccupied with constructed language systems to devote m uchtim e and effort to a n application of their views to th e description of o rdinar ylanguages. Carnap even believed (op.cit. 2) th a t 'the statem ent of t he formal

rules of f orm ation an d tran sform ation [of na tur al languages] would be so compli-cated t h a t it would hard ly be feasible in practice'. This belief is certainly correctfor a COMPLETE stat em en t of the rules, bu t fairly good approximations should beachievable w ith some eff ort . Th is effort has been expended, as a m atte r of fact,for th e rules of form ation ; the re is no good reason for not do ing th e sam e for th erules of tra nsfor ma tion. Inde ed, beginnings for such an underta king exist al-rea dy ; bu t these ar e th e work of logicians an d philosophers, who are often biasedby their underlying m etaphysical conceptions a nd their adherence t o A ristotelianor Scholastic ways of thinking.It is th e duty of th e structural. linguist to scrutinize Ca rnap 's conception eare-fully; after all, Carnap is not a linguist proper. If and when his conception isfound t o be linguistically soun d, as I think i t is, we shall have t o give u p Harris'sa The term 'structural linguist' is used throughout this paper to meau 'aome Americanstructural linguists', of whom Blocb, Harris, H oekett, Smith, and Trsger are a, representa-t ive sample.


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232 LANGUAGE, VOLUME 30, NUMBER 2contention (Methods 5) th a t 'the main research of descriptive linguistice, an d th eonly relation which will be acce pted as relevant ..., s th e distribution or arrange-m en t within t h e flow of speech of some par ts or features relative t o others'.Ins tead , LOGICAL ANALYSIS,ased upon the relation of DIRECT CONSEQUENCE:will have to be given equal rights with DISTRIBUTIONAL ANALYSIS.T hi s will enta il, of course, a radical change in th e official conception of elicita-tion techn iques. Un til now th e inform ant hras been required only t o supp lyrepe titions of sound sequences, to judge whe ther two sound-sequ ences ar e th esame or not, to tell whether certain sound-sequences are sentences or not, andto determ ine whether 'two item s ar e the "same" in a particular aspec t of meaningor "different1' '.6 I t now becomes necessary t o develop techn iques of elicitationfor logical analysis which will have th e sam e degree of relia-bility an d v alidity asthose developed fo r distribu tiona l analysis. Dire ct questioning ('Do oculist an deye-hctor mean the same to you?') may serve as a first approximation, to bereplaced in time by more objective methods. Notice th a t Ha rris h i i l f ndicates,a t one place, an elicitation technique to this effect when he says; 'one can readthe text sentence ... in company with an informant, and then s top and say tohim, in an expectant an d hesitant way, "Tha t is to say, ...,"waiting for him t osupply t he continuation, ' However, Harris seems not to be aware th at w hat hegets from th e informant by this technique is much more than information abo utdistribution. Since structura l linguists have no dou bt been using su ch techniquesin their practical work, it is of u tmo st imp ortance th a t they make these tech-n i q u e ~ xplicit, become aw are of their theoretical function, an d analyze a ndimprove upon them .Most structural linguists seem to have recognized that not all aspects oflinguistics can be handled b y distributional analysis alone; but there is one whoatte m pte d th e seemingly impossible. W ishing t o exploit this kind of analysis toits utmost, H arris has chim ed th at he can describe in purely distributional termsboth synonymy relations (say between oculist a nd eyedoc lor) and the act ive-passive relationship (say between plays and is played by) ; and h e would probablyundertake, if challenged, t o do th e same w ith respect t o th e difference betweenLat in aut and ue l . According to his basic pos tulate (Methods 7 fn . 4), 'It m ay bepresumed t h at an y tw o morphemes having different meanings also differ some-where in distribution. ' It would then seem to follow tha t a ny two morphemeswith t he same distribution have t he same meaning. If we were to grant thesepresum ptions, the n indeed m an y of th e transfo rm ationa l aspects of langu age, ifno t all of them, w ould be reducible t o the form ational aspects. B u t in spite ofsome initial plausibility, th e presumptions a re false. Whatever conviction theycarry is due to the fact t ha t man y of the term s involved are equivocal. It willbe wo rth w h le t o analyze some of these equivocations.T he first is language itself. This term is sometimes understood a s the to tal ityof ail possible sentence-types (or utteran ce-ty pes), som etimes a s th e tota lit y ofall actually uttered sentence-tokens: or perhaps as the to ta l ity of ail sentence-

