Markedness Theory 9780822382881

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Markedness Theory

Sound and Meaning: The Roman Jakobson Series in Linguistics and Poetics C. H. van Schooneveld, Series Editor

Markedness Theory The Union of Asymmetry and Semiosis in Language

= Edna Andrews = Duke University Press Durham and London, 1990

© 1990 Duke University Press All rights reserved. Printed in the United States of America on acid-free paper 00 Library of Congress Cataloging-in-Publication Data will be found on the last printed page of this book.

To my parents, Nick and Goldie

Contents

One

Two

Acknowledgments ix Introduction 1 The Principles of Jakobsonian Markedness Theory 9 Gesamtbedeutung and a Definition of Markedness A Brief History of Markedness: From Trubetzkoy to the Present Jakobson's and van Schooneveld's Morphological Features Mark or Feature? Deixis: A General Definition Deixis and Reference The Union of Conceptual Feature and Deictic Category: Shifters in the Russian Verb Peirce and Jakobson Revisited: A Reconciliation 44 Peirce's Influence on Jakobson Markedness Theory as a Theory of Interpretants Sign, Object, and Interpretant The Categories of Firstness, Secondness, and Thirdness The Ultimate Interpretant Meaning and Interpretants Icon, Index, Symbol, and Artifice? Dyads or Triads? An Application of Peircean Interpretants to Linguistic Analysis

viii

Markedness Theory

Three

Markedness Theory as Mathematical Principle 81 Mathematics: Topology and Its Relevance to Jakobsonian Linguistics The Role of Syllogisms and Different Types of Inference Deductive, Inductive, and Abductive Reasoning Continuity or Discontinuity? Dynamics and Structural Stability Catastrophe Theory and Linguistic Sign Theory An Axiomatic Base for Markedness The Morphological Conceptual Features and Group Theory The Laws of Form and the Form of Laws

Four

Myths About Markedness 136 Statistical Frequency Neutralization Markedness Assimilation Markedness Reversals Substitutability

Five

The Category of Grammatical Gender in Russian, Serbo-Croatian, and Modern Greek 166 Modern Greek (Dhimotiki/Demotic) and the Role of the -5 Marker Jakobson's Analysis of the Category of Gender in Modern Russian The Serbo-Croatian Gender Hierarchy Shifting Genders Grammatical Gender versus Declension: Syntagmatic Vs. Paradigmatic Is Gender Meaningful? Notes 189 Bibliography Index 211

199

= Acknowledgments =

In writing the present work I have been fortunate to receive the support of many of my colleagues and friends. I would like to thank the following people for their suggestions, comments, and interest in my project: Ron Butters, Ron Feldstein, Barbara Fennell, Michael Holquist, Michael Morgan, Stefan Pugh, and Rodney Sangster. Special thanks are in order to Laura Severin for patiently editing the manuscript at various stages in its development, to Sandy Bostian for photocopying drafts of the manuscript, and to Reynolds Smith for his professionalism and encouragement. I would also like to thank Krystyna Pomorska Jakobson for reading parts of my manuscript, even though she was very ill at the time. I only regret that she is not able to see the final product. Finally, I would like to thank Kees van Schooneveld for his constant support at every stage of my career. It was his gentle manner of teaching linguistics that originally motivated my interest in Slavic linguistics.

= Introduction =

The question of the relation between form and meaning, signifier and signified, is fundamental for modern linguistics in the Jakobsonian tradition. Although one may recognize that, in fact, the linguistic sign has these two components, the semantic theory resulting from such an approach has suffered from a serious lack of development, especially in comparison to phonological theory. The present work has three primary goals: to define the structure of linguistic meaning, to explain the laws of linguistic form, and to reconcile these two components with each other via a semiotic thirdthe interpretant. The interpretant is the third constituent in the sign/object/interpretant triad. It is only via the interpretant that semiosis, and hence the production of meaning through reference, can occur. The interpretant, as a rule (or law) mediating translation of the sign, provides the foundation for differentiating between that which is invariant and that which is variant in linguistic structure. In different terms, what is to follow is an analysis of markedness theory, a theory of interpretants. Markedness theory is a theory of qualitative oppositions that enables linguists to analyze the inherently asymmetrical relationships by which linguistic signs (signum, signans, and signatum) are created and thus posit a model for defining linguistic meaning in terms of invariant conceptual relations. Roman Jakobson first discovered the relation of marked and unmarked terms in 1921, although it was Nikolai Trubetzkoy who first used the term priznak (Russian "mark") for this particular type of opposition (Holenstein 1976:129). Jakobson defined the marked term as the necessary statement of a property A, while the unmarked term is divisible into two

2

Markedness Theory

parts: nonstatement of A or statement of non-A. The "property A" is defined by Jakobson as an intrinsically given property of meaning that is relatively autonomous to extra-linguistic reality. The category of tense in Russian can serve as an example of how to apply markedness to categories of grammatical meaning. The past tense in Russian is said to be marked, while the present tense is unmarked. Specifically, the feature marking of the past tense is the obligatory disjunction between the verbal process and the speech event; since the present tense does not have this feature marking, it mayor may not coincide with the speech event (that is, nonstatement of A or statement of non-A). In the case of statement of non-A, conjunction, not disjunction, occurs. Such a definition of the past tense in Russian explains usage of all potential utterances in Russian using a past tense verbal form. The form serves as the primary element for analysis, relating, in some cases, semantic categories that were traditionally considered to be distinct. In Russian, for example, this includes utterances having a past meaning as well as the conditional and hypothetical moods, which also require a past tense verb form. The present tense may indicate present time or past time (cf. historical present in narratives). Rather than defining the past tense in terms of multiple and disparate meanings, markedness theory, using markedness features, reveals the semantic invariant behind the form. As becomes clear from the example given above, the properties of meaning that will be representative of marked categories are not objects, nor are they absolutes. Rather, the markedness value(s) for a given category will be definable only in terms of relations and these relations at their most basic level are generally defined spatially. Such a theory of markedness, as described above, should be applicable to all levels of linguistic meaning, from phonology to morphology and syntax, including grammatical and lexical meaning. The range of disciplines and theories evoked in a study of markedness theory such as this one is broadly defined because only by means of an interdisciplinary approach can a relevant, semiotically defined theory of linguistic markedness be developed. In particular, mathematics provides us with quantitatively and qualitatively defined principles that are essential in substantiating any claims we would

Introduction

3

make concerning relational concepts, which play such a crucial role in markedness theory. There can be no question of the importance of Roman Jakobson's work in the discovery of markedness theory and in developing a coherent theory of signs for linguistics. And it is Jakobson's work that allows us now to bring together such major figures as C. S. Peirce, G. S. Brown, Rene Thorn, and C. H. van Schooneveld, all of whom have researched principles of invariance as they are represented by variant structures. By way of introduction, what follows is a brief analysis of the role that each scholar has played in establishing a theory of markedness within the framework of Jakobsonian linguistic thought. It is not so surprising to see the names of Jakobson and Peirce paired in a work on linguistic theory. In fact, it would be unjustifiable to pretend to discuss Jakobson in-depth without some evocation of Peirce. For many linguists Peirce is primarily known through Jakobson's work on him. In the last decade, however, semioticians, as well as linguists working in the semiotic tradition, have produced some very interesting studies on aspects of Peirce's works that were not included in Jakobson's interpretations. Where pertinent, these studies will be discussed, particularly those of David Savan, Michael Shapiro, Linda Waugh, and Elizabeth Bruss. However, my emphasis will be not only on Peirce the semiotician/philosopher but on Peirce the logician/ mathematician, for it is precisely Peirce's logical and mathematical works that reveal his attempts to develop a "speculative grammar" for semiotic systems. Furthermore, Peirce authored some remarkably insightful works on the structure of logical argument, from a mathematical perspective, as well as discussions concerning the utility of such tools commonly used in modern semantic theory as Euler's and Venn's diagrams, and essays on the general importance of mathematical systems, including those of arithmetic, algebra, and various geometries, such as topology. In works on Peirce's contribution to linguistics his specifically mathematical studies have, for the most part, been ignored in favor of his more accessible pieces on developing a theory of semiotics. Yet Peirce's mathematical studies become particularly important for this work,

4 Markedness Theory

since a major portion of the theoretical argumentation in my approach rests on an explication of the principles of Set and Group theory and their applicability to extending Jakobsonian markedness theory. Mathematical Set theory, as a theory of relations, provides axioms that explain how binary signs interrelate at their most fundamental level. Group theory, a natural extension of Set theory, allows us to analyze not only linguistic relations, but the binary operations that define these relations. The application of both set and group theory is crucial if we are to achieve any notion of how conceptual relations, or markedness features, combine to produce linguistic meaning through reference and, hence, enable communication to occur. Ultimately, it is via Peirce and G. S. Brown that we can clearly define both the fundamental differences between logic and mathematics and the crucial role played by the concepts of continuity and discontinuity in defining asymmetric sign systems. For example, Peirce argues that continuity "is the leading conception of science" and that cognition and perception are necessarily continuous categories. But, in order to discriminate between forms and structures, discontinuity is necessarily implied. Therefore, markedness theory, as presented here, will be defined in terms of a continuous, and hence dynamic, model that includes discontinuous factors. In other words, the oppositional relationship marked/unmarked is continuous, but the markedness values (or features) are discrete and discontinuous. Likewise, by clearly differentiating between the discipline of logic, which can only analyze structure, and the discipline of mathematics, which can both create and analyze structure, we are able to define more precisely the relevance of logical and mathematical principles to linguistic research. G. S. Brown nicely complements Peirce and Jakobson in his logical discussions of the laws of form. The theme of form as law, another theoretical manifestation of the concept of invariance, is consistently present in every chapter of this book, either explicitly or implicitly. In fact, it is Brown who provides us with a coherent statement of the differences between arithmetic and algebra, a crucial concept for understanding the defining mechanism underlying a theory of markedness and the actual markedness features themselves, by explaining how they are defined internally and manifested externally in the structure of language. Finally, it is Brown who provides us with a nonlinguis-

Introduction

5

tic justification of the importance of deixis, which is the act of making reference to a particular spatial or temporal point within a given utterance, and deictic structures (such as verbal tense and the personal pronouns) in perceptual categories as defined within the field of logic. Brown's argument can be summarized as follows (1969:69): The form is the vehicle providing distinction, that is, the key to the structure of meaning. Each distinction, via the form, necessarily yields reference. Two types of reference obligatorily occur in every distinction: (1) explicit reference to the "value" of the sign, that is, how it is marked, and (2) implicit reference to an "outside observer," that is, fixing the position of an observer so that an expression is interpretable and, hence, "meaningful." The first type of reference, as interpreted by Jakobsonian linguistic theory, is the obligatory reference given by any signifier to its signified via the features it possesses. The second type of reference-one more often ignored than noted-is the obligatory reference via the signifier to some deictically given observer. If we accept Brown's definition of implicit reference as obligatory reference to an observer, we are led to accept that all forms inherently possess some deictic referent in order to become meaningful. It is through deixis that one can explain the complicated relationship between context as representative of variant meaning and context, in the deictic sense, as invariant meaning. Context, via deixis, is coded into the forms themselves. Such a codification of variation leads to the assertion that there is no meaning without a context or, in other words, there is no meaning without deixis. Thus, one has yet another perspective on the crucial role of context and on the relationship between invariants and variants in the broad structural scheme of language. By defining deixis in such terms, we are able to better comprehend the necessity for including the Peircean interpretant in the definition of markedness features for language. Jakobson often wrote about the importance of mathematics in linguistic theory, particularly the field of topology, since he felt that all semiotic systems share the same fundamental structural principles, expressible in qualitative as well as quantitative terms. Rene Thorn, both a topologist and a semiotician, has made significant advances in using topology to develop a qualitative theory of catastrophes. Not only does Thorn offer a well-defined argument for the advantages

6 Markedness Theory

of a qualitatively defined theory within the framework of what has previously been considered a purely quantitative science, but he also makes some very interesting remarks on the role of semantic density in defining parts of speech in language. For Thorn, the semantic density of a category can be determined by measuring the energy and time required to reduce a concept to its representative sign. Semantic density is necessarily implied by structural stability, so the greater the complexity (or density) of a concept, the more regulators (or markedness values) it requires. The structural stability of a space or category is the quality that allows the space or category to exist over time and resist the extreme change that results from environmental pressure. (The substantive, or noun, is an example of the most structurally stable and semantically dense part of speech.) Most important, Thorn gives us a fresh view of the potentials existing within the framework of traditional quantitative science and of the applications of semiotics and qualitative theories. As one of the few scholars whose work has managed to bridge the gap between qualitative and quantitative science, Thorn has opened the door to future discoveries. Not only are Thorn's principles of structural stability and semantic density crucial to our argumentation of markedness theory, but the very spirit of his work, which repeatedly validates the potentiality of rigor in the qualitative sciences, is invaluable to the development of linguistic science. Although all of the scholars mentioned play an integral role in the development of a theoretical foundation for Jakobsonian markedness theory, this work is predominantly about the linguistic applications of markedness, so it is to this point that we must return. The works of C. H. van Schooneveld represent the closest philosophical parallel to the various theoretical principles from the fields of mathematics, logic, and semiotics. In particular, van Schooneveld offers an advanced theory of markedness features, as defined by grammatical and lexical meaning. Certain implicit principles of his theory become explicit as we scrutinize the underlying notions intuited by Jakobson and van Schooneveld in their conceptualization of a markedness theory. Specifically, van Schooneveld has concentrated on developing the Jakobsonian principles initially set forth in Jakobson's studies on the Russian case system (1936, 1958). In addition, van Schooneveld has made significant progress in developing a theory of deixis, the

Introduction

7

importance of which cannot be overstated. It is van Schooneveld's work on deixis that gives true life to Jakobson's shifter and integrates it into the linguistic structure as one of the necessary components of linguistic perceptual categories. Returning to our original thesis, this work attempts to present a coherent and workable theory of markedness as a universally defined system that is applicable to any linguistic system. The conceptual features presented here, as developed by van Schooneveld, have been applied to other languages, namely Serbo-Croatian and Arabic (cf. Levenberg, Fradkin), and appear to be universals as well. However, the fundamental thrust of this work is to present one particular version of Jakobsonian-based markedness theory, to explain why such a theory is necessary in linguistic analysis, and to define specifically what this theory can and cannot do. This includes addressing certain misapplications of the theory that have occurred. In addition, I have tried to expose any and every tacit assumption involved within such a theory of markedness and to present a multidisciplinary foundation that justifies the viability and utility of markedness theory in general. The following supplementary goals support a discussion of Jakobsonian markedness theory: (1) Expanding the applicability of Peircean semiotics in Jakobsonian linguistic theory by demonstrating where these two approaches are compatible, where they are incompatible, and where resolution of differences is possible. (Mathematics is particularly instrumental in reconciling incompatibilities between Jakobson's emphasis on seconds, or binary oppositions, and Peirce's emphasis on thirds, or ternary oppositions.); (2) Explaining the mathematical and logical assumptions found in Jakobson's and van Schooneveld's theoretical principles and applications'of markedness and markedness features; (3) Applying the results, as listed above, to linguistic data. The final chapter includes an analysis of the category of grammatical gender in Russian, Serbo-Croatian, and modern Greek. In each of these languages we find a tripartite gender system (masculine, feminine, neuter), but the relationship among these three categories is redefined for each language. In particular, I will examine cases of sllifting gender types and explain what meaning gender categories can potentially convey. The question of the "latent semantic value" of gen-

8 Markedness Theory

der oppositions will be addressed, as well as the role of grammatical gender in the poetic and emotive functions of language. The need to present a complete analysis of Jakobsonian markedness theory without logical gaps requires that certain sections of this work include portions of previously published articles, which have been reworked and expanded here. In particular, portions of these articles can be found in the final sections of chapters one and two, sections five and six of chapter three, and all of chapter five, which is a combination of two separate articles with additions. Bibliographical entries referring to the Collected Papers of Charles Sanders Peirce, volumes 1-8 (Harvard University Press: 1931-1958) will be listed in the following manner: (5.467) = volume 5, section 467. Carolyn Eisele's edition of The New Elements of Mathematics by C. S. Peirce, volumes 1-4 (Mouton: 1976) will be listed by volume and page number: (Eisele 3:387) = volume 3, page 387.

=One= The Principles of Jakobsonian Markedness Theory

Gesamtbedeutung and a Definition of Markedness There is no SIGNATUM without SIGNUM.-Roman Jakobson

The goal of any linguistic analysis is to describe or explain a particular phenomenon of language, and a multitude of approaches can be applied to achieve this goal. Whatever the approach, however, the linguist is faced with the problem of describing what is potentially infinite in a finite, meaningful manner. One means of linguistic analysis is based on the principle that there are certain invariants in language which recur at different levels within the structure of any given language and which generate a multitude of variations. Roman Jakobson, in the Saussurian tradition, is one of the greatest champions of explicating a theory of invariants by distinguishing between general versus contextual meaning (or Gesamtbedeutung and Grundbedeutung) in morphology and semantics. Jakobson's major contribution to establishing a theory of general meaning came in his 1936 analysis of the Russian case system. In this pioneering work, Jakobson demonstrated that the various uses of each of the six Russian cases can be described in terms of three invariant, semantic features. Later, in his 1958 article, "Morfologiceskie nabljudenija nad slavjanskim skloneniem," Jakobson expanded his definition of these three semantic features, further demonstrating their relationship to the morphology of the case system. In these two major works and in other morphological studies, Jakobson combined the principle of Gesamtbedeutung (or general meaning) with semantic features, defining them in terms of the marked/unmarked relation-

10

Markedness Theory

ship. In his article "Shifters, Verbal Categories, and the Russian Verb" (1957) Jakobson defined the relation marked/unmarked as follows: the marked term gives the statement of a property A; the unmarked term can be divided into two components: (1) a general meaning = nonstatement of A; (2) a specific meaning = statement of non-A. I Gesamtbedeutung is given in every instance by means of a marking (or feature) or a bundle of features. Therefore, the definition of markedness in morphology includes both a general and a specific meaning, whereas the definition of markedness in phonology does not provide for a distinction in the unmarked term; only the "specific" definition occurs. Note the diagrams in figure l. Of course, Jakobson's theoretical approach has frequently been criticized on the premise that although such analyses are elegant, they are inherently unverifiable, are not self-explanatory, and have very limited predictive power, so limited that Wierzbicka, in The Case for Surface Case, argues that "the predictions they generate are very often incorrect" (198o:xv). Wierzbicka goes on to say that Jakobson's formulations are "too vague, too general to be empirically adequate" (xvi), Figure

1

Universe

In General:

Thus, I. General Meaning A. Marked: Statement of A B. Unmarked: Nonstatement of A

II. Specific Meaning A. Marked: Statement of A B. Unmarked: Statement of non-A

@© @© A.

B.

A.

B.

Principles of Jakobsonian Theory

11

and she also criticizes form-content linguistic analyses in the Diverian school (cf. Garcia) as suffering from the same lack of specificity, the same vagueness and unverifiability. As an alternative to looking for one invariant definition for each case category, Wierzbicka proposes an invariant meaning for each different "surface" manifestation of the Russian instrumental case. She gives seventeen invariant meanings for the instrumental and claims each to have full predictive power. Thus, she counters the validity of positing one invariant meaning for a given case and, in exchange, proposes seventeen so-called invariant meanings. Therefore, Wierzbicka does not abandon the notion that invariant meaning exists, but she redefines the line between invariance and variation, broadening the potential variation of invariance. Wierzbicka's accusations would be valid complaints against the Jakobsonian approach if Jakobson, concluding his linguistic analysis with his 1936 case study, had failed to further develop his conceptualization and application of Gesamtbedeutung. However, this is not the case. Rather, these early articles represent only Jakobson's first step in working toward a cohesive theory of meaning using the principles of invariance and markedness. Henrik Birnbaum has taken a slightly different approach in arguing against a theory of general meanings. Citing such eminent Slavic scholars as Potebnja and Kacnel'son, Birnbaum restates the question asked by Kacnel'son: Why should linguists, knowing very well that polysemy and synonymy exist in language, renounce these realities in search of some abstract belief in the isomorphism of form and content? Birnbaum concedes that Gesamtbedeutung is most likely "a genuine reality of language and not merely a construct invented by the linguist," but he ultimately decides that the concept is not terribly useful "when it actually comes to analyzing a grammatical form's overall meaning" ([in press]:7-8). As an example of the futility of working with general meaning, Birnbaum notes that Jakobson "compellingly illustrated his conception of general meaning as an invariant of lexical semantics," although he concludes his argument by pointing out that Jakobson did not develop "a systematic theory of general meaning of the lexicon" (21-22). However, C. H. van Schooneveld, working within a Jakobsonian framework, undertook precisely that task of developing a systematic theory of general meaning for the Russian

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Markedness Theory

lexicon (van Schooneveld: 1983, 1985). Although van Schooneveld has not completed his analysis of the Russian lexicon, his work to date is convincing in its own right. Unlike Wierzbicka and Birnbaum, I have argued that the quest for general meaning can be meaningful, can have descriptive power, and can provide a powerful pedagogical tool (Andrews 1984b, 1985a, 1986d, 1987a). The search for and application of general meaning can be a useful tool, even the essential one, in linguistic analysis. In the process of looking for general meanings, complex linguistic structures can be related and elucidated. Peircean semiotic theory, too, in particular Peirce's theory of interpretants, stresses the quest for general meaning. As Elizabeth Bruss states: "The meaning of a concept must be general, it cannot be exhausted on any single occasion of use but must extend to ever new instances. Peirce's logical interpretant is therefore a rule of interpretation which includes all possible uses and all possible users" (Bruss 1978:84). According to Peirce, the interpretant is the rule or law that permits the translation of the sign. Thus, we can derive a fundamental connection between Jakobson's definition of general meaning and Peirce's notion of interpretant. The inadequacy of the theory of general meaning, as described by its critics, seems actually to reflect a criticism of the manner in which the concept has been applied, not the concept itself. To make Gesamtbedeutung a useful concept, the linguist is faced with the task of avoiding extreme abstraction, which indeed is not always easy. However, there are ways to avoid this problem. Whenever a particular morphological or semantic phenomenon is being analyzed, the linguist must never stray too far from the actual linguistic data itself, even for the sake of theoretical elegance. If, in our quest for Gesamtbedeutung, we are better able to understand the languages we study, then such a quest is justified. However, we must at no time forsake detailed examination of language, which is our only true, measurable data, for vague abstractions. General meaning, if correctly applied, does not demand such a sacrifice. Erica Garcia succinctly states what the goal of linguistic analysis should be: A better understanding of that process which necessarily underlies the use of language, namely the creative synthesis of a coher-

Principles of Jakobsonian Theory

13

ent gestalt from a few abstract, well-defined clues. That knowledge will never be gained by solipsistic contemplation of elegant models. We must face up to the fact that language is used (and known!) by people, and consequently get our hands dirty with the nitty-gritty of controlled experimental research. (in press) It is precisely this point of view that the following chapters will exemplify: a theoretical demonstration of the need for understanding the structure of form in order to determine meaning.

A Brief History of Markedness: From Trubetzkoy to the Present Roman Jakobson first proposed the oppositional relation of markedness in 1921 (Holenstein 1976:126). The terms marked/unmarked (originally priznak in Russian, and secondly merkmal in German) were introduced and applied by Nikolai Trubetzkoy in his 1931 article on "Die phonologischen Systeme." The German term was "Merkmalhaltigkeit"-the property of containing a distinctive mark. However, Trubetzkoy's conception of markedness applied strictly to phonology. As early as 1927 Jakobson had already formulated certain notions which were later to serve as the basis of his definition of morphological markedness. Specifically, Jakobson addressed the idea of "correlation" as binary opposition in his Proposition to the First International Congress of Linguists, which was cosigned by Karcevskij and Trubetzkoy (1928): "A phonological correlation is constituted by a series of binary oppositions defined by a common principle which can be conceived independently of each pair of opposite terms." When Jakobson brought his theory to the United States, he adopted the phrase "distinctive feature," which was used by Leonard Bloomfield, for the German term merkmal (Bloomfield 1933:79). As a markedness theory began to take shape in those early days, the notion of binary opposition became very important in defining markedness relations. Yet, even in the early days of the Prague School, the two major figures of that school did not agree on what "markedness" meant. Specifically, Jakobson and Trubetzkoy defined the term "opposition" in very distinct ways.

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Markedness Theory

Trubetzkoy, never a proponent of the theory of purely binary oppositions in phonology, developed three types of phonemic oppositions: (1) Privative-Two phonemes are identical except that one contains a "mark" which the other lacks (e.g., /b/ vs. /p/). (2) Gradual-Different degrees of some gradient property (e.g., /i/ / e / rv / c.e /). (3) Equipollent-Each member has a mark that the others lack (e.g., / p / rv / t / rv / k /) (Sampson 1980 :108) 2

f"'J

Jakobson, long a proponent of binary opposition, on the other hand, expanded and modified his theory of binariness to encompass morphology and semantics. However, the primacy of binary oppositions in linguistic systems is not universally accepted. Although Jakobson firmly adheres to the notion of asymmetrically defined binary opposition, where the unmarked term is not on a par with the marked term, the phonological distinctive features define the relationship marked/ unmarked differently from the morphological conceptual features. In phonology, a given feature (e.g., voicing) is either present or absent in a particular class of phonemes (or, possibly, indifferent to the feature, as the feature sharpness is not applicable to vowels). Therefore, the opposition in phonology is privative, whereas in morphology, marked means the necessary presence of an element, while unmarked means the element mayor may not be present-it is simply not specified; therefore, unmarked does not merely imply negation. In short, the phonological features can be viewed as forming mutually exclusive sets (as shown in figure 1 under specific meaning), while the morphological features form an inclusion relationship. In his theory of morphological markedness Jakobson clearly does not equate the unmarked element with the element that occurs most frequently in syntagmatic contexts. Rather, Jakobson bases his determination of the marked/unmarked pair on the presence of a property of meaning. These "properties of meaning" are defined as intrinsic properties given by the linguistic system itself, not by external reality (1967:671). The fact that Jakobson views the linguistic system as defining its own order of reality does not prohibit a potential relationship between linguistic and extra-linguistic phenomena. Yet, Jakobson does state that the intrinsically defined properties and relationships

Principles of Jakobsonian Theory

15

of language should be analyzed first before considering extrinsically defined properties and relationships, implying that the linguistic object is defined within the linguistic system proper and is not the same thing as an object in reality. An important concept related to Jakobson's distinction between intrinsic and extrinsic relationships is the notion of relative autonomy. Thus, linguistic signs within the linguistic system are defined in terms of oppositional relations, which are relative, while the linguistic object is necessarily autonomous of extralinguistic reality. In order to fully appreciate the importance of relative autonomy, Peirce's definition of the sign-object relationship becomes essential. Of particular interest is the notion of iconicity, the first of three sign-object relationships defined by Peirce. For Peirce, an icon is "a sign which stands for its object because of some similarity to that object" (Fitzgerald 1966:55 [italics mine]). Furthermore, "the only way of directly communicating an idea is by means of an icon; and every indirect method of communicating an idea must depend for its establishment upon the use of an icon ..." (Peirce 2.278). Therefore, in language all forms of signified-signifier relationships, insofar as they convey ideas and make reference, must be iconic. The degree of iconicity inherent in a given signified-signifier relationship depends on the relative hierarchy, since icons do not occur alone and may only occur in combination with other types of signs, namely symbols and indices (Fitzgerald 1966:55). Examples of iconicity in language include the following: (1) plural versus singular nominal forms, where the plural, meaning "more than one," in many instances has an additional affix (cf. English "table/tables"); (2) positive, comparative, and superlative adjectives that show an increase in the number of phonemes in the affix (cf. English "big/bigger/biggest"). [For more examples of iconicity, see Jakobson 1971C:351-59.] The above discussion would be incomplete, of course, without asking how "similarity" between the sign and its object is determined. According to Peirce, this similarity is not created by the interpreter but, rather, is a given within the ground of the relation. In other words, the interpreter does not establish or create the similarity-he merely uses it (Fitzgerald 1966:46-48). An iconic relationship unused remains a merely potential iconic sign, but nonetheless iconic it remains. Those linguists and schools of linguistics which have adopted some

16

Markedness Theory

form of markedness theory can be divided into two major groups: (1) those who work with meaning, and (2) those who attempt to describe language as a purely "formal" system without utilizing meaning. In particular, the Generative school redefined markedness relationships as properties derivable from a syntagmatic context in phonology, excluding any application of meaning. Noam Chomsky and Morris Halle, for example, redefined phonological markedness features for English based on distributional criteria in the form of general rules. The fundamental difference between Jakobson's work in phonology and that of Chomsky and Halle is the need, in Jakobson's theory, for a distinct phonemic level in phonology. Halle criticizes the phonemic level in The Sound Pattern of Russian on the grounds that its presence prevents the statement of certain linguistic generalizations on their simplest level. However, most of Chomsky's and Halle's objections to the difficulties involved in maintaining an autonomous phonemic level can be resolved by granting that the phoneme is not the basic phonological unit in language. Rather, it is the distinctive feature which is the minimal phonological unit in language. Jakobson has carefully defined distinctive features as invariant oppositions which are paradigmatically given and are fundamental to both speech perception and production: "Any distinctive feature exists only 'as a term of relation'" (1971a:641-42).3 Phonological features defined by syntagmatic properties (cf. tenseness and gravity in the Russian vowel system) are distinct, but not distinctive, units. Distinctive units require the paradigmatic axis (the axis of replacement) in order to find positions of contrastive distribution (Schane 197}:40).4 Joan [Bybee] Hooper, working in the area of natural generative phonology, defines markedness in phonology by describing the unmarked term as a more "natural" and the marked term as a less "natural" phenomenon (1976:1}6). Hooper makes an additional point that "markedness" and "naturalness" are not two separate notions but are both derivable from a single set of rules (1976:135). In terms of rule development Hooper makes significant progress by including only phonological rules that have no exceptions with regard to surface forms. Leonard Babby's application of generative grammar to Russian uses two types of markedness-one having nothing to do with meaning and another which is loosely based on the Jakobsonian definition.

Principles of Jakobsonian Theory

17

Specifically, Babby adopts the terms "case marking" and "markable" from J. Ross. A case marking is a transformation that "marks every MARKABLE element of a NP (noun phrase) except elements dominated by a S (sentence)" (Babby 1975:164-65). In other words, a "case markable" element is any root or stem to which a case ending can be attached, that is, nouns and adjectives (in Russian, Babby means specifically long-form adjectives), but not adverbs and short-form adjectives. In his other application of markedness, Babby claims that the long-form adjective in Russian is "marked," in the Jakobsonian sense, for "reference to the subject's class," while the short-form adjective is "unmarked" in the same sense. Babby further states that "the unmarked term always has a wider range of meaning than the marked term" (1975:2°9). Since the transformational base that Babby sets up to analyze the short-form/long-form adjectives in Russian does not include "meaning," it is inconsistent to attempt to apply Jakobsonian markedness theory and to define the "property" of meaning of the long-form adjective without any reference to a consistent "system" of meanings. While Babby works with only one type of meaning, Jakobsonian linguistic theory necessarily distinguishes paradigmatic, or invariant meaning, from syntagmatic, or contextual meaning. In any Jakobsonian-based markedness theory a clear distinction must be maintained between paradigmatic/invariant meaning, given by the marking, and contextual/variant meaning, which is not necessarily a property of the paradigmatic base. (This statement is not meant to imply that context is the same thing as contextual meaning. As I will show in the following discussion of deixis, context can be coded into the linguistic structure itself. And it is context, as defined via Peirce's interpretant, that will find its place in the semiotic structure of meaning.) Later developments of generative theory in phonology have not been so preoccupied with markedness, but have demonstrated a distinct movement toward reconciling rule development more closely with actual surface forms (Anderson 1985:336-47). Representative of those linguists who have applied markedness theory with meaning as an integral component are Joseph Greenberg, John Lyons, and C. H. van Schooneveld, to name just a few. Particularly important to my discussion will be van Schooneveld's system of features of perception, which he developed to describe grammati-

18

Markedness Theory

cal and lexical meaning in modern Russian. Van Schooneveld's work is of particular interest because it continues and develops the Jakobsonian definition of markedness in terms of features of perception. Van Schooneveld's features share certain definitional principles with those that Roman Jakobson described in his 1936 article, "Beitrag zur allgemeinen Kasuslehre," and characterized more definitively in his 1958 article, "Morfologiceskie nabljudenija nad slavjanskim skloneniem." In A New Invitation to Linguistics Greenberg begins his discussion of "marking theory" by pointing out the intuitively natural "priority" a particular grammatical form seems to enjoy. For example, no one looks in the dictionary for the word "large" under the entry "larger." Therefore, he states, markedness is an "aspect of hierarchy" (1977: 53-54). Greenberg further suggests certain characteristics of the unmarked versus marked categories. As I will demonstrate in the following chapters, these so-called characteristics, such as the unmarked form's occurring more frequently, the marked form's usually having an additional morpheme, etc., are not axioms or theorems of markedness theory and can play no role in determining which elements are marked and which are unmarked. One further comment on Greenberg's work on markedness theory is appropriate here. Greenberg's Language Universals (1966) is devoted to establishing the concept of markedness as a language universal, applicable to phonology, morphology, and semantics; in other words, to establishing markedness theory as semiotic principle. It. is this view that I will attempt to clarify by connecting Jakobsonian markedness theory to C. S. Peirce's theory of interpretant. John Lyons offers a different perspective on the concept of markedness than is found in Greenberg's work. Instead of attempting to set up markedness as a language universal, Lyons views the theory as a concept that has been manipulated in such a way as to describe "a number of disparate and independent phenomena" (1977:305). Focusing his discussion and application of markedness theory to lexemes, Lyons distinguishes three types of lexeme markings. Like Greenberg, however, Lyons allows distributional criteria to influence his definition of markedness. (An in-depth discussion of Lyons' types of lexeme markings can be found in chapter three.)

Principles of Jakobsonian Theory

19

C. H. van Schooneveld has developed a markedness theory that encompasses new notions of how semantic features and deixis are defined, while consistently applying Jakobson's fundamental definition of markedness for morphology. Most of van Schooneveld's research has been devoted to analyzing the categories of grammatical and lexical meaning in Russian, using features of perception, which represent the properties of meaning expressed by marked/unmarked oppositions. In order to develop a theory of markedness, it is first necessary to define the morphological features as they were used by Jakobson and van Schooneveld in their analyses of Russian. Only after this step has been taken will it be possible to fully uncover the underlying principles of markedness relations as defined by this work. Jakobson's and van Schooneveld's Morphological Features In Jakobson's works on the Russian case system he derives three features based on general unified meanings to generate the Russian cases. The Russian case system consists of six so-called "full" cases and two "accessory" cases. Jakobson names his three features directionality (napravlennost'), marginality (periferijnost'), and quantification (ob"emnost') and sets up the case markings as follows: Nominative Case = Unmarked (0) Accusative Case = Directionality Instrumental Case = Marginality Dative Case = Directionality and Marginality Genitive Case (-u) = Quantification Genitive Case (-a) = Directionality and Quantification Locative Case (-u) = Marginality and Quantification Locative Case (-e) = Directionality and Marginality and Quantification Jakobson defines directionality as "the statement of the existence of directness" (1936:67); thus, the accusative case indicates the goal of the verbal process. Marginality defines a phenomenon of "peripheral status," that is, a background phenomenon (Jakobson 1936:82). Hence, the instrumental case represents an object that is replaceable

20

Markedness Theory Gen-u (+Quant)

~ - - - - ~ Gen-a

(+Dir,+Quant)

N om (-------+----fAcc (0) (+Dir)

Instr. (+Marg)

L--

Figure

Loc-u (+Marg, +Quant) __

Dative (+Dir,+Marg)

2

in, as well as non-central to, the content of the utterance. Quantification indicates that the referent's involvement in the content of the utterance is limited (Jakobson 1936:72); thus, the genitive case in -u serves as an example of how the notion of limitation becomes an expression of pure quantity. The markings for the Russian case system listed above can be represented by a cube as seen in figure 2. 5 Van Schooneveld's work on the Russian prepositional system and his analysis of the lexical meaning of the Russian verb took Jakobson's initial attempt to define morphological features a step further. He discovered the existence of six conceptual features, hierarchically ordered, that are capable of defining the invariant properties found in both grammatical and lexical categories (1978b, 1978c). These six features will be defined briefly in the following section, using examples from both grammatical and lexical meaning. 6 Van Schooneveld's six features can be presented in terms of a modified and a modifier-the two elements involved in every modification situation. The modified (MO) is the element being "restricted" while the modifier (MR) is the element that "restricts." (It should be noted that this approach is only one way of representing the perceptual features. My choice to define the features in terms of a modifier and modified is intended to achieve a greater degree of concreteness. Following a definition using the modifier/modified dichotomy, a more general definition of each feature will be offered.) In a basic noun phrase, the adjective is the modifier and the noun is the modified. In a sentence with a subject (noun) and a verb, the subject is the MO, the

Principles of Jakobsonian Theory

21

verb the MR. Each definition will be accompanied by prepositional examples from Russian. The first feature in the hierarchy, plurality, can be defined as follows: plurality creates a set in the universe and states that there will be more than one element. This fact implies that there will always be at least one MD and one MR in the prepositional system. Therefore, every preposition in Russian must have an object, but the prepositional object may be implicitly or explicitly stated. In general grammatical terms plurality defines the plural number one- and two-argument (or transitive) verbs (see figure 3). In more general terms plurality sets up "a multiple of perceptions" (van Schooneveld 1987:127). Examples of plurality from the sphere of grammatical meaning include the substantival plural, verbal passive, and the adjectival comparative. The second feature, dimensionality, creates a subset from the set given by plurality. In particular, dimensionality gives outlines to the MR, that is, it adds a second and, frequently, a third dimension to the MR because dimensionality is more "restricting" in its focus, limiting the number of points that remain perceivable. Note the following prepositional example: stol (MD) stoit v komnate (MR) = "The table is (standing) in the room." (The preposition v (in) is marked for dimensionality.) Dimensionality sets up the "room" as a container of the "table" (MD). In general terms dimensionality "assumes a set as background, but considers relevant only a segment [or subset] of this set as its perceptional objective" (van Schooneveld 1987:128 [brackets mine]). Dimensionality necessarily implies plurality and its very definition is dependent upon plurality.? Dimensionality is the feature marking of the perfective aspect in Russian (van Schooneveld 1978b) (see figure 4). Figure 3 Universe

MR o

MD o

22

Markedness Theory

Roo

MR

Figure 4

MR

MD

------[>

Order of perception

Figure 5

Van Schooneveld's third feature, distinctness, sets up more than one subset in such a way that the MD and MR must be perceived as distinct -they cannot merge. Furthermore, distinctness sets up an ordering of perception such that perception is directed from MR to MD, regardless of the observer's actual orientation (cf. the feature dimensionality, where the MD merges with the MR [cf. "the table is in the room"]). Note the following example: Mal'cik (MD) sidit za stolom (MR) == "The boy is sitting behind/at the table." In this case the "table" and "boy" must be viewed as distinct. The mandatory distinctness of MD and MR does not necessarily imply that there can be no contact between MD and MR (cf. Mat' vzjala rebenka za ruku == "The mother took the child by the hand"). The feature distinctness creates a subset within dimensionality such that the referent (as subset) must be identified by a previous perception situation (van Schooneveld 1987:132-33). This identification of a once-occurring choice of subset is part of the linguistic code. The phenomenon of verbal conjugation (in Russian, the indicative mood) is an example of grammatical distinctness (see figure 5).

Principles of Jakobsonian Theory

23

The fourth feature, extension, presupposes the existence of the two distinct, unrelated phenomena given by distinctness and also establishes a relationship between the two. Extension corresponds to Jakobson's feature directionality. Note the following example: Soldat (MD) sel po ulice (MR) == "The soldier was walking down the street." Here, the "soldier" and the "street" are connected only during the given narrated event. Extension, the first feature of the second triad of features, interestingly enough, resembles to a certain extent the first feature of the hierarchy, plurality. Extension calls for reidentification of the referent and, thus, introduces the concept of time into the semantic system (van Schooneveld 1987:134). The imperative mood in Russian is an example of extension (see figure 6). The fifth feature, restrictedness, cancels the tie between MD and MR that was established by extension. Thereafter, the MR will simply remain as a reference point. For example in Etot professor (MD) iz Leningrada (MR) == "This professor is from Leningrad," iz indicates that Figure 6

MR

MD

Figure 7

MR

MD

24

Markedness Theory

Figure 8

the MD (the professor) is no longer directly connected with the MR (Leningrad). Restrictedness corresponds to Jakobson's feature mar-

ginality. Restrictedness designates a cancellation between an initial and second period (or space) where only the second period remains relevant to the content of the utterance (van Schooneveld 1987:134). The past tense in Russian is an example of grammatical restrictedness. The sixth and final feature in the hierarchy, objectiveness, states that the MR is "potentially maximally distant" from the MD and, hence, no further subsets are derivable. Note the following example: Ona umerla (MD) pri Staline (MR) = "She died during Stalin's time." In this example the MR (Stalin) was present in the universe of the MD at the time the MD (she) "died." The MR is remotely connected to the MD and may indirectly be responsible for the resulting state of affairs. Objectiveness corresponds to Jakobson's case feature quantification. Objectiveness provides for an initial and a second space of equal importance, and the referent is necessarily maximally independent of both spaces (van Schooneveld 1987:135) (see figure 8). The hierarchical relationship formed by the six conceptual features can be represented by figure 9. Two points are essential in summing up the remarks given above. First, each conceptual feature defines a "range of reference," that is, the range of identifying a modifier (as referent) (van Schooneveld 1987:135). This way of conceptualizing the morphological features finds a nice parallel in Thorn (1983:270): "It must not be forgotten that above all signs are forms in space-time, and that consequently their spatio-temporal localisation is one of the first factors to consider." 8

Principles of Jakobsonian Theory

25

Second, each feature in succession contains information of the preceding feature (hence, the inclusive definition), and, thus, the definition of each later feature in the hierarchy is dependent on the previous one. A similar phenomenon is seen in Peirce's definition of the categories of firstness, secondness, and thirdness, where the definitions of secondness and thirdness are impossible without firstness (cf. chapter two). Before we can undertake a more detailed analysis of van Schooneveld's features in the context of Peircean semiotic theory, however, we need to address a fundamental question of terminology: the difference between the terms "mark" and "feature." In fact, what on one level seems to be a relatively trivial difficulty is actually indicative of a deep-rooted confusion tied to the definition of markedness itself. The following section is an attempt to resolve this confusion for the theory of markedness presented here. Mark or Feature?

