Linguistic Variables: Towards a Unified Theory of Linguistic Variation (Current Issues in Linguistic Theory) issue 0304-0763

LINGUISTIC VARIABLES

AMSTERDAM STUDIES IN THE THEORY AND HISTORY OF LINGUISTIC SCIENCE General Editor E.F. KONRAD KOERNER (University of Ottawa)

Series IV - CURRENT ISSUES IN LINGUISTIC THEORY

Advisory Editorial Board Henning Andersen (Los Angeles); Raimo Anttila (Los Angeles) Thomas V. Gamkrelidze (Tbilisi); John E. Joseph (Hong Kong) Hans-Heinrich Lieb (Berlin); Ernst Pulgram (Ann Arbor, Mich.) E. Wyn Roberts (Vancouver, B.C.); Danny Steinberg (Tokyo)

Volume 108

Hans-Heinrich Lieb Linguistic Variables

LINGUISTIC VARIABLES TOWARDS A UNIFIED THEORY OF LINGUISTIC VARIATION

HANS-HEINRICH LIEB Freie Universität Berlin

JOHN BENJAMINS PUBLISHING COMPANY AMSTERDAM/PHILADELPHIA 1993

Library of Congress Cataloging-in-Publication Data Lieb, Hans-Heinrich. Linguistic variables : towards a unified theory of linguistic variation / Hans-Heinrich Lieb. p. cm. -- (Amsterdam studies in the theory and history of linguistic science. Series IV, Current issues in linguistic theory, ISSN 0304-0763; v. 108) Includes bibliographical references and index. 1. Language and languages-Variation. I. Title. II. Series. P120.V37L49 1993 410--dc20 93-5760 ISBN 90 272 3611 9 (Eur.) / 1-55619-562-1 (US) (alk. paper) CIP © Copyright 1993 - John Benjamins B.V. No part of this book may be reproduced in any form, by print, photoprint, microfilm, or any other means, without written permission from the publisher. John Benjamins Publishing Co. • P.O. Box 75577 • 1070 AN Amsterdam • Netherlands John Benjamins North America • 821 Bethlehem Pike • Philadelphia, PA 19118 • USA

On This Book

The present book is an essay in the original sense: an attempt. It is an attempt at conceptualization — is it possible to develop a conceptual structure, preferably a theory, that can do justice to the more impor­ tant approaches currently followed or proposed in the study of linguis­ tic variation? Variation research offers a confusing picture. There are a number of competing approaches distributed over different fields of linguis­ tics, in particular, historical linguistics, dialectology, sociolinguistics, psycholinguistics, language typology, and contrastive linguistics. It is hard to see what if anything is shared by, say, Chomsky's notion of parameter (Chomsky 1981), implicational scale analysis (see Dittmar and Schlobinski 1988), Klein's variety grammars (Klein 1988), and Coseriu's conception of dialects and styles (Coseriu 1988/1981). Variation research is heterogeneous. Comparing its different ori­ entations requires a conceptual framework that is both sufficiently general and non-trivial. After a lot of experimentation I finally came up with a frame of reference that centers around the concept of a linguistic variable, in a sense that crucially differs from Labov's intuitive notion. Major approaches to linguistic variation can be distinguished by the types of linguistic variables emphasized by each. Such a distinction is not yet a theory. Struggling for conceptual clarity, I found myself more and more strongly pushed towards taking the notion of theory seriously: nothing much could be achieved with­ out formally defining key terms, without distinguishing definitions from assumptions and both from their consequences. In fact, it would be easy to disengage from the present essay a theory — however in­ complete — that is axiomatized. This is so not because I treasure pre­ cision and clarity, which I do; rather, there was no other way to

VI

ON THIS BOOK

achieve my primary aim, adequate conceptualization in the area of lin­ guistic variation. I consider such conceptualization as a matter of urgency. By a cur­ rent estimate, "the coming century will see either the death or the doom of 90% of mankind's languages" (Krauss 1992:7). Hopefully, this estimate will prove too pessimistic; even so a huge descriptive ef­ fort will be required of the community of linguists. There is, however, a real danger that descriptions of different languages may continue to turn out non-comparable: so far there is no clear answer to the ques­ tion in terms of what languages — or language varieties, for that mat­ ter — may differ; notions like 'parameter' await explication. The situation is harmful to the descriptive attempt itself: the field linguist can only grope for relevance in his descriptions if there is no clear account of linguistic variation per se. My second aim in writing this essay has therefore been a practical one, contribute, as a theorist, to the descriptive attempt that is demanded of linguistics. Adopting the proposed theory of linguistic variation should make it easier to deve­ lop a format for linguistic descriptions that are variation-sensitive, a point to be taken up in the last two chapters of this essay. From the very beginning I had a third aim in mind: simply, orien­ tation. Indeed, the present essay originated from an attempt to write a handbook article on "Syntax and Language Varieties" (now Lieb forthc. b, largely identical to Secs 1 to 3, below). A lot of spadework for such an article had been done in three recent handbooks (Besch et al. (eds) 1982/1983; Besch et al. (eds) 1984/1985; Ammon et al. (eds) 1987/1988). The third, in particular, contains excellent overviews of the literature on most variation aspects; I continue to draw on it and its predecessors in this essay. Still, I found it impossible to write the arti­ cle as planned since there was no obvious coherence to the field of var­ iation research in general, and research on syntactic variation in par­ ticular. In deciding on an essay devoted entirely to theory I did, how­ ever, keep an emphasis on informativeness: my essay is meant to pro­ vide orientation by characterizing major approaches and showing their interrelations. Equal coverage of all forms of variation research has not been at­ tempted. In particular, short shrift has been given to Creole and pidgin studies (for a recent overview, see Holm 1988/1989) and to research

ON THIS BOOK

Vll

on variation and language acquisition. Both language acquisition and Creoles and pidgins will be briefly considered, though, to make sure that the proposed theory can account for them. There are two other features that can be traced back to the essay's origins: it pays special attention to syntax, and it emphasizes languageinternal variation. These limitations are no matter of principle; the theory of language varieties to be outlined is conceived as part of a larger theory that also covers variation among languages, and the em­ phasis on syntax is largely a matter of exemplification. Most of the theoretical tools provided in this essay apply to interlanguage as well as language-internal variation, and an attempt to cover language typo­ logy is made in the concluding Part V of this book. Any linguistic theory should require a backdrop of heuristic as­ sumptions on language and linguistics that are not part of the theory it­ self. Such assumptions are drawn in this essay from the framework of Integrational Linguistics (cf. Lieb 1983), whose knowledge is, how­ ever, not presupposed. (Lieb's Tntegrational Linguistics' is entirely unrelated to 'integrational linguistics' as proposed by Roy Harris, e.g. (1981); for critical remarks on the latter, see Borsley 1991.) The present book is intended to be an essay also in the modern sense. Given the intended coverage, it is relatively brief. It concen­ trates on essential ideas, which are to stand out clearly rather than be smothered by lots of learned detail. Mostly, I have been satisfied with establishing main points, rather than supporting them from every pos­ sible angle. Also, a sharp selection is made from the relevant literature (which was systematically checked till the end of 1990, and in a more cursory manner since). References are to be informative by strategic placement rather than extensive quotation. Footnotes are avoided en­ tirely, even in places where they might have helped the flow of prose. Style has been kept as simple as possible. This does not mean, unfortu­ nately, that the essay is easy to read at all times: cutting out verbosity tends to increase information density, and parts of the essay presup­ pose knowledge of naive set theory. Time and again I have therefore included remarks and cross-references that are meant to direct the reader, running the risk of being tedious rather than obscure; and readers who are not trained for formal detail or are unwilling to both­ er with it are helped in still another way, by paraphrases in plain Eng-

Vlll

ON THIS BOOK

lish of most formulations of the theory, and by inclusion of simple ex­ amples. The problem with paraphrases is, however, that they may be misleading and, in minor ways, inaccurate; in a case of doubt it is al­ ways the original formulation that takes precedence over its para­ phrase. In summary, then, I try to be easy to disagree with by clearly sta­ ting my points. I do hope that some of them have been made. Berlin, December 1992

Hans-Heinrich Lieb

Contents

On this book

v Part I ORIENTATION

1

2

Linguistic variables

3

1.1

An elementary question

3

1.2

A concept of linguistic variable

4

1.3

Comments and examples

6

1.4

Classifying linguistic variables

7

1.5

Component variables

9

1.6

Holistic variables

Major approaches to linguistic variation 2.1

3

11 13

Component approach and holistic approach (variety approach)

13

2.2

Grammar approach and language approach

15

2.3

Examples: grammar approach

17

2.4

Examples: language approach

19

2.5

Aims and scope of the present essay

20

An overview of syntactic variation studies

23

3.1

A classification of current research

23

3.2

Conclusions

25

CONTENTS

X

3.3

Old biasses. Syntax in dialectology

26

3.4

Size of research. The role of theory

28

Part II SETTING THE STAGE 4

5

6

7

The diachronic perspective

33

4.1

Languages as communication complexes

33

4.2

Systems for communication complexes

36

4.3

Different systems for a stage: example

38

4.4

Chains of systems

39

4.5

States of systems. Language development

41

4.6

Lists of variables

43

Basic ideas

45

5.1

The variety relation

45

5.2

Details

45

5.3

Variety structures as classification systems

47

5.4

Classification criteria: external and system-based

48

5.5

Criteria correlation

49

In defense of variety structures: the problem of idiolects

51

6.1

Introduction

51

6.2

Idiolects as 'external' and 'speaker specific'

52

6.3

Idiolects as 'intermediate'

53

6.4

Idiolects as'homogeneous'

54

6.5

Remark: concepts of homogeneity

56

In defense of variety structures: classification systems on historical languages

57

7.1

57

Historical languages: general objections

CONTENTS

8

xi

7.2

Historical languages: specific objections

58

7.3

Classification systems: the problem of criteria

59

7.4

Classification systems: the problem of uniqueness

61

The variety structure of a historical language: overview 8.1

The historical period division and the basic dialect division

63 .....63

8.2

Problems of the basic dialect division

65

8.3

Other primary classifications

67

8.4

Classifications on historical periods

69

8.5

Other non-primary classifications

70

8.6

Summary

72 Part III

A THEORY OF LANGUAGE VARIETIES 9

Variety structures as classification systems

77

9.1

Divisions, classifications, partitions

77

9.2

Introducing criteria

80

9.3

Division systems, classification systems, partition systems

82

9.4

Auxiliary notions. Theorem

85

9.5

The notion of place

88

9.6

Explication of "variety structure"

90

10 External criteria

93

10.1 Example

93

10.2 Criteria-determining functions

95

10.3 Permissible types of non-language entities

97

10.4 Points of view and criteria

98

CONTENTS

Xll

11 System-based criteria

101

11.1 The criteria-determining function

101

11.2 Permissible types of systems

102

11.3 Points of view and criteria

104

11.4 Example

108

11.5 The correlation theorem

..

12 Languages, varieties, idiolects

111 115

12.1 Varieties and languages

115

12.2 Properties of the variety relation

118

12.3 Idiolect location in historical languages

121

12.4 Idiolect location in varieties

123

13 Varieties and idiolect systems

125

13.1 Location of idiolect systems

125

13.2 Position of system components

126

13.3 Variety-specific components

128

13.4 Variety-specific properties

130

Part IV INTEGRATING THE COMPONENT APPROACH 14 Variants and variables

135

14.1 Introduction

135

14.2 Orientation

136

14.3 Variants of relations

138

14.4 Variants of functions

140

14.5 The notion of a linguistic variable in a set of systems .... 143 15 Reconstructions: Chomsky and Seiler

147

15.1 On reconstructing Chomsky

147

CONTENTS

xiii

15.2 'Principles and parameters': definitions

149

15.3 Discussion

151

15.4 Parameter sets

153

15.5 'Representation': reconstructing Seiler

154

16 On the conception of evaluation grammars

157

16.1 Example

157

16.2 The notion of evaluation basis

159

16.3 A simple evaluation basis: rule status

161

16.4 Types of evaluation grammars

161

17 Evaluation grammars, variable rules, and linguistic variables 17.1

165 Rule-weight1

17.2 Rule interpretation 17.3

165 166

Rule-weight2

168

17.4 The values of rule-weight2 as linguistic variables

170

17.5 On reconstructing the variable rule approach 17.6 Grammar-independent variables: quantitative and qualitative

171

18 Solving the integration problem

173 177

18.1 Basic ideas

177

18.2 Property determination by linguistic variables

178

18.3 Specifying sets of systems by linguistic variables

179

18.4 Example

181

18.5 Permissible types of systems: integrating the component approach

183

CONTENTS

XIV

Part V EXTENSIONS 19 Going beyond varieties

187

19.1 A note on contrastive analysis and language acquisition . . 1 8 7 19.2 Language typology: basic ideas

188

19.3 Auxiliary concepts

191

19.4 Typological structures and types

194

19.5 Explanations

197

19.6 Variety structures and typological structures

200

20 Grammars and their terminology

203

20.1 Introduction

203

20.2 Types of 'grammars'

204

20.3 Comments

207

20.4 A sample grammatical statement

210

20.5 Grammatical terms: non-linguistic constants

213

20.6 Grammatical terms: linguistic constants

215

21 Grammatical statements

219

21.1 Claim on simple grammars

219

21.2 Comments

221

21.3 Complex grammars: a sample statement

223

21.4 Claim on complex grammars

226

21.5 Comparative grammars

229

21.6 Grammars, typologies, and linguistic variables

232

Bibliography

235

Index of names

245

Index of subjects and terms

248

List of symbols and abbreviations

259

PART I

ORIENTATION

1 Linguistic Variables

1.1

An elementary question

A first general step in dealing with linguistic variation should consist in giving a clear answer to the following question: what exactly is it that varies? Put differently: (1.1)

What is a linguistic variable?

An inadequate answer may seriously hamper both theoretical under­ standing and practical progress; cf. Cheshire's (1987a) critical discus­ sion of Labov's (since (1963)) conception of a linguistic variable, who made the term popular in linguistics — "It is sad that after 25 years or so of analyzing language in its social context, we have achieved so little in the analysis of specific varieties", Cheshire (1987a:278). I will pro­ pose an answer that was chosen after much experimentation. For initial orientation consider the notion of allophone as a tradi­ tional variation concept, used in statements of the form: (1.2)

A is an allophone of B.

(It is here immaterial whether or not the notion of allophone should be allowed in one's theory of language.) Formulation (1.2) would suggest that it is entities B — 'phonemes' — that vary; linguistic variables, then, would be units of linguistic systems, as in Labov's original con­ ception. Such a view is problematic, though. For one thing, it makes no­ thing of the fact that the notion of allophone is relative to 'language­ like entities' L such as idiolects, language varieties, languages, or sys­ tems of such; strictly speaking, formulation (1.2) is incomplete and should be replaced by:

4

ORIENTATION (I)

(1.3)

A is an allophone of B in L.

Not only may B vary — by having different allophones — but so may L, by including different pairs (A, B). Taking these pairs as 'L-values' of the relation Allophone — a three-place relation whose third-place members are language-like entities — the relation itself rather than B or L may be said to vary: it is the relation Allophone that would be a linguistic variable. Obviously, this also covers variation of B, and var­ iation of L with respect to the relation Allophone. In addition, the re­ lation Allophone provides a 'point of reference' for comparing varia­ tion in different language-like entities; all we have to do in the case of different L1 and L2 is compare the L1-values of Allophone with its L2values. This suggests: (1.4)

The relation Allophone is a linguistic variable.

A conception — somewhat expanded — by which the concept of lin­ guistic variable applies to relations like Allophone does prove adequate for characterizing the field of variation studies. It gives one possible answer to the question, much discussed in connection with comparative work of any type (see for example Heger 1990/91, Seiler 1990: Sec. 7, Krzeszowski 1990: Ch. 2), what exactly should be allowed as a tertium comparationis when two language-like entities are compared. (Differ­ ently from other authors I am not tying myself down to tertia comparationis that are semantic in one sense or other). 1.2

A concept of linguistic variable

For a more precise account of linguistic variables, the following sym­ bols are introduced as variables in the logical sense (i.e. as symbols used to refer to arbitrary entities of a certain kind): (1.5)

"L", "L 1 ", ... stand for any language-like entity, i.e. a. any idiolect, language variety, language or larger lan­ guage-like entity (in a sense where these are not iden­ tified with systems); b. any system of any entity (a); c. any grammar (understood as a description or a theo­ ry) of any entity (a) or entity (b).

LINGUISTIC VARIABLES (1)

5

Thus, there are three major types of language-like entities, each with its subtypes. Grammars are allowed as a separate type because they figure prominently in at least one kind of variation studies, so-called 'evaluation grammars'. Generalizing the Allophone example we might now identify lin­ guistic variables with relations whose last-place members are lan­ guage-like entities of a single type, more precisely, of a single subtype of one of the three major types distinguished in (1.5). (In the case of Allophone the relation is three-place, but two-place — or higher-place — relations may also occur, such as the two-place relation Phoneme: x is a phoneme in L.) There is, however, a complication. To account for the entire field of variation studies, it is not only relations like Allophone but certain functions (in the set-theoretical sense) that must be allowed as linguis­ tic variables. Such a function is either 'one-place' (assigns objects to individual objects), and its arguments (the objects to which others are assigned) are language-like entities of a single type; or the function is more than one-place (assigns objects to tuples of objects), and its argu­ ments (the tuples) have language-like entities of a single type as their last components. Such functions will be taken into account right from the start. No further requirements will be imposed on the relations and functions. This leads to a very general concept of linguistic variable; the concept is indeed adequate for discussing all major conceptions of linguistic variation. Assuming naive set theory and using "M" for any set (relations and functions are understood as sets of a specific kind), we define: (1.6)

Definition. M is a linguistic variable iff [if and only if] M is non-empty and (a) or (b): a. M is a relation, and the last-place members of M are language-like entities of a single type; b. M is an n-place function (n > 0), and either (i) or (ii): (i) n = 1, and the arguments of M are language-like entities of a single type; (ii) n > 1, and the last components of the arguments of M are language-like entities of a single type.

6

ORIENTATION (I)

Once again, "single type" means a single subtype of one of the three major types distinguished in (1.5). 1.3

Comments and examples

Informally, a linguistic variable may be (a) a non-empty relation, or set of ordered n-tuples (x1,.., xn) (2-tuples or pairs, 3-tuples or triples, etc.), such that all xn are language-like entities of a single type (either all of them are idiolects, or all of them are language varieties, etc., see (1.5)). Or else, a linguistic variable is (b) a non-empty function. This function may take language-like entities of a single type as arguments and assign to them entities whose nature is left undetermined in the definition of "linguistic variable". We may also have a function that takes not language-like entities but n-tuples (x1 .., xn) of entities, again assigning to each tuple exactly one entity of an unspecified type. In this case it is the xn in the various tuples that must all be language-like entities of a single type. (Something may be a linguistic variable on both accounts (a) and (b), due to the fact that any n-place function may be construed as an (n+l)-place relation of a specific kind but this need not concern us here.) For example, the relation Allophone in Sec. 1.1 is a linguistic var­ iable by (1.6a): x is an allophone of y in L; equivalently: (1.7)

(x, y, L) G Allophone;

Allophone is a three-place relation, and its last-place members L are language-like entities of a single type (such as idiolect systems). As an example of a linguistic variable in conformity with (1.6b), subcase (i), suppose that we introduce the notion of an allophone with respect to L, using the term "allophone1": (1.8) allophone1 (L) =df {(x, y) | (x, y, L)  Allophone}. ("=df" means, "is identical-by-definition with".) Function allophone1 as defined in (1.8) takes any language-like entity L of a specific type and assigns to it the set of allophone-phoneme pairs that exist in L, or the allophone-phoneme relation in L. In a similar way we may obtain an example of a linguistic variable covered by (1.6b), subcase (ii):

LINGUISTIC VARIABLES (1)

(1.9)

7

For any phoneme y of L, allophone2 (y, L) =df {x | (x, y, L)  Allophone}.

Function allophone 2 takes any pair consisting of (i) a phoneme of a language-like entity L of a specific type and (ii) L itself and assigns to the pair the (non-empty) set of all x such that x is an Allophone of y in L; i.e. allophone2(y, L) is the set of allophones of y in L. The two allophone functions were introduced only for the sake of exemplification. As a matter of fact variables that are functions as characterized in (1.6b) are of considerable importance for syntax; thus, 'grammatical relations' in a traditional sense like subject or pre­ dicate may be construed as functions that are linguistic variables covered by (1.6b), subcase (ii) (as in Integrational Linguistics: Lieb 1983, forthc. a); and this is also true of the 'rule-weight' functions in Evaluation Grammar (Sec. 17, below; see also Sec. 2.3). Indeed, we may propose to do away with linguistic variables of the relation type (1.6a), replacing them by functions on the pattern of de­ finitions (1.8) or (1.9). It seems preferable, though, to allow as lin­ guistic variables both functions like allophone1 and allophone2 and un­ derlying relations such as Allophone. The following point is worth emphasizing: the term "Allophone" — a name of the relation Allophone that is a linguistic variable — is, somewhat unfortunately, a constant of a theory of language, in the logical sense of "constant"; generally, linguistic variables as defined in (1.6) are, or may be, denoted by constants of linguistic theories. Given the notion of linguistic variable as defined in (1.6) we might go on to introduce various notions of value of a variable; for instance, if x is an allophone of y in L, we might say that the pair (x, y) is an Lvalue of Allophone. However, notions of value will not be used in this essay; a related but different terminology based on the notion of vari­ ant (Sec. 14) is employed instead. 1.4

Classifying linguistic variables

The most general characterization of variation research may well be this: variation research is the study of linguistic variables in the sense of definition (1.6). To substantiate this claim I will distinguish differ-

8

ORIENTATION (I)

ent types of linguistic variables and then define major approaches to linguistic variation by relating each to a certain type of linguistic vari­ able. Linguistic variables may be classified by two criteria: (1.10)

a. the type of language-like entities that are last-place members, or last components of arguments, of a lin­ guistic variable; b. the kinds of linguistic entities involved elsewhere in the variable.

For example, the Allophone relation requires linguistic systems as its last-place members (criterion (a)), and units of such systems elsewhere (criterion (b)). The two criteria result in two independent classifications (crossclassifications) on the set of linguistic variables:

The (a)-classification is easily explained by reference to the three types of language-like entities (see (1.5)): grammar variables involve gram­ mars in 'last position', non-grammar variables involve either entities like idiolects or languages (language variables), or systems of such (system variables).

LINGUISTIC VARIABLES (1)

9

The (b)-classification must be explained in greater detail. I begin by considering the first class in this classification. 1.5

Component variables

Consider, once again, the relation Allophone. If x is an allophone of y in L, then y is a phonological unit (a phoneme), and x a phonetic unit (a phonetic sound), of L. Generally, both x and y are 'components' of L. Components of L may be defined, informally and somewhat vague­ ly, as units, categories, structures, and relations of L and as 'parts' of L that are not themselves language-like entities. (Note that L may be a grammar; among its components, we have its symbols, its rules etc. Also note that the [linguistic] concept of component of L and the [settheoretical] concept of component of an n-tuple are entirely unrelated.) The relation Allophone is a component variable because of the way in which components of language-like entities figure among the relation's members. More precisely, a component variable is a linguis­ tic variable M that satifies one of two conditions (a) or (b). a.

b.

M is a relation whose members at a certain place i (other than the last place) have the following property: given such a member xi, xi is a component of the language-like entity L that is a relevant last-place member of M. — Consider, for example, the first-place members (i = 1) of the relation Allophone. If x is an allophone of y in L (put differently, if (x, y, L) e Allophone), then x must be a phonetic sound of L, therefore, a component of L. This makes Allophone a component variable. M is a function of the following kind. M may be oneplace. We then consider the values x of M (in the set-theo­ retical sense: the entities x assigned by M to the entities that are given): if M(L) = x ("M(L)" means "the value of M for L") and x is a component of the language-like enti­ ty L, then M is a component variable. — M may also be more than one-place. Then we have a component variable on one of two conditions (which may both be satisfied):

10

ORIENTATION (I)

-

-

at the i-th place of each argument (x 1 , .., x n-1 , L) of M (not allowing the last place), we have a component x1 of L; once again, if M(x 1, .., xn_1, L) = x, then x is a compo­ nent of L.

This characterization of component variables translates into the fol­ lowing definition: (1.12)

Definition. M is a component variable iff a. M is a linguistic variable; b. (i) or (ii): (i) M is an n-place relation (n > 1), and there is an i = 1, . . , n - l such that for any (x1 ..,x i , ..,x n - 1 , L)  M, xi is a component of L. (ii) M is an n-place function (n > 0), and either (α) or (ß): α. n = 1, and for any argument L of M, M(L) [i.e. the entity assigned to L by M] is a com­ ponent of L; ß. n > l , a n d ( ß 1 ) o r ( ß 2 ) : ß1 there is an i = 1, ..,n-l such that for any argument (x1 ..,x i , ..,x n - l ) of M, xi is a component of L; ß2 M(x1, .., x n-1 , L) is a component of L.

Allophone is a component variable by (a) and (bi) because, for any (x,y,L) G Allophone, both x and y are components of L. This is stronger than required by (bi); either x or y would have sufficed. Again, the function allophone1 as defined in (1.8) is a component variable because both (a) and (a) in (bii) are satisfied: allophone1 is a one-place function, and for any argument L of allophone1, the set of allophone-phoneme pairs in L may be assumed to be a component of L, given a suitable theory of language. The function allophone2 de­ fined in (1.9) is a component variable by (a) and (bii) because the first subcase (ß1) of (ß) holds: for any argument (y, L) of allophone2, y is a phoneme of L, hence, a component of L. In addition, allophone2 is a component variable because subcase (p2) of (ß) also holds: for any ar-

LINGUISTIC VARIABLES (1)

11

gument (y, L) of allophone2, the set of allophones of y in L is a com­ ponent of L. Components of L may be classified by the 'part' or 'linguistic level' to which they belong: they may be phonetic, phonological, etc. We may accordingly distinguish phonetic variables, phonological vari­ ables, etc.: (1.13)

Definition schema. Let "+" stand for any of the following expressions: "phonetic", "phonological", "morphological", "syntactic", "semantic", "pragmatic". M is a + variable iff [same as (a) and (b) in (1.12), adding the expression + in front of each occurrence of "compo­ nent"]

(If no pragmatic components of language-like entities are allowed, then of course there are no pragmatic variables.) Variables are purely phonetic if they are phonetic and not phonological etc.; similarly, for other 'levels'. Linguistic variables may but need not be 'pure' in this sense (level-specific). For example, Allophone is both a phonetic and a phonological va­ riable: its first -place members art phonetic components and its secondplace members phonological ones (case (bi) in (1.13)). The function allophone1 defined in (1.8) is both a phonetic and a phonological varia­ ble by (biiα) if the allophone-phoneme relation is assigned to both the phonetic and the phonological levels; and allophone2 defined in (1.9) has the same status by (biiß): allophone2 is phonological because in its arguments (y, L), y is a phoneme of L, and is phonetic because its val­ ues are sets of phonetic sounds of L. We next characterize the second class of linguistic variables in the (b)-classification (1.11). 1.6

Holistic variables

Consider a statement such as (1.14)

Bavarian is a variety of German.

Variety is a two-place relation whose last-place members are language­ like entities L, more specifically, 'languages', in some sense of the

12

ORIENTATION (I)

term. The relation Variety is therefore a linguistic variable, by (1.6a). It is not, however, a component variable; differently from variables like Allophone, it is not only the last-place members but all members of Variety that are language-like entities. Variety is, so to speak, 'ho­ listic' (takes as its members complete language-like entities rather than their components): (1.15)

Definition. M is a holistic variable iff a. M is a linguistic variable; b. for any x, if x is a member of M, then x is a language­ like entity.

The term "member" in (b) also applies if M is a function: any n-place function can be construed as an (n+l)-place relation. No holistic variable is a component variable, and conversely; this follows from (1.15b), (1.12b), and the assumption that no component of L is itself a language-like entity. Holistic variables other than Variety are Dialect (cf. "Bavarian is a dialect of German"), Sociolect etc.; or Parent Language etc. Variety is the most general holistic variable used in discussions of languageinternal variation (for the term itself, see Berruto 1987, whose explanations are, however, coloured by meanings specific to the Italian expression). Obviously, the distinction between component variables and holist­ ic variables is not logically exhaustive: the criterion of what entities figure in places that need not be filled by language-like entities also yields the set of 'other variables' (neither component nor holistic). As a matter of fact, such variables appear to be of minor importance in variation studies (for an example and discussion, see Sec. 10.2, below). Major approaches to linguistic variation are now distinguished by referring to the various types of linguistic variables, and the aims and scope of the present essay are characterized in greater detail.

2 Major Approaches to Linguistic Variation

2.1

Component approach and holistic approach (variety ap­ proach)

We may informally distinguish the component approach — emphasi­ zing component variables — from the holistic approach, which empha­ sizes holistic variables and has the variety approach as a subcase: (2.1)

{Definitions) a. By the component approach to linguistic variation I understand the position that component variables are basic to, if not sufficient for, dealing with variation both within and among 'natural languages' in a tradi­ tional sense. b. By the holistic approach to linguistic variation I un­ derstand the position that holistic variables are basic to, if not sufficient for, dealing with variation both within and among 'natural languages' in a traditional sense. c. The variety approach = the holistic approach to lin­ guistic variation restricted to language-internal varia­ tion.

In these informal definitions reference is made to 'natural languages' in a traditional sense. This is not to say that advocates of the approa­ ches must adopt them in their theories, or, if they are adopted, all con­ ceive them in the same way. The holistic approach has so far been applied largely to languageinternal variation, i.e. has taken the form of the variety approach. In particular, nothing larger than a historical language is traditionally al-

14

ORIENTATION (I)

lowed as a last-place member — or a last argument-component — of a holistic variable. Such restrictions are, however, not inherent to the holistic approach. Given the informal definitions in (2.1) we may distinguish a stronger and a weaker version of both the component approach and the holistic approach (hence, of the variety approach), depending on whether the variables in question are or are not considered to be sufficient for dealing with variation. The following diagram shows the interrelations among the approa­ ches that have been distinguished: (2.2)

Diagram

The distinction between the two major approaches is of funda­ mental importance for characterizing variation studies, in particular, studies on language-internal variation, where the holistic approach takes the form of the variety approach:

MAJOR APPROACHES TO VARIATION (2)

(2.3)

15

Claim on variation studies. All major work in the study of language-internal variation exemplifies either the compo­ nent approach or the variety approach.

Obviously, the distinction between component approach and holistic approach is non-exhaustive since it is based on the non-exhaustive dis­ tinction between component variables and holistic variables. This means that (2.3) is an empirical claim not a consequence of the definitions.The claim, which is eventually substantiated by the present essay taken in its entirety, will be made plausible in the present Sec. 2. There is a second major distinction between approaches, indepen­ dent of the first, that is related to if not based directly on the distinc­ tion between grammar variables and non-grammar variables (Diagram (1.11). 2.2

Grammar approach and language approach (2.4)

(Definitions) a. By the grammar approach to linguistic variation I un­ derstand the position that the study of linguistic varia­ tion is primarily concerned with (the linguist's) gram­ mars and the 'languages' they generate. b. By the language approach to linguistic variation I un­ derstand the position that the study of linguistic varia­ tion is primarily concerned with languages in a sense where they may be referred toby (the linguist's) gram­ mars and the 'languages' they generate.

On the language approach, variation occurs at the object-language lev­ el with respect to grammars and generated 'languages'. Obviously, the grammar approach emphasizes 'grammar variables' and the language approach 'language' or 'system variables'. The two approaches are dis­ tinguished by a criterion that is entirely independent of the criterion underlying the opposition of component approach vs. holistic ap­ proach. The grammar approach, strongly advocated in the seventies, is once more being superseded by the language approach, due to recent changes in linguistics. The major versions of the grammar approach

16

ORIENTATION (I)

were developed within Generative Grammar in the seventies as modi­ fications of an essentially Chomskyan framework, inheriting both Chomsky's original emphasis on the format of (the linguist's) gram­ mars and Chomsky's indirect way of dealing with a grammar's object (mental mechanisms, in the case of Chomsky) through a specification of properties of grammars. Since Chomsky (1981), there have been three relevant changes in the Chomskyan framework: (i)

the format of (the linguist's) grammars is left largely un­ specified;

(ii)

'mental mechanisms' are to be approached directly, not indirectly through a study of the linguist's grammars;

(iii)

for the first time in Chomskyan grammar, the Chomskyan framework includes a systematic means ('parameters') in­ tended to deal with interlanguage variation and, by exten­ sion, with variation within languages.

Because of (ii) and (iii), Chomsky now adopts the language approach, in theory if not in practice, and makes his own independent proposals for dealing with linguistic variation. Thus, the grammar approach of the seventies is out of touch with current Chomskyan grammar: while it may still be possible to adapt the approach to changes of detail in Chomsky's framework (as attempted by Bierwisch in (1988)), changes (i) to (iii) effectively cut the ties of the earlier work to Chomsky's framework (nor does this work easily relate to any other contempora­ ry version of generative grammar). In addition there has been a movement away from grammars in the 'variable rule approach', originally also tied to Chomskyan Gener­ ative Grammar (see Sec. 17.5, below). The grammar approach should still be considered carefully both because of its recent importance and its intrinsic interest: there is no necessary connection of the approach to Chomskyan grammar (or any other version of Generative Grammar), and the approach has produ­ ced some of the most carefully formulated proposals to deal with lin­ guistic variation.