'See Logical smlnlaz 170.6 Structure of English 8 fn. 6 .a Discourae anslyaid, Lg. 28.20 fa.13 (1952).7 Following the usage of Charlea S. Peirce, a &ION-TYPE s the abstract class of all coa-


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LOGICAL SYNTAX AND SEMANTICS 233tokens th at have been uttered or will be uttered until th e extinction of th e usersof this language.Now if we consider a language as th e to ta lit y of all possible sente nce- types ,Ha rris's presump tion is clearly false. Greenan d red ar e surelydifferent morphemes,bu t their distribution within this tota lity (with respect t o English, of course) isALMOST exactly the same, i.e, the same up to a subs et of special en vir on m en hwhich will cause trouble t o a n y consistent and would-be simple description. Th issubset, to use a fitting ma them atical metaphor-which is m eant, however, moreto help us dodge the problem th an to solve it-is of measure zero. It would con-tain, for instance, the environments -horn, into which only green would fit butnot red, and -skin, into which only red would fit but not green. Except for suchcases, within th e totality of all possible sentence-types, there is for any sente ncecontaining red a (significant) sen tence th at contains green instead, and vice versa.

However, if we take a language to be th e totali ty of all sentence-tokensuttere d u p t o a certain time (or alternatively, the totality of all sentence-typesof w h c h tokens hav e been uttered up t o a certain tim e), then-disregarding acoincidence of cosmic dimensions-no two morphemes will show th e sam e dis-tribution. For this interpretation Harris's presumption would indeed turn outto be true, b ut in such a trivial fashion th a t i t can hardly be wh at he meant.T he relations between oculist an d eye-doctor, oculist and dentist, oculist and beauty,ocuLi~t n d green are of four different types, each of which m ust be t h e concernof th e structura l linguist. T o stat e only t h at w ithin a given totality of sentence-tokens all these morphemes exhibit di ie re nt distributions is surely not t he w holetruth-in fact only a small par t of i t . Ev en to st at e th at oculist, eye-doctor anddentist have aImost equal distribution within th e total ity of all sentence-types,whereas o c d i s t and beauty have overlapping distribution, and oculist an d greenhave almost exclusive distribution, though incomparably more revealing, stillmisses th e essential difference between t h e first two pairs. Sameness of distribu -tion, within th e type -totality, is perh aps a necessary bu t certainly not a sufficientcond ition for sameness of meaning ; hence, difference of meaning is perhaps anecessary b ut certain ly no t a sufficient condition for difference of dis trib utio n,with respect to t he same totali ty .Since 'sameness of dis tributio n' and 'sameness of meaning' ar e cer tain ly no tconvenient terms, other terms are usually employed instead. Here, however,another equivocation becomes effective. Oculist and dentist are ~ U B S T I T ~ T A B L Ein th e sense tha t a nya sentence containing th e one will turn into a sentence (notnecessarily a sentence with th e same meaning or even w ith th e sam e truth-value)when this is replaced by th e other. Oculist and eye-doclor are substitutable in th esense that any sentence containing th e one wiIl turn into a sentence with neces-sarily the same truth-value when this is repIaced by the other. For both thesecrete SIGN-TOKENSwhich (by some criterion) belong-to-the-same-type. Cf. Y. Bar -Bille l,A quasi-arithmetical notation for syntactic description, Lg. 29.49 (1953); herry, Halle,and Jakobson, Toward the logical description of languages in their phonemic upect,Lg. 29.45 fn. 13 (1953).

From now on the qualifier almost will be omitted.