In 1974 Jakobson wrote an article entitled "Mark and Feature," in which he attempted to clarify some of the difficulties associated with certain definitional terms of the fundamental concepts of markedness theory. Unfortunately, the article itself has been a further source of Figure 9

26

Markedness Theory

confusion. One of the most problematic points is Jakobson's evocation of Hendrik Pos's definition of the concept of opposition. Although Jakobson repeats Pos's claim that "the presence of one term [of an opposition] necessarily educes the other" (1974:122), this definition does not hold for Jakobson's phonological or morphological features. Specifically, since the distinctive as well as the conceptual features are defined asymmetrically (cf. Jakobson, van Schooneveld), Pos's statement is only partially true, that is, true in one "implicational" direction. For example, in the opposition "voiced/voiceless," the presence of "voicing" implies "voiceless," but the opposite case does not hold -"voiceless" does not imply "voiced." In general, it should be noted that Jakobson did not waiver theoretically in his conviction that all such oppositions were asymmetrical, but in practice inconsistencies did occasionally arise (cf. compact/diffuse, instead of compact/noncompact, diffuse/non-diffuse). What precisely is the difference between mark and feature? Apparently, due to various permutations and translations via German and Russian, "mark" came to mean, in addition to its original definition as the presence of a more restricted pole of an opposition, the same thing as a distinctive feature (Jakobson 1974:123). The feature, called distinctive in phonology and conceptual (or semantic) in morphology, is the element that defines the invariant property or relationship of a given form. In phonology, distinctive features can be defined acoustically or articulatorily, but in morphology and semantics, the conceptual features are defined differently by different scholars. Jakobson and van Schooneveld, for example, define these features in a hierarchy, as paradigmatically given invariants. Jakobson found three features in his analysis of the Russian case system (1936, 1958); van Schooneveld posits six features in his analyses of the Russian prepositions, paratactic conjunctions, and Russian parts of speech (1960, 1978c) [cf. previous section]. For a specific example of the potential confusion of mark and feature, consider the Russian phonemes / t and / z /. These two phonemes differ by three distinctive features, as shown in figure 10. In general terms, one could state that the phoneme / t is relatively unmarked with regard to / Z /, or that / z / is relatively marked with regard to / t' /. Any statement of markedness in absolute terms would I /

I /

Principles of Jakobsonian Theory

27

be meaningless since there is no element in language, either in phonology, or in morphology or semantics, that is totally unmarked. Even the so-called unmarked element of an opposition (cf. the nominative case, the imperfective aspect) is nevertheless a part of a more general grammatical frame category. With reference to the example above, one could further state that / t' / is marked for sharpness, whereas / z / is unmarked for sharpness. Likewise, if / t' / is marked for sharpness, / z / is marked for continuancy and voicing (see figure 10). Van Schooneveld's morphological studies are systematic applications of markedness theory using conceptual features similar to those that Jakobson presented in his studies on Russian case (193 6, 1958). Here van Schooneveld seems to be taking the next logical step after establishing the markedness relationship of two categories. That is, he not only demonstrates which category is marked and which unmarked, but goes on to answer the question, "For what is the category marked?" Markedness theory can only realize its full potential and power as a theoretical framework, in my view, when this final step is taken. It is not sufficient simply to establish that two categories fit the marked/ unmarked relationship. As shown above with the Russian phonemes It'l and I z I, this statement is necessarily a relative one, and if no feature is ever posited, one ends up with a linguistic system full of M's and U's (marked and unmarked), but with no further discriminatory principles for distinguishing a perfective verb from a noun in the instrumental case. In this example, both categories are marked, but not vis-a.-vis each other, and for entirely different features. The extension from mark to feature brings us a step closer to understanding the intimate philosophical similarities between Jakobsonian markedness theory and Peirce's notion of interpretant. A conceptual feature in morphology is, for Jakobson and van Schooneveld, a relaFigure

10

/ t' /

+ sharp - continuant - voiced + consonantal

/z/

- sharp + continuant + voiced + consonantal

28

Markedness Theory

tionally determined, paradigmatically defined invariant that is part of every (potentially infinite) occurrence of a given form (signifier/SR). The feature is neither interchangeable with, nor actually, the signified (SO), or meaning of the SR, just as the feature directionality (Jakobson, 1936, 1958) is not the same as the accusative case. Rather, the feature, in this case directionality (or van Schooneveld's extension), is what Peirce calls an interpretant of the sign. Just as in Peircean logic the sign is tripartite (consisting of sign, object, and interpretant), so Jakobsonian markedness theory can be similarly defined using the SR, SO, and feature: Signifier Sign

Signified Object

9

Feature Interpretant

While Jakobson does not ever explicitly make this connection, our doing so is not a deviation from the fundamental theoretical principles established in Jakobsonian markedness theory, and what results thereby is a logical, even a necessary, extension of the Jakobsonian notion of sign. Shapiro (1983:97) makes significant progress in developing a Peircean theory of grammar by recognizing the crucial role of interpretants and, more important, of grammatical rules as interpretants: "Besides their status as interpretants, in a semeiotic theory of grammar rules cease to be viewed as divorced from the sign relations they implement. Rules are perceived necessarily as representing the relations constituting units and contexts and their hierarchies" [italics mine]. I am restricting the role of interpretant, however, by defining only distinctive and conceptual features as interpretants, not contextually defined, syntagmatic rules such as A ~ B/_C (that is, A goes to B in environment C). If the role of interpretant is limited in this way, interpretants will be more closely bound to categories of perception. Just as interpretants are fundamental to a Peircean grammar in order to understand, or translate, a sign, so the determination of a feature marking is fundamental to establishing a Jakobsonian-based grammar, or, linguistic calculus. One final point, which will be discussed in chapter 4 from a slightly different perspective, concerns the notion of markedness reversal. Like Andersen and Shapiro, working within the framework of a

Principles of Jakobsonian Theory

29

Peircean grammar, Jakobson sees no logical inconsistency in allowing reversals to occur in the synchronic linguistic system. My own argument, further, is that by definition the interpretant of a given sign/ object relationship cannot be "divorced from the sign relations [it] implements" (Shapiro 1983:87). Therefore, if the conceptual feature is an interpretant, it cannot be reversed or neutralized in synchrony. Rather, that feature, as interpretant, is an invariant and can only shift in time. 1O Finally, in view of the fact that Jakobson and van Schooneveld work with very few conceptual features (Jakobson-3, van Schooneveld-6), we must keep in mind that interpretants, like features, of one sign can also be the interpretants of another sign. Shapiro points this out in the following two statements: Every sign is at least potentially an interpretant of some othe~ sign, to which it is related through their shared object. In terms of antecedent and consequent, every sign is at least potentially the interpretant of an antecedent sign, and is interpreted by some consequent sign, which stands to the first as its interpretant. (Shapiro 1983: 48) Sign and interpretant are distinguished from each other by the fact that the interpretant is determined by the sign, whereas the converse does not usually hold true. (Shapiro 1983:48; Eisele 3: 839) Van Schooneveld, in developing a theory of deixis, has come directly to terms with the role of context and the question of its codification into the linguistic system. In other words, through deixis we come to understand how every sign can become an interpretant of another sign because deixis, by definition, codifies types of observers into the linguistic forms themselves.

Deixis: A General Definition "The conception of form lies in the desire to distinguish.If-G. S. Brown

In addition to a theory of conceptual features, van Schooneveld has also contributed to Jakobsonian-based markedness theory by developing the concept of deixis in linguistic sign systems. In traditional

30

Markedness Theory

terms deixis is defined as the act of making reference, or linguistic "pointing," to a particular spatial or temporal point within a specific utterance. In other words, deixis refers to the function of such grammatical and lexical features as verbal tense and the personal pronouns, which limit the term(s) to a particular point in time and space (Lyons 1977: 636). C. S. Peirce had a special designation, the Index, for deictic signs. An indexical sign in linguistics is a word that has no relevant meaning unless one is present at its utterance. For example, the words "I," "you," "now" are all deictic signs in that all are specific to a given speech situation. As Lyons states, "The addressee must be able to identify the referent of 'I' and also the referent of 'you'; and this implies that he knows that he is being addressed" (1977:575). Thus, the referent of a deictic sign "shifts," that is, varies, from one speech situation to another. In Saussurian terms, through deixis the parole is recodified into langue, that is, deixis is coded into the linguistic signifier and is an invariant of linguistic structure. The above definitions of deixis, however, all refer to only one type, which van Schooneveld calls transmissional deixis. An additional important component of transmissional deixis, as defined by van Schooneveld, is the presupposition of an observer of the given parole, where the observer is necessarily both speaker and addressee(s) (van Schooneveld 1983:161-62). Clearly, words such as sejcas == "now," ja == "I," and zdes' == "here" (representing temporal, person[al], and spatial deixis in all of their contextual occurrences) require the existence of an observer intimately connected with the given speech situation so that the referent defined by the temporal, person[al], or spatial deictic forms is identifiable. The speech situation, not being merely the act of emitting sound waves, includes all the observers who can potentially perceive the utterance and the identification of the surroundings in which the utterance occurs. Yet, how do we define the potentially deictic (that is, deictic in the traditional sense) relationship of words such as blizko (close[ly], nearby)? In the sentence On iivet blizko (He lives nearby), blizko sets up a relationship between the speaker and the subject of the sentence, which is determined by the given parole. However, blizko in the sentence Eto staroe, sinee zdanie naxoditsja blizko k Bol'somu teatru

Principles of Jakobsonian Theory

31

(That old, blue building is located near the Bolshoi Theater) does not set up a relationship directly involving the speaker and addressee, nor is this relationship determined by the given parole. The observer (or observers) presupposed by forms such as blizko is not necessarily restricted to the speaker and addressee, but can include an "objectivized" observer who is completely unconnected to the given utterance. Since any observer can perceive the spatial relationship between "that old, blue building" and the "Bolshoi Theater," this relationship, created by the word blizko, is a constant, existing both prior to and subsequent to the actual parole. Therefore, the relationship between the two buildings is defined by the narrated situation, not by the speech situation. The narrated situation is defined as any event in exogenous reality, potentially involving any observer, that may include the given speaker and addressee in the class of observers. The example On iivet blizko presents a case where blizko behaves very much like the transmissionally deictic forms sejcas, ja, zdes', in that each of their referents is restricted to a particular speech situation. But blizko can also define referents given by a narrated situation. Therefore, zdes' and blizko are both deictic, but in two different senses. Forms such as zdes' are restricted to the speech situation specified by the given parole, whereas forms such as blizko can involve the speech situation or the narrated situation. Van Schooneveld calls the type of deixis represented by blizko perceptional deixis. 11 Perceptional deixis involves an act of perception by any observer, which can include the speaker and addressee (as participants in the speech situation), but which may include an observer who is not a participant in the given speech situation. Blizko is an example of "lexical" perceptional deixis, whereas non-count (collective) nouns, verbal transitivity, and verbal aspect are all examples of "grammatical" perceptional deixis (van Schooneveld 1983:162-63). "Dimensionality," as Leech defines it, is another example of a perceptually deictic phenomenon. Since perceptional deixis can include any observer, it is not restricted to the speech situation, but may extend to the narrated situation. Based on the above characterization of transmissional and perceptional deixis, it is clear that perceptional deixis is an "unmarked" type

32

Markedness Theory

of transmissional deixis, being unmarked for a particular relationship to either the speech situation or the narrated situation, whereas transmissional deixis is marked for reference to the given speech situation. In other words, any anticipatory reference to the transmission of the utterance, or speech event, is defined by transmissional deixis; deixis that anticipates a reference to the narrated event, however, is perceptional. In relation to van Schooneveld's six features, perceptional deixis enters the system with the feature distinctness. This means that distinctness, extension, restrictedness, and objectiveness are all, inherently, perceptionally deictic features. Beyond perceptional and transmissional deixis, as defined above, van Schooneveld also posits two related types of deixis occurring on another level. (Actually, these other two types are subsets of the perceptional and transmissional deictic types.) This more restricted level of deixis is called singulative deixis because there is only one, unique reference to either the narrated event or the speech event, depending upon whether we are dealing with singulative perceptional deixis or singulative transmissional deixis. In singulative perceptional deixis (designated by'" in van Schooneveld's works), a reference is made to one, unique narrated event. 12 This reference must be perceived by the speaker, by the addressee, and, possibly, by a "specified" general observer. Examples of singulative perceptional deixis are the personal pronouns, demonstrative pronouns, proper names, and the phenomenon of anaphora. In singulative transmissional deixis (designated by ""), however, one unique reference is made solely to the actual, given pronunciation of the utterance. No "linguistic forms" correspond to this type of deixis except the iconicity of the sequential arrangement of morphemes. Singulative transmissional deixis provides the mechanism for bounding one morpheme to another, and such "boundedness" is always asymmetrical. For example, in the Russian word novost' ("news, novelty"), the -ost' is bound to nov-, but nov- is not bound to -ost'. Consequently, singulative transmissional deixis provides the potential to perceive broad "categories" that distinguish between such linguistic phenomena as lexical meaning, word formation, part of speech, grammar, and agreement. Figure 11 was designed by van Schooneveld for analyzing the morphology of Russian. The exact meanings of the four types of deixis, perceptional, trans-

Principles of Iakobsonian Theory 33

missional, singulative perceptional, and singulative transmissional, can be clarified by C. H. van Schooneveld's explanation (also cf. van Schooneveld 1987:125-26). A warship is at sea. The ship receives a message (or parole) from shore. The message states, "There is an enemy cruiser in your area. Start looking for it." The ship's radar begins scanning the area. Here, transmissional deixis would be preoccupied with the incoming message (the speech event), whereas perceptional deixis would be preoccupied with scanning for the enemy cruiser in extra-linguistic reality (the narrated event). In order to define the two singulative types of deixis, however, the story above needs to be expanded. Suppose that the incoming message to the ship is in a secret code such that every sentence of the message is in a different code (that is, each code is maintained for only one specific utterance). It would be impossible to decode the latter part of the message without knowing the first part. In this case the focus is completely on the actual pronunciation of the message and nothing more, that is, on a very restricted, once-occurring, speech event. This is precisely what singulative transmissional deixis does-it focuses on the pronunciation itself. Now suppose the message from the shore says, "Scan immediately or the enemy cruiser will be out of range." Therefore, the crew must begin scanning extra-linguistic reality at once because the command will be invalid next week, tomorrow, or even two hours from now. In this case we have an example of singulative perceptional deixis-the order is not valid outside of the moment in which it is acted upon, just as the referent of "I" is not an absolute. In marked/unmarked terms, perceptional deixis is the unmarked Figure

11

(/J" "

PL""

DIM""

DIST""

EXT""

RESTR""

OBI""

Lexical Meaning

WordFormation

Part of Speech

Grammar

Agreement

Agreement

Agreement

PL'

PL'

PL'

PL'

PL'

PL'

PL'

~

~

OBI'"

OBI'"

~

OBI'"

~

OBI'"

~

OBI'"

~

OBI'"

~

OBI'"

34

Markedness Theory

Perceptional Transmissional

~ ~ Figure

12

type of deixis since it refers to the narrated event, which is more general than and includes the speech event (see figure 12). Since each of the six conceptual features can occur on each of the four deictic levels, a total of twenty-four features is possible. In general, these six features occurring on four deictic levels (as shown in figure 11) can potentially generate 8.5 x 10 37 forms in modern Russian (that is, 2126 == 85,073,300,000,000,000,000,000,000,000,000,000,000). Deixis and Reference If nothing else is remembered from this work, the Jakobsonian tenet, There is no meaning without form, should remain with the reader, for every aspect of this work attempts to reiterate this principle, using linguistic analysis, mathematics, philosophy, and semiotics. Therefore, we are obliged to conclude that the form is inescapable and must play a role in linguistic analysis. According to the logician G. S. Brown, the form is the vehicle providing distinction, or differentiation, the key to the structure of meaning. Thus, each distinction, via the form, necessarily yields reference. Two types of reference necessarily occur in every distinction: (1) explicit reference to the "value" of the sign, that is, how it is marked; (2) implicit reference to an "outside observer" (Brown 1969:69). Explicit reference would be interpreted for Jakobsonian linguistics as the obligatory reference given by any signifier to its signified via the features it possesses. Implicit reference-a type more often ignored than noted-is an obligatory reference via the signifier to some deictically

Principles of Jakobsonian Theory

35

given observer. In fact, if we accept Brown's definition of implicit reference, we are led to accept that all forms must inherently possess some deictic referent in order to become meaningful. (This is precisely van Schooneveld's claim.) But Brown does not stop here. He goes on to note that "an observer, since he distinguishes the space he occupies, is also a mark" (1969:76). Van Schooneveld's theory of deixis supports such a statement in two crucial ways: (1) deixis is incorporated into the six semantic features and, hence, is part of the structure of the signified/signifier opposition; (2) all of these semantic features are spatially, as opposed to temporally, defined. Brown offers a very strong argument for the necessity of fixing the observer's position in order to make an expression meaningful. Briefly, Brown offers a Venn diagram representing the earth with brackets around the equator, Australia, and the South Island of New Zealand. Depending on the observer's spatial location, four different diagrams are possible (see figure 13). The four diagrams in figure 13 are not equivalent. Therefore, Brown argues, no expression is understandable without an indication of the observer's location (1969:102-3). Brown's requirement that an observer exist and be fixed in time and space parallels Peirce's requirement that an interpretant exist in order for the sign-object relationship to become meaningful. Figure 13

1. London

2. Cape Town

3. Melbourne

4. Christchurch

~ga

@~~b

@gc

36

Markedness Theory

Finally, van Schooneveld's system of deixis parallels Brown and Peirce by providing definitions for four such categories of observer, thereby giving linguistic science a key to understanding the role of context in a new way. Context, via deixis, is coded into the forms themselves. Therefore, it is both logical and consistent to assert that there is no meaning without a context and to mean that there is no meaning without deixis. Such a philosophy of the linguistic universe allows the linguist to search for invariants but requires the use of forms. Ultimately, this leads one to an understanding of the nature of reference and self-reference. As Brown has concluded: "Thus we cannot escape the fact that the world we know is constructed in order (and thus in such a way as to be able) to see itself" (1969:105). The Union of Conceptual Feature and Deictic Category: Shifters in the Russian Verb Roman Jakobson's analysis of "Shifters, Verbal Categories, and the Russian Verb" (1957) continues to be a major explication of the role of deixis in grammatical categories. Although his analysis focused primarily on the Russian verb, Jakobson was the first linguist to recognize the general importance of the relationships between the speech and narrated events (E S and En, respectively), as well as among their participants (P S , pn), in defining verbal categories. By defining the differences among verbal categories in terms of the speech and narrated events and their participants, Jakobson was able to define the Russian verbal categories using the same fundamental elements and, thereby, to go beyond the traditional definitions of the categories of mood, voice, tense, and aspect to a more profound level of linguistic analysis. Van Schooneveld's article, "Contribution a l'etude comparative des systemes des cas, des prepositions et des categories grammaticales du verbe en russe moderne" (1978b), presents a slightly different version of Russian verbal categories, in which the concept of deixis is expanded and each grammatical category is related to an invariant, semantic (or conceptual) feature. Specifically, the qualitative difference between categories such as voice and aspect, as opposed to mood and tense, can be stated in terms of perceptional versus transmis-

Principles of Jakobsonian Theory 37

sional deixis (van Schooneveld 1977a). By demonstrating that these two fundamental types of deixis are relevant to verbal categories, van Schooneveld has modified and expanded the entire concept of "shifter." By focusing now on the relationship between Jakobson's and van Schooneveld's work, we can determine the common denominator they share and make explicit the areas where their approaches differ. In doing so, the issue of which, if any, verbal category is more basic than the others and the relevance of establishing a hierarchy of verbal categories will also be addressed. I

Jakobson begins his analysis of verbal categories by defining the two basic vehicles of linguistic communication, message (M) and code (C), and their interaction (cf. message referring to message [M/M] [reported speech]; code referring to code [C/C] [proper names]; message referring to code [M/C] [meta-language]; code referring to message [C/M] [shifters]). Of the four structures given, only the last one, C/M, is defined by Jakobson as being deictic. Jakobson defines a deictic element as any element whose "general meaning cannot be defined without a reference to the message" (Jakobson 1957:131), and he calls such elements "shifters" (a term coined by Otto Jespersen), or, in Peircean terminology, indexical symbols. In order to better explain the nature of shifters, Jakobson translates the vehicles of message and code into the ultimate constituents of any communication act: the speech itself (s), the topic of the speech [or narrated matter] (n), the event (E), and any participants of said event (P), who necessarily include speaker and receiver. Thus, it is possible to combine these constituents to produce four defining categories: En = Narrated Event; E S = Speech Event; p n = Participant(s) of the Narrated Event; p s = Participant(s) of the Speech Event. Jakobson brilliantly organizes these categories in such a way as to define the exact relationship between the Russian verbal grammatical categories (see figure 14). To complete his analysis, Jakobson includes the concept of markedness and relates subcategories to each other as marked versus

38

Markedness Theory

P not involved

P involved

Non-shifter Shifter

Designator pn

Connector pnE n

gender/number

voice

pn/ps person

pn En/ps mood

Designator

En status/aspect En/E s tense

Connector EnE n taxis

En Ens /E s evidential

Figure 14

unmarked (cf. preterit vs. present [non-preterit], perfective vs. imperfective, plural vs. singular, etc.). (Jakobson had much earlier demonstrated the marked/unmarked correlations in the Russian verbal system in his 1932 article "Zur Struktur des russischen Verbums.") Before discussing van Schooneveld's extension of the shifter concept, it is appropriate to review the status of deixis as a linguistic concept. John Lyons presents an extremely detailed discussion of deixis and of how it has been used in linguistics, beginning with early Greek tradition (1977:636-724). In particular, Lyons defines deixis as a term referring "to the function of personal and demonstrative pronouns, of tense and of a variety of other grammatical and lexical features which relate utterances to the spatio-temporal co-ordinates of the act of utterance" (1977:636). Clearly, Lyons' definition echoes Jakobson's (1957:131), as well as Charles Fillmore's (1975:9), in that the key point in determining deictic elements, whether they be grammatical or lexical, is the obligatory connection between the deictic element and the utterance by means of the speech event (E and/or the participant(s) of the speech event (P S ) . S

)

II

As was shown, the notion of deixis developed by van Schooneveld has assumed a much broader sphere of influence than that found in Jakobson, Lyons, or Fillmore. Yet, van Schooneveld is clearly basing his conceptualization of deixis on Jakobson's work; like Jakobson, he views deixis primarily as a process by which parole is recodified into langue. However, van Schooneveld goes a step further by extend-

Principles of Jakobsonian Theory

39

ing the concept of deixis to all areas of language. Any traditionally deictic category, where such categories require redefinition in each unique context to become meaningful (for example, demonstratives, personal pronouns, etc.), involves a type of linguistic pointing, which is restricted to the actual speech event. Van Schooneveld realized that the act of reference itself is also a form of linguistic pointing. Hence, he considers all acts of reference to be inherently deictic. Such a principle implicitly requires that meaning, whether grammatical or lexical, be necessarily deictic. However, this definition of deixis is considerably different from the view held by most linguists. Consider the following examples, which are modeled on those given by Fillmore (1975:16), involving the lexical form "left." The two sentences below demonstrate that linguistic forms may have both deictic and non-deictic functions: (1) My friend stood to her husband's left. (2) Who is that standing to the left of that building?

In the first example the location of the participants of the speech event (P S ) is irrelevant to interpreting the sentence, whereas in the second example the location of the participants (PS) is crucial to decoding the message. From a slightly different perspective one could argue that the form "left" is deictic in both sentences but on two different levels. In the first sentence the location of p s is indeed irrelevant. Nevertheless, implicit to that sentence's message is a potential objectivized observer of the narrated event (or pn). Obviously, every human being has two sides and therefore potentially has two "left" sides. The most common reading of the first sentence assumes that one is looking at the faces of the husband and the friend. However, it is indeed possible that some pn is looking at the backs of the husband and friend. In such a case, an entirely different perspective is the result, and, hence, sentence one is equally deictic, not vis-a.-vis the E S or ps, but rather the En and pn. To further complicate the matter, sentence one could be interpreted in only one way if the perspective of a particular potential pn, the husband himself, is assumed. Clearly, when asked which is his left side, the husband would always point to the same side. Therefore, the role of pn is just as important as that of p s. Since lexical forms such as "left" can require the involvement of ps or

40

Markedness Theory

p n, whereas forms such as "now," "he," "here" always require ps, our

reformulation of deixis must take this difference into account. Therefore, the type of deixis represented by forms such as "left," "right," "near" is perceptional. 13 We can now understand why van Schooneveld defines perceptional deixis as an unmarked type of deixis, since it involves an act of perception by any observer (that is, ps or pn), whereas transmissional deixis is defined as marked for the involvement of the participants of the given speech event (PS only) (van Schooneveld 198}). What does van Schooneveld's redefinition of deixis imply for the verbal categories defined by Jakobson? First, van Schooneveld's system preserves exactly the model created by Jakobson using ps, ES , pn, En (cf. figure 14). Second, in van Schooneveld's system, since all categories are deictic, it is necessary to replace the terms non-shifter / shifter with the terms perceptionally deictic / transmissionally deictic. Third, and most important, as van Schooneveld has demonstrated (1978b: 42-5°), the verbal categories defined by Jakobson can be arranged in a hierarchy; each marked member of a verbal category is marked by means of a conceptual feature, defined similarly to those of the Russian nominal case system (Jakobson, 1936, 1958). Thus, not only does a hierarchical relationship exist between the marked and unmarked members of a given pair (cf. plural(M) vs. singular(U), preterit(M) vs. non-preterit(U), etc.), but the categories given as mood, voice, tense, and aspect can also be arranged in a hierarchy.14 In van Schooneveld's analysis of the Russian verbal categories, he discusses each category individually. With regard to voice, Russian distinguishes three types: active, passive, and reflexive. Jakobson views the passive as the most marked of the three (1932:6).15 Van Schooneveld supports this conclusion and views the passive voice as marked for the feature plurality (1978b:4)). Plurality requires that the verb form yield a result that is meaningful to any observer within the narrated event (Le., any pn), as well as tacitly naming a second point, which in non-ergative languages translates as the patient of the verbal process. In other words, the passive poses the problem of the action's manifestation; the process described by the passive becomes a fait accompli. In the category of aspect, Jakobson gives the perfective as the

Principles of Jakobsonian Theory

41

marked pole of the opposition, and van Schooneveld assigns the conceptual feature dimensionality to the perfective aspect. Dimensionality requires that the verbal process is bounded, that is, the focus will be either on the inception or completion (result) of the action, not on the process. Once again, the result implied is generally perceivable by any pn. The category of mood, particularly as it is manifested by the Russian imperative, is firmly implanted in the narrated event, yet its defining characteristic requires the involvement of some ps vis-a-vis the En and pn. The imperative constructs a direct line, or connection, between ps and pn. Van Schooneveld assigns to mood the conceptual feature extension, which requires that some ps be pulled into the realm of the narrated event. The final category analyzed by van Schooneveld, tense, involves an obligatory disjunction of the speech event and the given narrated event, described by a verb in the past tense. If the preterit is defined in terms of disjunction and not "past time," all categories expressed in Russian by so-called past tense forms can be adequately accounted for (cf. Russian conditional mood: Esli by u menja bylo mnogo deneg, ja by kupila novuju masinu = "If I had a lot of money, I would buy a new car"). In this example the verb is in the past tense form, but the narrated event being described could occur at any point in time, past or future, if the conditions are met; only the present moment given by the speech event is excluded. Van Schooneveld calls the feature that gives the obligatory disjunction with the speech event restrictedness (van Schooneveld 1978b:48). Van Schooneveld orders these features in the hierarchical system shown in figure 15. The one, totally unmarked verbal category, that is, the category Figure 15 Infinitive Passive (voice) Perfective (aspect) Conjugation Imperative (mood) Preterit (tense)

=C/J = Plurality = Dimensionality

(Least Marked)

= Distinctness

= Extension = Restrictedness

(Most Marked) 16

42

Markedness Theory

carrying minimal information, is in Russian the infinitive. Giving no information pertaining to ps, pn, E En, neither does the infinitive give any reference to person, number, or gender. The generalizations provided by van Schooneveld's system are essentially twofold. The first concerns the relationship between tense and aspect in verbal systems. As Lyons points out, aspect is a much more frequently occurring distinction than tense, if one considers all the languages of the world. He further notes that since children have been shown to master aspect before tense in languages that have both categories, aspect is therefore"ontogenetically" a more basic distinction than tense (Lyons 1977:705). One may see a reaffirmation of Lyons' view in van Schooneveld's hierarchy, if one assumes unmarked categories have a tendency to be acquired first. In our theory of markedness, however, language acquisition hierarchies are not considered to be an axiom of the theory. (This point will be dealt with in-depth in chapter 3.) The second concerns expanding the notion of deixis into perceptional and transmissional, whereby the most fundamental common denominator that unites all categories of meaning-the act of perception itself-is made explicit. S

,

III

This section is best concluded with a question: What is Jakobson's most significant contribution in the "Shifters" article? Certainly, one of the most broadly applicable principles Jakobson developed was his reinterpretation of the complex relationship between code and message in terms of the speech and narrated events and their respective participants. I ? Additionally, Jakobson defined the inherent hierarchy of verbal categories by conflating the shifter versus non-shifter distinction to the Russian verbal system. Van Schooneveld takes this implicitly given hierarchy and makes it explicit so that, if one were to shift Jakobson's chart, the hierarchy as given in figure fourteen would result. (The reader should recall at this point that the conceptual features themselves become inherently deictic beginning with the feature distinctness. ) Clearly, the potential participant in any event necessarily presupposes the reality of an event itself. Thus, Jakobson captured an

Principles of Jakobsonian Theory

ROJ Non-shifter

Shifter

Simplified

43

CHvS

n

p pnE n En EnE n

Plurality Dimensionality

pn/p s pn En/ps En/E s

Distinctness Extension Restrictedness

En Ens/E s pn En ps

Perceptional deixis Transmissional deixis

E

S

Figure 16

extremely significant distinction concerning the manner in which a linguistic utterance, as well as all discourse, is created. As van Schooneveld (1977a:1o) says in summing up Jakobson's contribution: Jakobson's entire work, from his literary beginnings on, is dominated by the search for what is invariable, and, as a corollary, variable, in semiotic systems. His vision has opened the way toward the invariance of invariants.

=Two= Peirce and Jakobson Revisited: A Reconciliation

Linguistics has a double object: it is the science of language and the science of languages.-Emile Benveniste One of the most felicitous, brilliant ideas which general linguistics and semiotics gained from the American thinker is his definition of meaning, as "the translation of a sign into another system of signs" (4. 127)·-Roman Jakobson on Peirce

Peirce's Influence on Jakobson The title of this section is perhaps a bit misleading when one considers the fact that Jakobson only discovered Peirce after having himself become an established scholar and linguist. In fact, one might argue that Peirce did not influence Jakobson at all. Rather, Jakobson simply brought Peirce's work to the attention of the international scholarly community. As Elizabeth Bruss says in summing up the situation: Most of Jakobson's attitudes have already matured by the time he draws upon Peirce; he has already formulated much of the basic framework for his semiotics. Thus he is a selective reader, using Peirce to supply additional support for his own positions, deploying him polemically as the exemplar of an alternative to the Saussurian tradition. His readings of Peirce never seem to demand any serious revisions of his own categories.... The Peirce that Jakobson presents is therefore Jakobson's Peirce (1978:81) .... Bruss goes on to argue that Jakobsonian semiotics is much more Saussurian than Peircean, but she also presents reasons for Jakobson's

Peirce and Jakobson Revisited

45

need to borrow from Peirce (1978:93-98). Bruss's particular point of view is insightful because it is certainly the case that Jakobson mainly discusses two of Peirce's notions: the icon/index/symbol trichotomy, and the importance of the interpretant (1974, 1975). Jakobson's focusing on only these two aspects of Peirce's work may be explained in one of two ways: either Peirce's other works are of no relevance to linguistics, or Jakobson did not entirely agree with Peirce's classification of signs. Bruss concludes that Peircean notions such as "firstness" are totally inconceivable for Jakobson and that they contradict the fundamental principles of Jakobsonian linguistic thought (1978:93). Bruss' assessment seems a bit unfair, however, when one recalls that Peirce's "iconic" sign, representing "firstness," was used liberally by Jakobson. My belief is that by using Jakobsonian principles, and in particular markedness theory, one can demonstrate that Peirce and Jakobson have a great deal more in common than even Jakobson himself realized. Specifically, I would argue that the essence of Jakobsonian markedness theory is derived from the principle of the Peircean interpretant, even that markedness theory is essentially a theory of interpretants. Supporting discussions of one trichotomy of Peircean interpretants (emotional/energetic/logical) and their relationship to Jakobson's six factors and functions of language will be offered later in this chapter, as will a discussion of Jakobson's attempt to add a fourth element, called artifice, to the icon/index/symbol trichotomy. What will not be discussed in this chapter, however, are Peirce's sixty-six sign classes, detailed presentations of which can be found in Savan (1976) and Shapiro (1983). My section on markedness theory as a theory of interpretants, though, will include definitions of firstness, secondness, and thirdness, as well as the three trichotomies relating the sign to itself, to its object, and to its interpretant.

Markedness Theory as a Theory of Interpretants Peirce's semiotic doctrine is the only sound basis for a strictly linguistic semantics.-Roman Jakobson

Although the literature contains numerous examples of the principles of markedness as applied to other semiotic systems (cf. Waugh 1982),

46

Markedness Theory

it was Michael Shapiro who first clearly articulated the notion that markedness is a uspecies of interpretant, fully compatible in its own way with the system of interpretants established by Peirce" (1983:17). Shapiro concludes that the interpretants of linguistic signs are markedness values (1983:17), a view with which I completely agree, adding, however, that these so-called umarkedness values" should not be seen simply in terms of 'marked' and 'unmarked'; they must also be ordered hierarchically, just as all interpretants in Peirce's theory are unequal and exist in a hierarchy. For the theory presented here, markedness values are the conceptual features as developed by van Schooneveld for grammatical and lexical meaning. 1 It necessarily follows that markedness, as expressed by asymmetrically defined properties of meaning which may be translated into an oppositional pair of the marked/unmarked type, is a fundamental semiotic principle that produces linguistic structure. If one sees that Jakobson's concept of markedness theory is compatible with Peirce's notion of interpretant, then it becomes obvious why Jakobson was so committed to the conceptualization of language as a system of signs and, hence, to the concept of language as semiotic. Shapiro offers three fundamental tenets of a semiotic perspective of language: (1) there exist semiotic universals that serve as organizing principles of linguistic data; (2) linguistic structure is coherent and explicable; (3) the coherence of the signified/signifier correlation is due to the Uinterpretative component of semeiosis" (1983:19). Thus, our discussion must begin at the beginning-with a definition of the Peircean concepts of sign, object, and interpretant. Sign, Object, and Interpretant Peirce's three types of inference, deduction, induction, and abduction, require three principles: result, rule, and case. Peirce's terms for these three principles (in his discussion of the structure of an argument) 2 are ground, reference, and leading principle, and they are crucial in the Peircean definition of the sign. Specifically, the ground of the argument provides the argument's uFormal Grammar"; the reference of the proposition yields its verifiability as true or false; and the leading principle represents the consequence rule of the argument, as well as

Peirce and Jakobson Revisited

47

providing the justification for inferring the conclusion (Savan 1976:3). Thus, deduction, induction, and abduction are all leading principles. Three possible definitions of the three types of inference may clarify Peirce's terms (see figure 17). First is the classification of inferences provided by Peirce (adapted from Fann 1970:7; see also Peirce 5.1711 8.388). A second way of distinguishing among the three types of inference employs the terms "cause" and "effect," where: (1) deduction is a form of a priori reasoning, inferring from cause to effect; (2) abduction is a form of a posteriori reasoning, inferring from effect to cause; (3) induction involves inference between the multiple effects of one cause (Fann 1970:15, Murphey 1961:60). Finally, a third and more direct way of defining inference is: "Deduction explicates and proves that something must be; induction evaluates and shows that something actually is operative. But abduction merely suggests that something may be" (Fann 1970 :51; see also Peirce 5.171,6.475,8.238). Using these same three principles, Peirce is then able to define the sign: A sign must first have an inner ground, an internal structure, character, or quality. [This is the sign proper, or representamen.] Second, it must stand for some correlate external to itself. [This is the object.] Third, it must exemplify some general rule which enables the sign to mediate between its object and some translation (or interpretation) of itself, such that this translation is a sign of the same object represented by the first sign. [This general rule is the interpretant.] (Savan 1976:3 [brackets mine]). Therefore, any sign must necessarily possess three elements: "representamen" (or vehicle), "object," and "interpretant" (Bruss 1978:86).3 Figure 17

/ Inference

Analytic (deductive) - conclusion necessarily follows from premise

~

abductive - reasons for selecting an hypothesis Synthetic

~inductive-

testing a hypothesis

48

Markedness Theory

For linguistics, this implies the presence of a signifier, signified, and feature. Furthermore, it is clear that without the interpretant, the sign becomes a mere potential and ceases to be a viable force (Savan 1976: 3). If we accept that any attempt to understand meaning is necessarily tied to a study of interpretants (Peirce 5.475), and that markedness theory is, in fact, a theory of interpretants, then we have found the philosophical legitimacy for using markedness in determining the structure of linguistic meaning. 4 The Categories of Firstness, Secondness, and Thirdness Firstness is representative of the possibility (or potentiality) of a quality that can be abstracted, perceived in and of itself, as a singular, unchanging "unity without parts," and without antecedents or consequences. Savan calls Firstness "quality space, a space which is occupied by existing qualities" (1976:6). Peirce uses ideas such as originality, freedom, and feeling to exemplify Firstness (1.302,1.531). Abductive inference is indicative of Firstness. Secondness is existence, or experience of a perception, and occurs in two forms: dynamic and passive (Peirce 1.358, 1.365, 1.372, 1.532). Secondness both exerts pressure on things and resists pressure of things external to it. The past, boundaries, and death are examples of Seconds "because in them something encounters its negation" (Savan 1976:7). Due to the double nature of Secondness, the dynamic form continues to produce subsequent correlative pairs of dynamic (0) and passive (P). Consider figure 18 (taken from Savan 1976:8). Inductive inference is representative of Secondness. (It is important Figure 18 IP IP

Secondness =

>

20

IP 20 20

Peirce and Jakobson Revisited

Thirdness =

>

49

3

Figure 19

to keep in mind that Jakobson's use of Peirce here is primarily, but not solely, limited to categories of Secondness. The extent of Jakobson's preoccupation with Seconds will be discussed in more detail in terms of one of two trichotomies of interpretants.) Thirdness is a generality that dictates rule-based change, that is, "any principle, function, or law which translates one form into another ..." (Savan 1976:7). Examples of Thirds are habit, intersection, continuity, inference-in short, "entities connecting two others" (Savan 1976:7; Esposito 1980:163). A Third is not a "single entity or event," but a generallaw which may change in time and space, so it is the interpretant that best depicts the character of Thirdness (Savan 1976:9). Deductive inference is representative of Thirdness. Like the Second, the Third also subdivides into a subordinate triad (Savan 1976:8) (see figure 19). Peirce notes that "Secondness is an essential part of Thirdness, though not of Firstness, and Firstness is an essential element of both Secondness and Thirdness" (1.530). These categories are "aspects [not things] of whatever can be known, and they occur always com-

50

Markedness Theory

pounded together" (Savan 1976:9 [brackets mine]). In other words, it is impossible to isolate one of these categories without evoking the other two. In this respect, a parallel situation occurs in the combinative quality of iconic, indexical, and symbolic signs in language (cf. iconic index, indexical symbol, etc).5 In terms of the three elements of a sign the representamen is a First, the object a Second, and the interpretant a Third (Savan 1976:10). In order to classify the signs themselves, based on the principles of Firstness, Secondness, and Thirdness, three perspectives are necessary: the sign in relation to itself, the sign in relation to its object, and the sign in relation to its interpretant.

The Sign in Relation to Itself The sign, when taken in relation to itself, "is the GROUND on which the object for which it stands is interpreted by the sign into which it is translated, or transformed" (Savan 1976:10). Note that the ground is not the same as the sign vehicle, since the ground of a sign is the essential component of a functioning sign; the sign vehicle, on the other hand, involves many characteristics secondary to the functioning of the sign (Savan 1976:11). Thus, the first trichotomy of signs is a trichotomy of grounds, consisting of qualisigns, sinsigns, and legisigns. Savan defines a qualisign as "a sign which signifies through its abstractable quality as such, through the Firstness of quality, apart from any empirical or spatio-temporal relation of the quality to anything else" (Savan 1976:11). In other words, "whenever a quality is a sign that is to be copied, imitated, mimicked, mirrored, it is acting as a qualisign" (Savan 1976:11). Furthermore, qualisigns are indispensable in communicating qualities: Given the fact that every sign obligatorily conveys information concerning the quality of its object, then every sign must partially involve a qualisign. The sinsign, a sign whose singularity of occurrence is essential to its being a sign, is an "object of direct experience." Therefore, "whenever some object or event is used as a clue to some other object or event, past, present, or spatially at some remove, this clue is a sinsign" (Savan 1976:12). Once again, note that every sign and every sinsign is partially a qualisign because there can be no Secondness or Thirdness without Firstness.

Peirce and Jakobson Revisited

51

The legisign, representative of Thirdness, is a sign whose law-like nature is essential to its character as a sign. Thus, a legisign is not "a single object, but a general type ..." (Peirce 2.246). Sayan notes that language is a good example of a system of legisigns (1976:13), but other examples include laws, social customs, and conventions (Savan 1976:14). The legisign, like the qualisign, cannot be directly encountered in experience. By implication then, this first trichotomy may be used only "to distinguish three different aspects of semiosis" (Savan 1976:14). Since no sign belongs completely to just one of these categories, every sign and sinsign has a part that is the qualisign, and every legisign is partially a qualisign as well as a sinsign. In fact, a legisign requires a sinsign in order to signify via its replica, which is one occurrence of the application of a legisign (Peirce 2.246). Finally, a legisign is "more than the sum of its actual REPLICAS" (Savan 1976:18), a statement that reaffirms the Gestalt principle so crucial to understanding lexical meaning in language (cf. chapter 3).

The Sign in Relation to Its Object This trichotomy, consisting of the icon, index, and symbol, is perhaps the best known, as well as the most utilized, of Peirce's sixty-six sign classes. Since this trichotomy will be discussed later in connection with Jakobson, it will suffice here to point out certain important aspects of the relationship between this second trichotomy and the first trichotomy of the sign in relation to itself. Specifically, any qualisign is an icon, but not all icons are qualisigns (Savan 1976:23-24). Every sinsign is an index, but some sinsigns are icons as well (Savan 1976:25). It then follows that any legisign is a symbol, but some legisigns are indices as well as icons. In linguistics the relation of the sign to its object is the most crucial relation of the three, and, within this trichotomy, the legisign plays a central role. Finally, it is worth notin~ that, according to Sayan, the icon/index/symbol triad represents the relationship of the sign to its dynamic (not passiv~ [or immediate]) object (1976:22).

