Modelling the Phoneme

F.H.H. KORTLANDT »•**M>«>>tUfo&ia*Kmtomrtn^^

MODELLING THE PHONEME

>IOUTON

\ Dis<. Amsterdam QU

197? UNIVERSITEITSBIBLIOTHEEK LEIDEN

00563267 MODELLING THE PHONEME MODELLING THE PHONEME

New trends in Fast European phonemic theory

ACADEMISCH PROEFSCHRIFT

TER VERKRÜGING VAN DE GRAAD VAN DOCTOR IN DE LETTEREN AAN DE UNIVERSITEIT VAN AMSTERDAM OP GEZAG VAN DE RECTOR MAGNIFICUS, DR. A. DE FROE, HOOGLERAAR IN DE FACULTEIT DER GENEESKUNDE, IN HEX OPENBAAR TE VERDEDIGEN IN DE AULA DER UNIVERSITEIT (TUDELIJK IN DE LUTHERSE KERK, INGANG SINGEL 411, HOEK SPUl) OP DINSDAG 30 MEI 1972, DES NAMIDDAGS TE 2.30 UUR

DOOR

FREDERIK HERMAN HENRI KORTLANDT geboren te Utrecht

1972 MOUTON THE HAGUE · PARIS PROMOTOR: PROF. DR. C.L. EBELING COREFERENT: PROF. DR. S.C. DIK SAMENVATTING

Het doel van deze Studie is tweeledig. In de eerste plaats tracht ik een overzicht te geven van de recente ontwikkelingen van de fonologie in Oost-Europa. De nadruk ligt hierbij op mathematische en semi-mathematische modellen van het foneem. In de tweede plaats geef ik aan wat naar mijn mening de fundamentele problemen zijn in een sluitende fonologische theorie. Bijzondere aandacht wordt geschonken aan het feit dat een definitie van het foneem als een klasse spraakklanken niet in overeen- stemming is met het distinctiviteitsbeginsel. In het eerste hoofdstuk geef ik een kort overzicht van de Russische fonologie voor 1962. Het tweede hoofdstuk is een kritische uiteenzetting van de fonologische theorie van S.K. Saumjan. In het derde hoofdstuk behandel ik verzamelingentheo- retische modellen zoals die van I.I. Revzin en S. Marcus. Het vierde hoofdstuk is gewijd aan identificatiemodellen. In het vijfde hoofdstuk geef ik een uiteenzetting van het model van de logicus T. Batog. Het zesde en zevende hoofdstuk hebben betrekking op algemene problemen van linguistische methodologie, en het achtste betreft de linguistische aspekten van het foneembegrip. Het negende hoofdstuk gaat over optionele distincties en het tiende over configuratieve eigenschappen. Dedicated to the memory of N.S. Trubetzkoy PREFACE

This study, which is submitted äs a doctoral thesis at the University of Amsterdam, has been accomplished under the inspiring guidance of Professor C.L. Ebeling. The opportunity to work with him has enabled me to draw heavily upon bis valuable insights and ample experience. I am most grateful to Professor A. H. Kuipers for his penetrating criticism of the manuscript. The stimulating discussions which we had together have greatly added to the value of this publication. I am also indebted to Professor S.C. Dik and Professor E.M. Uhlenbeck, and to my colleagues A.A. Barentsen, M.P.R. van den Broecke, N.S.H. Smith, H. Stein- hauer and W.A.L. Stokhof for reading the manuscript and commenting upon it. I thank Mrs. C.G. Blomhert for the copy editing and Miss A. Pols for the proof reading. Finally, I wish to express my gratitude to Mr. P. de Ridder for the quick publication of the book.

F.H.H.K. February 8th, 1972 TABLE OF CONTENTS

Preface 9 Abbreviations 14 Introduction 15

PART I THE DEVELOPMENT OF MODELS IN PHONEMICS 1. Russian phonemic theory before 1962 1.1. Baudouin de Courtenay 19 1.2. Scerba 20 1.3. Jakovlev 21 1.4. Trubetzkoy 21 1.5. The Moscow school of phonology 23 1.6. Thefifties 25 2. Saumjan's two-level model 2.1. Introduction 28 2.2. The antinomy of transposition 29 2.3. The identification antinomies 31 2.4. Saumjan's definition of the phoneme 33 2.5. The operator method of the paradigmatic identification of phonemes 35 2.6. Criticism 37 2.7. Social and individual variants 39 2.8. The operator method of the syntagmatic identification of phonemes 40 2.9. Criticism 41 2.10. Distinctive features 43 2.11. Prosodic features 44 3. Set-theoretical models 3.1. Introduction 46 3.2. The initial objects of Revzin's model 47 3.3. Revzin's definition of the phoneme 48 12 TABLB OF CONTENTS 3.4. A paradigmatic model . 51 3.5. Syntagmatic models 53 3.6. Phonetic and phonemic Systems 56 3.7. A fundamental hypothesis 59 3.8. Marcus' definition of the phoneme 61 3.9. Criticism 63 3.10. Nebesky's conception of relevant features 66 3.11. Graphic models 70 3.12. Kanger's model of the phoneme 71 3.13. Relations between models 72 4. Identification models 4.1. Introduction 76 4.2. The initial objects ofUspenskij's model 77 4.3. Identification rules 78 4.4. Uspenskij's definition of the phoneme 82 4.5. Beloozerov's model of the phoneme 83 4.6. Peterson and Harary 87 5. Batog's logical model 5.1. Introduction 91 5.2. Logical preliminaries 92 5.3. The initial objects of Batog's model 95 5.4. From phonetic chain to phonetic system 95 5.5. The distribution of sounds 99 5.6. Batog's definition of the phoneme 100 5.7. Criticism 103 5.8. The role of features 108

PART II FUNDAMENTALS OF PHONEMIC MODELLING 6. The use of mathematical methods in linguistics 6.1. The dehumanization of the study of language 113 6.2. Criticism 116 6.3. Conclusion 118 7. Models and modelling 7.1. Revzin's conception of modelling 120 7.2. Saumjan's conception of modelling 122 7.3. Apresjan's conception of modelling 124 7.4. Stoff's conception of modelling 126 7.5. Conclusion 129 TABLE OF CONTENTS 13 8. The phoneme 8.1. The motivation for taxonomic phonemics 131 8.2. Descriptive adequacy 133 8.3. Distinctiveness 135 8.4. Relevant features 137 8.5. Segmentation 140 8.6. Phonemic units 143 8.7. Identification 144 8.8. Uniqueness 147 8.9. Joint features 148 8.10. Conclusion. A characterization 150 9. Optional features and heavy phonemes 9.1. Phonemic overlapping 152 9.2. Phonemic interchange 154 9.3. Optional features and heavy phonemes 157 9.4. Theproof 161 9.5. Optional phonemes 162 9.6. Junctures 163 10. A note on configurational features 10.1. Inherent and configurational features 165 10.2. Relations between features 166 List of references 167 ABBREVIATIONS

Am. American Bu. Bulgarian Ch. Chinese Cz. Czech Dan. Danish Du. Dutch Eng. English Fr. French Ge. German Gr. Greek It. Italian Jap. Japanese Li. Lithuanian Po. Polish Ru. Russian Rum. Rumanian SCr. Serbo-Croatian Skt. Sanskrit Sp. Spanish Sw. Swedish Tu. Turkish INTRODUCTION

The purpose of the present study is twofold. Firstly, I will try to give a survey of the recent developments in phonemic theory that took place in Eastern Europe during the sixties. Emphasis is laid upon mathematical and semi-mathematical models of the phoneme. Since I am only concerned with theoretical phonemics in the present study, phonetic investigations remain out of the picture. Secondly, I will give an account of the problems which I regard äs fundamental in any consistent theory of phonemics. Special attention will be paid to the important but often neglected fact that a definition of the phoneme äs a class of speech sounds is incompatible with the principle of distinctiveness. Mathematical methods in linguistics fall into two classes, quantitative and non- quantitative. Quantitative methods are not discussed in the present theory-oriented study. This is a consequence of the fact that no linguistically relevant features are of the continuous-scale type (cf. Hockett 1955: 17). The mathematical disciplines that are relevant for THEORETICAL linguistics are, above all, algebra, set theory, and logic. However, only the most elementary notions from these disciplines play a part at the present stage in the development of linguistics. Mathematical concepts are introduced gradually in the course of this book in order to make the topics under discussion accessible to scholars without any previous training in mathematics. Formal definitions of basic mathematical concepts have been deferred to section 5.2. The only parts of the book where more mathematical sophistication than ordinary common sense is required are sections 3.10 and 5.4-5.6. I have purposely minimized the number of formulas in the second part of the book. In the first chapter I give a brief survey of Russian phonemic theory before 1962. The only aim of this chapter is to outline the background of the new developments in Soviet linguistics during the sixties. It is shown how all of the three main trends in phonemic thought, represented in Russian linguistics by Scerba, Jakovlev, and Trubetskoy, essentially go back to Baudouin de Courtenay, and how they finally stood with regard to each other. The second chapter is an exposition and discussion of S.K. Saumjan's two-level theory, which has hitherto found hardly any response outside the Soviet Union. Attention is focused on the paradigmatic and syntagmatic identification of phonemes, which I regard äs the main problem in phonemic theory. 16 INTRODUCTION In the third chapter I give an account of the set-theoretical models that have been proposed for various aspects of phonemic analysis. The main part of the chapter is devoted to the theories that have been put forward by I.I. Revzin and S. Marcus, who are the leading theoreticians on language models in Eastern Europe. Among the other models that are discussed in this chapter are some important contributions by L. Nebesky and S. Kanger. Here, äs well äs in the subsequent chapters, considerable attention is paid to the initial objects of the models under discussion and to the formal definitions of the phoneme. The models discussed in the third chapter are characterized by a lack of interest in and explicitness about the identification problem. This is why I have devoted the fourth chapter to models that are primarily concerned with the identification of phonemic units. This chapter contains an explicit Statement of identification rules and their logical implications. It is shown that different relative priorities of the identification rules lead to different phonemic Solutions. In the fifth chapter I give an exposition of the formally most elaborate model of phonemic analysis, which is the one that has been presented by T. Batog. The exposition is preceded by a short account of basic mathematical notions. The last two sections of this chapter are a review of my objections to the model put forward by Batog äs well äs, more generally, to any predilection for criteria other than the principle of distinctiveness. Chapter 6 deals with the possibilities and limitations of the application of mathematical methods in linguistic investigations, and Chapter 7 with the definition of the concept of 'model'. These chapters are not concerned with phonemic theory but only with general issues of linguistic methodology. Various Standpoints are set up against each other, and a tentative conclusion is drawn. In Chapter 8 I defend the thesis that a grammar lacking a taxonomic phonemic level cannot achieve descriptive adequacy because it cannot account for lexical innovations that do not conform to existing phonemic patterns. The existence of linguistically relevant units on the phonemic level derives from the fact that not only the presence vs. absence of features but also their relative ordering plays a part in the distinguishability of linguistic forms. As a criterion for both the paradigmatic and the syntagmatic delimitation of phonemic units I adhere to the principle of distinctiveness. The impossibility of assigning certain features to a single phonemic unit leads to the postulation of 'joint features'. In Chapter 9 the optional character of certain distinctive oppositions^is discussed. This phenomenon, which in theoretical linguistics has not yet received the attention which it deserves, is illustrated with a considerable number of examples from different languages. Chapter 10 is a small excursus on configurational features. PART ONE

THE DEVELOPMENT OF MODELS IN PHONEMICS l

RUSSIAN PHONEMIC THEORY BEFORE 1962

1.1. BAUDOUIN DE COURTENAY

Russian phonemic theory goes back to pre-revolutionary days. The first phonologist on the Russian scene was the famous Polish linguist J. Baudouin de Courtenay, who can be viewed äs the predecessor of both the Moscow and Leningrad schools of phonology.1 As early äs 1881 he wrote (1963: 122): The concept 'phoneme' is decomposed into two essentially different notions: 1) the mere generalization of anthropophonic [i.e., phonetic] properties, 2) the mobile [i.e., variable] component of a morpheme and the mark of a certain morphological category. This coincides with two categories of correlates. In the course of the further development of these ideas it will be necessary to make a strict distinction between the two aspects of the concept of a phoneme and at the same time to set up separate terms for them. It took Russian linguistics 75 years before the necessary distinction was finally established (Avanesov 1956). Particularly during the last twenty years of this period a great amount of unproductive discussion was wasted on the question of whether a phoneme should be regarded äs a family of phonetically related sounds, which was essentially the view held by the Leningrad school, or äs a family of automatically alternating sounds, äs the Moscow school maintained. It is remarkable that not only the first opinion goes back directly to Baudouin de Courtenay, but that the second opinion does äs well, for it corresponds rather closely to the same author's earlierviews. On the one hand the principal object of Baudouin de Courtenay's studies was the determination of strictly synchronic laws. On the other, his phonological theory required the comparison of morphemes for the investigation of synchronic relations in the sound system of a language. But relations between morphemes had not yet been touched upon by synchronic analysis. Baudouin de Courtenay regarded the establishment of morphemic correspondences äs being justified only historically, etymologically. There were two ways out of this profound contradiction. One could either give up morphological criteria in phonology or rebuild the description of

1 Cf. Jakobson I960, Leont'ev 1959, 1961, Schogt 1966, Häusler 1968. 20 THE DEVELOPMENT ÖF MODELS IN PHONEMlCS morphemic structure on a synchronic base. Baudouin de Courtenay went both ways. But if the comparison of morpheme alternants in phonemic identification is rejected and morphemic units cannot be identified on etymological grounds, a new criterion is needed for each problem. The criterion chosen by Baudouin de Courtenay, under the influence of psychologism in the linguistics of his day, was the feeling of the native Speakers.2 This notion, which is not present in his 1881 publication, became the cornerstone of his later work. His new ideas are most fully expounded in Proba teorji alternacyj fönetycznych (l 894), which appeared in a revised German translation the next year. His definitions of the phoneme and the morpheme now ran äs follows (1895:9f.): Das Phonem = eine einheitliche, der phonetischen Welt angehörende Vorstellung, welche mittelst psychischer Verschmelzung der durch die Aussprache eines und desselben Lautes erhaltenen Ein- drücke in der Seele entsteht = psychischer Aequivalent des Sprachlautes. Mit der einheitlichen Vorstellung des Phonems verknüpft sich (associiert sich) eine gewisse Summe einzelner anthropo- phonischer Vorstellungen, welche einerseits Articulations-Vorstellungen, d.h. Vorstellungen voll- gezogener oder in Vollziehung begriffener physiologischer Articulationsarbeiten, anderererseits [sie] aber akustische Vorstellungen, d.h. Vorstellungen gehörter oder im Gehörtwerden begriffener Resultate jener physiologischer Arbeiten, sind. [...] Morphem = jeder, mit dem selbstständigen psychischen Leben versehene und von diesem Stand- punkte (d.h. von dem Standpunkte eines selbstständigen psychischen Lebens) aus weiter unteilbare Wortteil. Dieser Begriff umfasst also: Wurzel (radix), alle möglichen Affixe, wie Suffixe, Praefixe, als Exponenten syntaktischer Beziehungen dienende Endungen, u.s.w.

1.2. SiERBA

These were the foundations of the Petersburg/Leningrad school in linguistics. During the twenties and thirties of the present Century Baudouin de Courtenay's most prominent pupil, L.V. Scerba, dominated the linguistic scene in the Soviel Union. The inherited phonological theory remained basically unchanged in these years though the stress laid on the psychological Interpretation of the phoneme varied considerably. In 1912 Scerba emphasized the word-differentiating function of the phoneme, which Baudouin de Courtenay had stated äs early äs 1869 (Ivic 1965: 133). This criterion is a sufflcient one for establishing the number of phonemes in a given position but not for the assignment of variants in different positions to the respective phonemes. Following Scerba, sounds in complementary distribution should be identified according to their resemblance. This can mean two different things. Firstly, the feeling of the Speakers can be resorted to: this was Baudouin de Courtenay's solution, which came to be known in Soviet linguistics äs the 'subjective method'. It met with sharp criticism in the young Soviet state because it was regarded äs a manifestation of subjective idealism. Besides, it did not yield a solution in many instances. Some of Scerba's disciples considered the first vowel of Ru.

a Cf. Panov 1967: 371ff. and Ivic 1965:133f. RUSSIAN PHONEMIC THEORY BEFORE 1962 21 golova [gslavä] 'head' a variant of /a/, others identified it with /i/ (which has an unrounded back variant after hard consonants in both stressed and unstressed positions). And, äs Panov puts it (1967: 376), "if the first solution of the problem turns out to be more widespread, then it is only because it is supported by Scerba himself, the very authority on 'linguistic feeling' ". The charge of idealism made Scerba stop referring to the feeling of the Speakers, but it did not basically affect his ideas (1958: HOff.). The only criterion left for the identification of phonemes in different environments was phonetic resemblance. This criterion, characteristic of the so-called Objective method', did not solve the Problem just mentioned either, because [a] resembles any unrounded füll vowel equally well. So there was simply a change of labels. However, it made linguistic theory less vulnerable from the Marxist methodological point of view. At the same time it opened a way back to traditional phoneticism, and this largely explains the popularity of Scerba's ideas among phoneticians after the elimination of psychological formulations.

1.3. JAKOVLEV There were two ways of avoiding the Scylla of psychologism and the Charybdis of phoneticism. The first possibility was to return to Baudouin de Courtenay's earlier views and to take into account the alternations that morphemes show in juxtaposition with other morphemes. This was the standpoint of the eminent Caucasist N.F. Jakovlev, who äs a result became the forerunner of the Moscow school of phonology. As early äs the beginning of the twenties he remarked that the individual feeling of the Speaker can hardly serve äs a particularly reliable basis for phonemo- logical [sie] investigations, and in fact it is no such basis in the works of the followers of phoneme theory [...] one should regard [the phoneme] äs wholly conditioned by a definite correlation of phonetic and semantic elements with the lexicon and morphology of a given language (1923:66f.) and a fewyears later he actually defined the phoneme äs asetof alternating sounds in different positions (1928).3 Thus, the first vowel of Ru. voda [vadä] 'water' is to be identified with /o/ because of the plural vody [vodi], not with /a/ äs in Scerba's theory. He clearly realized the consequences of this approach: "physically absolutely identical sounds are sometimes different grammatical sounds, diiferent phonemes" (Jakovlev and Asxamaf 1941: 407). One cannot but wonder why the Moscow school of phonology did not come into existence ten years earlier than it actually did.

1.4. TRUBETZKOY The other way was found by the outstanding Russian linguist, N. S. Trubetzkoy (Trubeckoj), a member of the Prague Circle, who in Western Europe is generally 5 Reformatskij 197Q; 129f,, cf, Zinder 196$; J9<5, 22 THE DEVELOPMENT OF MODELS IN PHONEMICS regarded äs the founder of phonology. In bis opinion, the final consonant of Ru. prud 'prut] should neither be identified with /t/ on the basis of phonetic resemblance nor with /d/ on account of its alternation with [d] before case endings, because neither phonetic nor morphological criteria should be decisive in the identification of phonemic units. Word-final [t] is in fact not identical with prevocalic [t] because it is not opposed to [d], so from the functional point of view it lacks a feature which is inherent in /t/. On the other hand, prud is homophonous with prut, so these words cannot be phonologically distinct: the Opposition between /t/ and /d/ is 'neutralized' in word- final position. This insight, which was fundamentally inspired by de Saussure, necessarily leads to the postulation of a new unit, the 'archiphoneme' (Trubetzkoy 1939:70f.).4 The notions of 'neutralization' and 'archiphoneme' have given rise to a lot of confusion and misunderstanding which eventually prevented them from gaining general acceptance. At least three interpretations have to be distinguished. The most widespread misconception is stated by Panov in the following words (1967: 397): "N. S. Trubetzkoy and his fellow-Praguists were the founders of syntagmatic phonology". This was NOT what Trubetzkoy was primarily interested in, however. The cornerstone of his whole theory is the concept of distinctiveness, which is a paradigmatic relationship (in the sense of Hjelmslev 1943: 36) and has nothing to do with tactics. If Ru. word-final [t] cannot be identified with /t/, this is not because fd] does not occur in the same position (which is a tactical characteristic) but because the Substitution of the latter sound for the former cannot yield a change of meaning. Consonants are always hard before unstressed [a] in Russian, but it does not follow that the Opposition hard ~ soft is neutralized in this position, äs Panov suggests (1967: 400). The non-occurrence of soft consonants before unstressed [a] is a necessary but insufficient condition for the phonemic identification of the sequence C + [a]. In the present instance, the vowel is an archiphoneme, not the consonant, äs is clear from the fact that [ν'αζύ] is interpreted äs vjazu '(I) knit', not vozu '(I) carry, conduct', and [nan'asu] äs nanesu '(I) shall inflict', not na nosu On the nose'. The second common misconception regards the notion of neutralization. Strictly speaking, it is incorrect to say that the Opposition between the final consonants of the words prud and prut is neutralized. These words are homonyms ending in [t]. The fact that this sound alternates with [d] and [t] respectively before case endings is irrelevant äs to its phonemic identification. Neutralization is non-distinctiveness of phonemes in a certain environment and cannot be established merely on the basis of morphemic alternations. Trubetzkoy's Interpretation of tense o in Ru. [sonca] 'sun' äs /öl/ is not based on morphemic alternation, äs Panov suggests, but on the non-distinctiveness between [o] and [öl].5

4 "Tout le mecanisme du langage [...] repose sur des oppositions de ce genre et sur les differences phoniques et conceptuelles qu'elles impliquent" (Saussure 1916: 167). & Cf. Trubetzkoy 1939: 56 and Panov 1967:400. The identification holds no longer for contemporary Standard Russian, which has ordinary [o], cf. Avanesov and Ozegov 1960:553. RUSSIAN PHONEMIC THEORY BEFORE 1962 23 Finally, a sharp distinction should be made between neutralization and defective distribution. The initial clusters [vzt] and [fxt] do not occur in Russian, but not for the same reason: whereas a native Speaker easily identifies the formet cluster with [fst], the latter cannot on the basis of phonetic cues be identified with any cluster actually occurring in the language. Though [on vztal] is easily understood äs on vstal 'he got up', the string [on fxtal] is uninterpretable but for the presence of extralinguistic indications in the Situation. Obviously, the Opposition between voiced and voiceless fricatives is neutralized, while the Opposition between dental and velar fricatives is not: the phoneme /x/ simply does not occur in the position under consideration.

1.5. THE MOSCOW SCHOOL OF PHONOLOGY

Political circumstances often have an important impact on the development of linguistic science. The very fact that Trubetzkoy had left his native country made it possible for his ideas to spread all over Western Europe but isolated them from Russian linguistic thought. The Russian translation of Trubetzkoy's Grundzüge der Phänologie (1939), a book filled with subtle observations on his mother tongue, appeared only in 1960. On the other band, the Moscow school of phonology, to which belonged such important linguists äs R.I. Avanesov, V.N. Sidorov, A.A. Reformatskij, and P.S. Kuznecov, remained almost unnoticed in Western countries until the present time. The fundamental theses of this school are summarized by Zinder äs follows (1968: 197).6 1. It is necessary for the characterization of phonological oppositions to distinguish a strong Position (in which the maximum number of distinctions is operative) from a weak position (where neutralization is possible). 2. Distinction is made between the basic shape of a phoneme (appearing in strong position), variations, which are tactically conditioned modifications of a phoneme in positions where the oppositions to other phonemes are not neutralized, and variants, i.e. tactically conditioned modifications in the case of neutralization. A Variation is always related to one phoneme, a variant to two phonemes. 3. The make-up of a phoneme is revealed only in strong positions. 4. The fact that a sound occurring in a morpheme belongs to a given phoneme is also revealed only in strong position. 5. If a morpheme contains a sound that cannot be placed in strong position (e.g., the flrst vowel of the word korova [i.e. [karovs] 'cow']), this sound cannot be assigned to any particular phoneme; it is a member of a 'hyperphoneme', i.e. a group of phonemes which are connected by positional or combinatory alternations. Thus, alternating sounds in different positions are to be regarded äs variants of the same phoneme. As a consequence of this Identification principle, different sounds

6 In 1970 an interesting book by Reformatskij appeared: it contains not only an excellent exposition of the ideas and development of the Moscow school of phonology but also a reader in which all 'classical' papers of the school have been reprinted, e.g., Jakovlev 1928, Avanesov 1947,1948, 1955, Kuznecov 1941, 1948, 1958, 1959, Reformatskij 1941, 1955, 1957, 24 THE DEVELOPMENT OF MODELS IN PHONEMICS may represent the same phoneme and different phonemes the same sound. The identification is based on the comparison of morphemes. There are several difficulties connected with this approach. First of all, a position which is 'strong' with respect to one pair of phonemes is not necessarily so with respect to another pair of phonemes. In Dutch, the Opposition /a/ ~ /a/, which is operative in stressed syllables, is neutralized pretonically in disyllabic words, so the word banaan 'banana' can be pronounced either [banän] or [banän], or something half-way between (Cohen etc. 1961: 49). On the other hand, the Opposition /Λ/ ~ /a/ is restricted to unstressed closed syllables and neutralized under stress and in open unstressed syllables (Ebeling 1968: 141 f.). Another example of an Opposition which is neutralized under stress is found in Tajik (Panov 1967: 195fn.). In Dutch and English the phonemes /h/ and /n/ are in complementary distribution, so there is no 'strong position' in which the Opposition is operative. Secondly, the choice of the 'basic shape' of a phoneme is rather arbitrary. In Russian, there is [i] instead of [i] after hard consonants and [e] instead of [ε] before soft consonants (cf. Kortlandt forthcoming b, ms. p. 2). There is no objective reason for [i] or [ε] to be more basic than [i] or [e] respectively, however. It could be argued that the basic shape of a vowel is found between pauses, but several languages (e.g., Arabic, German, Kabardian) have been described äs having no word-initial vowels. Such a criterion does not yield a satisfactory solution for consonants either, since word-initial and word-final neutralizations are especially common. Neither do consonants display their 'basic shape' intervocalically in view of the fricativization of stops that many languages (e.g., Danish, Spanish, Tamil) show in this position. The distinction between 'variations' and 'variants' rests upon the criterion of distinctiveness, which is basically alien to a theory that advocates phonemic identification through the comparison of morpheme alternants. Thirdly, the concept of the hyperphoneme requires some comment. This concept is a hybrid result of two lines of thought. The positionally determined neutralization of an Opposition leads to the impossibility of assigning at least some sounds (like [a] in the example cited above) to a definite phoneme and therefore, if one does not want to make an arbitrary choice, it also leads to the postulation of a new kind of units. This is essentially the justification of Trubetzkoy's 'archiphonemes'. In the theory under discussion, however, phonemic identification should be conformed to morphemic alternation. From this point of view, the sound [a] in Ru. [karovs] is assigned to a 'hyperphoneme' because it does not ALTERNATE with either [a] or [o]. This is quite different from what Trubetzkoy did when he assigned it to an 'archiphoneme' /A/ because it is not DISTINGUISHED from these sounds, that is, it can be replaced by [a] or [o] without impairing the intellegibility of the linguistic sign. Whereas Trubetzkoy's identification is a direct consequence of the view of language äs a code, the Muscovite introduction of 'hyperphonemes' results from a choice concerning the things to be described. Now, there are two possibilities. If one distinguishes a sound [a] that does not show alternation with [a] or [o] from another [a] RUSSIAN PHONEMIC THEORY BEFORE 1962 25 that does, one should also distinguish an [o] that alternates with [a] from one that does not. Consequently, the four sets of sound alternants [ο, a, a], [o, a], [a, a], [a], which characterize the first vowel of the words voda 'water', doktor 'doctor', topor 'axe', saraj 'barn', respectively, are four diiferent phonemic entities (cf. Gvozdev 1958: 84f. and Halle 1963: 15). However, if one does not want to make such a distinction and combines [o, s] with [ο, a, 9] into one 'phoneme' , there is no reason not to identify both [a, s] and [a, a, s] with one and the same symbol . This is just a matter of simplicity since "the morphophonemic rules [...] will always select the appropriate phoneme [the author means sound] regardless of what other Symbols are added to those already included in the brackets" (Halle 1963: 15). In that case, the arbitrariness of the choice whether to include [a, s] in or in is wholly irrelevant because either solution yields the same results, and that is the only restraint simplicity-minded authors would impose. So the 'hyperphoneme' does not originate from a single conception: on the one band, it does not fully take into account the automatic alternations that exist in the language and therefore does not give complete Information about them; on the other, the Information which it does convey is redundant within the framework of a System of morphophonemic rules. It is not quite clear what Panov means when he writes (1967: 404): "When speaking about the links between the Moscow phonological school and Jakovlev's group it needs to be emphasized that the 'Muscovites' made a very big step forward: the doctrine of the neutralization of phonemes emerged".7

1.6. THE FIFTIES

The 1950's are marked by two important trends in Russian phonemic theory: the search for a synthesis between the ideas advocated by the Moscow and Leningrad phonological schools, and the penetration of Western structuralism into Soviet linguistics. The controversy about structuralism started in 1952, when an article by S.K. Saumjan appeared under the title 'The problem of the phoneme'. In this article, which was written under the influence of both Trubetzkoy's and Hjelmslev's ideas, Saumjan emphasized the "dual aspect of Speech sounds, their physical and functional aspects" (1952: 334, cf. Milivojevic 1970: 17). His main objection against Trubetzkoy's phonemic theory concerned the absence of a consistent differentiation between the phonemic and the phonetic level of language. This view led Saumjan to a strict distinction between the 'level of observation' and the 'level of constructs' in his later work (1960, 1962, 1965). But at the time that the article appeared, Soviet linguistics was not yet ready for a favorable discussion of structuralism and Saumjan's paper met with sharp criticism from all prominent Soviet linguists.8 The discussion 7 This remark is all the more surprising in view of Panov's judgment on Trubetzkoy: "Trubetzkoy's theory is not free from contradictions; the very core of this theory, the doctrine of the archiphoneme, is vulnerable" (Panov 1967:401). 8 Avanesov 1952, Reformatskij 1952, contributions by Bernätejn, Gvozdev, Panov, Zinder and pthers ir» the following issues of ftv 4 N SS§R ÖL Ja, 26 THE DEVELOPMENT OF MODELS IN PHONEMICS was renewed in 1956, when the Russians suddenly feit the necessity of 'catching up and overtaking the achievements of Western structuralism'. The synthesis of the view that the phoneme is the smallest phonic component of a morpheme and the view that it is the smallest phonic constituent of a word form could be achieved in three different ways. One could either restate the Moscow defmition of the phoneme in terms of the Leningrad phonological school or vice versa, or devise a new, 'neutral' terminology in which both kinds of phonemes would find their proper place. Avanesov chose the first possibility, Kuznecov the second, Bernstejn the third.9 So the 'Moscow' phoneme, which remained the only true phoneme in Kuznecov's opinion, changed into a 'phoneme series' (fonemnyj rjad) in Avanesov's new terminology and into a 'phoneme of the second degree' according to Bernstejn's proposal. The 'Leningrad' phoneme became Avanesov's 'phoneme', Bernstejn's 'phoneme of the first degree', and Kuznecov's 'language sound' (zvuk jazyka), which of course is to be carefully distinguished from both the same author's 'speech sound' (zvuk reci) and Bernstejn's 'language sound' (not to mention Bern- stejn's 'speech sound'). Moreover, Kuznecov's 'speech sound' Stands for at least two essentially different things (1959: 30f.): on the one band, "any utterance by any Speaker in any language [...] consists of some sequence of speech sounds" in the sense of tokens of sound types, and on the other "we can recognize and identify [...] one and the same infinitely repeated speech sound" in the sense of a type of 'speech sounds' in the previous sense. The latter entity is commonly called a 'variant', but this term is inappropriate for Kuznecov because it signifies something quite different in Moscow phonological tradition (see above). Bernstejn, however, states that "the positional modifications of one and the same phoneme of the first degree are called the 'variants' of the phoneme" and "a language sound is an articulatory-acoustic- auditory formation used in a given language äs a variant of some phoneme of the first degree", while 'speech sounds' are in his opinion elements from a universal phonetic classification of sounds (1962: 66f.). In addition to phonemes of the first degree and phonemes of the second degree, Bernstejn distinguishes phonemes of the third degree, i.e., series of phonemes that show non-automatic alternation such äs [k] ~ [c] in Ru. [rukä] 'band', [rucnoj] 'band (adj.)'. Thus, a phoneme of the first degree, which is also called a 'variational series', is a set of positionally determined variations in the 'Moscow' sense; a phoneme of the second degree, which is also called a 'substitutional series', is a set of automatically alternating variants in the 'Moscow' sense; and a phoneme of the third degree, which is also called a 'trans- formational series', is a set of grammatically alternating variants (Bernstejn 1962: 73).10 If Bernstejn's exposition of phonemic theory had been published 25 years earlier, äs it was originally intended to be, it would have saved Soviet linguistics a lot of vain discussion.

9 Avanesov 1955, 1956, Kuznecov 1959, Bernstejn 1962. Cf. also Klimov 1967:90. 10 Cf. Reformatskij 1955b: 99 and Bloomfield 1926:160f. RUSSIAN PHONEMIC THEORY BEFORE 1962 27 At the time when the controversy around the nature of the phoneme was dying a natural death, the Isolation of Russian linguistic thought from Western structuralism was finally ended. The Russian translations of Trubetzkoy's Grundzüge der Phänologie and Hjelmslev's Prolegomena to a theory oflanguage were published in 1960 and the translations of Chomsky's Syntactic structures and a number of papers by Jakobson and Halle appeared in 1962. Jakobson's binarism gave rise to discussion on the possibility of identifying distinctive features with their phonetic correlates.11 This was the background of Saumjan's two-level theory, which we shall examine in Chapter 2.

11 Kuznecov 1958, 1959, Piotrovskij 1960, 1963, Reformatskij 1961, Ivanov 1961, 1962, Nork etc. 1962, Kibrik 1962, Grigor'ev 1962, 1964, 1967. 2

SAUMJAN'S TWO-LEVEL MODEL

2.1. INTRODUCTION

The year 1962 was, in a sense, a milestone in Soviel linguistics. Not only Bernstejn's article, which finally put an end to the discussion between the Moscow and Leningrad schools of phonology, but also the first two books of the new, mathematically oriented trend: I.I. Revzin's Models of language and S.K. Saumjan's Problems of theoretical phonology, were published in 1962. Since both of these important contributions to modern linguistics have been translated into English (the former in 1966, the latter in 1968), quotations will be made from the translations. This chapter is devoted to Saumjan's two-level theory. Revzin's ideas, äs far äs they directly concern phonemic theory, will be dealt with in the subsequent chapter, in which other set-theoretical models are also put under examination. An outline of Saumjan's theory had been published in 1960 in the fifth issue of Voprosy jazykoznanija, so when two years later the füll exposition of the theory appeared it did not entirely come äs a surprise. In fact, its main tenet, the complete Separation of the functional from the physical aspect of Speech sounds, is no more than the ultimate consequence of the view put forward in Saumjan's 1952 paper on the phoneme and goes back directly to Hjelmslev's ideas. The theory is presented äs a critique and, at the same time, äs a further elaboration of Trubetzlcoy's phonology, which Saumjan calls the 'relational-physical theory of the phoneme' (relja- cionno-fiziceskaja teorija fonemy). This name is based on Trubetzkoy's definition of phonological oppositions, which is reformulated by Saumjan äs follows: "phonological oppositions are these sound oppositions which can differentiate between the signifiants of two words of a given language" (1968:23f.). So phonological oppositions are sound oppositions, i.e., oppositions between physical entities. However, the property that makes sound oppositions phonological is their ability to differentiate between the signifiants of two words, i.e., refers to a relation within the System of the language. A member of a phonological Opposition is a 'phonological unit'. A phonological unit which from the standpoint of a given language cannot be further segmented into smaller consecutive phonological units is a 'phoneme' (1968: 32). This System of definitions "should be regarded äs a System of hypotheses whose function is to explain the principle of the invarjanee of sounds in any lan- SAUMJAN's TWO-LEVEL MODEL 29 guage" (1968: 33). Such a System of definitions which can be regarded äs a System of hypotheses about observable phenomena is what I will henceforth call a MODEL.1

2.2. THE ANTINOMY OF TRANSPOSITION

From the model outlined here two Statements evolve (Saumjan 1968: 35): (1) Phonemes are elements whose function is to differentiate between signifiants. (2) Phonemes are acoustic elements. The first Statement leads Saumjan to the following conclusion: If it is true that the function of phonemes is to differentiate between signifiants then it follows that there exists an inherent possibility of transposing the acoustic substance into other forms of physical substance — graphic, chromatic, tactile. Any System of distinctive features and phonemes can be presented not only äs acoustic properties but äs graphic, chromatic or tactile Symbols äs well. However, "if it is true that phonemes are acoustic elements it follows that they cannot be transposed into other forms of physical substance since in that case they would cease to be themselves, i.e. acoustic elements" (1968:36). According to Saumjan, the resulting contradiction, which he calls the 'antinomy of transposition', constitutes an inherent theoretical difficulty in Trubetzkoy's model of the phoneme. The reasoning is clearly incorrect. If we substitute 'green table' for 'phonemes', 'thing' for 'elements', and 'colour' for 'function', we obtain something like this: (1) A green table is a thing whose colour is green. (2) A green table is a table. If it is true that the colour of a green table is green then it follows that there exists an inherent possibility of transposing its table-ness into other forms of thing-ness. However, if it is true that a green table is a table it follows that it cannot be transposed into other things since in that case it would cease to be a table. Analogy is a bad argument and I am no supporter of the kind of debating exhibited in the preceding paragraph, but it certainly shows that a bit of superficial logic does not make up for the lack of explicitness with regard to the underlying assumptions. Saumjan's reasoning would hold true if the first Statement were reversible, but that is clearly not the case if the second Statement holds. In principle, there is nothing against defining phonemes äs acoustic elements whose function is to differentiate between signifiants. It just does not touch upon the real problem, which is IDENTIFICATIONAL. And it is with respect to the identification of phonemic units that different 'schools' propose different Solutions. Now, there are several questions to be answered. First of all, one may wonder whether justice is done to Trubetzkoy in the model that Saumjan ascribes to him. In fact, Trubetzkoy defines the phoneme NOT äs an entity possessing both physical 1 Saumjan does not mention the concept of 'model' in this connection but his use of the term elsewhere in his book (1968) does not seem to contradict the paraphrase given here, cf. the discussion on modellin g in Chapter 7 of this book. 30 THE DEVELOPMENT OF MODELS IN PHONEMICS and functional properties but äs "die Gesamtheit der phonologisch relevanten Eigen- schaften eines Lautgebildes" (1939: 35), i.e., a purely functional entity. His identification rules, however, refer to physical rather than functional phenomena, and this is where a confusion of levels arises. So even if Saumjan's argument against an admittedly fundamental inconsistency in a Statement concerning the NATURE of a defined concept — a Statement which is incorrectly attributed to Trubetzkoy — is based on an elementary logical error, it does point to a possible contradiction between the definition of the concept — which is an abstraction in the sense that it requires at least some generalization from directly observed data — and the IDENTIFICATION rules that make entities in reality correspond to the concept in a definite way. Every- thing is mixed up, but the spirit of Saumjan's criticism is basically right with reference to the spirit of Trubetzkoy's theory. Secondly, Saumjan does not overlook the objection that if phonemes are elements whose function is to differentiate between signifiants and, at the same time, acoustic elements, then the property of the differentiation between signifiants and the property of being an acoustic element are equally essential for the phoneme and the bond between these two properties must be considered indispensable within the limits of natural languages. Therefore, we are not justified in deducing from Statement l that the phoneme can be transposed from acoustic substance into other forms of physical substance. (1968:36) Since Saumjan's method of refuting this view is characteristic of the nonchalance that many contetnporary linguists show in referring to logic äs the sole basis of all trustworthy insight, I cannot resist the temptation of quoting his observations in füll. It must be noted beforehand that "a mental experiment is a deductive process which consists of the deduction of specific consequences from Statements acknowledged to be true which, although not confirmedly empirical facts, appear to be fundamentally possible" (1968:31). This is Saumjan's comment on the view expounded above. This objection can be answered äs follows. If we regard definitions äs convenient compressed descriptions of directly observed data then, since in natural languages phonemes are always sound elements, we are not justified in separating the functional properties of the phoneme from its acoustic properties. But the subject matter of science comprises not only empirical data, not only what is but also that which in principle can be; hence, if a mental experiment arrives at what can be, we disclose the essence of the studied subject. We regard the definition of the phoneme not äs a convenient compressed description of an empirical fact but äs a hypothesis, i.e. speaking in the words of H. Reichenbach, äs a nomological Statement. "In a general nomological Statement the ränge of the all-operator is given by all possible argument-objects and is not restricted to all real argument-objects." (Reichenbach 1947:401) The antinomy of transposition develops specifically at the level of the Interpretation of the relational-physical definition of the phoneme äs a nomological Statement. At this level there exists the question whether the communicative function of natural language would be violated if its acoustic substance were transposed into other forms of physical substance. Obviously, no such violation would occur. We are, therefore, justified in transposing phonemes, by means of mental experiment, from acoustic substances into other forms of physical substance. The results of the mental experiment contradict, however, the Interpretation of the acoustic properties äs the essential properties of the SAUMJAN'S TWO-LEVEL MODEL 31 phoneme, since if the acoustic properties are essential properties of the phoneme the phoneme cannot be transposed from an acoustical substance into any other form of physical substance. So if the definition of the phoneme is a description of directly observed data, the phoneme has both functional and acoustic properties. But if we take into account not only empirical facts but everything which is fundamentally possible, äs science should, the definition of the phoneme is a hypothesis or — even better — a nomological Statement. This gives us the chance to drop in at Reichenbach's, quietly aband- oning one of the two essential properties of the phoneme. The only question left after we have passed the heights of logic is "whether the communicative function of natural language would be violated if its acoustic substance [sc., of the phoneme] were transposed into other forms of physical substance". This is exactly what we have seen before, but the tail of the argument is nevertheless formulated with pain- staking care. Such a reasoning unduly discredits logic in the eyes of linguists and linguistics in the eyes of logicians. I should be noticed that all this is not an argument against Saumjan's two-level theory. I merely want to stress that there is no LOGICAL justification for this model of the phoneme.

2.3. THE IDENTIFICATION ANTINOMIES

Thirdly, one may wonder if the identification rules should reflect the physical and the functional aspect of speech sounds to the same extent. This is where the real difficulty is encountered. Sameness on the functional level need not coincide with sameness on the physical level. Saumjan Signals the existence of two identification antinomies, of which the first regards the 'paradigmatic' and the second the 'syntagmatic' identification of phonemes. These terms are explained äs follows (1968: 37): Every language differentiates two basic types of relations: paradigmatic and syntagmatic. Paradigmatic relations are relations of linguistic units which undergo a mutual alternation within the same position. Syntagmatic relations are linear relations between linguistic units within the speech flow. This is in conformity with general usage in modern linguistics.2 Saumjan points out correctly that the two kinds of relations do not, however, correspond to disjunction and conjunction in logic, äs Hjelmslev suggested. If two linguistic units can occur in the same position, a choice between them (and, possibly, other admissible units) is to be made in every occurrence of that position, so that the units are necessarily mutually exclusive: "the specific character of the paradigmatic relations precludes the coexistence of the members of the relations [...] Therefore, the paradigmatic relations can be analogous only to the so-called exclusive disjunction" (1968: 39). The digression on Hjelmslev's views makes it all the more striking that the meaning of the word 'paradigmatic' in Saumjan's 'antinomy of the paradigmatic identification of phonemes' is quite different from the one outlined here: it corresponds instead to 2 Cf. Martinet 1960:27 and Hjelmslev 1943:36. 32 THE DEVELOPMENT OF MODELS IN PHONEMlCS the traditional meaning of the word 'paradigm' in the sense of a set of word forms representing the same lexical item in its various syntactic environments, such äs, e.g., Skt. {devas, devam, devena, deväya, devät, devasya, deve, deva}. The 'antinomy' runs äs follows (1968: 40): If in the speech flow in Position PI we encounter a class of phonemes KI, then in position T?z there exists a class öl phonemes K2, which corresponds to the class of phonemes KI in such a way that the phonemes which differ in respect to their phonation are in identical correspondence while those phonemes which are identical in respect to their phonation are in non-identical correspondence. Thus, if we encounter [q], [k], [k'] before back vowels and [k], [k'], [c] before front vowels, functional identity does not coincide with acoustic identity. There is, however, one possible Identification which Saumjan does not take into consideration, though it violates neither the functional nor the physical properties of the phoneme. He writes: if, in accordance to Statement l [see above], phonemes possess a function of differentiation between signifiants, then phonemes which occur in different positions can be altered in respect to their phonation äs sharply äs desired äs long äs they do not get confused with one another. (1968:41) According to this view, one could, strictly speaking, regard any pair of sounds äs variants of one and the same phoneme provided only that they are in complementary distribution: thus [q] in position PI can be identified with [c] in position P2, and subsequently [k] and [k'] can be identified in accordance with their acoustic properties. It follows that Saumjan's antinomy cannot be logically derived from his Statements l and 2 alone, but that it rests upon an additional assumption concerning the mutual relations between phonemes äs well. This does not diminish the value of his argument because such an assumption is explicitly present in Trubetzkoy's work. The identification of phonemic units in different positions äs discussed in the preceding paragraph presupposes their paradigmatic and syntagmatic delimitation in any one environment. Here 'paradigmatic' is again used in the Hjelmslev sense of 'referring to equally admissible but mutually exclusive alternatives'. Within the relational-physical theory of the phoneme, two antinomies concerning the paradigmatic (in this sense) and syntagmatic delimitation of phonemes can be inferred. Saumjan mentions only the latter of these and calls it the 'antinomy of the syntagmatic identification of phonemes'. The former is wholly analogous to Saumjan's 'antinomy of the paradigmatic Identification of phonemes' except for the positional difFerence between the sounds involved: even in one and the same position it holds true that phonetically different sounds may be functionally identical and phonetically identical sounds may not be functionally equivalent. The first possibility is generally called 'free Variation'. Such a relationship holds between, e.g., apical r and uvular r in Dutch. The second possibility is no less common though rarely referred to in publications on THEORETICAL linguistics. This is the relationship between, e.g., e and ζ in Polish. The [e] in Po. [bjore] Ί take' and many other words can be replaced by [e] SAUMJAN'S TWO-LEVEL MODEL 33 without affecting the meaning of the word, while the same Substitution of the [e] in [xore] 'sick (nom.pl., no male persons)' and many other words yields a non-existing form.3 So these two phonetically and positionally identical sounds are nevertheless functionally different. The 'antinomy of the syntagmatic identification of phonemes' consists in the fact that on the one band phonetic sequences made up of e.g. stop + spirant or vowel + semivowel such äs [ts] or [ej] are in some languages interpreted monophonemically, cf. Ru. /c/ and Du. /e/, while on the other fairly homogeneous sounds may in some languages be identified with sequences of phonemes, like Du. [s] f- /sj/ or Sw. [d] l- /rd/.4 It is not clear whether Saumjan acknowledges the latter possibility because he discusses only the former. This antinomy again rests upoji an additional assumption, namely that there exists a natural segmentation of the speech flow into sounds which does not coincide with the segmentation into phonemes. According to Saumjan, "physical segmentation of the speech flow into separate sounds, i.e., into separate acoustic Segments, is an objectively ascertained phonetic fact" (1968:42).5 In that case a sequence of acoustic segments can, in principle, constitute a single phoneme.

2.4. SAUMJAN'S DEFINITION OF THE PHONEME The 'three fundamental theoretical difficulties' which Saumjan signalizes in the relational-physical theory of the phoneme and which he calls the 'antinomy of transposition', the 'antinomy of the paradigmatic identification of phonemes', and the 'antinomy of the syntagmatic identification of phonemes' lead him to a strict distinction between the level of observation and the level of constructs. The relationship that holds between 'sounds', which are directly observable entities, and 'phonemes', which are constructs, is termed the relation of 'embodiment' (voploscenie), denoted by the symbol /. The fact that the sound segment [ts] embodies the phoneme /c/ in Spanish is denoted äs follows (Saumjan 1968: 50): I(tS, "c") (2.1) In German, however, the sound segment [ts] embodies the phonemic sequence /ts/: / (i, "t"} (2.2) Ι(!,αη (2.3) This notation is equivalent to the one defined in footnote 4 of this chapter, and will be used throughout the present book: Sp. [ts] H /c/ (2.4) Ge. [ts] μ /ts/ (2.5) 3 Ebeling 1967:134f., cf. Chapter 9 of this book. 4 Cf. also Trubetzkoy's discussion of tense o in Ru. solnce, section 1.4. The symbol 'l-' Stands for 'is identified äs' or 'is the realization of, cf. Kortlandt, forthcoming d, and Stokhof 1972. 5 Here Saumjan refers to Fant 1960:21-24. 34 THE DEVELOPMENT OF MODELS IN PHONEMICS Then follows a discussion of Saumjan's own views on defining the phoneme (1968:51). Since this passage raises a number of questions I shall quote it in füll. In our theory phoneme is regarded äs a primary, undefinable concept. By the same token we also introduce the concepts of paradigmatic oppositions and syntagmatic oppositions äs primary, undefinable concepts. Both these oppositions we also rank among constructs. Phonemes are subject to the following rule: every phoneme must be in Opposition to at least one phoneme on the paradigmatic axis and to at least one phoneme on the syntagmatic axis. At the level of observation phonemes are embodied in sounds, and oppositions are embodied in contrasts which are established through an analysis of the informant's deposition. A definition of the phoneme äs a construct can be expressed in the language of symbolic logic thus:

P =fl/ (x)(ly)[S(x).S(y-).C(x,y) => I(x,P)}, (2.6) where P denotes the phoneme, S the sound segment, C relationship of contrast established on the basis of the informant's deposition, and / relationship of embodiment. Before the square brackets there occur the Symbols of quantifiers which are generally accepted in modern symbolic logic: the symbol (x) which Stands for "given any x" is a universal quantifier; the symbol (3χ) which Stands for "there exists at least one y such that" is an existential quantifier. This formula which is the correspondence rule between the construct 'phoneme' and the level of observation should be read äs follows: if x is a sound segment and is in relation of contrast to at least one sound segment y, then x is in relation of embodiment to the phoneme P. Though the phoneme "is regarded äs a primary, undefinable concept" its definition "can be expressed in the language of symbolic logic". On the other hand, the definition of the phoneme "is the correspondence rule between the construct 'phoneme' and the level of observation". Actually, it is not quite clear what the formula really Stands for. Since the symbol P occurs in both the definiendum and the definiens it cannot be the defined concept itself. The symbol P on the left side of the equality sign may stand for "P is a phoneme", but in that case it is not clear in what respect the phoneme P differs from any other phoneme because the variable x is bound by the universal quantifier.6 However, the main objection that can be made against the formula consists in the fact that it does not reflect Saumjan's own 'rules of correspondence for the paradigmatic and syntagmatic identification of phonemes' which will be discussed below. In fact, the expression on the right side of the equality sign can be viewed äs an unduly simplified minimal-pair identification rule: any sound segment x which can be contrasted with at least one sound segment y has some phonemic identity. Neither the paradigmatic and syntagmatic delimitation of phonemic units, nor the identification of units in different positions, are touched upon.7 The former component of Saumjan's assertion that "every phoneme must be in Opposition to at least one phoneme on the paradigmatic axis and to at least one phoneme on the syntagmatic axis" is a more precise formulation of the Statement contained in his formula, while the latter component is an unwarranted assumption about phonemic distribution because there exist in many languages words consisting

6 Cf. Reichenbach 1947:88, Tarski 1965:12. 7 Cf. in this connection the critical remarks in Leska 1966. SAUMJAN'S TWOLEVEL MODEL 35 of a single phoneme, such äs Fr. eau /o/ 'water', Sw. a 'river', Dan. 0 'island', Tu. o 'he, she, that'. Thus, the main probleras remain open: the paradigmatic and syntagmatic delimitation of phonemes depends on the effective Interpretation of the Symbols C and S, and the identity of phonemes in different positions depends on the nature of the phoneme, which so far remains unclear except for the fact that it is not a directly observable entity.