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234 LANGUAGE, VOLUME 30, NUMBER 2essentially different relations, the term substitutable (or replaceable, or commuta-ble, or even equwalentj is used indifferently, more often th an no t with out even aquahfying adverbial. A co nsi sk nt use of qualifiers like disttibudionally an dlogically (or, more fan cifully, s&a significalione an d s& a verktate) could assistin avoiding the pitfalls connected with this equivocation; but a convention touse, say, commuiabk for t h e first sense an d interckangeable for t h e second, wouldbe even better.There has been recently a lively discussion of th e degree of interdep ende nceof the various structural layer^'.^ I t seems to me t ha t pa rt of the purists' in-sistence on a sharp demarcation between phonology and grammar is based onth e assumption t h at a treat m en t of t he syntactical-transformational aspects oflanguage is in constant danger of succumbing t o an infestation by m eaning, a nevil from which those aspects of language th a t ca n be shown t o be independ entof s yn ta x can be sav ed . Inde ed, so long a~ syn tax, as traditionally handled, was aMEANING SYNTAX, it w as methodologically worth while to ado pt th e procedureof T rage r an d Smith i n An o d i n e of English structure (1951),which, based up onpurely distributional analysis, rigidly d is c ri m in ah between ascending levels ofcom plexity of organization . If only one could establish phonemics without re-course to gram ma r, th e danger of letting sema ntic considerations creep in wouldbe con siderably reduced if no t completely eliminated. I believe th a t some of t h eattractiveness of this a tti tu de is reduced by recognizing t h a t a description of th etra ns fo m at io m l aspects of sy ntax can be just as free of m eaning as other partsof a l inguistic tre atm ent.T h e fear of allowing meaning to in tru de is of course only one reason for thesharp-level approach. Ano ther, probably m ore im porta nt, is th e fear of circular-ity . If (say) th e term 'morpheme' is used in the definition of th e phoneme, an dvice versa, then certainly this procedure looks viciously circular, and the logicalsoundness of th e science th a t uses such definkions is grav ely jeopardized. Pike ,howev er, has given sound reasons why this fear, in it s generalized form , isground-less. M oreover, it is possible to sh ow tbat certain types of concept introductionswhich look circular are not so in fact-types in which th e elimination of th enewly introduced term does not involve an infinite regress. As a matter of fact,concept form ation s of these kinds a re in regular use in m athem atics, a nd espe-cially in mathem atical logic, where th ey are known as special cases of ~ECURSIVEDEFINITIONS. It seems rather likely (though a detailed proof would require m an yman-hours of work) that Pike's nine-step procedure (op.cit. 120) can be formal-ized an d adequately represented by a se t of such de hi tio ns . Since I have t reatedthis top ic elsewhere a t som e length,'O I s h d l say no more here.It is a n in kr es tin g fac t, deserving th e atten tion of sociologists of science, t h a ta t approximately th e same time, b u t in complete independence of each other ,Bloomfield and Carnap were fighting the psychologism that dominakd their

respective fields, linguistics and logic. They both deplored the mentalistic mud@ Kenneth L. Pike, More on grammatical prerequisites, Word 8.106-21, (1952), and the

references mentioned there.'0 On recursive definitions in empirical science, Proc. 11th Internal. Congresa of Philoso-

phy 5.16@5 (Bruswls, 1953).