52

Markedness Theory

The Sign in Relation to Its Interpretant As was mentioned earlier, Peirce often defined the interpretant as a rule mediating translation of the sign, or the "effect produced by a sign upon the mind of a person who receives and understands the sign" (Savan 1976:29-30). The interpretant, obligatorily a Third, must therefore be of the nature of a rule (or law). In fact, every interpretant is a sign and every sign an interpretant. However, sign and interpretant differ in that the interpretant "is determined by" (or follows from) the sign by deductive, inductive, or abductive inference, but the converse is not true (Savan 1976:32). Furthermore, since every interpretant implies an antecedent and a consequence, there can be no first or last interpretant in a sequence; rather, the interpretant is a general rule, or leading principle, and is necessarily a legisign that "mediates between its antecedent sign and its consequent interpretant (Savan 1976:33).6 Finally, the interpretant is contingent upon the dialogic principle in order to be fully realized. As Savan explains, "The full meaning of any sign emerges only as the dialogue expands into a conversation in which all the members of a community of interpretants take part" (Savan 1976:36). Before discussing the relation of the sign to its interpretant, Peirce's two triads of interpretants and their relation to one another must be briefly presented. The first trichotomy consists of the following categories: immediate, dynamic, and final. The immediate interpretant "is the total, unanalyzed impression which the sign might be expected to produce, prior to critical reflection upon it" (Savan 1976:40). Each sign has one immediate interpretant at most (Shapiro 1983:55). The dynamic interpretant "is whatever interpretation any mind actually makes of a sign" (Peirce 8.315). Contrary to the general definition of interpretant as a member of an infinite series, the dynamic interpretant (particularly any emotional or energetic one) is a "finite bounded event" (Savan 1976:48). Each sign has any finite number of dynamic interpretants, starting at zero (Shapiro 1983:55). According to Savan, there are three types of dynamic interpretants: emotional, energetic, and logical (1976:42-45). Fitzgerald also presents this triad as types of the dynamic interpretant (1966:76), but Shapiro, using Peirce and Short, presents these three interpretants as a pri-

Peirce and Jakobson Revisited

53

mary trichotomy, independent of the dynamic interpretant (1983:4958). It is difficult to determine who is being truer to Peirce's intentions because none of these authors gives evidence to support his interpretation. Savan and Fitzgerald at least acknowledge the controversy, but Shapiro does not even mention it (Savan 1976:42; Fitzgerald 1966:78 [note 9]; Shapiro 1983:49-5°). Since Peirce himself does not evoke these two triads of interpretants together in his published works, a definitive statement is impossible to derive from him. However, Peirce's definition of interpretants does make it clear that more than three distinct types of interpretants exist: "Now the problem of what the 'meaning' of an intellectual concept is can only be solved by the study of interpretants, or proper significate effects, of signs. These we find to be of 3 general classes with some important subdivisions" (5.475). Based on Peirce's statement above, my position will be more conservative than Shapiro's, following Savan's treatment of emotional, energetic, and logical interpretants as sub-types of dynamic interpretants. (This trichotomy of interpretants, crucial to linguistics, will be discussed separately in terms of the problem of acquisition of Russian verbal aspect in second-language learning and bilingualism.) The final interpretant "is the one Interpretative result to which every Interpreter is destined to come if the sign is sufficiently considered" (Peirce/Hardwick 1977:111). Providing a norm (or standard) by which one can measure dynamic interpretants, the final interpretant is a "living habit" (Savan 1976:48), the ultimate "self-control" (Peirce 8.372). In other words, the final interpretant is the total semiotic effect of a sign whose purpose has been realized (Savan 1976:49). At this point one can begin to define the relation of the sign to its interpretant. However, this relation is not to just any interpretant but, specifically, to the final interpretant. Three categories define the relationship of sign to final interpretant: rheme, dicent, and argument (Peirce 2.25°-52). Briefly, the rheme is a simple sign of qualitative possibility, representing a possible object and not considered to offer information (Peirce 2.250). All qualisigns are rhemes (Savan 1976:51). The dicent has an antecedent and a consequent and proposes information about actual existence. Every dicent has a part that necessarily involves a rheme (Peirce 2.251). The argument is a "sign of law" (Peirce 2.252);

54

Markedness Theory

Firstness

Secondness

Thirdness

sign in relation to itself [SR ~ SR]

Qualisign

Sinsign

Legisign

sign in relation to its dynamic object [SR ~ SO]

Icon

Index

Symbol

sign in relation to its final interpretant

Rheme

Oicent

Argument

sign as possibility

sign as actuality

sign as rule or law

[SR~MARK]

Figure

20

it represents "its object in its character as a sign" (Peirce 2.252). As Savan states, "an argument must be interpreted by its interpretant as deriving a conclusion validly from its premise (or premises) because it is one of a class of possible inferences which conform to a leading principle" (1976:52). Thus, only symbolic legisigns, not qualisigns or sinsigns alone, can be arguments (ibid.). Figure 20 represents an abbreviated schematization of the three sign relations described above (adapted from Shapiro 1983:64, with modifications)? The Ultimate Interpretant

One final type of interpretant mentioned by Peirce is the "ultimate logical interpretant" (5.476). Both Fitzgerald and Shapiro refer to ultimate versus non-ultimate logical interpretants (Fitzgerald 1966:14445; Shapiro 1983:5 0 ). In Peirce's general theory of signs he defines a sign process that is potentially infinite, where each interpretant is potentially a sign itself and every sign has an interpretant. The ultimate logical interpretant would "allow for a natural termination of the [sign] process ..." (Fitzgerald 1966:145 [brackets mine]). As defined by Peirce, the ultimate, or final, logical interpretant is a habitchange: "The deliberately formed, self-analyzing habit-self-analyzing because formed by the aid of analysis of the exercises that nourished

Peirce and Jakobson Revisited

55

it-is the living definition, the veritable and final logical interpretant" (5.491). To understand the function of an ultimate logical interpretant, we must understand what Peirce means by the term "habit." According to Fitzgerald, the Peircean habit "is a disposition to act or react in a certain manner under certain conditions" (1966:152). In this vein, a "habit-change," as a "self-analyzing habit," does not require the development of a completely new habit; rather, the habit, as a response to a sign, is modified and becomes stronger or weaker. Habit-changes may occur as a result of experience "forced upon us from without; from repeated muscular activities; or finally, from mental experiments in the inner world" (Fitzgerald 1966:146). The importance of the ultimate logical interpretant is that it prevents infinite regress and gives a termination to the sign process: "It is not sufficient then to be able to continually translate our signs into other signs. They must make a connection with the real world at the level of thirdness, not merely through indices" (Fitzgerald 1966:154). The discussion above was intended to acquaint the reader with the more salient points of Peircean sign theory. Obviously, much has been omitted, but the reader should now have a clearer understanding of the structure and complexity of Peircean sign theory, as well as a sense of how limited its application has been in linguistic analysis. Before we can make any specific statements about the relationship between markedness theory and Peircean sign theory, however, we must tackle the definition of "meaning" inherent in these two theories. Meaning and Interpretants If Jakobsonian-based markedness theory is a theory of interpretants, then we must demonstrate that these two approaches similarly define "meaning." Within the linguistic framework presented in chapter 1, using principles developed by Jakobson and van Schooneveld, meaning is defined by invariant conceptual features existing in a hierarchy, including four types of deixis that define kinds of observers necessary to interpret the general meaning given in the signans-signatum relation. Linguistic meaning, defined within the linguistic code itself, is not in an isomorphic relationship to so-called extra-linguistic reality. Thus, the linguistic and the extra-linguistic objects are distinct,

56 Markedness Theory

although they may overlap. Iconic meaning is one of the fundamental vehicles that makes accessible, and interpretable, meaning as given in the linguistic code itself. Likewise, indexical meaning, as exemplified by "shifters," is another distinct but no less relevant type of meaning. Markedness allows for the definition of the invariant, hierarchical, conceptual features in terms of a theory of general meaning. Peirce's theory of meaning is inextricably tied to his system of interpretants: "Now the problem of what the 'meaning' of an intellectual concept is can only be solved by the study of interpretants, or proper significate effects, of signs" (5.475). But what exactly is the "proper significate effect" of a sign? "It is all that is explicit in the sign itself apart from its context and circumstances of utterance" (Peirce 5.473). Therefore, by definition, any theory of markedness that pursues the revealing of the general, invariant meaning of a sign is a theory of interpretants. No less important to Peirce's definition of meaning, in its narrow sense, is the purpose of a sign (5.175; Fitzgerald 1966:84). In particular, Peirce refers to the traditional definition of meaning used by logicians, in which meaning is divided into: (1) internal/intrinsic meaning, as fulfillment of the purpose of the sign, that is, as signification, and (2) external meaning, as the referential aspect of the sign, where an idea indicates "something other than itself" (Fitzgerald 1966:84-85; Peirce 8.119). Peirce recodifies internal and external meaning into his triadic distinction of the sign-object relation, using icons, indices, and symbols. For Peirce, iconic meaning is related to internal meaning, indexical meaning to external (referential) meaning, and symbolic meaning to "principal meaning" (Peirce 8.119; Fitzgerald 1966:86). "Principal meaning" involves both internal and external meaning, but is a distinct type of meaning, because principal meaning, of the nature of a "habit," or law, involves purpose (Fitzgerald 1966:87). As Fitzgerald particularly emphasizes, internal, or iconic, meaning for Peirce is not the same thing as pragmatic, or principal, meaning (1966:87 [note 17]). All signs necessarily have internal meaning, but not all signs must have a pragmatic meaning (Fitzgerald 1966:169). In other words, every sign potentially has an interpretant, but its potential is not necessarily realized. If we focus our discussion on "principal meaning," which most

Peirce and Jakobson Revisited

57

closely parallels the Jakobsonian sense of Gesamtbedeutung, or general meaning, we find that principal meaning, being defined as habit or law, is essentially given by the "logical interpretant" (Peirce 5.486). But the ultimate logical interpretant cannot be the logical dynamic interpretant, since the logical dynamic interpretant does not require "a potentially infinite series of further habitual actions" (Savan 1976:48). Only the final interpretant can be the "living habit," the "full semiotic effect of a sign"-the ultimate logical interpretant. However, the dynamic interpretants, which are "finite, bounded events," in their successive evolutions, move toward the norm, or standard, set by the final interpretant (Savan 1976:48-49). If we return, for a moment, to the statement made earlier that markedness theory is a theory of interpretants, one important question arises. What justification can be offered to substantiate the claim that a markedness theory using linguistically defined conceptual features is preferable to one simply using marked/unmarked oppositional pairs? That justification can be found in Peirce's own hierarchy of interpretants. It can be argued that conceptual features derived from a Jakobsonian-based markedness theory are not simply interpretants, but are of the nature of final interpretants, that is, a "Third of Thirds." They are indi 2, these vector fields are necessarily not dense everywhere. 9 However, it must be noted that for M > 2, this fact does not imply the complete absence of structurally stable fields with density. Specifically, there is necessarily at least one open set where the structurally stable fields are everywhere dense (Thorn 1975:26). An open set in topology can be defined as follows: Given a set a == (all a 2 , . . • a q ) of q real numbers (i.e., points of IRq), A == state corresponding to a. M A == defining set of A in IRq. If a ==(a ll a 2 , ••• a q ) E MA (i.e., a is a physically realizable state of A), all sufficiently closed points B == (b I , b 2 , .•• b q ) are also realizable. Therefore, MA requires: if a E M A , then M A contains a ball with center a and sufficiently small radius r(a). Such subsets of IRq are called open. (Thorn 1975:332) The concept of a ball in topology must be understood in relation to a system. Thorn defines a system as "the content of a domain (0) of space-time" (1983:85). The domain is a non-empty set, or more pre-

Markedness as Mathematical Principle

91

cisely, for Euclidean space (IRq), where IR represents the real numbers and q is the dimension of the space, a domain is "a connected open set" (ibid.). (Thorn firmly rejects the notion of a 'system' as the union of "distinct objects.") The domain (0) is not only connected, but is contractable-that is, a topological ball. The distance between any two given points in IRq [where x == (Xli x2, ... xq) and y == (Yll Y2, ... yq)] is given by the formula: q

d(x, y) ==

lL (x

j -

Yj)2 j

1/2

j=l

The set {y; d(x,y) < r} is the open ball with center x and radius r (Thorn 1975:331-32). The fact that the domain (0) is a connected open space is essential because, if domain (0) were representative of a totally autonomous system, then no external forces or changes could permeate the system, nor could we observe the "flow of matter and energy in all their forms" coming from within the domain (0) (Thorn 1983:86). Thus, domain (D), as topological ball, has an outer boundary that allows both inflows and outflows and, like language, is only a relatively autonomous system. Another feature of systems, as defined above, is the notion of the characteristic of the system. Related to density, the characteristic involves regularity properties of the system that are independent of the history, or past developments, manifested in the system. (Recall that system, as defined here, is fixed in space and time.) The notion of characteristic corresponds in principle to what van Schooneveld calls the semantic dominant (1978c:46-47; 1985:496), meaning the principle that defines the structure of a given language. Van Schooneveld claims that defining the semantic dominant of a language would make it possible to transmutate semantic structures of different languages into each other. In other words, the semantic dominant would lead to the definition of an interlinguistic semantic calculus. lO The importance for Jakobsonian markedness theory of these definitions is that because we are necessarily dealing with a system which, in topological terms, has M > 2, not all subsets of the manifold are structurally stable fields everywhere dense. l1 But there is, nevertheless, a core of the system possessing both stability and density. While the markedness features describe qualitatively open sets of the type

92

Markedness Theory

given above, our model remains dynamic on the fringes, at least, to allow us to explain, via such a continuous model, language change through the catastrophe. Catastrophe Theory and Linguistic Sign Theory The extension and application of Thorn's theories to linguistics here do not necessarily follow Thorn's own conceptualization of catastrophe theory's application to language. In particular, Thorn is aiming for a theory of language where meaning, or signification, is part of the so-called global topology represented by the attractor(s) and the catastrophes they experience. In other words, the meaning (SO) of a form is defined purely contextually, that is, by its usage (Thorn 1975:321). The above statement can be understood in two different ways, only one of which supports the Jakobsonian definition of linguistic sign systems and the SO/SR relationship. In following the Jakobsonian model, my view of the relationship between SO and SR is as an invariant one that gives rise to a potentially infinite number of contextually defined variants. Whatever position one may ultimately take, and however one may choose to interpret the applicability of catastrophe theory to markedness theory, one should recognize that it is not so absurd to imagine geometrical, as well as algebraic, models as having at least some value to "almost every domain of human thought" (Thorn 1975: 324). In any case, it is essential to realize that context for semiotic linguistic theory is one manifestation of the "inflows" and "outflows" of the linguistic system. The system changes because of the pressures internal and external to it. Context provides the window revealing the directional flow of linguistic change. The critical piece of the puzzle that is still missing for linguistics is, of course, a more precise description of how the relationship between SO and SR changes in time. This missing piece can only be found, in my view, by continuing to develop and fine-tune our understanding of dynamic systems through the catastrophe. A theory of catastrophe can help us to define more precisely the interrelationship of synchrony and diachrony as an interaction of two different systems struggling for dominance and culminating in a third, resultant system. Catastro-

Markedness as Mathematical Principle

93

phe theory provides a tool for calculating such qualitative changes as "habit-change," especially when the catastrophe is seen as "a 'survival manoeuvre' of a system called on to leave its normal characteristic state" (Thorn 1983:90). As Thorn points out, catastrophe theory implies that "to a certain extent, existence is determined by essence, the set of all the qualities of being" (1983:91). In other words, catastrophe theory promotes the point of view that mappings involving the linguistically given signified and signifier proceed from signified (meaning) to signifier (form), not vice versa. The actual range of applications of catastrophe theory in biology and the social sciences has hardly been realized at this point in time. Continued research is required to calculate more exactly how qualitative changes can manifest themselves quantitatively through "catastrophes." An Axiomatic Base for Markedness Markedness theory, like all theories, is necessarily the outgrowth of a set of constructs. These particular constructs can most clearly be analyzed and formulated in terms of an axiomatic base. The fundamental axioms of set theory are the basic propositions from which all other propositions are derived. Thus, before discussing a specific markedness theory, one must understand the statements that give rise to it. The axiomatic base for markedness presented in this work is not simply a collection of axioms formulated for language, but is precisely the same group of axioms used to define mathematical set theory. Furthermore, these axioms systematically define the principles of markedness theory as well as the operating principles of binary signs; they will not be directly applied to linguistic "sentences" or "propositions." Jakobson, quoting Henry Sweet, made it very clear that language cannot be reduced "to strict logical or psychological categories" (1961a:457). Nor does Jakobsonian markedness theory lend itself to "truth table" implicational structures, since these implicational propositions involve symmetrical, privative oppositional types, not asymmetrical oppositions such as those explicitly given by the dis-

94

Markedness Theory

tinction general versus specific meaning (cf. chapter 4). Therefore, the axiomatic base will be used solely to make explicit the inner workings and implications of any binary system of signs. When Transformational Grammar became popular, axioms, mappings, and symbolic logic were applied to the sentence and propositional levels of language in order to define formal grammars. 12 Jakobson, however, never indulged in such a practice because of his fundamental belief that form and meaning cannot be separated. In "The Phonemic and Grammatical Aspects of Language," for example, Jakobson states: "The SEMANTIC MINIMUMS of a given language can be stated only with reference to their formal counterparts, and visa versa, the MINIMAL FORMAL UNITS cannot be determined without reference to their semantic counterparts" (1949:1°5). Furthermore, Jakobson was convinced that the best way to explain the connection between form and meaning was to begin by studying these "MINIMUMS" (that is, phonemes and morphemes). In fact, Jakobson stated that "these minimums must be investigated in terms of ORDER GROUPS and SUBSTITUTION GROUPS (in keeping with the mathematical group theory) . . ." (1957:1°5).13 In this vein, my proposal is that the distinctive features and conceptual features, or, what Jakobson called the "lower level of semiosis," can be stated in terms of mathematical groups as well. But before group theory can be applied, we must establish that the linguistic relations defined by markedness theory represent a consistent system such that mathematical principles are valid statements within this system; establishing such a consistent system is the role that the axiomatic base will play in the following discussion. Jakobson defined all linguistic units as signs, in the Saussurean and Peircean sense. Therefore, every linguistic sign is bipartite, consisting of a signans (or signifiant or acoustic image) and a signatum (or signifie or concept) (1949:1°3). Furthermore, "any linguistic, and in general semiotic, analysis resolves more complex units into smaller but still semiotic units" (Jakobson 1949:1°4). This statement opened the door for the breakdown of the phoneme into distinctive features and, later, for the morpheme's divisibility into conceptual features. The axiomatic base to follow will define the linguistic sign binarily and will be applicable to any level (the phonological distinctive feature, the conceptual

Markedness as Mathematical Principle

95

feature, the phonemic, the morphological, and the syntactic levels) on which the linguistic sign exists. Rodney Sangster sums up the essence of the linguistic sign as follows: "The concept of linguistic sign implies that there exists a constant, recurring formal property or set of properties correlated with an invariant of meaning" (1982:4). If we accept the notion of a binary linguistic sign, we then must establish how these two parts of the sign are interrelated. Following in the Saussurean tradition, Jakobson states that the "two constituents of any linguistic sign (and of any sign in general) necessarily presuppose and require each other" (1949:1°3), thereby explicitly binding the signified to the signifier in such a way that one cannot exist without the other. Therefore, to analyze semantic structure, the linguist must focus on the formal properties of sound in order to distinguish meanings., This principle is called the principle of formal determinism (a term coined by Sangster), which Jakobson stated as follows: "There is no SIGNATUM without SIGNUM." As was shown in chapter two, Peircean semiotic theory is a very important part of Jakobsonian markedness theory, but the sign at its most primitive level is, for Jakobson, binary, consisting of a signified and signifier. The interpretant, though no less important, only becomes a viable part of the system once the relationship on the level of secondness is established. The direct connection between form and meaning, as stated above, includes a rejection of true synonymy, but does not exclude homonymy (a fact that will be duly reflected by the first axiom of our theoretical base).14 The term homonymy can be understood in several ways. In its most superficial sense, homonymy means that the same form has more than one meaning. In a much more profound sense, homonymy means that a paradigmatically or syntagmatically given form of one particular meaning can coalesce with (that is, be identical to) a paradigmatically or syntagmatically given form with a different meaning. In other words, the second definition of homonymy allows two forms to coincide phonologically in one of their paradigmatic or syntagmatic occurrences, but not to be identical in every paradigmatic/syntagmatic form (cf. English bark [verb] vs. bark [noun] == difference in part of speech, but barked can only be a verb; Russian luk [nom. case] "onion"/ luku [gen. case] vs.luk [nom. case] "bow"/luka [gen. case] == difference in inflection).

96 Markedness Theory

An axiom is defined as a statement or definition that is accepted without proof. However, it is crucial to recognize that a given axiomatic base is much more than a set of random statements; rather, it is a cohesive, systematic structure of "demonstrable" and consistent (free from contradiction) statements that is accepted without proof. In general, axioms facilitate a simple form of expressing complex principles (Thorn 1983:124-25). Once our axiomatic base is developed, it will be possible to demonstrate rigorously what a markedness theory based on these axioms can and cannot do. (The question of mandatory substitutability of the unmarked element for the marked element, for example, is one of the problems which will be specifically addressed.) Any statements that are not fundamental to defining markedness relations can be set aside once an axiomatic base is formulated. Markedness theory is founded on the notion that opposition exists within language. In fact, opposition, as expressed through communication, is what gives language its particular identity. As Alfred North Whitehead defines it, "Equivalence implies non-identity as its general case" (1960:6). Thus, only through opposition can one ascertain difference. But the way in which opposition is defined is also crucial. The definition used in this work is based on that of Hendrik Pos: L'opposition n'est pas un fait isole: c'est un principe de structure. EIle reunit toujours deux choses distinctes, mais qui sont liees de telle fa~on que la pensee ne puisse poser l'une sans poser l'autre. L'unite des opposes est toujours formee par un concept, qui, implicitement, contient les opposes en lui et se divise en opposition explicite quand il est applique a la realite concrete. (1937:246-47) Opposition is not an isolated fact: it is a principle of structure. It always brings together two distinct things, but which are linked in such a way that thought cannot pose one without the other. The unity of the opposites is always formed by a concept which implicitly contains the opposites in itself and is divided into an explicit opposition when it is applied to concrete reality [translation mine]. Therefore, opposition will always be considered a "principle of the structure" of a given language. Furthermore, the notion of opposition

Markedness as Mathematical Principle

97

may be derived from our conceptualization of the sign relationship

within language. The next step involves the way to ascertain opposition within a given language system. In the sign theory view of language, a linguist has only a language's individual forms to work with when analyzing .that language. The sign theory concept implies that any analysis of the language must be based ultimately on only what we know to exist -the forms. Given any two unique forms in a language, we can determine a difference in meaning. An example would be the often evoked phrases "the morning star" and "the evening star." Although both refer to Venus, they do not mean the same thing, referring instead to two different phases of Venus in which a perceivable difference is manifested. Such a recognition of difference clearly reveals that although language is tied to reality, it is not directly tied. Rather, language is tied to perception of reality. (The end of this chapter will be devoted to explaining the laws of form.) Therefore, assuming only that linguistic, bipartite signs, as defined by a particular language, constitute a set, and that both difference and sameness are ascertainable, the following is true. IS

Axiom

1:

A Difference in Form Signifies a Difference in Meaning

This axiom is motivated by the fundamental axiom of set theory, namely the axiom of extension, which states, "Two sets are equal if and only if they have the same elements" (Halmos 1960:2). The axiom of extension allows mathematics to define sameness and difference, and this is also the first step to be taken in linguistics. We cannot systematize if we have no means to distinguish between sameness and difference. The first axiom allows us to formulate the relationship between form and meaning into axiomatic terms. By changing the conditional "if and only if" to an "if ... then" statement, we are allowing for the potential occurrence of homonymy in both its superficial and specific senses (as defined above). Furthermore, since the replacement of "if and only if" by "if . . . then" does not make the axiomatic base inconsistent, this modification is allowable. The function that will eventually result from this statement relating form and meaning will be from meaning onto form.

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The function F from meaning onto form allows us to define a given language at a certain synchronic stage and to generate the entire language. The function F does not specify the syntactic concatenations of the morphemes-it maps meaning onto individual forms. However, will the function between meaning and form be isomorphic? If we define the function F as one-to-one and onto, we have excluded the potential for synonymy and homonymy in language (in both the narrow and specific senses given in chapter two). If we accept that both "true" synonymy and homonymy exist, it is mathematically impossible to define any function from meaning to form, or from form to meaning. Therefore, we must accept only one of them as an actual phenomenon, or neither, if a functional mapping is desired. C. H. van Schooneveld has made a great deal of progress in developing a theory of meaning and reference. In his work, van Schooneveld explains that the tie between linguistic meaning and "reality" is indirect and not isomorphic, but that linguistic meaning is based on perception of external reality. And human perception of reality, as expressed by language, is defined by the conceptual features. It is clear, however, that homonyms do exist, for example, in English: read (past tense "to read"), red (color); blew (past tense "to blow"), blue (color); see (verb), sea (body of water). Based on the above evidence, the function F between meaning and form must be defined such that homonymity can exist in language. If we continue to define the function F as an onto function from meaning to form (not from form to meaning), and not as one-to-one, then the function F, as stated, is sufficient to generate a mapping between meaning and form, allowing for homonymity as well as ambiguity in general, for a specific synchronic stage. However, the function F, as defined, does not allow for diachronic change. Therefore, the function F must be redefined, and too the sets of meaning and form (the domain and range), as language experiences diachronic development. As the domain and range of a function begin to change, the function that defines their relationship may become into, not onto; it could cease to be a function and become a relation, or it could become one-to-one. In short, language systems can undergo changes so that the functions defining the relationship between meaning and form can go from the extreme of being a simple relation to being a one-to-one and onto

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function. An onto function is the most "neutral" function for defining human language (Andrews 1984a:87-89). Thorn (1983:192-93, 264) supports the point of view stated above, that is, the function that describes the relationship of form (SR) and meaning (SO) is best defined as SO ~ SR: "It would seem good to make use of the Saussurean schema: Signified ~ Signifier, to explain the structure of language. There is an immediate feeling from psychological experience that it is the 'signified' which determines the 'signifier'" (1983:193). Thorn also comments that "in the interaction 'signified-signifier,' it is clear that, borne along by the universal flux, the signified generates the signifier in an uninterrupted burgeoning ramification. But the signifier regenerates the signified each time that we interpret the sign" (1983:264). Thorn's statement is particularly important in clarifying our definition of function F as mapping from the signified onto the signifier because if, indeed, "the signifier regenerates the signified each time that we interpret the sign" (ibid.), then the linguist has a twofold task: to attempt to determine the definitive functional mappings that give rise to the invariant structure of meaning (SO ~ SR) via the constant reevaluation of the SO/SR relationship as given by multiple mappings of the type SR ~ SO. These SR ~ SO mappings are produced, in turn, via interpretants. Therefore, linguistic research cannot avoid the linguistic form, as given by the signifier. Now that Axiom 1 has given us a starting point, the next question to be posed is: Are oppositional relationships ordered, or do they occur at random? If we accept, at the minimum, that linguistic signs represent a set of elements, then the following axiom can be adopted.

Axiom 2: Every Set Can Be Well-Ordered (Halmos 1960:68). This axiom, more commonly known as the Well-Ordering Axiom, reflects a notion of "ordering" based on inclusion relationships of the type "If a C b and if b C c, then a C c." Ordering, far from being unique in a set, occurs in three fundamental types (Hall 1959.:17). For the purposes of this work, the difference between partial order, total order, and well-ordering must be explained in order to clarify the role played by the relation of inclusion in both set theory and markedness theory. Intimately involved with the notion of ordering is the equivalence

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relation, a definition of which presupposes an understanding of the mathematical concept of ordering. An equivalence relation is defined as follows: Let A be any collection (set) with the elements a, b, c (that is, a, b/c E A) and the binary relation rv on A (that is, a relation between the elements of A). Then rv is an equivalence relation on A if: a rv a (reflexive) a rv b implies b rv a (symmetric) 3. a rv band b rv c imply a rv C (transitive). (Herstein 1975:47) 1.

2.

An example of an equivalence relation from everyday life would be the set of all ten-year-old children. If A == {a, b, c} where a, b, care ten-year-old children, then (1) each ten-year-old is ten years old (reflexive); (2) if a, being 10 years old, is equivalent to b, being 10 years old, then b is equivalent to a (symmetric); (3) if a, being 10 years old, is equivalent to b, being 10 years old, and b, being 10 years old, is equivalent to c, being 10 years old, then a is equivalent to c (transitive). An example of an equivalence relation in mathematics involves the set of all integers. Given a, b E A, let a rv b be defined as "a - b is an even integer." Therefore: Since a - a == 0 is an even integer, then a rv a; If a - b is even (a rv b), then b - a, which is the same as - (a - b), is even, (b rv a). Thus, a rv b implies b rv a; 3. If a - band b - c are even (a rv b, b rv c)/ and a - c == (a - b) + (b - c) is also even (a rv c), then a rv band b rv c imply a rv c. (Herstein 1975:7) 1.

2.

Equivalence relations may seem trivial when viewed in the context of everyday life, but they represent the logical basis of the human ability to perceive equivalence. In mathematics, one of the most relevant applications of equivalence relations is the isomorphism (that is, a one-to-one relation). The difference between an equivalence relation and the three types of ordering is a crucial one in mathematics, and, as I will demonstrate, this difference is equally important in linguistics. A partial ordering of a set shares two properties with an equivalence relation, namely reflexiveness and transitivity. However, by definition, a partial ordering of a set is antisymmetric, that is, a rv b does not imply b rv a (Halmos

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1960:56). Therefore, we can define a partial ordering for a set A with elements a, b, c as follows: (1) a ::; a (reflexive); (2) if a ::; band b 2:: a, then a

b (antisymmetric); (3) if a ::; band b ::; c, then a ::; c (transitive). :=

Such an ordering is called "partial" because a partial ordering is an "unmarked" type of order-it leaves certain questions about the given order unanswered, unlike a total ordering or a well-ordering. The most obvious and important example of a partial ordering is an inclusion relation (Halmos 1960:54), for the inclusion relation is the basis for all markedness relationships in linguistics. Also important is the relevance of inclusion relations to the general structure of sets, that is, binary relations and ordering, to name a few. [An interesting note: the symbol C for inclusion was introduced by C. S. Peirce.] Although inclusion in its general case represents a partial ordering, in certain special cases inclusion can be representative of a total ordering (whenever the set in question is "empty" or has only one element) (Halmos 1960:55). The definition of a total ordering is: If for every a and b in A either a ::; b or b ::; a, then ::; is called a total (or simple) order, and such a set is often referred to as a chain. A more complete definition of a total ordering of a given relation is given a set A with elements a,b,c: (1) if a and b are distinct in A, then a < b or b < a; (2) if a < b, then a # b (a and b are distinct); (3) if a < band b < c, then a < c (Wilder 1952:46). The difference between a total ordering and an equivalence relation is that a total ordering requires the elements of the set to form a chain with one element preceding or succeeding every other element. An equivalence relation, however, does not state any conditions concerrling the absolute distinctness of its elements. An example of a total ordering in mathematics is the relation "less than or equal to" (::;) in the natural numbers. At this point allow me to recapitulate briefly and extract from the discussion of ordering the major points that are relevant for linguistic analysis. The antisymmetry of partial orderings is one of the most important notions that can be applied to markedness relationships. The linguistic sign may be asymmetrical, but this does not imply lack

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of order in the asymmetry. The concept of a partial ordering, in conjunction with the relation of inclusion, allows for the rigorous establishment of ordered, hierarchical relationships within any linguistic sign system and, thereby, for perceiving the structure of the language more clearly. Before the role played by total orderings in markedness theory can be determined, total orderings and partial orderings must be contrasted. For any two elements x and y which are partially ordered, then either x < y or x == y (for ::::;) is true. In a total ordering, x ::::; y means only x < y, not x == y, since for every x and y in the set, x # y (see Condition [2] above). Therefore, a partial ordering, allowing equality or distinctness of its elements, is an "unmarked" form of a total ordering. (Total orderings exclude equality of elements.) The third type of ordering, called a well-ordering, becomes very important if the set in question requires a smallest and/or greatest element. A partially ordered set is said to be well-ordered if, for every set X, every non-empty subset of X has a smallest (or least) element. The main implication of this definition is that every well-ordered set is totally ordered, that is, it has a first (or least) element (Halmos 1960 :66). It is necessary here to interject the distinction between a least and a minimal element, which are two entirely different elements in partially ordered sets. A least (or smallest) element "a" in a set X is defined as a ::::; x for every x in the set X. The property of antisymmetry, which is crucial to all partial orderings, requires that if there is a least element, there is only one at most (that is, the least element is unique) (Halmos 1960:56). An element "a" of a partially ordered set X is called minimal when "a" is the absolute smallest element in X, that is, when there is no element in X strictly smaller than a. In other words, if a is minimal and x ::::; a, then x == a. The key difference between least and minimal elements is that minimal elements are not necessarily unique. An example of a least element is the element 0 in the set of natural numbers (0, I, 2, 3, 4 ... ). [The set of natural numbers has no greatest element, only a least element.] An example of a minimal element is the collection of non-empty subsets of a non-empty set X within an inclusion relationship. Each singleton is a minimal, non-unique element of the collection of subsets, but the collection has no least element (unless

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X has only 1 element itself) (Halmos 1960:57). Another example of a minimal element may help to clarify the previous example. Suppose there is a collection of subsets consisting of twenty families. Ten of these families have three children each, while the other ten families have four children each. The subsets defined as families-with-threechildren are considered to be "minimal" because, of the ten families with three children, no one subset is "smaller" than another. But all ten subsets of families with three children are smaller than the ten subsets of families with four children. Thus, while a minimal element is not necessarily "unique," a least element must be "unique." In Jakobsonian-based linguistic analysis, the notion of a least element is more applicable to the conceptual features used in morphological markedness analysis than is the notion of a minimal element. We thus will require that a set be well-ordered unless otherwise specified. Furthermore, any concept of ordering, whether partial, total, or well-ordering, implies the establishment of a hierarchy. However, it is important to keep in mind that any given well-ordering may not have any relation to the structure which the set may already have. In other words, one and the same set can be ordered in more than one way, such that some orderings are well-orderings, but others are not (Halmos 1960:69). One major implication of requiring that each set be well-ordered is the possibility of then proving propositions about these well-ordered sets by the method of transfinite induction. The transfinite induction principle, which allows one to demonstrate that all the elements of a well-ordered set possess a specific property, is defined as follows: Given a well-ordered set X and a set S such that Sex, if for every x E X, s(x) C 5, then xES and S == X. [s(x) is the set of predecessors of x.] In layman's terms, if each predecessor of a given element in a well-ordered set always implies the presence of the given element itself, then the set must contain everything. Another principle often associated (and even confused) with transfinite induction is the mathematical induction principle. Although the mathematical induction principle is in many ways similar to the transfinite induction principle, there are some fundamental differences. The mathematical induction principle is much more "ordinary" in its definition and does not require that the set in question be well-ordered. The definition of the mathematical induction principle (sometimes re-

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ferred to as Peano Axiom III) is: Given w = set of natural numbers and 5 is a set, if 5 C w, if 0 E 5, and if n + E 5 whenever n E 5, then 5 = w. [n+ is the successor of n, that is, n+ = n U {n}.] (Halmos 1960:46). The most obvious differences between these two principles are: (1) transfinite induction involves going from the set of all elements which precede the element in question to that element, not from one element to the next (that is, set ~ element, not element ~ element); (2) transfinite induction does not assume that there is a starting element (like 0). [Remember: a starting element is not the same thing as a least element.] The first difference between the two types of induction implies that a well-ordered set may not have an immediate predecessor. Although this fact is not important when considering the well-ordered set of conceptual features used in our linguistic analysis, it will become crucial when discussing sets of cumulations of conceptual features, where there are most certainly "holes" in the linguistic sign system in which no formal correspondence occurs between form and potential meaning. Since open spaces exist in the linguistic system where not all theoretically possible cumulations are formally represented, there is not always, consequently, an element which is a strict predecessor, but only a set of cumulations which is a strict predecessor. Just as every sign has a potential interpretant, it is not necessarily true that all potential interpretants (or all signs, for that matter) will be realized. The second difference between transfinite and mathematical induction, that transfinite induction does not require a starting point, is not a crucial difference. 5ince all well-ordered sets must have a least element, then the predecessor of the least element will be the empty set, and the empty set is nevertheless a subset of the set. Therefore, no contradiction results, and the well-ordered set is still complete (Halmos 1960:67). In some special cases, such as the set of natural numbers, the transfinite induction and the mathematical induction principles become equivalent. This occasional equivalence is precisely why principles can become confused as one and the same principle (ibid. ). The purpose of the lengthy discussion following Axiom 2 was to clarify how important the notion of ordering a set is to linguistic analysis, and to show how the relation of inclusion is derived from the

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concept of ordering. As G. Spencer Brown states, "What the mathematician aims to do is to give a complete picture, the order of what he presents being essential, the order in which he presents it being to some degree arbitrary" (1969:79). It is the relation of inclusion that provides the principle for defining sets of meanings as sets of conceptual features. Just as secondness presupposes firstness in Peircean semiotics, each conceptual feature, as defined by markedness theory, presupposes its preceding feature. To endow the well-ordered elements of a set with life, a binary relation must be defined, since any ordering depends on binary relations for its very existence. [The term "binary relation" will be given preference over the term "binary opposition" whenever discussing mathematically based notions.] In an attempt to define a binary relation, the following axiom is required.

Axiom 3: Given a Set Which Is Ordered, a Binary Relation Can Be Defined to Explain the Ordering. In other words, a binary relation defines any given ordering. This axiom solidifies the relationship among the elements representing the signified/signifier relation in a given language set. The binary relation is necessarily an interpretant. Axiom 4: For Any Two Sets, There Exists a Set That They Both Belong To (Halmos 1960:9). This axiom, called the axiom of pairing, will be necessary when we look at more complex types of markedness relationships involving not all types of interpretants, but specifically final interpretants. To complete our axiomatic base, five more axioms are needed. The first (and one of the major principles of set theory) is called the axiom of specification (or Aussonderungsaxiom). Axiom 5: To Every Set A and to Every Condition Sex) There Corresponds a Set B Whose Elements Are Exactly Those Elements x of A for Which Sex) Holds (Halmos 1960:6). The set B which results from this axiom is necessarily unique. One of the most interesting mathematical applications of the axiom of specification results in what is commonly known as Russell's Paradox,

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which states that there is no universal set that can contain all elements. In axiomatic set theory, however, Russell's Paradox presents no problem since the existence of a "universe" or "universal set" is not assumed by the axiomatic base. In its linguistic applications, the axiom of specification will allow us to determine mappings which yield feature cumulations and, eventually, that culminate in assignments of final interpretants to the SD ~ SR relation. The next axiom, the axiom of unions, permits the elements of more than one set to be united in one large set.

Axiom 6: For Every Collection of Sets There Exists a Set That Contains All the Elements That Belong to at Least One (i.e., Some) Set of the Given Collection (Halmos 1960:12). The axiom of unions gives validity to the formation of "union" relations between sets, as in the following examples: If A and B are sets, then AU(/) == A, A U A == A, A U B == B U A, etc. (The exact role of union and intersection as binary relations which define markedness feature cumulations will be discussed in the next chapter.) The seventh axiom, the axiom of powers, allows any subset of a given set to constitute a set itself.

Axiom 7: For Each Set There Exists a Collection of Sets That Contains Among Its Elements All the Subsets of the Given Set (Halmos 1960:19). The axiom of powers is immediately applicable to the six conceptual features. Consider, for example, the features dimensionality and distinctness, which form a set/subset relationship of the kind: DIST C DIM. The axiom of powers allows us to say that distinctness can be a Figure 27 ~

Dimensionality

8

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set in its own right, not only a subset of dimensionality. The same generalization can be made for each of the other conceptual features. The penultimate axiom needed to complete our axiomatic base will yield the most profound results for partially ordered sets. This axiom is known by two names: the axiom of choice or Zorn's Lemma (Halmos 1960 :62).

Axiom 8: The Cartesian Product of a Non-empty Family of Non-empty Sets Is Non-empty (Halmos 1960:59). In other words, if two sets exist and if neither is empty, then their Cartesian product (that is, the relation that combines the elements of two sets into a new set, consisting of ordered pairs) must also have elements. Therefore, if a is an element of the set A and b is an element of the set B, then A x B (the Cartesian product of A and B) yields the ordered pair (a,b,) (Halmos 1960:24). At first glance, this axiom appears not to have any direct bearing on what has previously been discussed. Yet, this is not the case because any element (that is, ordered pair) of a Cartesian product represents the graph of a function. A function (or mapping) is a relation that yields an ordered pair, mapping an element of one set into a relation with an element in another set. Functions playa very important role, of course, in any sophisticated theoretical system that attempts to analyze and explain human language. Intimately connected with the notion of function is the isomorphism, which is a restricted type of function. As discussed earlier, via functions, we are able to define how the relation between the linguistic signifier and signified can be established. To the axioms listed above, we need to add the axiom of existence, which provides for the mandatory existence of at least one set.