2.5. THE OPERATOR METHOD OF THE PARADIGMATIC IDENTIFICATION OF PHONEMES

The principle of identification put forward by Saumjan is what he calls the Operator method'. This method should be used in both the paradigmatic and the syntagmatic identification of phonemes. The identification procedures, which are fully described in the second chapter of Saumjan 1968, are regarded äs 'rules of correspondence' between the level of constructs and the level of observation (1968: 113):8 Operations which enable us to determine the substrata of identical or different phonsmes on the paradigmatic axes, and the substrata of one or two phonemes on the syntagmatic axis, are, in principle, nothing eise but correspondence rules which facilitate identification of phonemes in sounds which embody them. Saumjan's 'paradigmatic identification of phonemes' involves the following operations(1968: 114): (1) selection of a Standard, (2) establishment of homogeneous sets of sounds, (3) measurernent of the action of positional operators, (4) establishment of paired sounds. The application of these operations is clarified with the help of an example, the Russian vowel System under stress. There are five vowels in this position: [a], [ε] (which is closed [e] before soft consonants), [i] (which is back unrounded [i] after hard consonants), [o], and [u]. All vowels undergo an articulatory shift forward and upward in the final phase of their articulation before soft consonants, idem in the initial phase of their articulation after soft consonants, and during the entire duration of their articulation if they stand between soft consonants.9 As a Standard Saumjan selects the set of sounds with a minimal palatal shading: Mi = {[a], [t·], [i], [o], [u]}. The position in which these sounds are found in Opposition to each other is designated by the symbol Pi. Other 'homogeneous' sets of sounds are labeled M%, which comprises the sounds with a palatal shading in the terminal phase of their duration, occurring in position P% (— before soft consonants), Ms, which comprises the sounds with a palatal shading in the initial phase of their duration, occurring in position PS

8 The translation is incorrect: the Russian text speaks of correspondence rules by means of which (blagodarja kotorym) phonemes are identified (Saumjan 1962:91). 9 Cf. Avanesov 1956b:95f., Kortlandt, forthcoming b, ms. p. 2. 36 THE DEVELOPMENT OP MODELS IN PHONEMICS (= after soft consonants), and M i, which comprises the sounds with a palatal shading over the entire Segment of their duration, occurring in position P i (= between soft consonants). These sets of sounds are called 'homogeneous' because the difference between them and the Standard is attributed to the influence of the same positional conditions. According to Saumjan, comparing various sets of vowels and consonants in various positions, we can always reduce the sets of vowels to a single set of vowels (Standard set of vowels), and the sets of consonants to a single set of consonants (Standard set of consonants). Sets of vowels and sets of consonants cannot be mutually reduced since the differences between vowels and consonants are not dependent on positional conditions. (1968:115)

Thus, Saumjan explicitly denies the possibility that, e.g., [i] and [j] belong to the same phoneme even if the choice between these two sounds is positionally determined. On the other hand, Saumjan admits that within the System of vowels or the system of consonants the difference between sounds in complementary distribution cannot always be attributed to the positions in which they occur, e.g., the difference between Ge. Du. Eng. [h] and [rj], so the Standard set does not necessarily coincide with the set of sounds actually occurring in some well-defined position. This makes the rules for the selection of a Standard all the more arbitrary. The effect of the operators in the above example is the degree of palatali/ation exhibited by vowels in different positions. Operator PI induces minimal palatalization and operator P$ induces maximal palatalization. However, the operators P% and Pz differ not äs to the degree, but äs to the placement of their palatalization: the set of vowels Mz in position Pz and the set of vowels M3 in position PS differ not in respect to the degree of palatalization but in respect to the fact that the set of vowels MZ has a palatal shading in the terminal phase of its duration while the set of vowels Ma has a palatal shading in the initial phase of its duration. (1968:117)

So the relation of the degree of palatalization represents a partial order. The establishment of paired sounds is based on Saumjan's 'law of reduction', which is formulated äs follows: "if a given set of sounds Mi is taken äs a Standard, then for every sound ai of this set one can find a corresponding sound O) of the set Mj, whose difference from the sound

2.6. CRITICISM

The Identification procedure outlined here contains several weak points which may call forth various kinds of criticism. First of all, the selection of a Standard is arbitrary. The idea of having a Standard goes back to the Moscow school of phonology, which made a distinction between the 'basic shape of a phoneme' and its 'variations' and 'variants' (cf. Chapter 1). The same objections that have been put forward against this distinction can be raised against Saumjan's 'Standard'. There is, e.g., the possibility that an Opposition which is operative in one position is neutralized in another while the distinctiveness of another Opposition may be restricted to the latter position (cf. Dutch /a/ ~ /«/ which is neutralized pretonically in disyllabic words and /Λ/ ~ /9/ which is neutralized under stress and in open unstressed syllables); or phonemes may happen to be in complementary distribution so that they are never encountered in Opposition to each other, like Ge. Du. Eng. /h/ and /n/. In Saumjan's example the sound [i] is chosen äs the Standard unrounded closed vowel because it occurs between hard consonants. Intuitively, however, it would be more natural to select the sound [i], which occurs word-initially and after soft consonants, äs the Standard and to regard the variant [i] äs resulting from the influence of a positional operator, which is the preceding hard consonant. This is, essentially, the treatment proposed in Lomtev 1962. According to Lomtev, the Standard variant of a vowel is the one used in Isolation. Back vowels (a, o, u) undergo a shift forward and upward in juxtaposition with soft consonants, while front vowels (i, e) undergo a shift backward under the influence of juxtaposed hard consonants. In fact, I see no reason why one could not take one more step and regard ANY actually occurring sound äs the realization of a phoneme acted upon by a positional operator: in that case, there is no need for a basic variant. The Standard can be postulated on the level of constructs without specifying the articulatory or acoustic characteristics of its physical correlates. Homogeneous sets of sounds arc established. According to Saumjan, "the criterion of homogeneity should be the dependence of sound changes on the influence of positional conditions" (1968: 114). But the 'measurement of the action of positional operators', which models the influence of positional conditions, is based on the comparison of homogeneous sets of sounds. This clearly is a vicious circle. It would be correct to call 'homogeneous' a set containing the sounds which occur in a fixed Position. Then one can advance the hypothesis that the differences between homogeneous sound sets can be described in terms of positional operators. It is not clear to me why vowels and consonants cannot, in Saumjan's opinion, belong to one 38 THE DEVELOPMENT OF MODELS IN PHONEMICS homogeneous set of sounds though the existence of such minimal pairs äs e.g. Ru. [vasknsenjs] 'Sunday', [vaskfisentia] 'resurrection', where [i] is automatic, points to the presence of an ordinary Opposition /i/ ~ /j/. Elsewhere I have argued that Sp. [i] and [j] are realizations of the same phoneme because the choice between them can be described in terms of surrounding phonemes, morpheme junctures and place of stress (Kortlandt, forthcoming a, ms. p. 6). Such a description is unacceptable in Saumjan's two-level theory because vowels and consonants "cannot be mutually reduced". The concept of 'positional operator' reflects a principle which is not at all new in linguistics. As a matter of fact, it has been one of the most populär descriptive devices ever since the Junggrammatiker, especially in historical linguistics. In contemporary synchronic studies it is, though hardly ever absent, not always referred to explicitly. An explicit Statement is found, e.g., in Martinet's discussion of Span- ish /c/: On pourrait etre tente de considerer le [s] du groupe [ts] comme une Variante combinatoire de i dont l'articulation castillane est assez voisine. Mais il faudrait pour cela que le voisinage de [t] justifle le caractere proprement chuintant de [s], caractere qui le distingue de [s], ce qui n'est pas le cas. (1939:97) I believe that one of the important merits of Saumjan's theory is that this principle, according to which the positional variants of a phoneme should be justified by the phonetic characteristics of their environment in the speech flow, has finally been put forward with such consistency. The requirement in bis theory that a set of phonemes in Opposition to each other should display a similar shift between different positions replaces Trubetzkoy's requirement that the variants of one phoneme in different positions should be characterized by identical oppositions to other phonemes. However, I do not think that Saumjan's Operator method' can be applied more successfully than the identification principle based on the analysis of distinctive features. There are two kinds of argument in favour of this view (cf. Kortlandt, forthcoming a). Firstly, the reference to directly observable phonetic characteristics in order to establish the relation of identity between constructs is, in my opinion at least, strikingly contrary to the whole spirit of the two-level theory. It simply does not make sense to first plead for a sharp distinction between the physical and the functional characteristics of speech sounds and then to identify the functional units on the basis of the physical characteristics of their phonetic substrata without any regard to their function within the System of the language. Secondly, it is not always easy to determine to what extent the position of a phoneme should justify its phonetic realization.10 The following rules can be stated for the Standard pronunciation of modern Russian :u (1) Dental consonants are palatalized by a following soft labial consonant, e.g., zmeja [zmiiä] 'snake'. 10 Cf. Reformatsldj 1957, Gvozdev 1957. II Cf. Panov 1967:92-96 and Kortlandt, forthcoming b, ms. p. 5. SAUMJAN'S TWO-LEVEL MODEL 39 (2) Labial consonants are hard before a soft dental consonant, e.g., ptica [pfitsa] 'bird'. Both rules can be formulated in terms of positional operators. The assimilation stated in the first rule is wholly analogous to the influence that soft consonants exert upon juxtaposed vowels. The second rule, which is a corollary of the fact that soft labials do not occur before any consonant except [j], can be traced to a dissimi- latory operator inherent in the following consonant. However, the action of these two operators is clearly opposite and the difference in the final result cannot reason- ably be explained from the labial or dental character of the sounds involved. If the concept of positional operator is meant to be more than a convenient device for the description of phonotactics, certain specifications should be made about the correspondence between such operators and the observed facts of the language. The establishment of paired sounds is based on Saumjan's 'law of reduction' formulated above. This law is a fallacy: it is simply not true that "for every sound ai of this set [= the Standard set Mi] one can find a corresponding sound a] of the set MJ whose difference from the sound 04 can be attributed solely to the action of the positional operator P/' because, äs we have seen above, phonemes may be in complementary distribution. In that case one cannot find such a correspondence per definitionem: if, e.g., /h/ and /η/ are in complementary distribution one can neither find a sound corresponding to /h/ in a position where /n/ occurs nor find a correspondent of/η/ in a position where /h/ occurs. The same diificulty is encountered in other cases of defective distribution. The objection can be eliminated by adding to any homogeneous set of sounds a number of non-occurring variants of defectively distributed phonemes. This is not äs queer äs it may seem: such a procedure is wholly in accordance with Saumjan's 'mental experiment', which is advocated for the verification of positional operators äs well. But even if the 'law of reduction' is by this means made to be true it does not remove the main problem because it is not reversible. The main problem arises not from DEFECTIVE DISTRIBUTION but from NEUTRALIZATION. The fact that e.g. Russian word-final stops and spirants are voiceless can be attributed to the action of an unvoicing positional operator. In that case voiced and voiceless Standard sounds have the same correspondents in word-final Position, so there can be no transitive relation of identity between couples of paired sounds. This is where different phonological schools propose different Solutions. It turns out that Saumjan does not propose any solution at all.

2.7. SOCIAL AND INDIVIDUAL VARIANTS

The Operator method' is also used by Saumjan for the description of social and individual variants. In such cases the 'normal pronunciation' is selected äs a Standard and the deviation from this norm is attributed to the action of 'contextual operators', which reflect the social, dialectic, stylistic and individual conditions that influence the pronunciation of sounds. 40 THE DEVELOPMENT OF MODELS IN PHONEMICS Thus, in French the uvular pronunciation of the sound r is the norm; however, there exists likewise an apico-dental pronunciation of r which represents a dialectal deviation from the literary norm. Hence, in French the difference between the uvular and the apico-dental r is determined by the location of the Speakers in relation to the literary norm of the language. [...] In Russian, side by side with the normal explosive pronunciation of the sound g there exists a fricative pronunciation of this sound. The contextual operator of the fricative pronunciation is the afflliation of the Speakers with deflnite dialectal areas of the Russian language. (1968:120f.) The establishment of paired sounds that belong to different contexts is wholly analogous to the establishment of paired sounds in different positions.

2.8. THE OPERATOR METHOD OF THE SYNTAGMATIC IDENTIFICATION OF PHONEMES

In Saumjan's paradigmatic identification of phonemes sounds are regarded äs operands which undergo a change äs a result of the action of positional operators. Within the Speech flow, juxtaposed sounds can themselves be regarded äs operators acting upon each other. This is the basis of Saumjan's syntagmatic identification of phonemes. If one of two juxtaposed sounds is eliminable, this sound is considered to be the operator, while the ineliminable sound is the Operand.12 If both sounds are eliminable, they represent mutual operators. Mutual operators are called bilateral if they can be interchanged and unilateral if they cannot. After the introduction of these concepts Saumjan states the following rules (1968: 129): (1) If the chain AB is indivisible, or if only one of its elements, A or B, is the operator, the chain is a physical substratum of one phoneme "X". (2) If the elements A and B of the chain AB are bilateral mutual operators, A is a physical substratum of the phoneme "A", while B is the physical substratum of the phoneme "B". (3) If the elements A and B of the chain AB are unilateral mutual operators then, depending on the structure of the phonological System of the given language, AB can be interpreted either äs a physical substratum of one phoneme "X", or äs a physical substratum of two phonemes, "A" and "B", The example adduced by Saumjan is the sound chain [ts]. In Spanish the occlusive element is ineliminable, so the complex should be interpreted äs a physical substratum of a single phoneme /c/. In German both elements of the chain can be eliminated, cf. Kutschen 'carriages', Kutten 'cowls', kuschen 'to lie down (about a dog)'. Here [t] and [s] are bilateral mutual operators because the chain [st] occurs äs well, e.g., in the word Stand [stant] 'position, stand', so they are the physical substrata of two phonemes: /t/ and /s/. In English both elements of the chain can also be eliminated, cf. chop [tsop], top [top], shop [sop], but "since in this language the chain st is fundamentally inadmissible, the elements t and s represent unilateral mutual operators" (1968: 130). Saumjan identifies Eng. [ts] äs the physical substratum of a

12 In this connection I must point out an annoying misprint on p. 129 of Saumjan's book (1968). The first two lines of this page should read: "If A is ineliminable and B is eliminable, theq A is the Operand and B is the operator," SAUMJAN'S TWO-LEVEL MODEL 41 single phoneme /c/ because the voiced counterpart of this aifricate cannot be interpreted biphonemically (cf. Martinet 1939: 99).

2.9. CRITICISM Various objections can be raised against this identification procedure. Some of them have already been mentioned in connection with other aspects of the problems involved. To begin with, the reference to phonetic reality for the identification of functional unHs is contrary to the basic idea of the two-level theory. If phonemes are constructs, their identily should be inferred from their mutual relations, not from the occurrence or non-occurrence of certain phonetic sound chains. Secondly, the identification procedure presupposes that there exists a natural segmentation of the speech flow into separate sounds. Both the existence and the relevance of such a segmentation are open to serious doubt. Thirdly, if we assume for a moment that we have found an acceptable segmentation of the speech flow into sounds, the identification procedure deals only with the conditions for uniting two successive phonetic segments into one phoneme, not with the possibility of interpreting a more or less homogeneous sound biphonemically.13 This is a one-sided phonetic restriction on phonemic identification, which is in my opinion unwarranted. I have to admit that it is not clear to nie whether Saumjan really precludes the possibility of identifying a single speech sound biphonemically because there is a passage in his book where he seems to leave the question open (1968: 138): Since the question of element permutation becomes meaningless in respect to a complex of simultaneous physical properties, these complexes resemble sound chains which do not permit permutation of elements. If this is the case, complexes of simultaneous physical properties, similarly äs sound chains which do not permit permutation, can be interpreted, depending on the phonological structure of the given language, in some cases äs substrata of two phonemes and in other cases äs substrata of a single phoneme. Apart from these general considerations, the three rules stated above are subject to specific criticism. Strictly speaking, no sound is eliminable because there is always some influence on the pronunciation of neighbouring sounds, so the sounds acted upon never exist by themselves after the elimination of the sound that influences them. This is most clear in the example that Saumjan adduces when criticizing the syntagmatic identification of phonemes on the basis of commutation or Substitution. In Common Slavic, which had open syllables only, the softness or hardness of consonants was concomitant with the quality of the following vowel: [a, o, u, a, i] occurred only after hard consonants and [ä, ö, u, 9, i] only after soft consonants. Neither the consonant nor the vowel is eliminable since either of them presupposes the presence of the other, so the chain constituted by them is phonemically indivisible. Saumjan agrees with the following Statement by Avanesov (1947: 48) :14 13 This possibility has been suggested above in connection with Du. [s] and Sw. [d]. 3* Reformatskij 1970:287f., quotation on p. 135 of Saumjan 1968, Cf, also 2uravlev 1966, 1967, 42 THE DEVELOPMENT OF MODELS IN PHONEMICS The question of what we face — different consonantal phonemes plus the identity of succeeding vowels, or different vowel phonemes plus the identity of preceding consonants — remains open. And this question remains open not because [of ] the imperfection of our knowledge or of our method, but äs a result of the fact that it has not been differentiated within the System itself. It is believed that the most effective state of affairs would be the positing of an interdependence, and not the establishment of a unilateral dependence of vowels on preceding consonants, or the reverse. In view of the impossibility of Isolation one could consider the function of the differentors of meaning to be carried, äs a unit, by the combination of the consonant with the succeeding vowel, i.e. the entire syllable. However, the same Situation can be observed in Russian: [i] occurs after hard consonants and [i] elsewhere, [e] before soft consonants and [s] in other positions. Thus, Saumjan's first rule yields prevocalized and postvocalized consonants äs single phonemic units, which is clearly incorrect. These observations show that the eliminability of soimds depends on the precision of the phonetic transcription. Martinet writes about Sp. [ts]: "[s] n'existe que dans ce cas, tandis que [t] se rencontre fre- quemment dans bien d'autres positions" (1939: 97). In fact, the predorso-alveolar stop in [ts] resembles the apico-dental stop [t] found in other positions no more than prepalatal [s] resembles alveolar [s]. So if one uses a more accurate transcription, it turns out that neither the occlusive nor the fricative element in Sp. [ts] is eliminable. On the other hand, it can be argued that the difference between alveolar and palatal sounds is not distinctive in Spanish, so that a less precise transcription will do. In that case, [s] can be considered a variant of [s], and [ts] should be interpreted biphonemically in accordance with Saumjan's second rule stated above. I say this only to point out that Saumjan's solution is no more satisfactory than Martinet's. According to the second rule, the elements of a sound chain are realizations of different phonemes if they can be interchanged. This criterion leads to diöiculties when applied to clusters with a different degree of fusion, such äs possibly Po. cz and trz, both [ts]. Saumjan adduces the following word pairs: czech 'Czech', trzech 'three (gen.)'; czysta 'clean (fern.)', trzysta 'three hundred'; paczy 'warps', patrzy 'looks'; oczyma 'eyes (inst.)', otrzyma Obtains'. Let us suppose for the moment that these words are not homophonous (cf. Kortlandt forthcoming d). In that case, they must be phonemically distinct. But Saumjan's permutation test leads to the conclusion that both cz and trz are realizations of biphonemic strings because after permutation both yield [st], though possibly with a different degree of fusion, which is phonemically irrelevant, however.If Saumjan nevertheless identifies trz biphonemically and cz äs the physical substratum of a single phoneme /c/, this is for one thing at variance with his own criterion, and for another, it is based on purely phonetic data. It is clear from this example that the classical minimal-pair identification rule takes precedence of Saumjan's operator method even within his own theory, and that phonetic criteria are resorted to for the final identification of the units involved when the operator method fails to distinguish between distinct entities. As I have argued above, this application of phonetic criteria is contrary to the basic idea of the two-level theory. Besides, I do not approve of the criterion of permutability in any case because it reflects distributional characteristics, which in my opinion SAUMJAN'S TWO-LEVEL MODEL 43 should be entirely eliminated from the identification procedure (cf. Chapter 8 of this book). Saumjan's main objection against the criterion of commutation or Substitution lies in the fact that it "cannot differentiate between two kinds of linearity, phonological linearity and subphonological linearity (i.e. between linearity at the level of constructs and linearity at the level of observation in phonology)". This criticism of the classical criterion is essentially correct, though I do not agree that the objection "strips it ultimately of any possible theoretical value" (1968: 136). It must be noted that in doubtful cases Saumjan himself does not give any rules for the phonemic segmentation of the speech flow: his third rule leaves the Interpretation of non- permutable sound chains to be made on the basis of the structure of the phonological System. This is logically unsound because the establishment of the phonological System is the very aim of the identification procedure. If any complex of simultaneous physical properties is subject to Saumjan's third rule, äs the passage quoted above suggests, it means that not a single phonemic unit can be established because its identification depends on the patterning of other units, which, for the same reason, cannot be established either. And even if we choose a more or less arbitrary starting- point, such äs Saumjan's 'natural segmentation' of the speech flow, it is in my opinion incorrect to leave the problem of monophonemic or biphonemic Inter- pretation open. If language is a code, the units of the code must be distinguishable. The dilemma is mitigated by Saumjan's 'principle of unification', which runs äs follows: "if some positions in the speech flow permit a single solution to the problem of the syntagmatic identification of phonemes while other positions permit a double solution, then the double solution should be reduced to a single one" (1968: 133). In English, [d] is ineliminable in jam [dzsem], Job [dzob], jug [dzAg], so word-initial [dz] is a single phoneme. On the other hand, intervocalic [dz] is opposed to [z]: ledger [ledza], leisure [leza]. The sound chain [zd] does not occur, however, so two interpretations of intervocalic [dz] are possible in accordance with Saumjan's third rule. Now the 'principle of unification' points to the monophonemic Interpretation. In my opinion, this principle not only fails to remove the real difficulty, but is itself unacceptable. As we have seen above, two phonetically identical sounds in complementary distribution need not be functionally equivalent, so there is no reason to accept their identifiability in the present case either.

2.10. DISTINCTIVE FEATURES

After this rather comprehensive discussion of Saumjan's views on the identification of phonemes I shall limit the exposition of the other problems raised in his book to a survey of the aspects that are closely connected with the concept of the phoneme. In Trubetzkoy's theory a phonemic unit is defined äs a bündle of distinctive features. Within the relational-physical theory of phonology the following two Statements on 44 THE DEVELOPMENT OF MODELS IN PHONEMICS the nature of distinctive features analogous to the above Statements concerning the phoneme can be formulated (1968: 62): (1) Distinctive features are diacritical elements whose function is to differentiate between signifiants of linguistic units. (2) Distinctive features are acoustic elements. From these Statements the same 'antinomies' which we have already encountered in connection with the phoneme can be derived. Saumjan's treatment is wholly analogous and leads to exactly the same solution (1968: 68): At the level of observation we differentiate between individual substrata of distinctive features and classes of the individual substrata of distinctive features. In order to denote the former we consider it expedient to introduce the term 'concrete differentoids', and to denote the latter by the term 'abstract differentoids'. At the level of constructs we differentiate individual distinctive features and classes of individual distinctive features. The former can be, for expediency, given the term 'concrete differentors' and the latter the term 'abstract differentors'. The concept of distinctive feature äs a construct is formally defined äs follows:

D =Df (x)(ly)[A(x).A(y).C(x,y) => /(*,/>)], (2.7) where D is the distinctive feature, A the acoustic property, Cthe relation of contrast, and / the relation of embodiment (1968: 66). The definition is identical with the formal definition of the phoneme quoted above except for the Symbols D and A, which replace P and S, respectively. The same cryptical remark is added äs an explanation of the definition: This formula which represents the correspondence rule between the construct 'distinctive feature' and the level of observation, should be read: if χ is an acoustic property and is in relation of contrast to at least one acoustic property y, then χ is in relation of embodiment to the distinctive feature D. Since everything is identical I will not repeat the criticism put forward above.

2.11. PROSODIC FEATURES

Finally, prosodic features are subject to the same treatment äs phonemes and distinctive features. According to Saumjan, the following Statements can be formulated in the relational-physical theory of phonology (1968: 77): (1) Prosodic features are relational elements which possess either a culminative function or a function of word differentiation. (2) Prosodic features are acoustic features. These Statements lead once more to the same antinomies. In order to overcome these antinomies we are compelled to split the concept of prosodic feature into two corresponding concepts: the concept of prosodic feature äs a construct and the concept of the substratum of prosodic feature. To the former concept we will assign the term 'prosodeme' and to the latter the term 'prosodempid', [.··] By the same token orte shpuld differentiate between concrete SAUMJAN'S TWO-LEVEL MODEL 45 prosodemoids and prosodemes, on the one hand, and abstract prosodemoids and prosodemes on the other. (1968:79f.) Concrete prosodemes which are identical in respect to their placement within the word unite into a class which is designated äs an abstract prosodeme. Concrete prosodemoids, äs the substrata of corresponding concrete prosodemes, unite into a class which is designated äs an abstract prosodemoid. Further discussion of prosodic features is referred to Chapter 10 of this book. (It must be remarked that Saumjan regards the Opposition between vowels and consonants äs a prosodic Opposition. I shall not enter into a discussion of this point here.) In the last two chapters of gaumjan's book, the 'method of binary patterning of phonological oppositions' and the 'methods of phonological syllable patterning' are discussed from the point of view of the two-level theory. Since both problems have no direct bearing on the identification of phonemic units and the discussion of them presents no fundamentally new insights — though it sheds an interesting light upon some of the questions involved — I shall not engage in a review of this pari of Saumjan's theory. The most important merit of Saumjan's book is, in my opinion, the criticism of existing theories and the explicit formulation of the identification problem rather than the proposed Solutions. In the exposition of phonemic modelling in the subsequent chapters I will focus on the problems that have been raised in the present discussion. SET-THEORETICAL MODELS

3.1. INTRODUCTION

In Eastern Europe the term 'mathematical linguistics' most often refers to set- theoretical modelling of linguistic phenomena. The starting-point of this new discipline is generally acknowledged to be Kulagina's well-known 1958 article.1 Her model was further elaborated and refined by a number of authors.2 The results of the rapid development that took place in this new branch of linguistics during the initial phase of its elaboration can be found in Revzin's Models of language, which appeared in 1962 and was translated in 1966 into English and in 1968 into French. The subsequent development was characterized by a growing interest in the mathematical properties of the proposed models and a diminishing preoccupation with their linguistic relevance.3 This is at least partly explained by the fact that the large majority of scientific workers in the field are mathematicians rather than linguists. The mathematization of the discipline led, in turn, to a diminishing interest on the pari of Professional linguists so that the whole Situation looks definitely less promising now than it did ten years ago. In 1968 F. Kiefer wrote, in the conclusion of his chapter on the 'Kulagina school' (1968:50), "We have pointed out that every part of Kulagina's theory is somehow trivial from a linguistic point of view. In spite of the many able formalizations the linguistic content is almost next to nothing." The Situation has not substantially improved since. In this chapter I shall connne myself to models of the phoneme that have directly or indirectly been inspired by the 'Kulagina school'. The following sections are devoted to the ideas expounded by Revzin in the second chapter of the book mentioned above (1962a). This book has been followed by another, published in 1967, in which the author returns to most of the problems tackled in the former publication, but not to the questions of phonemic analysis. The second book contains a list of corrections to be added to Models of language (1962a). It is stated in this list that the chapter on 'syntagmatic models in grammar' should not be used at all (1967:276). Since I am concerned here with phonemic modelling only, I shall deal exclusively with the

1 Cf. Abernathy 1963:119, Papp 1966:81, Kiefer 1968:10. 2 Dobrusin 1957, Uspenskij 1957, Xolodoviö 1960, Revzin 1960. 3 Cf. Gladkij 1963, Nebesky 1963, 1964, Novotny 1965, 1966. SET-THEORETICAL MODELS 47 chapter entitled 'Methods of making models in phonology' (Metody modelirovanija vfonologü) and the corrections that bear upon that chapter.4

3.2. THE INITIAL OBJECTS OF REVZIN'S MODEL

The initial objects of Revzin's phoneme model are (1966:15): (1) a set of speech-sounds; (2) a set of 'phonetic categories' or 'marks', generally called 'features' in other publications on the subject; (3) a set of registered sequences of speech-sounds which are called 'phonetic words'. A set can be defined äs a collection of identifiable objects. Every speech-sound is coordinated with a subset of the set of marks. To use more ordinary terminology, we shall say that every sound consists of n marks. The concept of phonetic word must be interpreted not äs 'a minimal segment between two pauses in an actually existing speech-segment of a given language' but äs 'a minimal combination of speech-sounds permissible in a given language between two pauses' because "the phonologist must take into consideration, not only the combinations realized in the words of a language, but also potential combinations of speech-sounds" (1966:16). Moreover, this is the only appropriate Interpretation in constructing a generative model and corresponds to the idea of having a 'set of registered phrases' in the construction of grammatical models. A combination of sounds is called 'permissible' (dopustimyj) "if every element of this combination is encountered in some actually stipulated word of the given language in the same environment äs in the given combination" (1966:16). Revzin explicitly rejects the possibility of defining the phoneme äs 'the smallest unit serving for the differentiation of meaning' and states that "starting from the phenomenon of distribution, it is possible to define a unit in the initial material given us sufficiently close to what is usually regarded äs a phoneme" (1966:17). This opinion is based on the following Statement by Jones (1931:77): "If two sounds of a language can occur in the same Position in respect to surrounding sounds, then by definition the two sounds belong to separate phonemes." The last Statement is clearly incorrect: sounds in free Variation occur BY DEFINITION in the same position in respect to surrounding sounds and yet belong to one and the same phoneme. The Statement does hold after free Variation has been removed, i.e., after a first step of the Identification procedure has been carried out. In fact, the establishment of Revzin's set of initial objects presupposes that not only the paradigmatic and syntagmatic delimitation of some kind of sound units has been carried 4 The general considerations in the first chapter of Revzin 1962a, 'Types of models of language' (Tipy modele/ jazyka), and the additions made in the first chapter of Revzin 1967, 'Principles of linguistic modelling' (Principy lingvisticeskogo modelirovanija), will be dealt with in Chapter 7 of this book. 48 THE DEVELOPMENT OF MODELS IN PHONEMICS out beforehand, but the assignment of features ('marks') to the respective sounds and the Identification of sounds in different environments also have taken place already (otherwise no Statement about phonotactics can be made). Thus, all initial objects are 'coastructs' in Saumjan's sense, lacking explicit correspondence rules with reality. It is to be noted that Revzin's 'pauses' are constructs too. They certainly do not correspond to observable pauses in the Speech flow, and I am not quite sure what they do stand for because every reference to meaning is avoided. Neither is the difference between distinctive features and junctures clear from Revzin's sets of initial objects. According to the Statement quoted above, "every speech-sound is coordinated with a subset of the sei of marks". It is not stated, however, whether the set of 'marks' is exhausted by their assignment to separate speech-sounds. If so, configurational features (such äs stress in Russian) remain out of the picture because they characterize speech-sounds not paradigmatically (in relation to speech-sounds coordinated with a different set of marks) but syntagmatically (in relation to other speech-sounds within the same Speech flow), cf. Chapter 10 of this book. Finally, the concept of 'permissibility' rests upon the concept of 'environment', which is ambiguous.5

3.3. REVZIN'S DEFINITION OF THE PHONEME

Two marks are 'consistent' (sovmestimyj, I would say 'compatible') in a given language "if there exists at least one speech-sound in which they appear together", otherwise they are 'inconsistent' (1966:18). Two inconsistent marks mi and mj are 'homogeneous' (odnorodnyj) "if there exists at least one sound of the given language such that the replacement of mi by m} (or nij by mi) also produces a sound of the given language", otherwise they are 'non-homogeneous' (I would say 'inhomogeneous'). Examples from Russian: voicelessness and fricativeness are consistent, voicelessness and voicedness are homogeneous and, therefore, inconsistent, voicelessness and openness are both non-homogeneous and inconsistent. Now "every sound can be represented in the form of an assembly of marks" and "every phonetic word is an ordered succession of assemblies of marks. For generality, we shall consider that the pause, too, is a speech-sound, coordinated with the mark 'silence' " (1966:18). If, in the given. permissible pair of sounds SiSg, one of the marks (let this be the mark m) of the sound Si (or 82) may not be replaced by any other such that, once again, a permissible combination of sounds is obtained, then we shall say that the given mark m is bound in the given pair. Consider now the sound Si and examine: (1) the set of all pairs in which this sound Stands in the first position, and (2) the set of all pairs in which this sound Stands in the second Position. If the mark m is bound in one or both of these sets, we shall call this mark non-relevant. We shall call the remaining marks relevant (it is obvious that the 'relevant mark' so defined is a much wider concept than the 'differential mark'). As an example Ru. [ε] and [e] are adduced: [e] occurs before soft consonants and [ε] elsewhere, so the closeness of [e] is bound by the following soft consonant. Mutual 5 Cf. the discussion of 'environment' in Batog 1967, see Chapter 5 of the present study. SET-THEORETICAL MODELS 49 replacement of [ε] and [e] leads to non-permissible combinations, therefore the marks that distinguish between them are non-relevant (1966:19). If a relevant mark is bound in a given combination, we shall call the given combination the Position of neutralization ofcontrast of the given mark and of all those homogeneous with it. For example, the position before the pause in Russian is the position of neutralization of contrast of the marks voicedness and voicelessness. Finally, we shall call a phoneme any assembly of relevant nonhomogeneous marks coordinated with a certain speech-sound. Two sounds corresponding to one phoneme are called allophones or variants of the one phoneme. Since homogeneity precludes consistency (see above), the word 'non-homogeneous' in the definition of the phoneme is superfluous and should be omitted.6 The ARCHI- PHONEME is defined äs the assembly of relevant marks common to two phonemes. If the marks differentiating the two phonemes have a position of neutralization, the archiphoneme is called 'real' (aktuaVnyj). "If two phonemes have a common real archiphoneme, i.e., differ only in that the mark nn is present in one and the mark mj in the other, we shall say that they belong to one elementary phonological category" (1966:20). The main difficulty inherent in any distributional analysis is that distinctive features cannot be distinguished from redundant features. If the closeness of Ru. [e] is bound by the following soft consonant, it can also be stated that the softness of this consonant is bound by the preceding vowel. The replacement of a soft consonant by a hard one in this position, like the replacement of [e] by [ε] before a soft consonant, yields an inadmissible combination. It follows that the hardness or softness of a consonant preceded by [ε] or [e] is non-relevant in Revzin's sense, which clearly is an unsatisfactory result in view of bis definition of the phoneme. The Situation is even worse: the criterion of relevancy stated above is not only insufBcient but also unnecessary from a functional point of view. Ru. [u] is distinct from [i] both by its roundedness and by its back articulation. Both of these features are relevant in Revzin's sense, but, äs I see it, only the former can be called distinctive. It is in this Interpretation that the concept of relevancy is wider than the concept of distinctiveness. Thus, Revzin's phoneme is nothing but a family of phonetically related sounds in complementary distribution.7 There is no place in this conception for phonetically similar and yet functionally different sounds. Likewise, the direction of an assimilation cannot be established on purely distributional grounds. If hard consonants occur in juxtaposition with hard consonants and soft consonants with soft consonants only (äs in Lithuanian), the hardness or softness of any pair of juxtaposed consonants is mutually bound, so both consonants are realizations of archiphonemes. This is clearly incorrect because the hardness or

6 Cf. Revzin 1964:63 fn.9 and Revzin 1967:275. 7 This corresponds to the definition of the phoneme put forward by D. Jones, who stated that "a phoneme is a family of sounds in a given language which are related in character and are used in such a way that no one member ever occurs in a word in the same phonetic context äs any other member" (1950:10), and also to Söerba's views, cf. Chapter l of this book. 50 THE DEVELOPMENT OF MODELS IN PHONEMICS softness of the PAIR is distinctive. It turns out that essential Information has been lost by the introduction of archiphonemes. The matter is more complicated indeed, äs can be illustrated by an example from Russian. "Dentals are soft before soft labials" (Kortlandt, forthcoming b, ms. p. 5). "A hard dental consonant cannot be followed by a soft labial" (Panov 1967:92). It follows from the first Statement that the softness of dentals before soft labials is bound, and from the second that the hardness of labials following hard dentals is bound. In both cases the Opposition hard ~ soft is neutralized. Now the replacement of either consonant in a string like /t'p/ by its correlate changes the other consonant into an archiphoneme, so the 'relevant' features are not independent from each other after all. Conversely, the palatality mark of either consonant can be inferred from whether or not the other is an archiphoneme. Here, Information is given twice because of the introduction of archiphonemes. The main objection against the definition of 'neutralization' and 'archiphoneme' on the basis of distributional analysis, however, is the indistinguishability of these phenomena from defective distribution. Since I have already pointed out this problem and shall return to it afterwards, I shall not take it up here.8 Finally, I have to point to some inaccurate formulations in the passages quoted above. From the Statement that "every sound can be represented in the form of an assembly of marks" it does not follow that "every phonetic word is an ordered succession of assemblies of marks" because some features may characterize several sounds simultaneously (emphasis in Arabic, syllabic softness in Common Slavic, maybe also Turkish vowel harmony and Sanskrit cerebralization) or in relation to one another (configurational features, such äs Ru. stress). It is stated that the mark m is 'bound' if it may not be replaced by ANY other such that, once again, a permissible combination of sounds is obtained. Even if we abstract from the possibility of free Variation, the formulation is incorrect because of the existence of gradual oppositions: the closeness of Ru. [e] is bound by the following soft consonant but the vowel in [p'et'J 'to sing' can be replaced by the even more closed vowel [i], in whicb case the word fp'it'] 'to drink' results. The same inaccuracy is present in the definition of 'neutralization'. If the contrast between two marks is neutralized, it is not true that the contrast between these marks and all those homogeneous with them is neutralized: the Opposition between Ru. [a] and [o] is neutralized if the vowel is unstressed but the difference between [a] and [u] is distinctive in all positions. And the two criteria stated in connection with the concept of 'elementary phonological category' do not coincide: the fact that two phonemes "differ only in that the mark nn is present in one and the mark mj in the other" does not necessarily mean that they have a common real archiphoneme, cf. Eng. [s] and [Θ], Ru. [r] and [1] or [o] and [u]. Conversely, there is no reason why two oppositions could not be neutralized simultaneously so that phonemes diifering in more than one feature may have a common real archiphoneme, cf. Ru. hard ~ soft and voiceless ~ voiced. 8 See Chapters l and 8 of this book. SET-THEORETICAL MODELS 51 3.4. A PARADIGMATIC MODEL

As to the other topics treated by Revzin, I shall limit myself to an exposition of the main ideas. His 'paradigmatic model' consists of an algorithm for the classification of phonemes within a Subsystem, e.g., the Subsystem of obstruents. The algorithm runs äs follows (1966:22ff.):

(1) We choose two phonemes having a common archiphoneme «i and we add to this class all tbe other phonemes having the given archiphoneme. We obtain the phonological class K(aj) = KI. We notice that any such class is defined uniquely by an arbitrary phoneme χ which belongs to it; for this reason we shall sometimes denote the class to which the phoneme χ belongs äs K(x). It should be noticed that the expression K(x) is unambiguous only if the archiphoneme «i is known. This is not quite clear from Revzin 's Statement. (2) Let i classes already have been constructed. We take from the remaining phonemes the maximum assembly of phoneroes such that: (a) all of them have the common archiphoneme 04+1; (b) it is possible to establish a one-one correspondence between 04+1 and 04 so that the corresponding marks are either homogeneous or coincide. In this way we construct The condition stated here in point (b) diflfers from the original formulation, cf. Revzin 1962a:27f. and 1967:275. (3) We exclude from our Subsystem the remaining phonemes which do not fit into our arrangement and we draw up a new arrangement for them. [...] Thus, we have obtained a division into classes within the bounds of the Subsystem, each class being uniquely defined by its own archiphoneme. The set of archiphonemes αχ, «2, ... o^ obtained by our procedure of arrangement uniquely defines a division into classes Kj.(1>, K2(1), ... Ki(1>, where the upper index indicates the number of the division and the lower index the number of the class. (4) Having selected an archiphoneme ßi, which does not coincide with any ΟΊ considered above, and having repeated the procedure considered in points 1-2 [...], we either exhaust all the phonemes and obtain a new division into classes each of which is defined by an archiphoneme ßi, or we do not obtain a division into classes, äs all the phonemes of the Subsystem will not be exhausted. In the second case we consider each of the remaining phonemes äs an isolated class and, at the same time, we obtain a division of the whole Subsystem into classes which is defined (with preeision down to the isolated classes) by the set of archiphonemes ßi, ßz, ··· ßm- (5) Now we again repeat the procedure described in point 4 and obtain a new division into classes, which is defined (with preeision down to the isolated classes) by the set of archiphonemes y\, yz, ··· Vk. The expression "down to the non-isolated classes" in the English text (1966:24, first line) is obviously incorrect. (6) The procedure described in point 5 is repeated until all archiphonemes common to at least two phonemes o} the Subsystem are exliausted. The italicized specification (my italics) has been added after the publication of the Russian original, cf. Revzin 1962a:28 and 1967:275. The algorithm clearly illustrates the shift of interest in 'mathematical linguistics': everything which is relevant from a linguistic point of view is supposed to be known 52 THE DEVELOPMENT OF MODELS IN PHONEMICS (the units, the features, their mutual relations and tactic properties), and the only problem left is the question of how to arrange the data, or even, how to state rules according to which the data could be arranged.9 The following concepts are defined in connection with Revzin's 'paradigmatic model' (1966:27). A Subsystem is 'phonologically homogeneous' if, for any two divisions and for any two phonemes χ and y, from the condition K<«(JC) n K<2>00 Φ 0 (3.1) (i.e. from the presence of a phoneme z which, in the division Kl1', belongs to the same class äs x, and, in the division K'2', belongs to the same class äs y), there follows Κ»>00 Π K<2>(;c) ^ 0. (3.2) Thus, if χ and z differ in one single feature and y and z in another single feature, then there must be a phoneme which on the one hand differs from χ äs y from z and on the other diifers from y äs χ from z. Two marks mi and mj are 'fully homogeneous' in a given Subsystem if the Substitution of mi for mj (and mj for mi) in any phoneme of the given Subsystem leads to a phoneme of the given Subsystem. If, in a Subsystem, there are two phonemes FI and F2 such that Fi is obtained from F2 by the Substitution of mt for mj — mi and mj however not being fully homo geneous in the given Subsystem — then we shall say that the Subsystem contains an empty cell. The Subsystem of Russian obstruents is not homogeneous because there is no voiced velar fricative supplementing the phonemes /k/, /g/, /x/. Since voicelessness and voicedness are not fully homogeneous, there is an empty cell, sc. the place of */γ/. Several theorems about phonologically homogeneous Subsystems are stated in the section under discussion. Two phonemes are 'adjacent' if it is possible to pass from one of them to the other by changing just one mark. The 'rank' of a phoneme is the number of phonemes adjacent to it in the given Subsystem. A Subsystem is 'füll' if any two phonemes in it can be joined by a chain in which every two phonemes occurring next to one another are adjacent (1966:29). The 'nucleus' of a phonological Subsystem is the maximal subset of phonemes forming a phonologically homogeneous Subsystem within that Subsystem. The last concept is redefined in Revzin 1967 äs any non-empty phonologically homogeneous Subsystem in view of the following definitions, which are absent in Revzin 1962a (but present in the English edition, 1966:30). A division is 'admissible' (dopustimyj) for a given nucleus if any two phonemes belonging to the same class of it either both belong to the nucleus or both do not belong to it. The nucleus which admits the maximal number of divisions is called the 'principal' (glavnyj) nucleus.10

9 This shift of interest, which is characteristic of non-mathematical theoretical linguistics äs well, is sharply criticized in Kuipers 1968. 10 The reason for me to be so explicit about the part of the terminological apparatus introduced in SET-THEORETICAL MODELS 53

3.5. SYNTAGMATIC MODELS

A syntagmatic model is a model of phonotactics. The first model of phonotactics known to me is the statistical investigation of Puskin's Evgenij Onegin by the Russian mathematician A.A. Markov, which appeared in 1913. Following Markov, one can regard a sequence of phonemes äs a series of successive states through which a speech generator passes during the articulation of an utterance. The consecutive transitions from any state (phoneme) to the next one can be viewed äs connected trials. Certain probabilities can be associated with these transitions on the basis of their frequency of occurrence, which turns out to tend to a fixed value. As an Illustration of bis theory Markov applied the method to the first 20,000 letters of Evgenij Onegin, disregarding the hard and soft signs. The scope of bis theory, which has subsequently become to be known äs the theory of Markov processes, is actually much wider. Nowadays it is the central topic in probability theory.11 One of the first syntagmatic models in modern phonemic theory, which is adduced by Revzin äs an example of syntagmatic modelling, is the one introduced by F. Harary and H.H. Paper in 1957. These authors very well realize that their model does not add anything new to phonemic analysis but, on the contrary, presupposes such an analysis: It must be noted at this point that the formulaticms just offered presuppose a completed phonemic analysis, the strategy for which we know from linguistic theory. [...] We assume the phonemic analysis äs given and we now devise a map for charting distribution in both the most general and the most specific terms in a mathematically rigorous manner. (Harary and Paper 1957:145) The following concepts are introduced. (1) The set P is the set of phonemes of a given language, including an element 'space' which I shall denote by the symbol +. (2) The relation R is the set of ordered pairs of juxtaposed phonemes that occur in the given language. (3) The 'alpha-field' «x is the set of phonemes that may immediately precede the phoneme χ in the given language. Symbolically:

Κτχ = - = Kax + Kßx - Sx (3.8) nP where Sx is the 'degree of symmetry' (see below). In the present instance, Käs = 8/29, Kßs = 10/29, Κτ$ = 12/29. Next to these concepts, another kind of distributional completeness is defined by Harary and Paper, viz. 'internal completeness'. The definitions are identical to the ones just quoted but for the determinator of the ratio, which is ητχ instead of nP. A phoneme χ is 'Symmetrie' with respect to a phoneme y if both of the sequences xy and yx occur. The set of phonemes that are Symmetrie with respect to a phoneme χ can be symbolized äs σχ = xx n ßx = {z e P : zx e R Λ χζ e R} (3.9) The 'degree of symmetry' of a phoneme χ is now defined by ησχ (3.10) nP In the above example, 5§ = 6/29. The 'degree of internal symmetry' of a phoneme χ is defined identically but for the denominator of the ratio, which is mx instead of nP. The set of phonemes that are 'anti-symmetric' with respect to a phoneme χ is defined by σχ = τχ — σχ = {z e P : z e τχ \ ζ φ σχ} (3,1 1) and the 'degree of antisymmetry' by

3* = — (3.12) nP

12 The method is applied to Russian graphemes in Toporov 1966. SET-THEORETICAL MODELS 55 A phoneme χ is 'reflexive' if the sequence xx occurs, i.e., if χ e τχ. If so, the 'degree of reflexivity' Gx is equal to 1. If the sequence xx does not occur, the phoneme χ is 'irreflexive' and Gx = 0. If we define ßxy = ßx n ßy = {z e P : xz e R Λ yz ε R} (3.13) then the 'degree of local transitivity' of a phoneme χ with respect to a phoneme y is

(3-14)

If ßy <= /fc then ZXy = l and the phoneme χ is 'locally transitive' with respect to the phoneme y, which is to say that whenever both xy and yz occur, xz also occurs. It should be noticed that ßxy — ßyx but Txy φ Tyx.13 The model outlined in the preceding paragraphs has been criticized by the Georgian scholar R.R. Mdivani (1968). The main point of criticism regards the concept of two-sided completeness defined in formula (3.8) above. If ßx <= ax then τχ = xx and Κτχ is independent of nßx. This is clearly an unsatisfactory result : the number of phonemes that may follow a phoneme χ can vary freely between l and the number of phonemes that may precede χ without aifecting the degree of completeness of its distribution, provided that any phoneme following χ is a member of the set of phonemes that precede x.u According to Mdivani, the 'degree of completeness' should intuitively be proportional to the number of ordered pairs of phonemes (= elements of R) in which the phoneme under consideration occurs. This leads to the following definition: „ n«x + nßx - Gx KX = 2nP-l (3'15) The denominator of this ratio is equal to the number of theoretically possible pairs in which χ is the first member, plus idem where χ is the second member, minus l because the pair xx must not be counted twice. The numerator is equal to the number of actually occurring pairs in which χ is the first member, plus idem where χ is the second member, minus l if the pair xx has been counted twice, i.e., if χ is reflexive. Thus, the degree of completeness of Jap. /§/ is Ks = 17/57.15 13 In addition to the concepts exposed here, a number of derived indices are defined in Harary and Paper's paper (1957). Since these generalized ratios do not immediately refer to any observable phenomena, I have omitted them in the present review. Revzin adduces in his book only two of these generalized concepts, viz. the 'degree of fullness' (which is a back-translation of the original 'degree of completeness') and the 'degree of reflexiveness' (i.e., Haiary and Paper's 'degree of reflexivity'), skipping the wliole apparatus in which they play their part. Moreover, Revzin's definitions differ from the original ones because he does not exclude the sequence + + from the set R, cf. Revzin 1966:34f. 14 The lower bound of the number of elements in ßx is l, not 0 äs Mdivani suggests, because any phoneme can be followed by at least one other phoneme. (It is recalled that + is an element of P.) In Markov chains terminology, there are no transient states: all phonemes are ergodic (cf. Feller 1957:353). 15 Other examples from Bloch's 'conservative dialect' : Ατή = Krj = Κτν/ = 7/29 and Χτ7 = 6/29 56 THE DEVELOPMENT OF MODELS IN PHONEMICS Another syntagmatic model was put forward in 1960 by Marcus and Vasiliu. These authors presented a description of Rumanian initial consonant clusters in terms of graphs.16 A graph (M, R) is a pair consisting of a set of elements M and a relation R defined on that set. The elements in the set are called 'nodes' and a pair for which the relation holds is a 'rib' (cf. Revzin 1967:40). Now, we consider the set of consonants occurring in initial clusters and number the positions in which they are found from the first vowel of the word backwards. Thus, we obtain a set M of elements of the type xt, where χ is a consonant and i indicates its position with respect to the first vowel that follows. We define R äs the relation of immediate juxtaposition. A part of the resulting graph is shown below (cf. Marcus and Vasiliu 1960:326).