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LOGICAL S Y N T A X AND SEMANTICS 235in to which the s tudy of meanings had fallen, and tried t o reconstruct their fieldson a purely formal-structural basis. I think it is correct t o say that th e differencebetween the structu ral linguist and th e formal Iogician is on e of str es s and degreerather than of kind. Both are essential ly at tempting to const ruct languagesystems that stand in some correspondence to nat ura l languages-though mo stlinguists would say t ha t th ey a re just describing th e latter . B u t whereas for th elinguist t h e closeness of thi s correspondence is the crite rion by w hich he willjudge th e adequacy of the language system he is setting up, which alone entitleshim t o consider himself as describing a given na tura l language, t he logician willlook primarily for oth er feature s of his system , suc h as simp licity of h and ling ,fruitfulness for science, an d ease of deduction a nd com putation , with closecorrespondence to a natural language as only a secondary desideratum. Con-structed Ianguage systems a re judged by th e linguist according to th e degree t owhich they approximate a natural language; natural languages are judged bythe logician according to the degree to which they approximate efficient, well-constructed language systems.I have gone into these generalities in order to emphasize the following point.A few years after Carnap's elaborate att em pt t o show th a t prima facie semsnticconsiderations can be satisfactorily mirrored in formal syntax, he reversed him-self completely, reintroduced semantics into logic, and dedicated t o it most ofhis later studies." This development is no t surprising if we remem ber th a tsemantics w a s no longer, by thii time, th e hodgepodge th at w ent under this namein th e first qu ar te r of ou r century an d so much repelled Bloomfield. In th e earlythirti es, P olish logicians of th e Warsaw-Lw dw school-mainly T. Kotarbinski,A. Tarski , and K . Ajdukiewice-gave this science a foundation which ma de i tfully competitive with LOGICAL SYNTAX. This was achieved both through anextensive an d skillful use of th e symbolism of ma them atical logic, and by delib-erately ab stra ctin g from th e users and usages of t h e signs under st ud y and con-sidering only their relations to wh at was signified by them . Bloomfield's stric ture sagains t sem antics an d th e use of meaning for linguistic description, though validagainst the st at e of th at field a t the tim e he wrote, do not hold against thisrevitalized science, in th e form g iven t o i t by T arski,12 Ca rna p, Q uine,la an dothers. I ha ve no intention of bridging th e abyss between those linguists whoSTILL use semantic considerations in their analysis and those who use themAGAIN, just as I do not wish to minimize the corresponding difference betweenphilosophers. I believe t ha t only those who have followed th e syntactical methodt o its very end will be able to appraise adequately th e sta tu s of th e new semanticsin descriptive linguistics.M y plea for th e reintroduction of sem antics into th e theatr e of operations of

11 Foundation8 of logic and m l h e m t i c s , International encyclopedia of unified science,V o l . 1, No. (Cbicago, 1939) ; ntrodwt ion to semantics (Cambridge, M as s,, 1942) ;Meaningand necessity (Chicago,1 9 4 7 ) .'9Der Wahrheitsbegriff in den formalisierten Sprachen [written 19331, Studia philaso-

phica 1 . 2 6 1 4 5 (1936);T h e semantic conception of truth an d the foundation of semantics,P h i h s o p h y a d henomenological research 4.341-76 (1944).The latter is reprinted in Readingsin philosophical analysis 52-84 (ed. H . Feigl find W. Sellars; Mew York, 1949) and in Se-m a t i c s and the philasophy of language 13-47 (ed. L. Linsky; Urbana, Ill . , 1952).


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236 LANGUAGE, VOLUME 30, NUM BE R 2descriptive Iinguiatics will be strengthened, I think, if we follow Carnap andQuine in showing th a t the term 'semantics' bas been understood, traditionalIyaswell as by th e Polish school of logicians, t o con tain two ra ther sepa rate theorimwith t w o different sets of concepts. T h e one theory deals with t he INTENSIONALor CONNOTATIONAL aspects of language or o ther sign systems, i.e. MEANING (in arestricted mnse of this word), the other w ith the EXTENSIONAL,ENOTATIONAL,or REFERENTIAL spects. Carn ap calk them u THEORY O F INTENSION and THEORYO F EXTENSION respeetiveIy, Quine calla them1 =THEORY OF MEANING and THEORYOF REFERENCE. T h e firstmem ber of e ach pair deals with such concepts as logicaltru th , logical equivalence, and synonymy; t he second member deals with tru th,equality in truth-v alue , an d coextensiveness. To find ou t w hether a given atate-ment is Iagically true, whether two statements are logically equivalent, orwhether tw o expressions a re synonymous, one needs to know only their intension(connotation, meaning) ; o find o ut whether a certain statem ent is true, w hethertwo statements have the same truth-value, or whether two expressions are co-extensive, one mu st a k a m ake detailed observations, or rely on experience. Buti t is certainly no t th e l inguk t 's business, or for th at m atter th e logician's, to h dthese things out. T h a t morning star and evening &P are coextensive (den ote thesame physical entity ) is hardly of intere st to th e logician qua logician or to th elinguist qua linguist; it is, rather, the astronomer's du ty to find this out . W hetherthe s t a temen t All cats have tails is true is certainly not an exclusively linguisticproblem, bu t ra ther one for th e zoologist.