Axiom 9: There Exists a Set Which Has No Elements. This principle posits that the "universe of discourse" is not totally void and, therefore, some set must exist. In this case, the set that exists is the empty set, which is necessarily unique. But it is t1)e axiom of extension that makes it possible to prove that the empty set is unique. Also, note that, to some degree, the axioms above contain redundancies. For example, the axiom of existence and the axiom of pairing can be

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proved from the rest of the axioms given (Hrbacek & Jech 1978:172). It is essential always to remember that the most important feature of any axiomatic base is its mandatory consistency. (The above system has been proven to be consistent in mathematics.) At this point, the axioms will be reordered and the status of Axioms 2 and 3 changed, while the consistency of the axiomatic base will be preserved. Axiom 2 can be called a theorem (that is, a provable statement) within the system above. Specifically, the well-ordering theorem can be proven by Axiom 8, the axiom of choice. (Without the axiom of choice, the well-ordering theorem is merely an axiom since its "provability" depends on the axiom of choice.) With regard to Axiom 3, we will call this statement a definition and restate it as follows: Given a set A which is ordered (that is, its elements are ordered pairs), then the set A is a binary relation (Hrbacek & Jech 1978:20). Definitions are true statements that can be included in the system of axioms and theorems. (It is important to note that the actual ordering of the axioms themselves is not important. Since no type of cyclic rules are required or relevant in this type of system, ordering is only distinctive within the sets in terms of the elements of the set.) In the traditional framework of the Zermelo-Fraenkel Set Theory plus the axiom of choice, two additional axioms are usually listed: The axiom of infinity and the axiom of substitution. The first of these, the axiom of infinity, provides for the existence of infinite sets by stating that an inductive set exists (Hrbacek & Jech 1978:54). For Jakobsonian markedness theory and the features defined within it, infinite sets are not required, since the phonological distinctive features and the morphological conceptual features are finite by definition. The axiom of substitution (sometimes referred to as the axiom schema of replacement) is required when there is a need to extend the process of counting beyond even the natural numbers (Hrbacek & Jech 1978:117; Halmos 1960:75). This axiom, also not crucial at this level for defining the principles of markedness theory, could be omitted along with the axiom of infinity, except for one problem. Because the definition of the axiom of choice presupposes the existence of these two axioms, they must be included in the axiomatic base for the sake of consistency. Similarly, the axiom of choice is required because it allows us to prove the well-ordering theorem, and all principles concerning ordering are

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very important in Jakobsonian markedness theory. Therefore, the new listing of axioms is as follows: Axiom 1: There exists in the universe of discourse a set that has no elements (axiom of existence) Axiom 2: A difference in form signifies a difference in meaning (axiom of extension) Axiom 3: To every set A and to every condition S(x) there corresponds a set B whose elements are exactly those elements x of A for which S(x) holds (axiom of specification) Axiom 4: For any two sets, there exists a set that they both belong to (axiom of pairing) Axiom 5: For every collection of sets there exists a set that contains all the elements that belong to at least one (that is, some) set of the given collection (axiom of unions) Axiom 6: For each set there exists a collection of sets that contains among its elements all the subsets of the given set (axiom of powers) Axiom 7: An inductive set exists (axiom of infinity) Axiom 8: Let S(x, y) be a property such that for every x there is a unique y for which P(x, y) holds. For every A there is a B such that for all x E A there is ayE B for which S(x, y) holds (axiom of substitution) Axiom 9: The Cartesian product of a non-empty family of non-empty sets is non-empty (axiom of choice). The remaining question is, what relevance will the system of axioms given above have to markedness theory and linguistic analysis? The key concepts of Jakobsonian markedness theory, binarity, asymmetry, hierarchy (or ordering), and opposition, are alII/well-defined" in mathematics, and mathematics thus allows the linguist to formulate these principles more clearly. Furthermore, mathematics demonstrates the compatibility and consistency of these principles, all of which are intimately related in presupposing and requiring each other. It is by means of the axiomatic formulation, in fact, that all of the primary assumptions of markedness theory (and mathematics) are laid bare. In particular, the ability to ascertain sameness and difference is the basis of human perception and, thus, of language. Only through opposition is difference perceivable, and Jakobsonian linguistic analysis has always considered opposition to be a "principle of structure" (Pos

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1938:246-47). Since the simplest oppositional relationship involves more than one unit (therefore, at least two), the fundamental oppositional relationship is binary (or dyadic). Furthermore, the sign theory view of language focuses on the interaction between the signans (form) and signatum (meaning). However, the linguistic sign is not symmetrical but asymmetrical, and in morphology and semantics, this asymmetry is weighted on the side of the signatum. The Jakobsonian definition of markedness specifically describes the linguistic sign's asymmetry by distinguishing between general and specific meaning. Since each linguistic sign can be reduced to smaller "but still semiotic units," the notion of hierarchy becomes crucial to defining not only the ordering of formal units at the "language" level, but also the ordering of the phonological distinctive features and the morphological conceptual features at the deepest level (Jakobson 1949:104). These four fundamental phenomena, united by Jakobson in linguistic sign theory, are rigorously unified in mathematics (as is especially clear in set theory) in such a way that they become the basis for defining all of higher mathematics' principles, definitions, and theorems. The present work neither requires nor suggests the need for developing new axioms or using logical postulates to describe language. Rather, employing an axiomatic base taken from mathematics here is an attempt to make explicit the definitions and operations giving rise to all possible set relations in order to define the principles on which markedness theory is based: binary relations, hierarchy, inclusion, and asymmetry. Therefore, set theoretical concepts are being connected to markedness theory and linguistic signs on the definitional level only; no statement about the actual linguistic "forms" is being made at this stage. One of the most interesting proofs relating to axiomatic systems was discovered by Kurt Code!. His work, On Formally Undecidable Propositions of Principia Mathematica and Related Systems (1931), demonstrated that the Continuum Hypothesis in number theory (or w-inconsistency) could not be proven with Russell and Whitehead's Principia Mathematica. Likewise, this hypothesis cannot be proven true or false within the Zermelo-Fraenkel (plus the axiom of choice) system. The implication of Codel's discovery is that no sufficiently powerful axiomatic system of the type described is complete. However, since the primary con-

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sideration for any axiomatic system is consistency, not completeness (Naps 1969:112), what Codel's theorems and proof did not achieve was making all usage of axiomatic systems obsolete. In fact, far from abandoning axiomatic set theory, mathematics has retained the ZFC (Zermelo-Fraenkel plus Choice), and mathematicians continue to seek "intuitively justifiable axiom[s] with important consequences outside of set theory which could be added to ZFC and which would decide the Continuum Hypothesis" (Hrbacek & Jech 1978:174). Furthermore, the importance of set theory to mathematics as a whole should not be underestimated, for it is set theory that gives rise to the principles of elementary mathematics, which, in turn, "act as a basis for every other branch of mathematics ..." (Naps 1975:111). Douglas Hofstadter eloquently sums up the major thrust of Codel's proof: "In short, G6del showed that provability is a weaker notion than truth, no matter what axiomatic system is involved" (1979:19). Similarly, this work neither claims that linguistic utterances must be "logical" (in the narrow sense of the word), nor urges linguists to invent new axioms and apply them to such utterances. Instead, my goal here is to explicate the mathematically based assumptions that allow us to define consistently those semiotic units believed, in approach, to make up language. Such an explication may also help to clarify the confusion over how closely language is related to mathematics and logic, a confusion that arises from linguistics' equivocal status as a discipline. Since many linguistic approaches are based on the belief that linguistics is a science, certain trends that focus on testing for truth and falsity in language have developed. However, to establish linguistics as a science requires a primary focus on testing our linguistic approaches and theories for truth and falsity (or rather, consistency), not in such testing of language itself. Civen a consistent paradigm that will allow us a more rigorous approach, our analyses of linguistic data will inevitably be more rigorous as well. C. S. Pierce sums up this notion in stating that" ... science, then, is not so much correct conclusions, as it is a correct method" (1957:192). Let us now consider a linguistic phenomenon having a mathematical counterpart: the qualitative difference between definitions of markedness relations in phonology and in morphology. The signatum in phonology, unlike that in morphology, is not more complex than

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the signans; it cannot be described in terms of general and specific meaning because the phonological signatum, representing only "mere otherness," does not reflect a particular property of meaning. However, what can be demonstrated is that the phonological sign as signans and signatum requires for its definition a binary operation more complex than that which defines the morphological sign. Although the signatum in phonology seems simpler than in morphology at first glance, the privative binarity of the phonological sign is, in fact, a more complex relationship that necessarily presupposes the type of binarity present in the morphological sign. In other words, the relationship presence vs. absence is presupposed by the relationship presence vs. nonstatement of presence/absence. This apparent reversal between phonology and morphology has a counterpart in mathematics, where, for example, the binary operation which defines addition presupposes subtraction; the binary relation of inclusion presupposes the relations union and intersect. Based on the axiomatic base above, it becomes evident that any theory of markedness, that is, any theory which attempts to define the oppositional relationship between invariant elements of a given language, must include "well-defined" notions of sets, binary relations, and ordering. This is no easy task considering that not even such a rigorous science as mathematics has a "well-defined" formulation of a "set." Just as mathematicians cope with this difficulty by working with an intuitive definition of a mathematical set, we will have to work with an intuitively defined formulation of a linguistic set. The nine axioms stated above are sufficient to motivate a powerful markedness theory. However, the fact that we still have no criteria for defining what types of elements (or features) will be applied by the axiomatic base reveals a crucial difference between mathematics and linguistics. Ultimately, some criteria must be developed for determining which types of elements are relevant. Unlike set theory's ability to focus on the relationships among the elements, rather than on the elements per se, linguistics, according to Jakobson's theoretical premise, must study not only the relationships between the parts, but also the parts (or elements) themselves (Holenstein 1978:6-8). Therefore, markedness is not simply a reductionist type of approach, but one that depends on balancing reductionist and holistic approaches to achieve

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the deepest understanding of how the features (representing meanings) and forms of a language interact. An equal and simultaneous focus on both of these levels will enable us to define the functional relationships between any given element or elements within a language or between different languages. What is it then that defines these relations? Invariants. In a given mapping from one set to the other, the forms themselves may not be preserved by the mapping, but the functional relationship will remain constant. Thus, the invariant rule determines both the relationship among the parts and the parts themselves. Modern Russian offers a possible application of this approach in the occurrence of "determinacy" in the category of adverb, as well as verb. C. H. van Schooneveld (1982) has shown that the adverbs skorol bystro ("soon, quickly" I"fast, quickly") differ in meaning for the same reason that the verbs idtilxodit' ("to go") differ-namely, that the first element of each pair is marked for "determinacy" (or Extension' , in van Schooneveld's system), whereas the second element of each pair is unmarked for this feature. The distinct endpoint given by EXT' , can be spatial or temporal. In other words, spatial and temporal are merely contextual variants which will be determined according to part of speech. But determinacy (or Extension' ') means that there must be an endpoint, which i~ necessarily different from the beginning point. Thus, idti cannot mean "round trip," and skoro, always implying a new endpoint, is incompatible with a past tense imperfective. (For example, *On skoro cital I "He quickly was reading" is an impossible construction since no new endpoint is required with an imperfective verb, whereas On skoro procital I "He quickly read I finished reading" is a possible one since the perfective verb form requires a defined endpoint). Although their parts of speech and lexical roots indicate great differences between the two sets of forms, the relationship between the two sets of examples is invariant. Furthermore, this marking of determinacy (or Extension' ') would be called a semantic (or conceptual) marking at the level of grammatical meaning. Yet what about the lexical meaning of the forms? These will require a different level of application of the markedness concept, which we will tentatively call formal markings. Although a given element's formal marking (lexical meaning) and its conceptual marking (grammatical meaning) are not necessarily the same, these two levels of markings are defined by the same features.

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Furthermore, the conceptual marking, not being restricted to only one form, can convey its invariant meaning to many different forms. Another application of mathematics to linguistics lies in theoretically explaining the precise difference between formal and conceptual markings by analyzing the mathematical distinction between belonging (E) and inclusion (C). Belonging means that a given object is an element of a set, that is, a E X. Inclusion (or set inclusion) means that one set is included in (is a subset of) another set, that is, A C B. It is important to realize that belonging is "the principle concept of set theory" (Halmos 1960:2). In fact, in an axiomatic set theory like the one presented here, belonging is the "principle undefined concept," that is, it is only intuitively defined, as is the notion of a set. For Jakobsonian linguistics, belonging and inclusion are fundamental concepts which define the difference between conceptual marking and what I have called formal marking. The relation of inclusion, both in general mathematics and in the axiomatic base developed above, is a well-defined concept. The differences between belonging and inclusion are also clear in terms of an equivalence relation. Inclusion is always "reflexive" (A C A) and "transitive" (A C B, B C C imply A C C); belonging is neither "reflexive" (A E A is false) nor "transitive" (A E B, B E C does not imply A E C) (Halmos 1960:3). Neither inclusion nor belonging is symmetric (as is equality). Thus, when we assign a formal or conceptual marking to a linguistic form, we do not consider the marking and the form to be equal; instead, they represent an asymmetrical relation between two qualitatively distinct entities. Since we are defining markings as interpretants of the signans-signatum relation, then, following Peirce, the interpretant is necessarily distinct from both the sign and its object. Therefore, by definition the linguistic marking cannot be equal to the signans or signatum. Recalling that a formal marking is restricted to one form in all of its contextual occurrences, whereas a conceptual marking is not so restricted, formal markings represent a type of inclusion and conceptual markings a type of belonging. The connection between markings and set membership can be clarified by representative examples of the two types of markings taken from Russian.

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The perfective aspect, according to van Schooneveld, is marked for Dimensionality (1978b:45) and, in Russian, occurs with many disparate verbal forms. For example, govorit' ("to speak") and pokazyvat' ("to show") are imperfective, but pogovorit' ("to have a talk") and pokazat' ("to show") are perfective. In terms of these examples, we cannot assign the feature Dimensionality, which represents perfectivity, to the suffix -it' nor to the prefix po- since neither of these forms necessarily gives perfectivity. This example of a conceptual marking is similar to the mathematical notion of belonging. Just as belonging is not "reflexive," that is, A E A is false, neither does a conceptual marking imply that the marking dimensionality is formally attached to any part of the linguistic form (that is, po-govor-it' or po-kaz-at'). In this case, neither po- nor govor nor -it' possesses the perfective marker as a "formal" marking, yet the overall form pogovorit' is marked for perfectivity (DIM). If markedness theory had been perceived from its inception as a theory of interpretants, the point concerning "belonging" would have been self-evident. Although any lexical morpheme could serve as an example of a formal marking, for our purposes, the Russian preposition/prefix ob(-) ("about, around, concerning") will do. Ob(-) ("about, concerning") is "formally" marked for Dimensionality and Extension (van S.chooneveld 1978c:lll), implying that no matter what concatenation the morpheme appears in, that is, whether as a preposition or a prefix (obstanovka, ob universitete, obmenjat'), ob(-) always bears the features DIM and EXT in all of its surface manifestations. In other words, Dimensionality and Extension, as final interpretants, are always included in all formal occurences of ob(-). The means to establishing the correspondence between ob(-) and DIM/EXT is by application of a mapping, or interpretation, in the Peircean sense. Although many verbs with the ob- prefix are perfective (obmenjat', obygrat', obstric'), the marking of perfectivity is not "included" in every formal occurrence of ob-. Perfectivity "belongs" to ob- only in certain syntactic concatenations with other word formative elements, never with ob- as a single unit. While perfectivity (DIM) "belongs" to the form pogovorit', the presence of Dimensionality in any component of the word is not implied (according to the rules of mathematical "belonging," belonging is not transitive), Dimensionality and Extension, being "included" in every

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occurence of ob(-), are necessarily present (that is, included) in the forms obmenjat' and obstanavlivat' (to name only two). In other words, perfectivity (DIM) "belongs" to the form pogovorit' but is not "included" in either po-, govor, or -it'. However, DIM and EXT are "included" in the form ob(-) when it appears as ob (alone) and when it appears in any other concatenation (obmenjat', obstanovka), that is, when it is a "transitive" relation such that if DIM + EXT C ob(-), and ob(-) C obmenjat', then DIM + EXT C obmenjat'. Regarding interpretants, we would state that two levels of interpretation of the sign are necessarily involved-the interpretant produced from the bundle of morphemes in the form of a word, and the interpretant produced by each minimal unit of meaning (that is, prefix, root, suffix, grammatical ending, etc.). The first level of interpretant is more distanced from the formal representation of the sign, while the second level is more aligned with the form. It is erroneous to assume that ob(-) is equal to the set containing DIM and EXT because the features DIM and EXT are only included in the formal representation of ob(-). And the difference between inclusion and equality is that while inclusion is antisymmetric (A C B does not imply B C A), equality is symmetric (A == B implies B == A). Markedness relations are, by definition, asymmetrical (or antisymmetrical); the marking follows from the signifier/signified relationship, just as the interpretant follows from the sign, not vice versa (cf. chapter 2). Once again, this observation, that two "types" of markings exist for linguistic forms, is supported by a similar distinction in mathematics. Here, the distinction between formal markings and conceptual markings is both quantitative and qualitative. With conceptual markings, the autonomous, self-standing linguistic form (cf. pogovorit') assumes an additional marking (DIM, representing perfectivity) that is "greater than the sum of its parts," both qualitatively and quantitatively, whereas with formal markings, the form constantly maintains the same marking-no more, no less (cf. ob(-)). An additional problem arises at this point with regard to a marked/ unmarked pair of linguistic forms. Mathematics does not concern itself with unmarkedness, only with markedness; mathematics is concerned only with the application of specific features (in the form of binary operations) to relevant sets.

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The Morphological Conceptual Features and Group Theory From Leibniz to Peirce, algebra is considered 'the most perfect illustration of the [figurative] characteristica' (Lambert 1764:3.35). The algebraic equation is an icon. It uncovers a multitude of relations among the quantities represented by signs.-Elmar Holenstein (1978:48)

One of the major difficulties in attempting to define the conceptual features, as developed by Jakobson and van Schooneveld, is due to their having been originally formulated in extremely abstract terms, albeit vis-a.-vis a particular grammatical or lexical category (Jakobson's definitions are stated in terms of the Russian case system and van Schooneveld's in terms of the Russian prepositions, prefixes, conjunctions, and verbs). The conceptual features were nonetheless rigorously defined by van Schooneveld, however, in the context of the linguistic system under scrutiny. Yet, it is also possible to define the six conceptual features as isomorphic to the definition of the set of natural numbers in mathematics. Consider figure 28. Each set in the series is formed solely from its previous constituents. Therefore 1/2" is equivalent to the set of elements containing {I} and {O}, which were themselves previously defined by the sets {O} and (/). The natural number 1/2" thus presupposes the existence of 1/1" and I/O." Stating that the six conceptual features are isomorphic (that is, in a one-to-one relationship) to the natural numbers 1/1" to 1/6" means that a one-to-one correspondence exists between the elements of the two sets so that the result achieved by applying a binary operation to the elements of one set corresponds to the result obtained by applying a similar operation to their images in the other set. In this particular case, it would have been possible to set up an isomorphic relationship Figure 28 Isomorphism 0 = (/) Plurality ~(-------~) I = 0+ = {O} Dimensionality ( ) 2 = I + = {O,l} Distinctness ( ) 3 = 2 + = {O,I,2} Extension ( ) 4 = 3 + = {O,I,2,3} Restrictedness ( ) 5 = 4 + = {O,I,2,3,4} Objectiveness ( ) 6 = 5 + = {O,I,2,3,4,5} (Halmos 1960:44)

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to the natural numbers "0" through "5," or "5" through "10," etc. The reason for choosing "I" through "6" is to better illustrate the fact that the first conceptual feature, plurality, implies the creation of more than one point in space (or the universe of discourse), whereas "0" is defined by nothingness. In linguistic systems, the notion of "absolute nothingness" would correspond to a totally unmarked element, such as silence, perhaps, but the existence of a totally unmarked, formally expressed element in language is impossible, since the so-called unmarked element exists only vis-a-vis the marked element (just as there is no nominative case in a language without case oppositions). A more interesting similarity between the set of conceptual features and the set of natural numbers x+ == x U {x} where x E {O, 1, 2, 3, 4, 5} is the graphic way in which the set of natural numbers illustrates the notion of hierarchy, including the manner in which each number, and hence each feature, is "included" by the previous feature. Yet, the more complex features in the hierarchy, while being "included" by each previous feature, are at the same time more specific. What the model above demonstrates is that although the final feature, objectiveness, is the most specific, the space covered by Objectiveness is potentially larger than the space given by each of the preceding features. Thus, Plurality establishes only one fundamental relationship, but it potentially contains all of the other, more specific relationships (that is, Dimensionality to objectiveness). Such a definition is in keeping with phenomenological theory, where "opposition simultaneously represents an exclusion as well as an inclusion [italics mine]" (Holenstein 1979:85). Note figure 29. What is even more interesting than the isomorphic relationship between the six conceptual features and the natural numbers is the extension to group theory to which the six features so readily lend themselves. In particular, certain principles concerning the features and how they combine were established by van Schooneveld independently of mathematics many years ago. One of his major principles concerns the noncommutative nature of the binary operation which defines how the conceptual features in a set combine with each other. Specifically, when the features interact at the most basic level of combination, the ordering is very important since the features are asymmetrically, not symmetrically, given. Also, at the sign level of language,

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Side View

Figure 29

when dealing with the signans and signatum, the sign's asymmetry was one of the basic notions set forth by the Prague School (Jakobson 1949: 1°5). The extension of markedness theory from set theory to group theory is not only a natural but a necessary one, since group theory analyzes sets' and binary operations, whereas set theory's focus is exclusively on the set and its elements, not on the binary relations and operations potentially connected with each set. The definition of a mathematical group is as follows: A group G is a non-empty set of elements and a binary operation * for which the following conditions are true:

* (i.e., no new elements result from applying the operation); (2) The Associative Law holds such that a * (b * c) = (a * b) * c where a, b, c E G; (3) There exists an identity element e in G such that e * a = a * e = a for every a E G; (4) For every a E G, there exists in G an inverse element of a denoted by a-I such that a * a-I = a-I * a = e (the identity). (Dinkines 1964:5)

(1) G is closed with respect to

It is important to understand that a mathematical group should be conceived of as a set with a particular binary operation, not as a set

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and a binary operation (Dinkines 1964:6). In other words, a set mayor may not be a group once the binary operation is changed. The mathematical development of the concept of a group had its origins in the set of mappings, or permutations, of a set onto itself (Herstein 1975:120). Since then, group theory has often been used in fields outside of mathematics. For example, groups have been invaluable to physicists and chemists in studying the structure of molecules (Dinkines 1964:17), as well as in describing the wave functions of molecules and crystals (Burns 1977:37). While the types of groups that exist are infinite, a particular group may be finite or infinite. The type of group best describing the six conceptual features would be a finite group containing six elements. But before giving examples of groups with six elements (that is, groups of Order 6), let's consider a simpler group in the following example: the set of numbers {I, -I} combined under the operation of multiplication. In this case, the inverse of 1 is -1; the inverse of -1 is 1; and the identity element is 1. This group can be represented by the chart in figure 30. This particular group is commutative, that is, the result is independent of the order of the elements (1 x -1 == -1 x 1 == -1). In fact, all groups with five elements or less must be commutative, or "abelian" (Dinkines 1964:14). Therefore, the smallest noncommutative group must have at least six elements. The application of group theory to the conceptual features corroborates van Schooneveld's claim that the set of conceptual features containing six elements is defined by a binary operation for which the commutative law does not hold. In the case of markedness theory, we can now establish an isomorphism between the six conceptual features and a noncommutative Figure 30

X

1

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Markedness as Mathematical Principle

A

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Figure

31

(or nonabelian) group of order six. The ability to define an isomorphism between any two finite groups is guaranteed by Cayley's Theorem, which states: Every finite group is isomorphic to a certain group of permutations (Alexandroff 1959:31). If, in fact, the isomorphism is a "faithful" representation, then certain properties of the conceptual features should become clearer through their association with a mathematical group. Before demonstrating the group of conceptual features, it might be helpful to present two nonabelian mathematical groups of Order 6 in order to demonstrate how groups work. The first group of Order 6 is called the permutation group Sand consists of the following permutations of three numbers 1, 2, and 3: 123)

(123)

(123)

(123)

(123)

(123)

(a) ( 123 ; (b) 132 ; (c) 213 ; (d) 231 ; (e) 312; (f) 321 .

The first permutation, 123) ( 123 ,

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is the identity since every number is in its original position. In chart form, we have the results in figure 31 when combining (a) * (b), (b) * (c), (a) * (c), etc.: (c) * (f) == 1 ~ 2; 2 ~ 2 2~

3~

1; 1 ~ 3 3; 3~ 1

123) Therefore, (c) * (f) == (d) ( 231

Any given element in a group can occur at most and at least once in a given row and a given column. In other words, each element must appear once in each row and each column. There are many versions of the S group, of which the above is only one variant. Another group of Order 6 can be generated from the set of six rotations on an equilateral triangle. The six motions are shown in figure 32. The resulting diagram and chart appear in figure 33. By definition, there can only be one identity; in this case the identity is A. Each element is its own inverse except for Band C, which are each other's inverses. The second group given above is isomorphic to the group of six conceptual features. Therefore, we can substitute PL (Plurality), DIM (Dimensionality), DIS (Distinctness), EXT (Extension), RES (Restrictedness), OBJ (Objectiveness) for A, B, C, 0, E, F, respectively (see fig. 34). The identity element is represented by the feature plurality, and each feature is its own inverse except Dimensionality and Distinctness, which are each other's inverses. The uniqueness of DIM and DIS with regard to their inverses is a very important distinction because

Figure

32

A = no shift in vertices B = clockwise rotation of 120 C = clockwise rotation of 2400 o = reflection/flip on the line L1 E = reflection/flip on the line L 2 F = reflection/flip on the line L 3 0

3 c----t-------....2

Markedness as Mathematical Principle 3

3 '------~2 A

2'------~3

'---

~3

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Identity = A Inverses are:

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Figure 33

it illustrates the qualitative difference of these features from the other four. Specifically, the difference is that, beginning with the operation which occurs in Distinctness, a new deictic level is imposed on the remaining features in the hierarchy, namely EXT, RES, and OBJ (van Schooneveld 1978c:242-49) [cf. chapter 1]. Since the formation of the features themselves, which is what the group above illustrates, is a

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*

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Figure 34

retrograde one in which each new feature is definable only in terms of the previous one (cf. 2 == {I,D}), then it is entirely consistent for PL, DIM, and DIS at this level to be qualitatively different from the remaining features (recalling that PL is totally unique as the identity feature, and that DIM and DIS have distinct inverses). Furthermore, the last row illustrates another important property of the conceptual features: Since OBJ is the final possible feature, the combination OBJ * OBJ necessarily goes back to beginning point, PL. (There are many other structural aspects of the conceptual features, stated in terms of group theory, that remain to be investigated.) Having established the axiomatic base of a markedness theory and given an overview of its historical roots, it seems appropriate now to focus on some specific applications of markedness principles. The work of John Lyons, C. H. van Schooneveld, and Joseph Greenberg in this area is particularly pertinent. John Lyons constructs a tripartite system of markedness for lexemes, as follows: (1) Formal marking-The presence of an additional word-formative

morpheme (for example, host/hostess).

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(2) Distributional marking-The marked form is more restricted in terms

of the contexts in which it can occur (for example, good vs. bad, lion vs. lioness). (3) Semantic Marking-The marked term is more specific (for example, man vs. woman). (1977:305-7) These three subclassifications are not inclusion relationships, but ones that intersect at various points, yielding the potential for a given pair of lexemes to belong to all three types (that is, lion/lioness). But this clearly contradicts Axiom 2, which states that every set can be wellordered, hence every set is made of inclusion relationships to define the ordering. [The definitions of conceptual and formal markings given in this work do not correspond to Lyons' categories (1) and (3). Therefore, this difference is far more profound than just a case of the addition of a distributional marking by Lyons.] The tradition in Jakobsonian analysis has been to work primarily with the paradigmatic axis. This approach implies that there is no place for distributional criteria in the fundamental axioms of the theory, as distribution is a syntagmatic phenomenon involving variants as well as invariants. Distribution, however, is a context-oriented phenomenon-and it is in this type of "context" that one finds variation, not invariance. (Distribution generates a different type of context than deictic relations.) If a markedness theory consists of elements that are invariants by definition, then there is no place for variable features. However, the omission of variable features in the paradigmatic base does not imply an absolute prohibition against using distribuFigure 35 Lyons' Classification

Axiomatic Classification Conceptual

8

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tional variations; these may be used initially to help determine which form is marked or unmarked, but they have no place at the most fundamental axiomatic base. Nor does the discussion above imply that context is unimportant; on the contrary, there is no potential determination of invariance without a context from which to work. With regard to differences over formal markings, Lyons includes only word-formative items, while this analysis would include both lexical roots and word-formative items. Lyons' semantic marking can correspond to either our conceptual or formal categories. Since all markings are semantic, however, we use the word conceptual in specifically referring to any feature that can occur with several different forms. For example, as we have already shown, perfectivity in modern Russian is not signaled by one single form but is realized in many disparate forms, such as the prefix po- in pomenjat' (perfective) versus menjat' (imperfective), or the suffix -it' in vkljucit' (perfective) versus vkljucat' (imperfective). The salient point to be recognized is that each type of marking may be analyzed by the same set of features or invariants. The variation that occurs in any given syntagmatic combination is ultimately reducible to an invariant. For example, the verbal suffix it' does not always give a perfective verb (as in govorit'). Such a cyclic type of relationship among features forms the basis of recursion, or, the same phenomenon occurring on different levels at the same time. Recursion, as demonstrated by the method of van Schooneveld, makes it possible to generate the entire Russian language with six features on four deictic levels. Although Lyons manipulates the notion of markedness correctly, the problem arises when these marked/unmarked relationships are based on such a priori established categories as male/female and animate/inanimate, which are not necessarily linguistic categories. Rather, linguistic markedness relationships should be based on linguistically given perceptual categories, although the perceptual categories will occasionally overlap with the descriptive ones, such as animate/inanimate. (For example, the so-called animacy distinction in the Russian accusative case distinguishes between masculine living and masculine non-living but not between feminine animate/inanimate, nor does it include plants, which are biologically "living" organisms.) Let us look briefly at an example of the complex relation between

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"formal" and "conceptual" markings from a van Schooneveldian point of view. Such an illustrative example would be the following verbal forms from Russian: obmenivat' (imperfective), obmenjat' and obmenit' (obs.) (both perfective). On the "conceptual" level, we have the opposition imperfective/perfective, where the perfective is marked (Dim') under Grammar (Dist '" ') [cf. figure 11 in chapter one]. The imperfective lacks the feature Dim'. However, on the level of "formal" marking, there are several things to consider: (1) The root -men- under Lexical Meaning (0'" '); (2) the preverb ob- under Lexical Meaning and Part of Speech (0' , , , & Dim' , , '); (3) the three verbal suffixes: -iva(t'), -a(t'), and -i(t') under Word-Formation (PI'" '). On the formal level, the higher marked features are combined first since they "set the stage" for the following features. Therefore, in van Schooneveld's system, the feature objectiveness comes before restrictedness and restrictedness before extension, etc. What this example illustrates is that, in any given word, there may be several different formal markings that compose the morphological shape of the word, whereas those same two forms may differ only by one feature on the conceptual level. Specifically, perfectivity or imperfectivity is not signaled by only one, unique form, as was shown above. To consider either of these markedness types without the other, therefore, would destroy the relevance of the methodology. The "formally" marked obmenivat', for the suffix -iva(t'), is in fact "conceptually" unmarked for perfectivity. Therefore, it is meaningless to say obmenivat' is unmarked with regard to obmenjat', unless the level of markedness (that is, conceptual or formal) is explicitly specified. Even then, this term must be used very carefully-marking of the M/U type is not absolute but a matter of degree; however, markings, as expressed by the conceptual features, are fixed within the synchronic linguistic system. This characteristic of markedness becomes particularly evident when dealing with meaningful linguistic units that consist of such word-formative elements as prefixes and suffixes, where many different features (or cumulation of features) apply to a given linguistic form. In his book Language Universals, Joseph Greenberg states that markedness is a language universal. Based on empirical information gathered from many of the world's languages, Greenberg has posited

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certain universal criteria for morphological markedness: (1) Formal syncretism in the marked category (for example, in Russian the locative and genitive plural adjectival endings are the same); (2) The presence of a "formal" element to indicate marking (for example, English "big"I"bigger"); (3) Facultative expression (or substitutability) of the unmarked for the marked term (for example, "man is an intelligent being" refers to men and women); (4) Hjelmslev's notion of "participation," or contextual neutralization (for example, in Russian the numerals 2, 3, and 4 take the genitive singular of the noun); (5) A lesser degree of morphological irregularity in the marked form (for example, compare the relatively highly marked Russian verb govorit' ["to speak"] to the unmarked verb byt' ["to be"]); (6) Hjelmslev's "defectivation"-where the marked category lacks categories present in the unmarked (for example, no future tense in the French subjunctive); (7) In the category of number, the unmarked category is used to represent a heterogeneous group (for example, in Serbo-Croatian, the masculine plural is used when referring to a mixed group: Ove reke(fem.) i brda(neuter) su bili(masc.) ovde == "These rivers and hills were here"); (8) The unmarked category occurs more frequently, (for example, the third person singular occurs more frequently than the first person in Russian) (Greenberg 1966:45). According to our axiomatic base, all of Greenberg's eight criteria for markedness would be recognized as "tendencies" but not as rules, since counterexamples can be given for each of the eight types. The fact that each statement can be shown to be both true and false, depending upon the linguistic context, excludes their presence from the axiomatic base, which must be consistent. Statements that can be either true or false are considered inconsistent, and, as such, they violate the validity of the axiomatic base. However, one problem always inherent in any sufficiently powerful and consistent axiomatic system is that of its completeness (that is, the entire system's being derivable only by utilizing the axioms stated). According to the proof of Kurt G6del, no axiomatic system that is sufficiently consistent can be complete. However, G6del's proof, as demonstrated earlier, does not imply that an axiomatic approach to a problem is useless, but that once the axiomatic base has become sufficiently sophisticated, other propositions must be adopted to give completeness to the system.

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Let us now consider some of the counterexamples to Greenberg's eight criteria for markedness: (1) Formal syncretism in the marked category: no syncretism in the Russian accusative case (marked) for feminine II declension nouns with the nominative case (unmarked) (kniga(nom)/knigu(acc)) versus syncretism in the accusative of neuter I declension nouns with the nominative (okno(nom)/okno(acc)); (2) presence of a formal element to indicate number: the Russian genitive plural in -(/) (cf. kniga (nom. sing.), knig (gen. pl.)); (3) substitutability of the unmarked for the marked term: in English, the pair "baron" / "baroness" ("baron" can never refer to "baroness"); (4) contextual neutralization: according to Jakobson, contextual neutralization does not exist in morphology or semantics since in these two areas, as opposed to phonology, we are dealing with properties of meaning, not with "mere otherness" [cf. chapter 4]; (5) less morphological irregularity in marked forms: highly marked deictic categories have a great deal of irregularity, as do lesser marked general categories (cf. the Russian personal pronouns are a highly marked deictic category and are "irregular" in their declension); (6) marked category lacks categories present in the unmarked category: the plural number maintains and expands the animate/inanimate distinction in Russian to include feminine as well as masculine; (7) unmarked category of number represents a heterogeneous group: Classical Arabic admits only feminine singular agreement of both verb and adjective for any nonhuman plural noun; (8) unmarked category occurs more frequently: the imperfective in Russian occurs 46.9 percent, the perfective 53.1 percent in usage, according to Greenberg; thus, here is one example of the marked category occurring more frequently than the unmarked. (Greenberg's third criterion, facultative expression, or substitutability, will be discussed in chapter 4 as one of the popular "myths" about markedness. ) In any scientific approach, an equitable use of the principles holism and reductionism seems to be the only means of achieving a complete understanding of how languages work. Although markedness theory may have sprung from the principle of reductionism, it is important to remember that markedness can make just as great an impact on the holistic level. What is truly remarkable about the kind of notions of markedness in morphology, as applied semiotically, is the truly in-

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variant nature of those features. Regardless of what level one is ad-

dressing, whether a conceptual marking or a formal one, the same prototype features (as final interpretants) can be used to describe the invariants on these two different levels. In any application of markedness theory, distinctions must be made regarding which level is being addressed (formal or conceptual) or the theory will lose much of its explanatory power. Thus, we return to the ultimate message of markedness theory as a methodology: There is sameness in difference. From this perspective, we are able to perceive some "method" to the "madness" of language and to continue attempting to describe language as a "system" of signs. At the present time the technique used to establish the "marked" or "unmarked" nature of a given linguistic item includes first analyzing all of a form's "contextual usages" and then extracting an invariant general meaning from the set of seemingly variable meanings. (Roman Jakobson uses this method in his "Beitrag zur allgemeinen Kasuslehre.") However, these two steps do not go far enough. Next, the discovered invariant meaning as a relational category must be integrated with the "paradigmatic system" of the entire language in order for it to attain significance. This step has already been taken in van Schooneveld's morphological analyses of Russian and in Andersen's analyses of the distinctive features in phonology (1974). Such re-integration with the language system leads the linguist to establish a hierarchical pattern, for without some notion of the system in its entirety, there can be no hierarchy. Whether or not this particular linguistic paradigm's subscribing to markedness theory is the only or even the best way to analyze language is still a matter of individual choice. The major advantage of markedness, as a theory of interpretants, is its being a multifaceted as well as logically consistent means of analyzing language. Perhaps this particular paradigm's commitment to rigor and logical formulations is what allows it to continue to play a major role in the development of linguistics as a science: Without commitment to a paradigm there could be no normal science. Furthermore, that commitment must extend to areas and to degrees of precision for which there is no full precedent. If it did not, the paradigm could provide no puzzles that had not already been solved. Besides, it is not only normal science that depends

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upon commitment to a paradigm. If existing theory binds the scientist only with respect to existing applications, then there can be no surprises, anomalies, crises. But these are just the signposts that point the way to extraordinary science. (Kuhn 1970:100-101) Peircean sign theory offers an alternative perspective, assurance, from which to determine that "the object for which it [the interpretant] stands is also the object of the sign which the interpretant interprets" (Savan 1976:53). Briefly, Peirce describes three types of assurance: instinct, experience, and form (Savan 1976:54-56). The third type of assurance, form, is most crucial for markedness theory. As Savan comments, "It is through unity of form that the interpretants of signs of laws and necessitants are assured of their validity" (1976:56 [italics mine]). Once again, we must acknowledge the importance of the form as the key to all structure. In closing this chapter, a return to the philosophical questions underlying our approach is appropriate. In particular, it seems useful to re-examine the relationship between the disciplines of logic and mathematics, between terms like demonstration and proof, substitution and replacement, and to address the relevance of the linguistic form. This should allow us to put the finishing touches on the mathematical principles of a Jakobsonian-based markedness theory. The Laws of Form and the Form of Laws If it was shown earlier that the immutability of the mathematical object, or linguistic signified, justifies our quest for invariant structures, there is also an alternative perspective concerning the form, or linguistic signifier, as a mutable entity. It is to this latter perspective that we will now turn our attention. As G. S. Brown proposes in eloquently uniting these two points of view: Although all forms, and thus all universes, are possible, and any particular form is mutable, it becomes evident that the laws relating such forms are the same in any universe. It is this sameness, the idea that we can find a reality which is independent of how the universe actually appears, that lends such fascination to the study of mathematics. (1969:v)

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Here, the relationship of form and meaning, as perceived through the prism of laws, is reaffirmed in a more universal context. And mathematics is presented as one field that can facilitate a deeper understanding of the relationship between the laws and forms of structure. In this section, the work of G. S. Brown will reveal philosophical considerations that are crucial to understanding Jakobsonian markedness theory.

Logic or Math? Some confusion concerning the relationship between logic and mathematics is commonly found in linguistics. Brown helpfully sums up this relationship in very simple terms: logic is to mathematics as applied science is to pure ground. The implications of this statement are very serious ones for any conclusions drawn about so-called "logical" reasoning. Particularly important is the implication that logic is merely a "form" derivative of a given work's creativity. In other words, logic is secondary to that which is mathematical in the sense that logic is a product of the mathematical structure; logic, in fact, is the means by which structure is perceived. But logic does not create structureit simply makes itself known once the work has been created. Therefore, a mathematical theorem is not proved by logic. Rather, logic adds coherence to the argument. As Brown explains: A theorem is no more proved by logic and computation than a sonnet is written by grammar and rhetoric.... Logic and computation, grammar and rhetoric ... can be seen in the work after it is created, but these forms are, in the final analysis, parasitic on, they have no existence apart from, the creativity of the work itself. (1969:102) When mathematical principles are applied to linguistic analysis, logic -in the narrow sense of the term-is not necessarily being applied. Rather, our goal is to achieve a better understanding of the structure of the form. Jakobson was convinced of the fact that "there is no signatum (meaning) without signum (form [as sign])," and, therefore, he consistently regarded the linguistic signifier as the key to the invariants connecting form to meaning (1971b:260). In fact, Jakobson main-

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tained that access to meaning must come through the form. Brown, supporting Jakobson's theoretical position concerning the form, notes that the form is unavoidable and that "the conception of the form lies in the desire to distinguish" (1969:69). In other words, there is no meaning without form.

Demonstration or Proof? "Understanding is an intentional process."-Elmar Holenstein (1978:62)

Intimately connected with mathematics, and also used synonymously, are the two terms "demonstration" and "proof." In many ways the relationship between these two terms parallels the one between logic and mathematics. In particular, demonstration and proof, like logic and mathematics, share a boundary: proofs exist outside the given calculus, demonstrations exist within the calculus. This fact implies that while a demonstration can be seen as a proof, the converse is never true. Therefore, demonstration is to proof as (in arithmetic) initial equation is to axiom (Brown 1969:93-94). When a proof is discovered, relevance is given to the theorem in question. But this leads to yet another dichotomy-theorem versus axiom. As we saw earlier in this chapter, an axiom is a statement (or rule) accepted without proof, while a theorem is a statement which is provable within a calculus external to that calculus under scrutiny. Both axioms and theorems, then, are "simple statements about the ground on which we have chosen to reside" (Brown 1969:44). But these two types of rules are also relatively defined, depending on the calculus under examination: what in algebra is a consequence may be a theorem in arithmetic, implying that "any demonstrable consequence is alternatively provable as a theorem ..." (Brown 1969:44). Thus, instead of demonstrating an equation in algebra, one can prove it by arithmetic. What results are two distinct levels of mathematical operations, with axioms required at the arithmetic level and theorems at the algebraic level. Similarly, the axiomatic base presented in this chapter is fundamental to defining the features of markedness theory, while the algebraic level is reserved for more complex marked/unmarked values, that is, how the features combine to yield linguistic structure.

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The distinctions above lead us to differentiate two final terms: understanding versus following. Understanding is connected to invariance: "whatever is said or done can always be said or done a different way, and yet all ways remain the same" (Brown 1969:96). Furthermore, understanding is not a "static grasp of relations"; rather, when a relation is viewed as one piece in a series of relations, understanding becomes "an intersubjectively accessible operation" (Holenstein 1978:60). Following, on the other hand, is associated with variationit is "a particular way of saying or doing something" (Brown 1969:96). (Brown's formulation of these two concepts is very reminiscent of Saussure's distinction between langue and parole.)

Equality: Substitution and Replacement One of the major obstacles to a consistent application of Jakobsonian markedness theory arises from a misunderstanding about the role of substitutability of the unmarked element for the marked one in an oppositional pair. Perhaps by briefly reanalyzing what the notion of substitution implies, we can determine once and for all if it can be a property of markedness theory, as defined here. In discussing the rules of structure of algebras, Brown points out two implicit rules obligatorily associated with the notion of equality (==): substitution and replacement. Equality, necessarily yielding symmetry, makes substitution and replacement possible (Brown 1969:26). However, since Jakobsonian markedness theory is built on the principle of asymmetrical opposition, substitution and replacement are not automatically rules of that system. In fact, the notion of equality itself, as represented through linguistic synonymy, is dubious within such a theory. If, as was shown earlier, no true synonymy can exist in language, then neither can there be synonymy, or equality, of markings. Thus, substitution, having no place in the fundamental rules of such an asymmetrically defined theory, is not a real criterion for justifying a given marked/unmarked oppositional pair.