MAJOR APPROACHES TO VARIATION (2)

17

The language approach, only recently embraced by Chomsky, has been the dominant approach outside the generative camp. However, the history of variation conceptions, where post-Saussurean European structuralism would figure large (for the Prague School, see, e. g., Vachek 1972, Spillner 1987: Sec. 3.3, and Sgall et al. 1992 for a major recent contribution), will not be discussed in this essay (for the history of variation conceptions, see the relevant parts of Besch et al. (eds) 1982/1983, Besch et al. (eds) 1984/1985, Ammon et ah (eds) 1987/ 1988). The two following subsections contain examples for all four major approaches, emphasizing language-internal variation. The examples are restricted to recent theoretical work, in an informal sense of "theo­ retical". The distinction between grammar approach vs. language ap­ proach will be used as a major classification criterion. The two subsec­ tions provide evidence for the Claim on Variation Studies (2.3). 2.3

Examples: grammar approach

Up to Chomsky (1981), the study of language-internal variation was programmatically excluded from Chomskyan generative grammar (most notoriously in Chomsky 1965:3: "Linguistic theory is concerned primarily with an ideal speaker-listener in a completely homogeneous speech community [...]"). This position did not go unchallenged even in Generative Grammar. In historical linguistics, King 1969 enjoyed some prominence for a while, subsequently, Lightfoot (1979); for a critical account, see Mayerthaler (1984). A few applications to dialect­ ology were attempted (for discussion, see Francis 1983:171-192, Petyt 1980:171-184, also Veith 1982). More importantly, an approach that may be called Evaluation Grammar (an approximate translation of German ableitungsbewertende Grammatik) was developed in the se­ venties mainly by German linguists (Kanngießer 1972, 1978; Klein 1974; Bierwisch 1976), working in parallel and partly proceeding from work done by Suppes (1970) and Salomaa (since 1969, see Salomaa 1973); for recent summaries of the various subapproaches, see Kanngießer (1987; unduly condensed); Klein (1988; 'variety gram­ mars'); Bierwisch (1988; 'connotation analysis'). A culmination of this work is Habel (1979), a careful formal study that unifies the various

18

ORIENTATION (I)

subapproaches under the general notion of ableitungsbewertende Grammatik. Bailey's (1973) informal proposals for a 'polylectal grammar' — see also Bailey (forthc.) — should again be for evaluation grammars if made precise (this is obscured by Bailey's rejection of 'sociolinguistic grammars' in Bailey 1987; the general format of evaluation grammars as characterized by Habel appears to be compatible with Bailey's inten­ tions). The work done by Krzeszowski on 'contrastive generative gram­ mars' (1974/1979), summarized in Krzeszowski (1990: Ch. VIII), is concerned with interlanguage rather than language-internal variation; it seems fairly obvious, though, that his 'contrastive generative gram­ mars' can be subsumed under the general notion of evaluation gram­ mar. This should also be true of the proposals made by Sankoff and Poplack (1981) for 'grammars for code-switching' (change from one language to another in the middle of speech). Finally, the 'variable rule' approach (cf. Sankoff 1988) in its ori­ ginal, grammar-dependent form also appears to be covered by the con­ cept of evaluation grammar (for discussion, see Secs 16.4 vs. 17.5, be­ low). I will argue in Secs 16f that Evaluation Grammar exemplifies the component approach to linguistic variation. A considerable amount of formal detail is required for the demonstration. Somewhat less formal­ ly, the argument may be summarized as follows. Very roughly, an evaluation grammar is a formal grammar that uses 'evaluated rules' to generate 'evaluated sentences' by 'evaluated derivations'. An evaluated rule etc. is a pair whose first component is a 'proper' rule etc. and whose second component is an 'evaluation' of the first component; the evaluation is a number, or tuple of numbers. The proper part of the evaluation grammar (consisting of its prop­ er rules) can be subdivided into a sequence of subgrammars; for each subgrammar, there is a function that assigns numbers to proper rules of the evaluation grammar. This function is itself a value of a more basic function that applies to the evaluation grammar as a whole: the function rule-weight. Rule-weight takes pairs (i, Γ) — where Γ is an evaluation grammar and i a positive integer not greater than the length of the subgrammar sequence of Γ — as arguments and assigns to each

MAJOR APPROACHES TO VARIATION (2)

19

pair a function that in turn assigns to each proper rule of Γ a number; the function assigned to (i, Γ) by rule-weight is a component of Γ. It now follows that the function rule-weight itself is a component variable by (1.12), where (ß2) applies. The language-like entity (1.5) involved in rule-weight is grammar Γ. (Starting from rule-weight, we may actually arrive at component variables that no longer involve grammars but 'systems' in the sense of (1.5b).) Rule-weight is obviously basic to dealing with linguistic variation through Γ; it also underlies the evaluations of proper sentences, which represent their 'variation properties'. It now follows from (2.1a) that the Evaluation Grammar approach exemplifies the component ap­ proach to linguistic variation. Evaluation Grammar does, however, demand that rule-weight can be justified, at least in principle, by criteria external to a grammar. The role assigned to such criteria differs with different authors. Thus, component variables are not sufficient for dealing with variation, it is only the weaker version of the component approach that is exemplified by Evaluation Grammar. While adherents of the grammar approach also subscribe to the component approach, followers of the language approach may adopt either the component approach or the holistic approach. 2.4

Examples: language approach

Component approach: Chomsky, Seiler Chomsky's current Principles and Parameters framework (since Chomsky 1981, summarized in Chomsky 1986, see also Chomsky 1988) is, in theory if not in practice, a case of the language approach and exemplifies the stronger version of the component approach. No­ tions like 'natural language' or 'variety' are simply not allowed. Vari­ ation, especially syntactic variation, is dealt with through component variables. The language-like entities involved in the variables are 'Ilanguages', i.e. certain mental mechanisms. More specifically, Choms­ ky's 'parameters' can be construed as linguistic variables; a 'parameter value' in the sense of Chomsky is another, more restricted linguistic

20

ORIENTATION (I)

variable 'contained' in the parameter. (For details, see Secs 15.1 to 15.4, below.) Hansjakob Seiler's UNITYP framework for typological and uni­ versality research, e.g. (1986), (1990), under development since 1972, exemplifies the language approach and the weaker version of the component approach', see Sec. 15.5, below. Holistic approach: Lieb, Heger, Coseriu The framework for linguistic variation that is part of Integrational Linguistics (Lieb 1970; 1982; 1983: Part A), and related proposals (Heger 1982) using Klaus Heger's 'noernatic linguistics' (Heger 1976), are clear examples of the language approach and the holistic approach in its weaker version; somewhat less clearly, Coseriu (1988/1981) may also be assigned to this approach. To the extent that language-internal variation is covered, the three proposals exemplify the weaker version of the variety approach. (For discussion of the Integrational frame­ work, see Part II, below.) Frameworks not mentioned explicitly (e, g., 'implicational scale analysis', cf. Dittmar and Schlobinski 1988) also appear to be assigna­ ble to one of the major approaches; generally, it has turned out possi­ ble to reduce a bewildering array of different orientations to a few ba­ sic categories. The aims and scope of the present essay can now be characterized in terms of the major approaches to linguistic variation. 2.5

Aims and scope of the present essay

Linguistic variation, either within or among languages, raises prob­ lems of different types: (i) (ii) (iii)

theoretical: in particular, how to develop an adequate con­ ceptual framework for dealing with linguistic variation; methodological in a strict sense: develop adequate meth­ ods of research; descriptive: develop an adequate descriptive format for variation studies;

MAJOR APPROACHES TO VARIATION (2)

(iv)

factual',

21

establish the actual facts of linguistic variation.

The emphasis in this essay is on theory (i); recent theoretical work is considered but the history of variation conceptions is not discussed. Questions of methodology (ii) may be touched upon if and when they affect theory (see Secs 7.2, 7.4, and 10.2). In Secs 16f, some attention will be paid to questions of descriptive format (iii) in the grammar approach, due to the fact that major repre­ sentatives of the component approach also adopt the grammar ap­ proach. My own proposals for a descriptive format in variation re­ search (Lieb 1980a; 1983: Part G; 1989; for a brief outline, forthc. a: Sec. 1.4), which presuppose the language approach, fit in with the the­ ory of language varieties to be presented in this essay and differ from the Generative Grammar formats that dominate the literature; Sections 20f, below, adapt my earlier proposals to the theory of variation pres­ ented in this essay. Generally, the most important recent publications on method and description in variation research may well be the collections of survey articles in: Parts VII to IX of Ammon et al. (eds) 1987/1988 (Vol. II), for sociolinguistics; Parts IV to VII in Besch et al. (eds) 1982/1983 (Vol. I), for dialectology; and Parts V and VI of Besch et al. (eds) 1984/1985 (Vol. I), for historical linguistics. Factual questions are again subordinated to theoretical problems. While no attempt will be made to summarize what is known about ac­ tual variation either within or among attested languages, the theoretical proposals must fit what is known. For syntactic variation facts the reader is, in particular, referred to the more specialized articles in Ja­ cobs et al. (eds) forthc. In dealing with the theoretical problems I clearly opt for the language approach and the holistic approach in its weaker version (Sec. 2.1), emphasizing language-internal variation, thus, the weaker version of the variety approach. As a first step, a theory of language varieties - or rather, a theory fragment - will be developed that does not refer to (the linguist's) grammars and ties in with a more comprehensive theory dealing with variation both within and among languages; more specifically, with the framework for language-internal and interlanguage variation devel­ oped in Integrational Linguistics (Lieb 1970, 1982, 1983: Part A).

22

ORIENTATION (I)

As a second step, versions of the component approach will be re­ constructed in a form that allows them to be integrated into the previ­ ously developed theory of language varieties. Integration is achieved also for the versions of the component approach that exemplify the grammar approach. We thus obtain a unified theory of languageinternal variation, in particular, syntactic variation, that ties in with a more general theory of linguistic variation, as demonstrated for typology in Sec. 19. While the unified theory is based on a holistic lan­ guage approach, it does in a way transcend the opposition between ap­ proaches. From a metatheoretical point of view the expanded theory of lan­ guage varieties may be objectionable: the theory makes reference to language-like entities of all major types (1.5), in particular, refers both to languages and to grammars that are descriptions of languages. This makes the theory part of a theory of linguistics rather than of a theory of language, a dubious consequence arising from the fact that the grammar versions of the component approach are directly recon­ structed within the theory of varieties. The grammar approach appears to be losing ground, though; if it is retained, it should eventually be reconstructed so as to allow for a theory of linguistic variation that is part of a theory of language. The theory of language varieties is presented in Parts II ("Setting the stage" — Secs 4 to 8) and III ("A theory of language varieties" — Secs 9 to 13) of this essay. Part IV ("Integrating the component ap­ proach" — Secs 14 to 18) reconstructs several versions of the compo­ nent approach and shows how it may be integrated into the variety ap­ proach through an appropriate extension of the theory of language va­ rieties. Part V ("Extensions" - Secs 19 to 21) considers interlanguage variation, with special reference to typology, and characterizes linguis­ tic descriptions that take variation into account. The theory covers component variables of arbitrary type (phonet­ ic, phonological, syntactic variables, etc. — see (1.13)) and correspon­ ding aspects of language varieties. Actual examples, however, are mostly taken from syntax. I conclude Part I by characterizing the more recent literature on syntactic variation.

3 An Overview of Syntactic Variation Studies

3.1

A classification of current research

Linguistic variation — and syntactic variation in particular — is stu­ died in a number of different areas in linguistics, notably, historical linguistics, dialectology, sociolinguistics, psycholinguistics, contrastive linguistics, and language typology and universality research. It is mainly because of this wide distribution that the actual size and other quantitative aspects of syntactic variation studies are hard to judge. I therefore initiated a bibliographical study (carried through by Annette Bruhns of the Freie Universitat Berlin) on syntactic variation studies published during the ten-year period from 1980 to 1989 and dealing with either language-internal or interlanguage variation. The source material used consisted of the standard bibliographies; more special­ ized bibliographies or reports on variation studies; the tables of con­ tents of nearly all linguistic journals as covered by the German biblio­ graphical service Current Contents Linguistics; and the Lists of Refer­ ences in a number of the most recent relevant papers and monographs. Coverage was to be comprehensive although it was clear from the be­ ginning that complete coverage could not be achieved. 740 titles were collected and classified; when no classification was possible by title alone, studies were inspected whenever feasible. Un­ avoidably, a fairly large number of unclear cases remained. The re­ sults are summarized in diagram (3.1). The diagram reads as follows. An expression immediately above a horizontal line, say, "area of linguistics", names a classification that subdivides a set of variation studies into classes; the classes may over­ lap. The basic set is named by the expression — say, "Syntactic varia­ tion studies 1980-1981" — that is connected with the classification name by a diagonal line. The elements of the classification — the clas-

ORIENTATION (I) 24

1 The years 1980 and 1989 are included. 2 Also included 14 earlier titles, mainly from the seventies. 3 Percentages (rounded). 4 Classes overlap, numbers add up to more than basic number. 5 Includes all work not primarily directed towards specific lan­ guages. 6 Both purely typological and universality studies, in about even numbers. 7 Other area or area unclear or no specific area. s Brackets: ±5. 9 Angles: precise number. I ° Family unclear. II Specific area, but not easily classified on the left. 12 Area unclear or no specific area. 13 Area unclear.

SYNTACTIC VARIATION STUDIES (3)

25

ses into which the basic set is subdivided — are named below the hori­ zontal line; e.g. "typology" names the set of those of the 740 studies which can be assigned to typology. Generally, any expression immedi­ ately below a horizontal line names a set of syntactic variation studies; the name hints at the defining feature of the set. Numbers in brackets or angles refer to number of studies, other numbers indicate percent­ ages. There are three independent classifications (cross-classifications) on the set of all studies, one using theoretical vs. language orientation as a criterion; the other, the 'area of syntax' that a variation study is concerned with; the third, the 'area of linguistics' that a variation study may be assigned to. In addition there are two cross-classifications on the set of language-oriented studies, one using as a criterion: language family to which the language or languages investigated belong (only Indo-European and Non-Indo-European are considered); the other classification is by rough geographical area relative to which the lan­ guages are investigated (thus, a study on English in the U.S.A. is as­ signed to the 'North America' class). 3.2

Conclusions

The bibliographical study summarized in the diagram has its obvious limitations which must be respected in interpreting its results. For one thing, the classes labelled "unclear" are rather large; their ultimate dis­ solution might affect classes in the same classification that have rela­ tively few elements. Even so, we should be justified in drawing the following conclusions: (3.2)

Conclusions a. The sheer number of syntactic variation studies pub­ lished in such a short period is stunning. b. Work with a theoretical emphasis — in a broad sense of "theoretical" — is strongly represented. c. Work of a more 'empirical' type is in its entirety lop­ sided in two respects: (i) Indo-European languages strongly dominate among the languages investigated;

26

ORIENTATION (I)

(ii)

d. e. f.

g.

h.

two thirds of all languages investigated appear to be spoken in Europe, and studied as they are spoken in Europe. Studies appear to be distributed fairly evenly over ma­ jor areas of syntax. Roughly fifty percent of all studies are either from ty­ pology or from historical linguistics (one third). Sociolinguistics and psycholinguistics (including the study of ontogenetic language development) jointly ap­ pear to contribute a mere twenty percent of syntactic variation studies. Contrastive linguistics (mostly of a comparative type rather than programmatic 'contrastive grammar') ap­ pears to be the third largest contributor. Syntactic studies in dialectology (including 'dialect geography') are negligible percentage-wise.

These conclusions exhibit both perseverance and change in the study of syntactic variation, in mostly unexpected ways. 3.3

Old biasses. Syntax in dialectology

Old biasses Conclusions (ci), (f), and (h) testify to the perseverance of structures in variation research that might have been expected to change: just as the rest of linguistics, syntactic variation research is overwhelmingly 'Indo-European' (Conclusion (ci)), for all the emphasis on non-IE lan­ guages in typological work; sociolinguistics continues to have a hard time with syntactic variation (Conclusion (f) — "the most controver­ sial area of research in sociolinguistics", Wald 1988:1164), despite a lot of theoretical efforts spent in the seventies to remedy the situation (see Secs 16f, below); and dialectology (Conclusion (h)) has yet to mo­ dify its traditional emphasis on phonetics, phonology, morphology, and the lexicon. Since geographical dialects are generally considered a prototype case of language varieties, dialectology merits a closer look.

SYNTACTIC VARIATION STUDIES (3)

27

Syntax in dialectology None of the syntactic dialect studies covered by diagram (3.1) is restricted to single dialects. Still, the following table (3.3), based on Wiesinger et al. (1982) and Wiesinger (1987), suggests that their absolute number as given in (3.1) may be too small while the percent­ age should be roughly correct. The table testifies both to the virtual exclusion of syntax from dialectology and to what may be the beginnings of a change. The two Wiesinger studies jointly offer a complete bibliography of studies on the 'grammar' (i.e. aspects of form, from phonetics to syntax) of Ger­ man dialects, covering the period from 1800 to 1985/1986 (coverage of 1986 is incomplete). The following numbers can be established from Wiesinger (i.e. computed on the basis of the two bibliographies): (3.3)

Grammatical studies on German dialects 1800 - 1985/ 1986 Absolute number All studies

5179

Percentage 100

Syntactic studies

132

Syntactic studies 1980-1986

26

16,4

Number of years

7

3,7

2,55

These numbers for the first time substantiate a frequent claim, also made by Wiesinger et al. (1982:.XXIX), that syntax has received little attention in dialectology — how little could hardly have been suspect­ ed: over nearly two centuries of studies on the grammar of German dialects, a puny two and a half percent were devoted to syntax. The precise reasons remain to be established. In particular, we shouldn't jump to the conclusion that there is little syntactic variation among dia­ lects of a single language: 16 % of the syntactic studies on German dia­ lects were published during the last seven years (3,7 %) of the entire

28

ORIENTATION (I)

period, and the discrepancy would be even greater if we had started from 1979 rather than 1980. This recent increase in syntactic dialect studies may or may not re­ present an incipient change. There are two more drastic changes in the field of syntactic variation studies — not only dialect studies — that appear from diagram (3.1): sheer size and the prominence of theory. 3.4

Size of research. The role of theory

Size of research Conclusion (a) contradicts a fairly wide-spread impression among lin­ guists that syntactic variation studies have by and large remained a border-line interest also in current linguistics. Some reasons for this impression appear from Conclusions (c) and (g). While the increase in typological work is generally recognized (Conclusion (e)), the vast increase in work on 'diachronic syntax' (concentrating on actual change rather than on syntactic systems of older stages of languages) has gone largely unnoticed. (It is part of a general revival of historical linguistics over the past twenty years as documented in the Proceedings of the various Conferences on Historic­ al Linguistics, from 1973 [Anderson and Jones (eds) 1974] to 1987 [Andersen and Koerner (eds) 1990].) Moreover, the centre in syntactic variation research is very clearly Europe (Conclusion (cii)), which contradicts a general presupposition — not restricted to North America — that the United States of Ameri­ ca are the centre of linguistics. (In 1989, the European Science Foun­ dation, an organization of the European Community, created, for the five-year period of 1990 to 1994, a Programme in Language Typolo­ gy devoted to the languages of Europe; seven out of its nine Thematic Working Groups study syntactic variation.) Finally, the area of 'contrastive linguistics' is much more alive (Conclusion (g)) than the apparent decline of 'contrastive grammar' in a narrow sense would suggest. A second unexpected feature is brought out by Conclusion (b).

SYNTACTIC VARIATION STUDIES (3)

29

The role of theory Theory consciousness is a hall-mark of current research on syntactic variation. Of course, forty percent of 'theoretical' work does not mean that forty percent of all studies are devoted to developing a theory of syntactic variation, or presenting a format of description, or clarifying method — actually, all major theoretical and metatheoretical proposals go back to the seventies; what forty percent means is a predominantly theoretical orientation even where individual languages are investiga­ ted. Concluding remarks The bibliographical study on recent variation research in syntax was evaluated mainly from a quantitative point of view. For purposes of orientation — the main objective of the present Part I — this should be sufficient. The various approaches to linguistic variation naturally apply to syntactic variation, in particular, to syntactic variation within languages, and were partly characterized in view of such variation. Still, emphasis in the present essay is on a general theory of languageinternal variation rather than on syntactic variation as treated in vari­ ous areas of linguistics, for which a number of articles in Jacobs et al. (eds) forthc. provide good summaries. I therefore turn to my primary topic, first setting the stage for a theory of language varieties.

PART II

SETTING THE STAGE

4

4.1

The Diachronic Perspective

Languages as communication complexes

Language varieties are mostly discussed from a synchronic point of view, i.e. treated as entities that exist at a certain time. This is true even if varieties are characterized — as in classical dialectology — by tracing their development back to an earlier period. In contradistinction I take the position that a diachronic perspec­ tive is fundamental to both languages and their varieties: both should be construed as 'entities through time'. In Lieb (1970), (1982), (1983: Part A), see also (1976: Sec. 6.1), such a conception is worked out in considerable detail for languages but barely touched upon for varieties (attempts to extend a Liebian approach to varieties are made in Wildgen 1974, 1977, and Heger 1982; see also Heger 1992). The con­ ception will serve as a general background in Part III; it is informally sketched in the present Sec. 4. The key term "language" is to be understood as follows: (4.1)

"Language" is to cover a. complete historical languages through time, such as German — High German and Low German, so far — from its beginning to its end some time in the future; and b. certain proper parts of historical languages, to be call­ ed (historical) periods of historical languages, such as Old German (Old High German and Old Low Ger­ man).

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It is assumed that no historical language is a proper part of a historical language. This means, in particular, that no period of a historical lan­ guage is a historical language, and conversely. Furthermore, any historical language is to be a communication complex: a non-empty finite set of 'means of communication'. It fol­ lows that any subset of a historical language, such as a period of the language, is again a communication complex. Any means of communi­ cation is a set of form-meaning pairs or 'sentences', in a defensible sense. Means of communication that are elements of a language corre­ spond to 'idiolects', again in a defensible sense (see Sec. 6, below), and may indeed be called idiolects in the language. Idiolects are thus not identified with systems; rather, for each idiolect there is a system — a system of the idiolect — that determines the idiolect (which is a set of form-meaning pairs). We may wonder how pidgins and Creoles fit into this conception. There are three ways that may be considered (pidgins may well be treated differently from Creoles): (i)

Inclusion among the historical languages. In this case the pidgin or creole is no proper part, hence, no variety, of the underlying languages, see above.

(ii)

Inclusion among the proper parts, in particular, the va­ rieties, of an underlying language. In this case, the pidgin or creole is no historical language.

(iii)

Exclusion from the historical languages and their parts, but not from the communication complexes.

No problem arises for our conception in the first two cases. Since they are the only ones that can be seriously proposed for Creoles, these are covered by the conception. A good case can be made, though, for treating pidgins according to (iii). There is still no problem in applying the notion of communica­ tion complex to pidgins: even if it is no (part of a) historical language, a pidgin may be construed as a non-empty finite set of means of com­ munication. Pidgins would not be the only 'quasi-linguistic' communi­ cation complexes; such complexes also arise in language acquisition, which may be represented as a sequence of means of communication

THE DIACHRONIC PERSPECTIVE (4)

35

whose systems are increasingly similar to, and may eventually be iden­ tical with, systems of means of communication that are elements of languages (see also Sec. 19.1, below). The theory to be developed does not cover 'quasi-linguistic' communication complexes wherever the theory is specific to historical languages. This means, in particular, that the notion of variety does not apply to such complexes. Notions of change remain applicable, as may now be seen. An idiolect is a means of communication for some person during a certain time interval, and there is a system of the idiolect that is relevant for the person during this time, i.e. is essential to the person's mastery of the idiolect. Since a language is construed as a set of means of communication and each means of communication is related to speakers and time in­ tervals, languages, too, are related to speakers and times. This serves as a basis for associating a speech community with the language and for 'locating' the language in time, a prerequisite for describing how the language changes. For a description of change the following notions may be intro­ duced not only with respect to languages but more generally for any communication complex, where we speak of a user community rather than a speech community. First, a cross-section through the user community of a communi­ cation complex is the user community during a time interval when ex­ actly the same means of communication in the complex are in use. A stage of the complex is the set of means of communication in the com­ plex that is associated with a cross-section, i.e. the stage is the set of means of communication that are means of communication for any users during the time of the cross-section. The relation of physical time Earlier (is-earlier-than) between users may serve as a basis for defining a 'derived' temporal relation of precedence between cross-sections, and this in turn allows introducing a 'derived' temporal relation of precedence between stages. A section of a communication complex may then be defined as a stage of the complex, or the union of a set of consecutive stages. (A historical period, or period, of a historical language is as a rule no section of the lan­ guage but still contains a section as a subset.)

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So far we have abstracted away from individual means of commu­ nication, e.g. idiolects, only in a weak sense, by simply using the no­ tion of set. In particular, the traditional notion of system was not yet involved in characterizing languages and their periods. 4.2

Systems for communication complexes

Starting from systems of individual means of communication, we obtain systems for communication complexes by taking a number of steps. First, given a communication complex we associate with it a system class for the complex. This is a set of systems of means of commu­ nication that contains, for each means in the complex, exactly one sys­ tem of the means (which must be relevant for some person who is a user of the complex.) The systems in a system class may have shared properties. Consid­ er, for example, the 'standard clause property' (SCI) defined as fol­ lows ("S" stands for any system of any means of communication, in particular, for any idiolect system; "c" for any 'component' of any idi­ olect system S, in particular, any syntactic unit of S; for a slightly more general interpretation of the variables, see (4.8), below): (4.2)

Definitions a. For any idiolect system S [i.e. any system of an ele­ ment of a historical language]: c is a standard clause of S iff [if and only if] c is a onepredicate clause of S that is introduced by a particle or pronoun (counted as part of the clause) and whose predicate constituent has a finite part. b. SCI ["the standard clause property"] = the property of being an idiolect system S such that there are standard clauses of S.

(Definition (a) determines — in a preliminary fashion — what would be called "eingeleiteter einfacher Nebensatz" in German grammar.) Suppose that the communication complex we are dealing with is the set

THE DIACHRONIC PERSPECTIVE (4)

37

of all contemporary German idiolects, and consider a system class for the complex. Then each system in the class has the standard clause property. It is shared properties of this kind — properties of systems of in­ dividual means of communication — that are the building blocks of systems for sets of means of communication: a system for a communi­ cation complex is a 'construct from' properties shared by all systems (of individual means of communication) that belong to a given system class for the complex; it is thus a construct from properties shared by relevant systems of all means of communication in the complex. In the simplest case we might interpret "construct from" as "set of'; a system for a communication complex is then a set of properties shared by rel­ evant systems of all elements of the complex. We will indeed adopt this view for Part III even if it may have to be eventually replaced by a more sophisticated version. Thus, the standard clause property (SCI) — a property of idiolect systems — is an element of a system for 'con­ temporary German'. More specifically, SCI is an element of the syntactic part of a sys­ tem for contemporary German since SCI is a property of idiolect sys­ tems that concerns only the syntactic part of such systems. This exem­ plifies the way in which subsystems can be distinguished within a sys­ tem for a communication complex that is a stage — or larger section — of a language. The question of subsystems will, however, barely be touched upon in Part in. Both historical languages and their historical periods are commu­ nication complexes. We may therefore assume that it is not only stages that may have systems but also larger sections, or else, periods of his­ torical languages, or even entire historical languages. (The Saussurean conception by which stages would have to be identified with systems is altered: a stage is not itself a system but may have a system, and there may be systems for non-stages. Systems for communication complexes, such as historical languages, may have 'states', see Sec. 4.5, below. The Saussurean notion of état de langue is thus split up into two concepts, stage of a language and state of a system for the language.) We would not, of course, allow as a system for a complex just any set of properties shared by the systems of all means of communication

38

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in the complex; it may here be left unspecified exactly what additional conditions a set of properties must satisfy so as to count as a system. In any case there may be communication complexes for which no systems exist. 4.3

Different systems for a stage: example

We may have different systems for a single stage of a communication complex; actually, this is true not only of stages. The following exam­ ple, which continues (4.2), again starts from properties of idiolect sys­ tems: (4.3)

Definitions a. verb-final ["the verb-final property"] = the property of being an idiolect system S such that (i) S has SCI [i.e. there are standard clauses of S], (ii) final position of finite verbs is the dominant word order for standard clauses of S. b. free-order ["the free-order property"] = the property of being an idiolect system S such that (i) S has SCI; (ii) there is no dominant word order for standard clauses of S.

(In both (a) and (b), condition (ii) would have to be made more pre­ cise. "Dominant word order" is to be interpreted not in frequency terms but by reference to sentence structures.) The three properties SCI, verb-final, and free-order are related as follows: (4.4)

a. verb-final implies SCI but — for empirical reasons — not conversely. b. free-order implies SCI but — for empirical reasons — not conversely. c. verb-final implies non-free-order [i.e. excludes freeorder]. d. free-order implies non-verb-final.

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39

The meaning of "implies" is obvious. Because of (a) and (b) we may say that SCI is more abstract than both verb-final and free-order. Now assume two stages of German, one from the twentieth centu­ ry and one from the ninth. Free-order is a property of the systems of all idiolects in the earlier stage, and verb-final a property of the sys­ tems of all idiolects in the later (for the factual basis of this claim — whose second part may be doubtful — see the relevant syntax articles in Besch et al. (eds) 1984/1985). Therefore, verb-final is not a proper­ ty of the idiolect systems of the 9th century stage, and free-order not a property of the idiolect systems of the 20th century stage, by (4.4c,d), and SCI is a property of the idiolect systems of either stage, by (4.4a,b). Now suppose that each of the three properties is an element of sys­ tems connected with the two stages of German. We may postulate three such systems: a free-order, verb-final, and SCI system. The free-order system, which contains free-order as an element but does not contain the other two properties, is a system for the 9th century stage but not the 20th century stage; the verb-final system, which contains verb-final as an element but does not contain the other two properties, is a system for the 20th century stage but not the 9th century stage; and the SCI system, which contains SCI as an element but does not contain the oth­ er two properties is a system for either stage. (There may be several systems of each of the three types; we here assume that exactly one system of each type has been selected.) If not only SCI but all other properties in the SCI system are suffi­ ciently abstract, we may assume that the SCI system is indeed a system for any stage of German up to the present, and thus for German itself from its beginnings to this day. 4.4

Chains of systems

We may generally assume that the SCI system is abstracted from both the free-order and the verb-final systems; i.e. the SCI system is related to the free-order system (analogously, to the verb-final system) at least as follows: (i) each property in the first system is implied by some property in the second that it either does not imply or with which it is

40

SETTING THE STAGE (II)

identical; (ii) some property in the first system is not a property in the second (hence, is more abstract than some property in the second); and (iii) each property in the second system implies some property in the first. We may thus form two sequences of systems, one consisting of the free-order system followed by the SCI system, the other by the verbfinal system followed by the SCI system. The example highlights an essential point for languages and, gen­ erally, communication complexes: it is not just a single system that may be associated with a given stage of a language but an entire chain of systems for the stage such that each system in the chain is abstracted from its predecessors. As we travel up the chain, we reach systems that are also systems for other stages of the language, or systems for larger sections, until we arrive at a system for the language itself. The chain may not end here but go on to a system for a language together with its genetic predecessor, or eventually for the languages of an entire language family. A theoretical endpoint is a set of properties shared by the systems of arbitrary idiolects in arbitrary human languages. On a sufficiently liberal view of systems we may indeed assume that certain sets of this type are systems for 'human language', i.e. for the union of the set of human languages. A system that is abstracted from a given system for a communica­ tion complex, such as a language or stage or period of a language, is again a system for the complex but of a higher degree of abstraction. Any system for a communication complex is a set of properties shared by systems of the means of communication that belong to the complex; the more abstract and general the properties, the higher the degree of abstraction of the system. Allowing systems of different degrees of abstraction is an impor­ tant step towards distinguishing historical languages from their (histor­ ical) periods. We may postulate a smallest number n such that any his­ torical language has a system whose degree of abstraction is no greater than n, and a similar number m < n for periods of historical langua­ ges: intuitively, historical languages must exhibit a certain amount of systematicity, and so must their periods but for them more systematicity is required than for the languages.

THE DIACHRONIC PERSPECTIVE (4)

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As appears from the example a system for a communication com­ plex is also a system for any stage of the complex. It is, however, in different 'states' with respect to different stages. 4.5

States of systems. Language development

A state of a system for a communication complex is, roughly, the 'po­ sition' the system occupies in the system chains associated with a given single stage of the complex, in a specifiable sense of "position". Consider, once again, the SCI system of Sec. 4.3 as a system for (i) German up to the present and (ii) the 9th century stage of German. The SCI system figures in a chain of systems for the stage in which it is reached via the free-order system. The SCI system also figures in a chain of systems for the 20th century stage in which it is reached via the verb-final system. We may therefore say the SCI system — a sys­ tem for German up to the present — is in different states: a free-order state and a verb-final state, to use suggestive names. Each state is a construct from chains of systems for a stage of German. As explained in Sec. 4.1, there is a relation of temporal precedence between stages that is based on temporal precedence between cross-sections through the user community (this, in turn, is based on the Earlier relation in the physical world). Since states of a system for a complex are associated with stages of the complex, we may use tem­ poral precedence between stages to define a relation of temporal precedence between states. Temporal precedence between states plays an important role in re­ constructing the notion of 'development' (one linguistic entity develops into another), a major task for any theory of language change. Consid­ er the following statement ("OG" for "Old German", "ModG" for "Modern German", "G" for "German"): (4.5)

a. [Informally:] OG free order in standard clauses develops into ModG final position of finite verb. b. [Abbreviated:] OG free-order →G ModG verb-final

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SETTING THE STAGE (II)

c. [Set-theoretically: ] (G, (OG, free-order), (ModG, verb-final))  → By (4.5c), → (read: develops into) is a three-place relation whose members are, in particular, (i) a historical language, (ii) a pair consist­ ing of a historical period of the language and a property of idiolect systems (see (4.3) for "free-order"), and (iii) a second pair of the same type. (The relation → should be made to cover development in arbi­ trary sets of idiolects considered in historical linguistics.) The three statements in (4.5), meant to be synonymous, may be tentatively explicated as follows ("D", "D 1 ",... stand for any commu­ nication complexes; "S 1 ", "S 2 " for any systems of means of communi­ cation; "σ" stands for any systems for communication complexes, "Q 1 ", "Q 2 " for any states of systems σ): (4.6)

There are σ, Q1, Q2, D1 and D 2 such that: a. σ is a system for German [possibly, German-up-tothe-present]; b. Q1 is a 'free-order state' of σ; c. Q2 is a 'verb-final state' of σ; d. D 1 is an OG stage of German; e. D 2 is a ModG stage of German; f. Q1 is associated with D1; g. Q2 is associated with D2; h. Q1 precedes Q2 in σ and German. i. for any S1 and S2, if S1 is a system of an element of D1 and S2 a system of an element of D2, then 'free-order as a property of S 1 corresponds to verb-final as a property of S 2 '.

The inverted commas in i. isolate a part whose interpretation poses a notorious problem (there must be some kind of 'functional analogy' between the 'starting-point' and the 'endpoint' in a case of language de­ velopment). Whatever the details, the proposed framework provides a versatile formulation of the diachronic point of view in linguistics that allows

THE DIACHRONIC PERSPECTIVE (4)

43

its application not just to languages but also to larger sets (such as the union of a set of languages) and to proper subsets of languages, in par­ ticular, language varieties. 4.6

Lists of variables

We have outlined a theoretical framework in which a fairly large number of entities are distinguished, entities that must be talked about in a general way, i.e. by means of variables. (Once again, variables, in this sense, are symbols of the linguist's language, not to be confused with linguistic variables as defined in (1.6).) The following two lists collect, for reference purposes only and in systematic order, the most important variables to be used in Part III and, mostly, throughout this essay; if any variables are reintroduced at later points in the essay, this will be done — with a few exceptions in Secs 16 to 18 — in agreement with the two master lists (a colon means "each stand for" or "each have as their values"): (4.7)

List 1: variables from set theory a. "x", "x 1 ", ... : any set-theoretical entity (but not (e), (f) or (g)) b. "M", "M1", ... : any set of entities x c. "N", "N1", ... : any set of sets of entities x d. "O", "O 1 ",... : any set of sets of sets of entities x e. "α", "α 1 ", ... : any (admissible) property of set-theo­ retical entities x f. "A", "A 1 ",... : any set of α's g. "R", "R 1 ', ... : any set of pairs (M, α)

(4.8)

List 2: other variables a. "n", "m", "i", " j " [also with number subscript]: any non-negative integer b. "V", "V 1 ", ... : any object or event in space-time, in particular, any person c. "t", "t1", ... : any interval of time

44

SETTING THE STAGE (II)

d. "C", "C 1 ", ... : any set of form-meaning pairs of the 'sentence' type, in particular, any means of communi­ cation e. "π" (pi), "π 1 ", ... : any property of entities C f. "  " (capital pi), " 1 ", ... : any set of properties π g. "D", "D 1 ", ... : any set of entities C, in particular, any communication complex (such as a historical language or period of a historical language) h. "E", "E 1 ", ... : any set of entities D i. "F", "F 1 ", ... : any set of entities E j . "G", "G 1 ", ... : any set of entities F k. "S", "S 1 ",... : any system of any C 1. "c", "c 1 ", ... : any 'component' of any S that is a sys­ tem of an element C of a historical language m. "T", "T 1 ", ... : any set of entities S n. "ø" (phi), "ø1", ... : any property of entities S o. "σ" (sigma), "σ1" , ... : any set of properties ø p. "Σ" (capital sigma), "Σ 1 ", ... : any set of entities σ Note. A variable followed by an asterisk, such as "D*", or the italici­ zed version of a variable, such as "D", is an ambiguous constant, refer­ ring to a single though unspecified entity that belongs to the values of a corresponding variable ("D"). I continue setting the stage for the theory in Part III by explaining and motivating the key notion of 'variety structure' (Secs 5 to 8).