A linguist who decides that it is n o t his concern to find out which Englishstatements are true and which English expressions are coextensive is fullyjustified; he can safely disregard the se (pseudo)-sem antic aspe cts of language.Some linguists, however, ha ve thrown awa y the baby with th e b ath water. Bytotally discarding semantics, they have committed two sins. First, it is verydefinitely the linguist 's concern that oculist and eye-doctor are not only com-mutable but synonymous (co-intensive), and a description that contained nostatement of this fact would be seriously inadequate. (If this is agreed upon,the n i t mus t be equally th e linguist's concern to s ta te tha t f rom A ll Greeks aremen an d Socrates is a Greek, follows Socratea is a m n ; nd he should n o longer-exce pt for prag m atic reasons-leave such sta tem en ts t o his colleague th e logi-cian.) Secondly, both THEORY O F MEANING (in addition to meaning itself) andTHEORY OF REFERENCE (though not reference itself) are of v ital importance tohim, since-like every other scientist-he has to worry from tim e t o time abo utmethodological questions.

It ha s been th e purpor t of this pape r to establish t he following four points.(1) Th ere exists a conception of syn tax, du e t o Carnap , th at is purely formal(structural) and adequate in a sense in which the conception prevalent amongAmerican structural linguists is not. This conception entails a certain fusion'a For instance, Notes on existence and neeeesity, Journal of philosophy 40.113-27 (19431,reprinted in Sem ntica and th e philosophy of t a a gw z ge 77-91.14 80 far as I know, Carnap has not wed thew terms in print, but they fit the main

argument of Meaning and neceseily, and were used by him in correspondence.1 8 For instance, Two dogmaa of empiricism, l'hihsophical review 60.22 (1951).


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LOGICAL SYNTAX AND SEMANTICS 237between grammar and logic, with grammar treating approximately the forma-tional pa rt of syntax a nd logic its transformational pa rt. T he relation of COM-MUTABILITY may be sufficient as a basis for formational analysis, but otherrelations, such a s th at of formal CONSEQUENCE, must be added for transforma-tional analysis. Since modern techn iques of e licitation hav e been developedmainly with distributional analysis in view, a new approa ch is required th a t willyield reliable techniques of elicitation for th e establishm ent of syn on ym y an dthe l ike.(2) A recent at t em pt by H arris to reduce the transformational part of syntaxto it s formatio nal par t is based on a series of equivocations in th e term s language,eguiualent, commuhble, and their cognates, and so is without foundation.(3) Th e tendency exhibited by m any contemporary structural l inguists t o set

u p s har p dem arcation lines between th e variou s linguistic subfields is presumedto be based, f irst , on the at tempt to keep linguistics as far as possible inde-pend ent of concepts open to th e intrusion of meaning an d , secondly, on a fe arof circularity in th e definition of basic terms . B u t Car na p has shown th a t eventh e transform ational aspects of syn tax can be described witho ut appeal to m ean-ing ; and recent methodological studies of concept formatio n indicate th a t certainprocedures with a circular look are in fact harmless because th e term s introducedby them can be finitely eliminated.(4 ) T h e generalized fea r of letting m eaning intru de in to linguistics seems t orest mainly on the fact that in the first quarter of this century the study of

meaning was indeed in a bad methodological state. But since then, mainlythro ug h t h e efforts of Polish logicians, sem antics ha s become a w ell-defined,rigorous field. This change has caused Ca rnap to reintroduce semantics into logic,and should cause descriptive linguists to follow Carnap's lead.16If l For a somewhat different approach to the problems discuseed here, see Baskell B.Curry, Mathematics, syntactics, and logic, Mind 62.172-33 (1953).

hillel y. - logical syntax and semantics (1954)

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