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Sign Zero Jakobson demonstrated in 1938 how important the opposition between "something and nothing" is in the phonological and morphological structure of language. In particular, Jakobson emphasizes that the zero desinence is nonetheless a desinence and serves to distinguish meaning: "Language 'can tolerate the opposition between something and nothing' not only on the level of the signifier (signifiant), but also on the level of the signified (signifie),' (Jakobson 1984:152). We must ask, then, how the concept of zero relates to the axiomatic system presented in this chapter. Is there any common ground between the definitions of the linguistic versus the mathematical zero? The answer to this question is "yes." In classifying types of expressions for his algebraic calculus, Brown states that any step, including zero, is significant (1969:37). Therefore, a zero step is a step. But a step (in mathematical terms) "is not intended to cross a boundary" (Brown 1969:37). In other words, the zero step is a function of the principle of naming, and naming, which is multi- (or pan-) directional, does not require redefinition, as does the notion of crossing (Brown 1969:80). This conception of step explains why the linguistically given sign zero can signify, alternatively, both the zero morphological function, as well as the positive morphological function (Jakobson 1984: 153). At this point the current status of markedness theory needs to be reviewed and an explanation of how the theory presented here differs from other approaches that use markedness needs to be made. The following discussion, therefore, will cover the most well-known catchwords and concepts that usually accompany generic markedness theory, as well as demonstrating their applicability within markedness theory, as defined here.

=Four= Myths About Markedness

Opposition means incompatibility at some point.-Andre Martinet

As defined in the first three chapters, the markedness theory conceived and developed by Jakobson is a qualitative theory of oppositional binary relations and one that would share certain properties with Peirce's interpretants. Jakobson did not devote any particular written work to giving a comprehensive discussion of markedness in general, choosing, rather, to apply markedness to specific problems within the areas of phonology, morphology, and semantics. Nowhere in Jakobson's works, for instance, do we find an explanation for the qualitative difference expressed by the definitions of markedness for phonology versus morphology (cf. chapter 1). Although we have already made this distinction, absent in Jakobson's formulation, explicit, this is only the initial step in presenting a logically consistent theory of markedness in morphology and semantics. (The following chapter will discuss some particular issues that have arisen and subsequently caused misunderstandings over what exactly Jakobsonianbased markedness theory can and should be.) Statistical Frequency

Ever since Trubetzkoy's application of markedness to phonology (1930) and Jakobson's application of it to phonology and morphology (1931), linguists have debated the pertinence of a given form's statistical frequency in determining a marked category. Trubetzkoy writes: "Zdes' statistika ni pri cem, a delo v samom, tak skazat', 'idejnom soderianii' korrelacii" (1930/1975:162) [Statistics has nothing to do with it. The crux

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of the matter rests in the so-called "intrinsic content" of the correlation (translation mine).] Trubetzkoy clearly felt that statistical frequency should not be considered an indicator of markedness relations in phonology, and, in my view, no logical inconsistency would arise from generalizing this statement to markedness relations in morphology and semantics. Yet, despite Trubetzkoy's clear denial of statistics' relevance in establishing markedness correlations, confusion has abounded over precisely this point. For example, John Lyons states that although the perfective aspect is usually considered the marked member of the perfective/imperfective aspectual opposition in Slavic, the "relatively high frequency" with which perfective verbal forms occurred in texts suggests that the perfective was, at some point, unmarked (1977:709). My own view, however, is that, within the framework of Jakobsonian-based markedness theory, the justification for and determination of markedness correlations cannot be established based on statistical frequency. The purpose of markedness theory is to explain properties of meaning that are invariant, not to justify a system based upon statistical frequency, which, by definition, is a context-specific phenomenon. If the perfective aspect in Russian is marked, it is not because the perfective occurs less frequently in actual usage, but because the perfective is defined by a property of meaning absent in the imperfective. As Maslov, the leading Soviet aspectologist, demonstrates, one can modify the definition of perfectivity to accomodate contextual variation without abandoning the integrity of the perfective's marked status: "The perfective, being the 'strong' member of the opposition (semantically marked and intensive, and by the same token having a narrower meaning) depicts an action in its indivisible integrity [or as an individual whole]" (Maslov 1984:15-16; brackets and translation mine). Maslov emphasizes that his definition takes into account all basic types of aspectual usage in Russian. Instead of referring to frequency of occurrence, Maslov takes all possible contextual meanings and gleans an invariant property of meaning. On a different level, Jakobson shows in his article, "Relationship between Russian Stem Suffixes and Verbal Aspects" (1966:27-31), the "iconic congruence" of correlative perfective/imperfective verbal pairs by analyzing their phonemic composition. Jakobson demonstrates how the aspectual oppo-

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sition, which is semantic, is reiterated in the phonemic oppositions via the use of both diffuse versus compact vowels and noncompact versus compact ones in the verbal stems of each aspectual type (1966:28). Jakobson was himself briefly tempted to associate the statistically more frequent form with the unmarked, as his 1936 article "Beitrag zur allgemeinen Kasuslehre" reveals. In particular, Jakobson argued that the Russian locative 2 (ending in -u) and the genitive 2 (ending in -u), were the marked correlates of the locative I-locative 2/genitive 1genitive 2 oppositions, as locative 2 and genitive 2 are very restricted in their distribution. However, Jakobson later reanalyzed these case forms in his 1958 "Morfologiceskie nabljudenija nad slavjanskim skloneniem" and reversed the markings based on semantic criteria, not on statistical and distributional frequency. Some scholars (cf. Worth 1984) feel that Jakobson was right the first time and that the locative/ genitive 2 are indeed the marked case forms of the opposition, but it should be noted, regardless of the correct interpretation here, that Jakobson originally posited locative/genitive 2 as marked primarily because of their restricted distribution and not because of a restricting property of meaning. As this debate suggests, most of the "myths" about markedness are, in fact, somehow related to this fundamental issue of statistical/distribution frequency. Greenberg (1966:21), for example, is also seduced into tacitly assuming that the marked form of a correlation in both phonology and morphology is less frequent statistically while the unmarked form is more frequent. But why are so many linguists convinced that statistical frequency is significant? Actually, as a general tendency, the unmarked element of the marked/unmarked opposition often does occur more frequently (both in the statistical and distributional sense) than the marked element. However, two important points follow directly from this statement: first, and most important, statistical frequency is representative of a tendency, that is, of a variant, not an invariant, rule of markedness relations and, so, is not expressed in the axioms of markedness given in chapter three; secondly, statistical frequency may seem to be relevant in oppositions of the perfective/imperfective type, but what about more complex oppositions such as masculine/feminine/neuter genders, first/second/third persons, or nominative/accusative/genitive/dative/locative/instrumental cases? It is precisely in these last ex-

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amples that statistical frequency can be very misleading, if not totally unsystematic (cf. Greenberg 1966:45). In the majority of instances (and perhaps this overlooked fact is another cause of markedness misinterpretations and chaotic application), markedness oppositions in morphology and semantics involve more than two categories. It is hardly rewarding simply to use marked/unmarked in describing triadic gender distinctions or singular/dual/plural numbers without also attempting to uncover the properties of meaning that distinguish these categories. Yet, it is precisely in dealing with these more complex correlations that the true explanatory power of markedness theory can be realized. Neutralization The misnomer of neutralization is another area in morphology "leftover" from phonology. Neutralization entails the systematic cancellation of an opposition in a particular syntagmatic environment (cf. voicing before obstruents) (Jakobson & Waugh 1979:28). Once again, Jakobson very clearly described how this concept fits into his theory of morphological markedness: "Notion of neutralization in the Russian case system is a characteristic example of phonological contraband in grammatical analysis" (1958:111). However, even some linguists working in the Jakobsonian tradition have failed to acknowledge this denial of the possibility of neutralization in morphology and semantics. Shapiro argues, for instance, that neutralization in grammar "is an important semeiotic process" (1983:82). As an example of neutralization outside the realm of phonology, he presents the equivalence achieved in synonymy, where the equivalence results from the "neutralization of the base/suffix hierarchy which accompanies the juxtaposition of words with identical suffixes but different bases" (1983: 202). Likewise, Lyons speaks of neutralization of semantic elements in certain contexts, such as lion/lioness, where the contrast is neutralized in the collocation "female lion" vs. "lioness" (1977:307), but Jakobson has claimed that such a neutralization is impossible in morphology (1958:111). The fact that certain Russian verbs require a specific case form for the verbal objects does not imply that the case loses its inherent meaning due to the absence of an opposition. Furthermore,

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as was demonstrated by the axiomatic base and functional mapping, there can be no true synonymy in language if the Jakobsonian model is rigorously and consistently applied. In fact, absolute synonymy completely destroys the integrity of linguistic form, as signifier, in its relation to the signified. The controversy concerning neutralization in morphology can be better understood through a reevaluation of precisely what constitutes neutralization in phonology from a Jakobsonian point of view. Greenberg (1966:13), beginning his section on phonology with an introduction of the concept of markedness, correctly states that the history of the concept in phonology is most certainly connected with the problem of neutralization and, particularly, the archiphoneme. Paired phonemes, differing by one feature, form a correlative pair. In certain environments, these two phonemes may not be able to occur in contrastive distribution, and their difference is consequently neutralized. The term archiphoneme was dropped by the Prague School when the alternation problem was resolved at the distinctive feature, rather than the phonemic, level (Sangster 1982:22-23). Andersen and Shapiro have been instrumental in refining the phonological definition of neutralization. Briefly, Andersen posits two types of neutralization for discrete segments, sequential and concomitant. I Shapiro expands this notion of neutralization from discrete units to entire groupings, or "blocs," of segments. Examples of bloc neutralization from Russian include forms like scastlivyj [s':is'l'ivijl (1983:113), where certain phonemes are not realized in speech production. All of these theories share a basic understanding of neutralization as a systematic nonoccurrence of a (distinctive) feature in particular syntagmatic environments/positions. But the situation becomes a bit less clear when another term, syncretism, appears in similar contexts. In general, syncretism or syncretization is the phenomenon whereby "distinctions existing in the unmarked member are often neutralized in the marked categories" (Greenberg 1966:27). The common Russian example concerns gender types expressed in singular declensions that are lost in plural declensions. Greenberg calls syncretization a "characteristic" of the marked/unmarked distinction, but he also uses the word "neutralized" in his definition of syncretism, which only

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adds to the confusion between the two concepts. Moreover, Greenberg lists yet another characteristic of markedness called defectivation (Hjelmslev's term), which he claims can be considered in some cases a form of syncretism (cf. inflectional categories in Greenberg 1966:29). Clearly, Greenberg uses syncretism as a term applicable to morphology, whereas neutralization is a phenomenon restricted to phonology. Nonetheless, their joint usage here implies a type of parallelism having profound implications for their applicability in morphology. Jakobson makes a similar equation: The opposition of soft and hard consonants is suppressed before the vowel e: the presence of an opposition is, consequently, opposed to its absence.... Likewise, the syncretism of morphological forms which appear in certain grammatical categories or, on the other hand, the opposition of meanings whose suppression we witness in a given context-all these point to the large scope of the problem of "zero opposition" for linguistic and for general semiology.... (1938:159) It is important to note that although Jakobson makes a comparison between neutralization in phonology and syncretism in morphology (including both grammatical and lexical meaning), he is not implying that meanings are neutralized. In any case, Jakobson's statement here predates by twenty years his statement of this principle in "Morfologiceskie nabljudenija" (1958:111). Therefore, one may conclude that while neutralization and syncretism are similar phenomena sharing certain properties, they are nonetheless distinctive processes as defined within the spheres of phonology and morphology. Consider figure 36. Figure 36

Phoneme Morpheme

Signifier

Signified

Bundle of Distinctive Features Mere Otherness

Mere Otherness Bundle of Conceptual Features 2

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Supported by arguments presented by Jakobson (1958) and Sangster (1982), it is possible to conclude that the inherent difference in meaning between two or more distinct grammatical categories (or, on a different level, between two or more distinct lexical categories) is never completely neutralized. Such a neutralization would destroy the integrity of the fundamental differences between the phoneme and the morpheme. Phonological elements express distinctiveness, and that is all; morphological elements, however, express more than mere distinctiveness-they are "endowed with their own meaning" (Sangster 1982:134), as given by the invariant conceptual features expressed in the signified. Although an opposition in meaning may indeed be "suppressed" (Jakobson 1938:159) in a particular context, it is never completely deprived of its meaning. In fact, the "zero opposition," where suppression of an opposition occurs, is a special one in its own right. Jakobson claims that such oppositions are important not only for linguistics but for "general semiology" as well (1938:159). The conceptual features (or markings) inherently given 'in a particular signified are an invariant for the given synchronic language state and can only "mutate" or change in time. Verbal government in Russian provides an interesting example of how zero oppositions can be used. Consider the Russi~n verb vladet' (lito master, possess, own"), which requires an object in the instrumental case. One could argue that the instrumental case is meaningless here, since no other case is possible, but a close examination of the situation will show this not to be entirely accurate. Consider the sentence On vladeet restoranom ("He owns a restaurant"). This example, taken out of the Russian context, gives us very little information about the nature of syncretism. However, if we look for similar constructions in Russian, either from the point of view of the form itself or of the meaning, an argument begins to take shape. First of all, Russian verbs of governing, ruling, directing, leading all require the instrumental case (cf. Russian pravit', upravljat', vlastvovat', rukovodit', vladet'), so it is obvious that instrumental verbs form a definite semantic group. Second, consider alternative ways in Russian of expressing the sentence, "He owns a restaurant." Another possibility, for instance, would be On imeet restoran ("He has/owns a restaurant").

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In the second example, the object is in the accusative case. Yet, the difference between these two examples is very striking, particularly as vladet' (with the instrumental) conveys more of a feeling of nonpermanency, while imet' (with the accusative) gives a stronger connection between subject and object. Also, the example with the instrumental could be construed in a slightly different sense, where the subject has control over the restaurant and its management. The instrumental case most certainly retains its meaning in these instances, even though an opposition with another case is impossible. By way of concluding this section, the definitions of neutralization and syncretism will be reformulated for the type of Jakobsonianbased markedness theory proposed in this work. Van Schooneveld defines neutralization as a phenomenon restricted to phonology in which there is a systematic nonoccurrence of a particular distinctive feature in a given syntagmatic position; syncretism is then a phenomenon restricted to morphology where a given form simultaneously fulfills two functions in all instances of realization and in all contexts. Van Schooneveld's definition of syncretism is very similar to Lyons', where syncretism is said to occur when "two distinct morphosyntactic words may be realized by one word-form" (cf. I loved [past tense] versus I have loved [past participle]) (1977:73-74). In other words, syncretism in morphology, unlike neutralization in phonology, is not a purely distributional phenomenon, but is a paradigmatic double signaling by a particular form. In fact, all denials of neutralization in morphology, as expressed by Jakobson and van Schooneveld, are nothing more than a reaffirmation of the invariant and indestructible nature of paradigmatically-based categories, despite potential distributionally-based instances of suppression of meaning. Jakobson's and van Schooneveld's interpretation of syncretism in morphology, as well as of the absence of neutralization in morphology, directly accords with C. S. Peirce's semiotic perspective on the essence of signs. If the sign is indeed a mere potentiality, whose nature, in the case of the symbol, is "esse in futuro," then syncretism, as defined above, precludes the realization of a particular "potentiality" in a restricting context. Yet, the essence of this potentiality, as well as its very exis-

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tence, is in no way negated or eliminated by its nonrealization (or suppression). The fact of the potentiality remains as ever-essentially unchanged, but interpreted within the confines of a specific context. Markedness Assimilation Henning Andersen (1969, 1972) formalized a principle for combinatory tendencies of phonetic features, which he called markedness assimilation, and which Shapiro identifies as "universally valid semeiotic" (1983:84). Briefly, the principle of markedness assimilation states: "the normally unmarked value for a given feature occurs in an unmarked (simultaneous or sequential) context, and the normally marked value in the marked context" (Shapiro 1983 :84). This wording is very close to Andersen's (1972) and will serve as a working definition. Examples of the principle of markedness assimilation in phonology include "positions of neutralization," such as Russian obstruents being +voiced (marked) preceding voiced obstruents, but -voiced (unmarked) at word boundaries preceding segments unmarked for voicing, or pauses (Andersen 1972:44). Shapiro, arguing that markedness assimilation is not simply restricted to phonology (1983:85-86), presents the stress retraction in English verballnominal pairs like "permit" I"permit," "reject"I"reject." Shapiro claims that initial stress in English is unmarked, versus other positions (marked), and that substantives and adjectives are unmarked parts of speech relative to verbals, which are marked (1983:97). Therefore, we have an example of assimilation occurring not only between phonological categories but among lexical categories, as well. Although the preceding example assumes that the substantive is unmarked with regard to the verb, such an assumption should be substantiated in order to validate the example. What evidence is there, either pro or con, for the status of the substantive as a relatively "unmarked" part of speech? Jakobson (1980:105), by way of interpreting Rene Thorn, claims that "the verb [as] the marked category, a superstructure in relation to the noun . . ." follows from Thorn's analysis of parts of speech. What is particularly interesting here is Jakobson's interpretation of Thorn, for whom structural stability implies semantic density (Thorn's special

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terms), and who accordingly posits the following hierarchy for the traditionally defined parts of speech: Substantive (noun) Adjective Verb Adverb

Most semantically dense, most marked

Least semantically dense. (1975:327)

As Thorn explains, "the more 'complex' a concept is, the more its stability needs regulator mechanisms, the greater is its 'semantic density.' If it is fairly clear that a noun which represents a substance, an actual object, defines the most stable and least volatile of the grammatical categories, it is far from being true that all nouns are of comparable semantic density" (1983:248). Thorn goes on to say, however, that in any case the semantic density of the verb is "inferior to that of the noun" (ibid.).3 Semantic density is complementary to Andersen's notion that "markedness is a matter of conceptual complexity" (1974:893). (Shapiro also quotes this passage from Andersen (1983:109).) Thus, it seems incompatible to equate the noun with the "unmarked" category, if this judgment is based on Thorn's analysis. Independently of Thorn's proposed hierarchy for parts of speech, van Schooneveld posited precisely the same hierarchy for Russian parts of speech as early as 1960. In particular, van Schooneveld gives the following interpretation: These four parts of speech form a regular structure based upon two semantic markings: verb and substantive (in contradistinction to their unmarked counterparts, adverb and adjective, respectively) are marked by the fact that they envisage an element of exogenous reality in its entirety, whereas substantive and adjective are marked (in opposition to their unmarked counterparts, verb and adverb, respectively) by the fact that they denote an element of exogenous reality whose existence is ascertainable independently of the time of transmission of the speech message. (1960:40) Figure 37 captures van Schooneveld's hierarchically defined markedness relations for the Russian parts of speech. The feature objectiveness

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Markedness Theory Verb..--(_+_D_im_}

Adverb (+0)

S_u_b_s_ta_n_ti---..,ve (+Dim/ +Obj)

Adjective (+Obj)

Figure 37

is more complex and, therefore, more advanced in the hierarchy of six conceptual features than dimensionality. To summarize, markedness assimilation can be demonstrated only if one assumes in an a priori fashion what is marked and what is unmarked. In other words, every item, feature, and category must be previously ordered in the hierarchy for the principle of markedness assimilation to find support. Hence, a circular argument results. But the situation becomes even more complicated if there is no agreement concerning the hierarchy of a given category at the onset (cf. parts of speech). The solution to such a problem cannot be found in the principle of markedness assimilation. Rather, these are questions that must be dealt with initially, before one can establish whether the principle of markedness assimilation is a tendency or a rule/axiom. A similar problem arises when one assumes that truncation (defined as the absence of a given element of expression) "involves an unmarking" (Shapiro 1983:96). Shapiro argues that truncation necessarily involves an unmarking because "the absence of something (signe zero) is normally unmarked, whereas the presence of that same something is normally marked" (1983:96). The key word here is normally, or, in other words, not always (cf. Russian genitive plural - (/) ending for neuter first declension and feminine second declension nouns is an example of a zero that is marked). The theory of markedness supported in this work can permit only invariant rules in the axiomatic base, so more rigor is required in defining phenomena like truncation and augmentation, and such categories cannot be a rigorous proof for justifying the validity of the principle of markedness assimilation. 4 In conclusion, my own view is that the principle of markedness

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assimilation has general applicability within the realm of phonology, but there is not enough evidence to support its status as a rule for defining morphological and semantic categories. When the same set of data lends itself so easily to two diametrically opposed interpretations (cf. English verbal/nominal pairs given above), what becomes clear is the need for more groundwork in the markedness of individual categories, classes, and lexical forms before generalizations on the scale of markedness assimilation can be made. Therefore, at this point, all that has been demonstrated is the logical consistency of the axiomatic base given in this work. Markedness assimilation has not met the requirements for categorization as a rule since proving its validity requires such a large number of assumptions. In the next section, the principle of markedness assimilation will be encountered once again via its alterego-the markedness reversal. Markedness Reversals Markedness reversals are, perhaps, one of the most controversial aspects of Jakobsonian markedness theory. This section will develop an argument concerning reversals, beginning with Jakobson himself on the topic and going on to discuss its subsequent application by Waugh, Sangster, Andersen, and Shapiro. Counterarguments by van Schooneveld, Stankiewicz, and myself will conclude the section. The fundamental question must be whether the potentiality of a markedness reversal in synchrony is consistent with the basic principles of Jakobsonian markedness theory as a logically coherent, cohesive structure in its own right. This question necessarily encompasses the nature of conceptual features in morphology (as opposed to their phonological counterparts, distinctive features) and the qualitative differences in semiotic systems. In only one article does Jakobson mention a markedness reversal within a grammatical category (1959:185-86), claiming that the neuter gender, which occurs in second position in the gender hierarchy as given by the Russian cases, shifts to the unmarked position in caseless forms (that is, the verb, adverb). Further, Jakobson compares this "natural" shift to similar ones in the phonemic system of vowels and consonants with regard to the features compact/diffuse. Two

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crucial points must be made at this juncture in the discussion. First, Jakobson clearly implies that such "shifts," or markedness reversals, are natural and can be expected to occur. Secondly, Jakobson calls this shift, specifically, a shift "in the distribution of marked and unmarked categories" (1959:186). Distribution is a syntagmatically given category closely related to statistical frequency. However, in van Schooneveld's and Stankiewicz's alternative interpretations of the function of the neuter gender in Russian, distribution plays no role. Rather these two interpretations focus on the feature marking, not on the distribution of the marked/unmarked categories (cf. van Schooneveld 1977b; Stankiewicz 1968). My own goal is to demonstrate that, generally, conceptual features in grammar and morphology cannot reverse synchronically if the fundamental premises of Jakobsonian markedness theory, as Jakobson himself developed them for morphology, are accepted. Reflecting the Jakobsonian tradition, Waugh argues for reversals in other grammatical categories of Russian, as well as for extensions of the notion of reversal into other semiotic systems. One example of such a reversal in Russian involves the unmarked imperfective aspect's becoming marked in the imperative mood (Waugh 1982:229}18; Holenstein 1976:135). Reversals of markedness are also discussed by Sangster (1982:75 ff.), but in later work he reverses his position on this issue. Jakobson himself does not explicitly give such an interpretation to the Russian imperfective negated imperative. Jakobson's phonological studies include numerous references to reversals in phonology, involving shifts in consonant and vowel systems, as well as in emotive units (Jakobson 1980:82-83; Jakobson and Waugh 1979). However, it is important to acknowledge that even in "The Gender Pattern of Russian" Jakobson refers only to potential markedness reversals in grammatical categories/meaning, not in lexical meaning. Andersen, on the other hand, makes full use of the reversal of markedness values in phonology (1972, 1974). Of greater interest, however, is his extension of markedness reversals to grammatical categories and to all other human semiotic systems (1972). In each of Andersen's examples (cf. English subjunctive (M), where the past vs. present tense opposition, as well as the number opposition, is no

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longer found), an opposition is neutralized (1972:45). Consider Andersen's example, "I wish they knew." This example can be analyzed in the same way van Schooneveld analyzes the subjunctive mood for Russian. Russian, like English, uses a past tense verbal form for expressing subjunctives and conditionals. In fact, it is only via a past tense form that subjunctives can be expressed at all in Russian and English. When one undertakes the analysis of the past tense forms in Russian for an invariant property of meaning, all possible surface renderings using a past tense form must be included-the subjunctive is no exception to this rule. If the invariant meaning for past tense is defined as disjunction with the moment of utterance, then all meanings expressed by past tense forms are accounted for, including past time and subjunctives. Thus, to claim that a reversal has occurred, or neutralization, is unnecessary since the present tense can never be used to express a subjunctive in Russian or English. This definition of the past tense would also explain why the number opposition is potentially absent (that is, "I wish he were here")-the disjunction with the speech event leaves the number of participants unspecified. However, in modern English, the subjunctive can occur with verbs in the singular (cf. "I wish he was here"). Further support for including the English subjunctive mood with the past tense can be found in English modal conditionals, where once again a past tense form is used ("We would go to the theater every evening if we were in Leningrad"). The English modal conditional is not, however, the only possible function using these past tense forms (cf. "We would go to the theater every evening when we were in Leningrad") (Aronson 1977:15). In the case of both Russian and English, we are in no way required to claim that these instances are cases of neutralization based on an analysis of the forms themselves. In fact, what we can say is that English and Russian have no subjunctive mood in the sense that German does (cf. Sie konnte es tun / "She would be able to do it"; Ich wilnsche ich ware da / "I wish I were there"). Rather, each of these languages can only express the subjunctive mood via past tense verbal forms. (It is important not to confuse the linguistically given system of meaning with a priori established categories of meaning.) In attempting to analyze linguistic meaning, we are obliged to begin

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with the forms themselves-and the forms, via iconic structure, will lead us to the properties of meaning that define the signified of the linguistic sign. Let us now return to the question of markedness reversals in specific grammatical categories in modern Russian. As was mentioned earlier, Waugh and Holenstein adduce the imperative mood in Russian as an example of a markedness reversal. My argument is to the contrary, however, for two reasons. In the first place, when the perfective and imperfective aspects are seen to be dominated by the markedness relationship given by the category of verbal imperative, as opposed to aspect in abstracto or aspect in the verbal infinitive, the marking of the perfective is understood to be the same as in any usage of verbal aspect. According to Jakobson, Maslov, and van Schooneveld, the perfective aspect indicates that the verbal process has boundaries, and these become the focal point of the action in question. Thus, at the end of the verbal process, some result is required, often being manifested as a completed action (cf. On procital knigu = "He finished reading the book"). The verbal process indicated by an imperfective verb, however, mayor may not have boundaries-it simply remains unstated. The notion of a reversal's occurring arose because the perfective is, in fact, the usual way of stating a positive imperative (cf. Zakrojte okno! = "Shut the window"), whereas the imperfective is the usual way of expressing negative imperatives (cf. Ne zakryvajte okno! = "Don't shut the window"). Thus, statistical frequency, rather than the "meaning" of the perfective aspect, is the determiI1ing factor of this "reversal." If one looks at the meaning of the imperative as a category, which is a command to produce a result, one sees the complementary nature of the perfective aspect with the imperative. In the negative imperative, the focus is on not performing an action at all. The idea of non-result is precisely the contextual meaning manifested by the imperfective aspect in such negative declarative utterances as the following: fa ne slysal etoj opery = "I haven't heard (of) that opera"; fa ne pokupal etoj knigi = "I didn't buy that book"; Ona emu ne zvonil = "She didn't call him." Therefore, since no focus on the boundaries of the verbal process occurs in the negative imperative, no justification exists for saying that a reversal has occurred. The frame category of the im-

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perative will redefine the relationship perfective/imperfective to some degree, but the "feature marking" of the perfective aspect remains the same. My second reason for arguing that the imperative mood in Russian is not a case of markedness reversal is based on the very definition of markedness relationships as asymmetrical and binary (not polar); the type of "polarization" required for a markedness reversal, therefore, is impossible. Markedness theory in morphology cannot retain any consistency as a theoretical approach if it is defined by both asymmetrical and polar oppositional types simultaneously. Another, often cited example of a so-called "reversal" is the lexical pair female/male and its manifestations in certain social contexts. According to Waugh, "female" in the context of "doctor" or "professor" is marked as an occupation, whereas "male" is marked in the role of a secretary or nurse (cf. male nurse versus nurse) (Waugh 1982: 310). In this example, what is unclear is the marking that is being reversed. What does seem to be consistent in both examples of "reversals" is the reasoning used. Namely, the occurrence of the supposedly "marked" form becomes the normal state of affairs and, hence, becomes unmarked. However, the marking for the pair female/male is not actually derivable because of a fundamental error: two lexical items, which are, in their linguistic [not logical] form, the result of many conceptual features, are being juxtaposed as if they were "marked" for only one feature. Rather, these two lexical items are literally bundles of conceptual features that mayor may not differ by only one feature. Furthermore, these "features" or "marks," existing simultaneously within one and the same linguistic system, should form a consistent, systematic structure. Yet, the question remains as to the origins of these "reversing features." My own view is that, in each of the examples given, the reversal occurs not in the conceptual features but, rather, in "tags" taken from outside of the linguistic system and assigned to the categories in question. These extra-linguistically defined "marks" exemplify polarized oppositional relationships which, not being inclusive, cannot be applicable to asymmetrically defined markedness relationships. Each of the examples above is mistakenly perceived as representing markedness reversals because categories of extra-linguistic experience, such

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as gender and animacy, are misdefined as semantic invariants. Variation, however, is the key to these examples. The conceptual features for morphology, as conceived by van Schooneveld, define linguistic categories of perception; each feature is established within the linguistic system itself, only subsequently becoming applicable to interpretation of extra-linguistic phenomena. Oppositional pairs, such as male/female, good/bad, white/black, are treated as polar opposites in actual experience, but applying marked/ unmarked designations to them is not particularly relevant. The crucial point revolves around the necessity of defining the set of conceptual relationships (that is, features) first; only when that has been done can markedness theory be applied to a given sign system. One other problem connected with the attempt to use markedness in analyzing such cultural and social categorizations concerns the inseparability of a meaning from its form. Consider, for example, the following pairs: male versus female and black versus white. We have consistently argued for the principle that there can be no categories of meaning expressed independently of the form vehicles of language, and, thus, studying the structure of the signifier, as well as the mutual relations determined by a given system, is required. If this statement is correct, then the terms male/female and black/white cannot be analyzed without first analyzing their formal structure. Therefore, the sociocultural nuances attached to certain words (or other linguistic signs) in a given language cannot be fully grasped without first looking to the language itself. This conclusion is drawn in the recognition that no clear division can be made between language (in the sense of langue) and the sociocultural system in which a language is manifested. However, it is clear that the potential contextual meanings of linguistic signs are given their basic existence by the features that define them. In other words, if we are to discuss lexical items such as male/ female in any meaningful fashion, they cannot be removed from their linguistic context. This fact is merely a reiteration of conclusions drawn in chapter 3, namely: logical distinctions play a role, via mathematics, in defining the structure of markedness, but this does not imply that semantic categories should lend themselves to similar "logical" categorizations. Let us again review some of the defining characteristics of a lin-

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(Unmarked)

Figure 38

Universe

Figure 39

guistic sign system. All markedness relationships, being asymmetrical and binary, can therefore be conceived in a hierarchical fashion. This relationship can be demonstrated by a syllogism in the form of a basic inclusion relationship, where the marked set is a subset of the unmarked set. At the most primitive level the unmarked area corresponds to the universal set (see figure 38). However, since there can be no totally unmarked element in a linguistic system, this first illustration is not possible in actual linguistic systems. 5 Thus, figure 39 assumes a markedness relationship within a predefined system. The differentiation between the manifestation of the unmarked element in its general and specific meanings, on the levels of phonology, grammatical meaning, and lexical meaning, can be seen in figure 40. It is precisely Jakobson's definition of markedness, general versus specific, that provides the explanation for the qualitative difference between phonological and morphological markedness. In phonology, markedness relationships are restricted to the type given by specific meaning, whereas in morphology, markedness relationships can be

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Phonology I. Specific Meaning Only A. Marked: Statement of A B. Unmarked: Statement of non-A

Figure 40

I.A@e B .©

I.A@ e "© lIA@

Morphology. Grammatical Meanmg I. General Meaning (Gesamtbedeutung) A. Marked: Statement of A B. Unmarked: Nonstatement of A II. Specific Meaning (Grundbedeutung) A. Marked: Statement of A

B. Unma,hd, S""ment of non-A

Figure 41

of two types, involving general or specific meaning. Furthermore, it is important to note the additional complexity of lexical meaning, where three rather than two distinctions are required. If we define our system of features as interpretants, we can find an explanation for the qualitative difference in the features, as represented by grammatical and lexical meaning, using the Peircean categories of firstness, secondness, and thirdness. In order for an interpretant to be a sign, it must be triadically produced (Fitzgerald 1966:73; Peirce 5.473). Thus, figure 42 shows a rough sketch of what the conceptual features as interpretants might look like -they necessarily have three parts in their realization on the lexical level in language. Interpretants such as these are triadically produced and are of the order of thirdness. Figures 40 and 41 would also be representative of interpretants, but they are more of the order of firstness and secondness, respectively [recall the definition of these three categories in chapter 2]. Therefore, we are claiming that markedness features, as interpretants, are triadically produced on all three levels,

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that is, on the phonological, grammatical, and lexical levels, but that these interpretants are of different "orders"; namely, phonological features are of the order of firstness, grammatical features of the order of secondness, and lexical features of the order of thirdness. No one method has been used to determine which member of a given opposition is marked. In many cases, statistical data and "substitutability" of the unmarked for the marked term are used to establish the marked/unmarked relationship, but, as Waugh states, the "effects of markedness should not be equated with its definition" (Waugh 1982:302). In this vein, the following section will show that substitutability alone is not a valid test for determining markedness relationships since substitutability, at best, implies intersection, not inclusion. The essential premise on which markedness theory is based is the mandatory asymmetry of the linguistic sign, that is, the two parts are not equivalent, so the basic relationship that must be defined by such a theory is inclusion. A method of determining which element of a given opposition is marked and which is unmarked more rigorous than statistics and substitutability is essential if markedness theory is to continue to play Figure 42 Lexical Meaning (Conceptual Features)

PL

DIM

EXT

DIST

OBJ

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a role in analyzing linguistic structures. The basic methodology of Jakobson and others in morphology has been to derive a set of invariants from a definitive source of language data in order to explain the occurring phenomena. This methodology, seen in Jakobson's "Beitrag" and "Morfologiceskie nabljudenija" and in van Schooneveld's Semantic Transmutations, may need to be amended before being applied to other semiotic systems; it cannot simply be transferred since each sign system is qualitatively different. This statement is supported by data from language itself, for within one linguistic sign system, two entirely different types of markedness features are required to explain phonological as opposed to morphological structure. Although both are binary, phonological features are based on the interpretation of acoustic and articulatory phenomena, whereas conceptual features are based on perceptual categories. In applying markedness theory to diverse semiotic systems, it is crucial that the nature of the features used to characterize the semiotic correlations be consistent within the system they supposedly define. Otherwise, any statement of marked or unmarked will be meaningless. We may assume that markedness, as a theory of interpretants, is applicable to all semiotic systems, but it is necessary to establish initially what types of features (that is, properties of meaning) actually characterize the relationships of a given sign system. The need for well-defined markedness features can be demonstrated explicitly by following three sets of semantic oppositions in English: she/he, female/male, woman/man. As set forth by many linguists, including Jakobson and Lyons, among others, she, female, and woman are considered the linguistically "marked" forms (Lyons 1977: 305-10). But let us begin by considering the three pairs as purely "linguistic" terms, with no definite linguistic marking assigned to these terms other than stating that the "feminine" counterpart is marked. 6 Acknowledging the marked nature of the "feminine" form allows one only to assume that the marking is something like "a being who is perceived as having feminine gender and all this entails." (This feature definition is based on our experience in extra-linguistic reality.) If the above feature marking is correct, then every occurrence of the lexemes she/female/woman should carry this marking (except in the event of a re-

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versal, when the masculine counterpart would pick up this meaning). Immediately, several facts become apparent. If, in fact, all three "feminine" forms are marked for "femaleness," then why can the lexeme she also refer to ships, planes, hurricanes, and gay men? In fact, the U.S. National Weather Service now gives hurricanes both male and female proper names; pronominal usage corresponds to the gender indicated by the proper noun. This fact shows that pronominal gender is defined within the linguistic system itself; the pronoun agrees with the grammatical or lexical gender of its referent. Clearly, the invariant of these three forms has nothing to do with the actual difference between men and women but, rather, with a linguistically defined difference that intersects with exogenous categories of gender. Yet, what are these three forms marked for? No feature becomes convincingly apparent if we base our feature definition on exogenous reality. Furthermore, it might even be that she/female/ woman are not the marked forms of the opposition. From a purely "formal" point of view, the lexemes female and woman appear to be marked since they bear a formal marking that their counterparts, male and man, lack. But this same observation_ cannot be made about the lexeme she, which in modern English bears no such formal marking in relation to its masculine counterpart he. However, also note that in the two previous examples, the additional "morphemes" in the lexemes denoting female persons (called "initial residue morphemes" by Bolinger) are not productive in English, that is, no other "feminine" forms are made by these particular "residues" (cf. count/*wocount; boy/*feboy) (Bolinger 1965:187). The presence of a formal marker does not always indicate the presence of the conceptual markedness of a given linguistic item (cf. Russian obmenivat' [imperfective but formally marked] versus obmenjat'/obmenit' [perfective but not formally marked] [chapter three]). Such situations as the one above inevitably occur when the distinctions made by language are confused with extra-linguistic experience. In other words, there is no isomorphism between linguistic and extra-linguistic categories. The last example to be considered is more to the point of potential reversals in synchronic linguistic sign systems. As many linguists have noted, Black English (called NNE == Nonstandard Negro English

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and BEV == Black English Vernacular) often uses the lexeme "bad" to mean "good." The status of Black English in relation to contemporary standard English is somewhat controversial. Labov considers BEV to be a system in its own right, with its own phonological and morphological rules. However, at one point, some linguists were claiming that Black English was an African-based creole and, thus, was completely different from an English-based system in its historical origin and subsequent development (Labov 1969; Todd 1974; Turner 1949). If either of these latter theories were to become accepted, the question of a markedness reversal's occurring would not even be relevant since one would then be dealing with two autonomous linguistic structures. But, assuming for the present argument that Black English is a dialect or group of dialects of contemporary standard American English, what other evidence is needed to indicate that a reversal is occurring? As in the male/female example, if "bad" means "good," then a reversal would indicate that "good" should mean "bad." This, in fact, is not the case: "Good" does not mean "bad" in Black English, nor has "bad" ceased to mean "bad" in certain contexts of BEV. What one can say with assurance is that in Black English the lexeme "bad" has taken on a contextual (variant) meaning derived from its general meaning, which is given by its accompanying conceptual feature markings. Clearly, contextual variation of the "good/bad" type is common in language generally and to attempt to deny the existence of such phenomena would be absurd. Rather, we must attempt to explain how such contextual variation can occur. One way of accounting for these lexical "reversals" is to observe the connection between the principle of hierarchy and the categories of morphology and semantics. Lexical meaning, as part of semantics, is more complex than grammatical meaning. Thus, as we move up the hierarchy toward increasing complexity of the signified, we necessarily encounter more subtle differences in the referential ability of the sign. We have already seen that the conceptual features for lexical meaning are interpretants of the order of thirdness. Markedness theory, in using conceptual features defined as final interpretants, can hardly jump from form to form. But these features can lend themselves to a wide range of contextual shifting. In other words, markedness reversals in synchrony deny the very essence of

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markedness theory by focusing on variant relationships, not on invariants. It would be useful at this point to reconsider markedness reversals from a slightly different perspective. In doing so, my purpose is to demonstrate that Andersen and Shapiro are referring to markedness in a qualitatively different sense than the narrowly defined markedness theory presented in this work. To begin with, consider an example from Russian phonology. In word final position, voiced consonants become voiceless (cf. Russian sad [sat], lug [luk], etc.). In this position of neutralization, the unmarked element of the opposition occurs, that is, voiceless (or -voice). This state of affairs is the one generally expected, as was shown above: in positions of neutralization, the unmarked element of the opposition is the one to occur. However, there are counterexamples to this such as the one Shapiro and Andersen give of a situation found in standard German, where the tense feature is neutralized in obstruents functioning as "syllable codas." Andersen notes that this is a "marked function" for obstruents; his examples include schiidlich -"injurious" [dl > tI] and Pendler-"commuter" [ndl > ntI] (1972: 44-45). In this marked function, only + tense, that is, the marked element of the opposition, occurs. Here then is an example of a markedness reversal, since the unmarked term's occurring in positions of neutralization is generally expected. We would argue that this violated expectation, in and of itself, is not proof of a "reversal," however, because nowhere does the theory of markedness require that only the unmarked element may occur in positions of neutralization. In fact, if Russian regressive assimilation involving the voicing feature is considered a case of neutralization (cf. Andersen 1972:45), then how is it that both voicing and devoicing occur, depending on the environment (Russian avtobus-"bus" [aftobus]; vokzal-"train station" [vagzal])? Andersen claims that Russian regressive assimilation is both a case of markedness assimilation and one of neutralization, where the "markedness values are reversed"-+voicing requires +voicing, and -voicing requires -voicing (ibid.). Such examples as Russian regressive assimilation show how the phonological environment can determine the type of phoneme required, and

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both the marked or unmarked phoneme clearly can be involved. But the phonological distinctive features are inherently different in their essence from the conceptual features for morphology and semantics. In fact, phonological features have no meaning besides "mere otherness" and the indication of presence versus absence. Nonetheless, no explanatory power is gained by insisting that these examples are instances of markedness reversal. The fact that this assumption has not been made here has a two-fold significance. First, such assumptions cannot be supported as "consistent" with our axiomatic base for markedness. Second, the notion that the unmarked element should, in fact, occur in such a neutralized instance is indicative of another tacit assumption intimately connected with the notion of neutralization and reversal, that is, the notion of substitutability of the unmarked element for the marked one (cf. following section). Since there are numerous examples in phonology and morphology where so-called reversals occur, it would be just as economical and consistent to state that reversals do not occur at all, and, that in positions of neutralization or syncretism, either member of the opposition (marked or unmarked) may occur. This section will be concluded with one final phenomenon often cited as an example of a markedness reversal in grammatical meaning: truncation vs. augmentation. Truncation, defined by Shapiro as "the relation between forms which differ in part by the presence vs. absence of a given element of expression, involves an unmarking" [italics mine] (1983:96). Conversely, augmentation, the addition of an affix, is a marking (1983:186). This generalization is too simplistic, we would argue, since truncation is, in fact, more often a marking than an unmarking. Refusing to recognize the validity of such a generalization makes vacuous the argument that the Russian diminutive, as an example of truncation, is necessarily a markedness reversal. The importance of truncation and augmentation for modern Russian cannot be overstated, however. In particular, the entire Russian verbal system is built on the principle that truncation, versus augmentation, to the single stem is required to generate all verbal forms. However, in this example, truncation may occur in the formation not only of the infinitive (cf. citaj + t' = citat'), but also of the conjugated present/future tense and the past tense (cf. govor'i + at = govor'at;