5 Basic Ideas

5.1

The variety relation

As briefly pointed out in Sec. 1.4, "variety" is a relational term; in this it agrees with expressions like "period" and differs from the non-rela­ tional "language": German is a language, but Bavarian is a variety of German. (Treating expressions like "variety" and "dialect" not as rela­ tional but as property terms on a par with "language" leads, in particu­ lar, to the mistaken attempts to distinguish 'languages' from 'dialects', attempts that are bound to fail; for a recent example, see Hudson 1980: Ch. 2.) Both the first-place and the second-place members of the variety relation are language-like entities of the same type. On our account the second-place members are, in particular, historical languages con­ strued as communication complexes: i.e. as non-empty finite sets of means of communication, sets with which systems of various degrees of abstraction can be associated. Now in saying that Bavarian is a vari­ ety of German we treat Bavarian as an entity of the same kind as Ger­ man. Just as the second-place members, the first-place members of the variety relation — e.g. Bavarian — are communication complexes that have systems of various degrees of abstraction. This also means that the diachronic perspective is to apply not only to languages but to vari­ eties as well: all notions introduced in Sec. 4 that were not explicitly restricted to languages also cover varieties, which are thus treated, from the very beginning, as historical entities. 5.2

Details

Bavarian must certainly be a 'part' of German. If both Bavarian and German are communication complexes, i.e. sets, "part" may be under-

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stood simply as "subset"; this makes the variety relation a special case of the subset relation. Among the varieties of a historical language there are its temporal varieties or periods, the only varieties that are languages though not historical languages. Periods may again have varieties. For example, Medieval German — a period of German, see Sec. 8.1, below — intersects with Bavari­ an, a dialect of German. We may simply take this intersection, to be called Medieval Bavarian, as a variety of Medieval German, hence, of German, assuming that Variety is a transitive relation (which is not en­ tirely unproblematic — see Sec. 12.2, below). It is important to realize that Medieval Bavarian, though a variety of German, may not be a variety of Bavarian: German and Bavarian each have their own histories; Medieval German is determined by the history of German, and determining a certain subset of Bavarian by reference to the history of German (e. g., Medieval Bavarian as the in­ tersection of Medieval German and Bavarian) may not result in a tem­ poral variety of Bavarian — essential changes in a regional dialect of a historical language may happen right in the middle of a period of the language. A period of a historical language, such as Medieval German, has its own stages and may have its own periods, which are its temporal varieties. As for the period's non-temporal varieties, we may simply identify them with its intersections with non-temporal varieties of the language. This means that the non-temporal varieties of a historical language — say, Bavarian — must be given in order to determine the non-temporal varieties of the language's periods — say, Medieval Bavarian as a dialect of Medieval German (see also Sec. 8.4). So far we have allowed only languages (either historical languages or their periods) to have varieties. It is, however, customary usage to speak of varieties of varieties other than periods, e.g. Southern Bava­ rian is a variety of Bavarian which is a variety (but not a period) of German. Furthermore, if the Variety relation is transitive, any variety of a period of a historical language is a variety of the language since the period is. It appears, then, that we are confronted with a single basic prob­ lem: determining the varieties of historical languages. This would au-

BASIC IDEAS (5)

47

tomatically cover periods of historical languages and varieties of peri­ ods, due to the fact that the periods of a historical language are count­ ed among the varieties of the language. It is for solving the basic prob­ lem — determining the varieties of a historical language — that the notion of variety structure is introduced. 5.3

Variety structures as classification systems

The varieties of a historical language are 'given through' a system of classifications whose source is the language itself: this is the essential idea of the theory of varieties presented in Part III. The idea is by and large compatible with positions that are implicit in traditional discus­ sions of varieties, allowing for the fact that such discussions usually center not directly on historical languages but on their periods. (Habel, for one, comes close to including the idea explicitly in his own frame­ work, cf. Habel 1979: Sec. 2. The notion of variety structure is ana­ logous to Coseriu's 'architecture' or 'external structure' of a historical language — e. g., Coseriu 1988/1981:33 —, developed from Flydal's [1952] seminal architecture de langue. Flydal applies his notion only synchronically to an état de langue', similarly, if less clearly, Coseriu, who assigns dialectology to synchronic linguistics: 1988/1981:37. Nei­ ther envisages an actual classification system.) A classification on a given set — to be called its basis — is a set of (at least two) subsets that may partially overlap and jointly exhaust the given set. Two different classifications with the same basis are crossclassifications on their shared basis. If we take a classification and use one of its element sets as the basis of a new classification, then the sec­ ond classification is a suhclassification with respect to the basis of the first; and so is any classification obtained by repeating this procedure with an element set of a subclassification. A classification system on a set — to be called its source — is a non-empty set of classifications such that each is either a classification on the source or is a classification on some subset of the source that it­ self is an element of some classification in the set. A classification sys­ tem may, but need not, contain cross-classifications, subclassifications, or both.

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These informal definitions, to be made precise in Sec. 9, may suf­ fice to explain the sense in which the varieties of a historical language are said to be 'given through' a certain classification system on the lan­ guage: the varieties are simply those subsets of the language which are elements of elements of the classification system; note that varieties may overlap, even in a single classification. The system itself will be called the variety structure of the language. Saying that the varieties are 'given through' the variety structure does not mean that the concept of variety must be definable by the con­ cept of variety structure; "variety" may indeed be taken as a primitive term on which the definition of "variety structure" partly depends (see Sec. 9.5), As argued in Sec. 5.2, it is not only historical languages but also their varieties that may have varieties; hence there should be a notion of variety structure by which a variety of a historical language, not just the language, may have a variety structure. Consider, for this pur­ pose, a variety of a historical language and the set (possibly empty) of classifications in the variety structure of the language that are directly or indirectly based on the variety. It is this set that may be taken as the variety structure of the variety in the language. Obviously, the set is either empty or again a classification system, a system whose source is the variety. We thus arrive at two concepts of variety structure, one for his­ torical languages and another for their varieties; obviously, the second can be defined by means of the first (for definitions, see Sec. 9.5, be­ low). 5.4

Classification criteria: external and system-based

The classifications in a variety structure are not arbitrary: they are de­ termined by specific sets of criteria. Each criterion may be understood as a property of idiolects that delimits a certain variety, i.e. identifies the variety as the set of all idiolects that have the property. Criteria may be of arbitrary complexity; in particular, a criterion may be the 'conjunction' of various more simple properties. Criteria may be either external or non-external, in particular, system-based.

BASIC IDEAS (5)

49

External criteria are based on non-language entities: times, areas, social classes, situation types, individual persons, etc. A simple way of construing such criteria would be as follows (this is essentially Kanngießer's [1978] approach). We assume a system of classifications on the speech community that is defined by reference to the non-language entities. All external criteria are properties of the following type: being an idiolect that is used by speakers that belong to a certain class in the classification sys­ tem on the speech community. The problem with this approach is, of course, that for some lan­ guages, no such classification system may result in properties all of which qualify as variety-determining criteria: the classes of idiolects defined by some properties may not satisfy all conditions for a variety; in particular, the classes may not be definable by system-based proper­ ties. For this reason I will propose a different way of construing exter­ nal criteria (Sec. 10). System-based criteria are properties of idiolects defined by refer­ ence to systems, more precisely, by reference not to idiolect systems but to systems for sets of idiolects (see Sec. 4.2 for the difference). Very roughly, a system-based criterion is the property of being an idi­ olect that is 'covered' by a certain system of this type, and the criterion delimits a variety by identifying it with the set of all idiolects that have the property. The logical notion of classification criteria will be defined in Sec. 9.2; the linguistic concepts of external and system-based criteria are made precise in Secs 10f. 5.5

Criteria correlation

It is a fundamental feature of all variety research that it attempts to correlate 'the linguistic' and 'the non-linguistic'. There is both con­ fusion and difference of opinion as to their mutual roles: do we start from the linguistic or from the non-linguistic, or are both of equal im­ portance in delimiting varieties? In Part III, I will take the latter posi­ tion and assume a simple correlation between external and systembased criteria: each variety is independently delimited by an external and a system-based criterion (the two criteria need not, of course, be

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equally accessible, or applied with equal ease, but this is a point of methodology not theory). This then is the form that the correlation idea takes in my theory (Sec. 11.5). As a consequence, no system-based property of idiolects may figure as a criterion delimiting a variety unless the system-based prop­ erty is matched by a property based on non-language entities such that both delimit the same set of idiolects — and conversely. Since each variety is delimited by criteria of either type, the cor­ relation between 'the linguistic' and the 'non-linguistic' indirectly ap­ plies also to idiolects, idiolect systems, and components and properties of idiolect systems, once these entities are properly 'located' within the variety structure (Secs 12f). A strong version of the correlation idea supports the position that variety structures exist and are unique, rather than being methodolog­ ical expediencies (see Secs 7.3f, for discussion). Still, choosing a strong version may be considered as tentative, and indeed, there is little in the theory of Part III that actually depends on the Correlation Theorem (Sec. 11.5). The basic ideas of my theory of varieties have now been charac­ terized but should still be defended. This holds, in particular, of the key notion of variety structure, to be justified further in Secs 6f and applied, in a general way, in Sec. 8.

6 In Defense of Variety Structures: The Problem of Idiolects

6.1

Introduction

My defense of variety structures will take the following form: the no­ tion of variety structure is questioned (6.1) for three reasons (6.2), (7.1) and (7.6). Each reason is supported by claims, which are individ­ ually refuted: the first reason in the present Sec. 6; for the second rea­ son, see Secs 7.1f; for the third, Secs 7.3f. The questioning of the no­ tion of variety structure (6.1) is thus shown to be unwarranted. The first reason (6.2) concerns idiolects, the second (7.1) historical langua­ ges, and the third (7.6) the identification of variety structures with classification systems. Consider, then, the following claim: (6.1)

Claim. The notion of variety structure of a historical lan­ guage is problematic if not useless, either generally or on the conception proposed in Sec. 5.

This may be based on the following (6.2)

First Reason. On the conception proposed variety structure of a historical language built up from idiolects construed as sets of pairs. Such a notion of idiolect — possibly, is problematic if not useless.

in Sec. 5, the is ultimately form-meaning any notion —

This is not the place to discuss or defend the various conceptions of id­ iolect that may be found in the literature (cf. Oksaar 1987). The First Reason primarily refers to idiolects conceived as means of communi-

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cation in the sense of Sec. 4, which exemplifies a specific type of idio­ lect conception. There are four major claims (6.3) to (6.6) by which the First Rea­ son can be supported. 6.2

Idiolects as 'external' and 'speaker specific'

The first two claims concern the 'external' and 'speaker-specific' na­ ture of idiolects. (6.3)

Supporting Claim. As conceived in Sec. 4, idiolects are 'external languages' in the sense of Chomsky (1986). 'Ex­ ternal languages' are useless constructs in linguistics that should be rejected in favour of 'internal languages' (men­ tal mechanisms).

Refutation. The second part of the claim has been advocated most pro­ minently by Chomsky, e.g. in (1986). It is seriously questioned and re­ jected in Lieb (1987), (forthc. c), Carr (1990), Katz and Postal (1991). But suppose we do away with idiolects on the grounds that they are 'external languages'. Our conception of idiolects also provides systems by which idiolects are determined. Suppose that, as a second step, we put 'internal languages' (mental mechanisms) in the place occupied by idiolect systems (clarifying the point of whether there is anything — a set of 'internal sentences'? — that is 'determined by' such 'internal lan­ guages'). Except for a few obvious modifications, the variety theory outlined in this essay would remain unaffected, except for its interpre­ tation — true enough, an important change. (See also Sec. 15.3, below.) (6.4)

Supporting Claim. As conceived in Sec. 4, an idiolect is an 'external' set of sentences that is a means of communi­ cation for an individual speaker and may well be 'speak­ er-specific' (be an idiolect of just a single speaker). This makes it impossible to account for the social aspects of ei­ ther languages or linguistic communication.

This is a serious objection whose refutation would go well beyond the limits of the present essay; the reader is therefore referred to Lieb

THE PROBLEM OF IDIOLECTS (6)

53

(1983: Sec. 2.3) for the kind of counterarguments that I would consid­ er valid. The following claim questions the status of idiolects as entities in between sentences on the one hand and languages and their varieties on the other. 6.3

Idiolects as 'intermediate' (6.5)

Supporting Claim. As conceived in Sec. 4, idiolects have no theoretical justification as entities intermediate between individual sentences and languages and their varieties, which both should be construed simply as sets of sentences not as sets of sets of sentences.

This claim is implicit in all work done within the Evaluation Grammar approach (see Secs 2.3 and 16f), where it is made explicit in Habel's discussion (1979: Sec. 2.1.3) of part of a 1977 working paper by Lieb, a part that essentially agrees with Lieb (1983: Ch. 1). Refutation. Taking historical languages and their varieties simply as sets of sentences leads to a theoretical impasse: (i) Such a set must be determined by a system (represented as a grammar or by a grammar, on the Evaluation Grammar approach), (ii) Such a system has no indi­ vidual 'psychological reality' (in Generative Grammar terms, it does not represent any individual speaker's competence, be this speaker real or 'ideal': nobody 'knows' German as a historical language in its en­ tirety, and an 'ideal speaker' who does is obviously a useless ad hoc construct), (iii) Linguistic systems that determine sentences should have individual 'psychological reality'. — The desirability of (iii) is not questioned in Evaluation Grammar, and the resulting problem was noticed but played down (e.g. in Habel 1979: Sec. 4.1.1) essentially un­ til Bierwisch (1988). Bierwisch gets close to reassigning a basic theo­ retical role to systems (grammars) that determine sets of sentences which, on our account, would each be the union of a 'personal varie­ ty', i.e. the union of the set of idiolects of a single speaker that all be­ long to the same language. This would reintroduce speaker-specific sets of sentences as intermediate entities, and there is independent justi­ fication for choosing each idiolect in a personal variety, rather than

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the variety's union, as an intermediate entity. It is exactly avoidance of the Evaluation Grammar impasse that provides a major justification for idiolects as entities intermediate between sentences on the one hand and languages and their varieties on the other. The last claim in support of the First Reason would be accepted by many linguists. 6.4

Idiolects as 'homogeneous' (6.6)

Supporting Claim. As conceived in Sec. 4, an idiolect is a 'speaker-specific', 'intermediate' set of sentences that is also 'homogeneous', i.e. determined by a single system. Homogeneous sets of sentences of this kind are rarely if ever found.

Traditional objections against homogeneous sets of sentences receive their strongest support from (i) phenomena of 'style-shifting' (change from one register of a language to another in a single, complex situa­ tion, cf. Labov 1972b); this may, in principle, occur in a single utter­ ance (cf. the famous example in Labov 1970, to which Labov at the time still refers as a potential case of "code-switching": 1972a: 189); and (ii) from the phenomenon of 'code-switching' (change from one language to another in the same utterance — see Poplack and Sankoff 1988; also Poplack et al. 1987): it seems that some actual utterances cannot be explained on the basis of homogeneous sets of sentences; so this may be a useless notion to begin with. Refutation. As argued already in Lieb (1983: Secs 1.4f), claims like (6.6) lose much of their apparent force once an idiolect is clearly dis­ tinguished from a 'personal variety' of a language, i.e. a speaker's total share of the language, a distinction embodied in the theory of varieties in Part III (see Sec. 8.3). A personal variety is a set of idiolects each of which is homogeneous, i.e. determined by a single system; and there is a system for the set — a construct from shared properties of the sys­ tems of idiolects in the set — that may or may not be said to 'deter­ mine' the union of the set of idiolects. (This is similar to the structu­ ralist idea of 'coexistent systems'; for discussion, cf. Thelander 1988, where existence of such systems is, however, treated as a problem of

THE PROBLEM OF IDIOLECTS (6)

55

empirical detail rather than theory building.) For the problems raised by style-shifting and code-switching we may now envisage three solu­ tions: a.

First solution Some idiolects in a single personal variety are 'conflated', and so are their systems: we liberalize our notion of 'a single system' and allow some idiolects to contain other idiolects (e. g., idiolects that belong to different 'styles') as proper subsets (for further discus­ sion, see Sec. 6.5). b. Second solution The apparent shift or switch is reinterpreted as use of a single idi­ olect that is 'mixed' only if compared to two or more other sys­ tems (cf. the convincing counterarguments made in Weydt and Schlieben-Lange 1981:136ff against Labov's 'code-switching' ex­ ample). c. Third solution (i) Two or more different idiolects of the same speaker are used that belong α. to the same personal variety in a single language (e. g., as in style-shifting), or ß. to different personal varieties in different languages (as in code-switching), and (ii) to the extent that systematic features of such use are not cov­ ered by the idiolect systems, they are accounted for through a 'theory of speech' that may or may not be restricted to specif­ ic languages. The three solutions must obviously not be taken to present alternatives. Solution 1 may be fine to reconcile homogeneity and style-shifting in a single utterance but can hardly be extended to all idiolects in a person­ al variety, and certainly not to the case of 'code-switching'. As to Solu­ tions 2 and 3, either may be adequate depending on the situation; Solu­ tion 2, which excludes 'code-switching', would for example apply in cases analogous to the use of Creoles. (All three solutions allow for the construction of single grammars of an appropriate type; existence of 'code-switching grammars', such as the ones proposed by Sankoff and Poplack 1981, does not decide between Solutions 2 and 3.)

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In summary, then, claim (6.6) can be refuted, too. In this context the notion of homogeneity requires some comment. 6.5

Remark: concepts of homogeneity

In (6.6), "homogeneous" was understood as "determined by a single system". There appears to be a second sense of "homogeneous" when applied to idiolects, roughly: "belonging to a single variety of a lan­ guage". This is indeed a useless concept: given the fact that the variety structure of any historical language contains cross-classifications, any idiolect must simultaneously belong to several varieties of the lan­ guage. We may, however, retain the motivation for "homogeneous" in its second sense by adopting one of the following definitions: (6.7)

(Definitions) a. C is homogeneous in D iff (i) C  D; (ii) there is no proper subset C1 of C and variety D1 of D such that C1 G D1 b. C is homogeneous in D iff [as in (a), but adding "and C  D 1 " to (ii)].

Intuitively, (a) means that no proper subset of C may belong to any va­ riety of the language; (b) means, more weakly, that no proper subset of C may belong to a variety to which C itself belongs. I would indeed adopt "homogeneous" in the sense of either (a) or (b) rather than un­ derstand it as in (6.6). We are not forced to choose (a) (as Habel 1979: Sec. 2.1.3 mistakenly appears to assume in his criticism of Lieb); (a) is simpler but (b) must be chosen if certain varieties (in particular, styles or registers) are best construed as sets whose elements are idiolects that are subsets of certain other idiolects (for discussion, see already Lieb 1970: Sec. 4.2). The possibility of reinterpreting "homogeneous" along the lines of (6.7) may also be adduced against claim (6.6). We now turn to the second and third major reasons that could be given for rejecting variety structures.

7 In Defense of Variety Structures: Classifica­ tion Systems on Historical Languages

7.1

Historical languages: general objections

Claim (6.1) can also be based on the following (7.1)

Second Reason. The very notion of a historical language is problematic if not useless, either generally or on its conception in Sec. 4.

First, there are two general claims, independent of the conception pro­ posed in Sec. 4, that support (7.1). (7.2)

Supporting Claim. The notion of a historical language is a useless concept in linguistics generally.

Historical languages as objects of linguistics are rejected not only by Chomsky, e.g. (1986), but also by some non-Chomskyans: Hudson (1980:37), Carr (1990: Sec. 6.1). Refutation. (7.2) is incompatible with basic facts concerning linguistic variation. Variation among idiolects, idiolect systems or whatever else is assumed in their place tends to lead to a clustering of such entities in correlation with non-linguistic factors, and the same is true of varia­ tion among the clusters. Notions like 'historical language' in Sec. 4 are therefore useful, and may be indispensable, for dealing with linguistic variation. (7.3)

Supporting Claim. The notion of a historical language cannot be made precise.

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SETTING THE STAGE (II)

Refutation. It is true that explication of the concept presents a serious challenge; still, the claim is unwarranted. There has been at least one serious attempt at a precise explication of the notion of historical lan­ guage (Lieb 1970: Ch. 17), and there is a set of definitional criteria that can be used in any such attempt (see, e. g., Ammon 1987: Sec. 2). The two following claims against natural languages are directed specifically against the conception of historical language proposed in Sec. 4. 7.2

Historical languages: specific objections (7.4)

Supporting Claim. Assuming a concept of historical lan­ guage as in Sec. 4, no historical language is ever com­ pletely available to the investigator; hence, no historical language can be effectively studied for aspects like language-internal variation that involve the language as a whole.

Refutation. This is a methodological claim and as such, invalid: due to the hypothetical nature of all research in the 'empirical' (not just the natural) sciences, effective study of an object from a holistic point of view does not presuppose complete availability of the object. It may, however, be true that practical problems increase for variation studies when languages are, from the very beginning, construed as languages 'through time'. (7.5)

Supporting Claim. On the conception of Sec. 4, historical languages, and also language varieties and idiolects, are not construed as systems or constructs from systems. This is not only contrary to linguistic tradition but is generally an inferior conception.

Refutation. Linguistic tradition is not really unified on this point. More importantly, a traditional Saussurean opposition of langue as sys­ tem vs. parole as speech is known to be inadequate because of its in­ ability to account for sentences understood as objects different from concrete utterances; sentences are, as it were, intermediate between system and speech. Making languages, language varieties, and idiolects

CLASSIFICATION ON HISTORICAL LANGUAGES (7)

59

constructs based on the ontological level of sentences, we can deal both with the systematic aspects of languages, language varieties, and idio­ lects and with their relation to speech. Such a conception is superior, rather than inferior, by avoiding a traditional paradox: all linguistic entities belong either to langue or to parole — sentences are linguistic entities — sentences do not belong to parole because they differ from concrete utterances — sentences do not belong to langue because they are determined by, rather than part of, langue. This refutation, although primarily concerned with languages, also takes care of a potential objection against idiolects, not yet considered in Sec. 6. There remains the objection against historical languages in the sense of Sec. 4 that they are construed as sets of idiolects and idiolects are subject to the objections raised in Sec. 6. This objection need not here be considered since refuting the claims in Sec. 6 takes care of it. We now turn to the last major reason that might be offered for ac­ cepting claim (6.1). 7.3

Classification systems: the problem of criteria

The third major reason that might be given for rejecting the notion of variety structure concerns its nature as a classification system: (7.6)

Third Reason. On the conception of variety proposed in Sec. 5, the varieties of a historical language are 'given through' exactly one classification system on the language, viz. the variety structure of the language. Both the exist­ ence and the uniqueness of such a classification system is problematic.

Existence of the system may be questioned mainly by pointing out problems — or apparent problems — that are raised by classification criteria (supporting claims and refutations will be formulated in a more condensed form; for the uniqueness problem, see Sec. 7.4). (i)

Vagueness Claim: Criteria for varieties, if they exist, or names of criteria are vague. This means that varieties are 'ill-de-

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fined'; hence, this is also true of the variety structure, which is a set of sets of varieties. But set theory doesn't allow 'ill-defined sets'. Such an objection may be motivated by a realization that 'similarities' and 'degrees' must be accounted for. In this case, the objection can be countered (see (ii)). Otherwise, I simply proceed on the assumption that solutions exist to the general problem of vagueness — one of the worst un­ derstood phenomena in any field of research — that do not invalidate my approach; I have nothing to offer in this area beyond what may be found in more recent summa­ ries of relevant work such as Ballmer and Pinkal 1983. (ii)

Similarities vs. properties Claim: There are no properties that can be used as criteria for delimiting varieties; rather, there are α. various similarities between entities like idiolects, and ß. prototypes (entities, e.g. idiolects, that may fruitfully serve as reference points for similarity judgments). (In an even stronger version of the claim, only (α) is al­ lowed. The stronger version would indeed create serious difficulties for our approach; it is, however, clearly false.) Formally, similarities (α) are similarity relations of one type or other. The opposition between (α) and (ß) on the one hand and properties on the other is, however, spuri­ ous: given similarity relations (at least one) of an approp­ riate kind plus 'prototypes', there are properties definable by reference to the relations and the prototypes (see Kutschera 21975, Lieb 1980b), and in the case of (α) and (ß), these are exactly right for delimiting varieties. Hence, if the second part of the claim is true, its first part is false: there are similarity-based properties that can be used as criteria for delimiting varieties. Such properties should also account — from a theoretical if not a methodological point of view — for the use that has been or could be made in linguistics of numerical

CLASSIFICATION ON HISTORICAL LANGUAGES (7)

61

taxonomy (esp. Goebl 1982a, 1982b, 1983, 1984) or cluster analysis (on cluster analysis and classification, see Bock 1989: esp. Sec. 6, with references to recent litera­ ture). Generally, similarity-based properties may be de­ fined on the basis of functions whose values are numbers. Recognizing similarity-based properties, we might replace the original claim by an assertion that only similaritybased properties can be used as criteria for delimiting va­ rieties. This appears to be false at least for external crite­ ria but even if true it would not present a theoretical problem: similarity-based properties have a perfectly good theoretical standing. Allowing that a suitable classification system exists, we may still ques­ tion its uniqueness. 7.4

Classification systems: the problem of uniqueness

The problem of uniqueness may be construed either as theoretical or as methodological. (i)

Theoretical problem Claim: Postulating exactly one classification system, ra­ ther than at least one, is unrealistic. The requirement of exactly one system is based on the following heuristic assumption: we may eventually arrive at a theory of varieties that characterizes criteria for vari­ eties precisely enough to warrant a single variety struc­ ture (remember that varieties are to be 'given through' such a structure). It may still turn out that "exactly one" should indeed be replaced by "at least one". In this case the notion of variety will have to be relativized to variety structures, i.e. instead of "variety" we would have "F-variety" ("variety with respect to F" — F: a variety struc­ ture): "D1 is an F-variety of D". The theory of varieties in Part III uses the simpler notion of variety.

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(ii)

Methodological problem Claim. Even allowing that the theory may postulate exact­ ly one classification system, in actual research we will never be able to proceed beyond incomplete proposals for specific systems that may differ from one researcher to the next. This may well be correct. There is, however, an impor­ tant difference between two types of situation in classifi­ cation studies: in a situation of the first type, we are look­ ing for a specific classification or classification system whose existence and uniqueness are guaranteed by a pre­ supposed theory; any proposal, however hypothetical, is subject to the criterion of right or wrong. In a situation of the second type, no such theory exists, and classification proposals are subject only to criteria of expediency, or fruitfulness for whatever aims we may be pursuing. Postulating a unique classification system firmly places us in the first type of situation.

My defense of variety structures in Secs 6 and 7 does not, of course, prove that the notion of variety structure must be adopted; it does prove that it is defensible and, I hope, plausible. The following Sec. 8 informally characterizes the variety structure of a typical historical language. Given this characterization we may then proceed to formulate the theory of varieties itself (Part III).

8 The Variety Structure of a Historical Language: Overview

8.1

The historical period division and the basic dialect di­ vision

We begin by considering 'primary' classifications that are either neces­ sary for or typical of any historical language. By a primary or firstlevel classification in a classification system we understand a classifica­ tion whose basis is the source of the system; primary or first-level classes are elements of first-level classifications (for more precise defi­ nitions; see (9.9), below). Primary or first-level varieties of a histori­ cal language are the first-level classes of its variety structure. All pri­ mary classifications in the variety structure are cross-classifications (see (9.4)) on the language itself, independent of each other. Let D be any historical language. There is a classification in the variety structure of D whose elements are the historical periods of D; it is assumed that there are different periods (such periods may over­ lap). This classification is the (historical) period division of D. For example, if D = German (including both High German and Low German), then the historical periods of D are, so far, Old Ger­ man (up to early Medieval times), Medieval German, and Modern German (still in progress). "Medieval German" is here used to denote the union of traditional 'Middle High German' or Mittelhochdeutsch and 'Middle Low German' or Mittelniederdeutsch; for details, see Besch et al. (eds) 1984/1985, Vol. II, Parts XI and XII. (Setting up Medieval German as a period of German may be questioned but should still supply a realistic example.) According to some, Modern German would have to be replaced by (i) Early Modern German and (ii) Mod­ ern German in a more restricted sense (again, still in progress).

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Historical periods of a historical language may have periods, too. These will not be considered to be periods of the language though (the period relation will not be allowed to be transitive; this allows the gen­ eralization that all periods of historical languages are themselves lan­ guages, see (4.1), above). All periods of a historical language are to be first-level varieties, they are the historical periods (Sprachepochen) of the language, the largest parts that can be distinguished by appropriate external or system-based criteria as proposed in historical linguistics. External criteria for identifying historical periods all involve the time relation either between speakers or between utterances. There is no agreement in the literature on such criteria, and corresponding dis­ agreement on the periods of given languages (cf. Wolf 1984, for Ger­ man). System-based criteria appear to be applied on an ad-hoc basis. (For Lieb's 1970 proposal to use 'degrees of systematicity' for period delimitation, see Sec. 4.4, above.) In addition to historical periods, a historical language will as a rule have basic 'dialects' (traditionally, 'regional dialects' and 'stan­ dard varieties'; the term "regional" is mostly avoided in this essay be­ cause of problems to be discussed in Sec. 8,2). Thus, typically present in the variety structure of D there is the basic dialect division of D, a classification whose elements are the primary varieties of D of the fol­ lowing type: they can be determined by criteria that are essentially based on speaker location in space. Three points should be made. First, basic dialects of a historical language D are primary vari­ eties of D and correspond, in this respect, to historical periods of D. However, differently from the period relation, we allow the dialect re­ lation to be transitive, at least when restricted to historical languages: for any historical language D, if D 2 is a dialect of D1 and D 1 a dialect of D, then D 2 is a dialect of D. Second, it is worth emphasizing that we are dealing with dialects 'through time' not with 'varieties at a specific moment of time', which is a frequent restriction in dialectology. Third, just as historical periods may overlap so may basic dialects, i.e. some idiolect may simultaneously belong to different basic dialects (or, generally, may belong to any two dialects — basic or non-basic — that are elements of a single dialect division in the variety structure). Applying a synchronic point of view, dialectologists tend to speak of

VARIETY STRUCTURE OF A HISTORICAL LANGUAGE (8)

65

dialect transitions or transitional dialects, and dialect nuclei or nuclear dialects (see Wiesinger 1983: Sec. 1.4.2). These notions may also be applied to dialects through time; a dialect transition would be the non­ empty intersection of two dialects that coexist in time and none of which is a subset of the other; dialect nuclei would be the non-intersec­ ting parts of the two dialects. If no speaker has idiolects from both dia­ lect nuclei, it is exactly the speakers of the dialect transition that create an overlap between the two dialect areas. There are three problems raised by the basic dialect division that must be discussed in some detail. 8.2

Problems of the basic dialect division

Problem 7. It is customary to contrast 'regional dialects' with 'in­ terregional varieties' (überregionale Varietaten), usually denoted by terms such as "standard language" or "standard variety". (Concerning interregional varieties, see Besch 1983 for terminology, problems, and application to German; more general, and formally more explicit but making decisions somewhat different from our own, Ammon 1987. The feature of 'standardizing' or 'codification' through laying down norms may here be disregarded.) The distinction is usually made from a synchronic point of view. On closer analysis it cannot be reconstructed for dialects through time: a single dialect, whether basic or not, may be 'regional' at one time and 'interregional' at another. This means that the very notions of re­ gional and interregional are time-relative; they cannot be lifted from the area of the synchronic to the domain of the diachronic and used as a basis for distinguishing 'regional' from 'interregional' dialects through time, except in a limiting case: there may be dialects that are never interregional, or always interregional; these may indeed be con­ trasted as (strictly) regional vs. (strictly) interregional. True enough, for such a confrontation we would still have to lay down what dialects may be contrasted; otherwise any dialect of a his­ torical language would turn out to be interregional with respect to its own dialects (which are dialects of the language, too). To solve the problem, only dialects from a single classification in the variety struc­ ture should be contrasted, such as different basic dialects.

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In summary, insofar as varieties through time can be classified as (strictly) regional vs. (strictly) interregional, the basic dialect division of D — and any other dialect division in the variety structure — con­ tains all relevant regional and interregional varieties. Problem 2. Traditional dialectology tends to be ambiguous on the status of entities that might qualify as basic dialects — are they indeed to be construed as varieties (sets of idiolects, on our conception) or ra­ ther as groups (i.e. sets) of varieties? In the case of German, are High German (Hochdeutsch) and Low German (Niederdeutsch) basic dia­ lects (primary varieties of German) whose dialects include the so-cal­ led Stammesdialekte ('tribal dialects') Bavarian, Alemannic, Lower Saxonian etc. plus, on our conception, 'standard' varieties like Modern Standard German; or are High German and Low German sets of basic dialects of German? On the first conception the immediate dialects of High German, it­ self a basic dialect of German, would be or include Upper German (Oberdeutsch) and Central German (Mitteldeutsch), and possibly, Modern Standard German; Alemannic and Bavarian — two 'tribal dia­ lects' — would be immediate dialects of Upper German. On the second conception, High German would not be a basic dialect of German but a set of dialects: if Upper German etc. are allowed as dialects — they might again be construed as sets of dialects — High German could be the set {Upper German, Central German,...}; Upper German etc. would then be basic dialects of German. (For the history of this ques­ tion in German dialectology, see Wiesinger 1983: Sec. 1.2; Wiesinger himself is ambiguous on the problem.) Both a broader view of basic dialects (where High German is al­ lowed as a basic dialect of German) and a narrower view (construing High German as a set of basic dialects) is compatible with variety structures as classification systems; on the narrower view, groups of basic dialects could be isolated in the variety structure by means of properties attributed to varieties not idiolects. The broader conception is, however, theoretically simpler and will here be preferred despite the fact that it leads to formulations ("High German is a dialect of Ger­ man") that are strange on the narrower conception. Problem 3. There is a certain amount of vagueness in the litera­ ture concerning the criteria that are or may be used in setting up dia-

VARIETY STRUCTURE OF A HISTORICAL LANGUAGE (8)

67

lects, be they basic or non-basic (for classical dialectology, see Putschke 1982: esp. Sec. 3; on structural dialectology, Jongen 1982). Differ­ ently from what terms like "regional dialect" would suggest, external criteria for dialects need not be purely geographical (for discussion, see Heger 1982:429). System-based criteria for dialects are over­ whelmingly phonetic or phonological; there is an additional concern for morphological and lexical data but little attention has so far been paid to syntax (as stunningly proved by German dialectology: see above, Sec. 3.3; also, Henn 1983). There are additional first-level classifications that either may or must occur in the variety structures of historical languages. 8.3

Other primary classifications

As a primary classification that may be expected to exist for most his­ torical languages D we have the basic sociolect division of D, a classi­ fication that supplies the basic sociolects of D: varieties such as Lower Class D (e.g. Lower Class German, for D = German), Middle Class D, Upper Class D, and, possibly, Class-Neutral D. Basic sociolects as here understood correlate with the speakers' membership in large social classes (soziale Schichten); this sense of "sociolect" corresponds by and large to Kubczak's (1987:269) sense (c); see Kubczak for further discussion of relevant terminology: in ad­ dition to "sociolect", terms like "social dialect" and "code" (but cf. Bernstein 1987:574: "Codes are not varieties"); and also Kubczak on the conditions that must be satisfied for sociolects to exist in a lan­ guage. Class-Neutral sociolects must be allowed as a limiting case if the basic sociolect division is to be a classification on the entire histori­ cal language. The basic sociolect division is independent of the other primary classifications, all of them being cross-classifications on the language. (Independence of the basic sociolect and dialect divisions is doubtful, though, if the framework of classical dialectology is assumed; see be­ low, Sec. 10, esp. (10.1).) A basic sociolect may therefore include idi­ olects from different 'basic registers', a position not generally shared in the literature: the sociolect may intersect with all basic registers of

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SETTING THE STAGE (II)

the language, contrary to what Bernstein's early work would suggest (see Edwards 1987, Bernstein 1987, for relevant discussion). Basic registers are the elements of the basic register division of D; again, this division may not exist for every D. The concept of register, developed in English (British) linguistics, and the related but different concept of 'functional style' first intro­ duced in the Prague school continue to give rise to a host of unresol­ ved problems (for details, see Spillner 1987: Secs 3.4 and 3.3). It is, however, in agreement with at least part of this tradition if registers are construed as varieties that are "the linguistic reflection of recur­ rent characteristics of user's use of language in situations" (Gregory 1967:185, in an early summary of the English school). Following a tradition in stylistics that "dates back to classical anti­ quity and permits the stylistic classification of lexemes as well as of grammatical constructions" (Spillner 1987:282), we may propose ex­ actly three basic registers of D: Neutral D, Below-Neutral D, AboveNeutral D. The three terms are taken from Ludwig (1991: Ch. 4: neutral, unter neutral, über neutral) rather than from tradition, which has "middle", "low", and "high" (Spillner 1. c ) ; "neutral" suggests usabili­ ty 'in arbitrary situations'. Varieties that might have been proposed as basic, such as Colloquial (Umgangssprache in its second sense, where it is a 'style' rather than a basic interregional variety — see Domaschnev 1987), are treated as non-basic registers, e.g. Colloquial is a variety of Below-Neutral (see also Ludwig 1991: Ch. 4). Registers are considered to be varieties, i.e. sets of certain idio­ lects. It might be suggested that these idiolects should have a special status: they should be construed as subsets of non-register idiolects. This would mean that a proper part of a means of communication may again be a means of communication, a complication that I shall here avoid (see above, Sec. 6.5, for discussion). Historical periods, basic dialects, basic sociolects, and basic regis­ ters exemplify four variety types frequently called diachronic, diatopic, diastratic, and diaphasic (the terms are Coseriu's, who borrowed the second from Flydal 1952: see Coseriu 1988/1981:17); note that on our account the last three types of varieties are varieties through time, too.