These figures show the possible Rumanian word-initial triconsonantal clusters beginning in [s] and ending in [e] and [a], respectively. The authors introduce a number of concepts (redundancy, cohesion, adherence) in connection with their model. These concepts will not be discussed here.

3.6. PHONETIC AND PHONEMIC SYSTEMS

When Saumjan and Revzin published their books in 1962, the new trend in Soviet linguistics was finally established. In the following year the third leading theoretician in linguistic modelling, the Rumanian mathematician S. Marcus, published his but Ki) = K) = 12/57 while Kw = 8/57 and Κ"> = 6/57. All vowels have Κτχ = l but they differ according to Mdivani's criteiion: Ka. = 55/57, Ko = 54/57, /fu = 53/57, Ke = 50/57, and Ki = 49/57. 16 The description is based on Vasiliu 1957. Another model is deflned and applied to the same Rumanian material in Vasiliu 1963. Cf. also Maicus 1962 on the use of graphs in linguistics. SET-THEORETICAL MODELS 57 model of the phoneme (1963b). The model was taken over in the second chapter of bis book Lingvisticä matematicä, which appeared the same year (1963c:56-68). Since this book has been translated into French (1967a) and into Czech (1969), the formulation of the model is available in these languages äs well.17 Marcus' model looks very much like Revzin's but covers a wider ränge of phenomena and is formalized to a greater extent. Its initial objects are a set of sounds E, and a set of 'values' (Rum. valori, Fr. valeurs, Cz. hodnoty) V which is partitioned into a number of disjoint subsets such that V= u Vi (3.16) ί

Two values are 'homogeneous' if they are members of the same subset Vi, otherwise they are 'heterogeneous'. These 'values' correspond to 'features' in ordinary terminology, but Marcus reserves this term (Rum. träsäturi, Fr. traits, Cz. rysy) for values that are not homogeneous with any other value (1967a:51). Every sound χ (x e E) is associated with a set of values V(x) such that it holds for every number i that if Vi is not empty there is one and only one element v such that v€Vir\V(x) (3.17) This means that every sound is associated with one and only one value from every non-empty subset of V. If two sounds x, y are associated with the same set of values V(x} = V(y) (3.18) then they are 'absolutely equivalent'. Since this relation is an equivalence it partitions the set of sounds into a number of classes, which Marcus calls 'abstract sounds' and which he marks by means of square brackets: [x], [y], etc. The 'distance' between the sounds x and y is defined äs the number of values that are different for x and y. It follows from formula (3.18) that the distance between two absolutely equivalent sounds is equal to zero. Two values n and v% are 'compatible' if there exists a sound x (x e E) such that both vi e V(x) and v% e V(x), otherwise they are 'incompatible'. It is clear from this definition that compatible values are heterogeneous and, äs a corollary, homogeneous values are incompatible. As an example of compatible values Marcus mentions 'voiceless' and 'fricative', while the values 'hard' and Open' are incompatible.18 The latter example raises a problem in connection with the non-emptiness of the subsets of V. If Marcus were to stick to acoustic features of the Jakobsonian type there could, at least in one possible Interpretation of the theory, always be

17 Marcus 1967a:45-60 and Marcus 1969:49-63. It must be noted that^the Czech edition is not complete, but this does not regard the chapter on phonemic analysis. A slightly simplified exposition of the model in English can be found in Kiefer 1968:135-139. There is no chapter on phonemics in Marcus 1967b. 18 Kiefer's Statement according to which "the values 'fricative' and 'unvoiced' are incompatible" (1968:136) is obviously incorrect. 58 THE DEVELOPMENT OF MODELS IN PHONEMICS found one and only one 'value' satisfying formula (3.17) above. The very use of the terms 'hard' and Open' suggests that this is not the case, however. But if v Stands for an articulatory feature, there may be no 'value' satisfying formula (3.17) at all for at least some values of i and x. Thus, a 'hard' consonant is neither open nor closed : it has no degree of openness at all. One could formally save the model either by uniting some vocalic features with some consonantal features into one 'homogeneous' set of values, or by the assignment of arbitrary values in irrelevant cases, e.g., by assigning the value 'closed' to every consonant. Both of these Solutions are unsatisfactory. Two values vi and vz constitute a 'contrastive pair' if there exist two sounds x, y (x, y e E) such that V(x) - V(y) = {νχ} (3.19) and

V(y) - V(x) = {v2} (3.20) In words, two values are contrastive if there is at least one sound where the replacement of either of them by the other yields another sound of the language. This corresponds to the ordinary concept of minimal pairs in phonological tradition. It can easily be proven that values which constitute a contrastive pair are homogeneous, and therefore incompatible (1967a:48f.). The converse does not hold.19 A 'phonetic system' is now defined äs a quadruple Π = [V, P, E, φ} (3.21) where V is a set of values äs introduced in the beginning of the present section, P is a partition of Finto homogeneous subsets, £ is a set of speech sounds, and φ is a function that assigns a set of values to every speech sound in accordance with the rule stated above in formula (3.17). A phonetic System is 'complete' if every pair of incompatible values is a contrastive pair, and 'semi-complete' if every pair of homogeneous values is contrastive. Several theorems are stated in connection with these concepts. A 'phonemic system' is defined äs a quintuple Φ = [V, P, E, φ, S] (3.22) where S is the 'set of registered sequences of sounds' (Rum. muljimea de simri reperate, Fr. Vensemble des suites reperees, Cz. mnozina vyznacenych posloupnosti).20 This quintuple is practically identical to the set of initial objects presupposed in 19 It should be noticed that Revzin's concept of homogeneity is identical to the concept of contrast- iveness put forward in the model under discussion. The definition of compatibility (consistency) is the same in both models. 20 The symbol S is taken from Marcus 1963b. In Marcus 1967a, 1969 the same entity is denoted by F, which is confusing because this symbol refers later to a set of 'pertinent' values, cf. below. Kiefer writes Σ instead and calls the members of this set 'distinguished sequences of sounds' (1968:137). SET-THEORETICAL MODELS 59 Revzin's model: the sets E, V, S correspond to the ones posited in (1), (2), (3) of section 3.2 and φ embodies the Statement quoted immediately thereafter. The partition of V into a number of classes is not explicitly present in Revzin's model but can be inferred from bis concept of homogeneity: if the replacement of the feature (mark, value) vi in the sound χ by the feature v% produces a sound y that exists in the language, there is a sound (viz. the sound y) such that the replacement of va by vi produces a sound of the language (viz. the sound x), and if the replacement of vi by va and the replacement of V2 by vs stand the test, then the replacement of vi by va will also yield a positive result.21 Consequently, the relation of homogeneity in Revzin's sense partitions the set of features into a number of classes. Since the two models are so much alike, I shall not repeat here the criticism put forward above in connection with Revzin's model.

3.7. A FUNDAMENTAL HYPOTHESIS

Marcus formulates the following 'fundamental hypothesis' (1967a:54): "If one replaces a sound χ in a registered sequence by a sound absolutely equivalent to it, then the new sequence obtained is also registered." Rather than being a hypothesis about observable data this is a specification of the concept of registered sequence. Several interpretations of the above 'hypothesis' are possible. Firstly, it can be reduced to a triviality. It is stated above that every sound χ is associated with a set of values V(x), but there are no rules according to which this is done except the condition stated in formula (3.17). Within the model the Symbols χ and V(x) are, so to speak, in complementary distribution, so there is no formal reason not to identify them. If they are, in fact, identified with each other, the fundamental hypothesis turns into a triviality because two 'absolutely equivalent' sounds are per definitionem associated with the same set of values, cf. formula (3.18) above. Secondly, the above 'hypothesis' can be reduced to a definition. One can either redefine the set of registered sequences of sounds by adding to it the sequences that can be obtained through the replacement of any sound occurring in a sequence by any sound absolutely equivalent to the one substituted for, or, alternatively, define S

21 This is a simplification. If features need not be binary, the latter Statement does not necessarily follow from the definition of homogeneity. Thus, we can state that Ru. [p] is bilabial and [f] is labiodental, while [t] and [s] are apicodental consonants. If we put v\ = bilabial, V2 = apicodental, and vs = labiodental, then we can replace vi in [p] by vg (and obtain [t]) and replace V2 in [s] by vs (and obtain [f]), but we cannot in any sound replace vi by vs (or conversely) and obtain another sound existing in the language because there are neither bilabial fricatives nor labio-dental stops in Russian. The difficulty is easily overcome by considering the transitive closure of Revzin's homogeneity relation instead of the relation itself. But even in that case it cannot be excluded on theoretical grounds that two compatible features end up in the same homogeneity class thus established (though I cannot imagine this Situation actually occurring in practice), so the partition P introduced by Marcus turns out to be a necessary and independent entity after all. 60 THE DEVELOPMENT OF MODELS IN PHONEMICS as a set of sequences of ABSTRACT sounds.22 In both cases the fundamental hypothesis stated by Marcus becomes a part of the definition of S. Thirdly, the above Statement can be viewed as a real hypothesis, i.e., a Statement about observable phenomena that can be tested. In that case there must be a way to determine whether an arbitrary sequence of sounds belongs to S or not. Since explicit correspondence rules are lacking in Marcus' model, as in Revzin's, we are in need of additional criteria for linking the concepts defined in the model with observable entities. At least four interpretations of the concept denoted by the symbol S are possible. Firstly, S can stand for the set of actually registered sequences. Since all observations are finite, the set S is finite too. Any sequence of sounds observed after the set S has been established cannot be a member of S because it cannot have been registered before it was actually observed. Consequently, the test of the hypothesis that a newly observed sequence of sounds (e.g., obtained through the replacement of one sound by another in some registered sequence of sounds) belongs to S can on logical grounds yield a negative result only. The Interpretation under discussion does not seem to have any relevance from a linguistic point of view. In a second Interpretation the symbol S denotes the set containing not only the actually registered sequences but also the newly observed entities that cannot be distinguished from the actually registered sequences because they have the same physical characteristics. In fact, however, any two utterances can be distinguished from each other if the Instruments used for their measurement are sensitive enough. Thus, a strict application of the present criterion in testing the hypothesis on new material yields the same negative results as in the preceding case, only not for logical but for observational reasons. The only way out of this difficulty is the use of less precise Instruments. This leads us to two other interpretations of the symbol S. One possibility is registering a sequence of sounds only in so far as it is characterized by a number of features, e.g., the features that are associated with the sounds occurring in the sequence. In that case we have returned to the Interpretation of the 'fundamental hypothesis' as a more precise definition of the symbol S, viz. the Interpreta- tion according to which S is a set of sequences of 'abstract sounds'.23 This Interpreta- tion shifts the Identification problern to the correspondence rules linking the elements of V with observable features. The other possibility which I have in mind is the use of an informant in identifying a newly observed sequence of sounds as an element of S. This is, in my opinion, the only linguistically meaningful solution to the problem. Linguistics comes in where informants do, and the converse should hold as well. This Interpretation is closely connected with the problem of determining the physical correlates of the

22 Both possibilities amount to the same thing. The only difference lies in the TYPE of S, which contains sequences of sounds in the first case and sequences of classes of sounds in the second, cf. the above definition of 'abstract sounds'. 23 The features resorted to for the identification of the elements of S need not coincide with the elements of V, of course, but this would not alter the problem essentially. SET-THEORETICAL MODELS 61 elements of V. Since such problems are not tackled by Marcus, I shall defer them to a later chapter. The only point I want to stress here is the insufficiency of formulating a 'hypothesis' about observable facts in a model where correspondence rules are lacking.

3.8. MARCUS' DEFINITION OF THE PHONEME

The value v e V(x) is a 'relevant value' of the sound x if there is a sound y e E such that V(y) = (V(x) - {v}) u {v'} (3.23) for some value / e V. It follows from this definition that v and v' constitute a contrastive pair.24 It is clear that a relevant value of a sound χ is also a relevant value of any sound absolutely equivalent to x. It is therefore meaningful to speak of relevant values of ABSTRACT sounds. The value v e V(x) is a 'bound value' (Rum. valoare legatä, Fr. valeur liee, Cz. νάζαηά hodnota) with respect to χ if for any registered sequence of sounds containing χ either (1) v is not a relevant value of x, or (2) for every value v' e V such that v and v' constitute a contrastive pair and for every sound y e E satisfying formula (3.23) the sequence of sounds obtained from any registered sequence of sounds containing x through the replacement of x by y is not registered.25 The former condition is trivial, the latter essential. The intuitive meaning of the concept of boundness is clear: it corresponds to a complementary distribution identification rule in traditional phonemic theory. At the same time it reveals what I regard äs the principal weakness in any distributional analysis: it does not distinguish neutralization from defective distribution. In fact, the features differentiating between [h] and [η] in the languages in which these sounds are in complementary distribution satisfy the second condition stated above and are therefore 'bound values', which is contrary to linguistic Intuition. (Marcus defines some other concepts and states a number of theorems in connection with the 'boundness' of values but these will be omitted here because they have no direct impact on his definition of the phoneme.)

24 Marcus' definition runs äs follows (l 967a: 55): the value v e V(x) is a relevant value of the sound x if there exists a value v' such that v and v' constitute a contrastive pair and if there exists a sound y such that formula (3.23) holds. It is clear, however, that the flrst condition is but a corollary of the second. The term 'relevant values' is taken from Marcus 1967a, 1969 (Fr. valeurs relevantes, Cz. relevantni hodnoty) and differs from the original terminology in Marcus 1963b (Rum. valoripertinente, translated äs 'pertinent values' in Kiefer 1968). The Czech linguist M. Romporti deflnes a 'phonological distinctive Opposition' äs a pair of phonemes for which there is a position where formula (3.23) holds (1966:212). 25 Kiefer 1968 uses the term 'connected' instead of 'bound', but I shall not follow him because the concept introduced here has nothing to do with connectedness in the mathematical or logical sense of the word, cf., e.g., Ahlfors 1966:54ff., Tarski 1965:94ff. 62 THE DEVELOPMENT OF MODELS IN PHONEMICS Finally, Marcus introduces an equivalence relation R defined on the set of registered sequences of sounds. Two sequences of sounds are jR-equivalent if they have the same meaning. The value v ε V(x) is a 'pertinent value' of the sound χ if it is not bound and differentiates between meanings in at least one instance, i.e., there is a sound y E E such that formula (3.23) holds for some V e V and there exists a registered sequence of sounds s containing χ such that the sequence of sounds obtained from s through the replacement of χ by y is also registered, but not Ä-equivalent to s.26 Thus, a value is 'relevant' if it can be replaced in such a way that another sound of the language is obtained, and it is 'pertinent' (I would say 'distinctive') if it can be replaced in such a way that a sound sequence with a different meaning is obtained. The 'phoneme' associated with the sound χ e E is now defined äs the set [x, F(x)], where F(x) is the set of pertinent values of x. Two sounds χ and y are 'phonemically equivalent' if F(x) = F(y). This relation is an equivalence and therefore partitions the set of sounds into classes. If C(x) designates the set of sounds that are phonemically equivalent to x, the 'general phoneme' associated with the sound x is defined äs the set [C(x), F(x)], where C(x) is the 'physical component' and F(x) is the 'relational component'. The members of C(x) are called 'allophones' or 'variants'. If v is a pertinent value of x and y is a sound satisfying formula (3.23) for some v' e V and s is a registered sequence of sounds containing x such that the sequence of sounds obtained from s through the replacement of x by y is also registered but not .R-equivalent to s and if there exists a registered sequence of sounds t containing x such that the sequence of sounds obtained from t through the replacement of x by y is both registered and Ä-equivalent to t then the difference between v and v' is 'neutralized' in the position of x in t. If the second condition (replacement of x by y in t does not change the meaning of i) holds for every y that satisfies the first (pertinency) condition, then the difference between v and all values that are homogeneous with v is neutralized. If there is a sound z e E such that

F(z) = F(x) n F(y) (3.24)

then F(z) is called the 'archiphoneme' associated with the sounds x and y. This archiphoneme is the relational component of the phoneme [z, F(z)]. The definition of the phoneme put forward by Marcus is in accordance with Saumjan's Interpretation of Trubetzkoy's theory.27 The definition above of the archiphoneme, however, conforms to the one proposed by Trubetzkoy himself. It would seera more logical to define both concepts either äs sets of features or äs

26 Here again I stick to the terminology of Marcus 1967a, 1969 (Fr. valeurs pertinentes, Cz. pertinentm hodnoty), which differs from the one used in Marcus 1963b and Kiefer 1968 (Rum. valori relevante, 'relevant values'). The first line of Kiefer 1968:139 contains a disturbing misprint: the formula stated there should be identical to my formula (3.23), with u instead of n. The same formula contains a different misprint in the original (Marcus 1963b:417), where a parenthesis should be added immediately after the equality sign. 27 Cf. Chapter 2 of this book. SET-THEORETICAL MODELS 63 pairs consisting of a physical and a relational component.28 The hybrid solution in Marcus' model, where an archiphoneme is a component of a phoneme, does not conform to any phonological theory known to the present author. This is only a matter of labels, however. More important is the concept of neutralization defined above. The relevance of the criterion adduced here depends, once again, on the Interpretation of the symbol S, which I have discussed in section 3.7. If this Symbol Stands for a set of actually registered sequences of speech sounds, the above condition will not yield satisfactory results because the physical realization of an archiphoneme generally depends on its environment. Thus, though the [s] in Ru. [fstal] 'got up' is never replaced by [z] in ordinary speech, it is an archiphoneme in Trubetzkoy's sense. Moreover, the Interpretation of 'registered' äs 'actually occurring' renders the distinction of neutralization from defective distribution impossible. Such a distinction becomes meaningful only if sound sequences are identified on the basis of an informant's indications. This Interpretation evokes a number of new problems, however. Firstly, if sound sequences are assigned to .R-classes on the basis of an informant's indications, the relation R may not turn out to be an equivalence, e.g., the transitivity may be lacking. Secondly, the identity of meaning of two differently valued sound sequences does not necessarily point to a neutralization because of the existence of doublets: Ru. Ja videl skap and Ja videl skaf both mean Ί saw a cupboard' but the Opposition between [p] and [f] is certainly not neutralized. Thirdly, even if we remove this kind of doublets from the material the possibility of replacing χ by y in a sound sequence t without a change of meaning and the impossibility of the same replacement in another sound sequence need not be positionally conditioned, cf. Po. [bjore] and [bjore] Ί take', but [xore] 'sick', not *[xore]. Here the latter [e] is non-nasal, while the former is indifferent with respect to nasality. Though we can write F(x) <= F(y) there is no neutralization because χ and y occur in the same Position.29 It is clear from these observations that many linguistically essential questions remain unanswered in Marcus' model. Its main deficiency is the absence of correspondence rules.

3.9. CRITICISM

The model outlined above evoked various kinds of criticism. In the present section I shall deal with some alternative possibilities that have been suggested by three authors, viz. the author of Models oflanguage, 1.1. Revzin, the Czech mathematician L. Nebesky, and the Rumanian linguist A. Avram.30 These suggestions, all of which concern minor points in the formal apparatus, are in a way characteristic of the

28 The former solution is chosen in Marcus 1961:505, where a phoneme is defined äs a set like F(x). 29 This topic is treated at length in Chapter 9 of this book. 30 Cf. Revzin 1964, Nebesky 1966a, Avram 1967. 64 THE DEVELOPMENT OF MODELS IN PHONEMICS different outlook that scholars with different backgrounds display with regard to the same data. In bis 1964 article Revzin gives an exposition of the model proposed by Marcus, mysteriously leaving out the concepts of 'Ä-equivalence', 'phoneme', 'neutralization' and 'archiphoneme'. Two marks nn and mj (or two values V{ and v;) are 'concomitant' (soprjazennyj, literally 'conjugate' in the mathematical sense of the word) in the sound χ if both of them are elements of V(x) and the replacement of one of them by another from the same homogeneity class does not yield a set V(y) for any y e E while the simultaneous replacement of both of them by other marks (values) from the respective homogeneity classes does yield a set V(y) for some y e E. Thus, the features of voicelessness and tenseness in Russian (and some other languages) can only simultaneously be replaced by their counterparts. The article also contains a revision of Revzin's 'paradigmatic model', which was expounded in section 3.4 on the basis of Marcus' partition introduced in formula (3.16) above. If the homogeneity classes are numbered we can restate the algorithm äs follows.31 (1) There is for any sound χ only one feature m\ ε Mi. We define Ki^ äs the class of sounds that differ from χ only by the absence of mi and the presence of a feature homogeneous (in the new sense) with mi. (ΐ (2) Let the classes Ki, ... KI^ have been constructed. We define Kl+i^ äs the class of sounds containing the maximum assembly of sounds that differ from each other only in features from MI. This procedure is repeated until all sounds of the Subsystem are exhausted. (3) This is repeated for every class of features Mj. Nebesky's criticism regards above all the concept of 'pertinent values', which he calls 'relevant values' in accordance with Marcus 1963b. The phonemic System defined in formula (3.22) does not determine the set of phonemes of a language because the concept of 'phoneme1 depends on the concept of Ä-equivalence äs well. Now Nebesky introduces a function ψ which is analogous to the function φ but associates every Speech sound only with its linguistically relevant features. He defines a System which he calls 'F-system' äs a septuple F = [V, P, E, φ, S, R, ψ] (3.25) where V, P, E, φ, S, R have the meaning attributed to them in the foregoing sections and ψ Stands for a function that assigns a set of values to every speech sound χ e E such that (1) ψ (χ) <= φ (χ) for every x e E, and (2) if for every registered sound sequence s e S containing χ the replacement of

31 In accordance with Revzin's formulation I shall write M and m instead of the Symbols V and v used by Marcus, cf. Revzin 1964:65.1 shall not speak of 'phonemes', however, because this concept remains undefined in Revzin's exposition. Moreover, it is not clear whether the premisses of the algorithm hold for phonemes äs well äs for sounds. SET-THEORETICAL MODELS 65 x by y yields anolher registered sound sequence, then the number of elements in ψ(χ) is less than or equal to the number of elements in ψ()>). If ψ fulfils these conditions then it is called a Fo-mapping and F is called a Fo-system. There are at least two .Fo-mappings, viz. the function φ and the function that associates every speech sound with the empty set (i.e., ψ(χ) = 0 for every χ e E). The function ψ- associates a sound sequence with the sequence of sets of values that ψ associates with the sounds that occur in the sound sequence. Formally, if s (s e S) is a sequence consisting of the sounds xi, ..., xn (xi £ E for /=!,...,«), then yr~(s) is defined äs the string ψ(χι)

... ψ(χη). If ψ is a Fo-mapping then ψ is a Fi-mapping and F is a Fi-system if for every pair of sequences p, g e S that are not .R-equivalent Ψ~(Ρ) * ψ-(9) (3-26)

If ψ is a Fi-mapping then ψ is a iVmapping and F is a F2-system if for every Fi- mapping ψ' such that ψ'(χ) c ψ(χ) for every χ e E, it holds that ψ' = ψ (3.27) Thus, ψ is a F2-mapping if it is the unique Fo-mapping that associates every sound with a minimal number of features under the condition that every pair of sound sequences conveying different meanings are kept apart.32 It cannot be doubted that Nebesky's remarks constitute an important extension of the model proposed by Marcus. Two things should be kept in mind, however. Firstly, there is a clear shift äs to the emphasis that is laid on various identification principles. Revzin's analysis is entirely distributional, and every reference to meaning is excluded from his model. Marcus introduces meaning in the form of a given equivalence relation in the very tail of his model. In Nebesky's proposal, however, the criteria of jR-equivalence and simplicity (in the sense of minimizing the number of relevant features) are crucial. The priority of the latter criterion is, in fact, explicitly stated in Nebesky's model, which will be discussed in the following section. Secondly, the lack of correspondence rules involves the puzzling question: what linguistic phenomena are actually modelled ? The answer to this question is far from obvious. In fact, the second condition that ψ must fulfil in order to be a Fo-mapping is precisely the condition characteristic of 'heavy phonemes': if we put χ —- Po. [e] and y — Po. [e] then χ can always be replaced by y but not conversely, so χ is always irrespective äs to nasality whereas y is sometimes irrespective äs to nasality (e.g., in [bjore]) but definitely non-nasal in other cases (such äs [xore]).33 Consequently, φ(χ) and φ(γ) contain the features 'nasal' and 'non-nasal' respectively, ψ(χ) contains

32 Two remarks about the original formulation have to be made. Nebesky uses the symbol S not only äs a designation of the set of registered sound sequences but also äs a designation of a sound sequence from that set. This may be confusing. Furthermore, the implication in the third paragraph of Nebesky 1966a:455 has been inverted, so that the Statement becomes false. (If the Statement holds äs it is formulated, the introduction of ψ is senseless.) 33 Cf. Chapter 9 of this book. 66 THE DEVELOPMENT OF MODELS IN PHONEMICS no nasality feature, and ψ(γ) contains the feature 'non-nasal' in some instances and no nasality feature in others. It follows that the number of elements in ψ(χ) is less than or equal to the number of elements in y/(y). Since 'heavy phonemes' are hardly ever referred to in theoretical linguistics, however, it is highly improbable that Nebesk^ had this kind of language data in mind when he wrote his remarks on the model put forward by Marcus. Avram's article is not a direct answer to Marcus but can be viewed in connection with the model outlined above. Marcus defines the 'distance' between two sounds äs the number of values (features) that are diiferent for them. Thus, the distance between Ru. [p] and [b] is equal to l because there is only one feature where these sounds differ. In Avram's conception the distance between two PHONEMES should be defined äs the number of features present in one of them and absent in the other plus the number of features present in the latter and absent in the former. Consequently, the distance between Ru. /p/ and /b/ is equal to 2 because /p/ lacks the voicedness of /b/ and /b/ lacks the voicelessness of /p/. This approach makes it possible to make allowance for the irrelevancy of features: according to Marcus, the distance between [b] and [m] is equal to the distance between fp] and [b] but to half of the distance between [p] and [m], while the distance between /b/ and /m/ is equal to the distance between /p/ and /m/ and to l i times the distance between /p/ and /b/ according to Avram's criterion. In my opinion, it should be possible to define diiferent kinds of distance according äs the purpose of the investigation may require. At the moment I have to admit that I do not see how ANY kind of distance between sounds or phonemes can lead to meaningful Statements about languages (though I may have to alter my view in the future). The proposals by Marcus and Avram make in any case more sense than the one put forward by Peterson and Harary, which will be examined in Chapter 4.

3.10. NEBESKY'S CONCEPTION OF RELEVANT FEATURES

The three kinds of criticism discussed in the preceding section are possible extensions of the model put forward by Marcus. As such, they introduce additional criteria, which are not, however, used for an evaluation of the basic properties inherent in the model. Such an evaluation is a more fundamental kind of criticism and presupposes, in fact, an alternative model containing alternative criteria äs to its basic properties. This more fundamental kind of criticism is found in Nebesky 1966b. According to Nebesky, the set of relevant features of a language unit should fulfil the following requirements (1966b: 35f.). The set that has been denoted by the symbol S is now called the 'set of well-formed strings of sounds'. 1. It must be able to differentiate two units (sounds) in all cases within the set of well-formed strings of units (sounds), where it is necessary to dißerentiate every two well-formed string[s] in case they were differentiated by the sets of all features of units. 2. The sets must possess some 'reasonable' property. SET-THEORETICAL MODELS 67 3. With regard to the requirements l and 2 the System of sets of relevant features of the sounds äs well äs the sets themselves must have the smallest number of elements.

The requiremenis l and 3 correspond to identification rules on the basis of complementary distribution and economy, respectively. As will be pointed out in Chapter 4, these criteria are rather weak identification principles from a linguistic point of view and the linguistic value of Nebesky's model is thereby considerably diminished.34 The requirement of 'reasonability' is interpreted äs a kind of minimal pair identification rule. The evaluation of this reasonability requirement is not discussed in the paper under examination because it "lies outside the formal devices" (1966b: 36). The initial objects of Nebesky's model are given by (3.22).35 The restriction on φ is relaxed so that there is now for every χ and z MAXIMALLY one value v such that formula (3.17) holds. The sei of functions/: £·-> V* (where V* is the set of sets of elements from V} that fulfil the latter requirement is denoted by T.36 It follows that φ e T. Henceforth I shall write φ(χ) instead of V(x), which is in accordance with Standard mathematical notation, and (p~(s) for the string of sets of values that φ associates with the elements of a sound string s e S. (This is analogous to the notation y/~(s) in the preceding section.) The symbol U (φ, S) will denote the set of such fe T that for every pair of sound strings p, q e S if

Ψ-(Ρ) Φ φ~(9) (3.28) then

/-(P) Φ /-(«) (3.29) where /-(j) Stands for the string of sets of values that /associates with the elements of a string s e S.37 The set U(q>, S) is interpreted äs the set of those/e T which for each χ e E satisfy the above requirement 1. From the linguistic point of view this Interpretation makes sense only if FREE VARIATION HAS SEEN REMOVED at the very outset. The set of possible environments of a sound χ e E is defined by ) = {(p,q):pxqeS} (3.30) The length of a string s e S is defined äs the number of elements which it contains and denoted by A(i). Thus, if

s = χι ... xn (3.31)

34 According to Nebesky's criteria, the phonemes /h/ and /n/ must be identified with each other if they are in complementary distribution. 38 Nebesky writes A for E, B for V, C for P, d for S, and e for φ. Members of A, B, C are designated by a, b, c, respectively. Other Symbols are defined in the sequel. In order not to complicate matters unnecessarily, I shall stick to the notation introduced above. 36 Ein Nebesky's notation. 37 Nebesky writes F(d,e) instead of U(,S) and G%(,5) ^ 0 (3.34) or, respectively, γ(χ,5Γ) η Ky,S) Φ 0 (3.35) then #(*,.)/) Φ 0 or $?(*) = 9>(j). The symbol F((p,S) will denote the set of those /: E -* F* for which there exists a function g e G((p,S), which depends on/, such that for every x e E f(x) = u £(*,>·) (3.36)

and, analogously, Fi(,«S), respectively, with the same property. It follows that F*(q>,S) «= /i(p,S) c F(fl»,S) (3.37)

It is easily proved that F^S) «= T and Fa (?»,S) c U (,S) is interpreted äs the set of 'reasonable' subsets of the sets of sound features. The set of fe T fulfilling both the first and the second requirement formulated in the first Paragraph of the present section is defined by

38 Nebesky writes K instead of G, G instead of Γ, J instead of γ, and H instead of λ. His notation is not always unambiguous: his k(a,a'), which is my g(x,y), Stands for the value that g may assign to (x,y) in the first requirement and for the set consisting of maximally one value that g assigns to (x,y) in the second requirement, cf. Nebesky 1966b:37. SET-THEORETICAL MODELS 69

H(,S) and Fz(,S) the number of elements in {f(x): xe E] is smaller than or equal to the number of elements in {f'(x) : χ e E}. The symbol H"((p,S) will denote the set of such/e H'((p,S) that for every/' e H'(

39 My F and H stand for Nebesky's L and M, respectively. Ι Π 40 These functions are denoted by ea, and ea in Nebesky's paper. 70 THE DEVELOPMENT OF MODELS IN PHONEMICS

In Nebesky's 'theorem 2' it is stated that

ει, εζ e Ρ(φ,3) (3.43) for all φ and S, and that every one of the following situations may occur for some φ, S, provided that the number of sounds and the number of features are not too small:41

Sl,£zeF(

ei, £2 e H(f,S) - H'(

ει, ε2 e Η'(φ,8) - Η"(φ,8) (3.46)

ει, ε2 e Η"(φ,8) (3.47)

εχ e F((p,S) - H(

ει e Η(φ,3) - Η'(φ,Ξ), ε2 e Η"(φ,3) (3.49)

In view of the importance of these results I shall quote Nebesky's conclusion in füll (1966b: 41f.).42 From the theorem 2 [i.e., the Statements about formulae (3.43)-(3.49)] it follows that while the mapping ει always satisfied our requirement 2, it does not always satisfy our requirement 1. But the requirement 2 — the requirement of 'reasonability' — was chosen in this work so that ei always satisfies it. The requirement l, which, however, has a more principal character, is not always satisfied, and this is a considerable shortcoming of the mapping ει. Moreover, even when ai satisfies both the requirements, it behaves in a very different way with respect to its minimalizations [requirement 3]. The mapping 82 behaves in a similar way. Also, in case ει satisfies both the requirements, BZ behaves still worse. It behaves better only in case ει behaves very badly, i.e. when it does not satisfy the requirement 1. The aim of this remark was to draw attention to the fact that the notion of relevant characteristics of language units (relevant features of sounds) is not by far so clear äs it might seem, and that its general satisfactory solution is very difficult.

I cannot disagree with the last remark, though I may have a different conception of relevancy.

3.11. GRAPHIC MODELS

The preceding section clearly illustrates the mathematization of linguistic modelling which I referred to at the beginning of this chapter. This development entails a growing number of Symbols and formulas which are used for the clarification of a scholar's thoughts. However, most linguists are not accustomed to their use. Another, in fact

41 Nebesky's article is füll of misprints. Three of them are especially annoying, viz. the three Symbols K (= my G) instead of L (== my F) in theorem 2 sub l, 2, and 6 (corresponding to the formulae (3.43), (3.44), and (3.48) stated here). I II 42 I have substituted ei, «2 for his ea, e

Such illustrations have been common in phonemics for äs long äs it has existed.43 An extension of this kind of 'models' to three-dimensional representations is proposed in Evdosenko 1963.44 In this article, a 'feature' is represented by a plane. The intersection of two planes is a line, representing a 'phonemic row'. The intersection of three planes is a point, representing a 'phoneme'. The model is easily extended to more-dimensional spaces. An interesting characteristic of this kind of models is that the suggestiveness of a graphic representation requires a minimalization of the number of dimensions. Thus, Evdosenko unites openness and nasality of vowels into one dimension, and also voicedness and nasality of consonants. This practice is diametrically opposed to the general trend in contemporary linguistics of reducing rt-ary oppositions to the presence versus absence of binary features. It must be noticed that any graphic representation is not a model but PRESUPPOSES a model which allows certain set-theoretical operations. As far äs I know, the conditions under which graphic modelling of the paradigmatic relations between phonemes is possible have never been stated formally.

3.12. KANGER'S MODEL OF THE PHONEME

In all models discussed so far in the present chapter the set of Speech sounds E belongs to the initial objects of the analysis. Alternatively, one can proceed from a given set of strings. This approach is chosen in the model put forward in 1964 by the Scandinavian mathematician S. Kanger, who defined a 'phonology' äs a quadruple F = [U, ·, R, S] (3.50) where U is a non-empty domain, · is an associative binary Operation in U, R is an equivalence relation in U, and S is a non-empty subset of U that is closed under R (i.e., if χ e S and χ R y then y e S). It is furthermore assumed that if x-z = y-z or z-x = z-y then χ = y, and that if χ R y then x-z R y-z and z-x R z-y. Linguistically, (7is interpreted äs the set of possible sound sequences, · is the Operation

43 Cf. Sapir 1925, Bloomfield 1933, Trubetzkoy 1939. 44 The possibility of a 'stereometrization' was suggested in Reformatskij 1961a:118ff, Three- dimensional representations had been used earlier, 72 THE DEVELOPMENT OF MODELS IN PHONEMICS of concatenation (juxtaposition), and R and S have the same meaning äs in the above models. The symbol A Stands for a subset of U. Henceforth I shall write xy instead of x-y etc. The 'concatenation set' of A, which is denoted by A*, is the least subset of U such that A <= A* and xy e A* whenever x, y eA*. It is stated that χ is a 'part' of y (notation: χ P y) if there are z, w such that y — zx or y — xw or y = zxw, and that χ is a 'variant' of y (notation: χ var j;) if it holds for every z and w (which may be empty) that if zxw e S or zyw e S then zxw R zyw. Now A is a 'phonematic base' and the members of A are 'phonemes' if there exists a subset A of U such that (1) Ä <= Λ*, (2) if χ e /i then there is no y e A such that Λ: Ρ y,

(3) S <={z: 2 var χ, χ e yi}*, and (4) the number of members of A is minimal under these conditions. The linguistic relevance of Kanger's model is limited because the concept of relevancy remains out of the picture. There is no distinction between sounds and phonemes except for the elimination of free Variation. The linguistically important question of determining whether the relation A: P y holds or not (one or two phonemes) is left open. But there is one most interesting novelty in the above proposal: in the definition of 'variant' it is stated that if zxw e S OR zyw E S then zxw R zyw. Thus, two sound sequences can have the same meaning even though one of them may not occur äs a member of S. This novelty, which is not exploited in the model under discussion because S is closed under R, is in fact the key to a sound functionality test.45

3.13. RELATIONS BETWEEN MODELS

It will be clear from the foregoing sections that different models most often Supplement rather than replace each other. The diflference generally concerns the object which is modelled and the requirements that the investigator imposes on the input and the Output rather than the internal characteristics of the model. Thus, we have seen how meaning was absent in Revzin's model, crept in at Marcus', became one of the two cornerstones in Nebesky's adaptation of Marcus' System, and feil out in Nebesky's own model. Rev/in's 'paradigmatic model' is a classifying algorithm, while Evdosenko's 'Stereometrie model' is a picture of a classification: they refer to the same linguistic facts but reflect different aspects of them. The syntagmatic models outlined in section 3.5 all deal with phonotactics, but the underlying assumptions and the aims of the proposed models differ.46 Two consequences derive from this 45 This point will be taken up in Chapter 8 of this book. 46 This may require some comment. Harary and Paper take into account only immediately juxtaposed phonemes while Marcus and Vasiliu consider strings of consonants. (Markov's model can be interpreted either way.) There is an additional assumption about phonemic distribution in Marcus and Vasiliu's model, viz. ifboth ;>.*:;># Andpx'y'g occur, theapxy'q andpx'yq must also occur. As to SET-THEORETICAL MODELS 73 Situation. On the one band, the evaluation of one model in terms of another can easily lead to a misrepresentation of the model which is evaluated.47 A strict distinction should be made between criticism of the starting-point or the aim of an investigation, and criticism regarding the inherent properties of a model. On the other hand, this distinction opens the possibility of combining two models and investigating the relations between the concepts defined in one of them and the concepts defined in the other. In particular the relations between the paradigmatic (distinctive) and the syntagmatic (tactic) properties of a phoneme can be considered. The idea is not new: the avoidance of meaning led American distributionalists to the identification of phonemic units on the basis of their occurrence in different positions (cf., e.g., Bloch 1948). Conversely, one can try to describe certain distributional characteristics of Speech sounds in terms of their inherent properties. The latter possibility was suggested in 1966 by the Yugoslav phonemicist Z. Muljacic, who asked the following questions (1967:273): 1. Les contrastes des phonemes contigus dans la chaine parlee (sur Taxe syntagmatique, in praesentia) dependent-ils des traits distinctifs inherents qui servent a opposer ces memes phonemes dans le Systeme (sur Taxe paradigmatique, in absentid)1 2. S'ils en dependent, en quoi donc consiste le rapport entre la combinabilite mutuelle des phonemes et leur base subphonemique ? The first question was answered in the affirmative. For determining the relation between the tactic properties of a phoneme and its distinctive features, Muljacic introduced a distance between phonemes which turns out to be identical with the one proposed by Avram. The hypothesis put forward in Muljacic's paper can be formulated äs follows: the (paradigmatic) distance between phonemes that occur in juxtaposition is generally neither very small nor very large but fluctuates around an average value. This hypothesis was tested on a set of word-initial clusters consisting of two consonants in Serbo-Croatian and Italian. The idea was taken over by Tolstaja, who tested the hypothesis on the sets of initial and final biconsonantal clusters in Polish, Czech, Russian, Serbo-Croatian, and Bulgarian (1968). The two analyses of Serbo-Croatian initial clusters differ considerably. In the first place, the allotment of distinctive features to various phonemes is different (e.g., /r/ is {vocalic, consonantal, interrupted} according to Muljacic and {non-consonantal, diffuse, acute, discontinuous, non-nasal} according to Tolstaja). This causes the distance between /s/ and /n/ to be 3 according to Muljacic and 8 according to Tolstaja whereas the distance between /s/ and /t/, which is also 3 according to Muljacic, is 2 according to Tolstaja. In the second place, their analyses are based on different material. Both authors allude to a possible universality of the property stated in the hypothesis. the aims of the models, Markov is interested in the prediction of a sound on the basis of the preceding sound(s) whereas Harary and Paper are interested in a numerical characteristic of occurring sound combinations for typological reasons and Marcus and Vasiliu in a suggestive representation for descriptive purposes. 47 Cf. Nebesky's criticism of Marcus in 1966b:40, and Revzin's criticism of Evdosenko in 1964:61. 74 THE DEVELOPMENT OF MODELS IN PHONEMICS One of the striking characteristics of counting linguists is the absolute disregard of statistical regularities.48 The very fact that nearly the same numerical results are obtained on the basis of so widely divergent initial assumptions should be a hint at the statistical interference which is the decisive factor. Let us consider the following artificial example. tdszpbfvcsszkgxy compactness — — — — — — — — + + + + + + + + graveness — — — — + + + + — — — — 4- + + + continuousness — — + + — — + + — — + + — — + + voicedness —· + — + — + — + — + ·— + — + — + If there are no restrictions whatever on distribution, we obtain the following average displaying function, which approaches the normal distribution function if the number of features is increased (cf. Feller 1957: 168ff.). distance between phonemes number of pairs of juxtaposed phonemes 0 16 2 64 4 96 6 64 8 16 In fact, the Situation is more complicated because Muljacic and Tolstaja allow the possibility that a phoneme has neither + nor — in one or more cells. Let us therefore consider the following example, again artificial, where I have assumed (by way of convention) that the positively marked members of any Opposition do not participate in the subsequent Opposition. t t' d s s' p p' b k k' g χ x' compactness ______-J__L..J--J.-|- graveness ______|_-j_-|_ continuousness _ _ _ _|_ _j______|_ _|_ voicedness — — + _ _ _|_ _ __ -j_ checkedness — + — + — + — + — + If there are, again, no restrictions on distribution, we obtain the following function. distance between phonemes number of pairs of juxtaposed phonemes 0 13 1 0 2 10 3 36

48 Cf. my criticism of Apresjan 1967 in Kortlandt 1971:78f. For the consequences of this deplorable attitude see Kuipers 1968:78ff. SET-THEORETICAL MODELS 75

4 18 5 28 6 36 7 20 8 8 Here we observe that a second maximum and several local minima can emerge on purely statistical grounds EVEN IF THERE is NO RESTRICTION ON DISTRIBUTION AT ALL. The actual figures calculated by Muljacic and Tolstaja manifest a pattern somewhere in between the two artificial examples adduced here. I would therefore maintain that they are no indication whatever of any linguistically relevant fact. There is of course a possibility of obtaining more interesting results, viz. by relating the number of actually occurring pairs of juxtaposed phonemes to the number of theoretically possible pairs within each distance class.49 However, since the 'distance between phonemes' has no real significance for me, I shall not enter into an elaboration of this idea.

49 It will then become clear that neutralizations lead to a shift of the distance modus downwards and to a favouring of even distances between nearby phonemes and odd distances between remote phonemes. These tendencies, which are quite understandable, are clearly shown in Tolstaja's illustrations, especially in the one on p. 70 of her article. IDENTIFICATION MODELS

4.1. INTRODUCTION

There is one important property that all models discussed in Chapter 3 have in common: THEY PRESUPPOSE IDENTIFICATION. The underlying assumptions of Revzin's model, which reappear in Marcus' formula (3.22), are never abandoned. On the contrary, they remain the ultimate basis on which all modelling rests. These models are preoccupied with the determination of the predictability of features on the basis of known distributional characteristics, not with the identification of units on the basis of their inherent properties. In Fillmore's terminology, they model the 'phonetic characterization' of a representation on the basis of its 'phonetic description', while the 'physical specification' of Speech remains wholly out of the picture (1962: 13f.). Since any phonetic description is stated in terms of some kind of units, the delimitation and identification of phonemic units is generally implied. In my opinion, however, this is the only linguistically non-trivial problem in phonemics. The problem has four aspects:

(1) the paradigmatic delimitation of phonemic units, (2) the syntagmatic delimitation of phonemic units, (3) the identification of phonemic units in different positions, (4) the identification of phonemic units on account of meta-theoretical considerations ('pattern congruity', 'economy', 'simplicity').

The last point differs fundamentally from the three others because it bears exclusively upon the model, not upon the object which is modelled; this kind of argument can be invoked only if the other criteria do not yield a unique solution. The problem of the delimitation of units is not posed in any of the models presented in Chapter 3. The identification of units in different positions is generally carried out on the basis of phonetic similarity, which is not, however, stated explicitly äs an identification principle. The identification of units because of meta-theoretical considerations takes place quite frequently in the models above, though the linguistic sense of the restrictions under which such an identification is allowed remains out of the discussion. IDENTIFICATION MODELS 77 In this chapter and in Chapter 5 I shall deal with some of the models that have been proposed for the identification procedure itself.1

4.2. THE INITIAL OBJECTS OF USPENSKIJ'S MODEL Two such models were published in the last issue of Voprosy jazykoznanija 1964: one by V.A. Uspenskij, and the other by V.N. Beloozerov. The initial objects of Uspenskij's model are the following (1964: 40ff.). (1) There is a set of Speech fragments, which are called 'initial pronouncings' (isxodnye proiznesenija). These are not supposed to be pronounced in isolation, but they are thought of äs being cut out of the speech flow. They can, e.g., be interpreted äs utterances, sentences, phrases, word forms, or morphs. (2) There is a segmentation of the initial pronouncings into 'concrete sounds' or 'speech sounds' (zvuki reci) such that every initial pronouncing can be identified with a linear sequence of (concrete) sounds.2 The segmentation introduced in this postulate remains the only one in the whole model. Thus, THE SYNTAGMATIC DELIMI- TATION OF PHONEMIC UNITS is NOT DiscussED. The model presupposes a one-one correspondence between phonemic units and the Segments exhibited in the phonetic description of their physical correlates. (3) There is a classification of the concrete sounds (speech sounds) which occur in the initial pronouncings into classes of 'identicaP (odinakovyj) sounds. This classification, which is arbitrary, can, e.g., depend on the discriminatory power of the Instruments used for observation. A class of identical concrete sounds is an 'abstract sound' or 'language sound' (zvuk jazyka).3 (4) Some pairs of language sounds are 'phonetically similar' (foneticeski blizkij). The relation of phonetic similarity is reflexive and Symmetrie, but not necessarily transitive. (5) There is a 'transcription alphabet' (transkripcionnyj alfavit) exactly containing one sign for every language sound. The signs can be identified with the (abstract) sounds which they represent. (6) Every initial pronouncing can be written äs a string of transcription signs by replacing every concrete sound with the corresponding abstract sound. Transcriptions of initial pronouncings are called 'initial expressions' (isxodnye vyrazenija). Every initial pronouncing is called a pronouncing of the initial expression derived from it. It is clear from the definitions that different initial pronouncings may have the same transcription and one and the same initial expression may have different pronouncings. 1 It should be noticed that the 'sets of postulates' presented in Bloomfield 1926 and Hoch 1948 belong to this category of models. Since every phonemicist is familiär with these publications I shall exclude them from the present exposition. 2 Cf. the terminology in Saumjan 1962 and Kuznecov 1959. 3 These concepts are not identical to the ones introduced by Saumjan and Kuznecov, äs the terminology might suggest. 78 THE DEVELOPMENT OF MODELS IN PHONEMICS (7) Every initial pronouncing has one or several meanings, viz. the one(s) which it had in the context of which it was cut out. It is not necessary to know what meaning an initial pronouncing had in its initial context, but one must be able to characterize two meanings äs either 'same' or 'different'. Two initial expressions are called 'equivalent' (ravnoznacnyj) if they have the same set of meanings. It is clear that this meaning equivalence is an equivalence relation. The set of language sounds (or transcription signs representing them) with the relation of phonetic similarity defined on it and the set of initial expressions with the relation of meaning equivalence defined on it are the initial objects of Uspenskij's model. In accordance with the symbolization introduced in the preceding chapter we can represent this 'phonetic system' by F=[E,D,S,R] (4.1) where E is the transcription alphabet (or the set of abstract sounds), D is a reflexive and Symmetrie (but not necessarily transitive) relation defined in E, S is the set of initial expressions (= strings of elements from E), and R is an equivalence relation defined in S. Henceforward the elements of E and the elements of S will be called 'sounds' and 'sound sequences', respectively. The model itself is of course independent from the way these elements are distilled from observed facts. A comparison of formula (4.1) with formulae (3.21), (3.22), and (3.25) shows the two important characteristics that distinguish the present model from the ones discussed in Chapter 3: the replacement of features by the less clear-cut notion of phonetic similarity, and the central position of the meaning equivalence R. The concepts denoted by S and R are liable to the same criticism äs I have put forward in connection with the models already discussed, so there is no need to repeat it here.4 The influence of the context on the meaning of a pronouncing entails certain minimum conditions äs to the size of S. Besides, the jR-equivalence in formula (4.1) is a weaker datum than the original same-or-different criterion referring to separate meanings because the former reflects only the identity of SETS of meanings. If 'heavy phonemes' are taken into account, the .R-equivalence is an insufficient datum because the unilateral character of such phenomena cannot be stated in terms of equivalences. Thus, all meanings of Fr. [zdire] Ί would say' are meanings of [zdire] Ί will, would say', but the converse does not hold.5 The inclusion of one set of meanings in another follows from the above same-or-different criterion, but cannot be derived from the JR-equivalence.