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iiv + I = iiI)? The examples above make it impossible to determine how one can justify truncation as necessarily an unmarking in Russian, since truncation potentially occurs in any verbal form, depending on the verbal classifier. Additional examples of signe zero categories in Russian are the imperative mood and the genitive plural. (Note that not all instances of "sign zero" in Russian yield truncated stems.) Clearly, these examples are related to highly marked categories and fail to support the notion that truncation is an unmarking. Further, Shapiro states that "this assignment of markedness values accords well with the notion that the absence of something (signe zero) is normally unmarked, whereas the presence of that same something is normally marked" (1983:96). Intuitively, this statement seems to be true. However, we need evidencesomething more than intuition, or what one might call intuitive logic -to support such a statement. One way of supporting its truth to some degree would be to discriminate between formal and conceptual marking (cf. chapter three). In this fashion, one can say that secondary imperfective forms in Russian like obmenivat' are formally marked for the -IVAJ suffix, yet simultaneously are conceptually unmarked for perfectivity. Once again, the markedness relations expressed are relatively stated and cannot express an absolute on all levels of linguistic meaning. So truncation cannot absolutely be an unmarking, nor is it a marking-it is at once both and neither. In conclusion, let us return to Shapiro's example of dimunitive formation in Russian. Shapiro states that the Russian diminutive Misa, as well as the English diminutive Mike, is marked vis-a-vis the neutral full-form Mixail/Michael. Thus, we have an example of an unmarking, truncation, used to form a highly marked category, the diminutive. Yet, there are numerous augmented diminutives in Russian (cf. Annuska < Anna). How would these examples be explained-as a double markedness reversal? What seems clear is that the phenomena of truncation and augmentation are only formal signals of much more complicated morphological processes, and that to generalize them as an unmarking and marking, respectively, cannot be entirely justified on the basis of the data. The system of markedness proposed here, therefore, is not equivalent to a markedness system in which the distinction between formal

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and casual dress could be discussed (cf. Andersen 1972:45; Shapiro 1983:94; Waugh 1982:310). Rather, the markedness theory being developed here necessarily goes beyond merely setting up a hierarchical relational opposition; such a markedness theory is also preoccupied with the feature marking that defines the relationship. In other words, the feature is still not a "thing" but a relation. However, the feature represents not just any relation but an invariant relation. The other theory of markedness is more preoccupied with the pure relationship, the hierarchy, with the mark, not the feature. In the markedness theory developed here, however, features may not jump from form to form, from category to category. For example, the Russian perfective aspect is marked in opposition to the imperfective aspect, but, beyond this, the perfective aspect bears a feature marking (cf. van Schooneveld's dimensionality). The feature dim states the following relationship for the verbal process: the action is bounded, or contained. The feature dim is present in infinitely many contexts where Russian perfective verbs may occur, including the imperative mood. The fact that in the negative imperative the imperfective is the most common (or "natural") choice does not necessarily imply a reversal or shift in feature markedness. Rather, the imperfective becomes the usual choice for negative imperatives in Russian because the imperfective aspect is more complementary than the perfective to the meaning of the negated imperative. As was demonstrated earlier in this section, applying a feature approach endows our theory with as much, if not more, explanatory power as any theory assuming the existence of a markedness reversal. Substitutability Perhaps the most problematic "myth" about markedness is that of substitutability (or Greenberg's facultative expression). The notion of obligatory substitutability of the unmarked for the marked category has been used by some scholars (for example, Kucera) to prove that the ascribed markings are incorrect and that the theory is not rigorous enough. But what does substitutability in a given context actually imply? First, substitutability must be explicitly defined: Are two items substitutable for one another as long as the "truth value" in exogenous

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reality is maintained, or should substitutability be defined in terms of its effect on the linguistic value of the utterance? Consider, for example, the sentences, Cary Grant was an Englishman versus Archibald Leach was an Englishman. Although Cary Grant and Archibald Leach were the same person in reality, in the linguistic context, each sentence signifies a different aspect of his personality. Is our entire theory of markedness invalid if substitutability of the unmarked for the marked element is not always possible? The answer is yes, but only if we place the notion of substitutability into our axiomatic base. In fact, the nature of substitutability gives it no potential for becoming part of the axiomatic base because it can be both true and false within the system. Furthermore, if each form possesses an invariant property of meaning, which is necessarily represented by a bundle of conceptual features, then substitutability becomes absurd. Dokulil states that the possibility of substitution of the unmarked category for the marked one "is not only an optional symptom of the unmarked member but ... a necessary condition in order for us to be at all able to judge such a category as unmarked" (Kucera 1980:32). Since substitutability has been used as a necessary condition for establishing the unmarked category in previous analyses, the results of analyses made on such a basis must be reexamined. Yet, the question as to why substitutability is not credible within the present markedness system has not been fully addressed. Supposing one were to reject the axiomatic base, what other argument can be made against substitutability as a criterion? In an article entitled "Markedness in Motion" Kucera has stated, "If the pair of morphological categories is indeed to be viewed as a hierarchical correlational opposition, then it logically follows that the unmarked category should be capable of replacing the marked one" (1980:32). Kucera's statement raises the question of why it is necessarily "logical" that "the unmarked category should be capable of replacing the marked one"? Based on rigorous mathematical logic, the following proof regarding substitutability as a necessary condition can answer this question. Substitutability implies intersection, not inclusion, for a hierarchical correlational opposition. However, since a hierarchical correlational

164

Markedness Theory

opposition is defined as an inclusion relationship, substitutability cannot be a defining point of such an opposition. The following simplistic mathematical proof demonstrates this point: Prove: Given two distinct sets, M and U, defined as "marked" and "unmarked," show that M = U. Proof: Suppose there exist two sets, M and U, where M is the "marked" set and U is the "unmarked" (according to the Jakobsonian definition of marked/unmarked in morphology). Therefore, M = {x} and U = {x, X-I}, where X-I represents "non-x." Given M = {x} and U = {x,x- I } Therefore M C U (M is a subset of U) But U et M (by definition of subset) Therefore, M ¥= U (since M = U implies M C U and U C M) Using the above proof that M = U, but M C U, prove that U is substitutable for M. M and U are substitutable if and only if for any statement M = Z, then U = Z, and for any statement U = Z, then M=Z. Prove: Given the above definition of substitutability, prove substitutability implies equivalence, that is, if U is substitutable for M, then U = M. Proof: A set Z exists. Let M = Z. If U is substitutable for M, then U = Z. Therefore, M = U (by definition of an equivalence relationtransitive law) But the first half of the proof showed M ¥= U. This yields a contradiction. Therefore, U is not substitutable for M. Q.E.D. Therefore, it is apparent that substitutability, in the strict, paradigmatic sense, is impossible in the case of a hierarchial correlational opposition, since the notion of hierarchy implies that the two elements in the hierarchy are not equivalent but, rather, are asymmetrically defined. Given this fact, finding examples where substitutability is

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impossible only reinforces the idea that substitutability is not a criterion for establishing a markedness opposition. However, neither is the converse of the above, that is, those cases where substitution can occur, sufficient to prove that substitutability should be a criterion for determining markedness oppositions. Furthermore, recall that the notion of substitutability implies intersection, not inclusion. Two sets (of linguistic forms) can share a feature (for example, Russian ob vs. s share Dim'), but such sharing does not indicate whether one set is included by the other, that is, whether we are dealing with a marked or an unmarked relationship. At best, syntagmatic substitution of one form for another illustrates the potential that two forms share a feature. The final chapter will attempt to demonstrate specific applications of the theory of markedness developed in the previous four chapters. Only through actual application to linguistic data can the utility of such a theory of markedness be judged. Our markedness theory will be tested by a particularly difficult linguistic category for analysis: grammatical gender.

=Five = The Category of Grammatical Gender in Russian, Serbo-Croatian, and ~1odern Greek

ou tout se tient. [Every linguistic fact is part of a whole in which all parts are interrelated. ]-Antoine Meillet

Chaque fait linguistique fait partie d'un ensemble

The category of grammatical gender has always posed a difficult problem for the linguist. No single theory of linguistics has been able to explain adequately how gender assignments are made within languages or why languages differ drastically in this particular grammatical means of distinguishing forms. Therefore, this chapter will apply markedness theory to an analysis of the lexical and grammatical gender relationships of modern Greek (Dhimotiki), Serbo-Croatian, and Russian. Our attempt will be to determine if the relationship maintained by declensional paradigms and gender is systematic and meaningful. Modern Greek, Russian, and Serbo-Croatian, all Indo-European case languages distinguishing three gender types (masculine, feminine, neuter) in the noun and adjective, will be used to demonstrate several fundamental principles of linguistic gender systems generally. In particular, Jakobsonian-based markedness theory will be used to demonstrate that the feminine gender is not always (or necessarily) the "marked" gender in languages, and that the degree of interdependence between declensional paradigms and grammatical gender may vary greatly from language to language, a variability which is meaningful. In order to establish the hierarchy of gender in Dhimotiki and Slavic, markedness theory, as defined throughout this work, will be applied. But first, since both formal and semantic criteria are fundamental in determining markedness relations, the declensional

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167

systems of all three languages will be outlined briefly, and then particular modes of expression using gender in each language will be analyzed. Specific topics will include nouns with ambiguous gender, word formation in the noun (including diminutives), and gender shifts occurring from singular to plural number. Finally, a return to a definition of the relationship between gender, case, number, and declension will be made in order to show that the category of gender is indeed meaningful within language. The formal marker that will be the key to defining the gender hierarchy for Dhimotiki is the -s affix, which occurs in the nominal declension system. Modern Greek (Dhimotiki/Demotic) and the Role of the -5 Marker The Greek nominal declensions in their development from the classical period to the present have redistributed the -s desinenee in such a way that this affix takes on a much more distinctive role in the modern period than it had had at an earlier stage. Namely, in Dhimotiki, -s is the only consonantal ending that occurs in any of the singular paradigms of all three genders. In classical Greek, both -s and -n occurred in the singular declensions, while in the modern and classical plural declensions, both -s and -n occur. However, a striking pattern occurs in Dhimotiki with regard to the -so In summarizing the Dhimotiki system, most paradigms correspond to the system shown in figure 43. Figure 43 Singular Declensions NOMINATIVE:

Masculine VS

ACC/GEN/VOC:

V

Feminine

Neuter

NOM/ ACC/VOC:

V

V

GENITIVE:

Vs

Vu/Vtos

Feminine Vs on

Neuter V(ta)/Va on

PI ural Declensions NOM/ ACC/VOC: GENITIVE:

Masculine Vs/V on

NOM/ ACC/VOC: GENITIVE:

(Note: V represents the vowels a, e, i, 0.)

168 Markedness Theory

The most striking case opposition occurs between the nominative and genitive in both the singular and plural paradigms. Either the nominative (most unmarked case) is opposed to all other cases (acc/gen/voc), as in the masculine declensions, or the genitive (most marked case) is opposed to all other cases (nom/acc/voc), as in the feminine and neuter singular, and in all plural declensions, regardless of grammatical gender. Essentially, Dhimotiki has one fundamental case opposition from the point of view of the nominal case endings. Of course, in most contexts total case syncretism does not occur in the masculine and feminine declensions due to the presence of articles, which are still fairly distinct in form (cf. masc. 0 [nom], to(n) [acc], tou [gen]; fern. i [nom], ti(n) [acc], tis [gen]). In Dhimotiki one masculine declension and one feminine declension type, in which four distinct case endings are preserved, still remain:

masculine "brother" adherfos ACC: ton adherfo GEN: tou adherfou voc: - adherfe NOM: 0

feminine "entrance" i eisodhos tin eisodho tis eisodhou - eisodhe

The use of the n in the accusative of certain feminine nouns is optional in Dhimotiki. In most instances, the use of the n is associated with Katharevousa (Puristic Greek). All other singular paradigms in Dhimotiki distinguish two cases formally (that is, by nominal affix). [There does exist one feminine paradigm which distinguishes three forms: i dhespoinis "Miss" (nom/voc = -is; acc = -idha ; gen = -idhos )]. The modern Greek case system exhibits yet another peculiarity in addition to the system presented directly above. Due to the presence of Katharevousa declensions and forms that are often mixed together with Dhimotiki forms, the modern Greek case system seems even more irregular. Note the following examples: Singular "secretary" [masc] NOM: [0 grammateasl Dh. o grammateus Kath. ACC: to grammatea

Plural

1.

oi grammateis tous grammateis

Grammatical Gender GEN:

voc: 2.

tou grammatea - grammatea

ton grammateon - grammateis

"secretary" [fern]

NOM: ACC: GEN:

voc:

[i grammateas] Dh. i grammateus Kath. ti grammatea tis grammatea - grammatea

oi grammateis tis grammateis ton grammateon - grammateis

3. "blabbermouth" [fern] NOM: ACC: GEN:

voc:

i polilogou tin polilogou tis polilogous - polilogou

oi polilogoudhes tis polilogou.dhes ton polilogoudhon - polilogoudhes

4. "type, kind" NOM: ACC: GEN: VOC:

to eidhos to eidhos tou eidhous - eidhos

ta eidhi ta eidhi ton eidhon - eidhi

5. "lesson" NOM: ACC: GEN:

voc:

to mathima to mathima tou mathimatos - mathima

ta mathimata ta mathimata ton mathimaton - mathimata

6. "light" NOM: ACC: GEN:

voc:

to fos to fos tou fotos - fos

ta fota ta fota ton foton -fota

7. "class" NOM: ACC: GEN:

voc:

DhimotikilKatharevousa i taksi/taksis tin taksil taksin tis taksisl takseon - taksiltaksis

Dhimotiki oi takseis tis takseis ton takseon - takseis

169

170

Markedness Theory

8. "identity" NOM:

Ace: GEN:

voc:

Dhimotiki/Katharevousa i tautotita/tautotis tin tautotita/tautotita tis tautotitas/taut6titos - tautotita/taut6tis

Dhimotiki oi taut6tites tis tautotites ton tautotiton - taut6tites

In each of these examples the distribution of the -s affix follows two patterns: In the Dhimotiki singular, -s appears only in either the nominative case or the genitive case of masculine and feminine nouns, never in both cases. In example eight, where two forms exist for every case, notice that the Dhimotiki form corresponds exactly to the system given above (that is, nom/acc/voc == vowel, gen == s), whereas the Katharevousa form deviates from this pattern. For neuter nouns, examples four and six have the -s affix in every form, but in the genitive case the -s is accompanied by either a vowel shift (cf. eidhos > eidhous) or an additional infix is involved (cf. fos > fotos). In any event, the genitive is distinct from the other case endings. Even in the more unusual declension types listed above, the genitive plural ending for all types is -on; -s never appears in the genitive plural. In order to fully understand the distinctive role the -s marker plays in modern Greek, as well as its connection to gender, let us turn to Jakobson's analysis of the Russian gender system by way of introducing an analysis of the modern Greek gender system.

Jakobson's Analysis of the Category of Gender in Modern Russian The Russian nominal declension system, unlike the Greek one, is more developed in terms of the number of cases (Russian has 6 [plus 2 marginal cases]; Greek, 4), and no single consonantal or vocalic ending is distributed with the same regularity as the -s desinence is in Dhimotiki. However, both languages possess a tripartite gender distinction: masculine, feminine, neuter. In the Russian plural number, gender distinctions are no longer signaled, whereas a distinction is maintained in Greek by the presence of articles. By analyzing lexically given gender in Russian nouns, Jakobson

Grammatical Gender

171

(1960c:141) demonstrates that the feminine is the most marked gender in Russian, since feminine nouns designating persons or animals cannot designate males "unless in expressive, particularly pejorative language" (cf. Russian oslica refers only to female "donkeys," whereas osel (masc) refers to donkeys in general and may include both genders; the fern. nouns svoloc' "bastard" and sterva "bitch" may refer to male persons). Feminine nouns, then, have a more limiting semantic range of reference. While gender in Russian is signaled syntactically, in many cases, declension coincides with a particular gender (cf. Russian 1st declension = masc/neut; 2nd dec!. = fem/masc; 3rd dec!. = feme only).l Thus, simply because a noun ends in -a (Nom.sg.) does not mean that it is necessarily feminine (cf. moja sestra (f) "my sister," but moj deduska (m) "my grandfather"). However, no first declension noun ending in - 0 or -0 may be feminine. Clearly, the feminine gender is more semantically restricting than the masculine in Russian. Formally, that is, declensionally, the feminine nouns are distinguished from non-feminines (masc. & neut.) consistently throughout the singular, whereas neuter and masculine nouns merge in oblique cases in the singular. Given that the feminine is both semantically and formally more restricting, Jakobson is able to justify the following gender hierarchy for modern Russian: Most Marked Least Marked

Feminine Neuter Masculine

Continuing in the Jakobsonian tradition, van Schooneveld (1977b) has recontextualized Jakobson's analysis of Russian gender into semantic features. In doing so, van Schooneveld has developed a bilevel system of gender that is defined by a distinction between agreement gender (masculine inanimate, masculine animate, neuter, feminine) versus declension gender (-0 [1st declension masculine/3rd declension feminine], -0 [1st declension neuter], -a [2nd declension feminine and masculine]).2 Van Schooneveld expresses the relationship between these two types of gender as shown in figure 44. Although van Schooneveld's hierarchy matches Jakobson's, there is one major difference: Van Schooneveld adds the category of animacy to the hierarchy in order to yield the following system:

172

Markedness Theory -a

111 Decl./

/ /

/ /

/ /

Masc. an.

Fell" /

/

/

-0 1Decl.)

-0 /

/ /

/ /

/ /

/

(0)

/

Masc. inan.

/

Neuter

Figure 44

masculine inanimate neuter masculine animate feminine

== == == ==

+ + + +

(/J (unmarked) Distinctness Extension Distinctness, + Extension

Unfortunately, Jakobson's analysis of Russian gender categories does not explain in detail how nouns with feminine grammatical gender are more limiting in their semantic range of reference. Van Schooneveld, however, does offer an explanation of the restrictedness of the feminine grammatical gender by using the notions of narrated and speech event: the narrated event is any event in extra-linguistic reality involving any observer and may include the speaker and addressee; the speech event is not only the act of emitting sound waves, but includes all observers who can potentially hear the utterance (speaker and addressee are necessarily included). The unique feature of syntactically signaled gender, as found in Russian, Serbo-Croatian, and modern Greek, is that its realization is dependent upon a given parole. That is, the gender of a substantive is signaled by agreement and declension, or, how the substantive reacts with the other parts of speech. Clearly, the gender's actual signaling is given by its agreement with articles and adjectives. The declension merely restricts the possibilities; agreement specifies the grammatical gender. But what is gender? For van Schooneveld, gender "poses the problem to what extent a referent identified in a given narrated situation by a given parole remains identifiable outside that conjoint identification in narrated situation and parole" (1977b: 132). In other words, gender is primarily a category defined by the enduring identification

Grammatical Gender

173

of the referent. The gender most identifiable beyond the confines of the given narrated event is the gender most marked. Van Schooneveld states that animate substantives are necessarily more identifiable and retain their identity beyond the narrated event expressed by a given parole (1977b: 132). The conceptual feature that best expresses the essence of the category, animacy, is extension. Requiring that the referent be reidentifiable in each of its manifestations, extension thereby signals the integrity of the referent with regard to the narrated event (van Schooneveld 1982:445). Because animacy is conceptually tied to identifiability and is formally inextricable from gender, and since a coincidence of form signals a potential semantic correlation, disassociating animacy from gender in Russian is practically impossible. One cannot overlook the fact that, among linguists, opinion is divided on the status of the category, animacy. While neither Jakobson (196oc) nor Shapiro (1983:174-75) considers animacy a gender category, van Schooneveld (1977b) and Stankiewicz (1968) both include animacy in their gender analyses. Emily Klenin calls animacy a " subgender" (1983:118). My own view favors the inclusion of animacy as a gender for the following reasons: First, van Schooneveld includes the category of animacy because it is only by means of agreement genanimacy is formally signaled in Russian (cf. fa viiu bol'soj stol [masc. inan, 1st decl]/ moego druga [masc. an, 1st decl]/ moego djadju [masc. an, 2nd decl], etc.)-the expressions of animacy and gender are, in short, formally inseparable; secondly, all neuter nouns except one are inanimate (cf. moe ditje/ditja-"my child"), and so strong is this rule that even in cases where the ending appears to be neuter, the noun, if animate, is reinterpreted as masculine (cf. staryj volcisce-"the old, big wolf")-evidence again for animacy and gender as highly interrelated categories. 3 Finally, it is interesting to examine where animacy and gender find their broadest range of expression in Russian. Only in the accusative case is the animate/inanimate distinction formally expressed. Specifically, only masculine animate versus masculine inanimate is expressed in the accusative singular; only non-neuter (masc/fem) animate versus neuter inanimate is expressed in the accusative plural. Further, the marking for the Russian accusative case (as was shown in chapter one) is extension. If the category of animacy is also marked for ex-

174

Markedness Theory

tension, as van Schooneveld claims, then a double signaling occurs -one type of extension on the level of case, the second on the level of agreement via the category of animacy. Even if we accept extension as the marking of animacy, however, we still have not solved the problem of the second feature, which distinguishes masculine animate from feminine, masculine inanimate from neuter. The Russian neuter's referent, according to van Schooneveld, gives a referent that must be identified for each given parole, but the identity of the referent itself does not change. Van Schooneveld calls this feature distinctness. In conjunction with extension, distinctness makes the feminine grammatical gender capable of representing both animate and inanimate objects, and this cumulation of features gives a more restricting range of semantic reference, as well. One final point of interest regarding van Schooneveld's analysis of gender is directly connected with the relative hierarchy among the three Russian genders: "It seems that, from a formal point of view, the feminine occupies an intermediate position between the animate masculine and neuter. Semantically, there are indications in the same direction" (1977b:134-35). Richard Schupbach (1984:66-67) makes a similar observation, based on the formal expression of gender and declension in modern Russian. Additionally, the neuter gender is more restricted distributionally than the other two genders in Russian, but, as we have shown in chapter four, statistical frequency is not directly related to establishing markedness hierarchies. At first glance, one might interpret these remarks to mean that the neuter is more marked than the feminine. However, van Schooneveld's interpretation is that the feminine gender seems to occupy an "intermediate position" visa-vis the animate masculine and neuter because the feminine is the union of the two semantic features, extension and distinctness, that define the animate masculine and neuter, respectively (1977b: 137).4 My argument, essentially, is for understanding grammatical gender as a meaningful, iconically given linguistic cafegory, that is, one in which the formal representations reflect the functional signification of the category. Such an approach, having been very useful in explaining grammatical gender in German (cf. Zubin and K6pcke 1984), reminds us that instead of attempting to reduce gender distinctions to those sex-related categories given by extra-linguistic reality, we should

Grammatical Gender

175

search for a semantic invariant that is given by the linguistic code itself. This type of approach is fundamentally in keeping with our definition of the linguistic system as open, allowing both inflows and outflows (cf. chapter three; see also Zubin and K6pcke 1984:42). Recalling Jakobson's 1960 gender article, which includes his only reference to the occurrence of a markedness reversal, we find Jakobson specifically noting that the neuter is marked vis-a.-vis the masculine in case-forms (nouns and adjectives), but is the unmarked gender in caseless forms (1960c:142). If we briefly reconsider van Schooneveld's feature hierarchy for the Russian gender system, we find that the unmarked gender is the masculine inanimate, with the neuter assuming the second most unmarked slot, before the masculine animate. In caseless forms (verbs, adverbs), the animate/inanimate opposition is not realized. Thus, the masculine inanimate/masculine animate opposition collapses in favor of the animate (since most verbal agents of transitive verbs are animate), and the neuter remains as the basic gender for indicating either agreement with the agent of the verbal process or the absence of agent in impersonal constructions. This line of reasoning allows us to explain the apparent "shift" in categories, but without invoking the concept of markedness reversal. More importantly, if we recall that van Schooneveld's marking for Russian verbal conjugation (indicative mood) is distinctness, we see that the neuter gender bears the same feature, which argues for semantic compatibility of verbal conjugation and the neuter, as well as supporting the use of neuter verb forms in impersonal constructions. Given that distinctness requires a reidentification of the referent in every given narrated event, this doubling of distinctness would imply that the referent also has to be redefined in each speech event. Thus, the neuter verbal form would be used for impersonal constructions or for utterances lacking a grammatical subject. The Serbo-Croatian Gender Hierarchy The category of gender in Serbo-Croatian is, in many ways, similar to that of Russian. The feminine is kept distinct in singular declensions, whereas the non-feminine genders (m/n) merge in all oblique cases (that is, m # n (nom, acc, voc); m == n (gen, dat, instr, loc». Most

176 Markedness Theory

importantly, the feminine is more semantically restricted in SerboCroatian, as in Russian. Therefore, as Stankiewicz correctly suggests (1968: 33), Serbo-Croatian maintains basically the same gender hierarchy as Russian: Most Marked Least Marked

Feminine Neuter Masculine

However, this statement needs to be qualified in the following manner. First of all, the Serbo-Croatian gender system is different from the Russian one in two significant ways: (1) while Serbo-Croatian includes substantives that have one gender in the singular and a second, different gender in the plural, which we will call a "gender shift," Russian does not allow such a shift; (2) the animate/inanimate distinction does not play a role in the Serbo-Croatian accusative plural, as it does in Russian (cf. Serbo-Croatian s'inovi (n. pI) > s'inove (a. pI) "sons;" prozori (n. pI) > prozore (a. pI) "windows;" but Russian sinovja (n.pl) > sinovej (a. pI) "sons"; okna (n. & a. pI)) "windows." Secondly, the Serbo-Croatian gender system singles out the feminine gender by never permitting feminine nouns to shift their gender as non-feminines (m/n) do. Therefore, although the feminine gender is marked in Serbo-Croatian, the feature marking of the feminine involves a qualification of the invariability of its gender, unlike nonfeminine substantives. (Further research is required in order to posit conceptual features for the Serbo-Croatian gender system. 5) Based on the Jakobsonian gender model for Russian, many linguists have assumed that, in languages with gender distinctions, the feminine is generally the "marked" gender. However, this generalization is challenged by the gender hierarchy of modern Greek.

The Dhimotiki Gender Hierarchy The key component in establishing a hierarchy of markings for the Dhimotiki gender system, if applying the methodology proposed by Jakobson, must rest on the semantic and formal restrictedness, or

Grammatical Gender

177

specification, of one of the three genders. Lexically-given gender in Greek, as expressed by feminine nouns, may refer to male persons, and masculine nouns may refer to female persons. This usually occurs via augmentatives in both genders (cf. a koritsaros (m)-"very pretty girl," from to koritsi (n)-" g irl"). Examples of masculine nouns referring to both sexes, as in Russian, also occur (cf. a anthropos-"person, human being, man"). However, as the first example indicates, Greek is much freer than Russian in assigning lexical gender to persons, and the striking imbalance found in Russian lexical gender is missing here. The formal aspects of gender signalization in Dhimotiki are intimately tied to declension and, more specifically, to the -s desinence. While Russian always maintains a distinct nominative/accusative in second declension feminine nouns, Dhimotiki maintains this distinction with masculine nouns. The distinctness of nominative and accusative hinges solely on presence versus absence of the -s desinence. Although this observation is not meant to equate gender and declension, the acknowledgment of gender expression as intimately connected with case and declension in both Russian and Dhimotiki is crucial. Formally speaking, the typically "masculine" declension in Dhimotiki bears the formal marker -s in the nominative singular, as opposed to the zero ending found in the Russian masculine first declension. Gender in Dhimotiki is expressed syntactically, as in Russian, being specifically expressed via the article, as well as through pronominal and adjectival agreement (cf. a grammateas (m)-"secretary," or i grammateas (f)-"secretary;" a dhikig6ros (m)-"lawyer," or i dhikig6ros (f)-"lawyer") (Householder et al. 1964:39). However, unlike Russian, Dhimotiki does not systematically express a category distinguishing animacy in nouns. Before positing a gender hierarchy for Dhimotiki, the following categories must be considered: dimunitive formation and names for couples, as in the examples in figure 45. In the first category, the shift from nonemotive to emotive naming, Dhimotiki and Russian disallow exact opposites in declensional types: masc > neut (Greek); fern> neut (Russian). In the second category, Dhimotiki requires a feminine form to refer to mixed couples, whereas Russian uses a plural form, unmarked for gender. 6

178

Markedness Theory

Based on the evidence given above, the following gender hierarchy for Dhimotiki can be proposed: Most Marked Gender Least Marked Gender

Masculine Neuter Feminine 7

If these hierarchies for Russian and Dhimotiki are now analyzed within the contexts of the two languages' morphological systems of case and number, what are the implications for the systems as a whole? The nominative is considered the "unmarked" case in all of the socalled "nominative/accusative" languages. If this holds true in modern Greek, then what is that language's most marked case? Since the only formal distinction found in many nominal paradigms involves the nominative and genitive cases, the genitive is probably the most marked case in Dhimotiki. This statement is further supported by the Figure 45 I. Diminutives

A. Dhimotiki full form masc > fern > fern > fern > masc > j *masc

diminutive masc fern neut masc fern neut

B. Russian full form masc fern *fem fern masc masc

> > j

> > >

diminutive masc fern neut masc fern neut 8

II. Names for Couples A. Dhimotiki: feminine is used (Kazazis 1982: 234) 1. 0 kirios kai i kiria Kontou. "Mr. and Mrs. Kondu" 2. I kina kai 0 kirios Kontou. "Mrs. and Mr. Kondu" 3. Eleni kai Gi6rgos Kontou. "Helen and George Kondu" (*The masculine form of the name is Kontos) B. Russian: plural is used (no gender) 1. Nikolaj i Ol'ga Ivanovy "Nikolaj and Ol'ga Ivanov" 2. Gospodin i gospoza Ivanovy *"Mr. and Mrs. Ivanov" (for foreigners only)

Grammatical Gender

179

semantic range of the genitive case in Dhimotiki. One evidence of the restrictedness of the genitive is evidenced in limited usage of neuter nouns (particularly those ending in -aki and ouli) in the genitive case (Householder 1964:57). Formally, the genitive plural is the only instance in Dhimotiki of a case desinence that never involves an -5 and is never found in any other case form (cf. -on [gen. pI]). In this manner, the ending -5 juxtaposes the unmarked case (NOM) to the most marked case (GEN). But the placement of the -5 is reversed (nom. vs. gen.) in nouns with masculine, as opposed to non-masculine, gender, giving the following system: Therefore, if the masculine is the most marked gender in Dhimotiki, the -5 aligns the unmarked case with the marked gender, the marked case with the unmarked gender. But the Dhimotiki nominal declension system goes a step further to distinguish the nominative/genitive opposition by never allowing the -5 affix to appear in any paradigm in the genitive plural ending; the genitive plural is a doubly marked category, with the marked nature of the plural number added to the marking of the genitive case. Although the -5 affix never occurs in the genitive plural, it does occur in the genitive singular of non-masculine nouns. While the gender distinction is nondistinctive in the plural, the genitive versus non-genitive case distinction is the fundamental opposition in the plural. The major case, gender, and number distinctions in Dhimotiki are realized in most instances by means of the -5 affix, that is, either by its presence or absence (excluding a very small percentage of anomalous paradigms). Only in the neuter paradigms in -i and -0 may the -5 be totally absent Figure 46 Most Marked Gender masculine

Least Marked Gender non-masculine (feminine/neuter)

Most Marked Case genitive

Unmarked Case nominative

Affix -5 masculine nominative singular

Affix -5 non-masculine genitive singular 9

180

Markedness Theory

(cf. NOM/ACC paidhi; GEN paidhiou; VOC paidhi [sing]; NOM/ACC paidhia; GEN paidhi6n; VOC paidhia [pl]-"child[ren]"). Likewise, only in the neuter singular paradigms may the -s affix indeed be present in every case form (cf. NOM/ACC meros; GEN merous; VOC meros [sing]; NOM/ACC meri; GEN mer6n; VOC meri [pl]-"place; toilet [provincial]"). Of the three categories-case, number, and gender-the case opposition is the most important and is always signaled by the substantival declensions (in the masculine and feminine genders by -s and in the neuter gender by -u or occasionally an additional suffix), that is, either nominative vs. non-nominative or genitive vs. non-genitive. Even when the gender distinction collapses in the plural, the genitive versus non-genitive distinction remains. Shifting Genders Given the general assumption that substantives have invariable gender, it is interesting to find cases where this corollary does not hold, that is, where substantives express a change, or shift, in their gender. However, what exactly is meant by the term gender shift must be clarified. In general, there are four possible types of gender shifts within synchronic linguistic systems: (1) Shift in agreement and declension gender of a substantive from singular to plural (cf. modern Greek 0 ploutos (m) > ta plouti (n)-"riches"; Serbo-Croatian sluga (m) > sluge (f)-"servants");l0 (2) Shift in overall gender oppositional categories from singular to plural (cf. Rumanian: SING: feminine vs. non-feminine; PL: masculine vs. non-masculine [Jakobson 1959:187]); (3) Agreement gender shift-nouns with double gender in singular [this category is often referred to as "common" gender.] (cf. Russian sirota "orphan," p'janica "drunkard," kollega "colleague"; Greek o/i grammateas "secretary," o/i dhikig6ros "lawyer," o/i giatr6s "doctor"; o/i sizigos "spouse"; Serbo-Croatian vecer "evening," pijanica "drunkard," blebetalo "tattler" (masc/neut)-all examples, except for blebetalo are ambiguously masculine and feminine [vece-'~evening" [neut] also occurs]);l1 (4) Declension/gender shift-in rare instances an augmented noun may change its declension without changing its gender (cf. Russian dom/domisko/domisce (all masc)-"house, house [pejora-

Grammatical Gender

181

tive], huge house"; volk/volcisce (both masc)-"wolf, big wolf"; modern Greek tokoritsi (n) > 0 koritsaros (m)-" girl, pretty girl"; SerboCroatian decko (m) > decki (m)-"child/children;" auto (m) > automobili (m)-"car/cars"). (In Serbo-Croatian, augmentation is not a requirement for this type of declensional gender shift [for example, decko >

decki].) My focus here will be on the first type of shift, where both declension and agreement gender shift in the switch from singular to plural number. Of the three languages in question, only Russian does not allow gender shifts of the type given in number one, since Russian necessarily collapses all gender distinctions in the plural. SerboCroatian and Greek, however, maintain a three-way gender distinction in the plural of the nominative, accusative, and vocative cases. In all three languages, declensional types are ambiguous in their signalization of gender. Serbo-Croatian, like Russian (cf. above), has three declensions with precisely the same gender distinctions, but modern Greek shows a somewhat different pattern: First declension includes masculine and feminine, whereas second declension includes feminine and neuter. (Of course, modern Greek, as well as Russian and Serbo-Croatian, includes other anomalous and nonproductive paradigms, but these are the exceptions rather than the rule. 13 The fact that gender distinctions are collapsed in the plural (cf. Russian) corroborates Joseph Greenberg's 37th universal: A language never has more gender categories in non-singular numbers than in the singular" (1966:75). Thus, syncretism in the marked plural number and in shifts is not an unexpected occurrence, although implicit in Greenberg's universal is the understanding of a tendency to reduce the number of marked categories imbedded in other marked categories (Jakobson 1959: 188-89); this is only a tendency of markedness theory, not a rule. Here, we have the gender categories imbedded in the marked number. If Greenberg's statement is correct, we would then expect the gender shift in Dhimotiki to go from a more highly marked gender to a less marked one. The Dhimotiki shift of masculine nouns to neuter in the plural number supports, but does not prove, the markedness hierarchy suggested in this chapter. However, there would be no system-based explanation for a masculine to neuter shift II

182

Markedness Theory

if the masculine in Dhimotiki were considered the unmarked gender, as it is in Russian. Although declension and gender are not isomorphically related in Russian, modern Greek, or Serbo-Croatian, the degree of interdependence between these two categories does vary among the three languages. The validity of such a claim can be established by a closer look at the gender shifts that can occur in modern Greek and SerboCroatian. Consider the following examples: In Serbo-Croatian, all genders except feminine may shift from singular to plural, doublets in plural may occur (akta/akti), doublets in singular may occur (blebetalo, kino), and all masculine nouns ending in -0 must either change gender or declension in the plural (cf. kino, auto). In modern Greek, only nouns of the masculine gender may shift from singular to plural number, doublets in plural may occur, and no real doublets occur among those nouns that change gender. 14 From the data given above, it is clear that declension type in SerboFigure 47 A. Modern Greek (Dhimotiki): Singular

PIural

> ta plouti (n) > ta sana (n)

riches hay

Doublets in Plural 3. 0 vraxos (m) 4. 0 ouranos (m) 5. 0 dhesmos (m) 6. 0 kapnos (m) 7. 0 logos (m) 8. 0 xronos (m)

> > > > > >

oi vraxoi (m)1 ta vraxia (n) oi ouranoi (m)1 ta ourania (n) oi dhesmoi (m)1 ta dhesma (n) oi kapnoi (m)1 ta kapna (n) oi logoi (m)1 ta logia (n) oi xronoi (m)1 ta xronia (n)

rock (s) sky (ies), heaven (s) bond (s) I fetter (5) smoke I tobacco word (s), reason, speech year (s), tense (5), time 15

B. Serbo-Croatian: 1. sluga (m) 2. akt (m) 3. oko (n) 4. maee (n)

> > > >

sluge (f) akta (n) [also tikti (m)] oei (f) maeici (m)

servant (s) document (s) eye (5) kitten (s)

1. 0

2. 0

ploutos (m) sanos (m)

Masculine Forms Ending in - (/) 5. kino (min) > kina (n) 6. auto (m) > automobili (m)

movie theater (s) car (s)

Grammatical Gender

183

Croatian can force a gender shift (cf. -0 ending in singular), whereas in Greek this is not so. Therefore, it is useful to maintain a distinction between agreement and declension gender, since declension may indeed affect gender assignment. Such a distinction also allows us to sort out gender shifts involving both syntagmatic and paradigmatic information from those shifts that are either purely syntagmaticallydefined or purely paradigmatically-defined. One final point about declensional systems concerns the distribution of the zero ending in Slavic versus its conspicuous absence in modern Greek. As was discussed in chapter 3, the zero sign is one of the basic organizational principles of the Russian nominal declension system (Jakobson 1938,1958). The same is true of Serbo-Croatian. However, in modern Greek, no zeros are found in the nominal declension system; instead, one finds the -5 desinence. In particular, the -5 formally sets up a masculine/non-masculine opposition in the singular, yielding the following alliance between the masculine and feminine gender categories in declension: Ending

-0 ::::} - 5

::::}

Russian and Serbo-Croatian (1st dec!. nom. masc./ 3rd dec!. nom. and acc. fern.) Modern Greek (masc. nom. sg./non-masc. gen. sg.) Grammatical Gender Versus Declension: Syntagmatic Versus Paradigmatic

The arguments presented here to support a masculine vs. non-masculine gender opposition in Dhimotiki involve both the semantics of gender, that is, lexically given gender, as well as the formal expression of gender types. However, the exact relationship between gender and declension has not yet been established. Specifically, are these categories unrelated, relatively autonomous, or totally dependent upon each other and, hence, inseparable? Traditional approaches to grammatical gender call for maintaining a distinction between gender and declension, essentially arguing that the two categories are unrelated. It is certainly true that Russian has three declensions and three gen-

184

Markedness Theory

ders, while Dhimotiki has many declensions (at least five) and only three genders. Yet, grammatical gender is manifested only in the linguistic code via the various declensional paradigms. Significantly, a shift of gender in Dhimotiki necessarily requires a shift in declension. Since gender is expressed syntactically, the complementary declensional shift is not essential for the gender shift to occur. From the perspective of paradigmatic versus syntagmatic categories, one can better see the exact relationship between gender and declension: Namely, gender and declension are relatively autonomous categories that intersect with each other at the same point where paradigmatic and syntagmatic phenomena overlap. To illustrate this point, let us consider the one counterexample from Dhimotiki which supports the argument that the masculine gender in Greek is unmarked visa-vis the feminine: the interrogative pronoun "who" (Gk. poios, poid, poio (m/f/n». Kazazis (1980:252) states that the masculine interrogative is used in instances where the pragmatic referent is known to be a female (cf. Poios einai-"Who is it?" [imagine a phone conversation]). The feminine variant (Poid einai) is considered less polite. However, when the speaker switches from third person to first or second person, the interrogative form must agree with the pragmatic referent (cf. Paid eiste-"Who are you?"-must be used if the referent is female). Therefore, the masculine interrogative pronoun in Dhimotiki does not, to my mind, inherently signal gender at the grammatical level; further, this lack of gender signalization parallels the situation found with Greek nouns in general, where only declension type is signaled. Remember that forms ending in the -s affix potentially express all three gender types in Dhimotiki, or, put another way, nominative case forms ending in -s are the only words that express their potential gender ambiguously. Therefore, we may reasonably conclude that the masculine gender is not only semantically but formally marked, as well. While the -s affix does not mandatorily signal the masculine gender, all masculine nouns, pronouns, and numerals must end in -s; there are no exceptions to this rule. Furthermore, we may argue that poios is used only in the third person for either sex precisely because only the -s form can be ambiguous in its gender. The fact that poios is one of three forms of the interrogative pronoun implies a paradigmatic relationship; since gender

Grammatical Gender

185

is signaled syntactically in Dhimotiki, declensional (or paradigmatic) signalization of gender is necessarily ambiguous. A second point concerning poi6s directly relates to the systemic balance of morphological categories in Dhimotiki. The use of the most marked gender (masc) with the least marked person (3rd) is another example of the language's maintaining its balance (Jakobson 1959: 189). This principle, as stated by Jakobson, contradicts that of markedness assimilation, but, to reiterate, neither of these principles is a rule in the markedness theory presented here; rather, each is merely a tendency. The same "balance" is seen in the distribution of the -s desinence (masc. nominative [marked gender, unmarked case], non-masc. genitive [unmarked gender, marked case]), as well as in the masculine> neuter gender shift in the plural. If the masculine gender were unmarked, there would be neither a system-motivated explanation for the distribution of the -s desinence, nor an explanation for the masc > neut gender shift; thus, two significant generalizations would be lost. Is Gender Meaningful? Do languages assign lexemes to different gender types systematically? Householder answers this question with a resounding No: "Given a meaning like 'chair' or 'table', you have no way of guessing what gender the Greek word for it will have" (Householder 1964:40). One must agree with this statement because, from the outside looking in, gender assignments do seem arbitrary and meaningless. However, another possible perspective, that is, looking from the inside out, was adopted by Jakobson and Peirce, both of whom attempted to redefine arbitrariness, based on the relationship between the signified and signifier of the linguistic sign. Jakobson argues in "Language and Culture" that "latent semantic value" exists in gender oppositions of inanimate, as well as animate, nouns (1972:109). To support his hypothesis, Jakobson presents a study by the Moscow Psychological Institute (1915) on the human ability to personify inanimate objects and to make abstractions. The study revealed that subjects consistently personified abstract, inanimate nouns parallel to their grammatically-given gender in Russian.