VARIETY STRUCTURE OF A HISTORICAL LANGUAGE (8)

69

The four types do not, however, exhaust the primary classifica­ tions that may figure in the variety structure of a historical language, if less typically so. Thus, we may have a basic medium division of D that provides varieties like Spoken D and Written D; a basic gender (or sex) variety division of D correlating with differences in speakers' biological sex (again, a neutral variety may be included). Such a divi­ sion must be kept separate from mere differences in language use (see Klann-Delius 1987: Secs 2f), which may prevail in the case of age- and generation-specific differences (Cheshire 1987b). Even where classifi­ cations such as a gender variety division exist in the variety structure of a language, they may not be first-level classifications. So far we have specified only one first-level classification that must be present in the variety structure of any historical language D, the historical period division of D. The second first-level classification that is obligatory is the personal variety division of D: its elements are the personal varieties of D, i.e. greatest subsets of D such that each consists of elements of D (idiolects) that are means of communication for a single person at some time during his or her life. It should be noted that personal varieties cannot be obtained by subclassifications on regional dialects, they are no 'mini-dialects'; a personal variety may contain elements of different regional dialects. First-level varieties, such as historical periods, may serve as a ba­ sis for additional 'secondary' classifications. 8.4

Classifications on historical periods

By a secondary classification in a classification system we understand a classification whose basis is an element of a primary classification in the system; generally, an n-ary (n-th level) classification (n > 1) is a classification whose basis is an element of an (n-l)-th level classifica­ tion (see (9.9), below). Again, an n-ary (n-th level) class (n > 1) is an element of an n-th level classification; an n-ary (n-th level) variety is an n-th level class in the variety structure. Among the secondary clas­ sifications we first consider classifications on historical periods. These are of one of two types. Let D 1 be a historical period of historical language D. D1 may again have several periods. In this case there is a period division of D1'

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SETTING THE STAGE (II)

a second-level classification in the variety structure of D; its elements are varieties of D1. It is indeed defensible to assume that a period divi­ sion of D1 must exist. The period division is a classification on D1 of a first type: it is a classification obtained by criteria of the same kind as the criteria that underlie the historical period division of D itself. There may be classifications on D1 of a second type, supplying the now-temporal immediate varieties of D1 These classifications, which again are second-level classifications in the variety structure of D, have the following property: the elements of each are obtained by in­ tersecting D 1 with the elements of some first-level classification other than the period division of D (see also Sec. 5.2, above). Thus, if the basic dialect division of D consists of n dialects Dial1 ..., Dialn and if the intersections of D1 with the basic dialects are non-empty, then the dialect division of D1 = {D1 ∩ Dial1, ..., D1 ∩ Dial n }; its elements are immediate dialects of D1 and second-level dialects of D. Similarly, the intersections of D1 with elements of the personal variety division of D form the personal variety division of D1 which must exist since this is true of the personal variety division of D. It is defensible to introduce the following general assumption: gi­ ven any historical period D1 of D and any non-temporal primary vari­ ety D 2 of D, D 1 ∩ D2 is a (non-temporal) variety of D1 unless empty. No such assumption may be made if D1 is a non-temporal primary va­ riety of D; such varieties may again have immediate varieties but these must be elements of secondary classifications that are obtained by inde­ pendent criteria not by set-theoretical intersection. 8.5

Other non-primary classifications

Suppose that D 1 is any primary variety of D other than a historical pe­ riod, such as a personal variety or basic dialect, sociolect, or register of D. D1 may but need not be the basis of a secondary classification in the variety structure of D. Let D 1 be a basic dialect of D; if D = German, D1 may be High German (for discussion of such a view, see Sec. 8.2, Problem 2). Nor­ mally, there is a period division of D1 i.e. D1 has several periods, each of which is a variety of D1 and a variety (but not a period) of D. In the case of High German, we have, on a traditional view, the peri-

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71

ods Old High German, Middle High German, and Modern High Ger­ man {Neuhochdeutsch, frequently replaced by two periods, Early Modern High German — Frühneuhochdeutsch — and Modern High German in a more restricted sense). As argued above (Sec. 5.2), periods of a basic dialect are not ob­ tained by simply intersecting the basic dialect with a period of the lan­ guage. Such an intersection is a dialect of the language period (see Sec. 8.4), hence, a variety (dialect) of the language; it may or may not be a period of the basic dialect. Analogous remarks apply to periods of any (primary or non-primary) variety of a language. In addition to a period division on basic dialect D1 we may have a dialect division of D1 whose elements are immediate dialects of D1 and second-level dialects of D (i.e. dialects of D that are second-level varieties of D). If D1 = High German, then Upper German (Oberdeutsch) would be an immediate dialect of High German. Both the pe­ riod division and the dialect division of D1 are second-level classifica­ tions in the variety structure of D; hence, while dialect D1 (High Ger­ man) is a primary dialect of D (German), any immediate dialect of D1 (Upper German) is a second-level dialect of D. Let D 2 be a variety in the dialect division of D1? say, D 2 = Upper German, for D1 = High German. D2 may again have periods, there may be a period division of D2 This is a tertiary or third-level classification in the variety structure of D, and its elements are third-level varieties of D. Thus, the periods of Upper German are third-level va­ rieties of German. D 2 in turn may have dialects, there may be a dialect division of D 2 , which again is a third-level classification; it supplies third-level dialects of D. Indeed, if D2 = Upper German, then Bavarian and Alemannic are immediate dialects of D2 and third-level dialects of German. Generally, given an n-th level dialect of D (for 1 ≤ n < some fixed number depending on D), we may always ask whether there is (i) a pe­ riod division of the dialect and (ii) a dialect division of the dialect. The elements of each division are (n+l)-th-level varieties — dialects, in case (ii) — of language D. We certainly need not stop at n = 3. For ex­ ample, if D = German, then Bavarian is a third-level dialect of D; Southern Bavarian (see, for example, Wiesinger 1983: §3.3.2) a

SETTING THE STAGE (II)

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fourth-level dialect; and any period or dialect of Southern Bavarian — there are such periods and dialects — is a fifth-level variety of D. Analogous statements hold not only for dialects but for any type of non-temporal varieties. It is, however, unclear from current usage of terms like "variety", "period", "dialect" etc. whether there are — be­ yond general set-theoretical conditions — minimal size requirements for varieties that may serve as a basis for period divisions, dialect divi­ sions, or similar classifications in the variety structure of a language. 8.6

Summary

The proposed view of variety structure is summarized in Diagram (8.1); actually, Secs 8.1 to 8.5 may be read as an extended commentary on the diagram. The following conventions are used: (8.2)

Conventions a. Expressions above diagonal lines, or expressions from which lines do not originate, refer to sets of idiolects (a historical language; a first historical period of the language — period1; a first period of the first histori­ cal period — period11; etc.) b. Expressions above horizontal lines are names of classi­ fications: the historical period division (of the given historical language), etc. c. Diagonal lines, read from bottom to top, mean "is a classification on": "the historical period division is a classification on the historical language". d. Horizontal lines read "has as its elements": "the histor­ ical period division has as its elements period1 ...." e. A line of dots indicates an unspecified, finite number of entities that are of the same type as the entities — either classifications or their elements — named to the left of the line: "period1 " means "period 1 , period2,..., periodn", for some n > 1.

Variety structure of a typical historical language (incomplete)

VARIETY STRUCTURE OF A HISTORICAL LANGUAGE (8) 73

74

SETTING THE STAGE (II)

The background to the theory of varieties and its basic conception have now been explained, and the theory itself may be formulated (Part III, Secs 9 to 13).

PART III

A THEORY OF LANGUAGE VARIETIES

9 Variety Structures as Classification Systems

9.1

Divisions, classifications, partitions

In the present Section 9, the informal notion of variety structure will eventually be explicated by two different though closely related con­ cepts (Sec. 9.6). These concepts are linguistic not logical but are based on logical concepts centering around the notion of classification, in a broad sense of "logical" where set theory is included. In Secs 9.1 to 9.5, the necessary set-theoretical concepts will be defined. Definitions in Secs 9.1 and 9.2, leading up to "division system" and "classification system" in 9.3, are standard (see also Juilland and Lieb 1968, for de­ tails). The set-theoretical concepts are introduced in systematic order and partly for reference purposes. A first intuitive understanding of Sec. 9.6 and Secs 10ff should also be possible on the basis of Secs 5 and 8. In dealing with purely set-theoretical concepts we use variables "x", "X1", ... for any set-theoretical entity; "M", " M 1 , ... for arbitrary sets; "N", "N 1 ", ... for any set of sets; and "O", " O 1 , ... for any set of sets of sets (variables conform to (4.7)). Ordinary set-theoretical sym­ bols are employed; in particular, "e " means "is an element of'; "" — "is a subset of'; "" — "is a proper subset of'; "Ø" denotes the empty set. Formulations that are partly symbolic will as a rule be paraphra­ sed in plain English; non-linguistic notions may be exemplified by sim­ ple examples and counterexamples using positive integers. This ren­ ders the entire Sec. 9 rather longish but may still be defended as a help to readers. As a preliminary step we introduce a suggestive term for the rela­ tion between M and O if M is an element of some element N of O:

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(9.0)

Definition. M is a class in O iff [if and only if] M is an el­ ement of an element of O.

Given any set O whose elements are sets N whose elements are again sets, the classes in O are exactly the sets that are elements of the sets N. — The definiens of (9.0) could also be replaced by "M  O" or "M is an element of the union of O", where ""is defined as follows for arbitrary sets N whose elements are again sets: N = the union of N = the set of all x such that for some M  N, X  M (the union of N is the set of elements of elements of N). Examples (9.0) N1 = { { 1 , 5 } , {1,3}} N 2 ={{2,4}} O ={N 1 ,N 2 } = {{{1,5}, {1,3}}, {{2,4}}} The classes in O are {1,5}, {1,3}, {2,4}. The notion of class in O is useful because classification systems are sets of classifications, whose elements are again sets; we may therefore use (9.0) to speak, in particular, of the classes in a classification system; these are exactly the elements of the classifications in the system. Classifications are a special type of 'divisions': (9.1)

Definition. N is a division of M iff a. N has at least two elements; b. N = M.

A division of a set M is a set whose elements are sets; that has at least two elements; and whose union is again M. It follows that this set con­ sists of subsets of M and that every element of M is an element of one of the subsets. — The basis of a division N of M is M. Examples (9.1) M = {1,5,3} N1 = N1 in Ex. (9.0)= {{1,5}, {1,3}} is a division of M. N 2 = {{1}, {1,5}, {3}} is a division of M. N 3 = {Ø, {1,5,3}} is a division of M.

VARIETY STRUCTURES AS CLASSIFICATION SYSTEMS (9)

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N 4 = {{1, 5, 3}} is not a division of M. (9.2)

Definition. N is a classification on M iff a. N is a division of M; b. of two different elements of N neither is a subset of the other.

A classification on (not: of) a set M is a division of M that does not contain different elements — subsets of M — such that one is a subset of the other. This implies that all elements of the division are non­ empty sets (the empty set is a subset of any set), and are proper subsets of M; i.e. M may not itself occur in the division. On the other hand, two different sets in the division may overlap, i.e. may have shared elements (the intersection of the sets may be non-empty). Examples (9.2) M = M in Ex. (9.1) = {1,5,3} N1 = N1 in Ex. (9.1) = {{1,5}, {1,3}} is a classification on M. N 2 to N4 in Ex. (9.1) are no classifications on M. (9.3)

Definition. N is a partition of M iff a. N is a division of M; b. two different elements of N have no shared elements.

A partition of (not: on) a set M is a division of M in which different elements do not overlap. This excludes different elements one of which is a subset of the other. Hence, any partition of M is also a classifica­ tion on M. Examples (9.3) M = M in Ex. (9.2) = {1,5,3} N = {{1}, {5}, {3}} is a partition of M. N1 to N4 in Ex. (9.2) are no partitions of M. (9.4)

Definitions. N and N t are cross-divisions / -classifications / partitions on M iff both N and N1 are divisions of / clas­ sifications on / partitions of M.

The three concepts take care of the case where two divisions, which

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may or may not be classifications or partitions, have a shared basis. Examples (94) M = M in Ex. (9.3) = {1,5,3} N1 = N1 in Ex. (9.1) = {{1,5}, {1,3}} and N = N in Ex. (9.3) = {{1}, {5}, {3}} are cross-classifications on M, hence, crossdivisions on M. N5 = {{1,5}, {3}} and N in Ex. (9.3) are cross-partitions on M, hence, cross-classifications on M, hence, cross-divisions on M. In a division other than a partition, the sets which are elements may overlap. It is sometimes useful to single out those x which belong to just one set in a division, the ones 'specific to' the set: (9.5)

Definition. Let N be a division of M. x is specific to M1 in N iff a. x  M1; b. M1  N; c. for all M2, if x  M2 and M2 N, then M2 = M1

In a division of M, the entities x specific to a certain set in the division are those elements of this set that do not occur in any other set in the division. It follows that in a partition, all elements of a set in the parti­ tion are specific to the set. Examples (9.5) M = M in Ex. (9.2)= {1,5,3} N1 = N 1 i n Ex. (9.2) ={{1,5}, {1,3}} 5 is specific to {1,5} in N1 3 is specific to {1, 3} in N1 1 is not specific to any element of N1 9.2

Introducing criteria

We have so far explicated traditional notions of classification without making reference to 'criteria' by which the sets in a classification are 'determined'. Criteria may be understood as properties of elements of

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the classification basis. (For details on the following definitions and theorems, see Juilland and Lieb 1968: Ch. 5.) Let "à", "α 1 ", ... stand for any (admissible) property of set-theo­ retical entities. ("Admissible" is a reminder of the fact that allowing certain properties leads to inconsistencies; how to exclude such proper­ ties is a question that need not concern us here.) Generalizing the use of the term "property", we allow 1-place properties (i.e. properties in the normal sense), 2-place properties, ..., n-place properties, where the higher-place properties are properties of ordered pairs, ..., ordered ntuples. (The higher-place properties are sometimes called relations-inintension; and "attribute" is frequently used instead of our "property".) We define: (9.6)

Definition. The a-set = the set of all x such that x has a.

Examples (9.6) ("n" for any positive integer) α1 = the property of being an n such that n = 1 or n = 5 α2 = the property of being an n such that n = 3 α3 = the property of being an n such that n = the immediate successor of 2 (in the progression of positive integers) The α1-set = {1,5}. The α2-set = the α3-set = {3}. Next, let "A", "A 1 ",... stand for any set of α's. We extend the no­ tions of division, classification, and partition as follows: (9.7)

Definitions. N is a division of / classification on / partition of M by A iff a. N is a division of / classification on / partition of M; b. for each Mx  N, there is exactly one α  A such that M1 = the α-set; c. for each α  A, the α-set  N.

Examples (97) M = M in Ex. (9.5) = {1,5,3} N = N 5 in Ex. (9.4) = {{1,5}, {3}}

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A1 = {α1 in Ex. (9.6), α2 in Ex. (9.6)} A2 = {α1 in Ex. (9.6), α3 in Ex. (9.6)} A3 = {α1 α2,α3} N is a partition of (hence, a classification on and a division of) M by A1 as well as by A2 but not by A3. In a division of M by A (hence, a classification or partition), each a  A is called a criterion of the division. N is a division etc. of M iff there is an A such that N is a division etc. of M by A; and if there is a division etc. of M by A, there is exactly one such division etc. Criteria, on this conception, are properties, and for each classifi­ cation there must be several criteria. At least in the case of a partition we may also proceed form a single equivalence relation -— the criteri­ on of the partition — to determine the elements of the partition (cf. Juilland and Lieb 1968:33-35; Carnap 1960: Sec. 34a, for 'definition by abstraction'; in a more sophisticated form, Kutschera 2 1975: Sec. 2.4.7, Lieb 1980: Sec. 3.2; see also Sec. 7.3, (ii), above). Indirectly, criteria are also involved in the notion of a 'division system', the most important set-theoretical concept required for defi­ ning "variety structure". 9.3

Division systems, classification systems, partition sys­ tems

We continue to use "O" as a variable for any set whose elements are sets N of sets, and define: (9.8)

Definitions. O is a division system / classification system / partition system on M iff a. O is non-empty; b. O is finite; c. for every N  O, there is an M1 such that: (i) N is a division of / classification on / partition of (ii)

M1 = M, or M1 is a class in O.

(See (9.0) for "class in".) It follows that every partition system on M is also a classification system on M, and every classification system a di-

VARIETY STRUCTURES AS CLASSIFICATION SYSTEMS (9)

83

vision system; moreover, the unit set of a division etc. of any M is a division system etc. of M. Informally, for a division system we start from a (non-empty) set M. We next choose a division N1 of this set. (If this is to be a classifi­ cation, M must contain at least two elements.) The set {N1} already satisfies the conditions for a division system on M. We may have another division N2 of M; then N1 and N2 are cross-divisions on M, and {N1, N 2 } is a division system on M. Or else, there may be a divi­ sion N3 of some element M11 of N1; then {N1 N3} is a division system on M, and so is {N 1 ,N 2 , N 3 }. In this way we may go on as long as there are any subsets of M to subdivide — but not forever: O must be finite. If M itself is finite, then there is only a finite number of divi­ sion systems on M, and each element of a division system is a finite set of finite sets. In the present essay we will have to deal only with divi­ sion systems on finite if large sets. Division systems whose elements are finite sets may be denoted by diagrams — as previously used in various places in this essay (see dia­ grams (1.11), (2.2), (3.1), and (8.1)) — of the following form. A name of set M (of the 'source' of the system) is connected by slanting lines with names of any divisions on M that belong to the system. Under each of these names there is a horizontal line sprouting short vertical lines that lead to names of the elements of the division. If any such element is again the basis of a division in the system, the same procedure is applied to its name. Schematically: Sample diagram schema (9.8)

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Examples (9.8) M ={1,3,4,5} N1 = { { 1 , 5 } , {1,3}, {4}} N 2 = { { 1 } , {5,3}, {4}} N3 = { { 5 } , {3}} N4 = { { 4 , 5 } , {1}} O1 = {{{1}, M}} is a division system, but no classification system, on M. 0 2 = {N1} is a classification system, but no partition system, on M. 0 3 = {N2} is a partition system, hence, a classification system and di­ vision system, on M. 0 4 = {N1, N 2 } is a classification system, but no partition system, on M. 0 5 = {N 2 , N3} is a partition system on M. 0 6 = {N1, N2, N 3 } is a classification system, but no partition system, on M. 0 7 = {N1, N 2 , N 3 , N4} is not a division system, hence, neither a parti­ tion system nor a classification system, on M. (N4 does not satis­ fy condition (c) in (9.8): although N4 is a division of subset {1, 4,5} of M, this subset is neither the same as M nor is it a class in 0 7 , i.e. an element of N1 N2, N3, or N4.) Using the convention for diagrams, 0 6 may be denoted by sample diagram (9.8) (next page). As appears from the diagram, a single class in 0 6 , viz. {4}, occurs as an element in different classifications; generally, different divisions may have shared elements in arbitrary division systems. The following auxiliary notions are defined for division systems, hence, for classification and partition systems; they either render more precise notions used informally in Secs 5ff, or else are needed for sub­ sequent discussion.

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Sample diagram (9.8)

9.4

Auxiliary notions. Theorem

We define: (9.9)

Definitions. Let O be a division system on M. a. The source of (O, M) = M. b. M 1 is an endpoint of O iff (i) M1 is a class in O; (ii) there is no N  O such that N is a division of M1 c. N is a terminal element of O iff (i) N  O; (ii) for every M1  N, there is no N1  O such that N1 is a division of M1 d. For n ≠ 0, N is an n-th level (n-ary) element of O iff (i) N  O; (ii) either (α) or (ß): α. n = 1, and for all M1 if O is a division sys­ tem on M1, then N is a division of M1; ß. n ≠ 1, and N is a division of an element of an (n-l)-th level element of O.

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e. For n ≠ 0, M1 is an n-th level (n-ary) class in O iff there is an N such that (i) N is an n-th level element of O; (ii) M1  N. f. For n > 1, N is an n-th level subdivision o f / subclassification on / subpartition of M1 in O iff (i) N is an n-th level element of O; (ii) N is a division of / classification on / partition of M1. g. For n ≥ 1, N and N1 are n-th level cross-divisions / classifications / -partitions on M1 in O iff (i) N and N1 are n-th level elements of O; (ii) N and N1 are cross-divisions / -classifications / partitions on M1. h. Let M1 be a class in O. The M1-part of O = the set of all N such that (i) N  O; (ii) for some M2  M1 N is a division of M2 Informally, the source is simply the set from which we start. The endpoints are the classes in the division system (i.e. the elements of the di­ visions that belong to the system) on which no further division is based that again belongs to the system (this allows for endpoints that may in­ deed be subdivided — but only by subdivisions outside the system). We may speak of first-level, second-level, ... n-th level divisions in the system in the following sense: first-level divisions are exactly the di­ visions on the source of the system; for n > 1, n-th level divisions are the divisions in the system that are divisions of sets that belong to (nl)-th level divisions; e.g. second-level divisions are divisions of ele­ ments of first-level divisions. Assigning each division to a certain level we may characterize the classes in the system in a similar way: the n-th level classes in the system are simply the elements of n-th level divi­ sions. (Differently from the divisions, a class may belong to several levels simultaneously.) Subdivisions etc. are relativized to levels to be­ gin with: the n-th level subdivisions etc. of a given set are the n-th lev­ el divisions that are divisions of this set (it follows that the set must be an (n-l)-th level class in the system); similarly, for cross-divisions.

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Finally, we have the important notion of M1-part of a division system, where M1 is any class in the system: intuitively, we take that part of the system that originates from class M1, i.e. the set of divisions that are subdivisions of M1 or of some proper subset of M1. This set is empty if class M1 is an endpoint of the system; otherwise, the M1-part is itself a division system etc., not on M but on M1. The terminology introduced in (9.9) is suggestive of the diagrams by which division systems may be denoted. The definitions may there­ fore be exemplified by reference to sample diagram (9.8), which names 0 6 in Ex. (9.8): Examples (9.9) M = M in Ex. (9.8)= {1,3,4,5}. O = 0 6 in Ex. (9.8)={N 1 ,N 2 ,N 3 }. The source of (M, O) = {1,3,4,5}. The set of endpoints of 0 = {{1,5}, {1,3}, {4}, {1}, {5}, {3}}. The set of terminal elements of O = {N1 N 3 }. The set of first-level elements of O = {N1, N 2 }. The set of second-level elements of O = {N 3}. e. The set of first-level classes in O = {{1,5}, {1,3}, {4}, {1}, {5,3}}. The set of second-level classes in O = {{5}, {3}}. f. N 2 is a second-level subpartition of (hence, subclassification on and subdivision of) {5, 3} in O. g. N 1 and N2 are first-level cross-classifications (hence, cross-divi­ sions) on M = {1,3,4,5} in O. h. For any class M1 in O: if M1 = {5,3},the M1 part of 0 = {N3}; if M1 ≠ {5, 3}, the M1 part of O = Ø.

a. b. c. d.

A number of consequences of the definitions are summarized by the following theorem (proof omitted): (9.10)

Theorem. For any division system O on M:

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a. there are endpoints of O; b. for any endpoint M1 of O, the M1-part of O = the empty set; c. for any class M1 in O that is not an endpoint of O, (i) the M1-part of O is a division system on M1; (ii) if O is a classification system / partition system on O, then the M1-part of O is a classification system / partition system on M1; d. for any class M1 in O, (i) M1 is an endpoint of O iff there is no M2 such that M2 is a class in the M1-part of O; (ii) if M2 is a class in the M1-part of O, then the M2part of O  the M1-part of O; (iii) if O is a classification system on M, then M1 is a non-empty proper subset of M. This theorem concerns various aspects of classes in a division system, in particular, endpoints; it will be needed for proving theorems of the theory of language varieties. We finally consider individual elements x in the source M of a di­ vision system (the following Sec. 9.5 is needed only for Secs 12.3f and 13, below). 9.5

The notion of place

Any x from the source M of a division system O will eventually ap­ pear in some endpoint of O; the 'place' of x in O can be characterized by the endpoints of which x is an element. Consider, once again, sample diagram (9.8) (next page). The diagram is a name of classification system 0 6 on M = { 1 , 3 , 4 , 5 } . 1  M belongs to three endpoints of system 0 6 , {1,5}, {1,3}, and {1}. The 'place' of 1 is given through these endpoints. Similarly, 5 belongs to endpoints {1,5} and {5}; 5 is also in {5,3}: this can be inferred from the fact that {5}  N3 and N3 is a division of {5,3}.

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Sample diagram (9.8)

The notion of 'place' is explicated in two steps. First, we introduce a concept of place assignment. A place assignment for x in a division system is a set of endpoints to which x belongs. Now x may belong to different endpoints that are elements of a single division; e.g. 1 be­ longs to both {1,5} and {1,3}, which in turn are elements of N1. A place assignment is to contain at most one set from any given division in the system. This means that there must be at least two different place assignments for 1 in 0 6 . The place of x in a division system is identified with the set of place assignments for x. More precisely (in (aii), N = the intersection of N = the set of all x such that for every M1  N, X  M1; cf. N in (9.1), above): (9.11)

Definitions. For any division system O on M and x M: a. N is a place assignment for x in O iff (i) every M1  N is an endpoint of O; (ii) x  N; (iii) for every element N1 of O, there is at most one M1  N1 such that M1  N; (iv) N is a greatest set that satisfies (i) to (iii), i.e. there is no N1 such that N1 satisfies (i) to (iii) and N  N1. b. The place of x in O = the set of all place assignments for x in O.

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(A simpler notion of place, which may be sufficient for most purposes, would identify the place of x in O with the set of endpoints of O that contain x as an element.) Obviously, for any x  M, the place of x in O is a non-empty set of non-empty sets; in this sense, any x  M 'has its place' in O. Examples (9.11) O = 0 6 in Ex. (9.8). The place of 1 in O = {{{1,5}, {1}}, {{1,3}, {1}}}. The place of 5 in O = {{{1,5}, {5}}}. In the case of a historical language, we consider the place of an id­ iolect in the variety structure of the language, i.e. in a certain classifi­ cation system on the language. The meaning of "variety structure" can now be made precise. 9.6

Explication of "variety structure"

In Sec. 5 we informally introduced a key assumption that may now be formulated as follows ("D", "D 1 ", ... are understood as explained in (4.8), as variables for any set of C's: for any set of sets of form-mean­ ing pairs, in particular, any set of idiolects; "E", "E 1 ", ... stand for any set of D's, e.g. any set of dialects; and "F", " F 1 ' , . . . for any set of E's): (9.12)

Assumption 1. For any historical language D, there is ex­ actly one F such that a. F is a classification system on D; b. for any D1, D1 is a variety of D if and only if D1 is a class in F.

(See (9.0) for "class in".) Assumptions, definitions, and theorems are numbered by Arabic numerals if they belong to the theory of varieties rather than just to logic or set theory. In Ass. 1, we start from a historical language D, which is a non­ empty, finite set of idiolects C, just as in our numerical examples we started from a set of numbers such as M = {1,3,4,5} in Ex. (9.8); the idiolects C correspond to the numbers. We require that there should be exactly one classification system F on D that satisfies a certain condi-

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tion (b). F corresponds to 0 6 in Ex. (9.8); just as 0 6 is a set of sets N of sets M1 of numbers, F is a set of sets E of sets D1 of idiolects; and it is exactly these sets D1 that are the varieties of D, by condition (b). The elements of F are classifications E on subsets of language D, just as the elements of Oó are classifications N on M = {1,3,4,5}. The ele­ ments of the classifications are sets D1 of idiolects C, just as the ele­ ments of classifications N1, N2 and N3 on subsets of M are sets M 1 of numbers, viz. the sets {1, 5}, {1, 3}, etc. Just as these sets are 'given' through classification system 0 6 on M, so are the varieties of D1 'given' through classification system F on language D. Assumption 1 is far from trivial; Secs 6 and 7 contain a detailed defense that is here presupposed. Given Assumption 1, we easily define the notion of variety struc­ ture for historical languages: (9.13)

Definition 1. Let D be a historical language. The variety structure of D = the F that satisfies (9.12) with respect to D.

Sec. 8 contains an overview of the variety structure of historical lan­ guages; at least Sec. 8.6 may here be consulted. Consider any variety of a historical language, say, Medieval Ger­ man as a variety of German. This is not an endpoint of the variety structure of German, i.e. there are classifications in the variety struc­ ture of German that 'originate from' (whose bases are proper or im­ proper subsets of) Medieval German; see the "period1"-part of Dia­ gram (8.1) in Sec, 8.6, above. The set of these classifications — the 'Depart' of the variety structure of German (see (9.9h)) — is the variety structure of Medieval German in German. Generally, using Def. 1, we introduce a second concept of variety structure that applies not to historical languages but to their varieties, in particular, their histor­ ical periods: (9.14)

Definition 2. Let D be a historical language and D1 a vari­ ety of D. The variety structure ofD1 in D = the D1-part of the va­ riety structure of D.

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If D1 is an endpoint of the variety structure of D, then of course the variety structure of D1 in D is empty. Assumption 1 and the two definitions belong to a general theory of language; in an analogous form, they may have to figure in any theory of language that takes the notion of variety seriously. The two defini­ tions presuppose the concept of historical language, which is used in their antecedents. The antecedent of the second definition also uses the concept of variety; more importantly, this notion appears in Assump­ tion 1 and is thus indirectly involved in the definiens of either defini­ tion: "variety structure" is defined by means of "variety" and not con­ versely. For reversing the definitional relationship, we would have to characterize classification system F in Assumption 1 independently of the notion of variety, a problem that I have been unable to solve. In the present version of a theory of varieties, the term "variety" is not defined; it is a basic term in the technical sense. Naturally this does not mean that nothing more can be said about varieties. In particular, the logical notion of criterion (Sec, 9.2) may be used to explicate the idea that varieties are delimited by linguistic criteria.

IO External Criteria

10.1 Example Two types of criteria were distinguished in Sec. 5.4 in connection with variety structures, external and system-based ones, and a correlation between them was postulated. Both the distinction and the correlation must now be made more precise. I begin by considering the first type of criteria. External criteria are "based on non-language entities: times, areas, social classes, situation types, individual persons, etc," Exactly how may this be understood? Consider the basic dialect division E in the variety structure of a certain historical language D* — the division is a classification on D* — and assume that all elements of E are regional dialects (i.e. there are no basic interregional dialects of D*). Furthermore, let us pre­ suppose the dialect theory of 'classical' dialectology (see Putschke 1982) in a suitably adapted form, disregarding its diachronic orienta­ tion (we may thus be closer in parts to 'dialect geography', see Goossens 1987). Let D1 be a dialect in E. A property of idiolects that singles out D1 from the rest of D* can be obtained by starting from the conditions on informants found in a typical study of classical dialectology (Baur 1982:317): (10.1)

Angehörige der ältesten Generation aus der sozialen Grundschicht, die im Ort geboren und aufgewachsen sein und möglichst wenig außerhalb gewohnt oder gearbeitet haben sollten. Auch ihre Eltern sollten möglichst aus dem Ort stammen. (Members of the oldest generation from the basic social class that should have been born and grown

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up in the village or town, living or working away from it as little as possible. Their parents, too, ought to be from this place.) Using "V" for, in particular, persons; "t" for times; and "p" for smal­ lest inhabited places 'in the sense of dialectology' (Orte), we define: (10.2)

Definition. V is a potential dialect informant at p during t iff V and p satisfy conditions (10.1) during t.

The relation of dialect informant is a complex relation of 'belonging' that holds between a person and a place p (during a certain time): be­ longing to the oldest generation at p, and to the 'basic social class' at p; being born at p; having grown up at p; having lived and worked more or less exclusively at p; and having parents from p. Following classical dialectology it would be defensible to identify dialect D1 with the set of idiolects C in D* that are 'acceptable' to po­ tential dialect informants at some place in the area of dialect D1 where the area must be construed, on our account, as an 'area through time'. (We are considering dialects in their entire historical extension; a cer­ tain geographical location may belong to the area of a dialect at one time and not belong to it at another; the area need not be connected in space.) Put differently, if Area1 = the area of D1 then D1 may be de­ termined by the following property: (10.3)

acceptable-in-Areaj-of-D* = the property of being a C such that: a. C G D*; b. for some p, V, and t, (i) p is in Area1; (ii) V is a potential dialect informant at p during t; (iii) C is acceptable to V during t.

It agrees by and large with classical dialectology (and dialect geogra­ phy) if property (10.3) is taken as an external criterion that determines dialect D 1 : being 'acceptable' to potential dialect informants — a no­ tion that would have to be made more precise — is implicitly assumed when idiolects of such informants are taken to be 'representative'. Of course, there are obvious problems; in particular, nowhere in Area1

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must there be potential dialect informants to whom different C and C1 from non-overlapping dialects are acceptable; generally, the areas of non-overlapping dialects of D* must not overlap either. This will here be assumed for argument's sake. As our next step we generalize the example by considering 'crite­ ria-determining functions' and 'permissible sets of non-language enti­ ties'. 10.2 Criteria-determining

functions

A dialect area through time is a region (not necessarily connected) in space-time. Let us use "r", "r1", ... for such regions, and let "D" stand for any set of C's, see (4.8). We may then generalize (10.3) by means of the following definition: (10.4)

acceptable-in-r-of-D =df the property of being a C such that: a. C  D; b. for some p, V, and t, (i) p is in r; (ii) V is a potential dialect informant at p during t; (iii) C is acceptable to V during t.

The expression defined in (10.4), "acceptable-in-..-of-..", is a name of a function in the set-theoretical sense. Its arguments are pairs (r, D): it takes any (r, D) and assigns to it the property of being an idiolect C in D that is acceptable, at some time, to some potential dialect informant V at a place p contained in region r. (There may be no C with this property.) The function acceptable-in-r-of-D is, as a matter of fact, a linguis­ tic variable in the sense of (1.6) if arbitrary sets of idiolects are allow­ ed as language-like entities in the sense of (1.5) (see (ii) in (1.6b)), and so is any non-empty subfunction of acceptable-in-r-of-D. Acceptability and its subfunctions are neither component variables (1.12) nor holis­ tic variables (1.15). Their status as linguistic variables is, however, not a major feature. Essentially, they provide a basis for external criteria, in the following way.

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Suppose that there are n basic-dialect areas for D*, r1,..., r n, n > 1. We may then identify the basic dialect division E of D* by means of function (10.4), as follows. First, for each (r, D*) the function supplies a property of idio­ lects, i.e. the function supplies the following set * of properties π ("π" stands for any property of C's): (10.5) * =df {π|π = acceptable-in-r1.-of-D*, for some i = l,..,n}. Intuitively, we take the basic-dialect areas for our historical language; for each area we consider the property of being an idiolect that is ac­ ceptable in this area in the sense of (10.4), i.e. the property of being an idiolect in the language that is acceptable, at some time, to some dialect informant at some place in this area; the set of these properties is n*. This set now identifies the basic dialect division itself: (10.6)

E=

{D | for some π  , D = the π-set},

i.e. E is the set of idiolect sets that are defined by properties from * (see (9.6) for "π-set"). Intuitively, a basic dialect of our language is the set of all idiolects of the language that are acceptable in the same basicdialect area. * may be taken as a set of external criteria with respect to D* (* is a set of criteria for E in the logical sense, see Sec. 9.2). * con­ sists of the values of a certain subfunction of the acceptability function defined in (10.4): of that subfunction whose arguments are the pairs (r, D) with D = D* and r  {r1,.., r n }, see (10.5). It may be claimed that the areas r, can be identified only after the dialects themselves have been delimited by system-based criteria; in this way the external criteria would depend on system-based ones. While this may be true as a point of methodology, it is irrelevant in the present context: all we require is a way of characterizing the areas in non-linguistic terms, or rather, without making reference to linguis­ tic systems; we certainly do not require that the areas should be discoverable by non-linguistic methods, such as purely geographical in­ vestigation. IT*, then, is the set of values of a certain subfunction of acceptabil­ ity as defined in (10.4). It is existence of such subfunctions that makes

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acceptability a criteria-determining function: the value of acceptability for any argument (r, D) — a certain property of elements C of D — is, so to speak, a 'potential' external criterion with respect to D. If (r,D) is also an argument of an appropriate subfunction, then the value of acceptability for (r, D) is an external criterion with respect to D. The general condition on such subfunctions — eventually to be called 'external points of view' — is this: the arguments of each subfunction must agree in their second components, and the set of their first components must be a 'permissible type of non-language entities'; it was assumed that the set of basic-dialect areas {r1, ..,r n } of D* is such a type. "Permissible type'5 will now be explained. 10.3 Permissible types of non-language entities The acceptability function involves regions in space-time in its argu­ ments. Instead of a spatiotemporal region we may allow any other non-language entity to which a speaker of an idiolect, or utterances ba­ sed on an idiolect, can be related: a social class, person, time etc. We must also allow tuples of such entities, say, a pair consisting of a re­ gion and a social class, if speakers or utterances are to be related to several non-linguistic entities simultaneously. (For example, if the so­ cial class of potential informants had not been fixed in (10.1), we might have wished to consider in (10.3) acceptability relative to both a region and a social class of which potential informant V is a member.) For simplicity's sake tuples of non-language entities will again be taken to be non-language entities. The notion of permissible type of non-language entities is now un­ derstood as follows, (i) Such a type is a non-empty 'homogeneous' set of non-language entities, i.e. a set of single entities of the same kind: regions, persons, etc., or a set of tuples of single entities where the i-th components of all tuples are single entities of the same kind; and (ii) there is a 'relation of belonging' that relates to each non-language enti­ ty in the set either some person or some utterance: they 'belong to' the non-language entity. Any such relation may be called associated with the permissible type. Additional requirements may be proposed for permissible types and associated relations but will not here be consid­ ered.

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These definitions, which are admittedly vague, may be exemplified as follows: the set of basic-dialect areas {r1 .., rn of D* is a permissi­ ble type of non-language entities because (i) it is a set of regions, and (ii) the relation defined as follows has the required properties: (10.7)

Definition. V is an informant in r during t iff for some p, a. p is in r; b. V is a potential dialect informant at p during t.