4.3. IDENTIFICATION RULES

Every initial expression is now coordinated with a string of phonemes. Since the segmentation of the speech flow is supposed to be given (see above), every language 4 Cf. sections 3.7 and 3.8 of this book. 5 See Chapter 9 of this book. IDENTIFICATION MODELS 79 sound in an initial expression corresponds to exactly one phoneme. Moreover, one and the same sound cannot correspond to two or more different phonemes: there is no phonemic overlapping.6 Consequently, a phoneme is defined äs a set of disjoint classes of speech sounds. A sound that corresponds to a given phoneme in some initial expression is called an 'allophone' of the phoneme. The sounds of the language (= the elements of E) are now united into phonemes in accordance with the following identification rules. The first and the second rule are 'prohibition rules', the third one is a 'prescription rule', the fourth and the fifth are 'recommendation rules'.7 (1) Sounds which are not PHONETICALLY SIMILAR cannot be coordinated with the same phoneme. (2) Sounds for which there exists a MINIMAL PAIR cannot be coordinated with the same phoneme. (3) Sounds which are in FREE VARIATION must be coordinated with the same phoneme. (4) Sounds which are in COMPLEMENTARY DISTRIBUTION should if possible be coordinated with the same phoneme. (5) Sounds should be coordinated with phonemes in such a way äs to yield maximal PATTERN CONGRUITY. The last criterion is subject to widely divergent interpretations. For the sake of comparison I shall restate Uspenskij 's other rules in terms of the concepts introduced above. A phoneme is denoted äs a class of allophones; therefore we can write [a] e /a/ instead of [a] i- /a/ etc., in the discussion of the present model.

Rl. For every x, y e E if (x,y) φ D then there is no phoneme Z such that both χ e Z and y e Z. R2. For every x, y e E if there are strings p, q (which may be empty) such that pxq e S and pyq e S and (pxq,pyq) φ R then there is no phoneme Z such that both x e Z and y e Z. R3. If there are sounds x, y e E such that for every pair of strings p, q (which may be empty) such that pxq, pyq e S it holds that (pxq,pyq) e R then there is a phoneme Z such that both x e Z and y e Z.8 Two sounds are in free Variation IN A GIVEN ENVIRONMENT (p,q) if the requirement holds for the string pairs containing (p,q) äs an environment of x, y.

6 This rule precludes the existence of heavy phonemes, cf. below. 7 Cf. Uspenskij 1964:44f. In fact, there is an additional prescription rule, which is implicit in the phonetic analysis, viz.: sounds that are 'identical' in Uspenskij's sense (see above) must be coordinated with the same phoneme. It is this rule which renders phonemic overlapping impossible. 8 This is one Interpretation, viz. the one according to which sounds that are in some positions in free Variation must be in complementary distribution elsewhere. If one imposes the (strenger) requirement that sounds must in every position be in free Variation, the formulation becomes: if there are sounds x, y s E such that for every pair of strings p, q such that pxq e S1 or pyq e S it holds that (pxq,pyq) ε R and both pxq e S and pyq e S then there is a phoneme Z such that both x e Z and y e Z. The latter Interpretation, which is suggested in Uspenskij 1964:46, involves an extra requirement äs to the size of S äs well. 80 THE DEVELOPMENT OF MODELS IN PHONEMICS R4. If there are sounds x, y e E such that for every pair of strings p, q (which may be empty) either pxq $ S or pyq φ S (or both) then it is recommended to set up a phoneme Z such that both χ e Z and y e Z. These rules do not necessarily yield a unique solution. The fifth criterion can be interpreted in such a way that a unique solution is attained. It should be kept in mind that the formalization given here remains subject to the criticism of S and R outlined above. The minimal pair and complementary distribution rules make sense only if S is large enough. Besides, the concept of free Variation in a given positio n is not purely phonemic because of the existence of doublets: it is hardly in accordance with linguistic practice to state that "in Russian the sounds [f] and [p] are in free Variation in the environment ([ska], +)" (Uspenskij 1964: 46). Uspenskij states the following theorems in connection with the concepts of minimal pair, free Variation, and complementary distribution. Tl. The relation of free Variation, FV, is an equivalence. T2. The relation of NOT having a minimal pair, MP', is reflexive and Symmetrie but not necessarily transitive. Thus, if S = {axb, cyd, azb} and R is empty, then (x,z) e MP, but (x,y), (y,z) e MP'. T3. The relation of complementary distribution, CD, is Symmetrie and irreflexive. From the example just stated it is clear that the relation is not transitive: both (x,y) and (y,z) e CD, but (χ,ζ) φ CD. T4. There may exist a minimal pair for two sounds that are in some environment in free Variation. Thus, if S = {axb, ayb, cxd, cyd} and R — {(axb,ayb)} then

(x,y) e Ρνα$ but cxd and cyd constitute a minimal pair, so (x,y) e MP. T5. If (x,y) e FV then (x,y) φ MP. T6. If (x,y) ε CD then (x,y) φ MP. T7. There may exist x, y e E such that (x,y) φ MP, (x,y) φ CD, and (x,y) φ FV. This is the Situation, e.g., if S = {axb, ayb, cxd} and R = {(axb,ayb)}.g T8. If there are no x, y e E such that (x,y) e R, then for every two x, y e E it holds that (x,y) φ FF and, moreover, (x,y) e CD if and only if (x,y) φ MP. This theorem is the theoretical foundation of the contrastive-or-complementary-distribution principle which has been so populär in American structuralism. The next issue examined in Uspenskij's paper (1964) is the question of contra- dictoriness and completeness of the identification rules above. As Uspenskij correctly points out, a strict contradiction may arise only between a prohibition rule and a prescription rule. This possibility leads to the following AXIOM. If two sounds are in free Variation, then they are phonetically similar. Symbolically: (x,y) eFV=> (x,y) e D (4.2)

9 In this case y may be a 'heavy phoneme': take e.g. a = [bjor], c = fxor], b — d — [+], x = [e], y = [e], then. Ebeling's example cited above is obtained. Cf. also Chapter 9 of this book. IDENTIFICATION MODELS 81 It is clear from the theorems 5 and 6 that the second identification rule cannot be in contradiction with rules 3 and 4, even if rule 4 is considered a prescription rule instead of a recommendation rule. On the other band, it follows from theorem 7 that the set of identification rules above is incomplete, even if rule 4 is regarded äs a prescription rule. We can try to achieve completeness by modifying the identification rules in several ways. (2a) Two sounds must be coordinated with the same phoneme if and only if there is no minimal pair for them. This rule can easily lead to a contradiction in view of the fact that the relation MP' is no equivalence, cf. theorem 2 above. (4a) Two sounds must be coordinated with the same phoneme if and only if they are in complementary distribution or coincide. Here the term 'coincide' Stands for 'are phonetically identicaF, i.e., are denoted by the same transcription sign (see above). This rule also leads to a contradiction because CD is not an equivalence either, cf. theorem 3 above. Even the weaker principle of considering complementary distribution a sufficient but not necessary condition for coordination with the same phoneme yields a contradiction: (4b) Sounds that are in complementary distribution or coincide must be coordinated with the same phoneme. If there are no meaning-equivalent initial expressions, then it follows from theorem 8 that the identification rules 2 and 4b are together equivalent to 2a äs well äs 4a (which coincide in that case) and therefore lead to the same contradiction. (Cf. the example stated in connection with theorem 2.) Complementary distribution is a poor identification principle in any case. If we put S = {xiyi, xzyz} and (xiyi, xzyz) Φ R then the identification x\, xz l·- /x/, ji, yz l- /y/ yields the same phonemic transcription /xy/ for two sound sequences with different meanings, which is counter to the very principle of distinctiveness. According to Uspenskij, the whole difficulty is due to the fact that the criterion of complementary distribution (äs well äs the criterion of minimal pairs) refers to PHONEMES rather than sounds: two distinct, 'phonetically similar' phonemes cannot be in complementary distribution (and must have a minimal pair). This is why Uspenskij builds his model not on the identification rules above but upon the following requirements relating to the phonemes that result from the identification (1964: 50f.).10 1. Phonemes serve for distinguishing between meanings: consequently, different initial expressions, having different meanings, must not merge when the sounds that constitute them are replaced by the corresponding phonemes (i.e. if e.g. the initial expressions ax and bx have different meanings then α and b cannot belong to the same phoneme: otherwise, the two initial expressions would merge into one when the sounds are replaced by phonemes).

10 This solution was anticipated thirty years earlier by the Chinese linguist Y.R. Chao, cf. his defmition of the phoneme: "A phoneme is one of an exhaustive list of classes of sounds in a language, such that every word in the language can be given äs an ordered series of one or more of these classes and such that two different words which are not considered äs having the same pronunciation differ in the order or in the constituency of the classes which make up the word" (1934:39f.). This definition does not exclude the possibility of the same sound belonging to more than one phoneme, cf. Chao's discussion of Foochow [ei]. 82 THE DEVELOPMENT OF MODELS IN PHONEMICS

2. A further amalgamation of phonemes must be impossible (i.e. if e.g. there are phonemes A and B then the merger of A and B into one phoneme Υ must be impossible).

4.4. USPENSKIJ'S DEFINITION OF THE PHONEME

Uspenskij's model partitions the sei of sounds into phonemes, which are sets of allophones. All partitions in the present section are partitions of the transcription alphabet. The first step toward a phonemicization is the removal of free Variation. Since the relation of free Variation is an equivalence, it partitions the set of sounds into classes of sounds in free Variation. A partition 'removes free Variation' if every two sounds in free Variation belong to one and the same class. A partition is 'in concordance with the relation of phonetic similarity' if every two sounds belonging to the same class are phonetically similar. The axiom stated in formula (4.2) is equivalent to the assertion that there exists a partition which removes free Variation and is in concordance with the relation of phonetic similarity. The string of Symbols that is obtained from a sound sequence when every sound is replaced by a symbol representing the class to which it belongs, is called an 'image' (obraz) of the sound sequence. A partition is 'distinctive' (smyslorazlicitel'nyj) if every two initial expressions with different meanings have different images.11 Sounds belonging to one and the same class of a distinctive partition cannot have a minimal pair. It follows from the above axiom and theorem 5 of the preceding section (section 4.3) that there is a partition which (1) removes free Variation, (2) is in concordance with the relation of phonetic similarity, and (3) is distinctive. Such a partition is called 'quasi-phonemic' (pocti fonematiceskij). If we take E = {x, y, u, v}, every pair of sounds ε D, S = {xy, yx, xu, yv}, and R is empty, then u and y cannot belong to the same phoneme because (u,y) e MP, and the same holds for v and χ because (v,x) e MP. Moreover, χ and y cannot belong to the same phoneme because (xy,yx) is a minimal pair. The following partitions are quasi-phonemic: W> W} P* = {{*}, {y}, {«, v}} ^3 = {{x}, {»}, {y, v}}

P4 - {{x, u}, {y}, {v}}

P5 = {{x, u}, {y, v}} A partition A is an 'enlargement' (ukrupnenie) of a partition B if every two members of a 5-class are members of one and the same ^4-class. The enlargement is non-trivial if A and B do not coincide. A partition is 'phonemic' (fonematiceskij) if it is quasi- phonemic and if there is no quasi-phonemic non-trivial enlargement of it. The 11 It is clear that the property of distinctiveness depends only on the partition, not on the Symbols designating the classes. IDENTIFICATION MODELS 83 classes of a phonemic partition are 'phonemes'. Obviously, the existence of a quasi- phonemic partition is a necessary and sufficient condition for the existence of a phonemic partition. In the example above the partitions Pz and PS are phonemic. It is clear from this example that the phonemicization of a phonetic System is not necessarily unique. The cause of this non-uniqueness is the same äs in Chao's well- known 1934 paper, viz. the principle of grouping sounds into classes not on the basis of their own properties but on the basis of requirements concerning the resulting phonemes. A comparison of the model outlined here with the identification rules formulated in the preceding section (section 4.3) shows that the prohibition and prescription rules are complied with by any quasi-phonemic partition and that the choice of phonemic partitions from among the quasi-phonemic ones reflects to a certain extent the recommendation rules. Neither of the phonemic Solutions in the example above is in accordance with a strict application of the complementary distribution rule because such an application would conflict with the principle of distinctiveness: (x,y) e CD but (xy,yx) is a minimal pair. However, no two phonemes resulting from the analysis are in complementary distribution.

4.5. BELOOZEROV'S MODEL OF THE PHONEME

Thus, sounds in complementary distribution are grouped into phonemes with preservation of the distinctions between elements of S until no further grouping is possible. The resulting phonemes are not necessarily unique. Uniqueness can be achieved by modelling the very procedure of grouping sounds into phonemes. This problem, which is left open by Uspenskij, is tackled in Beloozerov 1964. The criterion on which Beloozerov's identification procedure is based is phonetic similarity. Those sounds in complementary distribution which resemble each other phonetically more than others are identified first, and so on. Instead of the above relation D Beloozerov introduces the concept of distance between sounds äs a measure of their similarity. Since the way of determining the distance between sounds falls outside the model and free Variation is removed at the outset by the assumption that all initial pronouncings conform to some norm, the initial objects of his model can be symbolized by F = [E, r, S] (4.3) where E is the transcription alphabet, r is a distance function, and S is a 'vocabulary' (slovar').12 The elements of S are called 'words'. There is one additional assumption,

12 In fact, r is a real, non-negative, Symmetrie function defined on Ez such that r(x,y) — 0 if χ = y and > 0 if χ ^ y. The triangulär inequality need not hold because distances between sounds are never added in the model under discussion. As to the symbolization, my E, r, S, MP, CD, IT, Φ stand for Beloozerov's A, ρ, Σ, P, S, Φ, [Φ], respectively. 84 THE DEVELOPMENT OF MODELS IN PHONEMICS viz. that no pair of sounds is characterized by the same distance äs any other pair.13 This assumption, which is based on the supposition that the distance between phonemes is measured experimentally and therefore depends on physical characteristics, enables the establishment of a strict Order in the set of pairs of sounds:

r(xi,yi) < r(xz,yz) < ... < r(xm,ym) (4.4) where m = %n(n—\) if n is the number of sounds. (It holds that χι φ yi for i = l, ..., m because pairs of identical sounds are not taken into consideration.) A pair of sounds (x,y) is called 'contrastive' (protivopostavlennyj) if there are two words s, t e S such that s = pxq and t — pyq, where p and q are sound sequences over E (p and q may be empty). If a pair of sounds is not contrastive, it is 'complementary' (sopostavlennyj). The sets of contrastive and complementary pairs of sounds are denoted by MP and CD, respectively.14 We now define a phonetic System äs Π = [E, r, CD] (4.5) From this phonetic System a phonemic System is obtained by grouping together those sounds in CD for which r is minimal and repeating this procedure until CD is empty.15 The distance between two sets of sounds is defined äs the minimal distance between any sound in the first and any sound in the second set: r(X,Y) = min r(x,y) (4.6) xeX je 7 The distance between intersecting sound sets is zero. We can now consider sets of

sounds only by defining a quasi-phonemic System [E0, C0], where

E0 = {{x}:xeE} (4.7) and

C0 = {({x},{y}): (x,y) e CD} (4.8) and uniting sets of complementarily distributed sounds äs follows. Because of formula (4.4) there is a pair (X, Y) e C0 such that r(X, Γ) is smaller than the distance between any other pair of quasi-phonemes in C0. We can therefore define recursively Ei = (Ε,_ι - {X, Y}) U {X u Y} (4.9) d = {(U, V): (U, V) e C,_i n E?} u {(X u Y, Z): both (X, Z) and (F,Z) e Ci_i} (4.10)

13 It must be noted that Beloozerov's own example (1964: 55) does not meet this requirement. 14 This symbolization is possible because of Uspenskij's theorem 8, cf. above. 15 The formalization of this procedure given here differs from the one proposed by Beloozerov because I prefer not to increase the number of different types of sets unnecessarily. IDENTIFICATION MODELS 85 where (X,Y) is the pair of quasi-phonemes in Ci_i which is characterized by the smallest distance. Thus, the number of quasi-phonemes is reduced by one in every step of the procedure until CK is empty for some k (k < «). Then we have reached the phonemic System

Φ = Eh de = 0 (4.11) The solution Φ is a partition of E into classes such that (1) there is a minimal pair for every pair of phonemes, (2) sounds belonging to one and the same phoneme are in complementary distribution, and (3) the minimal distance between phonemes äs defmed in formula (4.6) is maximal within the set of possible Solutions fulfilling (1) and (2). The following examples illustrate how Beloozerov's model can be applied to actual problems (1964: 58ff.). In English there are four a-like sounds, viz. open [3^] word-finally in sofa etc., slightly velarized [3·] in the neighbourhood of [k] and [g], neutral [3] elsewhere, and lengthened [3-] before the Suffixes ed (past indefinite, past participle) and s (third person of the present tense, plural of nouns) in words ending in er. We have ([a], [3-]) e MP because of sofas [soufsz] ~ suffers [sAfa~z]. Other sound pairs are in complementary distribution. Now we can write

E0 = {3, a- 3-, 3-} (4.12) and assume that φ,3·) < r (3,3-·) < φ,3~) < φΛ,3~) < φ·,3-) < φ·,3Λ) (4.13) Following the above procedure we define

31 = 3 u 3- (4.14) It follows from formulae (4.6) and (4.13) that φι,3-) < φι,3-) < φ-,3-) (4.15) Next we introduce

32 == 3l U 3~ (4.16) and obtain

φ = Ez = {/3/, 1^1} (4.17) where

M = 32 = {[3], [3·], M}, /S'/ = {M} (4.18) In Russian [a] and [o] occur in stressed syllables only. They are in complementary distribution with [a], which occurs in the first pretonic syllable, and [3] in other positions. Only ([a], [o]) e MP, We write 86 THE DEVELOPMENT OF MODELS IN PHONEMICS Eo = {a, ο, α, 3} (4.19) and assume that φ,α) < r(a,a) < φ,ο) < Φ,&) < Φ,ο) < r(a,d) (4.20) In accordance with the above procedure we define αϊ = 3 U α (4.21) &z = αϊ \J a (4.22) and obtain

Φ = £2 = {/a/, /o/} (4.23) where

/a/ = a2 = {[a], [a], [a]}, /o/ = {[o]} (4.24) It is clear from this example that the assumption of [3] being more similar to [o] than to [a] does not necessarily involve the identification of [3] with [o]. The third example is slightly more complicated. In Common Slavic there existed next to a reduced front vowel [t] a reduced [ü] which was in complementary distribution with both [t] and füll [i], the latter two vowels being opposed to each other. In 'weak position' [t] and [ü] were strongly reduced; the resulting vowels will be designated by [i] and [j], respectively. Thus, we can write

E0 = {i, Ϊ, j, Ϊ, 1} (4.25) and assume that r(\,\) < r(ü,i) < r(i,t) < r(i,ü) < r(i,i) < r(l,l) < r(\,i)

< r(i,i) < r(t,i) < r(V,i) (4.26) We now define U = i U i (4.27)

i2 = ϊ υ i (4.28)

18 = u u ΐ (4.29) and obtain

φ = E3 = {/i/, /i/} (4.30) where N = ia = {W, P]}, N = t8 = {M, h], [i]} (4.31) If we interchange (i,j) and (i,ü) in formula (4.26) then we obtain A/- {W, PL Ci]}, A/ = {FLW} (4.32) IDENTIFICATION MODELS 87 However, if we interchange (ΐ,ϊ) and (ϊ,ϊ) then ß/ = {H}, N = {K, W, W, [i]} (4-33) This example clearly shows in what way the identification procedure depends on the assumption of phonetic similarity. It is possible that the identifications presented here reflect different stages in the historical development of the language.16 The weakest point in Beloozerov's analysis is, in my opinion, the very starting- point. Beloozerov's phoneme is, like Revzin's and Scerba's and Jones', a family of phonetically related sounds in complementary distribution. Since this conception was already criticized in the preceding chapters, I shall confine myself here to three in my view essential remarks. (1) Sounds in complementary distribution should not be identified according to phonetic criteria but according to their functional value, which is embodied in their Substitution possibilities. UldalPs identification of Dan. initial [t], [d] with final [d], [δ] respectively is not possible in Beloozerov's model of the phoneme.17 (2) It is incorrect to reject the possibility of phonemes being in complementary distribution, cf. Ge. Du. Eng. /h/ and /rj/. (3) Even if one agrees with Beloozerov in precluding complementarily distributed phonemes and identifies /h/ with /rj/ in the languages just mentioned, the criterion of complementary distribution cannot be applied to SOUNDS. If E = {x,y} and S = {xy,yx} then (x,y) e CD but the identification of χ and y with each other leads to the phonemic indistinguishability of xy and yx.ls

4.6. PETERSON AND HARARY

Besides, it is not quite clear how the phonetic distance between sounds can be measured in any satisfactory way. One possibility was suggested in 1960 by G.E. Peterson and F. Harary. These authors distinguish five classes of parameters for determining the order of phonetic difference, viz. 1 = secondary articulation, 2 = laryngeal action, 3 — air direction, 4 = place of articulation (for vowels: tongue hump relative to pharynx), 5 = manner of articulation (for vowels: tongue height). Within each parameter class the individual parameters (features) are assigned decimal indices, so e.g. the value 3.1 means 'ingressive' for both consonants and

18 It must be noted that Beloozerov's identifications implicitly depend on formula (4.26) though he assumes explicitly that KU) < ΐ"(\,ΐ) and adduces even arguments in support of this assumption. It can easily be verified that the assumption leads to identiflcations different from the ones stated above. 17 Uldall 1935:54, cf. Fischer-J0rgensen 1956:150. 18 It is striking to notice that this problem was overlooked by Beloozerov though it had been pointed out already 25 years earlier by Trubetzkoy (1939:46). 88 THE DEVELOPMENT OF MODELS IN PHONEMICS vowels, while 4.3 Stands for 'alveolar' (consonants) or 'back central' (vowels). The phonetic distance between the sounds x, y is now defined äs the sum of the phonetic differences within each parameter class:

d(x,y) = y dt(x,y) (4.34)

These differences are calculated in accordance with the following formula:

di(x,y)j/· χ = i. +, a0i(x,y)., ^ — — — - ,„(4.35 ,« ) 10 10.ti(x,y) where qn(x,y) == 0 if the sets of parameters of χ and y in the z'th parameter class coincide, otherwise l ; rn(x,y) is the number of parameters by which χ and y differ in the ith parameter class; 9t(x,y) — 0 if the set of parameters of χ or y in the rth parameter class is empty, otherwise l ; st(x,y) is the sum of the absolute values of the differences between all pairs of decimal indices formed by parameters contained in χ but not in y and all parameters contained in y but not in x; and ti(x,y) is the number of terms in st(x,y). (Peterson and Harary 1961: 151) The rather formidable defining equation for di(x,y) actually expresses a simple number. The first term of the equation is an integer which is zero if x and y do not differ in a parameter class and otherwise is the index number of the parameter class. The digit in the tenths Position in the value of di(x,y) is determined by the second term in the equation and is the total number of parameters within the parameter class by which the two phones differ. The digit in the hundredths position (third term in the equation) is the sum of the differences, expressed äs absolute magnitudes, between the indices for the parameters within a given class for which x and y differ, normalized by the number of differences. The arbitrariness of the measure proposed above is obvious. There is no reason whatever to attach to the difference between 'dental' and 'alveolar' consonants, which is rarely distinctive, four times the weight that is attached to the difference between 'rounded' and 'unrounded' vowels. The decimals make no sense at all. Any figure calculated from formula (4.35) is rather an ordered triad than a single number liable to ordinary mathematical operations. But even in that case it remains completely unclear why velarized consonants are three times äs queer (= remote from plain consonants) äs palatalized consonants and six times äs queer äs labialized consonants. Acoustic reality is of the continuous scale type and should be measured accordingly. The possibility of attributing numbers to entities on the basis of a classification is restricted to the level of constructs and has nothing to do with measurement. More interesting than Peterson and Harary's phonetics is their phonemics. In order to eliminate free Variation the authors introduce the concept of 'functional similarity'. Two sounds are 'functionally similar' if they have phonetically similar environments and occur in semantically equivalent utterances. Though it is explicitly IDENTIFICATION MODELS 89 stated that "the relation of functional similarity is an equivalence relation", this assertion is contrary to the example given in the very same paragraph: Am.Eng. [F], which may occur in either latter or ladder, is in the first instance functionally similar to [t] and in the second instance functionally similar to [d] (1961: 156). Consequently, either the relation is not an equivalence or the two instances of [F] are not functionally similar to each other. The former solution leads to the necessity of assuming heavy phonemes while the latter, which reminds of the Moscow school of phonology, is essentially nonphonemic. In both cases there remains the possibility that "an utterance in which [F] occurs is ambiguous: i.e., [t] may be functionally similar to either [t] or [d]. The instances of [F] which occur under these circumstances are clearly different from those indicated above and thus they lie in a third set of functionally similar phones". This is a 'basic archiphoneme' in the former and a 'hyperphoneme' in the latter Interpretation.19 The concept 'allophone' is defined äs follows. A phonetically relatedset is a set of phones obtained by taking the union of a maximal set of phonetically similar phones and all sets of functionally similar phones which contain a member of that set. An uncoveredphonetically relatedset is a phonetically related set which is not contained in the union of one or more other phonetically related sets. A primary phonetically related set is an uncovered phonetically related set excluding those phones which lie in sets which generate other uncovered phonetically related sets. An allophone is the set of phones contained in the intersection of a maximal set of phonetically similar phones and a primary phonetically related set of phones. It is a pity that Peterson and Harary give no Illustration of the procedure of delimiting allophones because the sense of it is far from obvious, and even the formal side of the model is rather obscure to me. If there is no phonemic overlapping, there is no reason for distinguishing between the four concepts introduced in the above quotation. But in the case of phonemic overlapping there is no 'uncovered phonetically related set' unless all phonetically related sets involved are covered by one among them, and in that case the concepts of 'uncovered phonetically related set' and 'primary phonetically related set' coincide because the uncovered set is unique. Consequently, the concept of 'allophone' coincides with the concept of the 'maximal set of phonetically similar phones' whenever the 'allophone' is defined at all. Thus, if we denote the 'maximal sets of phonetically similar phones' by t, d, r in the above example, the corresponding 'phonetically related sets' are T = t V f, D = d U f, Γ = ί U J U r (4.36) and the only 'uncovered phonetically related set' is Γ because Γ, D <=. Γ and Γ — Γ u D. The word 'uncovered' can be replaced by 'primary' and the allophones are t r\r=t,dr\r= d, and f n Γ = f. Nothing is gained, nothing is lost.

19 Cf. Chapters l and 9 of this book. It seems that Peterson and Harary prefer the solution of the Moscow school of phonology, cf. their Statement (1961:158): "Thus, higher ordered linguistic Informa- tion (morphology etc.) is required to resolve certain phonemic ambiguities, i.e., on the basis of phonetic data alone it is not always possible to identify the phoneme to which an allophone belongs." 90 THE DEVELOPMENT OF MODELS IN PHONEMICS

A canonical allophone is a maximal set of phonetically similar phones which generates a primary phonetically related set. [...] A phoneme is the set of allophones which lie in primary phonetically related sets having nonsimilar phonetic environments, and which have canonical allophones with pairwise minimal phonetic differences (not to exceed some speciflc upper limit). According to these definitions the only canonical allophone in our example is f and the phonemes are /t/ = {t, f}, Id/ = {d, f} (4.37) both containing the canonical allophone f. The result is not unacceptable but the way of obtaining it is at the very least awkward. The authors propose the following identification of the phonemically ambiguous allophone f:

W H ^ (4-38)

The intention of Peterson and Harary's definition of the phoneme seems tobe the identification of complementarily distributed sounds on the basis of their phonetic similarity, i.e., precisely the concept formalized by Beloozerov. The main deficiency of their model is the absence of a formal analogue of such concepts äs 'position' and 'distribution'. On the other band, the model allows for free Variation and phonemic overlapping. Especially the latter phenomenon causes considerable trouble in the identification procedure. As a conclusion to this chapter I shall give a hypothetical Illustration of the problems involved. The table presented here is a modification of Peterson and Harary's Table 4 (1961:158), We consider four phonemes and distinguish six positions. Members of the same phoneme occurring in the same position are in free Variation. 123456 /P/ P P P P,b p,b p,b /t/ t t,F t t,d t,d /d/ d d,r- d d t,d /k/ k k k g g g In position 6 the Opposition between /t/ and /d/ is neutralized. In position 5 the Situation is more complicated because any [t] can be replaced by [d] without a change of meaning but the converse does not hold: this is the optionality condition, which will be discussed in Chapter 9. In positions 3 and 4 the non-occurrence of /d/ and /t/ respectively can be due either to neutralization or to defective distribution. The choice between these two possibilities cannot be made on the basis of the phonetic facts presented in Peterson and Harary's Table 4, but is not arbitrary either (cf. below). In position 2 there is partial overlapping of /t/ and /d/. This Situation will be discussed in connection with the concept of optionality. Any satisfactory phonemic theory must yield some Interpretation of such types of sound distribution äs the one presented here. 5

BATOG'S LOGICAL MODEL

5.1. INTRODUCTION

The formally most elaborate model presented in phonemic theory up to now is the one formulated by the Polish logician T. Batog. The first Version of this model was published äs early äs 1961 in the Polish periodical Studio, logica. The double language barrier connected with this publication, which is written in Polish äs far äs it does not consist of formulas, seems to have prevented any reference to it by Western authors. The following year a modified Version of the model appeared in the same periodical, this time in English, but frequent references to the preceding paper made it hardly more accessible to Western scholars. Finally, in 1967 a füll exposition of the theory appeared, again modified in many important respects, and published in English äs a separate book. In view of the major differences between the three versions of the model I shall present all three of them here. However, the extensiveness of the model makes it impossible to do justice to all the aspects involved. I shall therefore confine myself to an exposition and discussion of the linguistically essential parts of the model, in particular the identification rules. Consequently, I shall neither state the axioms and theorems formulated by Batog, nor enter into the problem of minimizing the assumptions and smoothing the derivations. Paying the price of formal incom- pleteness, I hope to gain a greater accessibility for colleagues who would indeed like to be informed about the formal properties of phonemic analysis but do not have the time and the will to work their way through dozens of pages of logic before reaching a linguistically non-trivial Statement. Batog was not the first to use the apparatus of mathematical logic for defming the foundations of phonemic theory. A similar approach had been proposed in Green- berg's axiomatization (1959). However, Greenberg's model is füll of formal inade- quacies and therefore I shall not examine it here.1 In the Soviel Union the use of logic in phonemic theory has been advocated by Saumjan since 1959.2 As we have seen in Chapter 2, however, Saumjan's own use of logic is very limited and, in relation to bis theory, marginal. Thus, Batog's System is the only complete axiomatization of phonemic theory thus far.

1 The interested reader should consult Greenberg 1959 and the criticism in Batog 1961b. 2 Saumjan 1959, 1960, 1962, 1963, 1965, 1966b. 92 THE DEVELOPMENT OF MODELS IN PHONEMICS 5.2. LOGICAL PRELIMINARIES

Before passing on to the exposition of Batog's models it is necessary to give an account of the notation to be used.3 Apart from the Symbols that have been used in the preceding chapters, such äs Χ η Υ = {x:xeX\xe Y} (5.1) X U Υ = {x:xeXvxe Y} (5.2) X' = {χ:χφΧ} (5.3) X- Y = {x:x<=X\x$ Y} (5.4) 0 = {χ: χ Φ χ} (5.5) we define \JA = {x: V xeX} (5.6) XeA i.e., u/4 is the set of elements χ which are a member of a member of A, As a corollary we have Xe A -> X ^ u A (5.7) In accordance with general usage in logic, a 'partition' is called a 'classification' and formally defined äs follows : the family A is a classification of the set X if and only if X — u A and Λ (Γ=ΖνΓηΖ=0) (5.8) Υ,ΖεΑ In that case we say that A e From the theory of relations we need the following defmitions :

R'X = {y. y Rx} (5.9) R"x = {y.xRy} (5.10) R(X) = {y: V yRx} (5.11) xeX R(X) is called the 'image' of X. It is easily verified that R'x = *({*}) (5.12) R(0) = 0 (5.13) jR(irur) = Ä(IO υ Ä(y) (5.14) 3 My notation differs slightly from Batog's. Most concepts defined in this section have been used earlier but so far I have omitted their formal definitions in order to minimize the number of linguistically irrelevant formulas. In view of the more highly formalized character of Batog's models I add them here for the sake of completeness. Like Batog, I write Λ and V (instead of V and 3) for the universal and existential quantifier, respectively. BATOG'S LOGICAL MODEL 93 If for every χ e X there is exactly one y such that y R x, then the unique y contained in R'x will be denoted by the symbol R'x: in that case we have R'x = {R'x} (5.15) Furthermore we define R n S = {(x,y): χ R y A. χ S y} (5.16) Λ u S1 = {(x,y):x R y v χ S y} (5.17) R' = {(x,y): ~ χ R y} (5.18) A" = {(*0'):j'Ä*} (5.19) Ä/S = {(x,y): VxRzAzSy} (5.20) and call R" the 'converse' of R and jR/S the 'relative product' of R and S. The concept of equivalence relation is formally defined äs follows : κΆ(Χ) = {£: Λ xRx} (5.21) xeJSf sym(JT) = {R: Λ χ £ >> -^ ;> Ä χ} (5.22)

trans^T) = {R: Λ ^ÄJA^ÄZ-^^ÄZ} (5.23) x,y,zeX eq(JT) = refl(JST) n sym(Z) n trans(JT) (5.24) A relation R e eq(Jf) partitions the set X into classes. The family of /J-equivalence classes in X is formally defined by

e(R,X) = {Y: YC χκ v Λ y e Y <-* y R χ} (5.25) xeX yeX Besides, Batog makes ample use of some mereological concepts (1967: 17ff.).4 The primitive Symbols in mereology are: P and T; denoting certain binary relations between in- dividuals. The expression χ P y means that the thing χ is a pari of the thing y; the expression χ Τ y means either that the whole thing χ precedes the whole thing y in time, or that the last time slice of χ coincides in time with the first time slice of y. Thanks to the introduction of the relation P, objects of different types can be identified with each other by means of the concept of 'mereological sum' : S - {(y,X): X = p'y Λ Λ Ρ(Χ) ο Ρ'ζ Φ 0} (5.26) zPy

4 These mereological concepts are based on Tarski 1937. 94 THE DEVELOPMENT OF MODELS IN PHONEMICS i.e., y S X(= y is the mereological sum of the set X) means: y is the whole composed of all elements and only of elements of the set X. It is clear from formulae (5.15) and (5.26) that χ — S'{x}. The concepts of 'point' and 'momentary thing' are formally defined by pnt = {x: P'x == {x}} (5.27) mom = {χ: χ Τ x} (5.28) Now we can introduce the following operations, which are completely analogous to the union and intersection of sets : x u- y = S'{x,y} (5.29) x n- y = S'(P'x n P'y) (5.30) In the models that will be outlined below objects like x, y will be identified with Segments in the speech flow. The definitions given in formulae (5.29) and (5.30) open the possibility of speaking about segments that consist of other Segments. The usual set-theoretical operations cannot be applied to segments because segments are not sets : they do not consist of elements of a lower type. The relation between a larger and a smaller segment cannot be a membership relation because they are necessarily of the same type, but the latter segment can be a part of the former, or they may partly coincide. The impossibility of regarding segments äs sets originales from the arbitrariness of any tentative segmentation of the speech fiow at the very outset. This is where the need for mereology comes in. The following definitions are added for the sake of completeness ; I shall not enter into a discussion of their formal properties. Two momentary things x and y are 'coincident' in time if Λ: C y where C = T n T" (5.31) i.e., if both x T y and y T x. The thing x 'completely precedes' the thing y in time if x Tc y where the relation of complete precedence is defined by

Te = cp'/rypy (5.32) i.e., if no part of y precedes any part of x in time. The relation of 'immediate precedence' is defined by

Ti = Te n (Tc/Tc)' (5.33) The set of 'momentary world-sections' is defined by mws = mom n {x: C'x <=: P'x} (5.34) The set of 'linear objects' is defined by

ttn = {χ: Λ x Te y Λ y Tc' x -> x rv y e pnt} (5.35) yemws BATOG'S LOGICAL MODEL 95 5.3. THE INITIAL OBJECTS OF BATOG'S MODEL

The initial objects of Batog's models consist of three or four primitive terms and a set of axioms. The number of axioms varies from eleven (ten of which are used in the definition of the phoneme) in Batog's original paper to fifteen in his book. I shall not state the axioms here because all of them are trivial from a linguistic point of view. The primitive terms of Batog's first paper are the following: 77i = [t, D, O, E] (5.36) where ι is an idiolect, in the sense of a "sufficiently representative sample of a dialect" (1967: 28), D is the set of all Segments in the idiolect i, O is the set of all pauses (zero Segments) in the idiolect, and E is the relation of 'phonetic similarity' between Segments. In Batog's second paper the idiolect ι has been replaced by the set of all idiolects /: 77.2 = [/, D, O, E] (5.37) and the symbol D now Stands for the set of all Segments that can be recognized in the whole of human Speech. The totality of human speech is identical with S'I. In Batog 1967 the relation E is transferred from the set of primitive notions to the set of defined concepts by replacing D with a higher type concept. Two sounds are phonetically equivalent if they are characterized by the same set of features. Thus, if a feature is identified with the set of elementary segments characterized by it, the relation of phonetic equivalence holds for any two segments belonging to the same features. The features themselves belong to kinds of features, such äs laryngeal action, place of articulation, or manner of articulation. We now define

Π3 = [I, K, O] (5.38) where K is the set of all kinds of phonetic features. It follows from formula (5.6) that u K is the set of all phonetic features, and that u (JK is the set of all elementary segments, i.e., the concept denoted by D in the original Version. The elementary segments are conceived of äs being "such minimal elements the impressions of which cannot be further divided by the ear" (1967: 30). They are in Batog's final publication (not in his earlier articles) distinguished from phonemic segments, which are called 'unit-length segments'. Apart from this distinction, the above symbols K, OK, u u K replace the respective symbols P, V, E introduced in Chapter 3 and used extensively in the preceding chapters.

5.4. FROM PHONETIC CHAIN TO PHONETIC SYSTEM

On the basis of the notions introduced in section 5.3 the concepts of 'phonetic chain' (= 'sequence' in American linguistic usage), 'utterance', and 'phrase' are formally defined. The formal definitions stated in the models under discussion 96 THE DEVELOPMENT OF MODELS IN PHONEMICS differ from each other, but essentially they come down to the same thing: a phonetic chain is an uninterrupted sequence of elementary segments, an utterance is a phonetic chain that begins and ends in a pause, and a phrase is a fraction of an utterance between two immediately successive pauses (cf. Bloch 1948: 19). I shall confine myself here to a formal Statement of the main definitions in Batog 1967. The sets of elementary segments, phonetic chains, utterances, and phrases are denoted by esg, ch, ut, and phr, respectively. The relations of being a member of there spective sets within a larger entity are denoted by Esg, Ch, Ut, and Phr. Besides, the formal apparatus makes use of the relations p and s, which stand for 'immediately precedes' and 'immediately succeeds', and the symbols λ(χ) and θι(χ), which denote the length of the chain χ (= the number of elementary segments which it contains) and the ith elementary segment contained in the chain x, respectively. The formal definitions now run äs follows.5 esg = UUK u O (5.39) Esg = {(x,y): χ P y Λ χ e esg} (5.40)

l Ch — {(x,u) :ue^Jl/ixPuA.x~S Esg' χ Λ Esg' u n Tc~(Esg' x)

n Tc(Esg' χ) <= ρ'χ} (5.41) ch = CA(U/) (5.42) P ~ {(x,y)'· x e esg Λ x Ti y Λ x u· y e ch} (5.43) s = {(x,y) : x e esg Λ y Ti χ Λ je u- y e ch} (5.44)

Ut = {(x,y); x Ch y Λ U vK n P'x ^ 0 Λ θι(χ) e Ο Λ. θλ(χ)(χ) e O} (5.45) ut = Ut(vl) (5.46) Phr — {(x,y): x Ch y Λ P'x n O = 0 Λ ρ'χ e O \ s'x e O} (5.47) phr = Phr(Ul) (5.48)

The concept of phonetic equivalence, which is a primitive notion in Batog's earlier papers, is formally defined in his book:

E = {(x,y): x,y ech\ λ(χ~) = λ(γ) Λ Λ (θι(χ) e Ο Λ 04(j) e O ι^λ(χ) ν Λ θι(χ) e Χ <-> θι(γ) e Χ)} (5.49)

5 Chapters 4, 5, 6 of Batog 1967. More precisely, x is a predecessor (successor) of y if and only if x is aa elementary segment immediately preceding (preceded by) y in time and forming together with y a. phonetic chain. The condition x u· y e ch is included in formulae (5.43) and (5.44) inorder to guarantee that x and y are taken from the same utterance. The formal definition of θ(χ), which is the unique ordinal correlator of {(x,y): x Tc y v x = y} with its field limited to Esg' x and :£ with its field limited to the set of natural numbers from l to λ(χ), is not stated in. Batog 1967. BATOG'S LOGICAL MODEL 97 i.e., χ and y are phonetically equivalent if and only if χ and y are phonetic chains of the same length and for every z which is not greater than the length of these chains either θι(χ) and 6i(y) are pauses or θ{(χ) and 9i(y) have exactly the same phonetic features(1967:59).6 Now we come to the definition of sounds, and this is the first point where the three versions of the model differ essentially. Most important, Batog 1967 makes a distinction between 'sounds' and 'phones'. The latter term refers to entities BEFORE the establishment of unit-length segments, the formet to entities AFTER this has been done. Since the syntagmatic identification of units is not taken into account in Batog's earlier papers, there is no such difference there. From the linguistic point of view, however, the difference is essential. The set of 'phones' is the set of .E-equivalence classes in esg:

Γ0 = ε(Ε, esg) (5.50) with D instead of esg in Batog's earlier papers. The set of 'proper phones' is defined by (5-51) This is all there is in Batog 1961a. In bis later publications the symbol ι has been replaced by / in the set of primitive terms, so there arises the need of distinguishing between 'phones' and 'phones in the idiolect i'. We define

r0« = {X: X e Γ ο Λ X n Esg(i) Φ 0 } (5.52) Γω = Γο«> - {0} (5.53) If X e Γ o and Λ: is a segment belonging to X then Z is a 'phonic form' of the segment χ and we write X y x. Formally :

γ = {(Χ,χ) : χ ε Χ Λ Χ e Γ0} (5.54) It follows from formula (5.50) that the phonic form of an elementary segment is unique. Thus, we can write φι(χ) — γ'θί(χ) for the phonic form of the zth elementary segment contained in the phonetic chain x. We now define the 'phonic structure' of the chain x äs φ(χ) = γ/θ(χ) ' (5.55) where θ(χ) is the sequence of elementary segments contained in the chain x. The 'phonic System' of the idiolect ι is defined äs S® = [Γω, f»(PAr(v))] (5.56) i.e., the pair consisting of the set of proper phones in ι and the p-image (= the set of phonic structures) of the set of phrases in i. Next we turn to the uniting of elementary segments into unit-length segments. If any two or three segments always occur together in the Speech flow, then these 6 The definition of 'phonetic word' in Batog 1967:61ff. will be omitted here. 98 THE DEVELOPMENT OF MODELS IN PHONEM1CS two or three segments constitute one sound. This is the criterion of syntagmatic identification chosen in Batog (1967: 73). The elementary segments x, y, z (in this order) are inseparable in the idiolect z, in Symbols: ZspW (x,y,z), if and only if x, y, z are proper elementary segments of the idiolect ι, χ is the predecessor of y, y is the predecessor of z, and [...] in the environment in which thewhole chain x u· y υ· ζ occurs, there occurs neither the segment y alone nor the chain x u· y alone nor the chain y vj· z alone. Formally: Jip(') = {(x,y,z): x, y, z e u *JK n Ρ(ι) Λ χ = p'y Λ y = p'z Λ Λ veCA(i)

(A(v) = 3 -> ~ (?>i(v) = γ'ρ'χ Λ ρ2(ν) = y'^ Λ φ3(ν) = y Yz)

Λ λ(ν) — 4 -> ~ (ρι(ν) = y'/j'jc: Λ p2(v) = y'x Λ ps(v) = y'y

Λ ^4(v) = y'j'z v φι(ν) = y'/j'x Λ pa(v) = y> Λ 9>s(v) = y'z Λ ^(^^[yVz))} (5.57)

The set of 'three-segmental complexes in i' is defined by

sgam® = {X: V (X = {x, y, z} /, IspW(x,y,zy)} (5.58) *,J>>z The set of 'two-segmental complexes in i', sgcmzw, is defined more or less analogously (1967: 74). The set of 'compound segments in i' is defined äs follows. (5.59) = S(sgcmz^) (5.60)

(t) U ci^2 (5.61) The set of 'proper unit-length segments in i' and the set of 'unit-length segments in i' are defined by u (( u vK n P(i)) — u(jgcm3(l) u jgcwaW)) (5.62) u (O n P(i)) (5.63)

The relation of being a unit-length segment in x is defined by

1 Usg = {(x,y):xP y \xeusg 0M} (5.64)

The set of 'complete chains in i' is defined by = CA(i) n {χ: χ = 5" {/Jg^'x} (5.65)

The Symbols λι(χ) and ö'(x) are analogous to λ(χ) and θ(χ) but refer to unit- length segments instead of elementary segments. The following definitions are analogous to formulae (5.52)-(5.56) but with 'sounds' substituted for 'phones'. The adjective 'phonic' is replaced by 'phonetic'. BATOG'S LOGICAL MODEL 99

G0w = ε(Ε, usg0U) (5.66)

GW = G0W - (O n P(i)} (5.67)

eG0^} (5.68) (5-69) = [GW, ?>ιΟΡΜι))] (5.70) Thus, formulae (5.66) and (5.67) define 'sounds' and 'proper sounds', respectively, and formulae (5.68)-(5.70) define the concepts of 'phonetic form' of a segment, 'phonetic structure' of a chain, and 'phonetic System' of an idiolect.

5.5. THE DISTRIBUTION OF SOUNDS

The next step of the analysis is the paradigmatic identification of phonemic units. Since Batog's model is essentially a formalization of American distributionalist phonemics äs outlined by B. Bloch and Z. S. Harris, the identification rests upon the principle of contrastive versus complementary distribution. These concepts are defined in the present section. An 'environmental pair' in ι is defined äs a pair of complete chains in ι such that only the first unit-length segment in its first member and the last unit-length segment in its second member may be pauses. Formally:

ι epd) = {(n,r2): n e CCÄW n {χ: Λ (l < i ^ λ(χ) -> φ\(χ) e GW)} i

w Λ rz B CCÄW n {χ: Λ(1 < / < λ'(«) -* «*(*) e C? )}} (5.71) i

The environmental pair (ri,rz) is an 'environment' of the proper unit-length segment χ in i, in Symbols: (ri,rz) En*· x, if nxrz constitutes a complete chain in i: Enl = {((ri,ra), x)'. (ri,rz) e ep^ Λ χ e usg® Λ π Τι χ Λ χ Ti rz

Λ π u· x u· r2 e CCÄW} (5,72) The phonetic structure of an environmental pair is defined by

ι ι δ' = {((ψι,ψύ, (riSsj): (n,rz) e epW Λ ψι = φ (η) Λ ψζ = ρ(''2)} (5.73) We now define the 'distribution' of a proper unit-length segment äs the set of phonetic structures of the environments in which it occurs : 1> = Q-IErf- (5.74) KXe GW then Dl(X) is the distribution of the sound X in the idiolect i. The sounds X and Υ are in 'free Variation' in the idiolect ι if their distributions coincide:

Fv*· = {(X, Y): X,Ye GWA JD'(JO = &(?)} (5-75) 100 THE DEVELOPMENT OF MODELS IN PHONEMICS

The relation of complementary distribution is somewhat more complicated. It seems natural to say that two sounds are in complementary distribution if their distributions are disjoint:

Cw'i = {(Χ,Υ): Χ, Υ e GW Λ D<-(X) n £ι(Υ) = 0 } (5.76) This definition is inadequate, however, äs has been pointed out by Bloch (1948: 23): Occasionally two segments will appear to have some of their environments in common, if the environments in which they occur are stated merely in terms of immediately preceding and following sequences; but will prove to be actually in complementary distribution, if the description of their environments is expanded so äs to include a differentiating segment or sequence that is not contiguous with the segments in question. Thus, the segments [u·] and [ü-] in pre-English are in some phrases immediately preceded and immediately followed by the same sequences, and hence appear to have some of their environments in common — for instance in *[mvrs] 'mouse' and *[mü-si] 'mice' ; but if we state the environments of [u·] and [u·] in such a way äs to include the following vowel, the two segments turn out to be in complementary distribution: [ü·] occurs only in environments that contain the segment [i] or [j] in the following sequence, [u·] occurs only in environments that do not contain such a segment.