186

Markedness Theory

It is precisely this type of "latent semantic value" that is often exploited in the poetic and emotive (that is, noncognitive) functions of language. Linguistics (when it has been interested in studying meaning) has often carelessly rejected any conceptualization of meaning that cannot be directly connected to extra-linguistically-given referents or to traditional logical values. Gender assignment at the lexical level, however, is an area that merits further research. By comparing and contrasting the gender systems of Russian, SerboCroatian, and Dhimotiki, the significant hierarchies of meaning and their interlinguistic redistributions can be discovered. The importance of the -5 marker in modern Greek cannot be overemphasized, given its role as a formal signal of a semantic marking that defines a masculine versus non-masculine opposition in the gender system, as well as its role of reinforcing the complex internal network of markings expressed by the categories of case, gender, and number. Gender oppositions represent one of many morphological categories that are indeed meaningful as they are recodified by each linguistic system. In recognizing the ability of morphological categories to express meaning, one is confronted by the fundamental principle underlying all linguistic sign systems-the inseparability of linguistic form and content. As Jakobson stated in "Observations of the Russian Case System": Phonology and grammar prove to be indissolubly linked by a whole range of transitional, interdisciplinary problems, and chiefly by the indivisibility of speech sound and meaning. (195 8 : 128) Based on the analysis above of gender categories in Russian, SerboCroatian, and modern Greek, we may conclude by suggesting that although these three languages signal gender syntactically via adjectival, pronominal, and, in the case of modern Greek, article agreement, the declensional type also plays a role in signaling ambiguous gender, double gender, and gender shifts. Furthermore, we have seen a case in Serbo-Croatian where declension type forces a shift in gender (Ivic 1961:56-57); we have also seen that in modern Greek, declensional shifts mandatorily accompany agreement shifts when this is, in fact, not essential for the gender shift to take place. Therefore, it appears that the relationship between syntagmatically and paradigmatically

Grammatical Gender

187

expressed gender oppositions should be maintained, that is, agreement versus declension gender. However, one must carefully and constantly reevaluate the relationship between these two categories as it is redefined from language to language. In this manner, a clearer understanding of the invariant function of gender categories will become possible. Markedness theory is a tool that enables the linguist to define more precisely the systemically-given oppositions and hierarchies represented by linguistic categories. In making explicit the foundations and principles of structure, the linguist can intelligibly convey relevant truths about language systems in general. Clearly, markedness theory, as a theory of interpretants, cannot resolve all of linguistics' unanswered questions. But, if applied rigorously, markedness theory will prove indispensable in uncovering the fundamental principles that define the broad spectrum of linguistically-given oppositional relationships, encompassing all levels of linguistic meaning. Disassociating markedness from the principles of semiotics renders the theory essentially useless, for only when the linguistic content is considered in connection with its formal realization can a theory of linguistic meaning be developed. Such a theory necessarily requires some notion of how linguistic reference occurs. Using the concept of deixis, as well as a more sophisticated definition of context and contextual meaning, we can begin to explain the complex network of codification that gives rise to the linguistic system. The present work does not pretend to have answered all questions concerning the concept of markedness. Rather, what has been attempted is a demonstration of how a markedness theory, defined by the principles of mathematical set and group theory and couched in the broader context of sign theory, can be used in defining linguistic oppositional relations via conceptual semantic features. In essence, we have only taken the first step in defining a theory of markedness.

= Notes =

One. The Principles of Jakobsonian Markedness Theory 1 The markedness correlations given in Jakobson's "Shifters" are initially posited in his article, "Zur Struktur des russischen Verbums." In Selected Writings II (The Hague: Mouton, 1932/1971), 3-15. 2 Trubetzkoy's definition of markedness is still predominant in the works of some Jakobsonians (cf. Stankiewicz 1968, 1986). 3 For a detailed discussion of the difference in phonological features as defined by Jakobson versus Chomsky/Halle, see R. B. Sangster, Roman Jakobson and Beyond: Language as a System of Signs (Berlin: Mouton, 1982), 9-28. 4 S. A. Schane defines the difference between "distinct" versus "distinctive" as "distinguishability" versus"distinctiveness," in Generative Phonology (Englewood Cliffs, N.J.: Prentice-Hall, 1973), 40 . 5 For different perspectives on Jakobson's analysis of the Russian case system, see Chvany (1984), Sangster (1982), van Schooneveld (1986a), and Worth (1984). 6 It should be noted that van Schooneveld's final three features correspond in a general sense to Jakobson's three features for the Russian case system. However, van Schooneveld's features differ from Jakobson's in three fundamental ways: (1) they are defined solely in terms of paradigmatic information; (2) all reference to extralinguistic reality has been removed; and (3) the features are defined in terms of a hierarchy. Thus, van Schooneveld no longer defines extension (Jakobson's directionality) as the goal of the verbal process, but as a referent that is minimally affected by the verbal process; this referent continues to exist beyond its relationship to the ling~istic modified within the narrated situation. For a thorough discussion of van Schooneveld's extension of Jakobson's feature analysis beyond the Russian case system, see Sangster (1982) and van Schooneveld (1978c, 1982, 1983, 1986a). 7 Geoffrey Leech (1969:167) also uses the term dimensionality but in a very different sense. Dimensionality, for Leech, defines a particular spatial relation [an orientation] determined by the "perceptual apparatus of the human body." For more information concerning Leech's notion of dimensionality, see Lyons (1977:698-99). 8 It is interesting to note Thorn's assessment that"all ontology, all semantics necessarily depends on a study of space-geometric or topological" (1983:275).

190

Markedness Theory

9 C. S. Peirce defines the"object" not as a thing, but as a phase of the sign. Peirce distinguishes two types of objects: (1) immediate-lithe object as the Sign itself represents it"; and (2) dynamical-lithe reality which by some means contrives to determine the Sign to its Representation" (4.536). Thus, the immediate object is given within the sign (that is, not denoted by it), while the dynamical object is external to the sign, a part of reality itself (Fitzgerald 1966:43). 10 The Saussurian distinction of synchrony and diachrony is an abstraction that can be, in some instances, extremely problematic. In the present work, I am inclined to view synchrony and diachrony as interactive categories rather than dichotic ones. This view parallels a similar perspective of the interrelationship between langue and parole. If deixis is the recodification of parole into langue, then once again we are dealing with an interactive conceptualization of Saussure's langue/parole distinction. In fact, this type of interaction is at the very base of Jakobson's notion of "relative autonomy," whether as applied to the difference between the phonemic and grammatical levels of language or to lingustic signs as determined by relatively defined oppositions. 11 In recent articles, van Schooneveld has renamed "perceptional" deixis as "identificational" deixis. 12 Van Schooneveld uses prime symbols to designate the four levels of deixis: perceptional = '; transmissional = "; singulative perceptional = "'; singulative transmissional = "". 13 These sentences are examples of lexical perceptional deixis. Verbal aspect is an example of grammatical perceptional deixis. 14 Van Schooneveld (1978b) does not include the categories of number and person in his discussion since these categories are to some extent redundantly given in Russian and are not signaled purely paradigmatically, as are aspect, tense, etc., but, rather, syntagmatically. 15 Although both Jakobson and van Schooneveld agree that the passive is the marked voice, they differ in their understanding of the relationship of the active and reflexive to the passive. Specifically, Jakobson (1932:4) gives the following hierarchy: (1) Intransitivity of action (that is, passive & reflexive) (M) versus active (U); (2) Passive (M) versus reflexive (U). Van Schooneveld (1978b:43), on the other hand, views the reflexive as a subtype of the active voice: (1) Passive (M) versus active (U); (2) Reflexive (M) versus non-reflexive (U). In terms of the formal structure of the Russian verb, the reflexive is indeed more closely related to the active than to the passive. 16 An additional category can be included in van Schooneveld's system, which is missing from the 1978 article, but is present in his seminar discussions concerning the Russian verbal system. The category of conjugation, which in Russian always signals the indicative mood and a non-preterit tense (that is, either present or future), is assigned the feature distinctness. Distinctness requires a series of perception acts which are necessarily ordered. As the first feature in the hierarchy that requires an ordering of perceptions, distinctness is, thus, the first feature that is

Notes

191

inherently deictic. For a thorough discussion of van Schooneveld's views on the Russian verbal system, see Fradkin (1985). Van Schooneveld has renamed most of the six conceptual features. Note the following changes: plurality ~ plurality dimensionality ~ demarcatedness distinctness ~ pre-identity ~ verification extension restrictedness ~ cancellation ~ objectiveness objectiveness Also perceptional deixis is renamed as identificational. 17 Howard Aronson (1977:14-15) argues that the positions of mood and status, as given by Jakobson, should be reversed for the Bulgarian verbal system, yielding: En (non-shifter) ~ mood/aspect; En/p s (shifter) ~ status. This modification of Jakobson's description is important because it questions the placement of mood in the verbal system. Van Schooneveld's redefinition of mood, aspect, voice, and tense in terms of conceptual features has a very significant effect on how the grammatical category of mood is perceived since, according to lingustic form, the conditional mood in Russian is related to the past tense, given by the restrictedness feature, while the imperative mood is given by the extension feature. Aronson is primarily concerned with the conditional mood in Bulgarian and, relying on the lingustic form, can justify his definition of mood as related to En, not pnEn/ps. Although Aronson and van Schooneveld have two distinct goals in mind, their analyses using "shifters" complement one another in that each requires a reinterpretation of the category of mood in the Slavic languages.

Two. Peirce and Jakobson Revisited: A Reconciliation

This statement does not imply that there are only six interpretants which are capable of describing human language. As was shown in chapter one, these six features on four deictic levels can generate 8.5 x 10 37 forms. 2 For a more detailed account of the three types of inference, see chapter three. 3 For an explanation of the difference between representamen and sign, see Savan (1976 : 10). 4 Peirce never offers a precise definition of object, but two important points should be included to clarify the concept as much as possible: (1) the object of a sign exists prior to the sign and is known collaterally; (2) the object of a sign is shared by a sign and its interpretants, and is necessarily confined to and definable by a context, or community of sign users (Savan 1976: 16-17). Therefore, the Peircean "object" is not an absolute but a relativized object, dependent upon the context for identification. For further discussion of the relationship between object and context, see Savan (1976 :19). 5 For more information concerning compound signs, see Jakobson (1985:207).

192

6 7 8 9

10 11

12

13 14

15

16

17

Markedness Theory Savan (1976:35) notes that qualisigns and sinsigns cannot be interpretants without additional conditions. For a detailed discussion of these three trichotomies, see Peirce (2.243-54). Similar terminology is presented by Esposito (1980: 198). Esposito (1980: 180-82) argues that the dyad is critical to understanding the monad and that Peirce's metaphysics "actually begins with the dyad." Such a view, as expressed by Esposito, is not meant to imply that dyads are more important for Peirce than triads. Rather, it is both dyads and triads that provide the foundation for Peircean categories. For mention of the artifice, see Waugh (1984:389-438). Esposito (1980:91-92) presents two very concise definitions of interpretant: (1) "An interpretant ... is a medium that links subject and object (relate and correlate) in the form of representation"; (2) "An interpretant is unanalyzable because to analyze it is to regard it as a representation and to employ another interpretant in the process." This second definition comes very close to van Schooneveld's use of autopoiesis in connection with his conceptual features and deixis. Peirce's second trichotomy of interpretants includes the following three categories: immediate, dynamic, and final. For a thorough discussion of these three categories, see Shapiro (1983:53-56). This analogy is parallel to one given by Peirce (5.490). It should be noted that Peirce writes very little on the emotional interpretant, but more fully develops his conceptualization of the energetic and logical interpretants. This is perhaps due to the energetic and logical interpretants' being more easily perceivable and, hence, more easily definable linguistically. Maslov restates his definition of the perfective-imperfective opposition in "An Outline of Contrastive Aspectology" (1985:26,30). Although Maslov follows Jakobson's assessment of the marked nature of the perfective aspect, he further qualifies the type of "boundedness" given by grammatically-defined aspect. As a general meaning for the perfective, Maslov emphasizes that the perfectively given action is necessarily an "indivisible whole." Thus, boundedness is more than limitation in Maslov's general meaning of the perfective. This fact does not imply that Maslov's definition is incompatible with van Schooneveld's feature, dimensionality. The term pragmatics is used here to refer to a general theory of communication, and includes metaphor, stylistics, rhetorical devices, and all phenomena called thematic structure. For a more detailed perspective of this question, see Kempson (1977:192-96). The preceding examples from Russian, I would argue, demonstrate the constant dialectic that exists between the emotional and logical interpretants. The comprehension or production of these utterances is hampered if one or both systems of interpretants is skewed or underdeveloped. Weinreich (1968:76-78) also argues in favor of the primary significance of semiotic behavior over pragmatics. There is an implicit understanding in the teaching of a second language that native speakers are better, or even essential, at advanced levels of L2 instruction. The reasoning behind this assumption, although not usually made explicit, is necessarily

Notes

193

connected with the prejudice that non-native instructors are usually not bilingual and, so, cannot adequately handle the "nuances" of the L2 that are dealt with at the advanced level. 18 Language instruction conducted in the culture of the target language is one means of supplying the L2 learner with a community of speakers. However, as Dulay, Burt, and Krashen point out, not all communities of speakers are equal. An important factor in defining the community of speakers involves the presence of "peers who speak the target language natively" (1982:109). 19 This is but another example of Jakobson's linguistic theory as more a theory of Seconds than of Thirds. Jakobson's use of Peirce was generally expressed via the icon/index/symbol triad, which is a category of Seconds. This observation is not meant to imply that Jakobson never extended his theory to encompass Thirds. In fact, it is precisely by means of markedness theory that Jakobson achieves his own version of Thirdness. 20 My definition for bilingualism is simply a further specification of the definition given by Weinreich (1968: 1): "The practice of alternatively using two languages...."

Three. Markedness Theory as Mathematical Principle 1

2

3 4

5

6

7

Jakobson also recognized that linguistics should not be totally consumed by mathematics. Elmar Holenstein presents Jakobson's opinion concerning this issue in the following statement: "Intralinguistic integration is combined with interdisciplinary integration. Linguistics is not isolated from the natural sciences (biology, physiology, etc.) or from other formal sciences (logic, mathematics), nor is it absorbed by them" (1976:6). Esposito (1980:47) notes that Peirce took from Plato his belief that "the abstract is reaL" For more on Peirce as a Platonist, see Peirce (6.192, 6.194, 6.208). For a discussion of the Platonist's perspective of Codel's theorem, see Davis and Hersh (1981 :319-20) and Brown (1969:96). This definition of mathematics is a combination of Peirce's own definition, taken from his father, Benjamin Peirce ("the science of making necessary conclusions"), as well as a definition of the mathematical object and type of reasoning fundamental to the discipline. For a detailed discussion on defining mathematics, see Davis and Hersh (1981:6-9). Holenstein refers to Euler circles as the "superior illustration" of sign systems (1978:46). For a discussion of the limitations of Euler's system of diagrams and of Venn's improved system, see Peirce (4.356-67). The justification of this statement is found in Peirce's formulation of the basic trichotomies, where sign is related to itself, to its object, and to its interpretant (cf. chapter 2). Peirce also acknowledges that, given his definition of continuity and continuum ("there shall be a next following point" [4.126]), there is certainly room for "cracks," or discontinuities, in the system (Esposito 1980: 171).

194

Markedness Theory

8 The notion of structural stability was introduced into mathematics by A. Adronov and L. Pontryagin (1937, "Systemes grossiers," C. R. (Dokl.) Academy of Sciences, USSR 14, 247-51). 9 Density in language refers to the inherent stability of a category (cf. the noun is more stable than the adjective, the adjective more stable than the verb, etc.) (Thorn 1975: 327; 1983). A manifold, roughly speaking, is a topological space that is something like (that is, similar to) Euclidean space JR. For more on manifolds in topology, see Maunder (1980:89-90). 10 Van Schooneveld connects his notion of the semantic dominant to the biological theory of autopoiesis, developed by H. R. Maturana and F. J. Varela (1980). 11 Thorn (1983: 193) further states that morphologies could be represented by multidimensional spaces greater than four. 12 For specific examples of the application of symbolic logic and mappings (or functions), see Carnap (1935, 1956), Chomsky (1957, 1965, 1968), and Harris (1968). 13 For examples of set and group theory applications to language, see Ungeheuer (1959) and Lowe (1969). 14 Even Peirce avoids the term synonymy and speaks of "extensional equivalence" (Savan 1976:30). 15 Fuzzy sets are not discussed here. However, their absence is not meant to imply that they are insignificant. Rather, our definitions on ordering will be specific enough to demonstrate gradation in class membership without evoking fuzzy concepts. For applications of fuzzy sets in linguistic analysis, see J. Coates (1983). Four. Myths About Markedness 1 For a definition of sequential and concomitant neutralization, see Shapiro (1983: 111). 2 Esposito (1980: 163) defines a degenerate second as "a relation of mere otherness." 3 For more information on the parts of speech, see Thorn (1983: 237-38, 248-49). 4 Another concept, which is an extension of types of markedness assimilation in morphophonemics, is the principle of markedness complementarity (Shapiro 1972, 1974, 1983). Briefly defined, "this principle states that oppositely marked stems and desinences attract, identically marked stems and desinences repel" (Shapiro 19 83: 146 ). 5 The two logical possibilities, that is, the totally unmarked case and the totally marked case, do not occur as forms in language. Specifically, there is no completely unmarked element in language, while totally marked types would yield frame categories, as defined by singulative transmissional deixis. 6 This assumption is probably based on the notion that in languages with grammatical gender, the feminine is usually the marked gender. For more on this subject, see chapter 5. 7 In general, if truncation occurs in the infinitive or past tense of the Russian verb, no truncation will occur in the conjugated present/future tense forms, and vice versa.

Notes

195

Five. The Category of Grammatical Gender in Russian, Serbo-Croatian, and Modern Greek

2

3

4

5

6

7

8

Traditionally included in the Russian third declension is a set of neuter nouns ending in -a (vremja "time," imja "name," etc.), and one masculine noun (put' "path, way"). The distinction between agreement versus declension gender is based on discussions with van Schooneveld and has not yet appeared in print. Examples of this type are very significant because they demonstrate that in Russian the lexical root is more forceful than other word-formative elements in determining gender. Yet, there are instances where the suffix does have an influence on determining the gender of the substantive (cf. dom "house," but domina "house, casket" (masc/fem)). Stankiewicz (1968 :30) and van Schooneveld (1977:137) classify animacy with the other genders. Klenin (1983:120) maintains animacy as a "subgender" and states that inanimacy, not animacy, is the "marked member of correlation" in Jakobsonian terms. Stankiewicz (1968:34) suggests that a shift in the overall gender opposition occurs in Serbo-Croatian when going from singular to plural, where the opposition feminine/non-feminine in the singular number shifts to masculine/non-masculine in the plural. Stankiewicz argues that this is a reversal, indicating that the feminine loses its marked status in the plural. I would argue that this is not a reversal, but a reflection of the plural number's ability to obscure identifiability of referents, and, thus, the masculine is more compatible with the meaning of the plural. Serbo-Croatian uses a masculine plural form in the nominative case to refer to mixed groups. As Russian does not maintain its gender distinctions in the plural, a generic plural form is used in every instance. In general, in those Slavic languages where a gender distinction is maintained in the plural, a masculine form is required for mixed couples (cf. Polish, Panstwo Krynscy "The Krynskis" (mixed couple) versus Panie Kryfzskie "The Krynskis" (women only)). This analysis will not be complete until actual feature assignments are made to the Serbo-Croatian and Greek markedness hierarchies (cf. Andrews [forthcoming]). Based on my analysis of the modern Greek case system, I have initially determined that the equivalent of the extension and objectiveness features seems to define the Greek case system. I would also suggest that the equivalent of the restrictedness feature was lost, along with the dative case, in modern Greek. For another example of gender analysis in Slavic, see Aronson (1964:87-101). The data concerning diminutive formation in Dhimotiki was taken from a conference paper given by Kostas Kazazis (1984), in which he cites Mpoutouras (1912), Modern Greek Proper Names, Interpreted Historically and Linguistically, and Katranides (1970), "Some Rules for Modern Greek Nicknames" (Word, 26.3,402-9). Mpoutouras cites examples of masc > neut nicknames in the nonstandard dialects of Kymi and Cyprus. Below is a list of examples of each gender type:

196

Markedness Theory

mlm flf fin flm mlf

Dhimotiki Giorgos > Giorgakis Anna> Annoula Marina > Marinaki Loukia > Loukas Nikos> Nikoletta

min

Russian Vasilij > Vasik AlIa > Alkal Allocka AlIa > Alikl Alek Aleksandr > Sasa Vasilij > Vas'ka Ivan> Vanko/Van'ko

Certain Russian diminutives can be of ambiguous gender (cf. Sasa < Aleksandr [masc.]! Aleksandra [fern.]; Alik < Alla [fem.]1 AleksandrlAleksej [masc.]). In the Russian examples, verbal and adjectival agreement with proper names parallels the gender given by the nonderived proper name (cf. Vanko priexal-"Vanko has arrived" [masculine agreement]). However, the Greek examples, although similar to the Russian ones in the sense of declension shifts, are significantly different in terms of syntactic agreement. In Greek, verbal and adjective agreement is usually determined by the derivative proper name, not by the nonderived proper name (cf. To Irtiki [neut.] efnai tirrosto [neut.]-"Iris is sick" [To Irtiki [neut.] < I iris [fern.]]; the construction To Irtiki [neut.] efnai tirrosti [fem.] can also be found [example provided by K. Kazazis]). 9 The distribution of the Dhimotiki desinence "-s versus non-s" parallels the distribution of the zero desinence in the Russian nominative singular/genitive plural. 10 Gender shifts of this type can also be found in Romance languages (cf. Italian un lenzuolo (masc) > Ie lenzuola (fem)-"(bed)sheet"; French amour (masc) > amours (fem/masc)). Note, however, that the gender shifts in Serbo-Croatian and modern Greek are more numerous and not generally considered to be archaic, as they are in the Romance languages. 11 The first declension Russian noun vrac-" doctor" does demonstrate a limited tolerance with feminine agreement (cf. Vrac prisla-"The doctor's here; Simpaticnaja vrac-"nice [attractive] doctor"). However, this example is qualitatively different from those second declension nouns with "common" gender (cf. sirota, sud'ja"orphan, judge"). 12 In Russian, there are cases of declension shifts of augmented nouns that also exhibit a gender shift (for example, pozorlpozorisce [m > n] 'shame"; pes/psina [m > m/f] "dog/big dog, dog's smell, dog's meat"). 13 Compare the following partial declension tables of modern Greek, Russian, and Serbo-Croatian: Modern Greek I declension (mascl [fem]) o tintras man oli grammateas secretary 01i ithopoi6s actor, actress 01i dhikig6ros lawyer

II declension (femlneut) i ginafka girl to dhomtitio room

Notes

197

Russian I declension (masclneut)

II declension (feml [masc])

stol table pis'ma letter

kniga book deduska grandfather sirota orphan (m/f)

Serbo-Croatian I declension (masclneut)

II declension (fem I[masc])

prozor window selo village

knjlga book dedaldedica grandfather pijanica drunkard (ml f)

Note that third declension and anomalous paradigms have not been included in these tables (cf. Russian imja (n) "name", modern Greek i odhos (f) "street," etc.). 14 The only example of a potential doublet in the singular that undergoes a gender shift in the plural is the pair 0 skiloslto skill "dog." However, this pair also has a doublet in the plural (cf. oi skiloilta skiliti). 15 In some instances, the doublets occurring in the plural have distinct meanings (cf. oi dhesmoi "bonds (of friendship)" vs. ta dhesmti "fetters"; oi xronoi "years, tenses, times" vs. ta xronia "years"). For a detailed list of these differences in meaning, see Householder (1964:63).

= Bibliography =

Alexandroff, P. S. 1959. An Introduction to the Theory of Groups. New York: Hafner. Andersen, H. 1969. "A Study in Diachronic Morphophonemics: The Ukrainian Prefixes." Language 45:8°7-3°. - - - . 1972. "Diphthongization." Language 48(1):11-5°. - - - . 1974. "Markedness in Vowel Systems." In Proceedings of the 11 th International Congress of Linguists. Edited by L. Heilmann, 891-97. Bologna-Florence: Societ'a editrice il Mulina, Bologna. Anderson, S. R. 1985. Phonology in the Twentieth Century. Chicago: University of Chicago Press. Andree, R. 1971. Selections from Modern Abstract Algebra. 2nd ed. New York: Holt, Rinehart & Winston. Andrews, E. 1984a. "A Theoretical Foundation for Markedness: Asymmetry in Language from a Mathematical Perspective." Ph.D. dissertation, Indiana University. - - - . 1984b. "A Semantic Analysis of the Russian Prepositions/Preverbs 0- and OB-." SEEJ 28(4) :477-9 2 . - - - . 1985a. "A Synchronic Semantic Analysis of the Preverbs 0- and OB- in Modern Serbo-Croatian." In Papers for the Fifth Congress of Southeast European Studies, Belgrade, 7-18. Columbus, Ohio. Slavica. - - - . 1985b. "Markedness Reversals in Linguistic Sign Systems." In Memory of Roman Jakobson: Papers from the 1984 MALC, 169-180. Columbia: University of Missouri Press. - - - . 1986a. "A Reevaluation of the Relationship between Grammatical Gender and Declension in Modern Greek and Russian." IJSLP XXXIV:99-112. - - - . 1986b. "An Extension of the Concept of Shifter in Verbal Categories: Perceptional versus Transmissional Deixis." University of North Carolina Linguistics Circle, Chapel Hill: 73-80. - - - . 1986c. "Markedness Theory in Morphology and Semantics: The Reconciliation of Contextual versus General Meaning." The SECOL Review X(3):89-103. - - - . 1986d. "The Prefixes DE- and UN- in Modern American English." American Speech 61(3):221-32. - - - . 1987a. "Gender Shifts and Myths about Markedness." University of North Carolina Linguistics Circle, Chapel Hill: 1-8.

200

Markedness Theory

- - - . 1987b. "Jakobsonian Markedness Theory as Mathematical Principle." In Language, Poetry and Poetics. Edited by K. Pomorska, E. Chodakowska, H. McLean, & B. Vine, 177-97. Berlin: Mouton de Gruyter. ---.1989. "A Study in Linguistic Sign Theory: The Suffix -K-A/-KA in Modern Russian." In From Sign to Text in Linguistics, Literature and the Arts. Edited by Y. Tobin, 123-34. Amsterdam: John Benjamins. - - - . (in press) "Grammar and Pragmatics: The Two Axes of Language and Deixis." In New Vistas in Grammar: Invariance and Variation. Edited by Linda R. Waugh, Amsterdam: John Benjamins. - - - . (in press) "Markedness Theory: An Explication of its Theoretical Basis and Applicability in Semantic Analysis." In Memorial Volume to Honor J. Daniel Armstrong. Edited by C. Gribble, C. H. van Schooneveld, C. Townsend. Columbus, Ohio: Slavica. ---.1990. "Peirce's Emotional Interpretant: A Key to Bilingualism." lRAL 3. Aronson, H. I. 1964. "The Gender System of the Bulgarian Noun." IISLP VIII: 87-101. ---.1977. "Interrelationships between Aspect and Mood in Bulgarian." Folia Slavica 1(1):9-3 2 . Babby, L. 1975. A Transformation Grammar of Russian Adjectives. The Hague: Mouton. Baltaxe, C. 1970. N. S. Trubetzkoy and The Theory of Distinctive Features. Ann Arbor: University Microfilms. Baric, E., et al. 1979. Prirucna gramatika hrvatskoga knjiievnog jezika. Zagreb: Skolska Knjiga. Benson, M. 1971. Serbo-Croatian-English Dictionary. Philadelphia: University of Pennsylvania Press. Birnbaum, Henrik. (in press) "Gesamtbedeutung-A Reality of Language or a Linguistic Construct?" In New Vistas in Grammar: Invariance and Variation. Edited by Linda R. Waugh. Amsterdam: John Benjamins. Bloomfield, L. 1933. Language. New York: Henry Holt. Bolinger, D. L. 1965. Forms of English: Accent, Morpheme, Order. Cambridge.. Mass.: Harvard University Press. Brown, G. S. 1969. Laws of Form. London: George Allen and Unwin. Brown, H. D. 1980. Principles of Language Learning and Teaching. Englewood Cliffs, N.J.: Prentice-Hall. Bruss, E. W. 1978. "Peirce and Jakobson on the Nature of the Sign." In The Sign: Semiotics Around the World. Edited by R. W. Bailey, L. Matejka, and P. Steiner, 81-98. Ann Arbor: Michigan Slavic Publications. Buczytlska-Garewicz, H. 1984. "Peirce's Idea of Sign and the Cartesian Cogito." In Sign, System and Function. Edited by J. Pelc, T. A. Sebeok, E. Stankiewicz, and T. Winner, 37-48. Berlin: Mouton. Bums, G. 1977. Introduction to Group Theory with Applications. New York: Academic Press. Carnap, R. 1934. The Unity of Science. London: K. Paul, Trench, Trubner. - - - . 1947/1956. Meaning and Necessity. Chicago: University of Chicago Press. Carr, G. F., and I. Rauch, eds. 1980. The Signifying Animal: The Grammar of Language and Experience. Bloomington: Indiana University Press.

Bibliography

201

Carus, A. B. 1983. "Patterning of Form and Content in Russian Person: Personal Pronouns and Non-Preterite Personal Finite Verbal Forms." Ph.D. dissertation, Indiana University. Cernysev, V. I., S. G. Barxudarov, & S. P. Obnorskij, eds. 1950-1965. Slovar'sovremennogo russkogo literaturnogo jazyka, 17 vols. Moscow: ANSSSR. Chomsky, N. 1957. Syntactic Structures. The Hague: Mouton. - - - . 1965. "On Certain Formal Properties of Grammars." In Readings in Mathematical Psychology, vol. II. Edited by R. D. Luce, R. R. Bush, and E. Galanter, 125-55. New York: John Wiley & Sons. - - - . 1965. "Three Models for the Description of Language." In Readings in Mathematical Psychology, vol. II. Edited by R. D. Luce, R. R. Bush, and E. Galanter, 105-24. New York: John Wiley & Sons. - - - . 1966. Topics in the Theory of Generative Grammar. The Hague: Mouton. - - . 1967. Aspects of the Theory of Syntax. Cambridge: MIT Press. - - - . 1968. Language and Mind. New York: Harcourt, Brace & World. Chomsky, N., and G. A. Miller. 1963. "Introduction to the Formal Analysis of Natural Languages." In Handbook of Mathematical Psychology, vol. II. Edited by R. D. Luce, R. R. Bush, and E. Galanter, 269-321. New York: John Wiley & Sons. Chvany, C. V. 1984. "From Jakobson's Cube as Objet d'Art to a New Model of the Grammatical Sign." IISLP XXIX:43-70. Coates, J. 1983. The Semantics of the Modal Auxiliaries. London: Croom Helm. Davis, M., ed. 1965. The Undecidable. New York: Raven Press. Davis, P. J., and Hersh, R. 1981. The Mathematical Experience. Boston: Houghton Mifflin. Deely, J. 1982. Introducing Semiotic: Its History and Doctrine. Bloomington: Indiana University Press. de Groot, A. W. 1938. "Zur Grundlegung der Morphologie und der Syntax." In Algemeen nederlands tijdschrift voor wijsbegeerte en psychologie, 151. Dinkines, F. 1964. Elementary Concepts of Modern Mathematics. New York: Appleton. Dokulil, M. 1958. "K otazce morfologickych protikladu." Slovo a slovesnost XIX: 81-103. Drvodelic, M. 1953. Hrvatsko-engleski rjecnik. Zagreb: Skolska knjiga. Dulay, H., M. Burt, and S. Krashen. 1982. Language Two. New York: Oxford University Press. Eisele, C., ed. 1976. The New Elements of Mathematics by Charles S. Peirce (vols. 1-4). The Hague: Mouton. Esposito, J. L. 1980. Evolutionary Metaphysics: The Development of Peirce's Theory of Categories. Athens: Ohio University Press. Fann, K. T. 1970. Peirce's Theory of Abduction. The Hague: Martinus Nijhoff. Fillmore, C. J. 1975. Santa Cruz Lectures on Deixis 1971. Bloomington: Indiana University Linguistics Club. Fitzgerald, J. J. 1966. Peirce's Theory of Signs as Foundation for Pragmatism. The Hague: Mouton. Forsyth, J. 1970. A Grammar of Aspect: Usage and Meaning in the Russian Verb. Cambridge: Cambridge University Press.

202

Markedness Theory

Fradkin, R. 1985. "Markedness Theory and the Verb Systems of Russian and Arabic: Aspect, Tense and Mood." Ph.D. dissertation, Indiana University. Fraleigh, J. B. 1976. A First Course in Abstract Algebra. Reading, Mass.: Addison-Wesley. Garcia, E. 1975. "The Role of Theory in Linguistic Analysis." Amsterdam: NorthHolland. - - - . (in press) "Grasping the Nettle: Variation as Proof of Invariance." In New Vistas in Grammar: Invariance and Variation. Ed. Linda R. Waugh. Amsterdam: John Benjamins. G6del, K. 1931/1962. On Formally Undecidable Propositions. New York: Basic Books. Greenberg, J. 1966. Language Universals. The Hague: Mouton. - - - . 1977. A New Invitation to Linguistics. Garden City, N.Y.: Anchor Press/Doubleday. Greenberg, J., ed., C. A. Ferguson, and E. A. Moravcsik, assoc. eds. 1978. Universals of Human Language, vols. I-IV. Stanford, Calif.: Stanford University Press. Grosjean, F. 1982. Life with Two Languages. Cambridge, Mass.: Harvard University Press. Haldeman, S. S. 1871. Affixes in Their Origin and Application Exhibiting the Etymologic Structure of English Words. Philadelphia: E. H. Butler. Hall, M., Jr. 1959. The Theory of Groups. New York: Macmillan. Halle, M. 1959. The Sound Pattern of Russian. The Hague: Mouton. Halmos, P. 1960. Naive Set Theory. New York: Van Nostrand Reinhold. - - - . 1962. Algebraic Logic. New York: Chelsea. Hardwick, C. S., ed. 1977. Semiotics and Signifies: The Correspondence between Charles S. Peirce and Victoria, Lady Welby. Bloomington: Indiana University Press. Harris, Z. 1951. Methods in Structural Linguistics. Chicago: University of Chicago Press. - - - . 1968. Mathematical Structures of Language. New York: Interscience. Heilmann, L., ed. 1974. Eleventh International Congress of Linguists. Bologna: Mulino. Herstein, I. N. 1975. Topics in Algebra. New York: John Wiley & Sons. Hofstadter, D. R. 1979. Gadel, Escher, Bach: An Eternal Golden Braid. New York: Vintage Books. Holenstein, E. 1976. Roman Jakobson's Approach to Language: Phenomenological Structuralism. Trans. C. Schelbert and T. Schelbert. Bloomington: Indiana University Press. - - - . 1978. "Semiotic Philosophy?" In The Sign: Semiotics Around the World. Edited by R. W. Bailey, L. Matejka, and P. Steiner, pp. 43-67. Ann Arbor: Michigan Slavic Publications. - - - . 1979. "Prague Structuralism-A Branch of the Phenomenological Movement." In Linguistic and Literary Studies in Eastern Europe (vol. 1). Edited by John Odmark, 71-97. Amsterdam: John Benjamins. Hooper, J. 1976. An Introduction to Natural Generative Phonology. New York: Academic Press. Householder, F. W., K. Kazazis, and A. Koutsoudas. 1964. Reference Grammar of Literary Dhimotiki. The Hague: Mouton. Hrbacek, K., and T. Jech. 1978. Introduction to Set Theory. New York: Marcel Dekker. Innis, R. E., ed. 1985. Semiotics: An Introductory Anthology. Bloomington: Indiana University Press.

Bibliography

203

Ivanovic, S., and I. Petranovic. 1981. Russko-serbskoxorvatskij slovar'. Moscow: Russian Language Publishers. Ivic, M. 1961. "On the Structural Characteristics of the Serbo-Croatian Case System."

I/SLP IV:38-47. - - - . 1963. "Relationship of Gender and Number in Serbo-Croatian Substantives." I/SLP IV: 51-57. - - - . 1965. "On the Structure of the Slavic Simple Sentence." I/SLP IX:20-24. Jakobson, R. O. 1931/1971. "Principes de phonologie historique." In Selected Writings I, 202-20. The Hague: Mouton. - - - . 1932/1971. "Zur Struktur des russischen Verbums." In Selected Writings II, 3-15. The Hague: Mouton. - - - . 1936/1984. "Beitrag zur allgemeinen Kasuslehre: Gesamtbedeutungen der russischen Kasus." In Russian and Slavic Grammar: Studies 1931-1981. Edited by L. Waugh and M. Halle, 59-104. Berlin: Mouton. - - - . 1938/1984. "Zero Sign." In Russian and Slavic Grammar: Studies 1931-1981. Edited by L. Waugh and M. Halle, 151-59. Berlin: Mouton. - - - . 1949/1971. "The Phonemic and Grammatical Aspects of Language in Their Interrelations." In Selected Writings II, 103-14. The Hague: Mouton. - - - . 1953/1971. "Pattern in Linguistics." In Selected Writings II, 223-28. The Hague: Mouton. - - - . 1957/1971. "Shifters, Verbal Categories, and the Russian Verb." In Selected Writings II, 130-47. The Hague: Mouton. - - - . 1958/1984. "Morfologiceskie nabljudenija nad slavjanskim skloneniem." In Russian and Slavic Grammar: Studies 1931-1981. Edited by L. Waugh and M. Halle, 105-34. Berlin: Mouton. - - - . 1959/1971. "On the Rumanian Neuter." In Selected Writings II, 187-89. The Hague: Mouton. - - - . 1960a/1987. "Linguistics and Poetics." In Language in Literature. Edited by K. Pornorska and S. Rudy, 62-94. Cambridge, Mass.: The Belknap Press of Harvard University Press. - - - . 1960b/1971. "Introduction to the Symposium on the Structure of Language and Its Mathematical Aspects." In Selected Writings II, 568-69. The Hague: Mouton. - - - . 1960c/1984. "The Gender Pattern of Russian." In Russian and Slavic Grammer: Studies 1931-1981. Edited by L. Waugh and M. Halle, 141-43. Berlin: Mouton. - - - . 1961a/1971. "Henry's Sweet's Path Toward Phonemics." In Selected Writings II, 456-67. The Hague: Mouton. - - - . 1961b/1971. "Linguistics and Communication Theory." In Selected Writings II, 570-79. The Hague: Mouton. - - - . 1963. "Implications of Language Universals for Linguistics." In Universals of Language. Edited by Joseph Greenberg, 208-19. Cambridge, Mass.: MIT Press. - - - . 1965/1971. "Quest for the Essence of Language." In Selected Writings II, 345-59. The Hague: Mouton.

204

Markedness Theory

- - - . 1966/1984. "Relationship between Russian Stem Suffixes and Verbal Aspects." In Russian and Slavic Grammar: Studies 1931-1981. Edited by L. Waugh and M. Halle, 27-32. Berlin: Mouton. - - - . 1967/1971. "Linguistics in Relation to Other Sciences." In Selected Writings II, 655-96. The Hague: Mouton. - - - . 1968. "Language in Relation to Other Communication Systems." Lecture delivered at the International Symposium, "Languages in Society and in Technique," in Milan, October. - - - . 1971a. "Retrospect." In Selected Writings I, 631-58. The Hague: Mouton. - - - . 1971b. Selected Writings I: Phonological Studies. The Hague: Mouton. - - - . 1971C. Selected Writings II: Word and Language. The Hague: Mouton. --.1972/1985. "Language and Culture." In Selected Writings VII. Edited by S. Rudy, 101-12. Berlin: Mouton. - - - . 1973. Main Trends in the Science of Language. New York: Harper & Row. --.1974/1985. "Mark and Feature." In Selected Writings VII. Edited by S. Rudy, 12224. Berlin: Mouton. - - - . 1975/1985. "A Glance at the Development of Semiotics." In Selected Writings VII. Edited by S. Rudy, 199-218. Berlin: Mouton. ---.1977/1985. "A Few Remarks on Peirce, Pathfinder in the Science of Language." In Selected Writings VII. Edited by S. Rudy, 248-53. Berlin: Mouton. - - - . 1978. Six Lectures on Sound and Meaning. Cambridge, Mass.: MIT Press. - - - . 1980. The Framework of Language. Ann Arbor: Michigan Studies in the Humanities. - - - . 1981. Selected Writings Ill: Poetry of Grammar and Grammar of Poetry. Edited by S. Rudy. The Hague: Mouton. - - - . 1982. "Einstein and the Science of Language." In Albert Einstein: Historical and Cultural Perspectives. Edited by G. Holton and Y. Elkana, 254-64. Princeton, N.J.: Princeton University Press. - - - . 1984. Russian and Slavic Grammar: Studies 1931-1981. Edited by L. Waugh and M. Halle. Berlin: Mouton. - - - . 1985. Selected Writings VII: Contributions to Comparative Mythology. Studies in Linguistics and Philology, 1972-1982. Edited by S. Rudy. Berlin: Mouton. - - - . 1987. Language in Literature. Edited by K. Pomorska and S. Rudy. Cambridge, Mass.: The Belknap Press of Harvard University Press. Jakobson, R., S. Karcevskij, and N. S. Trubetzkoy. 1928/1971. "Proposition au Premier Congres International de Linguistes: Quelles sont les methodes les mieux appropriees a un expose complet et pratique de la phonologie d'une langue quelconque?" In Selected Writings I, 3-6. The Hague: Mouton. Jakobson, R., and L. Waugh. 1979. The Sound Shape of Language. Bloomington: Indiana University Press. Kacnel'son, S. D. 1972. Tipologija jazyka i recevoe myslenie. Leningrad. Kazazis, K. 1967. "A Case of Ambiguity in Modern Greek." In Languages and Areas: Studies Presented to George V. Bobrinskoj, 70-76. Chicago.