(Intuitively, the informants in a region during a certain time are the potential dialect informants that exist in the region during this time.) First, this is a relation of 'belonging5 — V 'belongs to' r during t — because of (a), (b), and the fact that the relation of potential dialect in­ formant is a complex relation of 'belonging', see our comments on (10,2); and second, we may assume, for each basic-dialect area ri, that there are informants in ri during some t, i.e. each ri is related to some person by relation (10.7), as required by our informal definition of permissible type. Suppose we choose a criteria-determining function like acceptabil­ ity in (10.4), select an appropriate permissible type of non-language entities and consider only arguments (x, D) where x is of the permissi­ ble type: we then obtain a subfunction of the criteria-determining function that is an external point of view for D. (We need not, how­ ever, actually start from a larger function but may directly consider a more restricted function with the right properties.) External criteria with respect to D are values of external points of view for D. 10,4 Points of view and criteria We begin by defining "external point of view" ("M" and "M1" stand for any sets; "x" stands for any set-theoretical entity and "D" for any set of C's, i.e. for any set of sets of form-meaning pairs): (10.8)

Definition 3. For any communication complex D, M is an external point of view for D iff M is a function such that, for some Mv a. M1 is a permissible type of non-language entities;

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b. the arguments of M are the pairs (x, D) such that x  M1; c. for any x  M1, M(x, D) [the value of M for (x, D)] is a property of elements C of D that is 'defined, or part­ ly defined, on the basis of a relation associated with M1. More informally, we take any (finite, non-empty) set D (of means of communication — any communication complex); in particular, this may be a subset of a language. An external point of view for D is a function. This function takes any pair (x, D) where x is from a given permissible type of non-language entities; all such pairs agree in their second component, which is D itself. With each pair the function asso­ ciates a property that only means of communication in D may have. The property is 'defined, or partly defined, on the basis of a relation associated with the given type of non-language entities. For example, if r  {r 1 ..,r n } and D = D*, then acceptable-in-rof-D is an external point of view for D: M1 = {r1, .., rn }, and the rela­ tion required by (10.8c) = the informant relation defined in (10.7); cf. the role of this relation in the definiens of (10.4), where (10.4b) may be reformulated as, "for some V and t, V is an informant in r during t and C is acceptable to V during t" (this exemplifies the formulation "defined, or partly defined, on the basis of", which should eventually be made more precise). In Sec. 10.2, the function acceptable-in-ri-of D*, for i = 1, ..,n, was used to define the set * of 'external criteria' (10.5), which was then used to identify the set E of basic dialects (10.6). A set like * of properties of means of communication C that is the set of values of an external criterion will be called an external set provided different properties in the set determine different sets of C; external criteria are the elements of external sets. More precisely: (10.9)

a. "π", "π", ... stand for any property of sets C of formmeaning pairs, in particular, any property of idiolects. b. "  , " 1 ", ... stand for any set of π'S. c. Definition 4 For any communication complex D,  is an external

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A THEORY OF LANGUAGE VARIETIES (III) set for D iff there is an M such that (i) M is an external point of view for D; (ii)  = the set of values of M; (iii) for any π1,π2 , if π1 ≠ π2, then the π1-set ≠ the π2-set [cf. definition (9.6)]. d. Definition 5 For any communication complex D, π is an external criterion with respect to D iff for some n , (i)  is an external set for D; (ii) π  .

This means, for sets D of idiolects: an external set for D is a set of properties of idiolects in D; the set must be the set of values of some external point of view for D, and different properties in the set must delimit different sets of idiolects. External criteria for D are the ele­ ments of external sets for D. * in (10.5) is an external set for histo­ rical language D*, and the property acceptable-in-r1-of-D*, among oth­ ers, is therefore an external criterion for D*: the property of being an idiolect C in D* such that C is acceptable, at some time, to some poten­ tial dialect informant somewhere in basic-dialect area 1, see (10.4). The set of idiolects C that have this property is a basic dialect of D*. We next consider 'system-based' criteria, the second major type of criteria underlying the variety structure of a language.

11 System-Based Criteria

11.1 The criteria-determining function System-based criteria are "defined by reference to systems for sets of idiolects such as languages and language varieties" (Sec. 5.4). Given our notion of system-for (Sec. 4.2), this formulation is more easily ex­ plicated than the corresponding one for external criteria; the explica­ tion is, by and large, analogous. Instead of external points of view we need 'system-based' ones to determine properties of idiolects that are system-based criteria. A sys­ tem-based point of view is again a function; it assigns properties of idi­ olects to pairs (σ, D), where σ is a system for a subset of communica­ tion complex D. System σ plays a role analogous to non-language enti­ ties in the case of external points of view. The property assigned by a system-based point of view to a given (σ, D) may be characterized as follows. σ is a set of properties of systems S of means of communication, in particular, of systems S of idiolects C. Consider the idiolects C whose systems S have specific properties from σ, for example, certain prop­ erties that all concern the syntactic part of idiolect systems; i.e. consid­ er the idiolects that are 'covered' by a certain subset of σ, possibly, σ itself. The property of idiolects assigned to (σ, D) by the point of view is exactly this: being an idiolect C  D that is 'covered' by a certain subset of σ, i.e. that has all the properties in the subset. The subset may be identical with σ; in this case we have an exhaustive system-based point of view. Only exhaustive points of view may be used for deter­ mining criteria that delimit varieties but it is still useful to allow for non-exhaustive ones. Points of view of either type are based on the single function of 'coverage'; whereas there are several criteria-determining functions

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that underlie external points of view, coverage is the only one for sys­ tem-based ones: (11.1)

a. "Ø", "Ø1", ... each stand for any property of entities S (where "S" stands for systems of entities C, such as id­ iolects). b. "σ", "σ 1 ", ... for any set of entities Ø. c. Definition 6. covered-by-σ-in-D = the property of being a C such that (i) C  D; (ii) for all S and all Ø, if S is a system of C and Ø  σ, then S has Ø.

The function covered-by-..-in-.. takes pairs ( σ ,D) as arguments and assigns to each pair a property. Informally, this is the property of be­ ing an element C of D, e.g. a certain idiolect, such that every system of C has every property in σ (σ is a set of properties of systems S). For example, if Ø1 = the property of being an S such that there is a definite article in S and σ ={Ø1} and D = Modern Standard German, then (be­ ing) covered-by-a-in-D = the property of being an idiolect C in D such that every system S of C has propertyØ1, i.e. is a system with definite articles. As a matter of fact, every idiolect in Modern Standard Ger­ man is covered-by-σ-in-D, for σ and D as just explained: there are de­ finite articles in the system or systems of every MSG idiolect. Note the analogies between (c) in (11.1) and (b) in (10.4), the def­ inition of "acceptable-in-r-of-D"; "a" in (11.1) plays the same role as "r" in (10.4). The definition of "covered" adopts the view that systems a for communication complexes are simply sets of properties of idio­ lect systems. This is not essential, though; if a is a more complex con­ struct from properties Ø, all we have to do is replace " " in (cii) by the name of a more complex set-theoretical relation. For system-based points of view we require coverage by systems that are, once again, of a 'permissible type'. 11.2 Permissible types of systems On the conception explained in Sec. 4, a single subset D1 of a language will have several systems of different degrees of abstraction, all based

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on the set of systems of idiolects in D l (on the 'D-system class for D 1 ') and arranged in a chain of increasingly abstract systems. We will ad­ mit only the initial members of such chains, to be called 'lowest' sys­ tems. "Permissible type" is therefore defined as follows, using approp­ riate variables: (11.2)

a. "T" stands for any set of entities S (where "S" stands for systems of entities C, such as idiolects). b. " Σ " (capital sigma) stands for any set of entities o (where "a" stands for any set of properties of entities S). c. Definition 7. Σ is a permissible type of systems with respect to D iff X is non-empty and for any σ, D 1 , and T, if σ  Σ and D1 = {C| C is covered-by-σ-in-D} and T = the D-system class for D1 then σ is a lowest TD 1 system.

This means we allow in X only systems that are lowest (least abstract) systems for the relevant set of idiolects (the relevant D-system class — for definitions of the terms used in (c), cf. Lieb 1970:196 and 230; in the definition of "unteres TD-System" l.c. 230, "S" must be replaced by "a"). Informally, Definition 7 may be understood as follows. Once again, we consider only subsets D of languages. In the case of system-based criteria, systems a are to play a role analogous to the role of non-language entities, such as geographical areas, in the case of external criteria. Just as permissible types of nonlanguage entities are sets of such entities, a permissible type of systems with respect to D should be a set of systems a; "X" is used as a variable for such sets. (Each a is a set of properties Ø of systems S, e.g. idiolect systems; hence Σ is a set of sets of properties of systems S.) In order to be a permissible type of systems w.r.t. D, X must be non-empty and satisfy the following condition. Take any σ from X, and consider the set of all C that are covered-by-σ-in-D, i.e. the set of all idiolects in D whose systems have all the properties in σ. Let this set be D1. D1 is a set of idiolects each of which has a system (at least one). We can therefore associate with D1 itself a set of idiolect systems; "T"

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is used as a variable for sets of systems S. The set of idiolect systems associated with D1 a set of idiolects, is, roughly, the set T that con­ tains, for each idiolect in D1, all systems of the idiolect that are 'rele­ vant' for the speaker or speakers of the idiolect. Set T is the D-system class for D1. In summary, choosing a σ from Σ we determine (i) the set D1 of idiolects in D whose systems have all properties in σ (D1 = the set of C that are covered-by-σ-in-D), and (ii) a certain set T of idiolect systems S (the D-system class for D1) that contains systems of each idiolect in D1. By a process of abstraction we next associate with D1 a chain of in­ creasingly abstract systems σ1 σ2, ... that are systems for D1 (for the entire set of idiolects covered-by-σ-in-D) not systems of the individual idiolects in D1. It is now required that σ = σ1 for some chain of sys­ tems associated with D1: this is the meaning of the condition that σ must be a lowest TD1-system. Definition 7 imposes this condition on any element σ of Σ: each σ must be a least abstract system for the set of idiolects that are coveredby-σ-in-D. An example of a permissible type of systems will be given in Sec. 11.4, below. It may be argued that the notion of permissible type of systems as defined in (11.2c) is still too broad and should be restricted by intro­ ducing additional conditions into the definiens. This would automatic­ ally strengthen all subsequent definitions and assumptions in Sec. 11. It will eventually turn out (Sec. 18) that a stronger version of definition (11.2c) is indeed necessary — and also sufficient — to integrate the component approach to language-internal variation into the variety ap­ proach; the notion of permissible type of systems thus occupies a key position. For now we stay with the weaker version (11.2c). System-based points of view are again obtained by combining the criteria-determining function with permissible sets. 11.3 Points of view and criteria The following definitions are largely analogous to the corresponding ones in Sec. 10.4 (the concepts defined in Sec. 11.3. are exemplified in Sec. 11.4):

SYSTEM-BASED CRITERIA (11)

(11.3)

105

Definition 8. For any communication complex D, M is a system-based point of view for D iff M is a func­ tion such that, for some Σ, a. Σ is a permissible type of systems with respect to D; b. the arguments of M are the pairs (σ, D) such that σ  Σ; c. for each σ  Σ, there is exactly one σ1  σ such that M(σ, D) [the value of M for (σ, D)] = the property of being a C that is covered-by-σ1-in-D.

As explained in Sec. 10.4, an external point of view (Def. 3) is a function that takes pairs (x, D) as arguments, where x is from a given permissible type M1 of non-language entities and all pairs agree in their second component, which is the given set D, say, a certain subset of a historical language. The function assigns to each (x, D) a property of elements C of D of a certain kind. In Definition 8, Σ, a permissible type of systems w.r.t. D, takes the place of M1, the permissible set of non-language entities; and the systems σ in Σ take the place of the non-language entities x in M r The function that is the system-based point of view again assigns to each (σ, D) a property of elements C of D. This is the property of being covered by a certain subset of σ1 i.e. being an element of C of D whose systems have all properties that are elements of σ1. There must be exactly one such subset, which may or may not be identical to σ. As mentioned in Sec. 11.1, it may be useful to allow 'non-exhaustive points of view', i.e. in considering a set σ of properties ø of systems of entities C we may wish to concentrate on some but not all of these properties; in this case the property assigned to (σ, D) by the point of view is: being covered by the set of selected properties not by a itself. 'System-based criteria' are determined via 'system-based sets', on the analogy of (10.9): (11.4)

Definitions 9 and 10 For any communication complex D, a.  is a system-based set for D iff there is an M such that (i) M is a system-based point of view for D;

106

A THEORY OF LANGUAGE VARIETIES (III) (ii)  = the set of values of M; (iii) for any π1 and π2  , if π1 ≠ π2, then the π1-set ≠ the π2-set. b. π is a system-based criterion with respect to D, iff, for some , (i)  is a system-based set for D; (ii) π  .

By (10.9) an external set for D is the set of properties of entities C that are assigned by an external point of view, where different properties delimit different sets. A system-based set is a set of properties obtained in the same way from a system-based point of view, and system-based criteria are the elements of system-based sets. System-based points of view — correspondingly, system-based sets and criteria — may but need not be 'exhaustive' in the following sense: (11.5)

Definitions 11 to 13 For any communication complex D, a. M is an exhaustive system-based point of view for D iff (i) M is a system-based point of view for D; (ii) for any a, if (a, D) is an argument of M, then M(G, D) = the property of being a C that is covered-by-G-in-D. b.  is an exhaustive system-based set for D iff [as in (11.4a), inserting "exhaustive" in (i)]. c. π is an exhaustive system-based criterion with respect to D iff [as in (11.4c), inserting "exhaustive" in (i)].

Intuitively, an exhaustive criterion is the property of being an idiolect that is covered by a complete lowest system for a certain subset of D, i.e. the property of being an idiolect in D whose systems have every property that occurs in the system for the subset of D. Among the non-exhaustive criteria we may distinguish purely pho­ netic, phonological, morphological, syntactic, and semantic ones by means of the following definition schemata ("+" stands for any of the italicized expressions):

SYSTEM-BASED CRITERIA (11)

(11.6)

107

Definitions 141-5 to 161-5 For any communication complex D, a. M is a purely + point of view for D iff (i) M is a system-based point of view for D; (ii) for any σ and σ1 if (σ, D) is an argument of M and M(σ, D) = the property of being a C that is covered-by-σ 1 -in-D, then for every ø e σ1 and any S that has ø: ø concerns only the + part of S [i.e. there is a property of parts of systems whose definition does not involve several parts, such that: ø is the property of being an S whose + part has that property]. b.  is a purely + set for D iff [as in (11.4a), substituting "purely +" for "system-based"]. c. π is a purely + criterion with respect to D iff [as in (11.4b), substituting "purely +" for "system-based"].

In (aii) the formulation "ø concerns only the + part of S" is explained in brackets and may be exemplified as follows. Suppose that the [ε]property w.r.t. S =df the property of being a part of S such that [ε] is a unit of the part. Suppose that ø1 = the property of being an S such that the phonetic part of S has the [ε]-property w.r.t. S (i.e. the phonetic part of S is a part of S such that [ε] is a unit of that part). Then ø1 con­ cerns only the phonetic part of S (+ = "phonetic"). A purely phonetic point of view is a system-based point of view. Such points of view specify properties of entities C that consist in be­ ing a C whose systems have all the properties ø in a given set σ1. For a point of view to be purely phonetic it is necessary by (aii) that all properties in σ concern only the phonetic part of systems S. Given the concept of a purely + point of view, the notions of a purely + set and a purely + criterion are defined as before, on the pat­ tern of (11.4). There are five expressions by which the plus-sign may be replaced in each of the three parts of (11.6). Definition schema (11.6) thus covers 15 different definitions. We obtain, in particular, the notions of a purely syntactic set and a purely syntactic criterion: this is the property of being an idiolect in D whose systems have cer­ tain properties each of which (i) occurs in a lowest system for a cer-

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tain subset of D and (ii) concerns only the syntactic part of idiolect systems. A fairly complex conceptual net was needed to explicate the intui­ tive notion of a system-based criterion. The following example is meant to show the definitions at work; although constructed, the exam­ ple should be sufficient for its limited purpose. It is not proposed that the two criteria introduced in Sec. 11.4 are actually sufficient for de­ limiting varieties. 11.4 Example Suppose that the two properties of idiolect systems, verb-final and free-order, are defined as in (4.3), roughly: (i)

verb-final = the property of being an idiolect system 'with final position of finite verbs as dominant clause order'.

(ii)

free-order = the property of being an idiolect system 'ha­ ving no dominant word order in clauses'.

Consider two sets σ1* and σ2* of properties of idiolect systems such that: (iii)

{verb-final} but not {free-order} is a proper subset of

(iv)

{free-order} but not {verb-final} is a proper subset of

(v)

For i = 1, 2, Di = the set of idiolects covered by σi.* in German and Ti. = the German system class for Di. (i.e. T. is a certain set of systems of the idiolects in Di.), it is true that σi* is a lowest Ti.Di.-system (i.e. σi* is a least abstract system for Di. that may be obtained from Ti.).

Suppose that (vi) Σ*=df {σ1*, σ2*}. It now follows from (v), (vi), and Definition 7 ("permissible type of systems", (11.2c)) that

SYSTEM-BASED CRITERIA (11)

109

(vii) Σ* IS A PERMISSIBLE TYPE OF SYSTEMS WITH RE­ SPECT TO GERMAN. Next, consider the function M* defined as follows: (viii)

M* =df the function M such that α. the arguments of M are the pairs (σ1*, German) and (σ2*, German); ß. M(σ 1 *, German) = the property of being an idiolect that is covered by {verb-final} in German (i.e. of be­ ing a German idiolect whose systems each have all properties in {verb-final}, i.e. have the property verb-final); γ. M(σ2*, German) = the property of being an idiolect that is covered by {free-order} in German.

It can be shown that (ix)

M* IS A SYSTEM-BASED POINT OF VIEW FOR GER­ MAN.

Proof. Definition 8 ("system-based point of view", (11.3)) is satisfied: M is a function, and Σ* is a Σ of the required type. First, Σ* is a per­ missible type of systems for German, by (vii). Moreover, by (α) in (viii) and (vi), the arguments of M* satisfy (b) in Def. 8. Finally, the sets σ1 required in (c) of Def. 8 are, for σ1*: {verb-final}, by (iii) and (ß) in (viii); for σ2*: {free-order}, by (iv) and (γ) in (viii). q.e.d. Moreover, (x)

M* is NOT AN EXHAUSTIVE system-based point of view for German.

This follows from either (iii) or (iv) (σ1 * ≠ {verb-final}, and σ2* ≠ {free-order}), (ii) in (11.5a), and the obvious assumption that for any σ1 ≠ σ2 and D, the property of being covered by σ1 in D differs from the property of being covered by σ2 in D. We next look for a system-based set for German that is properly related to M*. Let us define:

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(xi)

π1* =df the property of being an idiolect covered by {verb-final} in German.

(xii)

π2* =df the property of being an idiolect covered by {freeorder} in German.

(xiii)

*= df

{π1*,π2*}.

We show that (xiv) * IS A SYSTEM-BASED SET FOR GERMAN. Outline of proof . M* is an M as required for * by Def. 9 (11.4a). — M* is a system-based point of view for German, by (ix), and II* = the set of values of M*, by (xi) to (xiii) and (viii). Moreover, since verbfinal and free-order exclude each other (4.4), it should follow that π1* ≠ π2*. We may further assume that {C | C is covered by {verb-final} in German} ≠ {C | C is covered by {free-order} in German}. It then fol­ lows from (xi) to (xiii) that, for any different π1 and π2  *, the π1set ≠ the π2-set, as required by (iii) in (11.4a). Therefore, (xiv) holds, (q.e.d.) Obviously, (xv)

* is NOT AN EXHAUSTIVE system-based set for German,

In addition: (xvi) π1* and π2* ARE SYSTEM-BASED, BUT NOT EX­ HAUSTIVE SYSTEM-BASED, criteria with respect to German. Cf. Definitions 10 (11.4b) and 13 (11.5c). — Finally, (xvii)

M* IS A PURELY SYNTACTIC POINT OF VIEW FOR GERMAN.

Outline of proof We show that Def. 144 (11.6a) is satisfied. — First, M* is a system-based point of view for German, by (ix). Second, con­ sider (ii) in (11.6a). Either σ = σ1* and σ1 = {verb-final}, or σ = σ2* and σ1 = {free-order}. Suppose that ø = verb-final or ø = free-order.

SYSTEM-BASED CRITERIA (11)

111

Then for any S that has ø, ø concerns only the syntactic part of S, by (4.4). This, then, is true of every ø in σ1 i.e. condition (ii) in (11.6a) is also satisfied, (q.e.d.) System-based criteria π are in the last analysis determined by properties $ of idiolect systems where ø is an element of some system a for some subset of language D. These properties ø in turn may be de­ termined by linguistic variables, as explained below, in Sec. 18.2. Dis­ cussion in Sec. 18 therefore also exemplifies, in an indirect way, sys­ tem-based criteria. We now go on to formulate two assumptions on variety structures from which the 'correlation theorem' — relating system-based and ex­ ternal criteria — can be derived. 11.5 The correlation theorem By the following Assumption 2 external criteria underlie any variety structure: (11.7)

Assumption 2. For any historical language D and any E, if E  the variety structure of D, then there is a  such that a.  is an external set for D; b. E = {D1| for some π  , D1 = the π-set}.

Intuitively, any classification in the variety structure is obtained by ap­ plying the external criteria determined by some external point of view: the varieties in the classification are the sets of idiolects determined by the criteria. Assumption 3 assigns system-based criteria the same role as exter­ nal ones: (11.8)

Assumption 3. For any historical language D and any E, if E  the variety structure of D, then there is a  such that a.  is an exhaustive system-based set for D; b. E = {D1 | for some π  , D1 = the rc-set}.

The two assumptions yield the correlation theorem:

A THEORY OF LANGUAGE VARIETIES (III)

112 (11.9)

Theorem 1 (Correlation Theorem), For any historical language D and any E  the variety structure D, there is a  and a 1 such that a.  is an external set for D; b.  is an exhaustive system-based set for D; c. E is a classification on E by ; d. E is a classification on E by 1.

Proof. We prove (a) and (c), using the definition of "N is a classifica­ tion on M by A" (9.7), D is a historical language and E  the variety structure of D, by hyp. Hence, there is a  such that (a), by Ass. 2; and E is a classifica­ tion on some D1 by Def. 1 (9.13). D 1 = E by definitions (9.2) and (9.1). Therefore, E is a classification on E, as required by (9.7a). We show that (9.7b) and (9.7c) are also satisfied. By (b) in Ass. 2, if π   and D1 = the π-set, then D1  E; hence, (9.7c) is satisfied. Moreover, for each D1  E there is a π   s.t. D1 = the π-set, again by (b) in Ass. 2. Let π1  , π ≠ π1 Assume that D1 = the π1-set. Since  is an external set for D, the π1-set ≠ the π-set, by (iii) in Def. 4 (10.9c), therefore, D 1 π the π-set, which is a contradic­ tion. Hence, there is no π1   , π ≠ π1 s.t. D1 = the π1-set, Therefore, π is the only set such that D1 = the π-set, i.e. (9.7b) is also satisfied. Therefore, E is a classification on E by , by (9.7); i.e. (c) in (11.9) is true. In a strictly analogous way, using Ass. 3 instead of Ass. 2, we show that (b) and (d) in (11.9) also hold. Q.E.D. The correlation theorem is of fundamental importance to the con­ ception of variety structure; it states that any classification in the varie­ ty structure can be obtained both by a certain set of external criteria and a certain set of system-based criteria; as a consequence, any varie­ ty of a historical language can be independently specified both by an external and by a system-based criterion. Important as it is as part of the general conception, the correlation theorem will not figure in the rest of this essay, where independent parts of the theory are going to be developed. We now introduce two additional assumptions that further relate varieties either to historical languages or to other varieties and allow

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113

to explicate the sense in which varieties may be said to be 'given' through variety structures. Furthermore, the notion of 'idiolect loca­ tion' (either in a language or a variety) will be clarified by referring to variety structures. We directly resume Sec. 9.6.

12 Languages, Varieties, Idiolects

12.1 Varieties and languages On a traditional view, varieties are either varieties of 'languages' or varieties of such varieties. I adopt this view, identifying 'languages' with historical languages: (12.1)

Assumption 4. If D2 is a variety of D1 then there is a his­ torical language D such that either (a) or (b):

a. D1 = D; b. D1 is a variety of D. Intuitively, only historical languages and their varieties may have vari­ eties. Furthermore, it agrees with traditional conceptions to assume that the varieties D2 of a variety D 1 of D are exactly the classes in — i.e. elements of elements of — the variety structure of D1 (this does not yet follow from the definition of "variety structure of D1 in D", (9.14)): (12.2)

Assumption 5. If D is a historical language and D1 a vari­ ety of D, then D2 is a variety of D1 if and only if D 2 is a class in the variety structure of D1 in D.

Given Assumption 1 in (9.12) and Assumptions 4 and 5, we derive a second major theorem (note that Assumptions 2 and 3 are not used): the varieties of any D 1 are exactly the classes in the variety structure of D 1 if D1 is a historical language, or else they are the classes in the variety structure of D1 in some historical language; more precisely: (12.3)

Theorem 2. D2 is a variety of D1 if and only if there is a historical language D such that either (a) or (b):

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a. D1 = D, and D2 is a class in the variety structure of D; b. D1 is a variety of D, and D2 is a class in the variety structure of D1 in D. Intuitively, we consider any D1 The varieties of D1 are given differ­ ently depending on whether D1 is a historical language, or just a varie­ ty of a historical language. In the first case the varieties of D 1 are the classes in its variety structure; in the second case the varieties of D1 are the classes in the variety structure that D1 has in the historical lan­ guage. Theorem 2 thus shows that the notion of variety is related in a natural way to the two notions of variety structure defined in (9.13) and (9.14). Proof of T2. A. Let D 2 be a variety of D1 We show that there is a his­ torical language D such that (a) or (b). By Ass. 4 there is a historical language D such that either (a) D 1 = D, or (b) D 1 is a variety of D. Case a. In this case, D2 is a variety of D. Now D is a historical lan­ guage. Hence, D 2 is a class in the variety structure of D, by (9.13) and (9.12b). Therefore (12.3a) is satisfied. — Case b. (12.3b) holds, by Ass. 5. B. Suppose that there is a historical language D such that (12.3a) or (12.3b). If (12.3a), then D2 is a variety of D, hence, of D1, by (9.13) and (9.12b). If (12.3b), then D 2 is a variety of D 1 by Ass. 5. Q.E.D. It now follows that (12.4)

Theorem 5. If D2 is a variety of D1, then a. for some historical language D, D 1  D; b. D 2 is a non-empty proper subset of D1; c. D 2 is not a historical language; d. D 2 is a communication complex (a non-empty, finite set of means of communication).

Informally, only subsets of a historical language can have varieties (a); varieties are non-empty sets (of idiolects) and are contained in but dif­ ferent from what they are varieties of (b); they are not themselves his­ torical languages — to this extent the traditional attempts to distinguish

LANGUAGES, VARIETIES, IDIOLECTS (12)

117

'languages' from 'varieties' are legitimate: we must know if something is or is not a historical language if we wish to decide on whether it is a variety of anything (c); and, being a non-empty subset of some histori­ cal language, a variety is a communication complex (d). Proofs of T3a,b. Suppose that D2 is a variety of D1. By Th. 2, there is a historical language D such that either (12.3a) or (12.3b). Proof of T3a a. (12.3a) holds. — Then D1 = D, hence, (12.4a), since D is a his­ torical language. b. (12.3b) holds. — Then D1 is a variety of D, therefore, by (9.12b), a class in the F postulated for D in (9.12) (i.e. the variety structure of D), and F is a classification system on D by (9.12a). It now follows from (diii) in (9.10) that D1 is a subset of D. q.e.d. Proof of T3b a. (12.3a) holds. — D 2 is then a class in the variety structure of Dv since D = D1 This is a classification system on D 1 by (9.13) and (9.12a); therefore, D 2 is a non-empty proper subset of D1 by (diii) in (9.10). b. (12.3b) holds. — By the argument used in (b) of the Proof of T3a, D1 is a class in the variety structure of D, which is a classification system on D (hence, a division system on D). Furthermore, D 2 is a class in the variety structure of D 1 in D if (12.3b) holds, hence, a class in the Depart of the variety structure of D, by (9.13). D1 is therefore no endpoint of the variety structure of D, by (di) in (9.10). It now fol­ lows from (cii) in (9.10) that the D1-part of the variety structure of D is a classification system on D1 since the structure is such a system on D. As D 2 is a class in the D1-part, we have it by (diii) in (9.10) that D 2 is a non-empty proper subset of D1 q.e.d. Proof of T3c. By T3a, D1 is a subset of some historical language D. By T3b, D 2 is a proper subset of D1, hence of D. It now follows that D 2 is not a historical language, from an ASSUMPTION ON LAN­ GUAGES made in Sec. 4.1: no historical language is a proper subset of a historical language. Q.E.D. Proof of T3d. The theorem follows from Ass. 5 (12.2), T3b, and an­ other ASSUMPTION ON LANGUAGES made in Sec 4.1: any histori­ cal language is a communication complex. (Q.E.D.)

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It was emphasized that "variety" is a relational term. There are standard properties that may characterize a relation, such as reflexivity, symmetry etc. Such properties must also be established for the va­ riety relation if this relation is to be properly understood. 12.2 Properties of the variety relation It follows directly from Theorem 3b that (12.5)

Theorem 4. Variety is asymmetric and irreflexive.

(Asymmetry: if D 2 is a variety of D1 then D 1 is not a variety of D 2 ; irreflexivity: no D 2 that is a variety of anything is a variety of itself.) Proof: By Th. 3b, Variety is a subrelation of Proper Subset, which is asymmetric; hence, Variety is asymmetric, too, by a law of logic; and is irreflexive because any asymmetric relation is. Q.E.D. Furthermore, the variety relation is transitive if restricted to the 'varieties specific to' a single historical language. "Variety specific to" is understood as follows: (12.6)

Definition 11. Let D be a historical language. D 1 is a variety specific to D iff a. D1 is a variety of D; b. for any historical language D 2 , if D1 is a variety of D 2 , then D 2 = D.

Note that the term defined in (12.6) is not "specific to" but "(is a) vari­ ety specific to". Informally, the varieties specific to a given historical language are those of its varieties that are not varieties of any other language. It can be demonstrated, by a non-trivial proof, that (12.7)

Theorem 5. If D is a historical language, then Variety restricted to the set of varieties specific to D is transitive.

This is to say: for all varieties D3, D 2 , and D1 specific to D, if D 3 is a variety of D 2 , and D 2 of D1, then D 3 is a variety of D1. Informally, we allow only such varieties of a given historical language that are varie-

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119

ties specific to the language. In the set of these varieties, the variety re­ lation is transitive, i.e. take three such varieties of the historical lan­ guage and assume that the first (D3), in addition to being a variety of the historical language (D), is also a variety of the second variety (D2) of the language, which in turn is a variety of the third variety (D1) of the language: then the first variety (D3) of the language is also a varie­ ty of the third variety (D1) of the language. Thus, a variety of a varie­ ty of a subset of a language is also a variety of the subset as long as all are varieties of the language, and of no other language. Proof of T5. Suppose that (i)

D is a historical language;

(ii)

D 3 , D2, and D1 are varieties specific to D;

(iii)

D 3 is a variety of D2;

(iv)

D 2 is a variety of D1.

We show that (v)

D 3 is a variety of D1

by applying Th. 2 and Th. 3c. D 3 is a variety of D 2 by (iii). Hence, there is a historical language D* such that either (12.3a) or (12.3b), by Th. 2. Suppose that (12.3a). Then D 2 = D*. Now D2 is a variety of D1 by (iv), hence, D* is a varie­ ty of D1, therefore not a historical language by Th. 3c, which gives rise to a contradiction. Therefore, (12.3b), i.e. (vi)

D 2 is a variety of D*, and D 3 is a class in the variety structure of D2 in D*.

In an analogous way it follows from (iv), Th. 2, (ii), Def. 11(a) and Th. 3c that, for some historical language D**, (vìi)

D1 is a variety of D**, and D2 is a class in the variety structure of D1 in D**.

In order to prove (v), we must find a historical language that satis­ fies either (12.3a) or (12.3b) with respect to D 3 and D1. This language

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cannot be D1 itself, because of Th. 3c and (ii). Hence, only (12.3b) may apply. We show that D in (i) is itself an appropriate language. First, D1 is a variety of D**, by (vii). Now D1 is a variety specific to D by (ii). Therefore, D** = D, by Def. 11. Hence, D 2 is a class in the variety structure of D1 in D by (vii), which means, because of Def. 2 (9.14), (viii)

D 2 is a class in the D1-part of the variety structure of D.

By (ii), D1 is a variety of D; therefore, bv Def. 1 (9.13) and Ass. 1 (9.12b), (ix)

D 1 is a class in the variety structure of D.

It follows from (ix), (viii), and (dii) in (9.10) that (x)

the D2-part of the variety structure of D  the D1-part of the variety structure of D.

Second, D2 is a variety of D*, by (vi). Now D2 is a variety specific to D by (ii). Therefore, D* = D, by Def. 11. Hence, D3 is a class in the variety structure of D 2 in D by (vi), which means, because of Def. 2 (9.14), that (xi)

D 3 is a class in the D2-part of the variety structure of D.

It follows from (xi) and (x) and the definition of "class in" (9.0) that (xii)

D 3 is a class in the D1-part of the variety structure of D.

Therefore, by (ii), Def. 11(a), (xii), and Def. 2 (9.14): (xiii)

D 1 is a variety of D, and D 3 is a class in the variety struc­ ture of D 1 in D.

We now derive (v) from (xiii) and (i) by Th. 2b. Q.E.D. There is a strong intuition underlying informal talk on varieties that the variety relation is transitive. It turns out that transitivity of the relation can be proved only for the varieties specific to a single histor­ ical language. The relative complexity of the proof also demonstrates that the notion of variety is not easily handled intuitively.

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We next turn to the place that individual idiolects may have in the variety structure of a language or language variety. 12.3 Idiolect location in historical languages Given the concept of variety structure of a historical language (9.13) and the logical concept of place (9.11b), we define the 'location' of an idiolect in a language as its place in the variety structure: (12.8)

Definition 12. Let D be a historical language and C  D. The location of C in D = the place of C in the variety structure of D.

The location of an idiolect in a language D is a set of place assign­ ments (9.11a) for the idiolect in the variety structure. Each place as­ signment is a set of varieties that are endpoints of the variety structure and contain the idiolect; thus, a place assignment for an idiolect C is a set E of sets D 2 of idiolects, a set that is of the same type as the classifi­ cations that yield the varieties. E does not contain different classes that belong to the same classification in the variety structure. The idiolect C is an element of each element of E. A place assignment is a specific way of relating an idiolect to the variety structure. The set of assignments, or the 'place' (9.11b) of the idiolect in the variety structure of language D, is the location of the id­ iolect in D. The location of idiolect C is thus a set F of sets E of sets to which C belongs. The location of an idiolect is of the same type as the variety structure itself. Consider the following example for idiolect location. Let D be German and assume that the variety structure of German contains, among others, the following classifications where at least the classes listed are endpoints of the variety structure (see also Diagram (8.1)): (12.9)

a. b. c. d. e.

{Modern German1 (MG 1 ),...} {MG1  Bav(arian)1 ...} {MG1  Coll(oquial)5, ...} {MG1  P(ersonal) V(ariety)n, ...} {Per(iod)2 of Bav1 Per3 of Bav1 ...}

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f. {Per4 of Suab(ian)1, ...} g. {PVn, ...} Assume that h. MG1,  PVn = PVn Number subscripts in (a) indicate certain unspecified periods of Mod­ ern German, construed in turn as a historical period of German. (MG1 could be Early Modern German — the union of Frühneuhochdeutsch and the corresponding part of Niederdeutsch — unless EMG is itself construed as a historical period of German.) Number subscripts else­ where in (12.9) indicate certain unspecified periods or 'subforms' (non-temporal varieties) of non-temporal varieties of German; PVn , for some unspecified n, is an element of the personal variety division of German. Lines of dots indicate further entities of a given type. (Note that sets (a) to (g) can at present be specified only hypothetically and incompletely — the dots remain: the underlying period of German — Modern German — is still in progress.) Let C be a German idiolect such that in each of the classifications listed in (12.9), C is an element of the classes whose names are actually given. In this case, (12.10) The location of C in German = {{MG1, MG1,  Bav1, MG1  Coll5, MG1,  PVn , Per2, of Bav 1 , Per4 of Suab1 ...}, {MG1, MG1,  Bav1, MG1,  Coll5, MG1  PVn , Per3 of Bav 1 Per4 of Suab1, ...},

(In (12.10) the names of the two varieties that give rise to at least two place assignments are in italics. Because of C, the two periods of Bava­ rian1 overlap with each other and with the period of Suabian1 VPn in (12.9g) is accounted for in (12.10), cf. (12.9h).) We may also wish to consider the location of an idiolect not in a complete historical language but in a variety.