Thus, complementarily distributed sounds may have some environments in common, but these environments turn out to be different if they are properly enlarged. This is why Batog regards two sounds äs being in complementary distribution also when they do not conform to formula (5.76), provided that among the environments which they have in common there are no 'maximal' environments, i.e., environments beginning and ending in a pause. Writing λ for λι(ϊζ) we define

ι = epW n {(n/2): 0ι(/·ι) e Ο Λ 9\(rz) e O} (5.77)

l 1 l Cm 2 = {(Χ,Υ): X,Ye G< > Λ D<-(X) Φ ΐ)\Υ) Λ D (X) n D<-(Y) Φ 0 Λ D^(X) n D'(7) n Q^mepff) = 0 } (5.78)

l l Cm' = Cm i u Cm 2 (5.79) The sounds X and Υ are 'allophonically similar' in the idiolect ι if they are either in free Variation or in complementary distribution:

= Fv1 υ Cm1 (5.80)

5.6. BATÖG'S DEFINITION OF THE PHONEME

The relation defined in formula (5.80) is reflexive and Symmetrie but not necessarily transitive, so the phoneme cannot be defined äs a class of allophonically similar sounds. There are several ways out of this difficulty. Firstly, it is possible to introduce an axiom which makes the relation transitive. This is the way chosen in Batog's first paper (1961a): Z Cm1 ΓΛ YCnf-Z^* X Fv<· Z v X Cnt Z (5.81) BATOG'S LOGICAL MODEL 101 Thus, if Υ is in complementary distribution with both X and Z then X and Z must be allophonically similar. A phoneme can now be defined äs a class of allophones : p™ = e(Alf\ G(l>) (5.82) From a linguistic point of view the axiom (5.81) is obviously untenable. Not only can such phonemes äs /h/ and /η/ be in complementary distribution, but strictly speaking all sounds occurring in one position are in complementary distribution with all phones occurring in any other position. Prevocalic stops are in almost any language clearly distinct from Word-final stops so that the definition above would lead to an identification of all stops with each other. Here phonetic similarity plays its part. But in Batog's models phonetic similarity either belongs to the primitive notions of the system, or is equated to identity of features, which are, in turn, primitive terms, cf. formula (5.49). In bis second paper (1962) Batog abandons the axiom but does not resolve the problem pointed out in the preceding paragraph. The sounds X and Υ are 'phonologically equivalent' in the idiolect l if they belong to precisely the same allophones : Fef = {(X,T>: X, Ye (?w Λ Λ ( V Λ A cG<0 Z ε GW W G G® (W e A +* W Alf<- Z) -+ (X e A *-> Υ e A))} (5.83) Since Feq1 is an equivalence relation, the phonemes of the idiolect ι can be defined äs classes of phonologically equivalent sounds : F«·) = E(Feq\ G«) (5.84) While a consistent application of the criterion in formula (5.82) would lead to the merger of all stops, a strict application of the criterion in formula (5.84) would not lead to any mutual identification of prevocalic and word-final stops. Suppose that a language has [p'], [t'], [k'] before vowels and sonorants and [p'], [t'], [k'] elsewhere.7 The sound [t'] is in complementary distribution with and therefore allophonically similar to [p'], [t'] and [k'], but phonologically equivalent to none of them, because all of them are in complementary distribution with and therefore allophonically similar to [p'] and [k']. Thus, we are left with six phonemes where any linguist would do with three. The definition of phonemes äs classes of allophonically similar or phonologically equivalent sounds brings to mind the definitions of phones and sounds äs classes of phonetically equivalent Segments. This opens the possibility of defining the concepts of 'phonological form' (of a sound), 'phonological structure' (of a chain), and 'phonological System' (of an idiolect) analogously, cf. formulae (5.54)-(5.56) and (5.68)-(5.70) above.8 Using the auxiliary symbol

7 This is not so odd äs it may seem, cf. e.g. Georgian loan-words such äs t'ek'st'i 'text', t'rak't'ori 'tractor'. 8 The formalization of F0<" in Batog 1961a:177 and 1962: 75 is incorrect because the type of the 102 THE DEVELOPMENT OF MODELS IN PHONEMICS

F0M = P® υ {{Ο η Ρ(ί)}} (5.85) we define

/' = {(A,X): XeA^Ae F0«} (5.86) Φ'(«) = fll V A <= B) (5.90) BeF Λ Λ (XFVYvXCnfiY) (5.91) AeF X,YeA Λ (A Φ B -> V V (U φ VA. uA <= E/A ÜB <= V)) (5.92) A,BeF CeK U,VeC In addition to these requirements the number of elements in P (= the number of phonemes) should be minimal. Thus, a phonemic base is (1) a classification of sounds such that (2) sounds in free Variation belong to one and the same phoneme, and (3) any two sounds belonging to the same phoneme are either in free Variation or in complementary distribution, and (4) for every pair of phonemes (A,B) there is a pair of homogeneous phoneüc features (U, V), where 'homogeneous' means 'belonging to the same kind of features (C)', such that the sounds belonging to A are characterized by U and the sounds belonging to B are characterized by V, and (5) there is no grouping of sounds containing a smaller number of elements that satisfies the preceding conditions.10 The family of all phonemic bases of the idiolect t is denoted by PSW. entities is not taken into account. It should be clear that the expression AflX defined by formula (5.86) has the same meaning äs the expression X \- A used elsewhere in the present study. 9 Cf. sections 4.3 and 4.4 of this book. 10 In fact, the Situation is more complicated. Elementary Segments are either continuous or discontinuous, but this does not hold for unit-length Segments in view of the existence of affricates, BATOG'S LOGICAL MODEL 103 On the basis of this new definition of the phoneme and using the auxiliary notion Fo = Fu{{0 nP(i)}} (5.93) we can define the concepts of 'phonernic form' of a sound, 'phonemic structure' of a chain, and 'phonemic System' of an idiolect äs follows. /; = {(A,X) -.XeA/^AeFo^Fe PJ?<»> } (5.94)

Ι Φ Ρ(Χ) = />'(*) (5.95) S-M = [F, ΦχΡΑτ(ι))1 (5-96) As a conclusion of the present exposition of Batog's formal apparatus I shall state his definitions of the concepts of 'relevant feature' and 'distinctive feature' without going into detail. The former concept refers to sounds, the latter to phonemes.11 Ve VK\ XeG^ Λ uf£X <= V} (5.97)

l = {(V,A): Ve Rf p(A) Λ V V V (V e CA U φ ΓΛ ÜB <= U)} BeF CeK UeC (5.98) Thus, V is a relevant feature of the sound X in the idiolect ι and in respect to the phonemic base F if it is a feature of every sound Υ which belongs in F to the same phoneme äs X (i.e., which has the same 'phonemic form' äs X), and Fis a distinctive feature of the phoneme A in the idiolect t and with respect to the phonemic base F if it is a relevant feature of the sounds belonging to A and there exists a phoneme B in F and a relevant feature U of the sounds belonging to B such that U and V are homogeneous and do not coincide.

5.7. CRITICISM

The objections which I have against Batog's definition of the phoneme are scattered through the preceding chapters. I shall list them here for the sake of convenience. Firstly, meaning is not represented in Batog's model. Consequently, the most essential characteristic of the phoneme, its ability to distinguish between linguistic forms, is not modelled. which are characterized partly by one and partly by the other feature. The same Situation obtains for pre-nasalized and post-nasalized or pre-glottalized and post-glottalized sounds. The difficulty is obviated by the introduction of 'compound features' of the type discontinuous + continuous. The symbol K in formula (5.92) should accordingly be replaced by a symbol representing a set of generalized kinds of phonetic features. I have omitted this pari of the analysis from this book only for the sake of simplicity. The interested reader should consult Chapter 10 of Batog 1967. 11 Here again I leave the complication arising from the existence of 'compound features' out of consideration, cf. footnote 10. There is a misprint in Batog's definition of distinctive features (formula 13.20, 1967:113): one should read Υ e B instead of X e B (corresponding to my B e F). 104 THE DEVELOPMENT OF MODELS IN PHONEMICS Secondly, the influence of the relation of phonetic equivalence on the results of the analysis must not be underestimated. This relation, which is one of the primitive terms in Batog's earlier papers, is based on the identity of phonetic features in the last Version of the model. However, since these features themselves are included in one of the model's primitive notions, this is no more than a shift of the problem, not a solution. It should be clear that the number of phonetic features that are distinguished must be neither too small nor too large. On the one band, minimal pairs must be kept apart, so that whenever there is in the totality of human Speech a single idiolect where there is a single pair of utterances that is distinguished by the presence versus absence of a certain phonetic feature, this feature must be included in the set u K On the other band, a distinction between sets of features occurring in complementary distribution, like the distinction between aspirated stops and glottalized stops in the example above, leads inevitably to the non-identifiability of sounds in complementary distribution. Such cases are not so rare äs it may seem. Difficulties may arise even if a single language is examined. In Spanish, the feature of interruptedness is distinctive in voiceless but positionally determined in voiced obstruents. Thus, voice has priority over interruptedness. But voice itself is positionally determined in the alveolar fricative /s/. Altogether, the problem of uniting features into complexes remains largely outside the modelling. The trouble is that a reasonable identification of sounds in complementary distribution can be carried out only on the basis of phonetic similarity, i.e., on the basis of criteria which either belong to the 'input' of the model (E or K), or fall out of the model altogether (äs in the case of aspirated and glottalized stops mentioned above). Thirdly, I consider the phoneticism in Batog's model a serious shortcoming. The very first identification in the model is the identification of 'phonetically equivalent' segments. This is incorrect from the linguistic point of view. As has been pointed out at length in Chapter 2 of this book, there is no reason whatever to assume that phonetically similar entities are functionally similar äs well, nor conversely. UldalFs identification of Dan. initial [t], [d] with final [d], [ö] respectively, which has been commonly accepted among linguists, is impossible in Batog's model because it does not allow for phonemic overlapping. In fact, the Situation is even worse. The fifth requirement in Batog's definition of the phoneme entails not only the POSSIBILITY of an incorrect identification because of the points just mentioned, but in some cases it even entails the INEVITABILITY of an incorrect identification. Minimizing the number of phonemes forces the investigator to identify Dan. initial [t] with final [δ] after initial [d] has been identified with final [d] because of their phonetic equivalence. In section 2.3 of this book I have adduced the example of [q], [k], [k'] before back vowels and [k], [k'], [c] before front vowels. Such a distribution would inevitably lead to the identification of [q] and [c], which is obviously unacceptable. In the examples adduced in the preceding paragraph Batog's phoneticism induces the economy rule to yield an incorrect identification. In other instances there should BATOG'S LOGICAL MODEL 105 be no identification at all, viz. in the case of Ge. Du. Eng. [h] and [n]. The non- identity of /h/ and /η/ in these languages, which is hardly disputed among linguists, points to the fact that mere economy is a bad guide in linguistic analysis. The minimal pair identification rule in Batog's model, formula (5.91), is stated in terms of free Variation and complementary distribution. This is not unequivocally correct in view of Uspenskij's theorem 7 (section 4.8 of this book). Alternatively, one could formulate a rule that keeps different utterances apart. Such a rule does not necessarily involve a formalization of the concept of meaning because it can be stated in terms of actually occurring utterances. I would suggest the following possibility. The set of 'quasi-phonemes' of the idiolect ι is defined äs the set of free Variation equivalence classes of sounds: H = ε (Fv*·, GW) (5.99) H JA = H® u {{O n P(i)}} (5.100)

The concepts of 'quasi-phonemic form' of a sound, 'quasi-phonemic structure' of a chain, and 'quasi-phonemic System' of an idiolect are defined by

\AeH0®} (5.101) (5.102)

= [HM, to«(PAr(i))] (5·103) The minimal pair identification rule can now be stated äs follows : Λ (ω'(*) Φ ω'0>) -> Φ*(χ) ^ 00) (5.105)

The rules (5.104) and (5.105) state that quasi-phonemically different utterances must be phonemically different, and that the converse must hold äs well. The number of phonemes (= elements in F) should be minimized under these restrictions. The alternative above rernoves one of the most important deficiencies of Batog's model. If an idiolect contains the chains xy and yx, where the order of the sounds x, y is distinctive, and these sounds are elsewhere in complementary distribution, then the identification of χ and y äs realizations of the same phoneme is inevitable äs a consequence of Batog's minimalization rule because bis complementary distribution criterion in formula (5.91) refers to sounds, not to phonemes. The merger of χ and y in the phonemic transcription makes the distinction between xy and yx on the phonemic level impossible but does not affect the complementary distribution of 106 THE DEVELOPMENT OF MODELS IN PHONEMICS x and y because the latter is defined in terms of PHONETIC environments.12 Thus, Batog has sacrificed uniqueness without gaining distinctiveness in the last version of bis model. The same argument applies in the case of strings x\yi and xzyz which can both be identified äs /xy/ because χι and Xz occur before y\ and yz respectively, and yi and yz after χι and xz respectively. The minimalization of the number of phonemes requires the identification of complementarily distributed sounds without taking into account the merger of chains that are kept apart by the joint presence or absence of a number of sounds.13 The problem outlined in the preceding paragraph, which is closely connected with the problem of joint features, has not escaped Batog's attention. In the very last pages of bis book he introduces the following 'fundamental hypothesis' : x, y e ccA« Λ F e PB^ \ Φ^(χ) = Φ*(γ) -ν Λ 9lt(x) FV· ψ^(γ) (5.106) i.e., every two complete chains with the same phonemic structure rnust be composed of sounds that have the same phonetic form with an allowance for free Variation (i.e., in my terminology, must be composed of the same quasi-phonemes). This is an unduly relaxed Version of my formula (5.104): a correct Statement would include λι(χ) — Al(j>) in the consequent. Batog comments on this 'hypothesis': "although not being a thesis of our System of phonology, the proposition [viz. (5.106)] may in spite of this be empirically true" (1967: 119). This is the problem of eliminability, which has been discussed in sections 2.9 and 3.3 of this book. In Common Slavic, the vowels [a, o, u, 9, i] occurred only after hard consonants and [ä, ö, u, ä, i] only after soft consonants. According to any complementary distribution criterion based on PHONETIC environments, these sets of vowels should be identified with each other because the choice between thern depends on the preceding consonant. On the other band, hard and soft consonants should also be identified with each other because their quality is determined by the following vowel. This is exactly the Situation which is excluded by formula (5.106). The number of cases where the proposition does NOT hold depends on the initial objects of the model, viz. on the concept of phonetic similarity or the number of features that are distinguished from the very outset. In Dutch there are six clearly different [k]-like sounds in the words kiel 'keeP, keel 'throat', kuil [kAül] 'pit', kaal 'bald', kool 'coal', koel [kul] 'cool'. All of these sounds have different places of articulation. Their mutual identification is conditioned by the fact that they occur before different vowels. But these vowels are in complementary distribution themselves because they occur after different consonants. There is no way out of this vicious circle unless either meaning is taken into account or the concept of phonetic similarity is specified in such a way that an order of successive

12 The same argument has been put forward in connection. with Beloozerov's model, see section 4.5 of this book, in fine. 13 It is recalled that this is the problem which led Uspenskij to the abandonment of uniqueness. BATOG'S LOGICAL MODEL 107 identifications can be established. (The latter possibility, which is the one chosen by Beloozerov, does not yield a solution in the case of xy, yx l- /xx/ mentioned above.) The presence of formula (5.106), which corresponds to my formula (5.104), in Batog 1967 makes the absence of an analogue of my formula (5.105) all the more striking. Yet there is no guarantee that free Variation between chains can always be reduced to free Variation between the respective sounds that constitute the chains. There may also exist free Variation in the order of the sounds, cf. Bu. [skraben] or [skarben] 'sorrowful', [dlazen] or [dalzen] 'indebted'.14 Such cases cannot be accounted for in Batog's model. Moreover, there may be instances where a sound is in free Variation with a pair of juxtaposed phonemes. In English the word suffer may end in [a] or in the same vowel followed by an r-like sound. Other examples are Fr. enfaisant [äfzoj or [äfazä], and film tmgique [filmtrazik] or [filmatrazik] (cf. Zaliznjak 1966: 226). Cf. also Sw. för sent [fAsent] or [fArsent] 'too late'. Handling such cases requires a wider concept of free Variation than the one dealt with in Batog's model. We have now come to the problem of the syntagmatic identification of phonemes, i.e., the problem of inseparability, in Batog's terminology. One or more elementary Segments constitute a unit-length segment, which is associated with a phoneme by means of the function fl/gl. Thus, the possibility of interpreting a single sound biphonemically, e.g., the identification of Du. [s] H /sj/ and Sw. [d] i- /rd/ suggested above, is precluded. The slightly more complicated case of transitional Segments that are simultaneously characterized by features of both the preceding and the following segment, such äs the partial nasalization of oral vowels before nasal consonants which is quite common in many languages, cannot be accounted for either. Batog's segmentation of the speech flow into unit-length segments depends on two factors, viz. the segmentation of the speech flow into elementary segments, which reminds of Saumjan's 'natural segmentation', and the inseparability of juxtaposed elementary segments. Both of these concepts are subject to serious criticism. One might be tempted to regard the physically finest possible segmentation of the speech flow äs the segmentation into elementary segments, but in that case ANY pair of juxtaposed elementary segments turns out to be inseparable, so that every chain is interpreted äs a single sound. Thus, some kind of phonetic similarity is presupposed in the identification of elementary segments, and we are back to the discussion in the beginning of this section. The inseparability defined in formula (5.57) does not yield linguistically satisfactory results in many cases. In Russian, strongly velarized consonants occur only before the vowel [i], Consequently, chains consisting of such a velarized consonant plus [i] should be interpreted monophonemically in accordance with Batog's criteria. This solution is contrary to the generally accepted treatment of [i] äs an allophone of /i/.

14 This case is different from the existence of doublets such äs Du. precies, percies 'precise'. 108 THE DEVELOPMENT OF MODELS IN PHONEMICS Other cases are even more significant. Retroflex [t] occurs in Russian orily before [s], e.g., in [hitsa] 'better', and the inseparability of these two sounds leads to a monophonemic Interpretation. But retroflex [n] occurs before [s] äs well äs [z], cf. [puns] 'punch' and [xanza] 'bigot', and is therefore not inseparable from the following sound (cf. Panov 1967: 35). It turns out that the neutralization of voicedness before voiceless sounds, which is a rule without exceptions in Russian phonology, entails the monophonemic Interpretation of a group which is generally considered the realization of a combination of phonemes. Having considered these problems, which clearly show that the Identification principles formalized in the definition of the phoneme should refer either to PHONEMES (phonetic similarity and complementary distribution) or to CHAINS (free Variation and minimal pairs) but never to SOUNDS and that, consequently, the segmentation of the speech flow into phonemic units can only be accomplished AFTER at least a part of the PARADIGMATIC delimitation procedure has been carried out, I have to draw attention to an assumption in Batog's model which is, though seemingly almost generally accepted in phonemic modelling, in my opinion unwarranted. I am referring to the supposition that free Variation is an equivalence relation. In fact, the relation of free Variation is not necessarily transitive. In some variants of American English the intervocalic consonant in the words latter and ladder may, but need not, be the same: these words can be kept apart if they are pronounced in Isolation but are homonymous in ordinary Speech. The same holds true for Ru. domovoj [damavoj, damavoi] 'brownie' and dymovoj [damavoi, dimavoj] 'smoke (adj.)' (cf. Ebeling 1967: 137). Since phonemic overlapping is excluded in Batog's model, such facts remain out of the picture. But the relation of free Variation is not necessarily Symmetrie either. As has been pointed out above, Po. word-final [e] is in free Variation with [e] in such words äs biorg but not in such words äs chore. The final vowel of Fr. [zdire] is in free Variation with [ε] if the word meansje dirais but not if it meansye dirai (at least in some variants of the language). This is a consequence of the fact that Po. [e] and Fr. [e] can in word- final position be replaced by [e] without a change of meaning, but the converse does not hold.15 Consequently, the alternative proposed in formulae (5.99)-(5.105) is not a linguistically satisfactory adaptation of Batog's model. Free Variation between phonemes äs described in the last two paragraphs must not be confused with the existence of doublets such äs Ru. skaf, skap 'cupboard'.

5.8. THE ROLE OF FEATURES

Many of the problems indicated in section 5.7 originate from the fact that a minimum phonemically relevant entity is not a phoneme but a feature. According to Batog's definitions (5.97) and (5.98), a 'relevant' feature is any feature pertaining 15 This phenomenon will be discussed in Chapter 9 of this book. BATOG'S LOGICAL MODEL 109 to all realizations of a phoneme and a 'distinctive' feature is a relevant feature of a phoneme which is opposed to another phoneme by the presence versus absence of the feature. In this conception, the relevancy and distinctiveness of features are determined by the phonemicization of the idiolect. Thus, the nasality of e.g. Ge. Du. Eng. [n] is neither relevant nor distinctive in Batog's model because it turns out AFTER the identification of this sound with [h] that nasality is not a common feature of all sounds that are interpreted äs realizations of the same phoneme äs [rj]. This is, in my opinion, the wrong way round. It is distinctiveness of features which is the primary phenomenon in linguistic analysis, whereas the phoneme has an additional characteristic, viz. the quality of being a unit. Consequently, the identification of features should precede the identification of units. The essential difficulty which arises when one proceeds from units to features is that units and features are not necessarily coextensive. Thus, it is a fallacy that phonemes are in one-one correspondence with segments characterized by certain features. Features characterizing different phonemes may fully or partly coincide in time. The instances of Du. [s] and Sw. [d] and the partial nasalization of oral vowels before nasal consonants were mentioned in section 5.7. In the latter example, the transition from oral to nasal takes place before the transition from vowel to consonant. The transitional segment is certainly non-phonemic, but this i s a result that can be obtained only if the segmentation of the speech flow into units is accomplished AFTER the features have been investigated. Moreover, there are three kinds of features which are even on the phonemic level not coextensive with phonemes. First of all, the existence of 'joint features' cannot be excluded on theoretical grounds. By this term I mean features of juxtaposed phonemes which require each other's presence for being relevant. A possible instance is presented by Russian hard consonants before [i] and soft consonants before [i]. The relevance of the Opposition hard ~ soft is beyond doubt. However, loan words generally preserve [i], which palatalizes the preceding consonant. This may be an indication that the words byt' 'to be' and bit' 'to beat' are opposed to each other by the presence of both consonantal hardness and vocalic back articulation versus the presence of either consonantal softness or vocalic front articulation. In the cases where this kind of analysis is correct, there is one feature (on the phonemic level) jointly characterizing two juxtaposed phonemes. Secondly, there are features which characterize units not by their inherent properties but only in relation to other units in the speech flow. An example is stress in Russian or in Dutch. Whether the first vowel in Ru. muka is stressed depends not on its absolute prominence, but on its comparative prominence in relation to the second vowel.16 Thirdly, some features may be functionally relevant without being distinctive on the phonemic level. This is the case of so-called 'demarcative' or 'delimitative' features, or simply 'junctures'. The problem is clearly illustrated by Jakobson's 16 Cf. Chapter 10 of this book. 110 THE DEVELOPMENT OF MODELS IN PHONEMICS well-known example of Ru. pogoreli [pagar'el'i] 'they burned up' versus po göre U [psgar'el'i] 'along the hill?', which has recently been subject to criticism, however.17 The difference between [e] and [ε] is undoubtedly non-phonemic in Russian. The neglect of features in phonemic identification makes the distinction between neutralization and defective distribution impossible in Batog's model. Besides, any meaningful distinction between these two concepts requires some kind of reference to meaning. Finally, I have to point to the role of meta-theoretical considerations in Batog's model. Neither pattern congruity nor simplicity is taken into account, but economy plays its part in Batog's fifth identification rule: the number of elements in F must be minimal under the condition that the requirements (5.89)-(5.92) are satisfied. I would like to stress that there is no linguistic justification whatever for this rule, which is the one according to which [h] and [n] are considered realizations of the same phoneme if they happen to be in complementary distribution. I have nothing against economy considerations, provided that they are applied on the right level and with regard to the right entities, which is, in the present case, on the subphonemic level with regard to the identification of compound features in different environments. Minimalization of the number of phonemes may yield formal advantages but has nothing to do with linguistic facts. The choice of meta-theoretical criteria is closely connected to the way one looks at things. If the phoneme is conceived of äs a mere device used in the description of languages, then simplicity should be the decisive criterion wherever two possible Solutions reflect the facts equally well. But if one maintains that the phoneme is a real linguistic entity, i.e., an entity deriving from the nature of human Speech and having an observable physical correlate, then there cannot be two possible Solutions: an entity either is or is not a phoneme, tertium non datur. Since I hold the latter view, uniqueness is one of the meta-theoretical requirements which I would impose on a satisfactory model of the phoneme. Another important requirement is observational adequacy. Little is said about observations in all the models discussed in the preceding chapters. It is generally assumed that there is an initial body of texts to which the analysis is applied. But every practically registered text contains a number of miscarriages which a native Speaker of the language would reject. In fact, the negative indications of an Informant are just äs valuable äs the positive ones. The reactions of a native to the initial body of texts are just äs necessary a datum of the analysis äs the texts themselves. Some concepts, such äs free Variation and neutralization, cannot even be defined satisfactorily without reference to a native Speaker's Interpretation of the material. The informant's reactions to the initial body of texts should therefore, like the texts themselves, be given a place among the initial objects of the model. Before envisaging a way out of the problems raised in the last two sections of this chapter we shall first turn to some methodological questions of linguistic modelling. 17 Jakobson and Halle 1956:18, cf. Shapiro 1968:14. PART TWO

FUNDAMENTALS OF PHONEMIC MODELLING 6

THE USE OF MATHEMATICAL METHODS IN LINGUISTICS

6.1. THE DEHUMANIZATION OF THE STUDY OF LANGUAGE

In ] 965 the leading Soviet periodical Voprosy jazykoznanija published an article by V.l. Abaev bearing the significant title "Linguistic modernism äs the dehumanization of the study of language". As in the case of Saumjan's 1952 article about the phoneme, the editorial board of the periodical feit the necessity of explicitly dis- sociating itself in a footnote from the views put forward in the article. A comparison of the two articles reveals the profound change in the Soviet linguistic outlook which had taken place in the thirteen years in between: in 1952 the first glimmer of structuralism, which was in Saumjan's paper, had been scientifically stoned by the prominent linguists of the day because the Soviets were not yet ready for "catching up and overtaking the achievements of Western structuralism", and in 1965 Abaev's publication was accorded almost the same reception because the author warned against the catching up and overtaking of 'linguistic modernism', the 'mathematical fashion', and the 'dehumanization of linguistics', natural and inevitable phenomena in the decline of Western bourgeois society. Abaev's article falls into four sections, dealing with the evaluation of the history of Soviet linguistics, the role of structuralism in the history of linguistics, the use of mathematical methods in linguistics, and the escape from the dehumanization of linguistics. According to Abaev, one must distinguish three periods in the history of Soviet linguistics: the Marrist period (until 1950), the Stalinist period (until 1956), and the modernist period.1 Though Abaev admits that serious mistakes have been made during the first and the second period, he maintains that Soviet linguistics was in those days built upon a number of fundamentally correct ideas, viz. the view that linguistics belongs to and is closely connected with the social sciences and that the development of a language is inseparable from the development of the society where it is spoken, and the recognition that the historical method is the most important way of apprehending language phenomena (1965:23). However, these ideas, in his view basically correct, were tightly interwoven with the Marrist or Stalinist

1 For a short outline of Marr's ideas, see, e.g., Ivic 1965:102ff. A detailed exposition is presented in Thomas 1957. The Stalinist period was not characterized by any consistent linguistic conception at all. 114 FUND AMENTALS OF PHONEMIC MODELLING setting, which was to be eliminated with the liquidation of the Stalin cult in 1956. This elimination created, in Abaev's opinion, a vacuum in Soviet linguistics, which was subsequently, under the influence of the increasing international cultural links and exchange of ideas, filled with fashionable theories from abroad, amalgamated by Abaev under the name of 'linguistic modernism'.

When a society enters a period of spiritual crisis it Starts convulsively catching at everything which is new. But since this is done under conditions of ideological devastation and impoverishment, the search of novelties follows chiefly the line of form, formal means, formal methods, formal tricks, formal eccentricities. The content, however, if it exists at all, remains extremely poor and primitive. This is what modernism is. Every modernism is always formalistic: it allures people by its outward, illusory, formal novelties. The characteristic feature of contemporary modernism is its anti- humanism. "The mania of abstract, formalistic schemes and constructions, in which there is no place for the living, trembling human soul, is the most general symptom of contemporary modernism in literature, art and science" (1965:24). According to Abaev, formalism is not a bad thing if taken in the sense of primary interest in the formal side of phenomena, which deserves the same attention äs their content, but it becomes unacceptable when it "appears äs an ideology, i.e. when it attempts at making the form of phenomena pass for their essence or advocates the incognizability of the essence" (1965:27), which is characteristic of modernism. It is the latter kind of formalism which Abaev detests so whole-heartedly.2 Linguistic formalism äs an ideology goes back to the Junggrammatiker, who started disregarding the "indissoluble connection between the history of a language and the history and culture of the people" which had been the concern of von Humboldt.3 F. de Saus- sure's structuralism took up and promoted these "abstractionistic and formalistic tendencies" of the Junggrammatiker. More fundamental than the contrast of Saus- sure's structuralist approach with the atomistic approach of bis teachers is, in Abaev's opinion, the formalism that they have in common and which separates them from the adherents of Humboldt's Weltanschauung theory. The essence of Saussurean structuralism äs Abaev views it is the dehumanization of linguistics which is the consequence of (1) the view that language is a sign system connected with objective reality in an arbitrary way only, (2) the attachment of significance to pure relations independently from the entities that are related to each other, and (3) the rupture between synchrony and diachrony that resulted from the repudiation of the historical point of view. The dehumanization of linguistics, which is part of the general process of cultural dehumanization registered by Abaev in philosophy, sociology, history, music, art, and literature, reaches its pinnacle in the theory of glossematics, which for Abaev is the "most logical and consistent" and therefore most abject variety of structuralism.

2 It is remarkable that Abaev makes no distinction between 'form' äs opposed to 'content' and 'form' äs opposed to 'substance', not even in bis criticism of Hjelmslev's views. 3 Cf., e.g., Ivic 1965:48ff. MATHEMATICAL METHODS IN LINGUISTICS 115 The use of mathematical methods in linguistics is not to be rejected in Abaev's eyes if they are harnessed to the study of the origin and development of a language and its contacts with other languages. As an example of this kind of application he mentions the glottochronological method of establishing the date of disintegration of a linguistic Community. But beyond the use of statistics in historical investigations there is no room for mathematical methods in linguistics. Not the exactness of the method, but the value of the results, is Abaev's primary concern, and the latter has to do with the role of language in social history, not with mathematics. The following quotation about mathematical linguistics and machine translation is characteristic of both the style and the content of Abaev's article (1965:33).

It is said that mathematical linguistics is necessary for machine translation. Very well. Machine translation will, if the experiments are crowned with success, be a great technical achievement. Stenography was an outstanding achievement in its time. It's no joke to write speech down with the same speed äs it is uttered! Stenography required a particular approach to the division of speech into constituent elements in view of their frequency of occurrence and recurrence, etc. But nobody maintained that Stenography opened a new era in theoretical linguistics. Nobody claimed that the whole study of language should be attuned to conform to the needs of Stenography. Machine translation also requires a particular approach to speech analysis in view of frequency, distribution, etc., for conveniently putting it into a Computer. But there is no necessity at all for attuning the whole of linguistics to conform to the needs of machine translation, no more than in the case of Stenography. The fish canning industry also elaborated particular ways of dividing fish into parts for conveniently packing them into cans. But, äs far äs I know, the workers in the fish canning industry have never claimed that they had opened a new era in ichthyology äs a science. Machine translation, like Stenography, Stands outside the fundamental Problems in the theory and history of language, and there is no need whatever for interlacing the two. It is necessary to support and develop in every possible way any new methods and devices of descriptive and applied linguistics if they demonstrate their value in practice. But one must not think that it is necessary to rebuild the theoretical foundations of linguistics every time a new device shows up. Formal and mathematical methods will, äs far äs their usefulness is corroborated by experience, be adopted in various flelds without at all affecting the theoretical, philosophical basis of the humanitarian study of language.

What, then, is the course that (Soviet) linguistics should take ? Language is not only a communicative technique but also an expression of social consciousness, and the synthesis of these two aspects is possible only if the historical perspective is taken äs the guiding principle (cf. Abaev 1934). Linguistic modernism takes only the former aspect into account, which is easier to formalize and schematize than the latter, and therefore distorts the essence of the object of investigation. The more formalized linguistics becomes, the less humanitarian will it be (1965:39).

Modernist linguistics means not a new stage in the evolution of the study of language but the annihilation of the study of language äs a social science in exactly the same way äs modernist art means not a new stage in the development of art but the annihilation of art äs a social value.

No fruitful cooperation is, in Abaev's opinion, possible between modernist linguistics and the serious study of language. It is necessary to delimit their respective spheres of action instead of aiming at a synthesis. The indivisible unity with human 116 FUND AMENTALS OF PHONEMIC MODELLING thought and the indissoluble connection with social history are the most profound specificities of language and the study of language without regard to thought and history is not really linguistics because it does not correspond to anything in objective reality. Thought and history are the gates where the human factor comes in. Con- sequently, the essential task of linguistics is to regain its central place within the humanities. As a social science, linguistics should be rebuilt on the basis of Marxist ideology. Soviet linguistics should distinguish itself from modernism by the historical approach, the primacy of meaning over form, and a close connection with philosophy and the other social sciences (1965:42). Humanization, not formalization, should be its device. The struggle against formalization in linguistics is part of the general struggle against the dehumanization of culture.

6.2. CRITICISM

Abaev's article provoked a large number of sharp reactions. Together with Abaev's paper the editors of Voprosy jazykoznanija published an article by Revzin, who emphasized the unity of linguistics and the necessity for mutual enrichment of old and new fields of knowledge, and an article by Rozdestvenskij about object and method in contemporary linguistics. Revzin maintains that structural ideas have been quite fruitful in various 'traditional' fields of linguistics, such äs dialectology and the theory of translation.4 On the other band, he points out that structural methods can only be applied to the same material which 'traditional' linguistics is built upon. The connection between new trends in linguistics and earlier methods (Port Royal, Sanskrit grammarians) has often been stressed in both Western and Soviet linguistic literature. Structural linguistics advances hypotheses that must be verified experimentally, and the most important linguistic experiment is the natural development of a language, which is the very object of 'traditional' linguistics. Finally, the new fields of applied linguistics (machine translation, speech analysis and synthesis, Information retrieval and storing) are certainly not characterized by a minor interest in semantic problems in comparison with the old application of linguistic theory to language learning. Rozdestvenskij points out the fact that the object of a science is not only determined by the topics to be studied but also by the way one looks upon them. It is, in bis opinion, the latter aspect rather than the former which is characteristic of the different periods in the development of linguistics äs a science. In the course of the following year Voprosy jazykoznanija published a number of reactions to Abaev's article.5 The large response that the article called forth was due 4 For an example of structural methods in dialectology, cf., e.g., the phonologization of purely phonetic data in Stokhof 1972. 5 Rozencvejg 1966, Gladkij 1966, Zinder 1966, Filin 1966, Cikobava 1966, Kuznecov 1966. The discussion was concluded with a survey of unpublished reactions by Rozdestvenskij. Cf. in this connection also MaCavariam 1963, 1967, Deserieva 1970, Losev 1970. MATHEMATICAL METHODS IN LINGUISTICS 117 to its tone and style rather than to the facts and arguments adduced by Abaev, äs is especially clear from the fact that hardly any of the critics referred to an article by Filin which had been published in the preceding issue of Voprosy jazykoznanija and in which essentially the same views were enunciated, only with some restraint, without the aggressive glamour that characterized Abaev's polemics.6 In the present review I shall confine myself to an exposition of the Novosibirsk mathematician Gladkij's contribution to the discussion, which is the most lucid Statement of the 'modernist' point of view. The appearance of formal methods in linguistics is not, in Gladkij's opinion, a consequence of the modern linguist's predilection for formalities, but originates from the analogy of language with certain formal Systems studied in mathematics. The analogy became apparent in the course of this Century äs a result of two developments. On the one band, linguists became interested in the synchronic functioning of language äs a System. On the other, mathematicians started examining the logical structure of their own language. This led to the rise of a new MATHEMATICAL discipline, which could expediently be called 'mathematical linguistics'.7 The use of the term 'mathematical linguistics' äs a designationoflinguistic investigations in which some kind of mathematical method is used is quite unsatisfactory in Gladkij 's eyes because the use of a mathematical apparatus is not characteristic of any specific pari of linguistics. Both formal and traditional methods should be used in linguistics, and the choice between them, or rather the choice of the extent to which each of them is to be used, should depend on the nature of the phenomena under investigation. Abaev's insistence on the point that linguists should exclusively be concerned with such topics äs 'language and thought', 'language and history', 'language and culture' leads Gladkij to the view that Abaev's objections refer not only to the use of formal methods in linguistics but also to the very study of language äs a separate phenomenon. According to Gladkij, every science must above all be engaged in the investigation of the proper characteristics inherent in its own object of study. Abaev's thesis that the historical method is the only really scientific method in linguistics is therefore not only an arbitrary but also an incorrect view. Machine translation cannot be compared with stenography or fish canning because the latter techniques take into account linguistically or biologically marginal phenomena only, whereas translation is one of the most complex varieties of linguistic activity, requiring the use of most, if not all, essential features of linguistic structure. Gladkij agrees with Abaev that the essence of the most important linguistic phenomena cannot be revealed by quantitative methods. This is precisely why the most fruitful mathematical methods in contemporary linguistics are taken frorn such disciplines äs set theory and mathematical logic, not from the quantitative branches of mathe-

« Filin 1965, cf. Kuznecov 1966. 7 The theory of context-free languages belongs to this brauch of mathematics, cf., e.g., Ginsburg 1966. 118 FUND AMENTALS OF PHONEMIC MODELLING matics.8 Abaev's identification of mathematical with quantitative methods is certainly incorrect. There is one more essential point in Abaev's exposition that is rightly criticized by Gladkij, viz. the primacy imputed to modern linguistics of form over meaning. This misconception goes back to a confusion between the possibility of abstracting from certain qualities and the insignificance of these qualities. Gladkij maintains that the abstraction from meaning in many contemporary investigations is no denial of its vital pari in the functioning of language, but rather a necessary prerequisite for a successful inquiry into meaning itself. The methodological principle of abstracting from some aspects when studying others is common to all sciences and there is no reason to repudiate it in linguistics.

6.3. CONCLUSION

The confusion between abstraction and insignificance referred to in the preceding Paragraph would not be made by the best among the 'modernist' linguists. However, there are various passages in publications by other authors which can easily give rise to the kind of misunderstanding referred to above. An example is the following quotation from an article by the Hungarian Linguist F. Kiefer (1964:10). I think it will turn out that mathematical linguistics is not a branch of linguistics but it is modern linguistics, i.e., there is no reason to make a difference between mathematical linguistics and general linguistics at all. I think even the name 'mathematical linguistics' could be abandoned. It would be more suitable to speak simply about 'modern linguistics' or 'exact linguistics'. This standpoint is just äs uncompromising äs Abaev's. Its consequences should be viewed in the light of the following Statement about semantics (1964:10): Semantic aspects are, by far, more difficult to formalize than most other aspects of language. Obviously, it is impossible to prove that they are irrelevant to linguistic model construction, but it is equally obvious that mathematical linguistics must have a solid base and therefore, to be useful, mathematical linguistics must — so far — leave semantics aside. The quotations above exhibit the same dogmatic attitude which we met in Abaev's exposition. The assertion that "it is impossible to prove that they [sc. semantic aspects] are irrelevant to linguistic model construction" is characteristic of the way a creed should be formulated: the relevance of semantics is not questioned, but the impossibility of proving its irrelevance is stated instead. As if one would LIKE semantics to be irrelevant! Moreover, it is far from obvious how mathematical linguistics can "have a solid base" or "be useful", or even both, if semantics is left aside. Here, formalism has indeed turned into an ideology. It is clear, however, that the repudiation of this view does not involve the repudiation of mathematical methods in linguistics. One can hardly disagree with Gladkij s Cf. Kortlandt 1969:156f., Gladkij and Mel'cuk 1969:20ff. MATHEMATICAL METHODS IN LINGUISTICS 119 when he states that the choice between alternative scientific methods should depend on the nature of the investigation. On the other hand, Abaev rightly Stresses the fundamental importance of meaning at all levels of language, including the phonemic level. If we view language äs a code, its most essential property is the existence of a relation between the plane of expression and the plane of content. This relation involves the existence of relevant features, which are minimum differences in one plane corresponding to a difference in the other, and units, which are minimum sets of relevant features that are concatenated in the Speech flow. In this conception, a phonemic unit is characterized by three essential properties. Firstly, it is a set of relevant features, which are defined by their distinctiveness. Secondly, there is no strict order between its elements. Thirdly, it is part of an ordered whole; in other words, it is characterized by a POSITION. If we reconsider the models presented in the preceding chapters, it is remarkable that none of them regards the phoneme äs a unit in the sense outlined here. As to the ESSENCE of a phoneme, I think that Abaev is right in stressing its distinctiveness, which has in modern linguistics often been neglected in favour of other criteria (äs was pointed out in the preceding chapters). As to the METHOD of investigation, I think that his prejudice against mathematics, which is based on his lack of familiarity with non-quantitative mathematical disciplines, is simply unwarranted.9

9 It goes without saying that the incorrect use of mathematical methods in some linguistic investigations is no argument against the possibility of using them correctly in others, cf., e.g., Piöurin 1965. MODELS AND MODELLING

7.1. REVZIN'S CONCEPTION OF MODELLING

The concept of 'modeF has been very much en vogue in linguistics since its introduction by Hockett in the early fifties (cf. Hockett 1954). The popularity of the concept has not, however, led to a communis opinio about its content. In 1960 Y.R. Chao contributed a paper to the international congress for logic, methodology and philosophy of science in which he presented thirty different concepts of 'model' taken from half äs many sources.1 The number of different interpretations has considerably increased since. The terminological variety signalized by Chao is especially annoying in view of the fact that authors on linguistics are not accustomed to explaining their extralinguistic concepts in any detail. That this may easily give rise to misunderstandings is most clearly testified in an article by A.F. Losev entitled "On the methods of expounding mathematical linguistics for linguists" (1965). In search of the concept of 'model' the author started reading Revzin's Models of language and found, in the first section of the first chapter, the Statement that "the essence of [modelling] is the construction of a certain sequence of abstract schemes which should be a more or less close approximation to the data of actual reality" (Revzin 1966:3). This is a hazy formulation indeed. The following paragraph in Revzin's book reveals that modelling is a method in which the investigator proceeds from certain of the most general features of actual languages, formulates certain hypotheses dealing with the structure of the language äs an abstract semiotic System, and then establishes what is the relationship between the consequences of these hypotheses and the facts of actual languages äs described by actual linguistic disciplines. (1966:3) Losev is undoubtedly right when he remarks that, apart from the reference to an 'abstract semiotic System', which is highly unclear, this is exactly what linguists have always been concerned with and, consequently, does not create any need for the term 'modelling'. Disappointed by the first section of Revzin's book, Losev turned to the second, which begins äs follows (Revzin 1966:4). 1 Chao 1962. The various concepts are taken from publications by Hockett, Chomsky, Voegelin, Harris, and others. MODELS AND MODELLING 121 The model is constructed in the following manner. Out of all the great variety of concepts accumulated by the science, certain ones which can conveniently be regarded äs primary are selected. Certain relations between these primary concepts are determined and these may be adopted in the character of postulates. All the remaining Statements are drawn up on a strictly deductive basis in terms defined, ultimately, by means of the primary concepts. This paragraph will be quite clear to anybody familiär with Batog's model of the phoneme described in Chapter 5 of this book, but one can hardly blame Losev for bis doubts about the sense of these words, which only too easily give rise to a confusion between the PRIMITIVE (rather than 'primary') notions of a model and the IMPORTANT notions of a theory. This confusion leads Losev to accuse Revzin of subjectivist idealism and relativism. The theory of language models, unconnected with the concept Original' of modeis and the theory of reflection, is a highly vicious theory. Its consistent application presupposes a fundamental struggle with dialectical materialism and rests upon pointless structures of consciousness, disregarding altogether the problem of consciousness. (Losev 1965:18) This style of debating is unscientific, useless for linguistics, and harniful to dialectical materialism. In order to meet Losev's criticism Revzin added to his second book a chapter on the principles of linguistic modelling. Meanwhile Revzin's conception of modelling has thoroughly changed, however. A model is now regarded äs a mapping of a process in reality and defined äs a system of signs ('logical model') or a System of physical objects ('physical model') with an input and an Output corresponding to the sets of initial and final objects of the process (1967:25). Revzin distinguishes between three kinds of linguistic models. Firstly, there are synthetic models, the input of which is a description of a Situation in reality and the output is a phrase.2 The Inversion of such models yields analytic models, having a phrase äs their input and a description of the corresponding Situation in reality äs their output. Secondly, there are generative models, yielding an infinite number of phrases from a finite input. Chomsky's generative grammar belongs to this category. These models abstract from the actual content of utterances and take into account certain general grammatical and lexical classes only. Thirdly, there are meta-linguistic models, the input of which is a set of phrases with their meanings and the Output a set of morphological and syntactical classes and relations between such classes. Whereas models from the first and second category can be viewed äs performance and competence models respectively, the third category contains learning or description models, thus constituting a link between the preceding categories of models. This conception of modelling is much more specific than the ones found in Revzin's earlier publications. Consequently, it has lost the generality to which the concept of model owes its popularity. For the sake of completeness I shall add here two other definitions of the concept from Revzin's earlier work. In a discussion of the possibil- 2 Various models by MePcuk belong to this category, äs does the computerization of Russian conjugation in Kortlandt forthcoming c. 122 FUND AMENTALS OF PHONEMIC MODELLING ities of formalizing distributional analysis, a model is said to be an 'idealization of an actually existing Situation' (1962b:15). Though this definition is rather loose it reflects an essential property of models. A much more formalized definition, which is found in an article that Revzin wrote together with the philosopher A.A. Zinov'ev, runs äs follows. Let X be a set of propositions decribing (stating) the correspondences between the elements of two complex objects A and B. [...] Let Υ be a set of propositions obtained from the investigation of A and different from the propositions in X. [...] Let Z be a set of propositions concerning B and also different from [the propositions in] X. If Z can be inferred from the conjunction of X and Υ in accordance with the rules of logic then A is a model of the object B and B is an original of the model A. (Zinov'ev and Revzin 1960:82)

Thus, if the propositions about B that can logically be derived from the investigation of A and the correspondence rules between A and B hold true, then A is a model of B. This is quite a rigid requirement because it implies that any quality in B can somehow be mapped into A.

7.2. SAUMJAN'S CONCEPTION OF MODELLING

The other leading theoretician in Soviet linguistic modelling, S.K. Saumjan, paid ample attention to the concept of modelling in his book on applicational generative grammar (1965:63ff.). The author points out correctly that there is an essential difference between 'models' in mathematics and 'models' in the empirical sciences. The same difference is emphasized in Chao's paper referred to above (1962:558): "In mathematics a model is more concrete than what it is a model of, while in the social sciences a model is more of an abstraction." In mathematics a 'model' or 'Interpretation' of a theory is a system that satisfies the Statements of the theory.3 In Suppes' words, a model of a theory may be defined äs a possible realization in which all valid sentences of the theory are satisfied, and a possible realization of the theory is an entity of the appropriate set-theoretical structure. [...] A possible realization of the theory of groups is a model of the theory if the axioms of the theory are satisfied in the realization, for in this case (äs well äs in many others) the valid sentences of the theory are defined äs those sentences which are logical consequences of the axioms. (1962:252)

In the empirical sciences, the word 'model' is often used äs a synonym of 'theory', or something slightly different from it. Thus, Braithwaite establishes that a model for a theory T is another theory M which corresponds to the theory T in respect of deductive structure. By correspondence in deductive structure between M and ris meant that there is a one-one correlation between the concepts of T and those of M which gives rise to a one-one correlation between the propositions of Tand those of M which is such that if a proposition in Γ logically follows 3 More exactly, a model satisfies not the Statements of the theory, but the sentential functions obtained from them by replacing the primitive terms by variables, cf. Tarski 1965:123. MODELS AND MODELLING 123 from a set of propositions in T, the correlate in M of the first proposition in T logically follows from the set of correlates in M of the propositions of the set in T. (1962:225) (This definition is very close to the one put forward by Zinov'ev and Revzin, cf. above.) Elsewhere the same author uses the words 'model' and 'theory' to express "the distinction between two deductive Systems represented by the same calculus but differing epistemologically" (1968:90). In this conception, two deductive Systems which are interpretations of the same calculus are related äs 'model' to 'theory' if in the one which is the model "the Interpretation of the initial formulae containing the theoretical terms is epistemologically prior to that of the derived formulae not containing these theoretical terms" whereas in the one which is the theory "the reverse is the case, the derived formulae being the epistemologically prior" (1968:90). Here 'epistemologically prior' is taken in the sense that the Interpretation of a set of formulae comes after and is dependent on the Interpretation of the set of formulae that are epistemologically prior to them. Thus, in a model the hypotheses that are logically prior, in the sense that they serve äs premisses for the deduction of the derived hypotheses, are epistemologically prior äs well, whereas in a theory the logically prior hypotheses are the epistemologically posterior ones. This conception is in concordance with the idea of deriving from the model certain Statements about the thing which is modelled. It leaves no room for any substantial diiference between the concepts of 'model' and 'theory', however. According to Saumjan, the essential property that models in mathematics and models in the empirical sciences have in common is their cognitive function. The difference between the two kinds of models is due to the difierent role of theories in the process of cognition, not to a different role of models. This is a consequence of the fact that the original of a model is a theory in mathematics but a pari of reality in the empirical sciences. Thus, Saumjan agrees with Braithwaite that a model differs from a theory only in respect of its epistemological value, though the authors seem to disagree about the essence of the difference. Not quite in accordance with bis own exposition, Saumjan defines a model formally äs "a theory with a clear signification in the form of images that serve äs analogues of unobservable objects".4 This definition makes sense for the empirical sciences only, because the observability of objects is alien to mathematics. If, however, the 'clear signification' referred to in the definition is considered to be a self-evident triviality in mathematical disciplines, the concept of model in mathematics coincides with the concept of theory. Summar- izing, I would say that Saumjan regards models äs a variety of theories, characterized by the existence of an obvious Interpretation. For the rest the concept of model does not play a fundamental part in the main exposition of Saumjan's theory. Chao, like Braithwaite and Saumjan, sees the essential diiference between a model and the thing which is modelled in their epistemological role (1962:565):

4 The Russian text runs äs follows (1965:77): "model' — έίο teorija, imejuscaja nagljadnoe soder- zanie v vide obrazov, sluzascix analogami nenabljudaemyx ob'ektov". Cf. also the discussion in Piotrovskij 1966:15ff. 124 FUND AMENTALS OF PHONEMIC MODELLING In general, that which can more conveniently be handled — that is, seen, heard, remembered, re- corded, communicated, manipulated, experimented upon, inherited, etc. is the model and that about which corresponding Information or results are hoped to be obtained through such handling (in the broad sense) is the thing. This is a rather pragmatic approach to the concept of'model'.