Bibliography

205

- - - . 1974. "On Some Aspects of Linguist Hellenocentrism." In Proceedings of the 11th International Congress of Linguists. Edited by L. Heilmann, 1075-80. BolognaFlorence: Societ'a editrice il Mulino, Bologna. - - - . 1980. "On Modern Greek 1ToL-'Who?'" In Pronouns and Anaphora, 251-57. Chicago: Chicago Linguistics Society. - - - . 1982. "Reanalysis in Modern Greek Women's Surnames." I/SLP XXV/XXVI: 233-3 8 . Kempson, R. 1977. Semantic Theory. Cambridge: Cambridge University Press. Klenin, E. 1983. Animacy in Russian: A New Interpretation. Columbus, Ohio: Slavica Publishers. Krashen, S. D. 1982. Principles and Practice in Second Language Acquisition. New York: Pergamon Institute of English. Kucera, H. 1980. "Markedness in Motion." In Morphosyntax in Slavic. Edited by C. Chvany and R. Brecht, 15-42. Columbus, Ohio: Slavica. - - - . 1984. "The Logical Basis of the Markedness Hypothesis." In Language and Literary Theory. Edited by B. A. Stolz and I. R. Titunitz, 61-75. Ann Arbor: University of Michigan Press. Kuhn, T. 1970. The Structure of Scientific Revolutions. Chicago: University of Chicago Press. Labov, W. 1969. "Contraction, Delection and Inherent Variability of the English Copula." Language 45: 715-62. Leech, G. N. 1969. Towards a Semantic Description of English. Bloomington: Indiana University Press. Levenberg, J. 1980. "A Semantic Analysis of Verbal Aspect in Russian and SerboCroatian." Ph.D. dissertation, Indiana University. Lowe, I. 1969. "An Algebraic Theory of English Pronominal Reference." Semiotica 1(4): 397-421. Lyons, J. 1977. Semantics, vols. I-II. Cambridge: Cambridge University Press. Mackridge, P. 1985. The Modern Greek Language. Oxford University Press. Maretic, T. 1918. Rjecnik hrvatskoga iIi srbskoga jezika, vol. VIII, IX. Zagreb: Knizara jugoslavenske akademije Lav. Hartmana. Maslov, Yu. S. 1984. Ocerki po aspektologii. Leningrad: Leningrad State University Press. - - - . 1985. "An Outline of Contrastive Aspectology." In Contrastive Studies in Verbal Aspect. Edited by Y. Maslov, 1-44. Heidelberg: Julius Groos Verlag. Maturana, H. R., and F. J. Varela. 1980. Autopoiesis and Cognition (Boston Studies in the Philosophy of Science, 42). Dordrecht: Reidel. Maunder, C. R. F. 1980. Algebraic Topology. Cambridge: Cambridge University Press. Murphey, M. G. 1961. The Development of Peirce's Philosophy. Cambridge, Mass.: Harvard University Press. Naps, T. L. 1975. "Set Theory in Infinitary Languages." Ph.D. dissertation, University of Notre Dame. Neidle, C. 1982. "Case Agreement in Russian." In The Mental Representation of Grammatical Relations. Edited by J. Bresnan, 391-426. Cambridge-London: MIT Press.

206

Markedness Theory

Ogden, C. K. 1967. Opposition: A Linguistic and Psychological Analysis. Bloomington: Indiana University Press. Peirce, C. S. 1931-1958. Collected Papers of Charles Sanders Peirce, vols. 1-8. Cambridge, Mass.: Harvard University Press. - - - . 1957. Essays in the Philosophy of Science. New York: Liberal Arts Press. Pelc, J. 1984. "Sign and Inference." In Sign, System and Function. Edited by J. Pelc et aI., 319-28. Berlin: Mouton. Pos, H. 1938. "La notion d'opposition en linguistique." In Onzieme congres international de psychologie. 246-47. Paris: Alcan. Potebnja, A. A. [1888]1958. Iz zapisok po russkoj grammatike (I-II). Moscow: Gosucebped izdatel'stvo Minpros RSFSR. Rauch, I. 1978. "Distinguishing Semiotics from Linguistics and the Position of Language in Both." In The Sign: Semiotics Around the World. Edited by R. W. Bailey, L. Matejka, and P. Steiner, 328-34. Ann Arbor: Michigan Slavic Publications. Recnik srpskohrvatskoga knjiievnog jezika. 1969. vols. III-IV. Novi Sad. Richards, J. C. 1971. "A Non-Contrastive Approach to Error Analysis." In English Language Teaching, 25: 204-19. Ross, J. 1969. "A Proposed Rule of Tree-Pruning." Modern Studies in English (Readings in Transformational Grammar). Edited by D. Reibel and S. Schane, 288-99. Englewood Cliffs, N.J.: Prentice-Hall. Sampson, G. 1980. Schools of Linguistics. Stanford, Calif.: Stanford University Press. Sangster, R. B. 1982. Roman lakobson and Beyond: Language as a System of Signs. Berlin: Mouton. - - - . "Towards a Phenomenology of Syntax: Syntactic Analysis and Linguistic Sign Theory." Unpublished manuscript. Saussure, F. de. 1966. Course in General Linguistics. Trans. Wade Baskin. New York: McGraw-Hill. Savan, D. 1976. An Introduction to C. S. Peirce's Semiotics. Toronto: Victoria University. Schane, S. A. 1973. Generative Phonology. Englewood Cliffs, N.J.: Prentice-Hall. Schupbach, R. D. 1984. Lexical Specialization in Russian. Columbus, Ohio: Slavica Publishers. Shapiro, M. 1972. "Explorations into Markedness." Language 48(2):343-64. - - - . 1974. "Markedness and Distinctive Features Hierarchies." In Proceedings of the 11th International Congress of Linguists. Edited by L. Heilmann, 775-81. BolognaFlorence: Societ'a editrice il Mulino, Bologna. - - - . 1983. The Sense of Grammar. Bloomington: Indiana University Press. Short, T. L. "Peirce's Divisions of Interpretants." Unpublished manuscript. Stankiewicz, E. 1962. "The Singular Plural Opposition in the Slavic Languages." I1SLP V:I-15· - - - . 1964. "Problems of Emotive Language." In Approaches to Semiotics (held at Indiana University, 1962). Edited by T. A. Sebeok, A. S. Hayes, and M. C. Bateson, 239-64. The Hague: Mouton. ---.1968. "The Grammatical Genders of the Slavic Languages." I1SLP XI: 27-41.

Bibliography

207

- - - . 1986. "The Concept of Structure in Jakobson's Linguistics." Paper given at conference, Rome. Stenson, N. 1974. "Induced Errors." In New Frontiers of Second Language Learning. Edited by J. Schumann and N. Stenson. Rowley, Mass.: Newbury House. Thorn, R. 1975. Structural Stability and Morphogenesis. Reading, Mass.: Benjamin/Cummings. - - - . 1983. Mathematical Models of Morphogenesis. New York: John Wiley & Sons. Tiersma, P. M. 1982. "Local and General Markedness." Language 58(4):832-49. Todd, L. 1974. Pidgins and Creoles. London: Routledge and Kegan Paul. Tolstoj, I. I. 1957. Serbsko-xorvatsko-russkij slovar'. Moscow: Gosudarstvennoe izdatel'stvo inostrannyx i nacional'nyx slovarej. Trubetzkoy, N. S. 1931. "Die phonologischen Systeme." Travaux du Cercle Linguistique de Prague, NO.4, 96-116. Prague: Jednota Ceskoslovenskych Matimatiku a Fysiku. - - - . 1975. N. S. Trubetzkoy's Letters and Notes. Edited by Roman Jakobson. The Hague: Mouton. Turner, L. D. 1949. Africanisms in the Gullah Dialect. Chicago: University of Chicago Press. Ungeheuer, G. 1959. "Das Logistische Fundament binarer Phonemklassifikationen." Studia Linguistica Annee XIII(2):69-97. van Heijenoort, J., ed. 1970. Frege and G6del: Two Fundamental Texts in Mathematical Logic. Cambridge: Harvard University ~ress. van Schooneveld, C. H. 1960. "On the Word Order in Modern Russian." In I/SLP III: 40 -44. - - - . 1963. "Allomorph versus Morpheme in Contemporary Standard Russian." In American Contributions to the Fifth International Congress of Slavists, vol. I, 107-9. The Hague: Mouton. - - - . 1968. "On the Opposition Determinate-Indeterminate in the Contemporary Standard Russian Verb." In American Contributions to the Sixth International Congress of Slavists, vol. I, 351-58. The Hague: Mouton. - - - . 1973· "The Morphemic Structure of the Slavic Word and Greenberg's 28th Universal." In Slavic Word, 443-48. Edited by Dean Worth. The Hague: Mouton. - - - . 1977a. "By Way of Introduction: Roman Jakobson's Tenets and their Potential." In Roman /akobson: Echoes of His Scholarship, 1-11. Edited by D. Armstrong and C. H. van Schooneveld. Lisse: de Ridder Press. - - - . 1977b. "The Place of Gender in the Semantic Structure of the Russian Language." In Scando-Slavica 23:129-38. - - - . 1978a. "A Semantic Approach to the Analysis of Word Formation in Contemporary Standard Russian." In American Contributions to the Eighth International Congress of Slavists, I: Linguistics and Poetics, 597-615. Edited by Henrik Birnbaum. Columbus, Ohio. Slavica. - - - . 1978b. "Contribution a l'etude comparative des systemes des cas, des prepositions et des categories grammaticales du verbe en russe moderne." In Slavica 4

208

Markedness Theory

Hierosolymitana, vol. II. 41-50. Edited by Victor Raskin and Dmitri Segal. Jerusalem: Magnes Press. - - - . 1978c. Semantic Transmutations. Bloomington, Ind.: Physsardt. - - - . 1982. "The Extension Feature in Russian." In IISLP, XXV, Festschrift for Edward Stankiewicz, 445-58. - - - . 1983. "Programmatic Sketch of a Theory of Lexical Meaning." In Quaderni de Semantica IV(1):158-70. - - - . 1985. "Ancient Greek and Modern Russian Prepositions: A Speculative Comparison." In IISLP, XXXI-XXXII, Festschrift for H. Birnbaum, 495-514. - - - . 1986a. "Jakobson's Case System and Syntax." In Case in Slavic. Edited by R. D. Brecht and J. S. Levine, 373-85. Columbus, Ohio: Slavica Publishers. - - - . 1986b. "Baudouin de Courtenay's Methodological Premises for the Investigation of Language and Their Relation to Present-Day Linguistics." Ian N. Baudouin de Courtenay: A Lingwistyka Swiatowa, 11-16. Wroclaw. Zaklab Narodowy. im. Ossolinskich. - - - . 1987. "Linguistic Structure and Autopoiesis." In Language, Poetry and Poetics. Edited by K. Pomorska, E. Chodakowska, H. McLean, and B. Vine, 123-42. Berlin: Mouton de Gruyter. - - - . 1988a. "The Semantics of Russian Pronominal Structure." In American Contributions to the 10th International Congress of Slavists. Edited by A. M. Schenker, 401-14. Columbus, Ohio: Slavica. - - - . 1988b. "The Semantics and Syntax of Russian Pronominal Structures: A Feature Breakdown." In Coling Budapest, Proceedings of the 12th International Conference on Computational Linguistics, 22-27 August, 1988,705-7. Budapest: John von Neumann Society for Computer Sciences. - - - . (in press) "The Dual and Linguistic Structure: Singulative Identification Deixis." Folia Slavica 9. - - - . (to appear) "Mathematical Foundations of Meaning in Language." Waugh, L. R. 1982. "Marked and Unmarked: A Choice between Unequals in Semiotic Structure." Semiotica 38 (3/4):299-318. - - - . 1984. "Some Remarks on the Nature of the Linguistic Sign." In Sign, System and Function. Edited by J. Pelc et aI., 389-438. Berlin: Mouton. Weinreich, U. 1966. "Explorations in Semantic Theory." In Current Trends in Linguistics, 3. Edited by T. Sebeok, 395-479. The Hague: Mouton. - - - . 1968. Languages in Contact. The Hague: Mouton. Whitehead, A. N. 1960. A Treatise on Universal Algebra. New York: Hafner. Whitehead, A. N., and B. Russell. 1925-27. Principia Mathematica (vols. I-II). Cambridge: Cambridge University Press. Wierzbicka, A. 1980. The Case for Surface Case. Ann Arbor: Karoma Publishers. Wilder, R. L. 1952. Introduction to the Foundations of Mathematics. New York: John Wiley & Sons. Worth, D. S. 1984. "Russian Gen2, Loc2 Revisited." In Signs of Friendship, To Honour A. G. F. van Holk, Slavist, Linguist, Semiotician. Edited by J. J. van Baak, 295-306. Groningen.

Bibliography

209

Zubin, D. A., and K. M. K6pcke. 1984. "Affect Classification in the German Gender System." Lingua 63(1):41-96. - - - . 1986. "Gender and Folk Taxonomy: The Indexical Relation between Grammatical and Lexical Categorization." In Noun Classes and Categorization. Edited by C. Craig, 139-80. Amsterdam: John Benjamins.

Index

Abduction, 46 ff., 85-87 Accusative case: directionality and, 19, 28; extension and, 23, 28; Russian, 126, 129 Addressee, 75-76 Addresser, 75-76 Alexandroff, P. S., 121 Algebraic topology. See Mathematics; Topology Andersen, H., 28, 130, 144-45, 148-49, 162 Anderson, S. R., 17 Andrews, E., 12, 99 Animacy, 171-74 Arabic, 129 Archiphoneme, 140 Argument, 46, 53-54 Arithmetic. See Mathematics Aronson, H., 149, 191, 196 Artifice, 58-62; musical, 60; poetics and, 61 Aspect. See Imperfective aspect; Perfective aspect; Russian: verbal aspect Assimilation: markedness, 144-47; Russian regressive, 159 Associative law. See Group theory Assurance. See Peircean semiotic/sign theory Asymmetry: of sign, 119; asymmetri-

callantisymmetrical relationships, 100-101. See also Binary oppositions; Relations Aussonderungsaxiom. See Axioms: Axiom of Specification Autonomy: relative, 91 Axioms: Axiom of Choice (Zorn's Lemma), 107, 108, 109; Axiom of Existence, 107, 109; Axiom of Extension, 79, 97, 109; Axiom of Infinity, 108, 109; Axiom of Pairing, 105, 107-8, 109; Axiom of Powers, 106, 109; Axiom of Specification, 105, 109; Axiom of Substitution (axiom schema of replacement), 108, 109; Axiom of Unions, 106, 109; of markedness theory, 109, 12425, 126, 128; in set theory, 93, 97-108; Well-Ordering Axiom, 99, 108. See also Mathematics: induction principle. Axis of replacement (paradigmatic axis), 125, 143 Babby, L., 16-17 Baudouin de Courtenay, J., 82 Belonging vs. inclusion, 114-15 Benveniste, E., 44 Biculturalism, 77-78 Bilingualism, 64, 77-78 Binary operations, 4, 119-20

212

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Binary oppositions: in markedness relationships, 10-11, 14; in mathematics, 93 ff.; "Seconds" as, 57-58 Binary relations, 99-101 Binary signs: set theory and, 93 ff. Birnbaum, H., 11-12 Bloomfield, L., 13 Bolinger, D. L., 157 Brown, G. 5., 3, 4, 5, 29, 34-36, 81, 8990, 105, 13 1-33, 135, 193 Brown, H. D., 71, 73 Bruss, E., 3, 12, 44-45, 47 Buczynska-Garewicz, H., 88 Biihler, K., 75 Bulgarian, 191 Burns, G., 120 Burt, M., 193 Calculus, 133, 135 Carnap, R., 194 Case, case system. See Russian; specific cases Catastrophe theory, 92-93 Cayley's Theorem. See Group theory Chomsky, N., 16,72,74,189,194 Chvany, C. V., 189 Coates, J., 194 Code, 37 Competence: Chomskyan, 73-74 Conceptual features: defined, 73-74; distinctive features and, 94; hierarchy of, 20-25; interpretants as, 55-58; morphological, 117-31; natural numbers and, 117-18; Order 6 and, 120-24; union of, with deictic category, 29-34 Conceptual marking, 113-14, 125, 12627; belonging and, 114 Constructivism. See Mathematics: constructivism Context: contiguity and, 4-5; deixis and, 36; invariance and, 4-5, 126; syntagmatic, 125 Contextual meaning (Grundbedeutung), 9 ff.

Contextual neutralization, 128, 129 Contiguity: context and, 61; factual, 59; in poetics, 59 Continuancy: voicing and, 27 Continuity: discontinuity and, 87-90; mathematical, 87-90; semiotic, 88; continuous models, 90-92 Continuum Hypothesis. See Mathematics Cumulations: feature, 106; of conceptual features, 104, 127

Dative case: directionality and, 19; marginality and, 19 Davis, P. J., 78, 79, 82, 193 Declension. See Gender Deduction, 46 ff. Deixis: defined, 29 ff.; deictic levels, 123; deictic relation, 125; Jakobson's "shifter" and, 36 ff.; in markedness theory, 33-34; in reference, 30, 34 ff. See also Perceptional categories, deixis and; Singulative deixis; Transmissional deixis Demonstration. See Mathematics: demonstration Demotic. See Dhimotiki; Greek Density. See Semantics: semantic density Dhimotiki (Demotic, modern Greek), 16670, 176- 8 7 Diachrony: synchrony and, 92 Diagrams: Euler's, 3, 84; Venn, 3, 35 Dialogic principle, 52

Dicent, 53-54 Dimensionality, 21, 41 ff., 115, 117, 146; distinctness and, 122-24; perfective aspect as, 115, 192; plurality and, 21 Dinkines, F., 119, 120 Directionality: extension and, 23; Russian cases and, 19, 28 Discontinuity: in asymmetric sign systems, 87-90; continuity and, 4, 87-90; mathematical, 4, 87-90; Thomian,

90 -93

Index "Distinctive feature," 13, 16; distinctive features, 16, 25-29, 94, 130 Distinctive units vs. distinct units, 16 Distinctness, 22, 117; as deictic, 32; dimensionality and, 122-24; extension and, 23; referent in, 22; Russian indicative mood and, 40 ff. Distributional marking. See Markings Diverian school, 11 Dokulil, M., 163 Dulay, H., 71,193 Dyads, 62-64 Dynamic interpretant, 52-53, 57-58 Dynamics: structural stability and, 90-92

Eisele, C., 8, 29, 66 Emotional interpretants, 52, 76-78 Emotive functions. See Function: emotive Energetic interpretants, 52-53, 65 ff., 75 English, 129; iconicity in, 15; past tense, 149; Black English Vernacular (BEV), 157-5 8 Equality, 96-97, 114; substitution and replacement in, 134; vs. inclusion, 116 Equivalence relation, 99-101, 114 Errors: in aspect choice, 69-72; interlingual vs. intralingual, 70-71 Esposito, J. L., 49, 88, 192, 193 Euclidean space, 90, 91 Euler, L.: syllogistic diagrams, 3, 84, 193 Exclusion: inclusion and, 118 Explicit reference. See Reference Extension, 113, 115, 117, 127; dimensionalityand, 115; directionality and, 23, 28; Peirce's interpretant and, 28; pluralityand, 23; Russian adverb and, 113; Russian imperative mood and, 41 ff. Fann, K. T., 47 Feature: cumulations, 106, 127; feature/ SR/SD triad, 28; vs. mark, 25 ff. Features: grammatical, 38-43; as interpretants, 28; lexical, 113-16. See

213

also Conceptual features; "Distinctive feature"; Markedness features; Morphology: conceptual features in; Phonology: distinctive features in; Semantics: semantic features Feminine. See Gender Fillmore, C. J., 38, 39 Final interpretant, 52-54, 57, 115 "Firstness": markedness theory and, 25; Peirce's iconic sign and, 45 ff. Firsts: representamen as, 47, 50 Fitzgerald, J. J., 15, 52-53, 54-55, 56 Fluency, 77 Following vs. understanding, 134 Form: as law, 131-35; of laws, 131-35; laws of, 131-35; linguistic, 131; marked/ unmarked, 126; meaning and, 132-33; as signifier, 131; structure and, 131-32; as type of "assurance," 131; unity of, 131 Formal grammar. See Grammar Formalism. See Mathematics: formalism Formal marking. See Markings: formal Formal syncretism, 127-28, 129 Fradkin, R., 7 Frege, G., 79; Frege-Russell thesis, 78 French, 196 Function: conative, 75; emotive, 75; mathematical, 98-99, metalingual, 75; morphological, 135; one-to-one, 9899; onto, 98-99; phatic, 75-76; poetic, 75-76; referential, 75-76 Functional relationships, 113 Function F, 98-99 Garcia, E., II, 12-13 Gender, 166-87, 195-97. See also Dhimotiki; Russian; Serbo-Croatian General meaning (G~samtbedeutung):vs. contextual meaning (Grundbedeutung), 9 ff., 110; deictic elements in, 29-34; as invariant, 130; Jakobson's "shifter" and, 36-43; reference in, 34-36; theory of, 9-13

214

Markedness Theory

Generative grammar: markedness in, 16-17; school, 16 Genitive case, 146, 161, 167; quantification in, 19-20; Russian, 129 German, 149, 159, 174 Gesamtbedeutung. See General meaning Gestalt principle, 51 G6del, Kurt, 89, 110; G6del's Proof, 83, 111, 128; G6del's Theorem, 90, 111 Gradation, 62-63, 86. See also Binary relations Grammar: formal, 46; generative, 16-17; Peircean theory of, 28 Greek: classical, 167. See also Dhimotiki;

Katharevousa Greenberg, J., 17, 18, 124, 127-29; on Hjelmslev's "defectivation," 128 Ground: of argument, 46; of relation, 15; of sign, 50 Group theory: Associative Law in, 119; binary operations and, 119-20; Cayley's Theorem in, 121; commutative (abelian) group, law in, 120; identity, inverse elements in, 119, 122, 124; Jakobsonian markedness theory and, 119; morphological conceptual features and, 117-31; Order 6 in, 120-24; set theory and, 119; substitution group, 94 Grundbedeutung. See Contextual meaning Habit: change, 93; "living," 57 Hall, M., 99 Halle, M., 16 Halmos, P., 97, 99-108, 117 Hardwick, C. S., 53, 65 Harris, Z., 194 Hersh, R., 78, 79, 82, 193 Herstein, I. N., 100, 120 Hierarchy, 41, 52-58, 118, 123, 171-78, 189. See Ordering Hofstadter, D., 111 Holenstein, E., 1, 13, 81, 112, 117, 118, 133, 134, 193

Homonymy, 95, 98; vs. synonymy, 95 Hooper, J., 16 Hopkins, G. M., 60 Householder, F. W., 177, 179, 185, 197 Hrbacek, K., 108 Hypothesis. See Abduction Hypothetical mood. See Mood Icon: algebraic equation as, 117; artifice and, 58 ff.; iconic meaning, 15; index, symbol, and, 51; metaphor as, 61; sign as, 15, 45 Iconicity, 15, 51, 56, 58, 174 Immediate interpretant. See Interpretants: immediate Imperative mood. See Mood Imperfective aspect, 67-72 Implicit reference. See Reference Inclusion: vs. belonging, 114-15; vs. equality, 116; exclusion and, 118; relationship, 10, 84, 99, 118, 125, 152, 163-65; union, intersect relations, and, 112 Index: deictic sign as, 30; icon and, 59; sign as, 58-62; symbol and, 59-60; synecdoche as, 61 Indicative mood. See Mood Induction, 46 ff. Inference, 46-48 Instrumental case: marginality in, 19-20; Wierzbicka on, 11 Intension: set membership and, 79-80; vs. extension, 79 Interpretants: conceptual features as, 55-58; deixis and, 29; distinctive features as, 27-29; hierarchy of, 52-58; immediate, 52; markedness as theory of, 45-46; meaning and, 35, 55-58; reversal of in L2learning, 76-78; as rule/law, 1, 28-29; second trichotomy of, 64-67; as sign, 29; of sign, 52-54; vs. syntagmatic rules, 28; as "Third," 50; in triad (sign/object/interpretant),

Index 28, 50. See also Dynamic interpretant; Emotional interpretants; Energetic interpretants; Logical interpretant Interpretation: mapping or, 115; of the sign, 116 Invariance: in mathematics, 82-84; markedness and, 125, 126, 129-13°; understanding and, 134 Invariant: conceptual feature as, 20-25; distinctive feature as, 94; deixis as, 2934; general meaning as, 130; meanings, 114; rule, 113. See also Meaning Isomorphism: Cayley's Theorem and, 121; conceptual features to group of Order G, 120-21; conceptual features to natural numbers, 117; form-content, 98-99; isomorphic relationship, 117 Italian, 196 Ivic, M., 186 Jakobson, R. : "artifice" of, 45, 58-62; binariness theory of, 14; on binary oppositions, 13, 26, 58; C. H. van Schooneveld and, 6-7, 17-19, 19-25, 26, 27, 40; conceptual features of, 26, 27, 29, 117; on contiguity, 59-60; C. S. Peirce and, 3, 7, 15, 28-29, 44, 51, 58-59, 61, 94; on deixis, 36, 37, 38; distinctive features defined by, 16, 26; distinct phonemic level of, 16; on factors and functions of language; 45, 64, 74-76; on form and meaning, 34, 94, 132-33; on gender, 170-75, 185-86; generative school and, 16; Gesamtbedeutung applied by, 9-10, 11-12, 57; on invariants, 43; on linguistic zero, 135; marginality of, 19, 24; on markedness, 1-2, 19, 37, 110, 181; message and code, 37, 42 ; morphological features of, 19-25; non-shifter of, 40, 42; Prague school and, 13, 58; quantification of, 19-20, 24; on relative autonomy, 15; on Russian, 10, 19-20, 26, 27, 36, 37, 40,

215

67-68, 183; Saussurean tradition and, 9, 44, 78, 94, 95; sn/sR relationship of, 92; "shifter" of, 7, 37, 40, 42; sign theory and, 3, 45, 94, 95, 110; sR/sn/ feature triad of, 28; theory of general meaning of, 9, 10-12, 55; theory of morphological markedness of, 13, 14; R. Thom and, 5; topology and, 81-84; N. Trubetzkoy and, 1, 13; works by, 9, 10, 18, 25, 36, 38, 42, 62, 94, 130. See also Markedness theory Jakobsonian: linguistic theory, 34, 45, 8184, 92, 112, 114; markedness features, 19-20; markedness theory, 9-43, 45, 46,67,78,84-85,86-87,88,91,93,95, 108-9, 132-34; semiotics, 44, 88 Jakobsonian-based: linguistic analysis, 103, 109, 125; markedness theory, 55, 57, 13 1 Jech, T., 108 Jespersen, 0., 37 Kacnel'son, S. D., 11 Katharevousa (puristic Greek), 168-70 Kazazi~ K., 178, 184, 195, 196 Kempson, R., 192 Klenin, E., 173, 195 Kopcke, K. M., 174-75 Krashen, S., 193 Kucera, H., 162 Kuhn, T., 131 Labov, W., 158 Language: factors and functions of, 7476; as semiotic, 130; as system, 130. See also Greenberg, J. Language acquisition. See Second language acquisition Langue, 30, 73-74, 134, 152, 190 Leech, G., 31, 189 Legisign. See Sign: legisign Leibniz, G. W., 117 Levenberg, J., 7

216

Markedness Theory

Lexemes: markedness and, 124-25 Lexical meaning, 127 Linguistics: mathematics and, 114-16; schools of, 13-19; semiotics and, 44-46 Locative case and Jakobson's features, 19 Logic: G. S. Brown on, 132-33; mathematics and, 78, 131, 132-33 Logical interpretant: final, 115, 130; ultimate, 54-55, 57 Logicist school, 78 Lowe, 1.,194 L2learners. See Second language acquisition Lyons, J., 17, 18, 30, 38, 42, 124-26, 13943, 156 Marginality: in instrumental case, 19-20; restrictedness and, 23-24 Mark, 13-19, 25-29 Marked categories, 128 Markedness: assimilation, 144-47, 185; in generative grammar, 16-17; Greenberg on, 121-29; history of, 13-19; Jakobson on, 1-2, 19, 37, 110; Lyons on, 124-26; mathematics and, 116; in morphology, 129; myths about, 129, 136-65; in phonology, 10; Prague school and, 13, 58, 119; relations, 116, 126; reversals, 14762; values, 2, 46; van Schooneveld on, 126; vs. "naturalness," 16 Markedness features: arithmetical level of, 133; Peircean interpretant and, 15859 Markedness theory: applications of, 136 ff.; axiomatic base for, 124-25, 126, 128, 133; axioms of, 105-09; catastrophe theory and, 92-93; deixis in, 33-34; invariants in, 125, 129; as mathematical principle, 81-135; misapplications of, 136-65; relational concepts of, 910; semantic features in, 151-58; set and group theory applied to, 119; as theory of interpretants, 1, 45-64, 130;

as universal, 7. See also Jakobsonian: markedness theory Markings: conceptual, 113-14; distributional, 125; feature, 113-26; formal, 113, 114, 124, 126; as interpretants, 57, 114; lexeme, 113-16; linguistic, 114; of Russian, 114-15, 126; semantic, 113, 125, 126; set membership and, 114; synonymy of, 134 Masculine. See Gender Maslov, Y., 68, 137, 192 Mathematics: algebra, 117, 133, 135; arithmetic, 133; axioms, 133; belonging vs. inclusion, 114-15; binary/dyadic oppositions in, 62-64, 119-20; constructivism, 82-83; Continuum Hypothesis, 110-11; demonstration, 131, 133-34; discontinuity, 87-90; formalism, 82-83; geometry, 85; induction principle, 1034; linguistics and, 114-16; logic and, 131, 132-33; markedness and, 116, 131; Platonism, 82-83; proof, 131, 133-34; structure, 132; theorems vs. axioms, 132, 133; theoretical principles, 81-135; zero, 135. See also Group theory; Set theory; Topology Maturana, H. R., 194 Maunder, C. R. F., 194 Meaning: context and, 4-5, 126; deixis and, 30 ff.; form and, 132-33; grammatical, 9-13, 36-43; iconic, 15; and interpretants, 55-58; invariant, 114; lexical, 124-27; pragmatic, 86, 192; "principal," 56-57; reference and, 34 ff.; as signified, 1, 28; structure of, 9-13; theory of, 9-36. See also Contextual meaning; General meaning Merkmal. See Mark Message, 37 Metaphor, 61 Metonymy, 61 Mood, 38 ff., 150-51 Morphemes, 141-43

Index Morphogenesis, theory of, 89 Morphology: conceptual features in, 1943; general meaning in, 9 H., 153-55; markedness applied to, 19 H., 11416; semantic features in, 114-16; vs. phonology, 153-55 Murphey, M. G., 82 Naps, T. L., 111 Narrated event, 31 H., 37 H. Natural numbers and conceptual features, 117-18 Neutralization, 139-44 Nominative case: as "unmarked," 19-20 Non-shifter. See Shifters Noun, semantic density and structural stability of, 144-47 Object: in content of utterance, 95-98; extra-linguistic, 95-98; in icon, 15, 45; as "Second," 51; in sign/object/ interpretant triad, 28, 154. See also Sign Objectiveness, 117, 127; as perceptionally deictic, 32; MR- MD distance and, 24; "Quantification" and, 19-24 Observer, 35-36 Opposition: aspectual, 137-38; binary, 57; definitions of, 96-97; dyadic, 57; phonemic, 138; Pos's concept of, 26, 96; privative, 14; triadic, 62-64; voiced/ voiceless, 26 Ordering: of interpretants, 155; partial, 99-1°5; total, 99-105; well, 99-105. See also Deixis Paradigmatic axis. See Axis of replacement Paradigmatic base, 125 Parole, 30, 73-74, 134, 152, 190 Parts of Speech: singulative transmissional deixis and, 32-33; Thorn on, 144-47

217

Passive voice. See Russian Past tense. See English; Russian Peano Axiom III. See Mathematics: induction principle Peirce, B., 193 Peirce, C. S.: on argument, 53-54; on assurance, 131; G. S. Brown and, 4, 35; on continuity and discontinuity, 4, 8889, 193; "Firstness" of, 45, 48-5°, 54, 74-75, 88, 105; formal grammar of, 46; icon/index/symbol trichotomy of, 45, 51, 58- 60, 61-62, 63, 86; on iconicity, 15, 51; on inference, 46-47, 62, 65, 84, 85; interpretant, 5, 12, 17, 27, 35, 45, 46, 52, 54, 57, 65, 88, 95, 114; R. Jakobson and, 4, 5, 44-45, 49, 58-60, 61, 62-64, 65; logic, 3, 28; mathematical studies of, 3; mathematical theory, 8788, 101; "Secondness" of, 45, 48-50, 54, 58, 74-75, 88, 95, 105; sign/object/interpretant triad, 28, 46-48, 50, 58, 63, 65; sign-object relationship defined by, 15, 35, 56, 62, 63, 190; theory of grammar of, 28; theory of interpretants of, 12, 18, 46, 48, 57, 192; theory of meaning of, 56-57, 65; theory of pragmatism of, 86; "Thirdness" of, 45, 48-50, 51, 52, 54, 74-75, 88; triads of interpretants of, 52-53, 58, 63, 66-67, 72, 74, 75, 76 , 78; topology and, 3, 82; works by, 8 Peircean semiotic/sign theory, 3, 54, 62, 88, 105, 131; linguistic analysis and, 12, 45, 55, 58; markedness theory and, 18, 55, 63-64, 95; van Schooneveld and, 25, 30, 55. See also Icon; Index; Interpretants; Object; Sign; Symbols Perceptual categories, deixis and, 31 H. See also Conceptual features Perfective aspect: dimensionality as, 21, 41, 115 Personal pronouns as deictic structures, 129 Phonemes, 26-28, 141

218

Markedness Theory

Phonology: distinctive features in, 130; markedness applied to, 153-54; vs. morphology, 130, 153-54; natural generative, 16; sharpness feature in, 26-27 Platonism. See Mathematics: Platonism Plurality, 21, 40 ff., 117; dimensionality and, 21; extension and, 23; grammatical meaning in, 40 ff.; identity element/ feature as, 122, 124 Poetics and artifice, 61 Polish, 196 Pos, H., 26, 96, 109 Potebnja, A. A., 11 Prague school, 13, 58, 119 Prepositions, 20. See also Russian Property: of meaning, 1-2; regularity, 91

Qualisign. See Sign: qualisign Qualitative: science, 86-87; theory of catastrophes, 92-93 Quantification: in genitive case, 19; in locative case, 19; objectiveness and, 24

Reasoning: abductive, 85-87; analytic, 46-48; syllogistic, 84; synthetic, 46-48 Reference: deixis and, 34 ff.; "range of," 24 Relations: binary, 99-101; ground of, 15, 46. See also Binary operations; Set theory Replacement and substitution, 131, 134 Replica of a legisign, 51 Representamen, 50, 63, 191 Restrictedness, 19-20, 41 ff., 117, 127 Reversal: of interpretants, and L2learner, 76-78; markedness, 147-62 Rheme, 53-54 Richards, J. C., 73 Ross, J., 17 Rule: as "living habit," 57; interpretant as, 28. See also Inference

Russell, B., 78, 110; Frege-Russell thesis, 78; Russell's paradox, 78-79, 105-6 Russian: adverb, 113; case system, 126; grammatical gender in, 166-87; infinitive, 40-41; L2learner and, 67-72; paratactic conjunctions, 26; parts of speech, 127; past tense, 40-42, 68-70; personal pronouns, 129; phonemes, 25-29; verbal aspect, 41, 115, 12627, 192; verbal categories, 21, 36-43, 150-51 -s affix, 167-70 Sampson, G., 14 Sangster, R. B., 95, 189 Saussure, F. de, 30, 64, 74, 78, 82, 94, 95, 99, 134 Savan, D., 3, 45, 47, 48, 49, 50, 51, 52-54, 57, 62-63, 86, 131, 191, 192 Schane, S. A., 16, 189 Schupbach, R., 174 Science, 130-31; qualitative vs. quantitative, 86-87; Kuhn on, 130-31; linguistic, 111 Second language acquisition: bilingualism and, 77-78; fluency and, 77; reversal of interpretants and, 76-78; Russian verbal aspect and, 67-72; speech community and, 73; teaching and, 67-73 "Secondness": dynamic vs. passive, 48-49; inductive inference and, 48; markedness theory and, 49; "Second of Thirds," 57. See also Binary oppositions Self-reference. See Reference Semantics: "class-logic" and, 194; conceptual features in, 114-16; markedness and, 151-62; semantic density, 6, 144-47; semantic dominant, 91; semantic features, 114-16; semantic invariant, 152; semantic marking, 125 Semeiotic. See Semiotic Semiosis and interpretant, 46 ff., 51

Index Semiotic, 44 H., 72 Serbo-Croatian, 4, 166, 175-76, 180-86 Sets: fuzzy, 194; mathematical, 93 H.; of phonological features, 194 Set theory: axiomatic, 93 H.; axioms in, 93 H.; binary signs and, 93-94; consistency in, 111; group theory and, 117 ff.; inclusion vs. belonging, 114; Jakobsonian markedness theory and, 93 H.; membership, 79; Zermelo-Fraenkel, 108, 110-11 Shapiro, M., 3, 28-29, 45, 46, 52-54, 67, 76, 144-47, 160-62, 192, 194 Shifters, 36-43 Short, T. L., 52 Sign: asymmetry of, 119; definition of, 47-48; final interpretant relationship, 53; iconic, 15, 51, 58 H.; indexical, 29 H., 58 H.; as interpretant, 52-58; Jakobsonian notion of, 9 H.; legisign, 50-51, 54; morphological, 112; qualisign, 50-51, 53-54; phonological, 112; sign/object/interpretant triad, 28, 154; sign-object relationship, 51; signans, I, 94, 112; signatum, I, 9, 94-95, 112; signified, 1, 28; signifier, I, 28, 131, 132; signum, 1,9,95; sinsign, 50-51, 54; translation of, 46 H.; vehicle, 50; "zero," 135, 146, 160 Similarity: factual, 59; ground of relation and, 15, 50; imputed, 59. See also Iconicity Singulative deixis, 32 H. Sinsign . See Sign: sinsign Speculative Grammar. See Grammar; Peirce, C. S. Speech community, 74, 77 Speech event, 30 H., 37 H. Stankiewicz, E., 148, 189, 195 Statistical frequency, 136-39 Stenson, N., 73 Structural stability: dynamics and, 89; semantic density and, 6, 144-47

219

Structure: form and, 131-35; linguistic, 133; logic and, 132-33 Substitutability, 162-65 Substitution. See Axis of replacement Sweet, H., 93 Syllogisms, 84-85 Symbols: as signs, 51 H.; icons and, 51; indexlindices and, 51; metonymy as, 61 Syncretism, 140-41 Synecdoche, 61 Synonymy: and homonymy, 95; and neutralization, 139 Syntagmatic axis, 28, 125 Tense. See English; Russian; Verbal categories "Thirdness": deductive inference and, 49; "Third of Thirds," 57-58 Thorn, R., 3, 5, 6, 82, 83, 89, 90-91, 9293, 96, 99, 144-47, 18 9, 194; Thomian discontinuity, 88-89. See also Topology Todd, L., 158 Topology, 81-82, 90-93. See also Mathematics Transformational grammar. See Grammar Transmissional deixis, 30 H. Triads: sign/object/interpretant, 28, 5054; sR/so/feature, 28; vs. dyad, 62-64 Trubetzkoy, N., 1, 13-14, 189 Turner, L. D., 158 Ultimate logical interpretant. See Logical interpretant Ungeheue~ G., 194 Unmarked: form, 126; terms, 128; values, 133 van Schooneveld, C. H.: on context, 29, 36; dimensionality of, 21, 22, 31, 41, 68; distinctness of, 22-23, 32, 41; extension of, 23, 28, 32, 41; on grammatical and lexical meaning, 5; invariance and, 3; Jakobson and, 6-7, 18-25, 26, 27,

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Markedness Theory

van Schooneveld (continued) 43, 189; on Jakobson's "shifter," 37, 38; on markedness features, 6, 189; markedness theory and, 3, 19, 78; on meaning, 55; on modifier/modified, 20-24; morphological features of, 1925; on narrated event, 41; objectiveness of, 24, 32; on parole/langue distinction, 30-31, 38; Peircean semiotic theory, 25; perceptional deixis of, 31-33, 36-37, 40, 42; perceptual features of, 17-18, 19, 20; plurality of, 21, 40; on reference, 24, 39; restrictedness of, 23-24, 32, 41; on Russian case system, 20 ff., 189; on Russian gender, 171-75, 195; on Russian lexicon, 11-12; on Russian paratactic conjunctions, 26; on Russian parts of speech, 26; on Russian prepositional system, 20, 26; on Russian verbs, 20, 36, 40, 190; semantic dominant of, 91, 194; singulative deixis of, 32-33; theory of conceptual feature~ 7, 29, 46, 57, 104, 194; theory of deixis, 7, 29-34, 36, 38-39, 42, 55; theory of meaning and reference, 98; transmissional deixis of, 30-33, 35, 36 -37, 40, 42

Varela, F. J., 194 Variation: following and, 134. See also Invariant Venn, J.: diagrams, 3, 35, 193 Verbal aspect. See Russian Verbal categories, 36-43, 191. See also Russian Verbal conjugation: distinctness and, 41, 19 0 -9 1 Voiced/voiceless opposition, 26-27 Waddington, C. H., 89 Waugh, L., 3, 45, 148, 155, 162, 192 Weinrich, V., 192, 193 Whitehead, A. N., 79, 96 Wierzbicka, A., 10-12 Wilder, R. L., 78, 101 Word-formative: formation, 32-33, 127; singulative transmissional deixis and, 32-33 Worth, D. 5., 189 Zermelo-Fraenkel set theory. See Set theory Zorn's Lemma. See Axioms: Axiom of Choice Zubin, D. A., 174, 175

About the Author. Edna Andrews is Assistant Professor, Department of Slavic Languages and Literatures, Duke University.

Library of Congress Cataloging-in-Publication Data Andrews, Edna, 1958Markedness theory : the union of asymmetry and semiosis in language / Edna Andrews. p. cm.-(The Roman Jakobson series in linguistics and poetics) Includes index. ISBN 0-8223-°959-9 1. Markedness (Linguistics) 2. Semiotics. 3. Jakobson, Roman, 1896- . 4. Peirce, Charles S. (Charles Sanders), 1839-1914. 5. Grammar, comparative and general-Gender. I. Title. II. Series. P299.M35A5 1990 401 '. 41-dc20 89-7906 CIP