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12.4 Idiolect location in varieties The concept is defined in an obvious way: (12.11) Definition 13, Let D be a historical language and D1 a va­ riety of D with a non-empty variety structure, and C  D1 The location of C in D 1 and D = the place of C in the va­ riety structure of D 1 in D. Consider, for example, the location of idiolect C (Sec. 12.3) in Bavarian and German. This is a set rather different from the location in German (12.10): (12.12) The location of C in Bavarian and German = {{Per2 of Bav1, ...}, {Per3 of Bav1, ...},

The location of C in Bavarian and German is obtained by restricting the location of C in German to those varieties which are varieties of Bavarian. It is assumed that MG1  Bav1 in (12.10) is no variety of Bavarian. MG1  PVn (= PVn) may be taken to be a proper subclass of Bavarian but this is not sufficient to make PVn a variety of Bavarian; as a matter of fact, this personal variety is an element of the personal variety division of German, a first-level element of the variety struc­ ture of German. Personal varieties of a language are not miniature re­ gional dialects. The two examples (12.10) and (12.12) also emphasize the differ­ ence between an idiolect and a personal variety of a language: an idio­ lect simultaneously belongs to a large number of different varieties, which are sets of idiolects; and there is at least one personal variety of which the idiolect is an element. The personal variety may contain oth­ er idiolects, all of them means of communication for the same person. Some of these idiolects may actually belong to different varieties in the same classification, such as different regional dialects, without be­ longing to their overlapping parts.

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It is not only idiolects but idiolect systems, their components and properties that may be related to the variety structure of a language or language variety.

13 Varieties and Idiolect Systems

13.1 Location of idiolect systems Idiolect systems in a subset of a language are the systems of idiolects in the subset: (13.1)

Definition 14. Let D be a subset of a historical language. S is an idiolect system in D iff for some C  D, S is a sys­ tem of C.

An idiolect is a means of communication, a certain set of form-mean­ ing pairs. For any means of communication C there may be several S such that S is a system of C but for any S there is at most one C of which it is a system; this is part of the conception of a means of com­ munication. (Assumption of at most one C is compatible with a con­ ception, not ruled out in Secs 6.4f, by which subsets of idiolects may again be idiolects; such a subset would be determined by a part of a system S that is itself a system.) Also, for any S there is a C such that S is a system of C (which agrees with the interpretation of "S" in (4.8)). Therefore, for any S there is exactly one C of which it is a system, called the means of communication for S, mc(S). In particular, an idi­ olect system S in D is a system of exactly one C. Idiolect systems may be related to variety structures via the means of communication they determine: the location of an idiolect system is simply the location of this means of communication. More precisely, (13.2)

Definitions 15 and 16. Let D be a historical language, a. For any idiolect system S in D, the location of S in D = the location of mc(S) in D.

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b. Let D 1 be a variety of D with a non-empty variety structure. For any idiolect system S in D1, the location of S in D1 and D = the location of mc(S) in D 1 and D. The two terms "location" may be indexed to make them formally dif­ ferent from the corresponding terms in (12.8) and (12.11), changing them to something like "s-location". It is the two notions of variety structure in Sec, 9.5 that keep generating concept pairs like the ones in (13.2). As an example, assume that (i) S is an idiolect system in German and, more specifically, in Bavarian; (ii) the location of mc(S) in Ger­ man is as in (12.10), and the location of mc(S) in Bavarian and Ger­ man as in (12.12). Then these locations are also locations of S itself. 13.2 Position of system components It is not only idiolects and idiolect systems that must be related to vari­ ety structures but specific components of idiolect systems, such as: phonemes; lexical words; syntactic units, categories, and structures; entire subsystems of idiolect systems, etc. — system components, for short. (Actually, if S is a system of C, then C itself might be included among the components of C. For obvious reasons C is here excluded from the components, differently from the elements of C, individual 'sentences', which are included.) Relating system components (not necessarily understood as compo­ nents of idiolect systems) directly to varieties is standard practice in linguistics; thus, lexical words are characterized in lexicology as be­ longing to a certain regional or temporal variety, a register or style, etc. Evaluation grammars (see Secs 2.3 and 16f) take this practice for orientation. As a matter of fact there is a tendency to single out only such sys­ tem components that are 'specific to' given varieties; 'nonspecific' components that can be related to a large number of different varieties are left unmarked. But surely both 'specific' and 'nonspecific' compo­ nents occupy a certain 'position' relative to the variety structure of a language or language variety, and it is this more general concept of position that will be defined first.

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The position of a system component in a historical language is de­ termined by referring to the locations of all relevant idiolect systems in the language: for the component, we take any set E of varieties such that E belongs to the location — as defined in (13.2a) — of some idio­ lect system S that has the component; the set of such E's is the compo­ nent's position in the language. Similarly, (13.2b) is used to define the position of a system component in a language variety. For a more precise formulation, use "c" for any component of idiolect systems S (see (4.8)): in particular, for any subsystem (part) of S (on the conception that I here adopt, no part of S may again be an idio­ lect system), and for any unit, category, structure, or function in any subsystem of S, be it a formal subsystem (phonetic, phonological, mor­ phological, syntactic) or a semantic one. "Position in a language" and "position in a language variety" are now explicated for system components by the following definitions: (13.3)

Definitions 17 and 18. Let D be a historical language. a. The position of c in D = the set of all E such that, for some S, (i) S is an idiolect system in D; (ii) c is a component of S; (iii) E  the location of S in D. b. Let D 1 be a variety of D with a non-empty variety structure. The position of c in D1 and D = the set of all E such that, for some S, (i) S is an idiolect system in D1; (ii) c is a component of S; (iii) E  the location of S in D1 and D.

Informally, consider any historical language and any component of id­ iolect systems, say, a certain phonetic sound. The position of this sound in the language is a set whose elements E are given as follows. There must be an idiolect system in the language of which the sound is a component (note that existence of such a system is not presupposed in the definition) such that set E belongs to the location of the idiolect system in the language. By previous definitions, E is a set of varieties

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of the language such that the idiolect system that has c as a component belongs to each of these varieties. Any E that satisfies this condition belongs to the position of the sound in the language. Now there may be several idiolect systems in the language of which the sound is a compo­ nent. Any E in their locations enters the position of the sound. We may even have chosen a sound that is totally wrong for the language, i.e. is not a component of any idiolect system in the language. The notion of position would still apply: the position of the sound in the language would be the empty set. These explanations carry over to (b) in (13.3). We simply consid­ er the idiolect systems in a given variety of a language such that the sound is a component of each of the idiolect systems; the position of the sound is then obtained from the locations of these systems not just in the language but in the variety and the language. In any case the position of a system component is a set F of sets E of sets of idiolects; in this the position does not differ from the loca­ tion of an idiolect or idiolect system. However, while the location of an idiolect system is the same as the location of the idiolect, the posi­ tion of a system component is based on the locations of all relevant idi­ olect systems. We next define the concept of a system component being specific to a variety; this concept is independent of the notion of component position. 13.3 Variety-specific

components

Consider a classification E in the variety structure of a historical lan­ guage D, and a variety D1 in E. A system component c may be specific to D1, or specifically D1, in E and D in the following sense: any system S in D of which c is a component — such a system is assumed — de­ termines an idiolect C that (i) belongs to D1 and (ii) does not belong to any other variety in E, i.e. S determines an idiolect C that is 'specific to' D1 in E in the general sense of definition (9.5). For example, we may wish to say that a certain word, sentence construction etc. is 'colloquial', meaning that it is only or specifically colloquial in the following sense: it is related in the above way to the set Colloquial that occurs in a certain register division E based on

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some subset of Below-Neutral (which is a basic register, see Sec. 8.3), and it is not so related to any other register in E. Components may be variety specific only relative to a variety in a given classification E in the variety structure. Moreover, components of systems of idiolects that belong to a given variety may or may not be variety specific, a fact that is rarely noticed (but see Kubczak 1987:271). It is for these two reasons that concepts of component posi­ tion as defined in (13.3) cannot be replaced by the notion of 'variety specific'. "Specific to (a variety)" is defined as follows ("mc(S)" is short for "the means of communication for S", see Sec. 13.1): (13.4)

Definition 19. Let D be a historical language and E e the variety structure of D. c is specific to D1 [specifically DJ in E and D iff a. for some S, (i) S is an idiolect system in D, (ii) c is a component of S; b. for all S such that (ai) and (aii), mc(S) is specific to D1 in E [see (9.5)].

Informally, we take a classification that belongs to the variety struc­ ture of a historical language, and consider a variety that belongs to that classification. A system component may be specific to the variety in the classification and the language, in the following sense: first, the component is a component of some idiolect system in the language; and second, given any idiolect system in the language that has this compo­ nent, the following is true of the idiolect determined by the system: within the classification, the idiolect is specific in the logical sense to the variety; this means that the idiolect occurs in the variety and does not occur in any other variety from the given classification (the idio­ lect may well belong to varieties from other classifications in the vari­ ety structure). In this way the notion of variety-specific for system components is based on the set-theoretical notion of specific-in-a-classification, applied to idiolects, varieties, and the classifications in the variety structure of a language. For example, consider a word of some German idiolect system, and assume that all German idiolect systems in which the word occurs

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determine idiolects that are 'specific to' Bavarian in a (non-basic) dia­ lect division of German, in the logical sense of "specific to". Then this word itself is specifically Bavarian in the dialect division. Generally, variety labels in lexicology — and, it would seem, in Evaluation Grammar — name varieties to which a system component is specific. Note on (13.4). In Definition 19 we proceeded from a historical lan­ guage and a classification in its variety structure. "Specific to" was then relativized to a variety D1 in the classification (D1  E follows from (a) and (b) in (13.4) and (9.5b)). We might also introduce a fur­ ther concept "specific to" that is relativized to a variety D2 of a variety D 1 of a language D. Such a concept would, however, serve no practical purpose since D 2 again would be an element of some E in the variety structure of D, i.e. Def. 19 would still apply. In addition to components, it is properties of idiolect systems that may or may not be specific to a variety. 13.4 Variety-specific

properties

Suppose that c is a component of a German idiolect system S, say, is a sentence construction in S. System S then has a certain property ø*: the property of being an S1 such that c is a component of S1, i.e. such that c is a sentence construction in S1. Suppose, furthermore, that c is specifically Colloquial in an ap­ propriate register classification and German. It would then be natural to say that ø* — the property of being an S1 such that c is a sentence construction in S1 — is also 'specifically Colloquial'. In this example the two fashions of speaking appear to be equiva­ lent. But this is not generally so: a concept of 'specific-to' that applies to properties of idiolect systems has wider applicability than the con­ cept defined in (13.4) for system components. The reason is that all linguistic properties of idiolect systems may not consist in being a sys­ tem with a certain component. This also means that 'specific-to' for properties cannot be defined simply by 'specific-to' for components; an independent if analogous definition is required ("ø" stands for any property of entities S):

VARIETIES AND IDIOLECT SYSTEMS (13)

(13.5)

131

Definition 20. Let D be a historical language and E e the variety structure of D. ø is specific to D1 [specifically D1] in E and D iff a. for some S, (i) S is an idiolect system in D, (ii) S has ø; b. for all S such that (ai) and (aii), mc(S) is specific to D1 in E.

Informally, we consider a classification in the variety structure of a historical language, and a variety in the classification. A property of idiolect systems is specific to that variety in the classification and the language if it is a property of some idiolect system in the language and if any such idiolect system of which it is a property determines an idi­ olect that, in turn, is specific to the variety in the classification in the logical sense. The definition differs from Definition 19 only in substituting "<()" for "c" and, in (aii), "S has ø" for "c is a component of S". (The Note on (13.4) applies to (13.5) in an analogous form.) Differently from what the literature would suggest, it is 'specificto' for properties not components that is a key concept in variation re­ search: while different idiolect systems may share linguistic units, more complex components such as categories (sets of units) turn out to be typically different: the set of noun phrases in one idiolect system will hardly ever be the same as the set of noun phrases in another sys­ tem. At the same time the two systems will usually agree in the property of having a non-empty noun-phrase category. It is such proper­ ties, rather than system components, that are natural candidates for be­ ing or not being specific to a variety. Properties of idiolect systems also play a pivotal role in Part IV (esp. Sec. 18), in which the theory of Part III is extended so as to ac­ count not only for the holistic approach to language-internal variation but also for the component approach.

PART IV

INTEGRATING THE COMPONENT APPROACH

14 Variants and Variables

14.1 Introduction In Parts II and III I outlined a theory of language varieties that repre­ sents a specific version of the variety approach. The component ap­ proach, too, must now be given a more specific form, i.e. we are con­ fronted with the following problem: (14.1)

The explication problem, (a) Develop a specific version of the component approach and (b) demonstrate that rele­ vant proposals for dealing with linguistic variation are covered by this version.

Moreover, the two approaches must be linked. Since I am proposing to take the variety approach as basic, I must also solve (14.2)

The integration problem. Demonstrate how the compo­ nent approach (in its more specific version, and possibly restricted to language-internal variation) may be integra­ ted into the variety approach (in its more specific ver­ sion).

Nearly all examples used used in Secs 14ff will be from syntax; the solutions proposed for the two problems are, however, quite gen­ eral. Section 14 offers a solution to part (a) of the explication prob­ lem. Sec. 15 argues for its adequacy in connection with (b): it will be shown how conceptions of linguistic variation that are as different as Chomsky's ('Principles and Parameters') and Seiler's (the UNITYP framework) may be reconstructed within the proposed framework. This is followed in Secs 16 and 17 by a more detailed discussion of 'evaluation grammars', which where briefly characterized in Sec. 2.3,

13 6

INTEGRATING THE COMPONENT APPROACH (IV)

and the 'variable rule approach' originating from Labov. Secs 16 and 17 are unavoidably technical and may presuppose some previous knowledge of work on 'variable rules' and 'evaluation grammars' (since proposals for such grammars differ, they had to be harmonized to some extent). Discussion in Secs 16 and 17 is, however, no prere­ quisite for understanding Sec. 18, which offers a solution to the in­ tegration problem. In solving the explication and integration problems, certain basic ideas from Integrational Linguistics (Lieb 1983: Part G) will be em­ ployed: the conception of a grammar being 'formulated in terms of' a theory of language, which is essential to the integrational theory of lin­ guistic grammars (see also Lieb 1980a, 1989), is transferred to the level of the object of grammars; just as a grammar (description) of a language variety may be formulated in terms of a theory of language, systems for varieties may be 'specified', completely or in part, by lin­ guistic variables that 'apply to' certain sets of idiolect systems, or to any such set; i.e. systems may be specified by variables that are 'varia­ bles in' sets of idiolect systems. (It turns out, then, that essential ideas in recent Generative Grammar — among others — may be recon­ structed within the more general framework of Integrational Linguis­ tics.) A simple example may serve for initial orientation. 14.2 Orientation Consider an expression like "Noun Group" (ordinarily, "Noun Phrase"), traditionally taken to be a name of a syntactic category. As­ sume that categories etc. are relativized to idiolect systems (as in Inte­ grational Linguistics) not to systems for language varieties or langua­ ges. We thus start from terms like (14.3)

c is a Noun Group [NGr] of S,

where c is a syntactic unit of idiolect S ("c", " c " , ... stand for any components of idiolect systems, see Sec. 13.2, above; a more precise interpretation of "component" and "is a Noun Group of' depends on the presupposed theory of language). Formulation (14.3) is logically equivalent to (14.4)

c  NGr(-,S),

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137

where (14.5)

NGr(-, S) = NGr-of-S = the set of all c1 such that c1 is a Noun Group of S.

Now compare the two expressions: "is a Noun Group of', or "NGr" for short, in (14.3), and "NGr(-S)" in (14.4) and (14.5). The first is a name of a relation that holds between entities c and idiolect systems; set-theoretically, "NGr" denotes a set of pairs (c, S), a set that is a component variable in the sense of (bi) in (1.8). The second is a com­ plex term from which a term denoting a set of syntactic units is ob­ tained if we replace the variable "S" by a name, say "S", of a specific idiolect system: "NGr(-, S)" — or "NGr-of-S" — denotes a set of syntactic units of S that is a syntactic category of S. The transition from "NGr" (14.3) to "NGr(-, S)" or "NGr-of-S" (14.5) is effected by means of a general set-theoretical definition ("M", "M 1 ", ... stand for any sets, "x" stands for any set-theoretical entity, see (4.7)): (14.6)

Definition. Let M be an n-place relation, n > 1 (i.e. a set of ordered n-tuples). M n (-,.., - , x) [with n-1 occurrences of the hyphen] = Mnof-x = {(x 1 ,..,x n _ 1 )l(x 1 ,..,x n _ 1 ,x) M}.

More informally, M n ( - , . . , - , x) is the set of (n-l)-tuples that together with x form an element of M (if x is no last-place member of M, the set is empty). In (14.5), M = NGr, x = S, n = 2, and NGr(-,S) = NGr 2 (-, S) (the index is omitted when it can be inferred from the con­ text, in particular, from the expression in parentheses) = {c1 | (c1, S)  NGr}. (Strictly speaking (14.6) is a definition schema that defines the expressions "M 2 (-, x)", "M 3 (-, - , x)", "M 4 (-, - , - , x)", etc. The same is true of all subsequent definitions that depend on (14.6). This aspect will, however, be disregarded.) Suppose that S1 is a certain idiolect system different from S. We may expect that (14.7)

NGr-of-S ≠ NGr-of-S1'

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INTEGRATING THE COMPONENT APPROACH (IV)

i.e. the category of noun groups in S may be expected to be different from the category of noun groups in S1 — the two categories should differ in at least one element. While there are two categories in (14.7), there is of course only one relation NGr, see (14.3). We may say that the two categories NGr-of-S and NGr-of-S1 are 'the S-variant' and 'the S^-variant' of the relation NGr. Generally, NGr is a 'linguistic varia­ ble in' sets of idiolect systems; in a given set it may (but need not) have different 'variants' for different systems. Taking this example for orientation, we use definition (14.6) to arrive at general, set-theoretical definitions for "variant" and related concepts that combine with the notion of a linguistic variable in a set of idiolect systems (Sec. 14.5). 14.3 Variants of relations The following terms are purely logical, more specifically, set-theoreti­ cal (for the variables, see (4.7)): (14.8)

Definitions. Let M be any n-place relation, n > 1. a. The x-variant of the M-relationn = M n (-,.., - , x). b. M1 is a variant of the M-relationn iff, for some x, M1 = the x-variant of the M-relationn.

(Here, and in all subsequent cases of the same type, it should be noted that an expression like "the ..-relation11" is simply a proper part of the term defined, e.g. of "the ..-variant of the ..-relation11"; it would be a mistake to lift the expression out of its context and ask questions such as, what is the M-relationn?) Intuitively, we take any x and consider the set of entities that together with x form an element of relation M (M is a set of ordered n-tuples): this set is the x-variant of the M-relation. If M is a two-place relation (or set of ordered pairs), the xvariant is a set of entities x1 that are not themselves tuples; if M is three-place, the x-variant is a two-place relation, or set of ordered pairs; etc. If x itself is no member of relation M, the x-variant is the empty set. Definition (b) uses the notion of x-variant to define "is a variant of the ..-relation11"; this term denotes the sets that are xvariants, for any given x. Applying (14.8) to our example in Sec. 14.2, we obtain:

VARIANTS AND VARIABLES (14)

(14.9)

139

a. NGr-of-S = the S-variant of the NGr-relation. b. NGr-of-S1 = the S1-variant of the NGr-relation. c. NGr-of-S and NGr-of-S1 are different variants of the NGr-relation.

(The index "2" after "relation" is omitted in (14.9).) As second-place members of NGr we should allow arbitrary idio­ lect systems. Consider any set of idiolect systems. NGr may vary (have different variants) or not vary (be constant) in the set; it may be general (have non-empty variants for all systems in the set), vacuous (have no such variants), or local (be neither general nor vacuous). The corresponding set-theoretical concepts are defined as follows: (14.10) Definitions. Let M be any n-place relation, n > 1. a. The M-relationn varies in M1 iff for some x and x1  M1, the x-variant and the x1-variant of the M-relationn are different. b. The M-relationn is constant in M1 iff the M-relationn does not vary in M1. c. The M-relationn is general in M1 iff for every x  M1 the x-variant of the M-relationn is non-empty. d. The M-relation n is vacuous in M1 iff for every x  M1 the x-variant of the M-relationn is empty. e. The M-relationn is local in M1 iff the M-relationn is neither general nor vacuous in M1. For example, suppose that M = NGr, i.e. the two-place relation is-aNoun-Group-of. Let T be a set of idiolect systems. The NGr-relation varies in T if for some systems S1 and S2 in T, NGr-of-S 1 (the set of syntactic units that are Noun Groups of S1) ≠ NGr-of-S2. The NGr-relation is constant in T if there are no S1 and S 2 in T such that NGr-of-S1 ≠ NGr-of-S2; this would be trivially true if for some S, T = {S}. The NGr-relation is general in T if for every S  T, NGr-of-S is non-empty; informally, if there are Noun Groups in every idiolect sys­ tem that belongs to T.

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The NGr-relation is vacuous in T if for every S e T, NGr-of-S is the empty set; informally, if there are no Noun Groups in any idiolect system that belongs to T. Finally, the NGr-relation is local in T if for some S1  T, NGrof-S1 is the empty set, and for some S1  T, NGr-of-S1 is not the emp­ ty set; informally, if there are Noun Groups in some but not all idio­ lect systems that belong to T. It may well be true that the NGr-relation varies in any set of idio­ lect systems that has more than one element, and is general (hence, nei­ ther vacuous nor local) in any set of idiolect systems; this is a factual question not relevant to the example. There are the following obvious theorems: (14.11) Theorems. For any n-place relation M, if the M-relationn is constant / general / vacuous in M1 and M2  M1 then the M-relationn is constant / general / vacuous in M2. The variation concepts defined in (14.8) and (14.10) have wide ap­ plicability, as demonstrated in Sec. 15. Still, there is another case, not yet covered, where analogous concepts should also be available. 14.4 Variants of functions Consider a linguistic variable M that is a function (see (1.6b)) and whose arguments are either idiolect systems S or tuples (x 1 ,.., xN-1, S) where S is an idiolect system. It is awkward to apply to such variables the variation concepts of Sec. 14.3. Any n-place function is an (n+1)place relation, so the notion of x-variant (14.8) does apply: the xvariant of the M-relation n+1 = M n + 1 ( - , . . , - , x) = {(x1, .., x n - l , S) | ( x 1 . . , xn_1, S, x)}  M. But this isn't what we want: if n = 1, then (x 1 ? ..,x x) is disregarded and the x-variant of the M-relationn+1 = {S | (S, x)  M}, i.e. the x-variant is a set (possibly empty) of idiolect systems; if n > 1, then the x-variant is a set (possibly empty) of ntuples that all agree in having S as their last component. The variants of a linguistic variable should, however, single out a certain S (or other language-like entity) and cover exactly those entities which are related to but different from S. For example, take the two-place function allophone2 defined in

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(1.9). Assume that only idiolect systems are allowed as language-like entities. The function then takes any pair consisting of a phoneme x1 of S and S itself, and assigns to it the set of allophones of x1 in S. Con­ strued as a relation, allophone2 is a set of triples (x1 S, x), where x is the set of allophones of x1 in S. What we would like to have as the variant of allophone2 for S is something like the set of all pairs (x1, x) that can be obtained from triples (x 1 ,S, x), i.e. the set of pairs that each consist of a phoneme x1 of S and the set x of its allophones. But the notion of x-variant defined in (14.8) only allows to single out a set x of allophones and relate to it the set of pairs (x1 S) such that x is the set of allophones of xx in S; what we get is the set of pairs (x1 S) as the x-variant of the allophone2-relation2, and this is not what we want. The problem is solved by concentrating not on a last-place mem­ ber of a relation but on an immediately preceding member — in our example, not on component x in a triple (x1 S, x) but on component S. The relations to be accounted for are n-place functions, n > 0; the fol­ lowing concepts are therefore introduced for such functions (note that the variables are used differently in the example and the definitions: "S" in the former corresponds to "x" in the latter, and "x" in the for­ mer to "x n+1 " in the latter): (14.12) Definitions. Let M be an n-place function, n > 0. a. M n [ - , . . , - , x,-] [with n-1 occurrences of the hyphen before "x"] = Mn-of-x-hyphen = the M1 such that ei­ ther (i) or (ii): (i) n = l , a n d M 1 = {x n+1 l(x,x n+1 ) M}; (ii) n > 1, and M1 = {(x1,..,xn-1,xn+1)| (x1,..,xn-1' x, x n+1 ) M}. b. The x-variant of the M-functionn = M n [-,.., - , x, - ] . c. M 1 is a variant of the M-functionn iff for some x, M1 - the x-variant of the M-functionn. d. The M-functionn varies in M1 iff for some x and x1  M 1 , the x-variant and the x1-variant of the M-functionn are different. e. The M-functionn is constant in M1 iff the M-functionn does not vary in M1.

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The M-functionn is general in M1 iff for every x  M1, the x-variant of the M-functionn is non-empty. g. The M-functionn is vacuous in M1 iff for every x  M1, the x-variant of the M-functionn is empty. h. The M-functionn is local in M1 iff the M-functionn is neither general nor vacuous in M1.

f.

(Definition (c) corresponds to (14.8b), and definitions (d) to (i) corre­ spond to (14.10a) to (14.10e).) The functions allophone1 and allophone2 defined in (1.8) and (1.9) may once again serve as linguistic examples. Assume that idiolect sys­ tems have been chosen as language-like entities. Take any idiolect system S. Since allophone1 is a one-place func­ tion, the S-variant of the allophone1-function = allophone 1 [S,-] = {X2|(S,X2) allophone 1 }, by (ai) in (14.12); i.e., using function notation, allophone1 [S,-] = {x2| allophone1 (S) = x2} = {x 2 }, where x2 = the set of allophone-phoneme pairs o f S (see (1.8)). Thus, the Svariant of allophone1 is the unit set of the allophone-phoneme relation in S. On the other hand, allophone2 is a two-place function, and the Svariant of the allophone2-function = allophone 2 [-,S,-] = {(x1, x3) | (x1, S, x3)  allophone2} = {(x1, x3) | allophone2(x1, S) = x3} = the set of pairs consisting of a phoneme x1 of S and the set x3 of its allophones in S; see (aii) in (14.12), and (1.9). The two examples demonstrate that the concept of variant defined in (14.12b) for functions is indeed adequate in linguistics. The remain­ ing definitions in (14.12) need not be exemplified since they depend on the concept of function variant in exactly the same way as the corre­ sponding definitions in (14.8) and (14.10) depend on the notion of re­ lation variant. Once again, there are theorems analogous to (14.11): (14.13) Theorems. For any n-place function M, n > 0, if the Mfunctionn is constant / general / vacuous in M1 and M2  M1 then the M-functionn is constant / general / vacuous in M2. The concepts introduced so far in Secs 14.3f have been quite gen-

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143

eral In linguistics we wish to apply them only to relations and func­ tions that are linguistic variables. 14.5 The notion of a linguistic variable in a set of systems Consider the set of all idiolect systems ("S" continues to stand for any systems of means of communication): (14.14) Definition I. IDS ["the set of idiolect systems"] = the set of all S such that for some D, D is subset of a historical language and S is an idiolect system in D [see (13.1)]. (Non-logical, i.e. linguistic definitions and theorems that serve to ex­ plicate the component approach are numbered by means of Roman nu­ merals) A linguistic variable in a set T (where "T" stands for arbitra­ ry sets of S's) is, as a matter of fact, a variable in a subset of IDS: (14.15) Definitions II to IV a. For n > 1, the M-relationn is a linguistic variable in T iff (i) M is a non-empty n-place relation; (ii) for any M1 such that M1 = the n-th domain of M [i.e. the set of n-th-place members of M], α. T  M1; ß. M1  IDS. b. For n > 0, the M-functionn is a linguistic variable in T iff (i) M is a non-empty n-place function; (ii) for any M1 such that M1 = the set of arguments of M, for n = 1, or M1 = the set of n-th compo­ nents of arguments of M, for n > 1, α, T  M1; ß. M1  IDS. c. M is a linguistic variable in T iff (i) or (ii): (i) for some n > 1, the M-relationn is a linguistic va­ riable in T; (ii) for some n > 0, the M-functionn is a linguistic variable in T.

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The following explanations may be helpful. If the M-relation is a linguistic variable in T (Definition II), then M is a non-empty relation. It is required that T — a set of idiolect sys­ tems — be a subset of the set of last-place members of the relation, i.e. unless T is empty, some last-place members of the relation are idiolect systems. We might still have other last-place members that fail to be idiolect systems; this is excluded by condition (ß) by which the entire set of last-place members must be contained in IDS, the set of all idio­ lect systems. It should also be noted that T may be a proper subset of the set of last-place members of M; thus the M-relation may be a lin­ guistic variable in different sets T of idiolect systems. Nor need all idi­ olect systems be last-place members of M: the set of last-place members may be a proper subset of IDS. In the case of functions M, these remarks equally apply to M, T, and the set of (last-place components of) arguments of M, see Definition III. Definitions II and III contain the expression "linguistic variable" only as part of the longer expressions that are actually defined; the ex­ pression has no independent status. In Definition IV, "linguistic varia­ ble" is so to speak freed; "is a linguistic variable in" is now defined as an independent term, as would be expected. Obviously, if the M-relation / M-function is a linguistic variable in T, then M is a linguistic variable in the sense of (1.6); hence, this also holds of linguistic variables in T as defined by Definition IV although the notion of linguistic variable in the sense of (1.6) was not used in the definition. Let T1 be a set of idiolect systems. As an example for Defs II and III, consider the two-place relation NGr, i.e. is-a-Noun-Group-of. Assume that for any S  T1 there is an x such that x is a Noun Group of S. (This assumption is trivially true if T1 is empty.) It then follows that T1 is a subset of the second domain (set of second-place members) of NGr, and the NGr-relation2 is a linguistic variable in T1, by Definition II. Therefore, NGr itself is a linguistic variable in T1, by (i) in Definition IV. As an example for Defs III and IV, take the one-place function allophone1. Since this function takes arbitrary idiolect systems as argu­ ments, T1 is a subset of the set of arguments of allophone1. Hence, the

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allophone 1 -function 1 is a linguistic variable in T1? by Definition III, and allophone1 is a linguistic variable in T1, by (ii) in Definition IV. Finally, the concepts defined in (14.10) apply to linguistic varia­ bles M in case (i) of Definition IV, and the concepts defined in (14.12) apply to linguistic variables in case (ii) of Definition IV: the M-relation / M-function may vary, be constant etc. in T. For linguistic variables, Definition IV has the consequence that (14.16) Theorem I. If M is a linguistic variable in T and T1  T, then M is a linguistic variable in T1. Only linguistic variables covered by Definition II will figure in the following reconstruction of two current approaches (Sec. 15); Definition III will be involved in subsequent reconstructions (Sec. 17).

15 Reconstructions: Chomsky and Seiler

15.1 On reconstructing Chomsky Until roughly 1980, Chomsky tenaciously clung to the idealization of "an ideal speaker-listener, in a completely homogeneous speech-com­ munity" (Chomsky 1965:3); correspondingly, his framework offered no theoretical means to deal with language-internal variation. The re­ visions introduced in Chomsky (1981) resulted in what has come to be known as the 'Principles and Parameters' approach, which allows for a treatment of linguistic variation by (i) separation of 'core' and 'periph­ ery' in a mental grammar (more recently — Chomsky 1986 — called an 'internal language'), and by (ii) construing the core of a grammar as the result of 'parameter-setting' on the basis of 'principles': there are certain innate principles that determine 'parameters', and gram­ mars (internal languages) differ in the 'values' these parameters as­ sume in different mental grammars. Two variation aspects of (ii) have so far been recognized, the acquisition aspect (parameters are 'set' dif­ ferently in language acquisition through linguistic experience — see, for example, Hyams 1986), and consequences for language typology (natural languages, in a traditional sense, might fall into types, depend­ ing on the values assumed by parameters; most prominently discussed has been the so-called 'pro-drop' or 'null subject parameter', see Jaeggli and Safir (eds) 1989). Typology concerns variation among langua­ ges; it is obvious, though, that language-internal variation can also be approached in this way (e. g., Kenstowicz 1989). The basic concepts of 'principle' and 'parameter' have so far been left at a fairly intuitive level in the writings of Chomsky and his fol­ lowers. In particular, there are the following problems.

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(i)

The ontological status of both principles and parameters is foggy: "Suppose that we now take the pro-drop parameter to be (12) R may apply in the syntax" (Chomsky 1981: 257; R is a specific 'rule') — what exactly does (12) name? In Jaeggli and Safir (1989:2), parameters are 'de­ fined' as "language (class) specific options expressed as postulates that interact with universal principles to form the grammar of a specific language" — the clearest for­ mulation in the entire collection of Jaeggli and Safir (eds) 1989.

(ii)

The relation between principles and parameters can be construed in at least two different ways: a. Neither are principles a kind of parameters nor para­ meters a kind of principles but both interact in the specification of grammars (cf. Chomsky 1981:34, 95; Jaeggli and Safir, see (i)). ß. Parameters are, or may be, principles 'with different values' (Chomsky 1981:95: "general principles [...], perhaps also parametrized"; op. cit. 6: "principles with certain possibilities of parametric variation"; Hyams 1986:3).

(iii)

Parameters, distinguished by Chomsky from "collections of properties" of languages 'explainable' by the parame­ ters (1981:6), are identified with such sets by others (e.g., Brandi and Cordin 1989:111).

The following explication of 'principle' and 'parameter', which uses concepts defined in Secs 14.3ff, tries to solve (i); uses (ß) in (ii) for orientation; and takes a Chomskyan position with respect to (iii). The explication deviates from Chomsky in various respects and is non­ committal on questions of innateness but should still reconstruct essen­ tial features of his conception. For orientation we are going to consider the 'null subject parame­ ter', stripping it of generative grammar detail and rebuilding it within the current framework. (No attempt will be made to retain the rather 'abstract' nature of the pro-drop parameter in Chomsky's sense, see the quotation in (i).)

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15.2 'Principles and parameters': definitions Our starting-point are three informally defined relations, PS, PS 0 , and PS 1 ("c" stands for arbitrary components of idiolect systems): (15.1)

(Definitions) a. c is a pronoun-subject sentence (PS) in S iff c is a sen­ tence of S with a single subject constituent, which is an occurrence of a form of a personal pronoun of S. b. c is an optional pronoun-subject sentence (PS0) in S iff (i) c is a PS in S; (ii) the subject constituent of c 'may be dropped in S'. c. c is an obligatory pronoun-subject sentence (PS1 in S iff (i) c is a PS in S; (ii) c is not a PS0 in S.

"May be dropped in S" essentially means that there is a sentence c1 in S that differs from c only in not having the subject constituent. (Exist­ ence of c1 may depend on certain conditions that c must satisfy; these would have to be added in (bi) and (ci). Any conditions on c1 itself — such as, in generative terms, occurrence of an 'empty category' pro in the structure of c1 — are to be covered by the interpretation of "drop". The formulation "may be dropped" is not to suggest that c is 'unmarked' and c1 'marked' in S; the opposite may be true.) Now consider the Romance languages. It is well known that Italian and Spanish do and French does not allow for optional pronoun-sub­ ject sentences. Let "Rom-IDS" denote the set of all idiolect systems in Romance languages. Assuming the framework of Sec. 14, the situation in these languages may then be described as follows: (15.2)

a. The PS-relation is a linguistic variable in Rom-IS (cf. (14.15a)). b. For each M1  {PS 0 , P S 1 , the M1-relation is local in Rom-IDS (cf. (14.10e)).

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Moreover, from the definitions in (15.1) and the fact that neither PS 0 nor PS1 is the empty relation, we deduce that (15.3)

{PS0, PS1} is a partition of PS.

(See (9.3), for "partition"; remember that PS is a set — a set of pairs (c, S).) The following formulation is meant to be equivalent to the con­ junction of (15.2) and (15.3): (15.4)

PS is a parameter in Rom-IDS with respect to {PS0, PS 1 }.