7.3. APRESJAN'S CONCEPTION OF MODELLING

We now turn to one of the most lucid among contemporary linguists, Ju.D. Apresjan, who in 1966 published a short outline of the different kinds of models that are used in linguistics.5 According to Apresjan, the concept of model "occupies a central place in contemporary structural linguistics, which can above all be characterized äs the science of language models" (1966:78). The necessity of modelling arises wherever the object of investigation is inaccessible to direct observation. In that case, the comparison with an object which is examined more easily leads to a better understanding of the object which is modelled. Thus, "the sense of modelling consists in studying manifest properties of the model instead of inaccessible properties of the object and extending the laws that have been deduced for the model to the object" (1966:79). Models are, in Apresjan's opinion, characterized by the following properties. Firstly, a model must be FUNCTIONALLY SIMILAR to the object which is modelled. Consequently, a model and the thing modelled are alike with respect to their structure but differ äs to their physical characteristics. It is, for example, irrelevant whether a model of the flexion of the Russian Substantive has the shape of a written text or a punched tape or a set of impulses in a Computer provided that it reflects the rules of Russian substantival flexion. Secondly, a model is an IDEALIZATION of the object which is modelled. As an example Apresjan mentions the composition of a criminars portrait in police investigations. Such a portrait is made up of a number of essential features, while other features, though existent in reality, are left out. At the same time, an idealization may be characterized by certain features which are absent from reality. Thus, it is generally assumed that the number of utterances in a language is infinite and that the length of an utterance is not restricted by the System, though any actual corpus of utterances is finite and every actual utterance is limited. Thirdly, a model is defined not in terms of real objects but in terms of CONSTRUCTS, which cannot directly be derived from experimental data but are formulated on the basis of the general hypotheses that the totality of observations and scientific Intuition suggest to the investigator. The same conception is apparent from the following quotation from Einstein (1953:440): "Ich bin überzeugt, dass rein mathematische Konstruktionen uns befähigen, die Grundbegriffe und in gleicher Weise die Gesetze

5 An enlarged German translation of this book appeared in 1971 and an English translation is forthcoming. MODELS AND MODELLlNG 125 zu entdecken, die diese miteinander verbinden, die uns dann den Schlüssel für unser Verstehen der Erscheinungen in der Natur liefern." Fourthly, a model is a FORMAL SYSTEM in the sense that the initial objects, the State- ments connecting them and the rules according to which they are operated upon are explicitly stated. The exactness of a model does not ensure the coincidence of Statements derived from the theory with experimental data but enables the investigator to perform experiments that can confirm or disprove the theory. Fifthly, a model must have some EXPLANATORY VALUE, i.e., it must explain the results of an experiment and predict the results of new experiments. The better the predictions, the higher the explanatory value. A model which does not allow any Interpretation äs an explanation of empirical material is a fiction. Classical examples of prediction on the basis of models are Mendeleev's hypothesis about the existence of a number of chemical elements that were unknown in his days but have later been detected or synthesized, and Le Verrier's calculation of the existence of the planet Neptune, which had also not yet, at the time, been detected. An excellent example from linguistics is F. de Saussure's hypothesis about the existence of laryngeals in Proto- Indo-European, which has later been confirmed by the decipherment of Hittite.6 The history of linguistic decipherment is füll of such examples (cf. Doblhofer 1957). In synchronic linguistics, predictions can only be verified by arranging experiments. Apresjan distinguishes three types of linguistic models according to the object ofmodelling(1966:99).7 (1) There are models of concrete linguistic processes and phenomena, modelling human SPEECH activity. The first step in this direction was taken by the Prague structuralists. (2) There are models of the PROCEDURES that lead scholars to the discovery of linguistic facts, thus modelling the investigator's activity. The first step in this direction was taken by the American descriptivists. (3) There are meta-models of linguistic DESCRIPTIONS, modelling grammars of concrete languages. The first step in this direction was taken by the glossematicians. According to Apresjan, the first type of models is the most important, whereas the other types play an auxiliary pari. Moreover, the procedure models logically precede and the description models logically follow the proper speech models. The Output of a procedure model consists of a grammar and a dictionary. Consequently, SPEECH MODELS ARE CHARACTERIZED BY THE FACT THAT GRAMMAR AND DICTIONARY ARE KNOWN το THE INVESTIGATOR FROM THE VERY OUTSET. The procedure models fall into three classes according to their input (1966:101). The input of deciphering models consists of a text only, and all Information about the language System is extracted from the text. The inpul of a grammatical model consists of a text and the set of correct phrases of the language. This means that the investigator makes use

6 De Saussure 1879. The Situation is actually more complicated, cf. Lindeman 1970. The interested reader can try to repeat Saussure's discovery on the basis of the data offered in Zaliznjak 1963:147f. 7 This classification is based upon Fitialov 1964; cf. also Fitialov 1962. 126 FUND AMENTALS OF PHONEMIC MODELLING of an Informant in order to establish whether a phrase is correct or not. It goes without saying that the investigator can be his own informant. The input of a semantic model consists of a text, the set of correct phrases, and a set of semantic invariants. This means that the informant must not only give Information about the correctness of phrases but also about the semantic equivalence or non-equivalence of pairs of phrases. Proper speech models can also be divided into semantic and purely syntactic models (1966:106). The latter model the speaker's command of a grammar, i.e., his ability to understand and construct grammatically correct but not necessarily meaningful phrases, whereas the former model the speaker's command of a language, i.e., his ability to understand and construct meaningful phrases. Another classification of speech models is based upon the aspect of the speaker's activity which is being modelled. Apresjan distinguishes analytic, synthetic, and generative models. The input of a syntactic analysis model is a text, and its Output is a record of the syntactic structures of the sentences occurring in the text. The input of a semantic analysis model is also a text, but its Output is a representation of the meaning of the text in a specially devised semantic language. The input of a syntactic synthesis model is a record of the syntactic structures of sentences, and its Output is a set of correct sentences. The input of a semantic synthesis model is the representation of a Situation in a specially devised semantic language, and its Output is a set of sentences reflecting the Situation. Generative models occupy, in Apresjan's opinion, an intermediary place between analytic and synthetic models. Their input consists of an alphabet of initial Symbols and a set of formation (and transformation) rules operating upon strings of Symbols from the alphabet, and their Output is a set of correct sentences with a record of their structural characteristics (including, in the case of semantic models, a representation of their semantic structures). Finally, models can be classified into calculi and algorithms according to their mathematical form (1966:107). A calculus is a System of permitted operations and determines the members of a possibly infinite set by means of a finite apparatus. Generative models usually have the form of a calculus. An algorithm is a sequence of commands, the execution of which leads to a specific member from a set of possible outcomes. An algorithm that can be executed by a Computer is called a program. (A calculus cannot be handled by a Computer.) Most analytic and synthetic models have the form of an algorithm.8

7.4. STOFF'S CONCEPTION OF MODELLING

The concept of model plays its part not only in linguistics but in other sciences äs well. The first discipline where the word became current was architecture, where it

8 The most complete treatment of grammar in algorithmic terms which I am familiär with is the description of Russian nominal flexion in Zaliznjak 1967. MODELS AND MODELLING 127 has always been in general use in the sense of Standard, pattern, specimen, prototype, or something which is in some respect similar to something eise. In the middle of the nineteenth Century the concept was introduced into mathematics in the sense of a structure that is similar to another structure.9 Meanwhile two kinds of 'models' found their way into physics (cf. Hesse 1963:10ff.). Models of the first kind are mentally or practically constructed structures that imitate a part of reality in a simplified shape. This way of representing things goes back to the Ancient Greeks who viewed the world äs a flat cylinder. Models of the second kind are physical analogues, i.e., physically different but structurally similar Systems. Classical examples of this kind of models are the representation of light or electric current äs a stream, the picture of the motion of gas molecules äs the movement of billiard-balls, and the comparison of an atom with the solar System. In linguistics, it is generally hard to determine whether a 'model' is conceived äs a theory (i.e., a set of Statements about the object of investigation), a scientific representation (i.e., a construct reflecting the object of investigation), or an analogue (i.e., an object which is structurally similar to the object of investigation). But it is not until after the emergence of cybernetics in the late forties that 'model' became the most populär meta-theoretical term in nearly all fields of investigation. Consequently, the task of defining the concept has shifted to philosophy, where it became a central topic of scientific debate.10 It seems reasonable, therefore, to pass the word to a philosopher now. In 1966 a monograph by V.A. Stoff appeared, entitled Modelling and philosophy. Choosing from the many aspects of modelling discussed in this book, I shall limit myself to an exposition of Stoffs conception and classification of models.11 Like Braithwaite, Chao, and Saumjan, Stoff sees the difference between a model and a theory in their 'gnoseologicaP (which is, äs far äs I understand, the Soviel equivalent of 'epistemological') role. According to Stoff, the essential characteristic of a model in contra-distinction to a theory is not its level of abstraction or simplification (äs suggested in Frolov 1961:41), but the way of expressing abstractions and simplifications (1966:15). Whereas the content of a theory is expressed in a set of propositions that are connected with each other by the laws of logic, in a model the content is represented äs a number of typical situations, structures, or diagrams. Stoff agrees with Novik that essential properties of a model are, apart from its quality of reflecting the object of modelling, its ability to replace the object in certain phases of the investigation, the existence of definite rules for passing from information

9 Today mathematicians speak of isomorphem!» structures in this sense. The first to suggest the possibility of identifying isomorphous relations and operations was G.W. Leibniz, who adduced addition and multiplication äs an example, cf. Bourbaki 1960:36. 10 Cf. the rapidly increasing number of articles about modelling in Voprosy filosofii in the early sixties, especially Frolov 1961, Stoff 1961, Maslov 1962, Uemov 1962, Novik 1963, Stoff 1963, Gluäkov 1963, Amosov 1963, Venikov 1964. 11 A short outline of §toif's views and their relevance for linguistics is presented in Guxman 1970. Cf. also Hartmann 1965. 128 FUNDAMENTALS OF PHONEMIC MODELLING about the model to Information about the object, and the possibility of deriving Information that can be verified experimentally (cf. Novik 1963:92). Stoffs own definition of 'model' runs äs follows (1966:19): "A model is a mentally conceived or materially realized System which reflects or reproduces the object of investigation and can replace it so that the study of the model yields new Information about the object." This is, in bis opinion, what all models have in common. Models can be classified according to their form (i.e., the means by which the model is built up) and according to their content (i.e., the object which is modelled). On the basis of the means of modelling Stoff distinguishes two classes, viz. the class of material models and the class of ideal (= mental) models, each of which is divided into three subclasses (1966:23).12 Material models are divided into spatial, physical, and mathematical models. To the first subclass belong maquettes and a chemist's models of molecules and crystals. Physical models represent the dynamics of processes and various kinds of dependencies between structural parameters rather than the spatial characteristics of the object under investigation. Examples are models of ships and airplanes to be tested before the construction of a prototype, and also small animals that are used in biological and medical experiments instead of large animals or human beings. Such models are most often used in order to reduce the spatial and/or temporal scale of actual processes.13 Mathematical models are analogues (e.g., electrical models of mechanic or acoustic processes), Computer simula- tions, and various kinds of cybernetic Systems. Their common property is the absence of physical or geometrical similarity. Ideal (mental) models are divided into figurative (iconical) and symbolic models, and a class of mixed varieties. Examples of figurative models are the representation of light or electric current äs a stream and the conception of the repulsion between electrons äs a mutual bombardment with small missiles. Symbolic models are sign Systems, characterized by the complete and fundamental absence of resemblance between the elements of the model and the corresponding elements of the object. This fundamental absence of resemblance is Saussure's arbitraire du signe. Models in logic and mathematics belong to this category, and so do Computer programs and all kinds of economic and econometric models.14 This is also, in my opinion, the most sensible Interpretation of the concept of model in contemporary linguistics. Between the two ideal types of figurative and symbolic models there is a spectrum of intermediate possibilities, exhibited in various kinds of diagrams, graphs, geograph- ical maps, chemical structure formulas, drawings, etc.

12 The classification is chiefly based upon Venikov 1964. 13 The representation of a PROCESS is often considered the characteristic property of a model, cf. e.g.: "A model is a structure in which changes in time and space under physical influences are re- flected" (Amosov 1963:27). 14 Cf., e.g., Allen 1966, 1968, Johnston 1963. MODELS AND MODELLING 129

7.5. CONCLUSION The main difficulty in defining the concept of model is the avoidance of being either too general or too specific. On the one hand, hardly anything is being said when Kiefer defines a mathematical linguistic model äs "a more or less exactly formalized System, throwing light upon one or more aspects of language" (l 964:9). On the other, Andreev seems to be too exacting when he defines the same concept äs "a complete or partial System of language elements and their numerical (concrete äs well äs generalized) characteristics which could be formally represented and put into a Computer" (1962:186). Computerizability can hardly serve äs a criterion for being a model.15 Trying to be precise about the inherent characteristics, while leaving open äs many interpretations äs possible, and, consequently, at the risk of being vague about the latter and pedantic about the former aspect, I define a 'model' formally äs a triple M=[D,F,H] (7.1) where D is a set of definitions, F is a set of functional relationships between the defined concepts, and H is a set of hypotheses about the correspondence between the defined concepts and certain observable phenomena m reality. A concept which occurs in D and F but not in H is an auxiliary concept. A concept which occurs in F and H but not in D is an undefined concept. A concept which occurs in D and H but not in F is an irrelevant concept. In my opinion, two distinctions are fundamental for any classification of models, and these are based on the role of time in the registered relationships and on the possible allowance for the influence of factors that are not referred to in the model themselves. If F depends on a variable reflecting time, the model is DYNAMIC, otherwise it is STATIC. If F accounts for the influence of variables that are not found in D or H, the model is STOCHASTIC, otherwise it is DETERMINISTIC. In this conception, a model differs from a theory in two respects. Firstly, it is less pretentious because the elements of F refer not to phenomena in reality but to members of D. A relation in a model holds between constructs, not between real objects, whereas a Statement in a theory refers to reality (the latter concept being taken in the sense of the thing which it is all about). Secondly, a model is not 'true' or 'false', äs a theory is, but 'adequate' or 'inadequate'. Testing a model is testing H, not F. In a theory, however, the elements of D (the concepts between which relationships are posited) are equated with their correlates in reality, so there is no room for H, and F acquires a hypothetical Status itself. The possibility of positing relationships between constructs without the direct pretense of stating how things are in reality is at the very bottom of the so-called hocus-pocus approach in contemporary linguistics. It is therefore far from accidental 15 Cf. also Denisov's Statement that linguistic modelling is "the creation of all sorts of auxiliary artiflcial languages" (1965:5), and Voegelin's characterization that a 'model' is "identified by label" in contradistinction to a 'framework of representation' which is "attestable by citation from actual descriptions" (1959:9). 130 FUND AMENTALS OF PHONEMIC MODELLING that the rise of modelling in linguistics coincides with Householder's demarcation of the hocus-pocus and God's-truth attitudes. In view of the close connection between modelling and hocus-pocus, I cannot refrain from quoting Joos' characterization of the hocus-pocus outlook (1957:80). Hocus-pocus linguistics is pejoratively described äs a game played with symbols. Its practitioner may perfectly well share in the God's-truth faith that the language has an autonomous structure. But the conclusion that the structure is therefore accessible to frontal attack is for him a non-sequitur. If he happens to be a theorist on procedure, he will say that he is setting up maps or models for ('for', not Of') seemingly coherent areas of the phenomena, testing these each against its parallel phenomena by simple inspection, altering them repeatedly and observing the improvement in fit, combining them into larger maps and testing the combinations by observing how well they seem to fit larger phenomenal territories, and so on until the description is complete enough to be acceptable for the time being. Each fit is good when the map or model seems to predict all the observed phenomena and does not predict the opposite of any observed phenomenon. Now it usually turns out that it also predicts some phenomena that have not yet been observed. This is the great advantage of the hocus-pocus map: it leads to new discoveries. The corresponding disadvantage is that different workers may make different maps for the same phenomena; this is the 'arbitrariness' 'in' the 'description' which parallele the God's-truth 'uncertainty' 'about' the 'facts'. Probably no human thinker can stay always on the same side of the line between the God's-truth and the hocus-pocus attitudes. One is needed to supply the motive, the other to supply the tricks of method. For it is a fact of experience that the most grimly consistent God's-truth worker frequently discovers in bis symbolization something useful that was not in his raw data: he has done some hocus-pocus in spite of himself. And it is also true that the most consistently cynical hocus-pocus worker gets a good deal of his pleasure out of discovering what he feels to be the truth about his language, not all of it out of the refinement of his procedure. This description characterizes linguistic modelling quite well. In particular, it should be clear that 'modelling' refers to the method of investigation, not to the content of the Statements involved. THE PHONEME

8.1. THE MOTIVATION FOR TAXONOMIC PHONEMICS In the last paragraph of Chapter 7 we entered into a discussion of hocus-pocus and God's-truth. It is now time to consider the position that the concept of the phoneme occupies in this respect. In terms of formula (7.1), it is time to determine whether the concept 'phoneme' is a notion that can be introduced äs a member of D for the sake of convenience in formulating F, or a notion referring to certain phenomena in reality which cannot be adequately described without making use of the concept 'phoneme' or a substantially identical concept. The former view, according to which the phoneme is simply a handy tool for describing languages, has been especially populär among American linguists. Thus, Twaddell wrote in 1935 that the phoneme "is to be regarded äs a heuristic or pragmatic fiction, a mere terminological convenience in describing the phonological relations which obtain among the elements of a language" (1935:68). Hockett advocates 'pattern congruity' and 'economy' äs criteria for phonemic identification (1942: 9 and 1955: 158ff.), and so does Harris (1951: 63ff.). It is clear that any kind of simplicity criteria can only refer to entities that are introduced for the sake of convenience, not to entities that derive their identity from their functional properties. This is why Hockett could so easily do away with the phoneme in his Manual.1 If the phoneme is 'a mere terminological convenience', one can of course leave it out äs soon äs it turns into an inconvenience for one reason or another. This is not so, however, if one regards the phoneme äs a fundamental unit in linguistic structure. As I pointed out at the end of Chapter 6, the view of language äs a code, in the sense of a mapping of a plane of content on a plane of expression, necessarily entails the existence of relevant features, which I define äs minimum differences in one plane corresponding to a diiference in the other, and units, which I define äs minimum sets of relevant features that are concatenated in the speech flow. The fundamental unit in the plane of expression is the phoneme. I think that this view is quite in accordance with Trubetzkoy's, though I do not accept his iden- 1 Cf., e.g., Hockett's comment on Fox /c/: "We have not used the term 'phoneme' in our IC analysis, since we do not know where to introduce it. One could logically call all the elements in list A 'phonemes', or all those in list B, or all those in list C, or all those in list D. [...] the term 'phoneme', and just how to use it, is regarded äs of subsidiary importance" (1955:163f.). 132 FUNDAMENTALS OF PHONEMIC MODELLING tification rules. It should be clear that my 'relevant features' are Saumjan's 'differentors', not his 'differentoids', which I shall call simply 'features'.2 Taking the position outlined in the preceding paragraph I find myself diametrically opposed to Chomsky and Halle, who explicitly deny the existence of a justification for assuming a separate 'taxonomic' phonemic level in linguistic structure.3 Trying to clarify the issues involved I shall briefiy discuss the objections put forward in Chomsky 1964.4 The first problem which I have to face is that Chomsky takes 'taxonomic phonemics' to be a theory which requires that phonological representations meet the following conditions (1964: 78): (1) linearity (2) invariance (3) biuniqueness (4) local determinacy whereas I do not recognize any of these criteria in the strict Interpretation that Chomsky criticizes. I do adhere to linearity and invariance (which together define the phoneme) on the level of constructs, but not on the level of observation, to which Chomsky's criticism applies. (As to linearity, I have to make a reservation even on the level of constructs, cf. below.) Though Chomsky's arguments against biuniqueness are largely irrelevant from my point of view, I agree with him that it cannot serve äs a criterion for phonemic identification. I shall deal with linearity in section 8.5 of this book and with invariance and biuniqueness (äs well äs complementary distribution) in section 8.7. Local determinacy will be discussed in section 8.9 and finally refuted in Chapter 9. In search of a justification for 'taxonomic phonemics' Chomsky makes a distinction between 'internal' and 'external' evidence (1964: 99). The first category contains various kinds of simplicity and convenience arguments which I have presented in the first paragraph of this chapter. As I pointed out above, such arguments are irrelevant from my point of view because in my opinion the phoneme is not 'a mere terminological convenience' but a fundamental unit deriving its identity from its functional properties. Consequently, it may indeed seem more of an inconvenience than a convenience for those who are engaged in stating certain rules of grammar.5 Nevertheless, phonemes cannot be dispensed with altogether because they constitute

2 Cf. section 2.10 of this book. 3 It is interesting to note that their 'systematic' phonemic level essentially coincides with the phonemics of the 'Moscow school of phonology', cf. Chapter l of this book. 4 Since the arguments put forward in Postal 1968 essentially come down to the same thing I see no point in discussing them separately. The matter is not discussed at all in Chomsky and Halle 1968. 5 It should be clear, on the other band, that I do not deny the convenience of eliminating phonemes from certain morphological Statements, which is what Chomsky c.s. are really interested in. (Cf. in this connection the lucid discussion of Spanish semivowels in Mel'cuk 1965.) An extreme example of the fruitfulness of this approach is offered by Kuipers' excellent description of Kabardian (Circas- sian) morphemics in terms of clusters of features, which enables him to eliminate all vowels from his transcription (1960). THE PHONEME 133 an essenlial part of linguistic structure and a phonemeless description of a language is therefore incomplete. Thus, the reason for assuming phonemes is 'external', if I understand Chomsky's use of this word correctly: the existence of phonemes derives from the view of language äs a code, the essence of which is the existence of a relation between the plane of expression and the plane of content. On the one band, the possibility of distinguishing elements in the plane of content from each other necessarily involves the existence of relevant features. On the other, a small number of relevant features can only yield a large number of signs if Segments where the realization of an arbitrary relevant feature is present are concatenated with Segments where it is absent. Since two distinguishable utterances may differ either in the relevant features that characterize them or in the relative ordering of the relevant features (or in both), these two properties together determine the existence of units (which may, theoretically, coincide with features). It should be remarked in this connection that Chomsky's criticism of the role of phonemes in speech perception is entirely beside the point. For one thing, the question of whether "the hearer first uses only local phonetic cues to identify the invariant criterial attributes that determine the successive taxonomic phonemes, and he then goes on to determine the deeper structure of the utterance" (1964: 99) is totally irrelevant for the existence of phonemes, just äs the question of whether the recognition of a face is preceded by the identification of individual criterial attributes by means of local visual cues is totally irrelevant for the existence of features that distinguish different faces from each other and so enable one to recognize a face. For another, Chomsky's remark that "intelligibility is preserved under gross phonetic distortion, which may be completely unnoticed when grammatical constraints are met" is just äs irrelevant because phonemes do not DETERMINE the recognition of linguistic forms, but only make recognition possible. Similarly, gross semantic distortion does not necessarily impair intelligibility. Thus, if in a conversation with my colleagues I refer to "that article about Latvian phonology by Stokhof", all of them will understand that I mean Steinhauer because he is the one who is working on the subject. The interchange of names may even go unnoticed. But this certainly does not mean that 'Stokhof means 'Steinhauer' in the context 'Latvian phonology'. Linguistic units, such äs phonemes, determine the possibilities of encoding Informa- tion, not the actual use which is made of these possibilities.

8.2. DESCRIPTIVE ADEQUACY

Elsewhere Chomsky and Halle claim that "if we construct a grammar to generate the occurring forms (more precisely, to generate the well-formed sentences involving attested lexical items), then this grammar already makes a distinction between admissible and inadmissible" (1965:117). On the contrary, I would maintain that a 134 FUND AMENTALS OF PHONEMIC MODELLING grammar based on attested lexical items alone cannot achieve 'descriptive adequacy', which is one of Chomsky's desiderata.6 The problem involved is the distinction of structurally determined from 'accidental' gaps in the lexicon. Here I have to point to a missing link in Chomsky's discussion of the levels of adequacy in phonology. He writes (1964:30): To attain the level of descriptive adequacy, a grammar [of English] would have to provide, in addition [to lexical rules generating existing words], a general rule that sets up a specific barrier against /ftik/, but not against /blik/ (which would thus qualify äs an accidental gap, a phonologically permissible nonsense syllable). This level would be achieved by a grammar that contained the generalization that in initial position before a true consonant (a segment which is consonantal and non- vocalic, in terms of Jakobson's distinctive features), a consonant is necessarily /s/. But how do we know that the latter rule meets the level of descriptive adequacy? The obvious reason is that /bl/-like clusters occur word-initially while /ft/-like clusters do not. This is not a reliable criterion, however, äs the Norwegian Caucasist H. Vogt pointed out ten years before Chomsky published his Current issues (Vogt 1954: 29): The total number of initial clusters in Georgian, äs they occur in ordinary speech and in printed texts, runs into the thousands, and that of final clusters into the hundreds. The number of theoretically possible medial clusters should run into huudreds of thousands. Since it is reasonable to expect that the proportion of accidental gaps will increase with the number of clusters, we are left with the problem of determining the non- existent but structurally possible (in Vogt's terminology, VIRTUAL) clusters of the language. This problem is definitely more serious for Georgian than for English (Vogt 1954:31):

This distinction between actual and virtual members of a System may have no great interest in languages such äs English, Danish, and Norwegian, where the consonant clusters are comparatively few and relatively symmetrical in their arrangement. [...] But in Georgian this distinction is of para- mount importance, because the number of virtual clusters probably exceeds that of the actually occurring clusters. The combinatory possibilities of consonants in the Georgian language, äs determined by the phonemic structure of this language, have only partly been exploited in the vocabulary. How, then, can we determine the virtual elements of the System ? Vogt proposes pattern congruity äs a criterion. It is not clear, however, how this concept can be defined in a theoretically satisfactory and unambiguous way. Chomsky does not talk about virtualities, but he does about simplicity of rules: "To meet the level of explanatory adequacy, a linguistic theory must justify the descriptively adequate grammar on internal grounds" (Chomsky and Halle 1965: 101). But if the (?) descriptively adequate grammar is to be justified ON INTERNAL GROUNDS (which is, äs far äs I understand, on the basis of simplicity considerations, cf. above), there is 6 "A grammar that aims for descriptive adequacy is concerned to give a correct account of the linguistic Intuition of the native Speaker" (Chomsky 1964:29). "We say that a grammar meets the level of descriptive adequacy to the extent that it gives a correct account of the speaker's 'tacit knowledge' " (Chomsky and Halle 1965:99). THE PHONEME 135 no criterion at all for distinguishing virtual from inadmissible clusters.7 I think that we should not confine ourselves to attested lexical items but look instead for a more straightforward way of determining non-existent but structurally possible forms in a language. Besides, restricting oneself to attested lexical items can easily lead to incorrect results, äs Ebeling has recently pointed out (1967: 131). In Dutch (more accurately, in the variant of Dutch where voiced /z/ is distinct from voiceless /s/) one finds the borrowings mazzel /mo'zel/ 'luck' from Yiddish &nd puzzel /pAizal/ from English puzzle. If one excludes words of foreign origin from the material, the conclusion must be that a voiced [z] is impossible after a lax vowel, and that the Opposition /z ~ s/ is neutralized in this Position. But then it cannot be explained why the words were incorporated in the Dutch language in this shape, for borrowings are äs a rule adapted to the models of the receiving language. This course of events is understandable only if one concedes that the possibility of a combination of lax vowel plus /z/ existed already, at least shortly before the time of borrowing, and that /s/ was at that time relevantly voiceless in this position. A phonologist working immediately before a borrowing of this kind must have at his disposal a method for detecting the hidden possibilities. The experimental Situation required in such a method should be a close Imitation of the natural Situation found in the act of borrowing. This paragraph points not only to the problem but also to a possible solution. Thus, I would claim that Chomsky's grammar cannot achieve 'descriptive adequacy' (in my Interpretation of the term) because he does not account for the difference between a System where the word puzzle is incorporated in the lexical System äs /pAzsl/, yielding a combination of phonemes not previously attested in the language, and a System where it is incorporated äs /pAsel/ or /püzol/, in accordance with existing phonemic patterns, though the way of borrowing undoubtedly reflects certain aspects of the native speaker's linguistic competence, viz. his ability to perceive the form of unknown words and to incorporate them in his own lexicon. An admissibility criterion for sounds and sequences not attested in the material should be based on linguistic observations, not on considerations of simplicity.

8.3. DISTINCTIVENESS In the Interpretation that I have put forward above a phoneme is characterized by two properties, viz. its distinctiveness and its quality of being a unit. The former 7 Moreover, the 'linguistic Intuition of the native Speaker' cannot directly be resorted to because of "the simple truth that observations made by informants on their language are usually wrong. A glaring example of the unreliability of morphological analysis and semantic identiflcation on the part of the Speakers is given by Yakovlev (1948:255): his Kabardian informants, when asked which part of the word wm'k^a 'don't go!' (lit. 'you,sing. w- not -m- go &"V)means 'not', usually answered "w-", even though both the 2nd pers. sing, prefix w- and the negative prefix m- are often found äs the only prefix preceding a base, e.g. wk'°[an 'your going', 'you ... to go', mk'°lan 'not going', 'not... to go', and one easily arrives at an analysis different from the first reaction of the Speakers by comparing the forms k'°a 'go!', wm[k'°a 'don't go!' (both addressed to one person),/'A:'°a 'go!', fmlk'°a 'don't go!' (addressed to several persons, cf. the 2nd pers. plur. prefix/-)." (Kuipers 1960: 107, fn.4) 136 FUNDAMENTALS OF PHONEMIC MODELLING of these properties will be discussed in the present section, the latter in section 8.5 of this book. The concept of distinctiveness rests upon the concept of functionality, which has probably never been explained more clearly than by Martinet in the first issue of Lmgua(l947:37i.).

Le langage a pour l'homme im but qui est d'agir sur ses semblables. C'est un outil, d'une grande complexito certes, mais un outil tout de meme, et si nous en voulons saisir la nature proprement linguistique, il nous faut l'examiner, comme nous le ferions de tout autre outil, en considerant les elements qui en assurent le fonctionnement. C'est du point de vue de la fonction, et de celui-lä seulement, que nous pouvons nous prononcer sur Fidentite ou la non-identite des elements linguistiques. Soit un outil, au sens courant et vulgaire du terme, comme la clo. Sa fonction est de fermer et d'ouvrir une porte. [...] Le serrurier pourra, s'il le juge bon, donner ä l'anneau une forme particuliere ou employer un metal ou un alliage autre que celui de Fexemplaire qui a servi aux mesures. Cela n'empSchera pas l'usager d'accrocher les deux cles, l'ancienne et la nouvelle, au meme clou et de considorer qu'en pratique les deux cles sont interchangeables et identiques. Consequently, a functionality test involves two kinds of data: on the one band, a key and a keyhole, and on the other, a way of determining whether the door is open or closed. Translated into linguistic terms (Ebeling 1960: 13):

Briefly, the reasoning Starts from the assumption that there are always two facts immediately accessible for the inquirer: the utterance and the Interpretation of it by a native. The Interpretation depends on two things: the utterance (the input) and the set of rules applied to it (the code). Thus, knowing both utterance and Interpretation, one can draw conclusions about the code. Any distinct change in an utterance that is accompanied by a change in the Interpretation cogently points to a rule in the code. This is the basic idea of phonemic — or, in a wider sense, functional — thinking in linguistics.

Now I call 'distinctive' a change in an utterance that is accompanied by a change in the Interpretation of it by a native. Unfortunately, however, this is no immediately applicable criterion for practical purposes. First of all, the Informant may not react differently to phonemically distinct forms because of the existence of doublets, like in the case of Ru. skaf, skap 'cupboard'. On the other hand, "an Informant confronted with the pair wines — winds can assure us that they are different, even if he does not make any difference in his rendition of the items" (Contreras and Saporta 1960: 4, cf. also Gudschinsky 1958). It is clear from these examples that one cannot ask an Informant whether two words are 'same' or 'different' because in that case one asks two different questions at the same time, one about the form and one about the meaning. The above problems result from the fact that in normal conversation "the attention of the listener is concentrated on the message. Sound äs such does not concern him in the least: it is merely the means of transmission" (Ebeling 1967: 128). This led Cohen to assume "two entirely different modes of perceptual action: [...] (a) wholes are identified rather than parts, and (b) in the absence of meaningful wholes, parts are identified and may constitute completely new wholes" (1966: 182ff.). The fact that an unprepared informant is much more inclined to perform the first THE PHONEME 137 than the second kind of action has unequivocally been demonstrated by Contreras and Saporta: meaningfulness "is apparently so strong a factor, that repetitions of the grammatical nonsense syllable [klu] were consistently repeated äs the meaningful [klub] 'club'" by their Chilean Spanish Informant though word-final b does not occur in genuinely Spanish words (1960: 8, fn.15). Ebeling calls the above modes of perception 'listening to the message' and 'listening to the sound', respectively (1967: ISO).8 This terminology seems to be more appropriate in view of the fact that the second type of action presupposes not the ABSENGE of meaning but its IRRELEVANCE in the message, and the latter may derive not only from the former but also from a Situation where the meaning is known in advance, e.g., when somebody is being introduced. In that case, "what interests the listener is the form of the utterance, for the meaning is known to him in advance: he is going to hear the name of the man Standing in front of him" (1967: 130).

8.4. RELEVANT FEATURES

On the basis of these observations I propose to define the set of initial objects of phonemic analysis by Π = [K, R, S] (8.1) where K is the set of possible dimensions (back — front, oral — nasal) in the con- tinuum of sounds that can be produced by the human Speech organs, R is a relation between sound sequences reflecting the informant's ability to recognize and identify Hnguistic forms (e.g., words), and S is a set of sound sequences recognized and identified by the informant äs Hnguistic forms (e.g., words) belonging to bis own language. The elements of K are, like in Batog's model, sets of homogeneous features (in the sense of Marcus'). It follows from formula (5.6) that vK is the set of phonetic features. The number of phonetic features is determined by the investigator's ability to distinguish them and can be arbitrarily large. It is assumed that the members of K are ordered sets so that it makes sense to speak of the intermediate values of two homogeneous features. Alternatively, K could be introduced äs a set of variables that take values in a one-dimensional space. This would lead to a slightly different formulation in the sequel. In this chapter I shall assume that R is an equivalence relation.9 It partitions the set of recognizable sound sequences into classes of linguistically identical forms. The set S is the initial corpus. Every string s e S is segmented by an arbitrary dimension k e K into parts characterized by different features (different elements of k). Thus, 8 Cf. the earlier Statement by Hockett: "some speech events, under ideal hearing conditions (no background noise), sound the same to the native Speaker, regardless of any variations in actual articulatory motion which the analyst may be able to observe, while others sound different" (1955:144). This idea did not, however, receive due elaboration at the time. 9 This assumption will be dropped in Chapter 9. 138 FUND AMENTALS OF PHONEMIC MODELLING Ru. sumrak 'dusk' is segmented by one dimension into a voiceless, a voiced, and a voiceless pari, and by another into an oral, a nasal, and an oral part. The segmentation can be reflned by distinguishing intermediate degrees of voicing and nasality. I now define the 'elementary segmentation' ~(s) can be defined äs the smallest sequence of Segments the concatenation of which cannot be distinguished from s by the phonetic features in \JK such that every single segment is characterized by one and only one feature from every k e K. It should be clear that length (duration) is a member of K. An intermediate sequence of the sequences q>~(s) and φ~(ί) is defined äs a sequence of elementary segments characterized by intermediate values of the features which characterize the elementary segments in

φ(χ) = {X:xeX A Xe UK} (8.2) Now we turn to the functionality test (Ebeling 1960: 28). Our starting point is the supposition that certain oppositions exist in a given language. We take any word of this language and let its sounds (not bothering whether they are single or complex) move along one dimension in both directions. Several things may happen. Either the artificial word we obtain is not recognizable äs a possible form of the language. Or we get a word which native Speakers will Interpret äs a different, though not necessarily occurring, form. In the former case we have come outside the field of language sounds and find data for the distinction of speech sounds from nonspeech sounds in the given language, but not for the setting apart of the phonemes from each other. In the latter case we have discovered a relevant Opposition. It may also happen that before reaching a distinctly different form we first get a sound complex which is uninterpretable because it may be äs well the first äs the second form and does not occur in normal speech. Thus, replacing ANY part of the string s by a substring composed of different elementary segments one obtains one of three possible results. Either the new string is jR-equivalent to the original string, or it belongs to another Λ-equivalence class, or it falls outside the domain of R. Formally, if x, y, u, v are substrings of s, t such that s e S, s = uxv, t = uyv, then (1) if s R t then the features by which x, y differ are REDUNDANT in the environment (w,r), and (2) if ~ s R t then there is at least one relevant feature by which x, y differ in the environment (u,v).w In the latter instance, the procedure must be continued in order to separate relevant from redundant features. Ideally, there is an elementary segment z such that s = pzq and the string obtained from s by the Substitution for z of the segment w defined by

This is where the necessity of distinguishing between the level of constructs and the level of observation comes in. In Saumjan's terminology, the presence of a single differentor on the level of constructs is embodied in the simultaneous presence of two differentoids on the level of observation. A similar relationship is found between Du. postvocalic /r/ and /j/, the former of which is either a (uvular or apical) trill or a back semivowel, whereas the latter is a front semivowel(cf. Cohenetal. 1961: 39). Thus, Du. haai /haj/ 'shark' differs from haar /har/ 'hair' by the simultaneous presence of resonance and front articulation and the absence of a flap. Formally I define a RELEVANT FEATURE of an ARBITRARY segment χ which is part of i äs a family of sets of sequences of feature combinations (i.e., sequences of elements from the Cartesian product of the elements of K) such that the simultaneous replacement of all or part of the features that are present in the segment χ by sufficiently different homogeneous features changes the phonemic identity (i.e., the R- equivalence class) of s, whereas a partial replacement of the involved features cannot yield a third recognizable form. If we put s = uxv and denote by E the set of all possible combinations of features, which is a generalization of the set of elementary segments, and by E* the set of possible sequences of elements from E, then we can say that A is a relevant feature of the segment χ in the string s if it is a family of sets that fulfil the following requirements:

VA c E* (8.4)

Λ s R s' -> φ~(ζ) e U A (8.5) s'=uzv φ-(ζ)εΕ*

11 Cf. Marcus 1963b:414 and Romporti 1966:212. 140 FUNDAMENTALS OF PHONEMIC MODELLING V ~ s R t (8.6) i—uyv

Λ t R t' ~> φ~(ζ) φ υΑ (8.7) t'=uzv (p-(z}eE* Λ s R r v t R r (8.8) r—uzv where C(x,y) denotes the smallest subset of E* that contains φ~(χ) and qr(y) and their intermediate sequences. (In other words, the physical characteristics of r must at any time be somewhere between those exhibited by s and t. It follows from formulae (8.5) and (8.7) that φ~(χ) ε uΆ andq>-(y)<£ u A, respectively.) It goes without saying that u, v may be empty. I now assume, for the time being, that the procedure outlined here unequivocally reveals the relevant features of the language.12

8.5. SEGMENTATION

After the establisbment of the relevant features we turn to the problem of delimiting units in the speech flow. Though this problem has received a good deal of attention in structural linguistic literature, a generally accepted solution has not been reached.13 There is no need to repeat the entire discussion in this book, and I shall therefore refrain from presenting all arguments that have been adduced in favour of a monophonemic or biphonemic Interpretation in doubtful cases and confine myself to what I view äs the essence of the problem. As will be clear from the preceding chapters, I reject all arguments which are based on purely phonetic or meta-theoretical (simplicity, economy) considerations in this part of the analysis. Most of the trouble in linguistics originates not from the lack of criteria but rather from their abundance, which is indeed a serious threat to any coherent conception. Thus, Trubetskoy's rule l refers to syllables (which have, in spite of Haugen 1956, remained a purely phonetic notion), his rule 2 refers to articulation, rule 3 refers to length, rule 4 to distribution, and rule 5 to pattern congruity. Consequently, all of these rules run counter to his own definition of the phoneme äs a distinctive unit and should be regarded äs convenient devices for

12 In fact, this assumption is unwarranted because of two complications that will be dealt with in Chapters 9 and 10. 13 Apart from the relevant parts of Chao 1934, Trubetzkoy 1935, 1939, Pike 1947, Hockett 1955, and Ebeling 1960,1 want to point to the discussion in Martinet 1939, 1949, Hintze 1950, Morciniec 1958, Merlingen 1960, and Isaöenko 1963. THE PHONEME 141 practical purposes rather than äs theoretically decisive identification criteria. His other two segmentation rules run äs follows.14 Regel VI. Wenn ein Bestandteil einer potentiel monophonematischen Lautverbindung nicht als kombinatorische Variante irgendeines Phonems derselben Sprache gedeutet werden kann, so muss die ganze Lautverbindung als Realisation eines Eigenphonems gewertet werden. [...] Regel VII. Wenn zwischen einem Einzellaut und einer den obererwähnten phonetischen Voraus- setzungen entsprechenden Lautverbindung ein fakultatives oder kombinatorisches Varianten- verhältnis besteht, wobei die Lautverbindung als Realisation einer Phonemverbindung gewertet werden muss, so hat auch der Einzellaut als Realisation derselben Phonemverbindung zu gelten. Both of these rules state that a sound segment should be interpreted äs a sequence of phonemes unless it is phonemically distinct from any appropriate sequence of phonemes. Thus, they refer to distinctiveness and orderedness, which I have put forward above äs the (only) essential characteristics of the phoneme. The relevant features that constitute a phoneme are unordered in time. The phoneme, however, is characterized by its position in the Speech flow. Consequently, if we detect an order between two features they must belong to different phonemes. If we interchange dorsal and apical articulation in Du. kat [kat] 'cat' we obtain the word tak [tak] 'branch', and this is why these features belong to different phonemes. On the other hand, interchanging features belonging to one and the same phoneme does not lead to phonemically different forms. Thus, Saumjan's permutation test should not be applied to SOUNDS, äs its author originally proposed, but to FEATURES. (The same holds true for Martinet's commutation test.) In fact, the Situation is slightly more complicated because the relevant order of a feature with respect to ANY other feature in the neighbourhood should be taken into account. The issue has first been stated correctly by Ebeling (1960: 67): Theoretically we have a right to introduce the notion 'phoneme' only when we discover bundles of distinctive features for which the fact that they are grouped together is relevant. Does it happen that the same features in the same order constitute different linguistic forms according äs they are grouped together differently? If this question is to be answered in the negative, there are logically two possibilities: either there is no order between features at all, or all features are ordered with respect to each other. In the former instance the maximum number of possible utterances in the language is equal to the number of theoretically possible phonemes, which is 2n.3m if n and m are the numbers of the binary and ternary relevant features, respectively. In the latter instance the phonemes coincide with the distinctive features. In all the languages with which I am familiär reality is somewhere in between. The test proposed by Ebeling is äs follows (1960: 70). Suppose, we have detected in a given form the distinctive features +A and +B: if we change +A into —A, or +B into —B, we obtain a different form. Now the question is: do +A and +B belong to one phoneme /+A, +B ,../ or to two different phonemes /+A, .../ and /+B, .../?

14 Trubetzkoy 1939:54f. These rules are numbered 10, 11 in Trubetzkoy 1935. 142 FUNDAMENTALS OF PHONEMIC MODELLING If the latter solution is right, it is to be expected that the realization of the phoneme /+A, .../ is slightly colored by the feature +B of the contiguous phoneme, but this +B-color is phonemically of no importance. But if the feature +B, äs far äs it appears simultaneously (i.e. within the same phoneme) with the feature + A, is irrelevant, it may be omitted and even be replaced by — B without causing a change in the identity of the form. Consequently, we must find out whether the Word started from may be realized, äs to the features in question, in either of the two following ways: 1. /+A, -B, .../ /-A, +B, .../ ...; 2. /-A, +B, .../ /+A, -B, .../ ... If both interpretations are excluded (because, if we tried to pronounce these features defmitely in this order, the words we would produce would sound to native Speakers äs forms different from the one we started from), then we have to admit that the word contains a phoneme /+A, +B, .../. This procedure correctly points to a rnonophonemic Interpretation NOT if there is no relevant order between the features under investigation but only if there is a relevant unorderedness between them, and thereby excludes, e.g., the identification [s'] H /s'/ in a language where both /s/ and /?/ exist and both /s?/ and /?s/ are possible interpretations of [s']. I know of no reliable example from any actual language, however.1·5 Moreover, the procedure includes the familiär case of homorganic affricates for which it yields the same solution äs Trubetzkoy's rules (Ebeling 1960:71): As a rule, two opposite features belong to two different phonemes. However, there seem to be exceptions. A sound [ts] may have äs distinctive qualities both interceptedness (compared with [s]) and continuousness (compared with [t]). This is a special case where +A of the above formula is the opposite of +B, or: +A = —B. Our analysis depends on whether a form with the artificial cluster /+A, —B, .../ /—A, +B, .../ is interpreted äs identical with the form under study. This applies of course to all cases where two opposite features are contiguous, such äs nasal and nonnasal. It cannot be excluded a priori that in some language a trinary [sie] dimension will be discovered of the type /n - nd - d/. Thus, a phoneme je/ can exist only if its realization is functionally distinct from [ts]. The existence of prenasalized stops referred to in the last sentence has indeed been reported for Sinhalese, where [mb, nd, nd, ng] are phonetically and phonemically distinct from clusters of nasal plus stop, cf., e.g., kafidd 'trunk' and kandd 'hill' (Gair 1970:24). It should be clear that the procedure outlined here does not involve any simplicity considerations. Here I want to recall the case of the 'voiced h' in Chinese Wu-dialects (Chao 1934: 42). These dialects usually have an ordinary [h], which has different values according to the vowel following and may therefore be taken äs one phoneme [...] But in the case of the voiced h, not only the vowel quality (or the vowel articulation) begins at the very beginning of the breathing, but the breathiness also lasts till the very last moment of the vowel, so äs to form one homogeneous breathy vowel, and there is neither question of order of succession nor question of Substantive and adjective. [...] The only practical thing to do here is to consider voiced h äs one phoneme and write the vowel Symbols öfter it äs [Ha], [He], [Ho], etc., although we know that these digraphs represent perfectly homogeneous sounds. 18 In this case I would regard the order of /s/ and /'/ äs being neutralized, cf. below. The case must be distinguished from the existence of doublets such äs Du. wesp, weps 'wasp' where there is no neutralization of order, just äs in Ru. skaf, skap 'cupboard' there is no neutralization of the Opposi- tion between fricatives and occlusives. THE PHONEME 143 Indeed, writing the Symbols one after another is often practical for typographical reasons but it has nothing to do with phonemic analysis. If the breathiness referred to in the quotation above is inseparable from vocalic articulation, it is a feature of the vowel and not a separate phoneme. In that case the existence of an extra series of breathy vowels must be recognized, like the existence of a series of nasal vowels in French or palatalized consonants in Russian.