PS 0 and PS1 are the values of the parameter. Suppose that PS is a para­ meter, in the required sense, not only in Rom-IDS but also in IDS, the set of idiolect systems in any language. PS could then be called a principle because the PS-relation would be a linguistic variable in IDS, see (15.2a). (As a matter of fact, PS may hardly be taken to be a principle. While both PS 0 and PS 1 are local in IDS, the PS-relation may not be a linguistic variable in IDS. For this we would have to assume that the second domain of PS = IDS, see (14.15a), which implies that there are pronoun sentences in the sense of (15.1) in arbitrary idiolect systems, a doubtful proposition.) If M is a principle, then the M-relation is general in IDS (in the sense of (14.10c) — capturing Chomsky's requirement that principles be 'universal'). M may but need not be 'parametrized', i.e. be a parameter in (a subset of) IDS: there may but need not be an appropriate partition of M. Generalizing from the example we arrive at the following con­ cepts (variables are as in (4.7) and (4.8)): (15.5)

Definitions V to VII. For n > 1: a. M is a parametern in T with respect to N iff (i) the M-relationn is a linguistic variable in T. (ii) N is a partition of M; (iii) for every M1  N, the M1-relationn is local in T. b. Let M be a parametern in T w.r.t. N. M1 is a value of M in N iff M1  N. c. M is a principlen iff the M-relationn is a linguistic var­ iable in IDS.

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15.3 Discussion The notion of parameter but not of principle is relational: something — a certain relation M — is a parameter in a set T of idiolect systems with respect to a certain set N of 'parameter values'. T is an arbitrary subset of IDS, the set of all idiolect systems; in this sense parameters may be quite restricted. The M-relation is a linguistic variable in T, hence, M itself is a linguistic variable in T, therefore, a linguistic vari­ able in the sense of (1.6). On the other hand, not all linguistic variables are parameters in some set T with respect to some set N of 'parameter values'; in particular, the parameter values must form a partition of the parameter M itself, and there may be no partition that could be reasonably suggested. This shows that the notions of a linguistic varia­ ble and of a linguistic variable in a set of idiolect systems are more general; intuitively, parameters are just a special case of linguistic variables. Parameters — more accurately, the first-place members of the parameter relation — are linguistic variables in the sense of (1.6), and this is also true of principles. Definition V could be strengthened by requiring that M should be a component variable in the sense of (1.8); this would indeed conform to Chomsky's approach. Moreover, a value M1 of a parameter M in T w.r.t some N is a linguistic variable in the n-th domain of M1; this follows from: (15.5b), (ii) and (i) in (15.5a), (14.15a), and (14.15c). Therefore, M1 is a linguistic variable in the sense of (1.6), and is a component varia­ ble in the sense of (1.12) if M is; for examples, see PS 0 and PS 1 in (15.1). In addition, the definitions have the following desirable conse­ quences: (15.6)

Theorem II. For n > 1, if M is a principle", then a. the n-th domain of M = IDS; b. the M-relationn is general in IDS.

Part (a) follows from (15.5c) and (14.15a); part (b) from (a) and (14.10c). For example, if PS is indeed a principle, then the PS-relation is general in the sense that there are subject-pronoun sentences in any idiolect system in any language.

15 2

INTEGRATING THE COMPONENT APPROACH (IV)

In Def. VII we required that the M-relationn be a linguistic varia­ ble in IDS. A theorem analogous to Theorem II is obtained if the Mfunctionn is a linguistic variable in IDS. This suggests a generalization of Def. VII, with a change of terminology: (15.7)

Definition VII'. M is a universal variable iff M is a lin­ guistic variable in IDS.

("Linguistic variable" is understood as in (14.5c). For our example of how universal variables may figure in linguistic argumentation, see Example (18.5), below, Outline of Proof, (b).) A principle in the sense of Def. VII is simply a special case of a universal variable, and there may be no need for honouring it with a term of its own. Def. VII may then be replaced by Def. VII', which frees the term "principle" for its metalinguistic use as: formulation of a certain requirement, state-of-affairs, etc. The two concepts of parameter and principle (Defs V and VII) are proposed as explicata of Chomsky's 'parameter' and 'principle'. True, there are problems with the explicanda (see Sec. 15.1, (i) to (iii)), and the ontology underlying (15.5) is not Chomsky's but could easily be brought into line with his by making two changes in Definitions I to VII: (15.8)

a. "T" is reinterpreted as a variable for sets of 'mental mechanisms'. b. "IDS" is redefined to denote not the set of idiolect sys­ tems but the set of 'internal languages' in the sense of Chomsky (1986).

Neither change would affect the form of (15.5), which supports the claim that the definitions explicate Chomsky's notions of parameter and principle. These notions may or may not be useful (I believe they are both dispensable), and there may be other ways of explicating them. All I claim here is that my explicata, which incorporate Chomsky's notions into a specific version of the component approach, are, as explicata, plausible, especially when placed in a larger context.

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15.4 Parameter sets Chomsky's conception of a parameter includes the requirement that there is — or may be — a 'collection of properties' or 'clustering of properties' of languages 'related to' a given parameter (1981:240, for the pro-drop parameter). This set may be accounted for by postulating appropriate sets of parameters in the sense of Def. V. In such a set values of parameters covary, in the following sense. Given one parameter and its values (e. g., PS with PS 0 and PS1) and another parameter and its values (say, 'system of person markers of verb forms' with 'rich system of person markers of verb forms' vs. 'non-rich system of person markers of verb forms'), the following is true of any S in the given set of idiolect systems: the S-variant of a certain value of parameter 1 (say, PS0) is empty if and only if the Svariant of a certain value of parameter 2 (say 'rich system') is (for any S from a given set T, there are no optional pronoun-subject sentences in S if and only if there is no rich system of person markers of verb forms in S — a claim that may be factually incorrect for many T). We could now define a parameter set in an arbitrary set T as a non-empty set of parameters in T whose values covary. The require­ ment of property sets associated with parameters may then be account­ ed for by an assumption such as: (i)

For any M, T, and N, if M is a parameter in T with re­ spect to N, then there is a parameter set N1 in T such that α. M  N1; ß. N1 has at least two elements.

(Without (ß), (i) would follow from the definitions since {M} is a par­ ameter set in T.) Given a parameter set N1 as in (i), a set of properties of idiolect systems ('languages') is easily obtained: the property of be­ ing an S such that the S-variant of a certain value of M is non-empty, plus the corresponding properties for other elements of N1. Once again, there may be other ways to account for property sets associated with parameters; it is sufficient to have shown that this fea­ ture of a Chomskyan conception, too, can be plausibly reconstructed.

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15.5 'Representation': reconstructing Seiler The UNITYP approach to universality and typology research (see, e.g., Seiler 1986, and Seiler 1990 for a recent summary) was devel­ oped by Seiler and his Cologne research group over a period of twenty years, since roughly 1972. UNITYP is a complex (pre-)theoretical framework, not yet worked out in an unambiguous form, in which a conception of linguistic variation figures prominently. I suggest that an important feature of this conception — the way in which it relates 'lin­ guistic form' and 'cognitive content' (1990: Secs. 3.2f) — may be ex­ plicated as follows. Adopting Seiler's approach we distinguish 'cognitive domains' d and 'linguistic domains' c (where "c" ranges, as before, over arbitrary components of idiolect systems — restriction to such systems is ours not Seiler's). We now propose that constructions c and domains d be related by a relation of representation: (15.9)

c represents d in S;

for example, (15.10) [the construction of] Possessive Modifier represents [the domain of] Possession in S. A relation of representation is envisaged by Seiler but not assigned a key position. Represents is a three-place relation whose third-place members are idiolect systems S and whose first-place members are components of idiolect systems. Therefore, represents is a linguistic variable in any subset of its third domain (which might well be IDS), by (14.15); and is a component variable in the sense of (1.12). For any idiolect system S, the S-variant of the represents-relation is the set of pairs (c, d) such that c represents d in S; thus, the variant is a two-place relation between linguistic constructions and cognitive domains: 'representation in S'. There are still other two-place relations that can be obtained from the three-place relation represents, such as 'representation of Posses­ sion'. For suppose that "d" in (15.9) is replaced by "Possession":

RECONSTRUCTIONS: CHOMSKY AND SEILER (15)

155

(15.11) c represents Possession in S. Represents-Possession is a two-place relation, and the variant-variable terminology applies as before; however, the S-variant of the represents-Possession relation is a set of linguistic constructions, the set of constructions that represent Possession in S. Transition from a linguis­ tic variable (represents) to a 'special case' (represents Possession) again reconstructs a UNITYP feature. Differently from Chomsky, Seiler introduces a semantic relation­ ship as a linguistic variable; either author follows the component ap­ proach as now explicated. This is also true of the 'evaluation grammar' approach that was briefly characterized in Sec. 2.3. Demonstration is, however, non-triv­ ial and somewhat cumbersome. As a first step, an attempt must be made (Sec. 16) to unify the various subapproaches even beyond Habel (1979). As a second step appropriate linguistic variables must be de­ fined. This will be done in Sec. 17, where discussion will also be ex­ tended to cover the 'variable rule' approach. It should be noted that use of variables (letters like "ø", "r" etc.) in Secs 16 and 17 may not conform to the conventions adhered to else­ where in this essay (cf. (4.7) and (4.8)).

16 On the Conception of Evaluation Grammars

16.1 Example The basic conception of evaluation grammars may be explained by means of a fictitious example used by Habel (1979:196f). Imagine a language LAN (understood as a set of sentences) where all sentences consist of an adverbial plus a 'base part' that is a noun phrase followed by a verb phrase. There are two dialects (construed as subsets of the language), prae and post. In the sentences of prae, the adverbial precedes, and in post it follows the base part. Assuming that nothing else is relevant to the example, there may be a specific evalua­ tion grammar EG of LAN of the following kind (Habel 1979:197; "Adv", "NP" and "VP" are preterminal symbols; lexical rules are omitted): (16.1)

[= Habel (4.12)]

S → Adv S' S → S' Adv S' → NP VP

prae 1 0 1

post 0 1 1

Using terminology adapted from and partly identical with Habel's we may say that (16.2)

[Assumption] EG is an evaluation grammar such that: a. the three pairs in (16.1), ("S → Adv S'", (l, 0)) etc., are the evaluated rules of EG; b. the three first components of the evaluated rules are the proper rules of EG; the set of proper rules is the

INTEGRATING THE COMPONENT APPROACH (IV)

proper part of EG; the language generated by the proper part of EG is the proper language of EG; its elements are the proper sentences of EG; c. there is a two-place non-repetitive sequence G 1 G 2 of proper subgrammars of EG (i.e. certain subsets of the proper part of EG), the subgrammar sequence of EG, such that: (i)

G1: S S'

(ii)

G2:

s

—> —>

Adv S' NP VP

S' Adv NP VP S' —> (iii) the language generated by G1 = prae (iv) the language generated by G2 = post; as a matter of fact, {G1 G2} = the proper part of EG; d. ø = the rule evaluation of EG = the function that maps the proper part of EG into the set {0, l } 2 (i.e. the set of number pairs whose components are either 0 or 1) such that, for any proper rule p of EG: —>

(i) [ø (p)]i (i.e. the i-th component of ø (p), i = 1,2) = 0 iff p is not a rule of G1 (cf. (c) and (16.1)); if p is a proper rule of EG, ø (p) = the evaluation of p in EG; e. there is a function Φ based on ø, the sentence evaluation of EG, that maps the proper language of EG (see (b)) into the set {0, l} 2 (see (d)) such that, for any proper sentence s of G (see (b)), (i) [Φ(s)]i (see (d)) = 0 iff s  the language genera­ ted by Gi (see (c)); if s is a proper sentence of EG, Φ(s) = the evaluation of s in EG;

CONCEPTION OF EVALUATION GRAMMARS (16)

159

f. the evaluated language of EG = the set of pairs (s, Φ(s)) such that s  the proper language of EG; g. the restricted evaluated language of EG = the set of pairs (s, Φ(s)) from the evaluated language of EG such that for some i  {1, 2}, [Φ(s)] i = 1 (i.e. the evaluation of s contains 1 somewhere, which means that s belongs either to prae or post; in our example, (g) = (f), but this need not be generally so). EG is an evaluation grammar (of LAN) because it involves each one of the entities in (16.2), and a few more; EG must not, in particular, be equated with its proper part. In grammar EG, it is simply the criterion of 'rule status' — p is or is not a rule of subgrammar Gi — that is used to evaluate proper rules. Evaluation grammars may, however, have a different 'evalua­ tion basis'. 16.2 The notion of evaluation basis Assume that the notion of 'probability of use' makes sense for rules p that may figure as proper rules of evaluation grammars. We then have formulations such as (16.3)

the probability in G of p = r

where G is a non-evaluation grammar, in particular, a proper subgrammar of an evaluation grammar. Formally, (16.3) may be con­ strued as (16.4)

(prob(G)Xp) = r,

i.e. for a given G, prob(G) is a function that assigns a number to prop­ er rules p of an evaluation grammar. On a normal understanding of "probability", numbers r should be from the closed interval [0; 1] of real numbers, where 0 is 'zero-probability'. Understanding (16.3) as in (16.4), the term "prob" itself ("the probability in ...") is interpreted as a name of a function: prob is a function that takes non-evaluation grammars G and assigns to each G another function; this, in turn, is the function that takes proper rules p

160

INTEGRATING THE COMPONENT APPROACH (IV)

and assigns to each a number from the interval [0; 1]; this number is p's 'probability of use in G'. Now consider the subgrammar sequence G 1 .G n of an evaluation grammar. Suppose that the rule evaluation ø is construed as follows: its values are from [0; l ] n , i.e. are n-tuples of numbers from [0; 1]; and for i = 1, ..,n, [ø (p)] i = (prob(G i )(p), i.e. the i-th component of the evaluation of p is the number from [0; 1] that is the probability of proper rule p in the i-th subgrammar Gi of the evaluation grammar; we may require that this number is 0 if and only if p is no rule of Gi, Such an evaluation grammar is a 'probability assigning' grammar, as exemplified by Klein's (1974) 'variety grammars'. The rule evaluation ø is 'based on' the function prob; this function is the grammar's evaluation basis, in the following sense ("Γ" — "cap­ ital gamma" — stands for evaluation grammars, "γ" for relations be­ tween non-evaluation grammars G and functions that assign real num­ bers to the rules of such grammars): (16.5)

Assumption I. The evaluation basis of Γ is a function γ such that, if G 1 .G n = the subgrammar sequence of Γ (n > 0), then: a. the domain of γ= {G1 ..,G n }; b. for i = 1,.., n: γ(Gi) is a function that maps the proper part of Γ into [0; 1] such that, for each proper rule p of Γ, (i) (γ(Gi))(p) = 0 iff p is not a rule of Gi; (ii) if ø = the rule evaluation of Γ, then [ø (p)]i. =

(γ(Gi))(p). (For the present sketch it is sufficient to characterize the evaluation basis by an assumption rather than give a proper definition.) Since the sentence evaluation Φ (see (16.2e)) is based on the rule evaluation <> |, the evaluation basis γ also underlies the sentence evaluation. The evalu­ ation basis may be any function that satisfies (16.5); it is an empirical question which functions may be meaningfully suggested. The nature of the evaluation basis is the most important criterion for classifying evaluation grammars.

CONCEPTION OF EVALUATION GRAMMARS (16)

161

16.3 A simple evaluation basis: rule status In a grammar like EG (Sec. 16.1), the evaluation basis is 'rule status' in the following sense: (16.6)

Definition VIII. Γ-rule status (Γ-rs) = the function y such that, if G 1 .G n = the subgrammar sequence of T (n > 0), then a. the domain of y = {G1, ..,G n }; b. if G  the domain of y, then y(G) = the function that maps the proper part of T into {0, 1} such that, for each proper rule p of Γ, (y(G))(p) = 1 iff p is a rule of G.

On the pattern of (16.3) and (16.4) we may read: (16.7)

"(Γ-rs(G)Xp)" as "the Γ-rule status in G of p".

For appropriate G and p it follows from (16.6) that (16.8)

Theorem III. (Γ-rs(G))(p) = 0 iff p is not a rule of G.

Thus Γ-rule status is the function that assigns to each subgrammar G of Γ the function that assigns to each proper rule p of T the number 1 if p is a rule of G, and 0 otherwise. Now suppose that the evaluation basis of Γ = T-rule status. We then obtain from (16.8), (16.6), and (16.5): (16.9)

Theorem IV. If G1..Gn = the subgrammar sequence of Γ and <)| = the rule evaluation of Γ and i = 1,.., n, then a. [(ø(p)]i = 0 iff p is not a rule of G.; b. [ø(p)]i = 1 iff p is a rule of G1.

This is exactly the situation that holds for evaluation grammar EG in Sec. 16.1, see (16.2d). 16.4 Types of evaluation grammars Evaluation grammars may be classified as 'elementary' or 'non-ele­ mentary' depending on the role of rule status:

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INTEGRATING THE COMPONENT APPROACH (IV)

(16.10) Definition IX. Γ is elementary iff the evaluation basis of Γ = Γ-rule status. By this definition EG is elementary. It is also 'purely qualitative': the evaluation basis of EG assigns a two-valued ('either-or') function to each subgrammar. An evaluation grammar may be either 'quantitative' or 'qualitative' with respect to one of its subgrammars: (16.11) Definitions X and XL Suppose that i = 1,.., the length of the subgrammar sequence of Γ. a. Γ is quantitative at i iff, for y = the evaluation basis of Γ and G = the i-th subgrammar of Γ, γ(G) has more than two values. b. Γ is qualitative at i iff T is not quantitative at i. (The notion of 'quantitative' as defined in (a) is rather weak and may be replaced by a stronger one; we may, for instance, require that γ(G) be a measurement function.) The concepts of 'purely quantitative' and 'purely qualitative' are defined in an obvious way: (16.12) Definitions XII and XIII a. Γ is purely quantitative iff for all i = 1,.., the length of the subgrammar sequence of Γ, Γ is quantitative at i. b. Γ is purely qualitative iff for all i = 1,.., the length of the subgrammar sequence of Γ, Γ is qualitative at i. Concerning grammars that are purely or partly quantitative, see Habel (1979: Secs 3 and 4.2f) for relevant discussion. In particular, Klein's 'variety grammars' are purely quantitative; γ(G) here is a probability function for each subgrammar G. Moreover, Klein's 'variety gram­ mars' appear to represent the only attempt to utilize in syntax the con­ cept of variable rule as originally proposed by William Labov (1969) (for relevant discussion, see Romaine 1981, Cheshire 1987a). In this respect, then, our notion of (purely or partly) quantitative grammars also accounts for the variable rule approach. A more formal account of evaluation grammars may be found in Habel's excellent book; still, there are some questions where we may

CONCEPTION OF EVALUATION GRAMMARS (16)

163

have to go beyond Habel. In particular, I would argue that subgrammar sequences must be specified even if we start from an evaluation grammar conceived as a total grammar (Gesamtgrammatik), rather than 'unite' individual grammars to obtain a total one; and an evalua­ tion basis should be included among the components of an evaluation grammar. Neither point appears to be clearly accounted for in Habel's framework. Evaluation grammars provide a basis for linguistic variables in sets of idiolect systems. This will now be demonstrated by using two notions of 'rule weight'.

17 Evaluation Grammars, Variable Rules, and Linguistic Variables

17.1 Rule-weighty 1 Intuitively, an evaluation grammar assigns each of its proper rules a 'weight' with respect to its i-th subgrammar. This is made more pre­ cise by defining the following (first) function of rule-weight (a second function of rule-weight is introduced below, in Sec. 17.3): (17.1)

Definition XIV. Suppose that n = the length of the subgrammar sequence of Γ, and i = 1,.., n. rule-weight1(i,Γ) ["the i-th rule-weight 1 in Γ"] = the function assigned by the evaluation basis of Γ to the i-th subgrammar of Γ.

We may read ("r" stands for any real number): (17.2) "(rule-weight i ,(i, Γ))(p) = r" as "the i-th rule-weight1 in Γ of p is r". Because of (16.5) and the relationship between rule evaluation and sen­ tence evaluation (16.2d,e), the concept of rule-weightj may be used to define an analogous concept of sentence-weighty Evaluation grammars are language-like entities in the sense of (1.5c); therefore rule-weight1 (analogously, sentence weight1) is a lin­ guistic variable in the sense of (1.6b). Moreover, the function assigned by rule-weight1 to an argument (i, T) should be allowed as a compo­ nent of T. It then follows from the second part of (iiß) in (1.12b) that rule-weight1 itself is a component variable in the sense of (1.12).

166

INTEGRATING THE COMPONENT APPROACH (IV)

However, rule-weight1 is not yet suitable to reconstruct the evalua­ tion grammar approach within the framework of Sec. 14 and integrate it into the theory of varieties in Part III. First, rule-weight1 is a 'gram­ mar variable' not a 'language variable' or 'system variable' (see above, Diagram (1.11) — the language-like entities involved in rule-weight1 are grammars Γ) whereas no grammar variables are foreseen in either Sec. 14 or Part III. If grammar variables are to be allowed into our theory of varieties, these should at least serve as a basis for appropri­ ate language or system variables; because of the requirements of Sec. 14, these must be linguistic variables not just in the sense of (1.6) but linguistic variables in sets of idiolect systems (14.15). For rule-weight1 to satisfy these conditions two difficulties must be overcome. Strictly speaking evaluation grammars are descriptive devices of the linguist, they are metalinguistic with respect to entities such as idi­ olects, varieties, languages or corresponding systems as understood in Sec. 4. Moreover, evaluation grammars are more easily related to sys~ tems for sets of idiolects than to systems of individual idiolects; indeed, introduction of 'idiolects' is explicitly rejected by Habel (1979) (for discussion, see above, Sec. 6.3). What is required, then, is an interpre­ tation of an evaluation grammar's proper rules that relates them to idi­ olect systems while retaining all other essential features of the Evalua­ tion Grammar approach. The interpretation of rules depends on their form. For simplicity's sake I will consider only the special case of context-free evaluation grammars, i.e. grammars Γ such that all proper rules of Γ are con­ text-free (see (16.1) for examples). 17.2 Rule interpretation Each context-free rule is a pair (ß1? ß2), where ß1 is a single non-ter­ minal symbol like "S"' — or rather, the one-place 'unit sequence' of such a symbol — and ß2 is a sequence (possibly one-place) of non-ter­ minal or terminal symbols, like "NP VP" (the arrow in (16.1) may be disregarded). We first interpret each symbol as a name of a relation between (i) sequences of phonological words of idiolect systems and (ii) idiolect systems; e.g. "NP" is to denote the relation NP, i.e. the re­ lation is-a-noun-phrase-of (f is a noun phrase of S). For simplicity's

EVALUATION GRAMMARS AND VARIABLE RULES (17)

167

sake we also assume such relations for terminal symbols; e.g. "man" is to denote the relation man, i.e. the relation between any sequence f of phonological words and any idiolect system S such that f = {(1, /mæn/)} and f is a syntactic unit of S. More generally: (17.3)

Suppose that (i) Γ (i.e. the proper part of Γ) is contextfree and (ii) ß is any symbol in any proper rule of Γ. a. Assumption II. The denotatum of ß is a relation be­ tween (i) sequences (possibly one-place) of phonolog­ ical words of idiolect systems and (ii) idiolect systems. b. Definition XV. ß* = the denotatum of ß.

I now introduce a second concept of denotatum that applies to sequences (possibly one-place) of symbols and is relativized to idiolect systems S ("+" denotes the 'concatenation product' of two sets of se­ quences, i. e. the set of all sequences that result from concatenating a sequence in the first set with a sequence in the second): (17.4)

Assumptions III and IV. Suppose that (i) Γ is contextfree, (ii) ß1 and ß 2 are sequences of symbols in proper rules of r , and (iii) S is any idiolect system. a. If ß1 = ß 11 ..ß ln , n > 0, then either (i) or (ii): (i) n = 1, and the denotatum of ß1 in S [den(ß1, S)] = ß *(-, S); (ii) n ≠ l ' and den(ß 1 ,S) = ß 11 *(-,S) + . . + ßln * (- S). b. The denotatum of (ß1, ß2) in S [den(ß1, ß2 , S)] = (den (ß 1 ,S),den(ß 2 ,S)).

((aii) is admittedly simplistic.) For example, if ß11 = "NP" and ß1 = {(1, "NP")} = the unit sequence of "NP" (or "NP" 1 , for short), then den(ß1, S) = "NP"*(-, S) = the set of all sequences f of phonological words that are related to S by the relation denoted by "NP" = NP(-, S) = the set of all f such that f is a noun phrase of S. And for ß1 = "S"' 1 and ß2 = "NP" "VP" (or "NP VP", for short):

168

INTEGRATING THE COMPONENT APPROACH (IV)

(17.5)

The denotatum of ("S"'1 , "NP VP") in S = (S'(- S), NP (- S) + VP(-,S)).

To derive (17.5) we first determine the denotatum of the unit sequence of "S"'. This is done in the same way as for the unit sequence of "NP", using (ai) in (17.4); the denotatum is S'(-, S). Similarly, the denotatum of the unit sequence of "VP" is VP(-, S). Next, (aii) is applied to obtain the denotatum of "NP VP"; this is NP(-, S) + VP(-, S), i.e. the set of concatenations of syntactic units from NP(-, S) with syntactic units from VP(-, S). (17.5) is now derived by using (b) in (17.4). Assumption IV covers the interpretation of proper rules of Γ; As­ sumption III covers, in particular, the interpretation of proper senten­ ces of Γ (which are sequences of terminal symbols of Γ). Given the denotata of proper rules as specified by Assumption IV, we now introduce a second notion of rule-weight by which weights of grammar rules are transferred to their denotata. 17.3 Rule-weight 2 Rule-weight1(i, Γ) is a function that assigns to each proper rule p of T the number that is the i-th component of its evaluation. Rule-weight2 ( i , r ) is to be the function w that assigns to each (K, K 1 ,S) (where (K, K1) = the denotatum in S of some proper rule of T) the same num­ ber that rule-weight1(i, Γ) assigns to any appropriate rule p. ("K", "K 1 ", ... each stand for any set of sequences of phonological words of idiolect systems.) For a more precise account we first define: (17.6)

Definition XVI. For any idiolect system S and contextfree r , S is appropriate for p in Y iff a. p is a proper rule of Γ; b. the denotatum of p in S is a component of S.

The denotatum of p is a pair (K, K1) of sets of sequences of phonolog­ ical words of S, see (17.5). Being a component may be understood, in the context of (17.6), as a matter of degree; else, our notion of ruleweight2 might be charged with a trivialization. We next introduce a new variable:

EVALUATION GRAMMARS AND VARIABLE RULES (17)

(17.7)

169

"w" Stands for any function whose arguments are pairs (c, S) (for "c", cf. (4.8k) and Sec. 13.2) and whose values are real numbers r from the closed interval [0; 1].

This is used in defining rule-weight2: (17.8)

Definition XVII. Suppose that (i) T is context-free, (ii) n = the length of the subgrammar sequence of Γ (iii) i = l,..,n. rule-weight2(i, Γ) ["the i-th rule-weight2 in Γ"] = the w such that a. the domain of w = the set of all (c, S) such that S is an idiolect system and, for some p such that S is approp­ riate for p in r , c = the denotatum of p in S; b. for any p and idiolect system S such that S is appropri­ ate for p in r , w(den(p,S), S) = (rule-weight1(i, Γ)) (P).

The formula in (b) is to be understood as follows: (i)

w(den(p, S), S) = the number r assigned by function w t the pair consisting of (a) the denotatum of rule p in S an (ß) S itself. The denotatum of p is a certain pair (K, K1 of two sets that consist of sequences of phonologica words of S. Since S is appropriate for p, this pair is a component of S.

(ii)

(rule-weighty, Γ))(p) = the i-th rule-weight1 in Γ of p [see (17.2)] = the number r1 assigned to rule p of Γ by the function that the evaluation basis of T associates with the i-th subgrammar of Γ [see (17.1)].

(iii)

The number r = the number r1.

Therefore, function rule-weight2 may be informally characterized in the following way. Just as rule-weight1 does, rule-weight2 associates a function with each subgrammar of evaluation grammar Γ. This func­ tion w, however, operates not on the proper rules p of grammar Γ but on their denotata in appropriate idiolect systems. What function w does is simply this: it takes the rule-weight of the grammar rule and assigns

170

INTEGRATING THE COMPONENT APPROACH (IV)

it to the system component that the grammar rule denotes. We thus ob­ tain a 'rule-weight' in a second sense, the rule-weight of a system com­ ponent not a grammar rule. In analogy to (17.2) we may read (17.9)

"(rule-weight2(i, Γ)(c, S) = r" as "the i-th rule-weight, in Γ of (c, S) is r".

Once again, rule-weight2 is a linguistic variable in the sense of (1.6), and is a 'grammar variable' just as rule-weight1. Moreover, rule-weight2 is a component variable in the sense of (1.12) if the func­ tion w assigned by rule-weight2 to an argument (i, Γ) is allowed as a component of Γ (for this purpose, ' T " would have to range over 'in­ terpreted' evaluation grammars). It is not only rule-weight2 but each of its values that is a linguistic variable. 17.4 The values of rule-weight 2 as linguistic variables Consider any value w of rule-weight. This is a (non-empty) function whose arguments have idiolect systems S as their last components; hence, w is a linguistic variable in the sense of (1.8). Differently from both rule-weight1 and rule-weight2, w is a system variable not a gram­ mar variable (Diagram (1.11)): the last components of arguments of w are idiolect systems not grammars. In addition, w is a component vari­ able in the sense of (1.12). This follows from its status as a linguistic variable; (17.8a); (17.6b), which implies that in any argument (c, S) of w, c is a component of S; and the first part of (ß) in (bii) of (1.12). Finally, let T be any set of last components of arguments of w. Be­ cause of (14.5b) and (14.5c), w is a linguistic variable in T: (17.10) Theorem V. Assume (i) to (iii) in (17.8), and w = ruleweight2(i, Γ). If T c the set of last components of argu­ ments of w, then w is a linguistic variable in T. Linguistic variables w in (17.10) may be either 'quantitative' or 'qualitative' in the following sense:

EVALUATION GRAMMARS AND VARIABLE RULES (17)

171

(17.11) Definitions XVIII and XIX. Assume (i) to (iii) in (17.8). a. w is a quantitative variable in T with respect to i and Γ iff (i) w = rule-weight2(i, Γ); (ii) T  the set of last components of arguments of w [see (17.7)]; (iii) Γ is quantitative at i [see (16.11a)]. b. w is a qualitative variable in T with respect to i and T iff

(i)

Kai)]

(ii) [=(aii)] (iii) Γ is qualitative at i [see (16.11b)]. Our starting-point in Sec. 17.1 was the function rule-weightj which, although a component variable, was found wanting for our aim, a suitable reconstruction of the evaluation grammar approach. It was argued that we should proceed to component variables that are system variables and, more specifically, variables in sets of idiolect systems. These conditions are indeed satisfied by the values w of func­ tion rule-weight2, a function defined in terms of rule-weight1; thus, functions w, although system variables rather than grammar variables, are ultimately based on the grammar variable rule-weight1. We would eventually have to demonstrate that values of ruleweight 2 may be relevant linguistic variables, i.e. variables that may serve, in the way explained in Sec. 18, to determine varieties of a lan­ guage. This may indeed be argued for qualitative variables but is doubtful for quantitative ones. Relevant discussion is found in the lit­ erature mainly in connection with the variable rule approach, only partly covered by evaluation grammars, which may now be consid­ ered. 17.5 On reconstructing the variable rule approach Our notions of quantitative evaluation grammar in (16.11) and of quantitative variable in (17.11) should account for the 'variable rule' approach in syntax to the extent that it continues to presuppose gram­ mars. More recently, this approach has been vastly generalized and has

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INTEGRATING THE COMPONENT APPROACH (IV)

become quite independent of grammars (see Sankoff 1988 for a stateof-the-art review; it has been argued especially by Romaine [1981] that even Labov's original 1969 conception is — contrary to Labov —- in­ compatible with Chomskyan Generative Grammar; for a critical dis­ cussion of the variable rule approach in both its original and its more recent forms, with special reference to syntax, see García 1985). I sug­ gest that the essence of the generalized variable rule approach is cap­ tured by a reconstruction along the following lines. The reconstruction uses evaluation grammars as a contrastive background but results in grammar-independent linguistic variables. Doing away with evaluation grammars, we need something to take the place of subgrammar sequences and grammar-related evaluation bases: (i)

Subgrammar sequences are replaced by sequences CON of 'conditions'.

(ii)

The notion of evaluation basis is reintroduced for sequen­ ces CON: such a basis is a function S that assigns to each member of CON a function w (which, in turn, takes com­ ponent-system pairs (c, S) and assigns to them real num­ bers r, see (17.7)).

In subsequent definitions, the pair (CON, 8) takes the part previously played by Γ. We proceed as follows: (iii)

The notions of 'quantitative at i' and 'qualitative at i' are redefined for condition sequences CON ('quantitative / qualitative at i given S'), using 8 instead of y in (16.11).

(iv)

Rule-weight 1 and rule-weight2 are replaced by a single grammar-independent function weight whose arguments are triples (i, CON, 8) where 8 is an evaluation basis for CON, and i < the length of CON.

(v)

The notions of quantitative variable and qualitative vari­ able (17.11) are reintroduced, using the redefined con­ cepts of 'quantitative' and 'qualitative' and the weight function.

EVALUATION GRAMMARS AND VARIABLE RULES (17)

173

17.6 Grammar-independent variables: quantitative and qual­ itative Steps (i) to (v) will now be taken in a formal way. The following variables (in the logical sense — expressions) are needed: (17.12) a. "con", "con1" ... stand for any 'condition' (of unspeci­ fied ontological type). b. "CON": for any non-empty non-repetitive sequence of entities con. c. "8": for any function whose arguments are entities con and whose values are functions w (see (17.7)). "Evaluation basis" is now defined as follows: (17.13) Definition XX. S is an evaluation basis for CON iff a. the domain of S = the set of members of CON; b. for each con e the domain of δ, (i) the function 8(con) has at least two values, and (ii) for each con1  the domain of S, the domain of 8(con) = the domain of 8(con1). For example, CON might be the sequence of conditions con2 con 2 , where con1 = 'formal situation' and con2 = 'informal situation'; and 8 might assign to con1 and con2 functions w1 and w2 such that (i) the do­ main of w1 is the same as the domain of w2 and is a certain subset of NGr (a certain set of pairs (c, S) such that c is a noun group of S), and (ii) for each (c, S) in the domain of w1, i = 1, 2: w.(c, S) is the proba­ bility of use of (c, S) with respect to con.. Condition sequence CON may be either quantitative or qualitative at a given place with respect to an evaluation basis: (17.14) Definitions XXI and XXII. Suppose that (i) 8 is an evalua­ tion basis for CON, and (ii) i = 1,.., the length of CON. a. CON is quantitative at i given 8 iff for any con = the ith member of CON, the function 8(con) has more than two values.

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INTEGRATING THE COMPONENT APPROACH (IV)

b. CON is qualitative at i given δ iff CON is not quantita­ tive at i given S. Once again, the concept in (a) could be strengthened by putting more stringent requirements on δ(con) (cf. (16.11a)). We next define "weight": (17.15) Definition XXIII. Assume (i) and (ii) in (17.14). weight(i, CON, S) ["the i-th weight for CON and 5"] = the function w assigned by δ to the i-th member of CON. The expression "(weight(i, CON, 8))(c, S) = r" may be read as "the i-th weight for CON and 5 of (c, S) is r". The function weight is defined on the pattern of rule-weightj (see (17.1)) but corresponds to rule-weight2 (see (17.8)) in taking functions w as its values. Once again, values w are component variables, and: (17.16) Theorem VI. Assume (i) and (ii) in (17.14), and w = weight(i, CON, 8). If T  the set of last components of ar­ guments of w, then w is a linguistic variable in T. In strict analogy to (17.11) we now obtain notions of quantitative and qualitative variables that are grammar-independent: (17.17) Definitions XXIV and XXV. Assume (i) and (ii) in (17.14). a. w is a quantitative variable in T with respect to i, CON, and 5 iff (i) w = weight(i, CON,δ); (ii) T  the set of last components of arguments of w; (iii) CON is quantitative at i given 5. b. w is a qualitative variable in T with respect to i, CON, and δ iff (i) [=(ai)] (ii) [=(aii)] (iii) CON is qualitative at i given δ.

EVALUATION GRAMMARS AND VARIABLE RULES (17)

175

It is a defensible thesis that the variable rule approach in its gener­ alized form is concerned with quantitative variables in the sense of (17.17a). For a convincing demonstration the approach would have to be analysed in greater detail than I have so far been able to do. Strictly speaking my reconstruction of the variable rule approach is therefore based on a plausibility argument. Even allowing that quantitative variables in the sense of (17.17a) adequately account for the variable rule approach in its grammar-inde­ pendent form, we would still have to show that such variables may be relevant, i.e. play a part in delimiting varieties of a language. There have been claims and counterclaims concerning the theoretical status of 'measurement by variable rules' which carry over to our reconstruc­ tion in the following form: do the standard quantitative variables (ei­ ther in the sense of (17.11) or (17.17)) measure statistical variability within a corpus, or do they measure (objective or subjective) probabil­ ity that represents some 'probabilistic competence' of the speaker? (See Altmann and Grotjahn 1988:1037, for references and discussion; for a more recent discussion of 'frequency of use', García 1990.) Only in the second case would quantitative variables be relevant in the present context. In solving the explication problem for the component approach (14.1) we had to demonstrate that relevant proposals for dealing with (syntactic) variation are covered by our version of the approach. This has now been achieved. We may therefore turn to the integration problem (14.2) and demonstrate how the component approach — on our explication, and possibly restricted to language-internal variation — may be integrated into our version of the variety approach.