8.6. PHONEMIC UNITS

Summarizing, I define the PHONEMIC STRUCTURE of a string s e S äs the largest sequence of non-empty sets of relevant features for which there is a sequence of segments that are characterized by the respective sets of relevant features such that the concatenation of these segments is .R-equivalent to the string s. If we denote by oc(x) the set of relevant features of the segment χ in the string j and by ω(ί) a sequence of sets of relevant features ) (8.9) for which there is a segmentation of i

S — ΧιΧζ-..Xn (8.10) into segments that are characterized by the respective non-empty sets of relevant features

Λ flfo) - an (8.11) i then 0(s) is a phonemic structure of s if ω"(Ο (8.12) where s R s" and ωΑ(·5Λ) is characterized by the property that there is no s' such that s R s' and for which V «(οφ')) > «(ω%Ο) (8.13) ω

The uniqueness of Φ(Α) will be discussed below. The PHONEMIC UNITS of the language under investigation are defined äs the members of F={a: V αεΦ(*)} (8.14) seS Malecot's examples of English nasalized vowels before unvoiced stops cited by Chomsky äs an argument against the linearity condition do not constitute a problem 144 FUNDAMENTALS OF PHONEMIC MODELLING in the conception outlined here. The fact that Am.Eng. can't can be realized äs [kät] äs well äs [ksent] or any intermediate sound complex proves that nasality, which is the relevant feature that distinguishes the word from cat, is neither linked to the vocalic part of the word (äs the degree of closure of [ae] is) nor to its final consonantal part (äs the interceptedness of [t] is). Consequently, neither 'vocalic' nor 'consonantal' belongs to the phonemic unit which contains the relevant feature 'nasal'. On the other hand, nasality belongs neither to the unit which contains the degree of closure of [εε] nor to the unit which contains the interceptedness of [t]. The case of Am.Eng. writer ~ rider, which is the other example of non-linearity cited by Chomsky, is slightly more complicated and will be discussed below. Elsewhere I have pointed out that the segmentation procedure outlined here leads in some cases to a phonemic representation which is exactly opposite to the phonetic transcription (forthcoming d, ms. p. 2). The AUTOMATIC merger of two phonemes into one sound, like Du. /sj/ -> [s] or Sw. /rd/ -> [d], entails the biphonemic Inter- pretation of the sound: Du. [s] μ /sj/ and Sw. [d] μ /rd/. Consequently, the very process that transforms clusters into single complex sounds on the phonetic level involves the non-existence of the latter on the phonemic level. In literary Croatian there is a phoneme /c/ which is distinct from /tj/, cf., e.g., cerka 'daughter', tjerati 'to drive, pursue'. However, many people do not make this distinction and pronounce [cerka], [cerati] with an identical word-initial affricate. According to the above procedure this affricate must now be interpreted biphonemically: [c] μ /tj/. Thus, the pronunciation [c] of the cluster /tj/ in tjerati entails the Interpretation of the sound [c] in cerka äs a cluster /tj/. It should be clear that this identification is a direct consequence of the principle of distinctiveness.

8.7. IDENTIFICATION We have now defined phonemic units äs bundles of relevant features which cannot be decomposed into smaller entities of the same kind. Relevant features, however, have only been defined in relation to an environment (cf. above). So far nothing has been said about the identifiability of features (and, Consequently, phonemic units) in different environments. Since a phoneme is a set of relevant features, phonemes in different environments are identical if they are composed of the same relevant features (Martinet 1947: 43f.): ainsi donc si nous identiflons le [b] de banc et celui de baut, ce n'est pas parce qu'en comparant Tun ä l'autre nous jugeons qu'ils sont trop analogues pour ne pas representer la meme unite distinctive, ni exactement parce que le [b] de banc nous paralt plus pres du [b] de baut que du [p] de pou, mais uniquement et exactement parce que nous constatons que le [b] de banc se distingue des autres consonnes de la serie banc, pan, van, etc., par les memes caracteristiques qui assurent la distinction entre le [b] de baut et le [p] de pou, le [v] de vous, le [f] de fou, etc. Consequently, phonemic units that are composed of a different number of relevant features cannot be identified with each other. In Twaddell's words (1935: 74): THE PHONEME 145

We have no right to (and we don't want to) establish any 'phonemic' relations between the stops of a "pill" and of a "spill", for the stop of a "spill" is not in a phonetic sequence where it may contrast with a not-voiceless articulation. Any constituent member of the 'p-phoneme' must correspond to an articulatory complex which is in a phonetic sequence where it is different from a complex cor- respouding to a constituent member of the 'b-phoneme'. The stop of a "pill" and the stop of a "spill" cannot correspond to the same macro-phoneme, for the corresponding micro-phonemes are not similarly ordered. There is a phonological difference between the forms/»'//and bill; there is no similar phonological difference between the forms spill and *sbill. There appears to be no alternative to considering the stops of "spill, spare, spin", etc. äs corresponding to a different phoneme from the stops of "pill, pair, nap, lip, tapper", etc. The stops of "spill, spare", etc. are significantly bilabial and stop, but not significantly voiceless; the stops of "pill, nap, tapper", are significantly bilabial, stop, and voiceless. If an Opposition, like /p/ ~ /b/ in Twaddell's example, is unoperative in a certain environment, I say (following Trubetzkoy) that the Opposition is NEUTRALIZED in that environment. Formally, if for some γ e F V 7 = « π β (8.15) then γ is the ARCHIPHONEME of α and ß. Archiphonemes of three (or more) phonemic units are also possible, cf., e.g., Ch. [s] etc. before [i, u] versus [x, s, s] etc. elsewhere (Chao 1934: 48). A PHONEME is a phonemic unit which is not a proper subset of any other phonemic unit. It should be clear that, in my conception, the notion of neutralization depends immediately and exclusively upon the principle of distinctiveness. Consequently, the automatic ALTERNATION of a word form is not a sufficient condition for the establishment of a neutralization. In almost all Slavic languages the Opposition between voiced and voiceless consonants is neutralized in Word-final position. This rule seems to apply to Cz. Bu. v [f] 'in' äs well, in contradistinction to Ru. v [v] 'in'.16 However, my Bulgarian informants explicitly rejected [vimeto na narods] äs a possible realization of v imeto na naroda 'in the name of the people' and interpreted it äs vimeto na naroda 'the udder of the people' instead. It follows that the [f] under consideration is distinctively voiceless. (The Situation may be different in Czech.) Here again, the phonemic identity of a sound cannot be inferred from the generality of any possible rules but should be checked by means of a sound functionality test.17 Not only the Opposition between two phonemes, but also the Opposition between a phoneme and a cluster (e.g., between /c/ and /ts/) or the Opposition between two

16 Since voice assimilation in consonant clusters is a common phenomenon in the languages under discussion I take into consideration the prevocalic form of the preposition only. 17 It will be clear that Halle's example of voicing rules which operate on some consonants BEFORE and on others AFTER the phonemic level (Halle 1959 :22f., cited by Chomsky äs an argument against biuniqueness) is inappropriate from my point of view because the concept of neutralization refers to the relevance and redundance of FEATURES. Thus, distinctively voiceless /&/ differs from voice- irrelevant /ö/ just äs distinctively voiceless /t/ differs from voice-irrelevant /t/. I do not deny that phonemic units can be dispensed with in certain generation rules but I do maintain that descriptivc adequacy cannot be achieved if phonemic units are neglected, cf. above. 146 FUND AMENTALS OF PHONEMIC MODELLING clusters (e.g., between /s?/ and /?s/, cf. above) can be neutralized. A possible example of cluster nentralization is offered by some variants of Swedish. In this language there is an Opposition between dental and retroflex consonants, cf., e.g., mod [müd] 'courage' and mord [müd] 'murder'. The retroflex series should be interpreted biphonemically, äs is clear from the fact that even word-final r merges in sandhi with a following word-initial dental consonant into a fused unit sound: för sent [fAsent] 'too late'. On the other hand, the cluster /sj/ is realized äs a palatal [s], cf., e.g., mission [misün] 'mission'. Many Swedes do not distinguish between palatal and retroflex s, however, and pronounce [s] instead of [s], so that the Opposition between /rs/ and /sj/ is neutralized. So is the Opposition between either of these sequences and /rsj/, cf. version [vssün] 'version'.18 Thus, phonemes are identical if they are composed of the same relevant features. This does not solve the problem of phonemic identifiability, however, but merely shifts it to another plane, viz. to the problem of identifying relevant features, äs has correctly been pointed out by Saumjan (1968: 126). Here the criterion of distinctiveness fails because features in different environments cannot per definitionem be opposed to each other. But distinctiveness is, äs I have tried to point out above, the only principle that makes sense on the sub-morphemic level. So we are in need of a criterion. If the set of phonetic features UÄ" substantially coincides with the set of relevant features (here I abstract from the type and the nature of the respective elements, of course), then there is no problem at all. In that case, every dimension k e K contains a definite number of features which can be substituted one for another in such a way that any Substitution of this kind yields (or, in a slightly different Inter- pretation, can yield in an appropriate environment) a form which is not jR-equivalent to the initial form. Now relevant features in different environments can be identified with each other if they are coordinated with corresponding parts of the same dimension. Thus, in the familiär case of Dan. [e, ε, a, a] before [r] corresponding to [i, e, £, a] before other consonants, it seems quite sensible to identify the corresponding features of relative degree of closure in the respective environments with each other.19 This identification suggests the possibility of defining a more general type of 'dimensions' on the level of constructs such that relevant features in different environments can be identified if they are coordinated with corresponding parts of the same generalized dimension. A possible example is Dan. word-initial [t, d] and word-final [d, ö]: if word-initial [ö] i s interpreted äs a variant of word-initial [d]and word-final [t] äs a variant of word-final [d], then it seems reasonable to introduce a generalized dimension which runs from voiceless stops to voiced fricatives and regard

18 In fact, I do not think that this Interpretation is quite correct because not every [s] necessarily admits both [rs] and [sj] äs possible variants, which is an almost necessary condition for full-fledged cluster neutralization. It seems that the phenomena pointed out here are more satisfactorily described in terms of optional features, cf. Chapter 9 of this book. 19 Cf. Martinet 1947:43, Fischer-J0rgensen 1956:150. THE PHONEME 147

the first element in the pairs [t, d] and [d, ö] äs the 'strong' member and the second äs the 'weak' member of one and the same Opposition. In that case, the feature 'voiceless stop' that distinguishes word-initial [t] from [d] is identified with the feature 'stop' that distinguishes word-final [d] from [5], while the feature 'voiced' that distinguishes word-initial [d] from [t] is identified with the feature 'voiced fricative' that distinguishes word-final [ö] from [d].20 However, since I do not at the moment see any general LINGUISTICALLY interesting principle on which specific criteria for the identification of relevant features in difierent environments can be based, I shall refrain from a tentative formalization of any possible criteria here.

8.8. UNIQUENESS

Thus far, I have made no attempt at securing the uniqueness of <£(j). Yet I think that Φ($) should be unique indeed: its non-uniqueness simply means that there is a gap in phonemic theory. Adherents of non-uniqueness all too easily refer to Chao's famous article. Thus, Batog writes in his book on phonemics (1967: 98), which has been discussed at length in Chapter 5 of this book: The acceptance of a defiaition formulated according to (1) would mean that for each idiolect there is only one way of grouping sounds into phonemes. However, äs has been known for more than thirty years this assumption is false. (This fact was pointed out for the first time in 1934 by a Chinese linguist Yuen Ren Chao in his work under the significant title: The Non-Uniqueness of Phonemic Solutions of Phonetic Systems) The reference to Chao 1934 is at least inaccurate, if not simply incorrect. After an exposition of different Solutions that have been proposed by various authors äs representations of the Icelandic vowel system, Steblin-Kamenskij remarks (1964: 51): It is also clear from the survey of the six phonemic Solutions which have been proposed that the so-called non-uniqueness of phonemic Solutions is an Illusion. They are non-unique only äs far äs they are Solutions under diiferent conditions. The generally accepted thesis about the non-uniqueness of phonemic Solutions was suggested by Chao in his well-known article. After a closer examination, however, it turns out that this article is concerned either with Solutions that to a different extent take into account the facts [...], or, more often, with different representations of the same solution, viz. the representation of a phoneme by one or two letters, the use of different alphabets or Symbols, etc. It is of course possible to attain more or less simplicity or symmetry in the representation of a phonemic solution. But symmetry in this sense is a purely graphical problem that has no bearing on the phonemic solution itself. Even if we disregard the possibility of representing a string of phonemes by Symbols from different alphabets, the problem of uniqueness has some intricate aspects, however. Though I think that <3>(s) should be unique, it does not follow from this

20 It is evident that this identification is impossible if word-initial [d] turns out to be distinctively intercepted for in that case the Opposition that keeps word-final [d] and [ö] apart is operative word- initially äs well but the phoneme /ö/ is defectively distributed. It holds in the latter case that the Opposition /t/ ~ /d/ is neutralized in word-final Position, cf. Fischer-J0rgensen 1949:224. 148 FUNDAMENTALS OF PHONEMIC MODELLING supposition that there is ANY unique representation mapping Φ(Χ) onto a string of Symbols which meets the linearity and local determinacy conditions that are usually imposed on 'phonemic' REPRESENTATIONS. Three factors are responsible for this Situation. Firstly, the order between two successive phonemes may be neutralized in certain instances. This is the case of /s?/ and /?s/ referred to above. Secondly, a single feature may characterize two (or more) successive phonemes simultaneously. This is the phenomenon which I propose to call 'joint features' and which is to be discussed in section 8.9. Thirdly, local determinacy is impaired by the fact that R is not, in fact, an equivalence relation. The plural of Po. roza [ruza] 'rose' ends in a distinctively non-nasal [e]: roze [ruze] 'roses', whereas the accusative Singular ends in a vowel which may or may not be nasalized: roz% [ruze, ruze]. Consequently, the phonemic structure of the form [ruze] depends on the number of roses involved. This kind of problem will be discussed in Chapter 9.

8.9. JOINT FEATURES

The case of what I call 'joint features' is analogous to the case of different phonetic features jointly constituüng a single relevant feature, which was discussed in section 8.4 of this book in connection with Du. stom ~ stam. It turned out that the vowel /o/ which distinguishes the first word from the second must be both rounded and mid, whereas the vowel /a/ in the second word must be either unrounded or low (or both). In this example the features involved characterize the same, vocalic segment in the speech flow, but a Situation where phonetic features characterizing successive segments in the speech flow jointly constitute a single relevant feature is easily conceivable. In that case, either feature is relevant or redundant depending on the other. A possible example is presented by Russian hard consonants before [i] and soft consonants before [i]. If both the hardness of the initial consonant and the back articulation of the vowel are necessary to keep Ru. byt' [bif] 'to be' apart from bit' [b'it'] 'to beat' while, on the other hand, the presence of either consonantal softness or vocalic front articulation is sufficient to keep the latter word apart from the former, then the assignment of the relevant feature either to the consonant or to the vowel is arbitrary and must be rejected. The hardness or softness of a consonant is relevant before [i], not before [i], whereas the back or front articulation of an unrounded high vowel is relevant after a hard but not after a soft consonant. It follows from this example that the existence of joint features is an immediate consequence of the fact that relevant features have been defined in relation to a PHONETIC, not phonemic, environment. Polish obstruents are unvoiced before unvoiced obstruents, cf., e.g., sflaczec [sflacec] 'to get flabby' versus zwloczyc [zvwucic] 'to draggle'. Moreover, the phoneme /v/ is unvoiced AFTER unvoiced obstruents äs well, cf., e.g., tworzyc [tfoztc] 'to create' versus THE PHONEME 149 dworzec[dvozec] 'Station'. Thus, the Opposition between voiced and voiceless obstruents is neutralized before [f] and operative before [v] whereas the Opposition /f/ ~ /v/ is neutralized after voiceless obstruents. It is incorrect, however, to Interpret, e.g., [sf] äs a sequence of two voice-irrelevant archiphonemes because the complex [sf] is distinctively voiceless, and it is equally incorrect to Interpret [zv] äs a sequence of two distinctively voiced phonemes because there is only a single relevant feature which distinguishes the complex [zv] from its voiceless counterpart. This is an example of joint features. Li. vesti 'to lead' is pronounced [vcesti] in West Lithuania and [v'asti] in Hast Lithuania (Augustaitis 1964:38). 1t is possible that the two dialects have different phonemic Systems, the former containing an Opposition /a/ ~ /e/ and no palatalization correlation, and the latter possessing phonemic palatalization but lacking the vowel Opposition. It is equally possible, however, that both dialects exhibit variants of the same phonemic System, characterized by the joint relevance of consonant palatalization and vowel quality. In the latter case, the presence of either a palatalized consonant or a front vowel is sufficient to distinguish, e.g., tepti 'to smear' from täpti 'to become', geras 'good' from gäras 'steam', metas 'time' from mätas 'measure', retas 'rare' from rätas 'wheel', whereas the absence of both of these features is necessary to distinguish the latter word from the former. The essential characteristic of joint features is the fact that a single relevant feature is part of a number of successive phonemic units simultaneously. The existence of the phonemic units, the establishment of which should be based on the procedure outlined in the preceding sections of this chapter, is presupposed, and only the relative ordering of a specific relevant feature with respect to the relevant features which constitute the phonemic units is being questioned. If, however, the very existence of one of the units is involved, i.e., if there is no succession of previously ascertained sets of distinctively unordered features, the segmentation criterion discussed above should be applied. This is a simple consequence of the fact that a relevant feature cannot jointly characterize two units if one of the units does not, qua unit, exist. Thus, it cannot be inferred from the non-distinctiveness of Modern Greek [nd], [mb], [rjg] in relation to [d], [b], [g] äs well äs [nt], [mp], [nk] that the voicedness of the occlusive element or presence of a nasal segment is a joint feature, opposed to the joint feature constituted by voicelessness of the stop and absence of nasality. In fact, the feature which distinguishes, e.g., ankyres [arjgires] 'anchors' from akyres [akires] 'invalid (f.pl.)' is neither relatively unordered with respect to the features characterizing the velar stop, nor with respect to the features characterizing the preceding vowel. Consequently, it constitutes a separate unit on the level of constructs: /ankires/. The Situation is wholly analogous to the case of Sw. [d] i- /rd/ etc., discussed above. 150 FUND AMENTALS OF PHONEMIC MODELLING 8.10. CONCLUSION. A CHARACTERIZATION As a conclusion of the present chapter I want to present a characterization of the standpoint outlined here in terms of the criteria that have been put forward by C.J. Fillmore in bis important dissertation (1962). I shall not give a füll account of Fillmore's 'system for characterizing phonological theories' but limit myself to a characterization of my own views. As to the domain of the theory, I think that the aspect of the speech communication act that is under consideration consists of certain articulatory or acoustic events and their Interpretation by a native Speaker. I have not said anything about the style of the input, but I agree with Ebeling that it is the task of the investigator, not of the Informant, to ascertain the style of every single bit of material (cf. Ebeling 1960: 10f.). The elements of the domain are sound sequences identified by the informant äs belonging to his own language. Thus, the object of the description is a set of speech events interpreted by a single individual. The results of the analysis depend not only upon the Interpretation of the initial corpus but also upon the Interpretation of strings that may not have been uttered by a native Speaker of the language under consideration, cf. formulae (8.5)-(8.14). As to the power of the theory, the problem of functional equivalence has been discussed in section 8.3 of this book and will be taken up again in Chapter 9. Relevant features are qualities that enable the listener to recognize a linguistic form. The explanatory power of relevant features is the possibility of predicting the informant's ability to recognize linguistic forms previously unknown to him. On the level of constructs, every reference to phonetic similarity for 'explaining' the relevant features themselves is avoided. The number of phonetic features that are distinguished is arbitrarily large. The number of relevant features immediately depends on the relation R. A relevant feature is defined äs a set of possible combinations of phonetic features, cf. section 8.4. A phonemic unit is defined äs a set of relevant features and consequently does not contain any redundant features. (A stipulation must be made for joint features.) An arbitrary phonemic unit is either marked by the presence or by the absence of an arbitrary relevant feature, or unmarked by that feature (or marked jointly with another unit by the presence or absence of the feature). No binarism is imposed. Linearity on the level of constructs depends on the relative unorderedness of relevant features and cannot directly be derived from linearity on the level of observation. A single phonemic unit may correspond to a sequence of phones and a single physically homogeneous segment may be the realization of a number of successive phonemic units, cf. Sw. [d] l·· /rd/ and Gr. [d] l·- /nt/.21 No commitment to biuniqueness is made: a single phonetic description may have two different phonemic structures according to the substitutability of features under preservation of R-

21 Features characterizing strings of units without characterizing the individual units in Isolation will be discussed in Chapter 10 of this book. THB PHONEME 151 equivalence, cf. Po. [ruze] roze or τόζς. Two phonemic units are identical if they are composed of the same relevant features. However, no criterion for the identifiability of relevant features in different environments has been given in the present study. In an arbitrary phonemic structure the number of relevant features is minimized in formula (8.5), whereas the number of units is maximized in formula (8.13). No attempt is made to keep the number of units in the System to a minimum. Any kind of simplicity considerations have specifically been ignored. 9

OPTIONAL FEATURES AND HEAVY PHONEMES

9.1. PHONEMIC OVERLAPPING

In Chapter 8 I have assumed that the relation R, which reflects the informant's ability to recognize and identify linguistic forms belonging to bis own language, is an equivalence relation. In fact, there is a large number of examples in many languages contradicting this assumption. It is indeed quite surprising that the many examples which can be found in practical descriptions of various languages have hardly ever induced language theoreticians to draw the general conclusions that follow inevitably from the fact that phonemes, defined äs classes of Speech sounds, intersect. Bloch distinguished two kinds of phonemic overlapping in his well-known article on the subject (1941:93).

The intersection or overlapping of phonemes will be called partial if a given sound χ occurring under one sei of phonetic conditions is assigned to phoneme A, while the same χ under a different set of conditions is assigned to phoneme B; it will be called complete if successive occurrences of χ under the same conditions are assigned sometimes to A, sometimes to B.

Bloch adduces the following example of 'partial overlapping'.

In the speech of many Americans, the [t] phoneme includes äs one of its constituent sounds or allophones an alveolar flap (something like the r of London English very), which occurs intervocalically after a stressed vowel, and in this Position varies freely with the familiär voiced t and with the aspirated voiceless f, äs in butter, betting, kitty (contrast budded, bedding, kiddy). In the speech of some of these persons, the [r] phoneme includes äs one of its allophones the same alveolar flap, occurring after [Θ] in words like three, throw, less commonly after [ö] in dissyllabic pronunciation of words like withering, gathering. (The flap after [Θ] is often partly or wholly voiceless; but the voiced variety also occurs.) In this dialect of English, then, the [t] phoneme and the [r] phoneme appear to intersect in the alveolar flap; but the intersection is only partial and never leads to uncertainty or confusion: every such flap between vowels belongs to the [t] phoneme, every flap after a dental spirant belongs to the [r] phoneme. It is clear that such cases are not incompatible with .ft-equivalence. The alveolar flap is intervocalically in free Variation with [t] and consequently belongs to the same phonemic unit, äs distinct from, e.g., the r in berry. The same sound after [Θ] can be replaced by [r] without causing a change in the linguistic form and, consequently, belongs to the same phonemic unit äs [r]. OPTIONAL FEATURES AND HEAVY PHONEMES 153 The Situation changes, however, when we turn to 'complete overlapping'. I do not agree with Bloch that "examples are rare, and are always the result of an error in the analysis" (1941:94). On the contrary, examples are quite abundant because the phenomenon seems to be rather universal. I do agree with Bloch, however, that the tentative examples of 'complete overlapping' which he adduces in bis article may in fact be instances of other phenomena. Bloch's irrst example is the identification of the weak vowels in such phrases äs see them go, they could go, they will go, not so much, all of which are in his speech phonetically identical with the second vowel of sofa, with the stressed vowels in the phrases not them, they could, they will, not so, respectively (1941:95). In that case, "all the syllabic phonemes would intersect in their unstressed allophones". The example is not necessarily correct, however, since the identity of meaning does not always involve identity of form, cf. the case of Ru. skaf, skap 'cupboard' discussed above. Moreover, the phonemic System of a language cannot be determined on the basis of the alternating forms that a small number of high frequency words take under different circumstances. The evidence is therefore at least inconclusive, if not simply false. Bloch's second example is the vowel length Opposition in bomb ~ bahn, bother ~ father, sorry ~ starry. The long vowel also appears w.pa, star, card. But the utterance fraction pa'd in Pa'd go (if he could) is phonetically identical with pod in The pod grows (Bloch 1941:96). This is what Bloch regards äs "the most seductive example of apparent intersection". In fact, the simultaneous presence of several phenomena obscures the actual state of affairs. First of all, it is not clear whether the vowel in pa'd represents the same phonemic entity äs the vowel of the word pa pronounced in Isolation. Thus, Fr. pas [pa] is pronounced [paz] before vowels, and Fr. point is phonetically identical with poing except before vowels. The matter is even more obvious in Arabic: hardly anybody would claim that non-pausal accusatives ending in -an (e.g., baytan 'a house') and -ata (e.g., almaktabata 'the library') are phonemically identical with their pausal forms in -ä and -ah, respectively, so there is no reason to assume a priori that the vowels in Eng. pa and pa'd represent the same phonemic unit. Secondly, the Opposition that keeps bomb and balm apart may be neutralized before word-final [d]. This solution seems to be in accordance with Bloch's (though he does not, of course, speak of neutralization) since he identifies the vowel of pod with the one in balm. He does not state, however, whether the words cod and card are homonyms in his Speech. If they are, there is no problem. If they are not, there are, again, several possibilities: there may or may not be a phoneme /r/ in card, which may or may not be optional (and which may be realized either äs vowel length or äs retroflexion, or both), or there may exist a distinctive or optional vowel length Opposition between cod and card. It is seen from this example that the phonetic data which I regard äs conclusive for the phonemic Interpretation of a string are often absent from the description. Henceforth we shall be concerned only with cases of 'complete overlapping' where the presence of optionalities is less open to doubt than in Bloch's examples. 154 FUNDAMENTALS OF PHONEMIC MODELLING 9.2. PHONEMIC INTERCHANGE

In studying optionalities it is of primary importance to distinguish the phonemically determined from the phonemically unfounded. Phenomena that belong at one time to the formet category may in a subsequent period belong to the latter. Thus, the alternation *rqka ~ *rqce was automatic at one stage of the development of Slavic but the alternation r%ka ~ r%ce in contemporary Polish is certainly not phonemically determined. Consequently, the criterion of 'consistency of words' is valid only if certain kinds of alternation are eliminated. The problem was stated äs follows by Swadesh(1934a:118f.). The word sometimes has regulär variant forms; in this event, two forms may differ äs to one or more phonemes though they are in a sense the same word. Since variants sometimes confuse the phonemic problem, it may be well to point out some of the types of variants: I Free Variants (either variant is equally correct in any position) A Particular (applying to a single word or a limited number of isolated words), e.g., Nootka âpwînqis, âpw'inîs 'in the middle of the beach' B General (applying to all words of a given class), e.g., Chitimacha words of three or more syllables ending in -W vary with -V äs k'ahtW, k'ahti 'he bites'. II Conditional Variants (determined by position in the sentence) A Particular, e.g., Eng. a, an B General (a) Phonetically conditioned, e.g., Sanskrit punar, punah 'back, again' (b) Structurally conditioned, e.g., Tunica disyllabic words of the form CV'V have that form only when spoken in Isolation; in context they become CV äs: rf>i 'house', context form n. Conditional variants may be regulär, äs the examples given, or may be optional, äs the Eng. sandhi type of äs you [az yu, az(y)u], both of which are sometimes interchangeably employed by the same Speakers. It is evident that an alternation which is not general cannot be phonemically automatic. On the other hand, a general alternation is not necessarily determined by the phonemic System of the language. In this chapter we shall be concerned only with general free variants that are phonetically conditioned (which would be type Ι Β α in terms of the classification above). The existence of such variants is, in fact, signalized by Swadesh (1934a:120, cf. also 1934b:360ff.). It sometimes happens that one of a pair of free variants coincides with some other phoneme. Thus, Chitimacha \v', y\ m', «' may be pronounced with or without a glottal stricture, coinciding in the latter instance with the phonemes w, y, m, n. Another instance of this phenomenon, which may be called phonemic interchange, is the interchange of initial d with d in words like the and they in Edgecombe County (near Rocky Mount), North Carolina. Optional employment or omission of a phoneme occurs, for example, in the case of postvocalic r (e.g. barn) in certain sections of New England. Thus, Chitimacha w', y', m\ «' may be replaced by w, y, m, n respectively without changing the .R-class to which the string belongs whereas the opposite Substitution is not always possible. The checked and unchecked phonemes intersect because the ränge of realization possibilities (Martinet's champ de äispersion) of the latter is wholly contained in that of the former. OPTIONAL FEATURES AND HEAVY PHONEMES 155 In bis 'System of descriptive phonology' C.F. Hockett defines the phoneme äs a class of phones which, among other things, does not intersect with another phoneme (1942:9). In the same article, however, he gives a beautiful example of phonemic interchange (1942:12). There is sometimes, in some definable position in utterances, a free alternation between phones that must be assigned to different phonemes. In some dialects of Spanish, for instance, there is free alternation between /d/ and /r/ before a stressed vowel, äs inpedir 'ask' andparar 'prepare'. This is different, of course, from free Variation between phones of different homeophones but the same allophone. t1] Free alternation is a matter of phonemics because the conditions for the alternation can be given in purely phonological terms. In some other dialects of Spanish such words äs pedir have either /d/ or /r/, but such äs parar have always /r/. This is not free alternation, since one cannot predict on phonological grounds alone where the alternation will occur and where it will not; for this reason it is not part of phonemics, but rather of morphophonemics (a subdivision of grammar). In our terminology, the Opposition between /d/ and /r/ is neutralized before a stressed vowel in the dialects referred to in the first paragraph quoted here. The dialects referred to in the second paragraph show phonemic interchange: /d/ can be replaced by IT/ but the converse does not hold. If ANY /d/ before a stressed vowel can be replaced by /r/, the phenomenon certainly is phonemic and has nothing to do with grammar. In bis article about the phonemic System of Italian, Malmberg concludes bis discussion of the vowel system äs follows (1942a:39). II est vrai qu'on peut distinguer pesca de pesca a l'aide de la qualite de 3a voyelle accentuee de la meme maniere qu'on peut distinguer vile de vele, mais l'existence de la possibilite d'une homonymie complete entre les deux premiers mots (pesca dans les deux cas) affaiblit enormement la force de l'opposition. On peut dire que les oppositions / : e et e : e sont toutes deux des oppositions phonologiques, mais de stabilite differente (de mSme « : o d'un cote et o : a de l'autre). If the description in this paragraph is correct, the Situation is analogous to the one labelled 'phonemic interchange' by Swadesh. However, it is not clear whether Malmberg's description refers to the Speech of a single Informant.2 If it does not, it is quite possible that there are simply two different vowel Systems, characterized by a different number of phonemes. In the same issue of Acta linguistica Malmberg writes about vowel length in French(1942b:50): Der Unterschied zwischen tete und tette besteht nicht darin, dass das erste Wort einen langen und das zweite einen kurzen Vokal hat, sondern darin, dass der Sprechende eine Möglichkeit besitzt, das normalerweise kurze ε in tete, wenn es der Zusammenhang aus dem einen oder ändern Anlass fordert, zu verlängern, und dies ist nicht der Fall bei tette. [...] Die Opposition langer : kurzer Vokal ist also eine Möglichkeit, die die Sprache in besonderen Fällen zu Hilfe nehmen kann, die aber normalerweise nicht ausgenutzt wird.

1 "A homeophone is a class of phones such that all members of the class are characterized by all the features that characterize any one member" (Hockett 1942:9). 2 There is no doubt about this in the case of Chitimacha sonorants, cf. Swadesh 1934b:361f. 156 FUND AMENTALS OF PHONEMIC MODELLING Here again, long [ε] can always be replaced by short [ε] but the converse does not hold. Now we turn to English. Jakobson and Halle state (1956:6): For many American English Speakers /t/ and /d/ are ordinarily not distinguished between a stressed and unstressed vowel but can be produced distinctively when there is danger of a confusing homonym- ity: "Is it Mr. Bitter /bite/ or Bidder /bids/?" may be asked with a slightly divergent implementation of the two phonemes. This means that in one type of American English the code distinguishes the inter-vocalic /t/ and /d/, while in another dialectal type this distinction is totally lost. Here two different phenomena are confused. The first sentence of this paragraph refers to a single Speaker who produces a distinction which he ordinarily does not make: this is phonemic interchange. The second, however, refers to the co-existence of different phonemic Systems, different dialects, characterized by the presence or absence of an Opposition. It is evident that the existence of an Opposition in one dialect cannot, in a purely synchronic description, account for the fact that a Speaker of another dialect has an optional distinction at bis disposal.3 The case of Am.Eng. intervocalic t, d has not gone unnoticed by other authors, cf. the observations by Peterson and Harary discussed in section 4.6 of this book. Fillmore writes (1962:63): Of any two utterances appearing äs the yield of the same representation, one must 'semantically include' the other. For example, the meanings possible to [Isefa] include those possible to [lasL'e] äs well äs those belonging to [laeds], while no relation of this sort obtains between the latter two. Under this relaxed semantic power requirement, [Iser-s] is permitted äs the phonetic Output of either /Isetgr/ or /laedar/.

This phenomenon, which Fillmore calls 'multiple free Variation', "occurs where one phonetic segment is in free Variation with two or more other segments and these latter are in contrast" (1962:63). It is, in fact, a slightly more complicated case of phonemic interchange than the French, Spanish and Italian examples cited above. Here both [t] and [d] can be replaced by [r-] but the converse does not hold. Chomsky regards Am.Eng. writer [rayDir], rider [ra-yDir] äs an important violation of the linearity condition (1964:82f.; here I stick to bis transcription). If the transcription reflects the only correct pronunciation one cannot but conclude that there is a vowel length Opposition between the words under examination.4 It is not impossible, however, that the case is identical to the one discussed in the preceding paragraph. There is a third possibility, viz. that /d/ is realized either äs [d] or äs vowel length (or äs a combination of the two). In that case, the feature which distinguishes rider from writer is a joint feature (which, again, may or may not be optional). The correct solution can only be determined by means of an appropriate experiment. Bloch, in spite of the fact that he explicitly rejected the possibility of 'complete

3 Historically, the existence of optionalities may explain the gradual character of sound changes in a number of instances, cf. below. 4 Cf. in this connection the discussion in Joos 1942. OPTIONAL FEATURES AND HEAVY PHONEMES 157 overlapping' (see above), found the following instances of phonemic interchange in Japanese (1950:109).5 In three pairs of phones — [g, rj], [g', r)'], [dz, z] — themembersareinpartiallyfree Variation witheach other, but must nevertheless be kept apart. Nearly all phrases containing [n], [rj'], and [z] are paralleled, especially in slow or careful speech, by otherwise identical synonymous phrases containing respectively [g], [g'], and [dz] instead. But there are many phrases containing the latter three phones that are not paralleled by phrases containing the former; and these phrases are not marked by any phonetic or phonemic peculiarities. Both phones occur in [arjaru, agaru] rises, [marjo, mago] grand- child, [mas-surju, mas-sugu] straight; [karj'i, kag'i] key, [nyuurj'yuu, nyuug'yuu] milchcow, [nlrj'-rj'yoo, nlrj'-g'yoo] doll; [mizikäi, rnidzikäi] short, [nizuu, nidzuu] twenty, [sä'n-zuu, sä'n-dzuu] thirty. But there is no such alternation in [sonogo] öfter that, [donogurai] about how much?, [ärugak-koo] a certain school; [konog'yuunyuu] Ms (cow's) milk, [nihön-nog'ikai] the Japanese Diet, [ärug'irj-koo] a certain bank; [k'idzi] newspaper article, [ook'inadzislii-]agreatearthquake, [utsinodzotsuu]o«r7na/i/ servant. Since the alternations between [g, g', dz] and [n, rj', z] respectively are limited to certain phrases only, and since their common environments do not form a phonetically or phonemically definable set, the three pairs of phones must be treated separately in the phonemic analysis.

This Statement is clear enough if the word 'nearly' in the second sentence of the quotation is not to be taken seriously. Bloch's 'partially free Variation' refers to the same phenomenon äs Swadesh's 'phonemic interchange' and Malmberg's Opposi- tions phonologiques de stabilite differente'.

9.3. OPTIONAL FEATURES AND HEAVY PHONEMES

The existence of such cases äs Po. chore [xore] 'sick (nom.pl., no male persons)', biorg [bjore, bjore] Ί take', which is, again, what Swadesh called 'phonemic interchange', led Ebeling to the distinction between 'basic distinctive features' and Optional distinctive features', and also between 'basic phonemes' and 'heavy phonemes' (1967:134ff.). The fact that *[xore] is rejected äs a possible realization of chore points to the distinctiveness of nasality. But the suppression of nasality in such forms äs [bjore] never leads to a sound sequence which is rejected äs a possible realization of the initial form. Such features are called Optional', and a phoneme that contains an optional feature is called a 'heavy phoneme'. When a heavy phoneme loses its optional feature the linguistic identity of the form to which it belongs is not affected (like in the case of free Variation), but the converse replacement changes in a number of instances the linguistic identity of the form (like in the case of ordinary distinctiveness). In the above Polish example nasality is optional and /e/ is a heavy phoneme. Other examples given by Ebeling are: Du. fee [fe] 'fairy', vee [fe, ve] 'cattle', where voicedness is optional and /v/ is a heavy phoneme; Fr. peche [pese] 'sin', pecher [pese, pese] 'to fish', where the relative degree of openness is optional and /ε/ is a heavy phoneme; Ru. domovoj [dsmavoj, dccmavoi] 'brownie', dymovoj [damavoi, dimavoi] 'smoke (adj.)', koza [kozs, koza] 'skin (nom.sg.)', kozi [kozs, kozi] 'skin

6 I write [n] for Bloch's [n] etc. (palatalized consonants). 158 FUNDAMENTALS OF PHONEMIC MODELLING (gen.sg.)', koze [koza, kozi, koze] 'skin (dat.sg.)', where /a, e, i/ are heavy archiphonemes. The examples of phonemic interchange which have been given in the preceding section can easily be restated in Ebeling's terminology: Chitimacha /w', y', m', n'/ are heavy phonemes with glottalization äs an optional feature; Sp. dialectal intervocalic /d/ is a heavy phoneme with the absence of flap articulation äs an optional feature; It. /ε, oj may be heavy phonemes, analogous to the French and Russian instances cited above; length in Fr. tete is an optional feature; Am.Eng. intervocalic /t, d/ may be heavy phonemes; Jap. /η, ζ/ are heavy phonemes with nasality and continuousness äs optional features, respectively. Moreover, several problematic points that cannot be clarified in a strictly discrete phonemic theory can now satisfactorily be accounted for. I shall give some examples here without, of course, any pretension to exhaustiveness. Firstly, there is the case of the Slovak diphthongs ia, ie, iu. Though according to Czambel these diphthongs are not to be confused with the groups ja, je, ju; Häla stated that both acoustically and articulatorily the two kinds of groups are identical and must be identified äs clusters /ja, je, ju/. Jakobson rernarks that "to my ear, the relative length of each of the two diphthongal components varies considerably and can be freely interchanged while in the sequences ja, je, ju the quantitative relation of the first member to the second is that of a consonant to a short vowel" and that "one can frequently hear a qualitative difference between the first component of the diphthong and the consonant j, the former being acoustically closer to the vowel i than isj" and concludes (1962:222):

It is, however, very probable that an optional realization of the ascending diphthongs is identical with the sequence 'j + short vowel'. Nonetheless, such groups äs ia, ie remain integral diphthongs from the phonemic point of view. So it is quite possible that everybody was right in this discussion, viz. if /i/ is a heavy phoneme before /a, e, u/.6 L.I. Zirkov remarked in bis grammatical sketch of the Avar language (1936: ISO):7

In one and the same book or article, even side by side in one line, different vowels were written in one and the same word; e.g.: peq and piq 'fruit', habize and habizi 'to make', bugo and bugu 'is' were quite often found on one and the same page, sometimes in successive lines. [...] There is, however, a number of words that are defmitely differentiated äs to their meaning precisely by the presence in the root of one or the other vowel from the pairs mentioned; this is how the words beλ'ize 'to sow, plough' and btt'ize 'to divide', bocize 'to measure' and bucize 'to knead', and some others are opposed to each other.

6 It is striking to note that Pauliny mentions the problem neither in bis book about Slovak phonology (1961) nor in bis recent article about /i/ and /j/ (1967). He does give some interesting instances of optional neutralization, however: prijmes [prlmes], objimat' [oblmat'],p/-fe'(pri-ist') [prlst'], kyjftd] (1961:77f. and 1967:1500f.). 7 I have replaced 2irkov's spelling of Avar with the transcription in Ebeling 1966:62. OPTIONAL FEATURES AND HEAVY PHONEMES 159 The phenomenon is quite understandable if the distinction between /i, u/ and /e, o/ is optional. Avar diphthongs also offer an interesting example of optional features (Ebeling 1966:61): In Xunzax, words like doj 'she' (-j is the fern, ending) admil only one pronunciation: [doj]. For the word t'ohoje 'to the flower' (-je is the dative ending) the most frequent pronunciation is [t'ohoj]. The optimal System, however, offers a possibility to distinguish the final parts of the two words: one can say [t'ohoii], or even, in a very bookish style, [t'ohoj[e]. [...] The word for 'dog' [hoj or hwe] is, äs to its final part, potentially distinguished both from /oj/ and from /oi/; it shows a whole gamut of pronunciations [hue, hge, hog, hoj]. It can best be phonemicized äs hwe. Its pronunciation never coincides with the Xunzax form /doe/ of literary dobe 'thither'. The final vowel of t'ohoje is optional. The other example is more intricate because it follows from the last sentence of the Quotation that the feature which is optional is a joint feature. The final part of hwe is also distinct from its narrow counterpart in such words äs kwi [kui, km] 'ram' and kwine [kuine, kuine] 'to eat', which is, again, potentially distinguished from both rakuje [rakui, rakuii] 'manure (dat.)' and xaduj [xaduj] 'after (fern.)'. This example clearly shows that the relation R is certainly not transitive. It is reasonable to assume that optionalities sometimes play an important part in a Situation of linguistic change. On the one hand, a distinction which is disappearing may remain äs an optional distinction in the language for some time. On the other hand, the same may hold true for a new distinction appearing in the language. The first possibility is hinted at by JJ. Gumperz in his article about Vernacular Hin- dustani dialect differences. He concludes his article äs follows (1958:224). A third matter of interest is the decrease in the distinctiveness of a phonetic difference between two coutrasting features äs one approaches an isogloss. In villages R and K, for example, the difference between the allophones of /n/ and /n/ is clearly audible in all environments. Data from another village near Merut, which is probably very close to the isogloss, shows the allophones of /n/ to be much less retroflex and retracted than in R, so that the contrast is distinctly audible only in slow and careful speech. (Similar observations were made by William McCormack and H.A. Gleason for the contrast between the vowels /a/ and /A/ in the Dharwar dialect of Kannada.) If "the contrast is distinctly audible only in slow and careful speech", then retroflexion is optional and /n/ is a heavy phoneme. The possibility of partial coalescence and subsequent excision is implicitly referred to by Martinet in his recent discussion of the origin and development of French nasal vowels (1965). According to Martinet, the rise of nasal vowels cannot be separated from the loss of word-final [a]. Medieval French had paysan [an, an] /an/, paysanne [ans, ans] /ans/ whereas Modern French has paysan [ä] /ä/, paysanne [an] /an/. Thus, the nasalization of [a] before [n] was a redundant feature in the middle ages, (Martinet 1965:120) Mais lorsque le -e final tend ä s'amu'ir, paysanne s'articule d'une facon qui se rapproche de plus en plus de [peizän], c'est-ä-dire de ce qui etait une des realisations possibles de paysan; le maintien de la distinction roclame donc que relimination de Felement consonantique apres voyelle nasale dans 160 FUND AMENTALS OF PHONEMIC MODELLING paysan aille de pair avec l'elimination de -e. Comme toutefois une prononciation comme [peizän] pourrait rester, pendant longtemps, ambigue, les usagers vont tendre ä mieux distinguer le feminin [peizän] du masculin [peizä] en y eliminant progressivement la nasalite de la voyelle qui n'etait que l'anticipation de celle de la consonne: [peizän] pouvait, dans certaines circonstances, §tre ambigu; [peizän] ne Fest plus; il ne peut s'agir que du feminin. But how is [peizän] to be phonemicized in the case where it is, indeed, ambiguous ? It follows that the absence of nasality in the second vocalic segment of [peizan] is an optional feature and that /a/ is a heavy phoneme before /n/. The example above shows that the answer to the question ONE OR TWO PHONEMES? depends in a rather complicated way on possible optionalities. The words [peizän], [peizan] do not differ in the features that constitute their linguistic forms but only in the ORDERING of these features, viz. in the part of the form which is characterized by the presence of nasality. If there is no [peizan], then [peizän] l- /peizan/, but äs soon äs the former word appears in the language äs a distinct form the latter must be 'rephonemicized' äs /peizä/.8 In the case we are dealing with it is assumed that the sequence /an/ is optionally different from the (basic) phoneme /ä/. But the very existence of the latter AS A PHONEME depends on its being distinct from the sequence /an/. The case is analogous to Po. /c/ and /ts/: "C'est le langage intentionnel du polo- nais qui est caracterise par la distinction phonotique entre des mots comme czy et trzy" (Jacobsson 1966:86). Here the cluster /ts/ is optionally different from the phoneme /c/, the existence of which AS A PHONEME depends on its being distinct from the cluster. Another possible instance is presented by Martinet in his discussion of Fr./n/(l 947:47): Tous les Franc.ais paraissent roaliser le n mouille de agneau de fason sensiblement identique: il s'agit d'une occlusive nasale palatale suivie d'un leger yod. Certains parmi eux, surtout dans la partie Orientale du pays semble-t-il, articulent de la m§me facon le groupe ni de panier qui, dans la prononciation traditionnelle se realise au moyen d'un n ordinaire suivi d'un yod bien net. L'essentiel de la difference entre les deux usages est evidemment que les uns ont perdu la possibilite de distinguer entre l'agnelle et la nielle par exemple, tandis que les autres Tont conservoe. This case is more complicated indeed because several problems are interwoven. Firstly, the Opposition /i/ ~ /j/, which is operative in pays ~ paye, may or may not be neutralized in panier. Secondly, [n] may have to be interpreted either äs a single phoneme /n/ or biphonemically äs a sequence /nj/ (where j Stands for either the phoneme /j/ or the archiphoneme of /i/ and /j/, which depends on the first question). Thirdly, it is possible that some of the features involved are joint features. Fourthly, the Solutions to all of these problems may involve optionalities. It is, e.g., possible that we have peigner [pene, penje] and panier [panje, panje], in which case the absence of 0] in peigner and the absence of palatalization in the [n] of panier are optional. We have, then, an Opposition /ne/ ~ /nje/, characterized by the presence versus absence of a single basic relevant feature (palatalization). In the sequence /nj/ the

8 Cf. the 'rephoaemicization' [c] t- /tj/ of SCr. cerka when the intitial cluster of tjerafi coalesces with [c], äs discussed in section 8.6. OPTIONAL FEATURES AND HEAVY PHONEMES 161 relative ordering of the presence of palatalization with respect to the presence of nasalization is optional in one out of two ways: the palatali/ed and nasalized Segments are optionally either strictly unordered or strictly ordered with respect to each other. This example clearly shows that arbitrary decisions between, e.g., l'agnelle /l anel/ ~ la nielle /la njel/ and l'agnelle /l anjel/ ~ la nielle /la niel/ can easily lead to Solutions that are contrary to the principle of distinctiveness. There is no room for simplicity considerations here.

9.4. THE PROOF

The existence of optional features has been advocated in the preceding sections äs a possible explanation of phonemic interchange. In fact, I think that optionalities have already passed the hypothetical stage and that we can say that their existence has been PROVED. The proof has been supplied by Kloster Jensen in his excellent investigation of tönernes in West Norwegian dialects (1961), which undoubtedly is one of the most important contributions to phonemics since Trubetzkoy's Grundzüge. Jensen tested 612 subjects from the area under investigation for identification of paired test words (minimal pairs) äs spoken by themselves and subsequently listened to from a sound tape. Each test tape contained 58 items of test words from three minimal pairs in randomized order and was played back to the subject four times, so that in all 232 answers were given and taken down. The total number of observations amounts to over 140,000. Jensen's report includes an ample discussion of the limitations and reservations äs to the applicability of the method, the difficulties involved in the procedure of recording the test words, and the validity of the recognition test, äs well äs an account of the problems which show up in connection with various decisions that must be taken in the course of the investigation. The reliability of the method is checked by comparing the results obtained for groups of subjects constituted according to a variety of criteria. The recognition test rests on the supposition that a subject in whose dialect there is no tonemic contrast will normally make a 50 pct. recognition score whereas a subject whose dialect has tonemic contrast will make a score close to 100 pct. It follows from the conditions of the experiment that 99 pct. of the non-tonemic subjects will have a score between 35 and 65 pct. and that the probability of a tonemic subject's score being less than 95 pct. is negligible. Consequently, the assumption that tonemic contrast is either distinctive or not distinctive entails the almost complete absence of scores below 35 pct. and between 65 and 95 pct. In fact, the lowest score of all was 36 pct. but no less than 108 subjects (out of 612) scored from 65 through 85 pct. This most important result can only be accounted for by assuming that the tonemic oppostion is optional in a considerable part of the area. I cannot refrain here from quoting Jensen's comment on subject no. 260 (age 23, total score 81 pct). 162 FUND AMENTALS OF PHONEMIC MODELLING This subject may also be considered a 'semi-tonemic' Speaker. The rural district of Os is too near to Bergen [which is tonemic] to have tonemicity features much different from those of Bergen. The subject considers his own dialect äs a mixture Os-Bergen. He had not been told about tönernes at school. The subject thinks it possible to 'make the difference' in pronunciation. When asked why he could not then make better scores (79 % — 82 % — 83 %), he had no answer. The subject's mother is from Fjell, a rural district which was found to be non-tonemic. The father is a native of the locality represented. The informant's reaction was quite understandable because an optional difference is a difference which one can but ordinarily does not make. It would be interesting to see whether recognition failures of 'semi-tonemic' Speakers bear upon both members of a tonic pair or only upon a single member. (In the latter case, one of the tönernes is always recognized correctly whereas the other is ambiguous.) This kind of information cannot be retrieved from Jensen's publication, however.

9.5. OPTIONAL PHONEMES

A phonemic unit has been defined in formula (8.14) äs a set of relatively unordered relevant features. The optionality of phonemes can therefore arise from two origins: either the presence of the relevant features constituting the phoneme is optional, or the relative orderedness of the features that are present in the speech flow is optional. Some examples of the former kind of optional units have already been given, viz. the cases of postvocalic r (e.g., barri) in certain sections of New England (in the quotation above from Swadesh 1934a) and, possibly, word-final 3 in Fr. paysanne at the time when it was disappearing. It should be remarked that the final vowel in Avar t'ohoje [fohoi, fohoii] and rakuje [rakui, rakuji] is not an optional but a heavy phoneme because the ]i]-glide in the latter variant is automatic: the final parts of these words are to be phonemicized äs /oi/, /ui/ with a heavy /i/, the corresponding basic phoneme of which is /j/. However, the final ß] in Avar hej [he, hei] 'that (fern.), she' is an optional phoneme. The final vowel in the optimal realization of Avar λ-eje [λ-e, A-ei, A-eji] 'water (dat.)' is an optional heavy phoneme. An example of optional phonemes in French is the / in such words äs mülion and filiere, which can be pronounced with either [Ij] or just [j] (cf. Martinet 1964:354). The case of Fr. /n/ ~ /nj/ has been discussed above. A possible example in English is offered by such pairs äs wines [nz], winds [nz, ndz] in dialects where these words are not necessarily homonyms. If both pronunciations are acceptable äs realizations of either word, the Opposition is neutralized and the [d]-element has no distinctive value at all.9 The second kind of optional phonemes can be illustrated by Du. zingt [zirjt] 'sings', zinkt [zirjt, ztrjkt] 'sinks'. The k in the latter word is an optional phoneme 9 A definite example of non-distinctive sounds is [y] in Sp. agua [a^a] 'water', where the obstruent element has no distinctive value indeed, cf. Alarcos Llorach 1965:164 and Contreras and Saporta 1960:13. OPTIONAL FEATURES AND HEAVY PHONEMES 163 deriving its existence not from the presence of an optional set of features (because the features characterizing [zirjt] and [zinkt] are identical) but from an optional difference in the relative ordering of the features. In the form [zirjt] the presence of nasality and velar articulation are unordered with respect to each other because the segment that is characterized by velar articulation must be nasal äs well.10 In the form [zinkt], however, the presence of nasality and velar articulation are NOT relatively unordered and, consequently, do not belong to the same phonemic unit; here [η] is the realization of an archiphoneme in the sense that its place of articulation is determined by the subsequent phonemic unit (which is the optional one). An analogous case is presented by Du. Het stamt uit de oudheid [stamt] 'It dates from antiquity', Hij stampf de sneeuw van zijn schoenen [stamt, stampt] 'He kicks the snow from his boots'. An interesting instance of optionalities is possibly found in Tajik. In this language, the u in words like [xub] 'good' (Persian [xüb]) is identical to the one in words like [sud] 'he became' (Persian [sod]). In unstressed syllables, however, the length of the vowel in words of the second type may vary between the length of an unstressed u in words of the first type and zero: [xubi] 'good (subst.)', but [sudi, sdi] 'you (sg.) became'.11 Here the absence of a segment [u] in words of the latter type is optional (cf. the optional absence of [j] in Fr. peigner discussed above). A similar case is presented by Du. melk [melk, melak] 'milk' but billijk [bilak] 'fair, reasonable', not *[bilk].12 Optional phonemes must, of course, be distinguished from positionally conditioned phonemes such äs z and t in Fr. pas [ρα, ραζ] and point [pw£, pw£t], respectively (according to the traditional description). In the latter case the diiferent forms of the word do not occur in the same position, whereas they do in the case of optional phonemes. As an example of positionally conditioned phonemes Chao cites Southern English sore, which takes the form [s5] before throat and [sör] before eyes (1934:45). If the example is correct, the case of Eng. saw, sore is analogous to Fr. poing, point, not to pairs like cruel [krüel], cruelle [krÜ£l(3)] with an optional word-final 9 in some variants of French. It is conceivable, however, that in some dialects of English sore has before consonants an optional r by which the word can be distinguished from saw. The same remark can be made in connection with Eng. mica [maiks] and poker [pouko(r)] (Chao 1934:50).

9.6. JUNCTURES

One kind of optional features deserves special attention, viz. boundary Signals or 'junctures'. A juncture is a feature which occurs in the immediate environment of a

10 The converse does not hold because [ztrjt] and [zinftt] are phonemically identical to [zirjt]. 11 Cf. Sokolova 1949, cited in Panov 1967:195fn. 12 I am indebted to Mr. H. Steinhauer for this example. 164 FUNDAMENTALS OF PHONEMIC MODELLING morpheme boundary and which may distinguish a sequence of morphemes though it is not a distinctive feature of the morphemes themselves, cf. e.g. Du. een Noor [anor, an-or] 'a Norwegian', eenoor [anor, an?or] 'an ear'. Thus, a juncture is suprasegmental in the sense that it characterizes a segment containing more than a single morphemic unit, but segmental in the sense that its realization does not necessarily involve a segment containing more than a single phonemic unit. Junctures are, from this point of view, the very opposite of joint features: the latter characterize a segment not necessarily containing more than a single morphemic unit, but their realization involves a segment containing more than a single phonemic unit. Though it is theoretically conceivable that some junctures are not optional, I am not familiär with any reliable examples. Like in the case of optionalities in phonemic units, the optional character of junctures may explain the disputability of their distinctiveness. As an example I shall discuss the case of Ru. pogoreli [psgar'el'i] 'they burned up', po göre U [psgar'fil'i] 'along the hill?', which was introduced into linguistic literature by Jakobson.13 The existence of a difference between these two strings was not confirmed by Shapiro's (noninstrumental) experiments (1968:14): "The speech of the informants questioned showed no Variation in the realization of {e} before enclitics, close [e] being the only possibility". On the contrary, the influence of palatalized consonants upon a preceding vowel is, according to Durnovo and Usakov, not only operative within a morpheme and across morpheme boundaries, but optionally even across word boundaries: in their transcription of the phrase dve devocki 'two girls' they wrote an open vowel for the e in dve but remarked that this vowel could optionally be closed (1926:347, cf. Panov 1967:306). Shapiro's conclusion that "the original rule [viz. word-final e becomes narrowed before an enclitic with an initial soft consonant] is really an optional rather than an obligatory one not only before enclitics but before a word boundary within a phonemic phrase containing no enclitic äs well" (1968:14) is quite in accordance with the hypothesis that junctures are optional.

13 Cf. Jakobson and Halle 1956:18, Halle 1959:72. 10

A NOTE ON CONFIGURATIONAL FEATURES

10.1. INHERENT AND CONFIGURATIONAL FEATURES

One kind of joint features is especially interesting, viz. relevant features which are realized äs a relation between phonetic features that belong to difFerent phonemic units. The most important example is stress. It is certainly not true that "We can consider accent to be a distinctive feature similar to such distinctive features äs voicing, nasality, etc. Just äs we have voiced and unvoiced consonants, so also we have accented and unaccented vowels" (Chomsky etc. 1956:79). This view is incorrect because such features äs voicing and nasality are either present or absent in a segment whereas a vowel can only be stressed or unstressed in relation to another vowel in the same Speech flow. The issue was stated correctly by Jakobson and Halle (1956: 25f.): Any prosodic feature is based primarily on the contrast between two variables within one and the same time sequence [...] The recognition and definition of an inherent feature is based only on the choice between two alternatives admissible in the same position within a sequence. Thus, prosodic features are in CONTRAST whereas inherent features are in OPPOSITION, to use Martinet's terminology (1960:27). However, Jakobson and Halle do not remain faithful to the Statements above and use the term 'prosodic' in its traditional sense, to cover all kinds of tone, force, and quantity features (1956:22). Consequently, 'prosodic' and 'inherent' are no longer mutually exclusive concepts, äs has correctly been pointed out by Jensen (1961:73f.). Tones in tone languages are an example of features that are both inherent and prosodic (cf., e.g., Künstler 1968:180f.). The essential diiference between stress and inherent features was first formulated by Kuznecov (1948). His argument is summarized by Panov äs follows (1961:7). The sounds [u] (stressed) and [ü] (unstressed) are not different phonemes in Russian because they are not found in one and the same position. The stress of the first [u] in a disyllabic word conditions the absence of stress in the other vowel, and conversely: cf. muku ~ muku; there is no Opposition muku ~ muku or muku ~ mükü. [...] Consequently, stress is phonemically present in a sequence of phonemes only. It is therefore not the absolute prominence of the stressed vowel which is relevant from the functional point of view, but only its relative prominence in comparison with another vowel that is present in the same Speech flow. 166 FUND AMENTALS OF PHONEMIC MODELLINO Ebeling has tried to clarify the issue by coining the term 'configurational' äs a designation of features that are relevant but not inherent to a phonemic unit (1968:135): Among the multifarious attributes of linguistic units a sharp distinction must be made between those which characterize a unit, within the larger whole to which it belongs, in comparison with the other constituents of the same whole, and those which are established on the basis of a comparison with another element not necessarily belonging to the same utterance. I propose to speak of configurational and inherent features, respectively. For configurational features the compared object is in praesentia, for inherent features in absentia. Consequently, a phonemic unit can only be characterized by a configurational feature (e.g., stress) if there is at least one other phonemic unit in the same sequence such that the relation between the two units embodies the configurational feature.

10.2. RELATIONS BETWEEN FEATURES

It should be clear that a feature is not inherent or configurational per se but only in relation to the frame in which it is distinctive. As Ebeling has pointed out (1968: 136), The relationship between configurational and inherent features is such that a configurational feature of a lower-level unit constitutes an inherent feature of the unit of the next higher level. For example, in Ru. muka 'flour' the vowel /a/ carries the configurational feature consisting in the fact that it is prominent äs compared with the /u/ present in the same frame. For the word muka the accent is an inherent feature: it distinguishes the word in absentia from muka 'suffering'. Features that are configurational within the frame are inherent in relation to the frame itself. Another example of configurational features are Intonation contours, which are inherent features of the part of the Speech flow characterized by them, realized äs a sequence of contrasting pitches that mark Segments of the frame in relation to each other.1 The position of a phonemic unit in the Speech flow can also be viewed äs a configurational feature: äs in the case of stressed vowels, it is not by itself distinctive but determines the conditions under which phonemic invariants can occur.2 It seems that an intuitive identification of phonemic units in different positions is generally based on configurational rather than inherent features.3 The issue requires further investigation before any definite conclusions about the relation between inherent and configurational features can be reached.

1 Cf. the recent investigation of Gterman sentence Intonation in Isacenko and Schädlich 1966. 2 Cf. Gvozdev 1957:62 and Panov 1961:16. 3 Cf. Schatz 1954:49. It turned out in bis experiments that the k from [ki] was perceived äs t before [a] and äs p before [u]. LIST OF REFERENCES

ABBREVIATIONS

AL Acta Linguistica (Hafniensia) (Copenhagen). AnthrL Anthropological Linguistics (Bloomington, Indiana). BOMP Bjulleten' ob'edinenija po problemam masinnogo perevoda (Moskva). BPTJ Biuletyn polskiego towarzystwa jezykoznawczego (Wroclaw-Krakow). CL TA Cahiers de linguistique theorique et appliquee (Bucarest). CTiL Current Trends in Linguistics (The Hague). FRJ For Roman Jakobson (The Hague, 1956). UAL International Journal of American Linguistics (Baltimore). Izv AN fzvestija Akademii Nauk JC Jazykovedny casopis (Bratislava). JL Journal of Linguistics (London). L. Leningrad Lcs Linguistics (The Hague). Lg Language (Journal of the Linguistic Society of America) (Baltimore). Lingua Lingua (Amsterdam). Lque La Linguistique (Paris). M. Moscow MPPL Masinnyj perevod i prikladnaja lingvistika (Moskva). ÖL Ja Oldelenie literatury ijazyka P BML The Prague Bulletin of Mathematical Linguistics PFil Prace filologiczne (Warszawa). PKib Problemy kibernetiki (Moskva). PSL Problemy strukturnoj lingvistiki (Moskva). PSML Prague Studies in Mathematical Linguistics RJN$ Russkij jazyk v nacional'noj skole (Moskva). RMPA Revue (roumaine) de mathematiques pures et appliquees (Bucarest). SaS Slovo a slovesnost (Praha). SCauc Studia Caucasica (The Hague). SCL Studii ξι cercetäri lingvistice (Bucuresti). SCM Studii fi cercetäri matematice (Bucuresti). ScSl Scando-Slavica (Copenhagen). SGen Studium Generale (Berlin, Göttingen, Heidelberg). SiL Studies in Linguistics (Buifalo, New York). Slavia Slavia (Praha). SLing Studia Linguistica (Lund). SLog Studia Logica (Warszawa). SMiL Statistical Methods in Linguistics (Stockholm). TCLC Travaux du Cercle Linguistique de Copenhague TCLP Travaux du Cercle Linguistique de Prague THRJ To Honor Roman Jakobson (The Hague, 1967). TSTL Tijdschrift voor Slavische taal- en letterkunde (The Hague). 168 REFERENCES Uc zap Ucenye zapiski VF Voprosy filosofii (Moskva). V Ja Voprosy jazykoznanija (Moskva). Word Word (Journal ofthe Linguistic Circle of New York). ZfPh Zeitschrift für Phonetik und allgemeine Sprachwissenschaft (Berlin).

Abaev, V.l. 1934 "Jazyk kak ideologija i jazyk kak texnika", Jazyk i myslenie 2, 33-54 (M.). 1965 "Lingvisticeskij modernizm kak degumanizacija nauki o jazyke", V Ja 14/3, 22-43. Abernathy, R. 1963 "Mathematical linguistics", CTiL l, Soviel and East European linguistics, 113-132. Ahlfors, L.V. 1966 Complex analysis (New York, etc.). Alarcos Llorach, E. 1965 Fonologia espanola (Madrid). Allen, R.G.D. 1966 Mathematical economics (London, etc.). 1968 Macro-economic theory (London, etc.). Amosov, N.A. 1963 "Modelirovanie informacii i Programm v sloznyx sistemax", VF 17/12, 26-34. Andreev, N.D. 1962 "Models asatool in the development of linguistic theory" [== "The model äs a tool in linguistic analysis"], Word 18, 186-197. Apresjan, Ju.D. 1966 Idei i metody sovremennoj strukturnoj lingvistiki (M.). 1967 Eksperimental'noe issledovanie semantiki russkogo glagola (M.). 1971 Ideen und Methoden der modernen strukturellen Linguistik (Berlin) [Translation of Apre- sjan 1966]. Augustaitis, D. 1964 Das litauische Phonationssystem (München). Avanesov, R.I. 1947 "Iz istorii russkogo vokalizma. Zvuki i i y", Vestnik MGU l, 41-57 [Reprinted in Reformat- skij 1970, 278-299]. 1948 "O dolgix sipjascix v russkom jazyke", Doklady i soobscenija filologiceskogo fakul'teta MGU 6, 23-29 [Reprinted in Reformatskij 1970, 326-335]. 1952 "K voprosu o foneme", Izv AN SSSR, ÖL Ja 11/5, 463-468. 1955 "Kratöajsaja zvukovaja edinica v sostave slova i morfemy", Voprosy grammaticeskogo stroja, 113-139 (M.) [Also in Avanesov 1956b, 13-40. Reprinted in Reformatskij 1970, 422-450]. 1956a "O trex tipax naucno-lingvisticeskix transkripcij", Slavia 25/3, 347-371. 1956b Fonetika sovremennogo russkogo literaturnogo jazyka (M.). Avanesov, R.I., and S.I. Ozegov 1960 Russkoe literaturnoe proiznosenie i udarenie. Slovar'-spravocnik (M.). Avanesov, R.I., and V.N. Sidorov 1945 "Sistema fonem russkogo jazyka", Ocerk grammatiki russkogo literaturnogo jazyka l, Fonetika i morfologija, 39-64 (M.) [Reprinted in Reformatskij 1970, 249-277]. Avram, A. 1967 "Sur la distance entre phonemes", CLTA 4, 17-21. Axmanova, O.S., I.A. Mel'öuk, E.V. Paduceva, R.M. Frumkina 1961 O tocnyx metodax issledovanija jazyka (M.). Batog, T. 1961a "Logiczna rekonstrukcja poje.cia fonemu", SLog 11, 139-183. 1961b "Critical remarks on Greenberg's axiomatic phonology", SLog 12, 195-205. 1962 "A contribution to axiomatic phonology", SLog 13, 67-80. 1967 The axiomatic method in phonology (London). Baudouin de Courtenay, J. REFERENCES 169 1881 "Nekotorye otdely 'sravnitel'noj grammatiki' slavjanskix jazykov", Russkij filologiceskij vestnik 5, 265-344 [Partly reprinted in Baudouin de Courtenay 1963, 118-126]. 1894 "Proba teorji alternacyj fonetycznych. Czesc l, ogolna", Rozprawy Wydzialu Filologicznego Akademü Umiejetnosci w Krakowie 20, 219-364 (Krakow). 1895 Versuch einer Theorie phonetischer Alternationen. Ein Capitel aus der Psychophonetik (Strassburg) [Translation of Baudouin de Courtenay 1894. Russian translation in Baudouin de Courtenay 1963, 265-347]. 1963 Izbrannye trudy po obscemu jazykoznaniju l (M.). Beloozerov, V.N. 1964 "Formal'noe opredelenie fonemy", VJa 13/6, 54-60. Bernstejn, S.I. 1962 "Osnovnye ponjatija fonologii", VJa 11/5, 62-80. Bloch, B. 1941 "Phonemic overlapping", American Speech 16, 278-284 [Quoted from the reprint in Joos 1957, 93-96]. 1948 "A set of postulates for phonemic analysis", Lg 24, 3-46. 1950 "Studies in colloquial Japanese 4. Phonemics", Lg 26, 86-125 [Reprinted in Joos 1957, 329-348]. Bloomfield, L. 1926 "A set of postulates for the science of language", Lg 2, 153-164 [Reprinted in UAL 15 (1949), 195-202, and in Joos 1957, 26-31]. 1933 Language (New York). Bourbaki, N. 1960 Elements d'histoire des mathematiques (Paris). Braithwaite, R.B. 1962 "Models in the empirical sciences", Logic, methodology, andphilosophy of science, 224-231 (Stanford). 1968 Scientific explanation (Cambridge). Chao, Y.R. 1934 "The non-uniqueness of phonemic Solutions of phonetic Systems", Bulletin of the Institute of History and Philology, Academia Sinica, 4/4, 363-397 [Quoted from the reprint in Joos 1957, 38-54]. 1962 "Models in linguistics and models in general", Logic, methodology, and philosophy of science, 558-566 (Stanford). Cherry, B.C., M. Halle, R. Jakobson 1953 "Toward the logical description of languages in their phonemic aspect", Lg 29, 34-46. 1962 "K voprosu o logiceskom opisanii jazykov v ix fonologiceskom aspekte", in Zvegincev 1962, 279-298 [Translation of Cherry et al 1953]. Chomsky, N. 1957 Syntactic structures (The Hague). 1962 "Sintaksiceskie struktury", in Zvegincev 1962, 412-527 [Translation of Chomsky 1957]. 1964 Current issues in linguistic theory (The Hague). Chomsky, N., and M. Halle 1965 "Some controversial questions in phonological theory", JL l, 97-138. 1968 The soundpattern ofEngüsh (New York, etc.). Chomsky, N., M. Halle, F. Lukoff 1956 "On accent and juncture in English", FRJ, 65-80. Cikobava, A. 1966 "K voprosu o putjax razvitija sovremennoj lingvistiki", VJa 15/4, 45-61. Cohen, A. 1966 "On distinctiveness äs a criterion in language analysis", AL 9, 179-191. Cohen, A., C.L. Ebeling, K. Fokkema, A.G.F. Van Holk 1961 Fonologie van het Nederlands en het Fries (The Hague). Contreras, H., and S. Saporta 1960 "The validation of a phonological grammar", Lingua 9, 1-15. Denisov, P.N. 170 REFERENCES 1965 Principy modelirovanija jazyka (M.). Deserieva, T.I. 1970 "O roli matematiceskix metodov v jazykoznanii", Leninizm i teoreticeskie problemy jazykoznanija, 168-183 (M.). Doblhofer, E. 1957 Zeichen und Wunder. Die Entzifferung verschollener Schriften und Sprachen (Wien, Berlin, Stuttgart). Dobrusin, R.L. 1957 "Elementarnaja grammatiöeskaja kategorija", BOMP 5, 19-21. Durnovo, N.N., and D.N. Usakov 1926 "Opyt foneticeskoj transkripcii russkogo literaturnogo proiznosenija", Slavia 5/2, 342-347. Ebeling, C.L. 1960 Linguistic units (The Hague). 1966 "The grammar of literary Avar", SCauc 2, 58-100. 1967 "Some premisses of phonemic analysis", Word 23, 122-137. 1968 "On accent in Dutch and the phoneme /s/", Lingua 21, 135-143. Einstein, A. 1953 Mein Weltbild (Zürich) [Erstdruck: Amsterdam 1934]. Evdosenko, A.P. 1963 "K voprosu o primenenii stereometriceskoj modeli v oblasti fonologii", Issledovanija po strukturnoj tipologii, 200-207 (M.). Fant, G. 1960 Acoustic theory of speech production (The Hague). Feller, W. 1957 An introduction to probability theory and its applications l (New York, London). Filin, F.P. 1965 "Zametki o sostojanii i perspektivax sovetskogo jazykoznanija", V Ja 14/2, 15-28. 1966 "K Probleme social'noj obuslovlennosti jazyka", V Ja 15/4, 31-44. Fillmore, C.J. 1962 A System for characterizing phonological theories (Ann Arbor). Fischer-J0rgensen, E. 1949 "Remarques sur les principes de l'analyse phonemique", Recherches structurales (= TCLC 5), 214-234. 1956 "The commutation test and its application to phonemic analysis", FRJ, 140-151. Fitialov, S.Ja. 1962 "O modelirovanii sintaksisa v strukturnoj lingvistike", PSL, 100-114. 1964 "Transformacii v aksiomaticeskix grammatikax", Transformacionnyj metod v strukturnoj lingvistike, 3-11 (M.). Frolov, LT. 1961 "Gnoseologiöeskie problemy modelirovanija biologiceskix sistem", VF15/2, 39-51. Gair, J.W. 1970 Colloquial Sinhalese clause structures (The Hague, Paris). Ginsburg, S. 1966 The mathematical theory of context-free languages (New York, etc.). Gladkij, A.V. 1963 "Konfiguracionnye xarakteristiki jazykov", PKib 10, 251-260. 1966 "O formal'nyx metodax v lingvistike", VJa 15/3, 52-59. Gladkij, A.V., and I.A. Mel'cuk 1969 Elementy matematiceskoj lingvistiki (M.). Gluskov, V.M. 1963 "Gnoseologiceskaja priroda informacionnogo modelirovanija", VF 17/10, 13-18. Greenberg, J.H. 1959 "An axiomatization of the phonological aspect of language", Proceedings ofthe Symposium on sociological theory, 437-480 (Evanston, New York). REFERENCES 171

Grigor'ev, V.l. 1962 "DifferenciaPnye priznaki russkix glasnyx u, y, i", V Ja 11/1, 10-30. 1964 "Statisticeskoe raspoznavanie i differencial'nye priznaki fonem", V Ja 13/3, 63-69. 1967 "Moduljacionnaja priroda reci i differencial'nye priznaki fonem", VJa 16/1, 47-61. Gudschinsky, S.C. 1958 "Native reactions to tones and words in Mazatec", Word 14, 338-345. Gumperz, J.J. 1958 "Phonological differences in three Hindi dialects", Lg 34, 212-224. Guxman, M.M. 1970 "O roli modelirovanija i obscix ponjatijax v lingvisticeskom analize", Leninizm i teoreticeskie problemy jazykoznanija, 153-167 (M.). Gvozdev, A.N. 1957 "Obladajut li pozicii razlieitel'noj funkciej?", VJa 6/6, 59-63. 1958 "Voprosy fonetiki. Cto dajut tri tipa transkripcij ?", VJa 7/6, 76-86. Halle, M. 1959 The soundpattern of Russian, A linguistic and acoustical investigation (The Hague). 1962 "Fonologiceskaja sistema russkogo jazyka (lingvistiko-akusticeskoe issledovanie)", in Zvegincev 1962, 299-339 [Partial translation of Halle 1959]. 1963 "Phonemics", CTiL l, Soviel and East European linguistics, 5-21. Harary, F., and H.H. Paper. 1957 "Toward a general calculus of phonemic distribution", Lg 33, 143-169. Harris, Z.S. 1951 Methods in structural linguistics (Chicago). 1960 Structural linguistics (Chicago). Hartmann, P. 1965 "Modellbildungen in der Sprachwissenschaft", SGen 18/6, 364-379. Haugen, E. 1956 "The syllable in linguistic description", FRJ, 213-221. Häusler, F. 1968 Das Problem Phonetik und Phänologie bei Baudouin de Courtenay und in seiner Nachfolge (Halle [Saale]). Hesse, M.B. 1963 Models and analogies in science (London, New York). Hintze, F. 1950 "Zur Frage der monophonematischen Wertung", SLing 4, 14-24. Hjelmslev, L. 1943 Omkring sprogteoriens grundl&ggelse (K0benhavn). 1953 Prolegomena to a theory oflanguage (Baltimore) [Translation of Hjelmslev 1943]. 1960 "Prolegomeny k teorii jazyka", in Zvegincev 1960, 264-389 [Translation of Hjelmslev 1953]. Hockett, C.F. 1942 "A System of descriptive phonology", Lg 18, 3-21 [Reprinted in Joos 1957, 97-108]. 1954 "Two models of grammatical description", Word 10, 210-234 [Reprinted in Joos 1957, 386-399]. 1955 A manualofphonology (Baltimore) [= UAL 21/4, pari 1]. Horecky, J. 1967 "Sucasny stav vo fonologii", JC 18, 151-157. Householder, F.W., Jr. 1965 "On some recent Claims in phonological theory", JL l, 13-34. Isaöenko, A.V. 1963 "Der phonologische Status des Velaren Nasals im Deutschen", ZfPh 16, 77-84. Isacenko, A.V., and HJ. Schädlich 1966 "Untersuchungen über die deutsche Satzintonation", Studia Grammatica l, 7-67 (Berlin). Ivanov, V.V. 1961 "O priemlemosti fonologiceskix modelej", Masinnyjperevod, 396-412 (M.). 1962 "Teorija fonologiceskix razlißitel'nyx priznakov", in Zvegincev 1962, 139-172. 172 REFERENCES Ivic, M. 1963 Pravci u lingvistici (Ljubljana). 1965 Trends in linguistics (The Hague) [Translation of Ivic 1963]. Jacobsson, G. 1966 "Les affriquees slaves", CLTA 3, 81-89. Jakobson, R. 1931 "Z fonologie spisovne slovenstiny", Slovenska miscellanea, 155-163 (Bratislava). 1960 "Kazanska szkola polskiej lingwistyki i jej miejsce w äwiatowym rozwoju fonologii", BPTJ 19, 3-34. 1961 ed., Structure of language and its mathematical aspects (= Proceedings of symposia in applied mathematics 12) (Providence, Rhode Island). 1962 "Phonemic notes on Standard Slovak", Selected writings l, 221-230 (The Hague) [Translation of Jakobson 1931]. Jakobson, R., G. Fant, M. Halle 1962 "Vvedenie v analiz reci. Razlicitel'nye priznaki i ix korreljaty", in Zvegincev 1962, 173-230 [Partial translation of Jakobson et al. 1965]. 1965 Preliminaries to speech analysis. The distinctive features and their correlates (Cambridge, Mass.). Jakobson, R., and M. Halle 1956 Fundamentals of language (The Hague). 1957 "Phonology in relation to phonetics", in Kaiser 1957, 215-251 [Chapter 14]. 1962 "Fonologija i ee otnoSenie k fonetike", in Zvegincev 1962, 231-278 [Translation of Jakobson and Halle 1957]. Jakovlev, N.F. 1923 Tablicy fonetiki kabardinskogo jazyka (M.). 1928 "Matematiceskaja formula postroenija alfavita (Opyt prakticeskogo prilozenija lingvisti- ceskoj teorii)", Kul'tura ipis'mennost' Vostoka l, 41-64 (M.) [Reprinted in Reformatskij 1970, 123-148]. 1948 Grammatika literaturnogo kabardinocerkesskogo jazyka (M.). Jakovlev, N.F., and D.A. Asxamaf 1941 Grammatika adygejskogo literaturnogo jazyka (M., L.). Jensen, M. Kloster 1961 Tonemicity. A technique for determining the phonemic Status of suprasegmental patterns in pairs oflexical units, applied to a group of West Norwegian dialects, and to Faroese (Bergen, Norway). Johnston, J. 1963 Econometric methods (New York, etc.). Jones, D. 1931 "On phonemes", TCLP 4, 74-79. 1950 The phoneme. Its nature and use (Cambridge). Joos, M. 1942 "A phonological dilemma in Canadian English", Lg 18, 141-144. 1957 ed., Readings in linguistics l, The development of descriptive lingmstics in America 1925-56 (Chicago, London). Kaiser, L. 1957 ed., Manual of phonetics (Amsterdam). Kanger, S. 1964 "The notion of a phoneme", SMiL 3, 43-48. Kibrik, A.E. 1962 "K voprosu o metode opredelenija differencial'nyx priznakov pri spektral'nom analize (na materiale glasnyx novogreöeskogo jazyka)", V Ja 11/5, 81-89. Kiefer, F. 1964 "Some aspects of mathematical models in linguistics", SMiL 3, 8-26. 1968 Mathematical linguistics in Eastern Europe (New York). Klimov, G.A. 1967 Fonema i morfema (M.). REFERENCES 173 Kortlandt, F.H.H. 1969 "Exacte methoden in de lingui'stiek", Raster 3/2, 153-161 (Amsterdam). 1971 "The semantics of the Russian verb", Lingua 27, 53-81 [Review of Apresjan 1967]. forthcoming a "Sur l'identiflcation des unites phonologiques du castillan", Los. forthcoming b "Phonetics and phonemics of Standard Russian", TSTL 1. forthcoming c "Russian conjugation. Computer synthesis of Russian verb forms", TSTL 2. forthcoming d "O fonologii sovremennogo pol'skogo literaturnogo jazyka", ScSl 18. Kuipers, A.H. 1960 Phoneme and morpheme in Kabardian (The Hague). 1968 "Unique types and typological universals", Pratidänam, 68-88 (The Hague). Kulagina, O.S. 1958 "Ob odnom sposobe opredelenija grammaticeskix ponjatij na baze teorii mnozestv", PKib l, 203-214. Künstler, M.J. 1968 "Toward a phonologic Interpretation of tonematic Systems", BPTJ 26, 179-195. Kuznecov, P.S. 1941 "K voprosu o fonematiceskoj sisteme sovremennogo francuzskogo jazyka", Uc zap MGPI 5/1, 140-174 [Reprinted in Reformatskij 1970, 163-203]. 1948 "K voprosu o fonologii udarenija", Doklady i soobscenijafilologiceskogofakurteta MGU, 6, 12-17 [Reprinted in Reformatskij 1970, 360-367]. 1958 "O differencial'nyx priznakax fonem", VJa 7/1, 55-61 [Reprinted in Reformatskij 1970, 485-493]. 1959 "Ob osnovnyx polozenijax fonologii", VJa 8/2, 28-35 [Reprinted in Reformatskij 1970, 470-480]. 1966 "Eäce o gumanizme i degumanizacii", VJa 15/4, 62-74. Leont'ev, A.A. 1959 "Obscelingvisticeskie vzgljady I.A. Boduena de Kurtene", VJa 8/6, 115-127. 1961 "I.A. Boduen de Kurtene i Peterburgskaja gkola russkoj lingvistiki", VJa 10/4, 116-124. Leska, O. 1966 "K Saumjanove definici fonemu", SaS 27, 205-208. Lindeman, F.O. 1970 Einführung in die Laryngaltheorie (Berlin). Lomtev, T.P. 1962 "OtnositePno dvuxstupencatoj teorii fonem", VJa 11/6, 61-69. Losev, A.F. 1965 "O metodax izlozenija matematiceskoj lingvistiki dlja lingvistov", VJa 14/5, 13-30. 1970 "O predelax primenimosti matematiöeskix metodov v jazykoznanii (O sravnitel'noj xarakteristike jazykovogo i matematiceskogo znaka)", Leninizm i teoreticeskie problemy Jazykoznanija, 184-194 (M,). Maöavariani, M.V. 1963 "O vzaimootnosenü matematiki i lingvistiki", VJa 12/3, 85-91. 1967 "O predmete lingvistiki", Problemy Jazykoznanija, 33-38 (M.). Malecot, A. 1960 "Vowel nasality äs a distinctive feature in American English", Lg 36, 222-229. Malmberg, B. 1942a "A propos du Systeme phonologique de l'italien", AL 3, 34-43. 1942b "Bemerkungen zum quantitativen Vokalsystem im modernen Französisch", AL 3, 44-56. Marcus, S. 1961 "Structures linguistiques et structures topologiques", RMPA 6, 501-506. 1962 "Teorija grafov, lingvisticeskie oppozicü i invariantnaja struktura", PSL, 22-30. 1963a "Logiöeskij aspekt lingvisticeskix oppozicij", PSL 1963, 47-74. 1963b "Un model matematic al fonemului", SCM 14, 405-421 1963c Lingvisticä matematicä. Modele matematice in lingvisticä (Bucuresti). 1966 "Le modelage mathematique en phonologie. Methodes, resultats, significatioa", CLTA 3, 109-116. 1967a Introduction mathematique a la linguistique structurale (Paris). 174 REFERENCES 1967b Algebraic Unguistics. Analytical models (New York, London). 1969 Algebraicke modely v lingvistice (Praha). Marcus, S., and E. Vasiliu 1960 "Mathematiques et phonologie. La theorie des graphes et le consonantisme de la langue roumaine", RMPA 5, 319-340 et 681-703. Markov, A.A. 1913 "Primer statisticeskogo issledovanija nad tekstom 'Evgenija Onegina' illjustrirujuscij svjaz' ispytanij v cep' ", Izv AN, VI, 7/3, 153-162 (Sankt-Peterburg). Martinet, A. 1939 "Un ou deux phonemes?", AL l, 94-103 [Reprinted in Martinet 1968, 109-123]. 1947 "Oü en est la phonologie?", Lingua l, 34-58 [Partly reprinted in Martinet 1968, 59-76]. 1949 "Occlusives and affricates with reference to some problems of Romance phonology", Word 5, 116-122. 1960 Elements de linguistique generale (Paris). 1964 "Pour un dictionnaire de la prononciation frangaise", In honour of Daniel Jones, 349-356 (London) [Reprinted in Martinet 1969, 121-131]. 1965 "Les voyelles nasales du francais", Lque 1/2,117-122 [Reprinted in Martinet 1969,144-154]. 1968 La linguistique synchronique. Etudes et recherches (Paris). 1969 Le francais sans fard (Paris). Maslov, P.P. 1962 "Modelirovanie v sociologiöeskix issledovanijax", VF16/3, 62-78. Mdivani, R.R. 1968 "ZameCanie k modeli obscego iscislenija distribucii fonem", VJa 17/3, 124-125. Mel'öuk, I.A. 1965 "O fonologiceskoj traktovke poluglasnyx v ispanskom jazyke", VJa 14/4, 92-109. 1967a "Model' sprjazenija v ispanskom jazyke", MPPL 10, 21-53. 1967b "K postroeniju dejstvujus'cej modeli jazyka", Problemy jazykoznanija, 82-89 (M.). 1968a "O pritjazatel'nyx formax vengerskogo susöestvitel'nogo", PSL 1967, 326-343. 1968b "Model' sklonenija vengerskix suscestvitel'nyx", PSL 1967, 344-373. Mel'öuk, I.A., and A.K. Zolkovskij 1970 "Towards a functioning 'meaning-text' model of language", Los 57, 10-47 [Translation, of Zolkovskij and Mel'öuk 1969], Merlingen, W. 1960 "Über Ein- und Zweiphonemigkeit", ZfPh 13, 98-176. Milivojeviö, D.D. 1970 Current Russian phonemic theory, 1952-1962 (The Hague). Morciniec, N. 1958 "Zur phonologischen Wertung der deutschen Affrikaten und Diphthonge", ZfPh 11, 49-66. MuljaiSc, Z. 1967 "La combinabilite des phonemes sur Taxe syntagmatique, depend-elle de leur traits distinctifs?", Phonologie der Gegenwart, 273-286 (Graz, Wien, Köln). Nebesky, L. 1963 "O jednom algebraickem modelu jazyka", SaS 24, 231-237. 1964 "K odnoj modeli analiza predlozenija", PBML 2, 3-10. 1966a "K odnoj matematiceskoj modeli fonemy", RMPA 11, 453-456. 1966b "On the notion of relevant features", PBML 6, 35-43. Nork, O.A., Z.M. Murygina, L.P. Bloxina 1962 "O differencial'nyx priznakax fonemy", VJa 11/1, 42-50. Noväk, L'. 1969 "K spornym otäzkam fonologie". JÖ 10, 179-182. Novik, LB. 1963 "Gnoseologiöeskaja xarakteristika kiberneti&skix modelej", VF 17/8, 92-103. Novotny, M. 1965 "Ob algebraizacii teoretiko-mnozestvennoj modeli jazyka", PKib 15, 234-243. 1966 "On some algebraic concepts of mathematical linguistics", PSML l, 125-140. REFERENCES 175

Panov, M.V. 1953 "O znacenii morfologiceskogo kriterija dlja fonologii", Izv AN SSSR, OLJa 12/4, 373-377 [Reprinted in Reformatsldj 1970, 368-373]. 1961 "O razgraniöitel'nyx signalax v jazyke", V Ja 10/1, 3-19. 1967 Russkajafonetika (M.). Papp, F. 1966 Mathematical linguistics in the Soviel Union (The Hague). Pauliny, E. 1961 Fonologia spisovnej slovenciny (Bratislava). 1967 "Zum Verhältnis der Laute /i/ und /j/ im Slowakischen", THRJ 2, 1497-1502. Peterson, G.E., and F. Harary 1961 "Foundations of phonemic theory", in Jakobson 1961, 139-165. Piöurin, L.F. 1965 "K voprosu o primenenii matematiki v jazykoznanii", V Ja 14/4, 119-120. Pike, K.L. 1947 Phonemics. A techniquefor reducing languages to writing (Ann Arbor). Piotrovskij, R.G. 1960 "Esce raz o differencial'nyx priznakax fonemy", VJa 9/6, 24-39. 1963 "Pis'mo v redakciju", VJa 12/1, 146-149. 1966 Modelirovanie fonologiceskix sistem i metody ix sravnenija (M., L.). Postal, P.M. 1968 Aspects of phonological theory (New York, etc.). Puäkin, A. 1837 Evgenij Onegin. Roman v stixax (Sankt-Peterburg). Reformatskij, A.A. 1941 "Problema fonemy v amerikanskoj lingvistike", Uc zap MGPI 5/1, 103-139 [Reprinted in Reformatskij 1970, 204-248]. 1952 "K probleme fonemy i fonologii", Izv AN SSSR, OLJa 11/5, 469-473. 1955a "Soglasnye, protipostavlennye po sposobu i mestu obrazovanija, i ix var'irovanie v sovremennom russkom literaturnom jazyke", Doklady i soobscenija Instituta jazykoznanija AN SSSR 8, 3-23 (M.) [Reprinted in Reformatskij 1970, 374-397]. 1955b "O sootnosenii fonetiki i grammatiki (morfologii)", Voprosy grammaticeskogo stroja, 92-112 (M.) [Reprinted in Reformatskij 1970, 398-421]. 1957 "Fonologiceskie zametki", VJa 6/2, 101-102 [Reprinted in Reformatskij 1970, 481-484]. 1961a "Dixotomiceskaja klassiflkacija differencial'nyx priznakov i fonematiceskaja model' jazyka", Voprosy teoriijazyka v sovremennoj zarubeznoj lingvistike, 106-122 (M.). 1961b "Fonologija na sluzbe obucenija proiznoseniju nerodnogo jazyka", RJNS, 6, 67-71 [Reprinted in Reformatskij 1970, 506-515]. 1963 "Jazyk, struktura i fonologija", PFil 18/1, 105-111 [Reprinted in Reformatskij 1970, 516- 523]. 1970 Iz istorii otecestvennoj fonologii (M.). Reichenbach, H. 1947 Elements of symbolic logic (New York). Revzin, I.I. 1960 "O nekotoryx ponjatijax tak nazyvaemoj teoretiko-mnozestvennoj koncepcii jazyka", VJa 9/6, 88-94. 1962a Modelt jazyka (M.). 1962b "O nekotoryx voprosax distributivnogo analiza i ego dal'nejsej formalizacü", PSL, 13-21. 1962c "Ob odnom podxode k modeljam distributivnogo fonologiceskogo analiza", PSL, 80-85. 1964 "K logiceskomu obosnovaniju teorii fonologiieskix priznakov", VJa 13/5, 59-65. 1965 "Strukturnaja lingvistika i edinstvo jazykoznanija", VJa 14/3, 44-59. 1966 Models oflanguage (London). 1967 Metod modelirovanija i tipologija slavjanskix jazykov (M.). 1968 Les modeles linguisttques (Paris). 1970 "Nekotorye zamecanija v svjazi s dixotomiCeskoj teoriej v fonologii", VJa 19/3, 58-70. Romporti, M. 176 REFERENCES 1966 "K metode zvukoveho rozboru jazyka", SaS 27, 208-216. Rozdestvenskij, Ju.V. 1965 "O sovremennom stroenii jazykoznanija", V Ja 14/3, 60-69. 1966 "Obzor materialov, postupivsix v redakciju po povodu stat'i V.l. Abaeva 'Lingvisticeskij modernizm kak degumanizacija nauki o jazyke' ", V Ja 15/4, 75-79. Rozencvejg, VJu. 1966 "Jazykovaja praktika i lingvisticeskaja teorija", VJa 15/2, 30-39. Sapir, E. 1925 "Sound patterns in language", Lg l, 37-51 [Reprinted in Joos 1957, 19-25], Saumjan, S.K. 1952 "Problema fonemy", Izv AN SSSR, OLJa 11/4, 324-343. 1956 "O susCnosti strukturnoj lingvistiki", VJa 5/5, 38-54. 1959 "Logiceskij analiz ponjatija fonemy", Logiceskie issledovanija, 159-177 (M.). 1960 "Dvuxstupenöataja teorija fonemy i differencial'nyx elernentov", VJa 9/5, 18-34. 1962 Problemy teoreticeskoj fonologii (M.). 1963 "O logiCeskom bazise lingvistiöeskoj teorii", PSL 1963, 3-8. 1965 Strukturnaja lingvistika (M.). 1966a ed., Issledovanija po fonologii (M.). 1966b "Sovremennoe sostojanie dvuxstupencatoj teorii fonologii", in Saumjan 1966a, 3-23. 1968 Problems of theoreticalphonology (The Hague) [Translation of Saumjan 1962]. Saussure, F. de 1879 Memoire sur le Systeme primitif des voyelles dans les langues indo-europeennes (Leipzig). 1916 Cours de linguistique generale (Paris). Söerba, L.V. 1909 "Sub'ektivnyj i ob'ektivnyj metod v fonetike", Izv AN, Otdelenie russkogo jazyka i sloves- nosti, 14/4, 196-204 [Reprinted in Scerba 1958, 110-116]. 1958 Izbrannye raboty po jazykoznaniju i fonetike l (L,). Schatz, C.D. 1954 "The role of the context in the perception of stops", Lg 30, 47-56. Schogt, H.G. 1966 "Baudouin de Courtenay and phonological analysis", Lque 2/2, 15-29. Shapiro, M. 1968 Russian phonetic variants andphonostylistics (Berkeley, Los Angeles). Sokolova, V.S. 1949 Fonetika tadzlkskogo jazyka (M., L.). Steblin-Kamenskij, M.I. 1964 "O simmetrii v fonologiceskix resenijax i ix needinstvennosti", VJa 13/2, 45-52. Stoff, V.A. 1961 "Gnoseologiceskie funkcü modeli", VF15/12, 53-65. 1963 "Ob osobennostjax model'nogo eksperimenta", VF 17/9, 40-50. 1966 Modelirovanie ifilosofija (M., L.). Stokhof, W.A.L. 1972 "Notes on the extinct East Slovincian Kluki dialect", TSTL, forthcoming. Suppes, P. 1962 "Models of data", Logic, methodology, and phihsophy ofscience, 252-261 (Stanford). Swadesh, M. 1934a "The phonemic principle", Lg 10,117-129 [Reprinted in Joos 1957, 32-37]. 1934b "The phonetics of Chitimacha", Lg 10, 345-362. Tarski, A. 1937 "Appendix E", in Woodger 1937, 161-172. 1965 Introduction to logic and to the methodology ofdeductive sciences (New York). Thomas, L.L. 1957 The linguistic theories of N.Ja. Man (Berkeley, Los Angeles). Tolstaja, S.M. 1968 "Fonologiceskoe rasstojanie i soöetaemost' soglasnyx v slavjanskix jazykax", VJa 17/3, 66-81. REFERENCES 177

Toporov, V.N. 1966 "Materialy dlja distribucii grafem v pis'mennoj forme russkogo jazyka", Strukturnaja tipologija jazykov, 65-143 (M.). Trubetzkoy, N.S. 1935 Anleitung zu phonologischen Beschreibungen (Brno). 1939 Grundzüge der Phänologie (= TCLP 9) (Praha). 1960 Osnovy fonologü (M.) [Translation of Trubetzkoy 1939]. Twaddell, W.F. 1935 On defining the phoneme (Baltimore) [Quoted from the reprint in Joos 1957, 55-80]. Uemov, A.I. 1962 "Analogija i model' ", VF16/3, 138-145. Uldall, HJ. 1935 "The phonematics of Danish", Proceedings ofthe 2nd international congress of the phonetic sciences, 54-57 (Cambridge). Uspenskij, V.A. 1957 "K opredeleniju casti reci v teoretiko-mnozestvennoj sisteme jazyka", BOMP 5, 22-26. 1964 "Odna model' dlja ponjatija fonemy", V Ja 13/6, 39-53. Vasiliu, E. 1957 "Une classification des consonnes roumaines d'apres le critere de la distribution", Me- langes linguistiques, 97-112 (Bucarest). 1963 "Struktura konsonantnyx grupp v rumynskom jazyke", PSL 1963, 210-219. Venikov, V.A. 1964 "Nekotorye metodologiöeskie voprosy modelirovanija", FF 18/11, 73-84. Voegelin, C.F. 1959 "Model-directed structuralization", AnthrL l/l, 9-25. Vogt, H. 1954 "Phoneme classes and phoneme classification", Word 10, 28-34. Woodger, J.H. 1937 The axiomatic method in biology (Cambridge). Xolodoviö, A.A. 1960 "Opyt teorii podklassov slov", VJa 9/1, 32-43. Zaliznjak, A.A. 1963 "Lingvisticeskie zadaci", Issledovanija po strukturnoj tipologii, 137-159 (M.). 1966 "Opyt fonologiöeskogo analiza sovremennogo francuzskogo vokalizma", Lingvisticeskie issledovanija po obscej i slavjanskoj tipologii, 214-230 (M.). 1967 Russkoe imennoe slovoizmenenie (M.). Zinder, L.R. 1966 "O novom v jazykovedenii", VJa 15/3, 60-64. 1968 "Fonologija i fonetika", Teoreticeskie problemy sovetskogo jazykoznanija, 193-231 (M.). Zinov'ev, A.A., and I.I. Revzin 1960 "Logiceskaja model' kak sredstvo naucnogo issledovanija", VF 14/1, 82-90. Zirkov, L.I. 1936 Avarsko-russkij slovar' (M.). Zolkovskij, A.K., and I.A. Mel'öuk 1969 "K postroeniju dejstvujusfiej modeli jazyka 'smysl-tekst' ", MPPL 11, 5-35. Zuravlev, V.K. 1966a "Dvuxstupencataja teorija fonologü i metodika modelirovanija fonologiceskix processov", in Saumjan 1966a, 65-78. 1966b "Gruppofonema kak osnovnaja fonologiceskaja edinica praslavjanskogo jazyka", in Saumjan 1966a, 79-96. 1967 "Opyt fonologiöeskoj interpretacii praslavjanskix gruppofonem", Phänologie der Gegen- wart, 142-157 (Graz, Wien, Köln). Zvegincev, V.A. 1960 ed., Novoe v lingvistike l (M.). 1962 ed., Novoe v lingvistike 2 (M.). STELLINGEN behorende bij het proefschrift "Modelling the phoneme. New trends in East European phonemic theory" van F.H.H. Kortlandt, Amsterdam, 1972.

1. Binnen het wetenschappelijk onderzoek in de A-faculteiten verdient het beschrij- ven van uitstervende talen de hoogste prioriteit. 2. Bij de beschrijving van werkwoordstijden wordt in het algemeen onvoldoende rekening gehouden met het verschil tussen de tijd waarin een handeling of situatie plaats heeft en de tijd waarnaar door een werkwoordsvorm wordt gewezen. 3. Apresjan's beschrijving van de lexicale betekenis van werkwoorden in termen van hun syntactische eigenschappen berust niet uitsluitend op zuiver formele gegevens. Ju.D. Apresjan, Eksperimental'noe issledovanie semantiki russkogo glagola (Izd. "Nauka", Moskva, 1967). 4. In de nieuwe Academische Grammatica van het Russisch worden de suffixen a en iva in secundaire imperfectiva ten onrechte beschreven als allomorfen van eenzelfde suffix. Grammatika sovremennogo russkogo literaturmgo jazyka (Izd. "Nauka", Moskva, 1970), p. 342. 5. Leningen aan arme landen kunnen niet als ontwikkelingshulp worden beschouwd voorzover rente en aflossingen terugvloeien naar de rijke landen. 6. De gedachte dat arbeid in de ontwikkelingslanden goedkoop is omdat de Ionen daar laag zijn berust op een misvatting. 7. Door bij het onderwijs in Westerse economische theorieen mede aandacht te schenken aan de kritiek die door Marxistische economen op deze theorieen is uit- geoefend kan de kritische zin van economie-studenten worden gestimuleerd. 8. Hoogleraren die ten gerieve van hun Studenten een leerboek schrijven dienen uit de verkoop verkregen royalties af te staan aan hun werkgever.