18 Solving the Integration Problem

18.1 Basic ideas Any linguistic variable in a set of systems is either a relation whose members include idiolect systems, or a function that has idiolect sys­ tems among the components of its arguments. Logically, such variables may or may not be component variables in the sense of (1.12); we are interested only in the ones that are. Systems for varieties were conceived as constructs from properties of idiolect systems; more specifically, as sets of properties of such sys­ tems. A connection between varieties and linguistic variables may be established via properties of idiolect systems. We proceed as follows (where "linguistic variable" is to be understood as "linguistic variable in a set that is a component variable in the sense of (1.12)"). A linguistic variable may determine properties of idiolect systems, in a sense to be explicated (Sec. 18.2). Such properties may then ap­ pear as elements in systems for varieties. As a matter of fact, a set of variety systems may be partly specified by a set of linguistic variables in the sense that each variety system in the set must contain properties determined by the variables (Secs 18.3f). Suppose that the set of varie­ ty systems is a permissible type of systems (11.2) that underlies a sys­ tem-based point of view (11.3) which in turn defines a set of systembased criteria (11.4). We establish a direct link between linguistic variables and system-based criteria for varieties by strengthening the no­ tion of permissible type of systems: such a type, it will now be re­ quired, must be partly specified by a set of linguistic variables (18.5). In this way linguistic variables are assigned a specific role in the deter­ mination of varieties, and the component approach is thus integrated into the variety approach.

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As a first step towards realizing this idea, we clarify the sense in which a linguistic variable may be said to 'determine' properties of id­ iolect systems. 18.2 Property determination by linguistic variables Once again, consider NGr, a linguistic variable, and some idiolect sys­ tem S1. The S1-variant of the NGr-relation is a set of syntactic units of S1, viz. NGr(-, S1), the set of all units f of S1 such that (f, S1)  NGr. This set may have various properties a, in particular, the property a* of being identical with a certain set K of units: NGr(-, S1) = K. This, in turn, gives rise to a property ø* that S1 itself has: the property of being an idiolect system S such that the S-variant of the NGr-relation — NGr(-, S) — has property a*, i.e. is identical with K. Call ø* "the property determined by NGr and a*", or "prop(NGr, a*)", for short: (18.1)

prop(NGr, a*) = the property of being an S such that the S-variant of NGr has a*.

In this way the linguistic variable NGr together with a property that its variants may have determines a property of idiolect systems; such properties of idiolect systems may also be determined by linguistic variables that are functions, see (14.15b). Generally, if "a", "α 1 ", ... stand for any (admissible) property of set-theoretical objects, we define the following purely logical concepts of property determination: (18.2)

Definitions a. Let M be an n-place relation, n > 1. propn(M, α) ["the property11 determined by M and a"] = the property of being an x such that the x-variant of the M-relationn has α. b. Let M be an n-place function, n > 0. proptn(M, α) ["the property11 determined by M and a"] = the property of being an x such that the x-variant of the M-functionn has α.

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179

Properties ø that are determined, in the sense of (18.2), by linguistic variables may be elements of variety systems σ; and sets of systems σ may be 'partly specified' by sets of linguistic variables, in roughly the following sense. (Definitions in Sec. 18.3 are followed by an example in Sec. 18.4.) 18.3 Specifying sets of systems by linguistic variables Take a single classification E, say, the basic dialect division, in the va­ riety structure of a historical language D. By Assumption 3 on variety structures (11.8), the dialects in this division can be obtained by a set  of (exhaustive) system-based criteria: by a set of properties π of idi­ olects such that each π delimits exactly one of the dialects. By Defini­ tions 7 to 9 in (11.2) to (11.4) and 11 to 13 in (11.5), each criterion π is the property of being an idiolect that is covered by a certain system σ for the dialect, i.e. the property of being an idiolect that has all the properties ø in a; these properties are properties of idiolect systems. It is required that σ belongs to a 'permissible type' of systems, a set Σ of systems for subsets of language D (e. g., systems for varieties of D). The properties π that delimit the dialects are thus given, in the last ana­ lysis, through the systems σ that are elements of Σ, the 'permissible type' of systems. Each of these systems a is a set of properties of idiolect systems, and such properties may be determined by linguistic variables. We may indeed propose that there are some variables that determine prop­ erties in every c from Σ; for example, each σ in Σ might contain the property of being an idiolect system S in which the category NGr-of-S has a certain property a. These properties of idiolect systems might be different for different a due to differences in the properties a. Intui­ tively, the dialect systems 'vary along the same dimensions' (represent­ ed as linguistic variables), which is in agreement with traditional as­ sumptions. The 'dimensions' or linguistic variables may of course be n-place functions, n > 0. In summary, a set Σ of systems that satisfies such a requirement is partly specified in terms of two sets: a set of linguistic variables in the sense of (14.15) that are, in particular, component variables in the sense of (1.12), and a set of properties of variants; or rather, there are

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three sets to be considered: a set Σ of systems for sets of idiolects, a set N of linguistic variables, and a set A of properties of variants. The variables that are elements of N are variables in a set T of idi­ olect systems. T should depend on the given set Σ of systems (for sets of idiolects); more specifically, T = the Σ-set of idiolect systems, i.e. the set of idiolect systems such that each has all properties that are ele­ ments of at least one system in Σ ("Σ", understood as in (11.2b), stands for any set of entities a, where "a" stands for any set of properties ø of entities S, and "S" stands for any systems of means of communication, in particular, for any idiolect system): (18.3)

Definition XXVI. The Σ-set = the set of all S such that for some σ  Σ and all ø  σ, S has ø.

So we start from a set Σ. This is not a set of systems of idiolects but a set of systems for sets of idiolects. We associate with Σ a set of idio­ lects, called the Σ-set. The set is determined as follows. Take any sys­ tem σ from Σ. σ is a system for sets of idiolects. More specifically, σ is a set of properties ø. Each ø is a property of idiolect systems. Now consider an idiolect system S that has all the properties that are ele­ ments of a. S belongs to the Σ-set. Since the Σ-set is a set of idiolect systems, we may have linguistic variables in the Σ-set, in the sense that was specified in (14.15c), and indeed, the variables to be considered will all be variables in the Σ-set. Given a set Σ we consider a set N that contains at least some lin­ guistic variables in the Σ-set. In addition, we need a set A of properties that S-variants of linguistic variables may have. Given a linguistic var­ iable in N and a property a in A, we obtain a property of idiolect sys­ tems S: the property of being an idiolect system S such that the S-variant of the linguistic variable has a. Σ itself may be partly specified in terms of sets N and A, in the following sense: every system σ in Σ con­ tains a property of idiolect systems that is determined, as just ex­ plained, by some linguistic variable in N and some property of vari­ ants in A. In more precise terms the notion of partial specification is now ex­ plicated as follows ("N" stands for any set of sets, "A" for any set of admissible properties of set-theoretical objects):

SOLVING THE INTEGRATION PROBLEM (18)

(18.4)

181

Definition XXVII. X is partly specified in terms of N and A iff there is an M such that a. M  N; b. M is a linguistic variable in the Σ-set; c. for every σ  Σ, there is an α  A such that (i) or (ii): (i) for some n > 1, M is an n-place relation and propn(M, α)  σ; (ii) for some n > 0, M is an n-place function and proptn(M, α)  σ.

Condition (b) could be strengthened by adding, "and is a component variable in the sense of (1.12)". Less formally, a set Σ of systems for sets of idiolects is partly spe­ cified in terms of (i) a set N that contains a linguistic variable in the Xset and (ii) a set A of properties, provided every system in Σ contains the property (of idiolect systems) that is determined by the variable and some property from A, where the 'relation case' and the 'function case' of linguistic variables are treated separately. 18.4 Example The import of Definition XXVII will be clearer from the following example: (18.5)

Suppose that a. X = {σ 1 ,σ 2 ,σ 3 }, where σ1, σ2, and σ3 are 'lowest' sys­ tems for, respectively, the three registers of Early Modern German (EMG): Neutral G(erman)  EMG, Above-Neutral G  EMG, Below-Neutral G  EMG; b. N = {WOP, ...}, where WOP = the two-place relation Word Order Pattern ('c is a word order pattern of S'); c. A = {α1, ...}, where α1 = the property of being an x such that: x = {SVO, SOV, ...} and the elements of x are exactly the word order patterns of idiolect systems in EMG; d. WOP is a universal variable (see (15.7));

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e. for each σ  Σ, prop 2 (WOP,α 1 )  σ, where prop 2 (WOP, α1) = the property of being an S such that the S-variant of the WOP-relation has α1 i.e. prop 2 (WOP, α1) is the property of being an S such that W O P ( - S ) = {SVO, SOV, ...}. Then f. Σ is partly specified in terms of N and A. Outline of proof. We demonstrate that WOP is an M that satisfies (18.4a) to (18.4c). a. WOP  N, by (18.5b). b. Because of (18.5a), the Σ-set (see (18.3))  IDS (see (14.14)). By (18.5d) and definition (15.7) WOP is a linguistic variable in IDS. Therefore, WOP is a linguistic variable in the E-set, by Th. I (14.16). c. Suppose that σ  Σ. We show that α1 is as required by (18.4c). First, α1  A, by (18.5c). Second, WOP is a two-place relation, and prop 2 (WOP,α 1 )  σ, by (18.5e). Therefore, (18.4c) holds of WOP. It follows that (18.5f), by (18.4). (Q.E.D.) Note that in this example a single property α was sufficient for WOP to determine a property in each σ  Σ. Definition XXVII would allow, though, for a case in which different properties α are required for WOP to determine properties ø such that each σ  Σ ontains a WOP-determined property. As also appears from the example, partial specification does not require that the properties of idiolect systems determined by the lin­ guistic variables should be 'specific to' a given variety, in the sense of Def. 20 (13.5). Definition XXVII could be strengthened by making every M  N a linguistic variable in the Σ-set, and making A a minimal set of prop­ erties; or by generally requiring that M should be a set of principles in the sense of (15.5c) or universal variables in the sense of (15.7) — a condition true to the spirit of Chomskyan grammar that I would, how­ ever, consider overly restrictive. We are now ready to integrate the component approach into the variety approach: permissible types of systems are partly specified by sets of linguistic variables.

SOLVING THE INTEGRATION PROBLEM (18)

183

18.5 Permissible types of systems: integrating the compo­ nent approach By Definition 7 in (11.2c), a permissible type of systems (for sets of idiolects) is simply a non-empty set of 'lowest', i.e. least abstract sys­ tems. This is now modified by also requiring partial specification: (18.6)

Definition 7'. Σ is a permissible type of systems with re­ spect to D iff a. for any a, D1 and T, if σ  Σ and D1 = {C | C is covered-by-σ in-D} and T = the D-system class for D1, then σ is a lowest TD1-system. b. For some N and A, Σ is partly specified in terms of N and A.

Given the modified concept of permissible type of systems, we take the decisive step and both expand and modify the theory of language vari­ eties as follows: (18.7)

Integration of the component approach a. After Definition 6 (11.1), insert Definitions I to XXVII, Assumptions I to IV, and Theorems I to VI from Secs 14 to 18 (making variable use consistent — see Sec. 15, last paragraph). b. In (11.2c), replace Definition 7 by Definition 7'.

This move has the desired consequences, for the following reasons. First, "permissible type of systems" in the definition of "systembased point of view" (Def. 8, (11.3)) is interpreted in the new, strong­ er sense, which automatically strengthens the concepts of system-based set and system-based criterion (Defs 9 and 10, (11.4)) and the notions of exhaustive system-based point of view, set, and criterion (Defs 11 to 13, (11.5)). Therefore, Assumption 3 on variety structures (11.8) is also strengthened; it is now required of any classification in the variety structure of a historical language that the classification is given through a set of criteria of the following kind: each criterion is the property of being an idiolect 'covered by' a system a from a set Σ of

184

INTEGRATING THE COMPONENT APPROACH (IV)

systems that is partly specified in terms of (i) a set containing linguistic variables and (ii) a set containing properties of variants. True enough, direct integration of the component approach into the variety approach, as proposed in (18.7), leads to a theory whose metascientific status is dubious: since the component approach also in­ cludes the grammar approach (which involves reference to the lin­ guist's grammars), integration results in a theory that is part not of a theory of language but of linguistics. This consequence no longer ari­ ses if the grammar approach is eliminated from the component ap­ proach; obviously, the grammar approach need not be adopted in vari­ ation research and has indeed been loosing followers. In brief, construing variation in terms of components may be ta­ ken to be one aspect of a variety conception that is sufficiently far de­ veloped; rather than being an alternative to the variety approach, the component approach, restricted to language-internal variation and properly construed, turns out to be part of it. By definition, the variety approach is tied down to language-inter­ nal variation. This is not true of the holistic approach, of which the va­ riety approach is a subcase, nor does it hold of the theory presented in this essay, after integration of the component approach. Indeed, the framework outlined in Sec. 4 applies to arbitrary communication complexes. In Part V - "Extensions" - I first consider the possibility of extending the theory to interlanguage variation, concentrating on questions of language typology (Sec. 19). No attempt will be made to review the literature. The best theoretical work so far should be Vennemann's (esp. 1984, 1985); my own proposals, though partly germane in spirit to Vennemann's, take a rather different route. Section 19 has the limited aim of demonstrating that the extended theory does cover interlanguage variation in a sensible way and, in particular, does justice to language typology. The second extension to be introduced in Part V concerns linguistic descriptions: I will study questions of format for grammars in which variation is accounted for by means of linguistic variables (Secs 20f).

PART V

EXTENSIONS

19 Going Beyond Varieties

19.1 A note on contrastive analysis and language acquisition From the very beginning the theory developed in Parts II to IV was conceived as a fragment of a larger theory that would also do justice to interlanguage variation. This shows in a number of ways. First, the concept of linguistic variable as defined in (1.6) does not imply any restriction to language-internal variation (see also (1.5)), and this also holds of the notions relating to types of variables (1.11), in particular, the concepts of component variable (1.12) and holistic variable. Some of the variation concepts are not even linguistic but purely set-theoretical. This is true of the variant terminology (Sec. 14), prop­ erty determination (Sec. 18.2), and all notions centering around the concept of classification system (Sec. 9). The theoretical background presented in Sec. 4 covers arbitrary communication complexes (non-empty finite sets of means of commu­ nication) and thus applies to a language just as well as to the union of several or all languages. Notions like stage, system-for, or state of a system are introduced for arbitrary communication complexes. Simil­ arly, the notions of permissible type of non-language entities and per­ missible type of systems; of external and system-based point of view, set, and criterion apply in connection with any communication com­ plex (Secs 10 and 11). A linguistic variable may be a variable in any set of idiolect systems (Sec. 14.5). Consequently, the important notion of specification — a set of systems is specified in terms of a set of lin­ guistic variables (Sec. 18.3) — applies to sets whose elements are sys­ tems for arbitrary idiolect sets; and this also holds of the revised con­ cept of permissible type of system in Sec. 18.5.

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EXTENSIONS (V)

Due to its generality the framework easily accommodates all sorts of contrastive analysis. Such analysis typically compares varieties of different languages for certain 'features', which in our framework may be construed as linguistic variables. The varieties are compared rather than arranged into classes; we need not go beyond the theory of varieties to do justice to contrastive analysis, or any other work of a comparative type. (More on this below, Secs 20.3 and 21.5; see also Lieb 1980a, where the notion of a linguistic variable — not yet used — could easily be included.) The larger theoretical framework also accommodates first- and se­ cond-language learning. What develops in language acquisition is a se­ quence of systems of means of communication ('interlanguages') that may not yet be idiolect systems in any language; this is accounted for by our notion of communication complex (see Secs 3.If of Lieb 1980a). True, the notions of linguistic variable and linguistic-variablein presuppose systems of idiolects rather than systems of 'quasi-idiolects'; however, given an appropriate characterization of the 'quasi-idiolects' that develop in language acquisition, the concepts could be gen­ eralized (by allowing quasi-idiolects as language-like entities in (1.5a) and including their systems in (14.14)). The generality of the theoretical framework may also be exploited in dealing with language typology. However, a new feature must be ac­ counted for: typological studies aim at establishing 'language types', which, it would seem, must be construed as sets whose elements are entities such as languages. Whereas a variety is a set of idiolects, a lan­ guage type is a set of sets of idiolects; in dealing with language types, we move one up in the hierarchy of sets. 19.2 Language typology: basic ideas Language types result from classifications. Objections to this tradition­ al view are mostly analogous to objections raised against the view that varieties result from classifications, and can be countered in a similar way (see above, Sec. 7). I here adopt the classification approach to ty­ pology. More specifically, I propose that the essence of typology can be captured by assuming classification systems, to be called typological structures, whose classes are language types.

GOING BEYOND VARIETIES (19)

189

As a first step we characterize the sources of such classification systems. A typological structure is based on a set that may contain his­ torical languages, varieties of historical languages, or both. Typology is usually concerned not with complete historical languages but only with language varieties which may but need not be languages in their own right (if they are, the varieties must be periods of historical lan­ guages). Such varieties are as a rule from different historical lan­ guages but this need not be the case; the typological point of view may be applied to different varieties of a single language. A typology base may be defined as a set of D's that satisfy one of two conditions: (i) D is a variety of some D1, hence, a proper subset of some historical lan­ guage, or (ii) D has a variety, hence, may itself be a historical lan­ guage. A typological structure is a classification system on a typology base. How is this system determined? It is at this point that linguistic variables come in. Consider a simplified example meant to clarify the role of linguis­ tic variables. The linguistic variable to be considered is the two-place relation Phoneme: x is a Phoneme of S. For any idiolect system S, the S-variant of the Phoneme relation = {x | (x, S)  Phoneme} = the set of phonemes of S (see (14.8)). We define the following two properties for any set M (/w/ = the bilabial approximant in English window): (19.1)

a. +/w/ = the property of being an M such that /w/  M. b. -/w/ = the property of being an M such that /w/  M.

The relation Phoneme and the two properties +/w/ and -/w/ in turn de­ termine two properties of idiolect systems (cf. (18.2a)): (19.2)

a. prop2(Phoneme, +/w/) = the property determined by Phoneme and +/w/ = the property of being an S such that the S-variant of Phoneme has +/w/ (i.e. such that /w/  {x | (x, S)  Phoneme}, equivalently, such that /w/ is a Phoneme of S). b. prop 2 (Phoneme,-/w/) = the property determined by Phoneme and -/w/ = the property of being an S such that the S-variant of Phoneme has -/w/ (i.e. such that /w/  {x I (x, S)  Phoneme}, equivalently, such that

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EXTENSIONS (V)

/w/ is not a Phoneme of S). The two properties in (19.2) may be used to set up a classification on a given typology base E (a set of languages or language varieties D): (19.3)

a. The (Phoneme, +/w/)-class for E = the set of all D  E such that there is a system σ for D such that prop2 (Phoneme, +/w/)  σ. b. The (Phoneme, -/w/)-class for E = the set of all D  E such that there is a system σ for D such that prop 2(Phoneme, -/w/)  σ.

Intuitively, the first class consists of those languages or language varie­ ties in the typology base which each have a system G such that the property of being an idiolect system S with phoneme /w/ is an element of a (remember that a system G for a language or language variety is conceived as a set of properties shared by the systems S of all idiolects in the language or language variety). In the same way the (Phoneme, -/w/)-class is the set of those elements of the typology base which each have a system G such that the property of being an idiolect system S without phoneme /w/ is an element of G. Suppose that (19.4)

F = {the (Phoneme, +/w/)-class for E, the (Phoneme, ~/w/)-class for E}.

Obviously, F is a classification on E — even more strongly, a partition of E — unless one of the two sets in F is empty. A typological structure on E is a classification system on E whose elements — classifications on some subset of E, not necessarily on E itself — are obtained in essentially this way through linguistic varia­ bles and properties of their S-variants; the classes in the typological structure (i.e. the elements of the classifications in the structure) are its types. They should be called linguistic types rather than 'language types', since they may contain language varieties as well as languages. We accept this example for orientation after a three-way modifica­ tion. First, a linguistic variable involved in setting up a classification F is to be a variable in the set of idiolect systems which are associated

GOING BEYOND VARIETIES (19)

191

with F, briefly, in the E-set: the set of all S such that S is a system of an idiolect in a language or variety that belongs to a set E1 that is an element of F. For the relation Phoneme as a linguistic variable and set F in (19.4) as a classification, this condition is trivially satisfied: we tacitly assumed that Phoneme is a universal variable, i.e. a variable in the set of all idiolect systems (15.7), therefore, a variable in any set of idiolect systems. However, allowing only universal variables would be too stringent a requirement; we only demand that linguistic variables are variables in the F-set. Second, it would be overly restrictive to allow just a single lin­ guistic variable (Phoneme) and a single property of variants (+/w/ and -/w/, respectively) in setting up a class in the typological structure: in­ stead of a single variable/property pair we should proceed from a set of such pairs - or two-place relation - which as a limiting case may contain a single element. A relation R of this kind may be called a typological criterion, or t-criterion, relative to a given classification F; the linguistic variables that are the first-place members of the criterion must all be linguistic variables in the E-set. Third, a name is needed for the class that a given typology criteri­ on may define. In (19.3), we used expressions such as "the (Pho­ neme, +/w/)-class for E". Individual pairs like (Phoneme, +/w/) are now replaced by sets R of pairs; we may therefore speak of the R-class for E. The various auxiliary notions should be made more precise before "typological structure" is defined. 19.3 Auxiliary concepts The following definitions will be more easily understood if we re­ member the various types of entities that are presupposed (see also (4.7) and (4.8)). Three groups may be distinguished. First group. We start from idiolects, entities of type C. Languages and their varieties are sets of idiolects, i.e. entities of type D. A typo­ logy base is a set of languages or varieties, i.e. an entity of type E; the same is true of a 'language type'. A classification on a subset E1 of E is a set of subsets of Ev therefore, a set of entities E, i.e. an entity of type F. A typological structure on E is a set of classifications on sub-

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EXTENSIONS (V)

sets of E, therefore, a set of entities F, i.e. an entity of type G. Second group. We start from systems of idiolects, i.e. from enti­ ties of type S, and consider sets of such systems, i.e. entities of type T. We next consider properties of idiolect systems, i.e. entities of type ø. We proceed to systems for languages or language varieties, i.e. sys­ tems for sets of idiolects; such systems are sets of properties ø of idio­ lect systems, i.e. they are entities of type G. Third group. We continue to speak of arbitrary set-theoretical en­ tities x (other than properties, or set-theoretical entities that involve properties); of arbitrary sets M of entities x; sets N of entities M; ad­ missible properties a of entities x; sets A of entities a; and sets R of pairs (M, a). The following definitions continue the chain of definitions ob­ tained after integrating the theory of Secs 14 to 18 into the theory of varieties (see (18.7)): the 27 definitions of Secs 14 to 18 had to be in­ cluded with the 20 definitions of the theory of varieties (whose last definition is Def. 20 in (13.5)). The next definition number is there­ fore 48. We begin by defining the notion of typology base: (19.5)

Definition 48. E is a typology base iff E  the field of Variety.

This means that for every D  E there is a D 1 such that D is a variety of D1 or there is a D 1 such that D1 is a variety of D. Intuitively, a ty­ pology base is a set whose elements are varieties of something or themselves have varieties; the two conditions may of course both be satisfied. If D is variety of anything, D must be a subset of some his­ torical language, by (12.4a); and any historical language may occur in a typology base since it must have varieties by (9.12). (A typology base E may be empty but then of course it cannot be the source of a classification system.) We next introduce the two auxiliary terms "F-set" and "typology criterion": (19.6)

Definition 49. The F-set = {S | there are E1  F, D  E1, and C  D such that S is a system of C}.

If F is a classification that belongs to a typological structure, then the

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F-set is a set of idiolect systems: the set of systems of those idiolects which are elements of sets D — languages or language varieties — that are elements of sets E1 — 'linguistic types' — that are elements of classification F. The linguistic variables used for setting up F must be variables in the F-set of idiolect systems: (19.7)

Definition 50. R is a typological criterion [t-criterion] relative to F iff a. R is non-empty; b. every first-place member of R is a linguistic variable in the F-set.

A t-criterion is not a criterion in the logical sense of Sec. 9.2; still, the term is defensible: it could be shown for typological structures that their classes are obtained by criteria in the logical sense that are based on t-criteria. It is useful to have a concept of criterion that is not relativized to any F: (19.8)

Definition 51. R is a typological criterion [t-criterion] iff a. R is non-empty; b. For some T, every first-place member of R is a lin­ guistic variable in T.

It follows from the definitions that any t-criterion relative to F is a tcriterion in the sense of (19.8). In speaking of t-criteria relative to F, we may occasionally drop reference to F; it should then be clear from the context how the ambiguous term "t-criterion" is to be understood. Finally, the notion of R-class is introduced independently of any F, hence, independently of t-criteria: (19.9)

Definition 52. The R-class for E = the set such that for all (M, α)  R there is a a such a. a is a system for D; b. (i) or (ii): (i) for some n > 1, M is an n-place propn (M, α)  σ. (ii) for some n > 0, M is an n-place proptn(M, α)  σ.

of all D  E that

relation and function and

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("is logically implied by" may be preferable to "e " in (b), see (21.6c).) Informally, we take a set R of pairs (M, α) where M is an n-place rela­ tion (n > 1) or an n-place function (n > 0). In the intended application, R is a t-criterion relative to some classification in a typological struc­ ture. We further choose a set E; this is to be the typology base that is the source of the typological structure. The R-class for E is a certain subset of E that is determined entirely on the basis of relation R; in the intended application, the R-class is a 'linguistic type'. Determination is as follows. We collect all elements D of E (all languages or language varieties in E) with the following property. Consider the property of idiolect systems determined by any (M, a) — any variable/property pair — that belongs to R: this property of idiolect systems must be contained in some system for D. The property may be contained in more than one system, and the properties determined by different pairs (M, α) in R may well be contained in different systems for D. 19.4 Typological structures and types The definition of "typological structure" uses "typology base", "t-crite­ rion", and "R-class": (19.10) Definition 53. G is a typological structure on E iff a. E is a typology base; b. G is a classification system on E; c. for every F  G there is an N such that for every E1  F there is an R such that (i) the domain of R = N; (ii) R is a typology criterion relative to F; (iii) E1 = the R-class for E. The pretheoretical concept of language type is explicated by three dif­ ferent if closely related concepts: (19.11) Definitions 54 and 55. Let G be a typological structure on E. a. E1 is a type in G iff E1 is a class in G. b. The R-type for E in G = the E1 s.t. either (i) or (ii):

GOING BEYOND VARIETIES (19)

(i) (ii)

195

the R-class for E is a type in G, and E1 = the Rclass for E; the R-class for E is not a type in G, and E1 = Ø.

In addition, (19.12) Definition 56. E1 is a linguistic type iff there are G and E such that a. G is a typological structure on E; b. E1 is a type in G. Definitions 53 to 56 will be further explained in Sec. 19.5. I first give an example jointly for all four definitions. (A proof is added for the sake of completeness; it is not needed for understanding the example.) (19.13) Example for Definitions 53 to 56 Suppose that a. E = {Modern High German (MHG), Modern English (ME), Modern French (MF)}; b. N = {Phoneme} c. A = {+/w/,-/w/} d. R1 = {(Phoneme, +/w/)}; e. R2 = {(Phoneme,-/w/)}; f. σ1 : a certain system for MHG such that prop 2 (Phoneme,-/w/)  σ1 (where prop 2 (Phoneme,-/w/) = the property of being an S such that the S-variant of Phoneme has property -/w/, i.e. /w/ is not a phoneme of S); g. σ2: a certain system for ME such that prop 2 (Phoneme, +/w/)  σ2; h. σ3: a certain system for MF such that prop 2 (Phoneme, +/w/) e σ3; i. E1 = {ME, MF}; j . E 2 = {MHG}; k. F = {E 1 ,E 2 };

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1. T = {S | for some C  {MHG, ME, MF}, S is a system of C}; m. Phoneme is a universal variable; n. G = {F}. Then o. G is a typological structure on E; p. q. r. s.

E1 E1 E2 E2

and E2 are the types in G; - the Retype for E in G; = the Retype for E in G; and E2 are linguistic types.

Proof of (o). We prove that E and G satisfy conditions (a) to (c) in (19.10). a. All elements of E have varieties; hence, E is a typology base, by (19.5). b. F = {E 1 ,E 2 } = {{ME,MF}, {MHG}} is a classification on E = {ME, MF, MHG}, by (9.2); therefore G = {F} is a classification sys­ tem on E, by (9.9). c. There is just one element of G, viz. F = {E1, E 2 }. We show that N = {Phoneme} is a set as required for F by (19.10c). There are just two elements of F, E1 = {ME, MF} and E 2 = {MHG}. We show that for both E1 and E2 there is an R related to N, F, E1? and E as required in (ci) to (ciii). For E1, R1 = {(Phoneme,+/w/)} is such a set, and R2 = {(Pho­ neme,-/w/)} for E2: (i) The domain of R1 = the domain of R2 = {Phoneme} = N. (ii) R1 and R2 are t-criteria relative to F: R1 and R2 are non­ empty, and by Hyp. (m), Phoneme is a universal variable, i.e. a lin­ guistic variable in IDS, the set of all idiolect systems, by (15.7). Since T in Hyp. (1) is a subset of IDS, Phoneme is a linguistic variable in T, by (14.16). Moreover, T = the F-set: T is the set of all S that are systems of idiolects either in MHG, ME, or MF, by Hypothesis (1); and these are exactly the sytems of idiolects that are elements of elements D of elements E 3 of F, as required by (19.6). Therefore, Phoneme is a linguistic variable in the F-set, and both R1 and R2 are t-criteria, by

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197

(19.7). (iii) E1 = {ME, MF} is the R1 class for E, by (19.9): E1 is the set of those D from E such that for the only element (Phoneme, +/w/) of R1 there is a system for D that contains the property determined by this element; for ME, this is system σ2 in Hyp. (g), for MF, system σ3 in Hyp. (h). (Postulating such systems is realistic since in any ME idio lect system S, /w/ is a Phoneme of S, and the same is true of MF sys­ tems, cf. bois, oui.) There is no such system for MHG: this is excluded by the fact that MHG has a system, viz. σ in Hyp. (f), that contains the property determined by (Phoneme, -/w/) (/w/ does not exist in MHG idiolect systems). Since (Phoneme,-/w/) is the only element of R2, E2 = {MHG} is the R2-class for E, by (19.9). In conclusion, conditions (a), (b), and (c) of (19.10) are satisfied for G and E, and G is a typological structure on E. Proof of (p). E1 and E2 are the types in G: this follows directly from (o), (9.0), (19.11a), and the fact that G = {{{ME, MF}, {MHG}}}. Proof of (q) and (r), E1 = the {(Phoneme,+/w/)} class for E and E2 = the {(Phoneme,-/w/)}-class for E, by the arguments used in the proof of (o). Both are types in G by (p). Hence, E1 = the {Phoneme, +/w/)}-type for E in G, and E2 = the {(Phoneme,-/w/)}-type for E in G, by (19.11b). Proof of (s). E1 and E2 are linguistic types by (o), (p), and Def. (19.12). Q.E.D. 19.5 Explanations Typological structures Informally, a typological structure is a classification system on a typo­ logy base where every classification in the system satisfies the follow­ ing condition: there is a single set of linguistic variables such that each set in the classification is determined by some typological criterion whose first-place members are exactly these variables. Each variable is a variable in the set of systems of those idiolects which are ultimately 'contained' in the classification. The typological criterion for a given

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set (linguistic type) in the classification combines the variables with properties such that each variable/property pair determines a property of idiolect systems. The linguistic type is the set of all languages or language varieties from the typology base that satisfy the following condition: given any variable/property pair in the t-criterion and the property of idiolect systems determined by the pair, this property is contained in some system for the language or language variety. It is important to notice the logical structure of condition (c) in (19.10): for each classification in the typology structure G, there must be some set N of linguistic variables of a certain kind — there may be several such sets for a single classification, and there may be different sets N for different classifications; and for each set (linguistic type) in a given classification, there must be some typological criterion relative to the classification that determines the set — there may be several such criteria for a single set, and there must be different t-criteria for different sets (linguistic types) in the classification. The t-criteria for different sets employ exactly the same linguistic variables; hence, they differ only in their second-place members, the properties a of S-variants of the variables. The domain of a t-criterion — a set of linguistic variables — can be compared to a set of 'features'; its range — a set of properties of Svariants of variables — to a set of 'feature values', in some traditional sense of these terms: we take a single set of 'features' (linguistic varia­ bles) and combine each 'feature' with one (or more) 'feature values' (properties of S-variants of linguistic variables); a specific combina­ tion (set of pairs of 'features' and 'values') defines a set of languages or language varieties; different combinations define different sets, and all sets in the classification are obtained in this way. While this analogy may be helpful, it should not be pressed; the traditional terms "fea­ ture" and "feature value" are both ambiguous and vague. Types, linguistic types, R-types The intuitive notion of language type was replaced by three different if related concepts. The types in a typological structure are simply the classes in this structure, i.e. the elements of the classifications that are elements of the structure (19.11a). Linguistic types (19.12) — rather

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199

than 'language types', since varieties are also allowed as elements — are types in some typological structure. The concept of R-type allows formulations of the following kind: (19.14) R-type: (9.11). a. The b. The c. The d. The

further examples. Let G and E be as in example {(Phoneme, +/w/)}-type for E in G = {ME, MF}. {(Phoneme, +/ /)}-type for E in G = Ø. {(Phoneme, +//)}-type for E in G = Ø. {(Phoneme, +/s/)}-type for E in G = Ø.

Proof of (a). From (19.13q) (reformulation). Proof of (b). [I /: a click phoneme.] +/ / is the property of being a set M such that / /  M, by a definition analogous to the definition of "+/w/". Hence, by (19.9), (i)

the {(Phoneme), +/ /)}-class for E = the set of all D  E such that there is a system σ for D such that prop 2 (Phoneme, +/ /)  σ, where prop2(Phoneme, +/ /) = the prop­ erty of being an S such that / / is a phoneme of S (cf. (19.2)).

It follows that all systems of idiolects in D have / / as a phoneme. Now E = {MHG, ME, MF}, and in none of these varieties are there idiolects whose systems have click phonemes. Therefore, the {(Phoneme, +/ /)}-class for E is empty, therefore, no type in G by (19.11a); hence, the {(Phoneme,+/ /)}-type for E in G = Ø, by (19.11b). Proof of (c). [/i|/: the bilabial approximant in French cuisine, /k  iz i n/.] +// is defined as before. Hence, by (19.9), (i)

the {(Phoneme, +//)}-class for E = the set of all D  E such that there is a system σ for D such that prop 2 (Phoneme, +//)  σ, where prop2(Phoneme,+//) = the prop­ erty of being an S such that// is a phoneme of S (cf. (19.2)).

It follows that all systems of idiolects in D have// as a phoneme. Now

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E = {MHG, ME, MF}, and only the MF idiolect systems have phoneme Al/. Therefore, the {(Phoneme,+//)}-class for E = {MF}. By (19.11a), this is no type in G, since G = {{ME, MF}, {MHG}}, by (19,13). Therefore, the {(Phoneme,+//)}-type for E in G = Ø, by (19.11b). Proof of (d). Analogous to proof of (c); the {(Phoneme,+/s/)}-class Q.E.D. for E = E, and E is no type in G. The examples show that the R-type for a given E in a given G may be empty in three cases: either the R-class for E is empty (R doesn't apply in E at all — cf. (b)); or the R-class for E is a non-empty proper subclass of E but no type in G (R applies but yields an incorrect result — cf. (c)); or the R-class for E = E (R applies but doesn't discriminate in the typology base, it yields the base itself — cf. (d)). Only in the first case is the R-type of E in G = the R-class for E = 0 ; hence, the notion of R-type cannot be generally replaced by the concept of Rclass. The proposed explications for the notions of typological structure and type may not yet be optimal in all respects; I do believe, though, that they are true to the spirit of current typological research. Typolo­ gical studies are concerned with typological structures, which are anal­ ogous to variety structures only in part. 19.6 Variety structures and typological structures The following points A to D are worth emphasizing. A. Typology and varieties. Typological structures are classifica­ tion systems on typology bases, which are subsets of the field of the Variety relation. It turns out, then, that language-internal variation is presupposed in typology research: the objects to be arranged in types are languages and language varieties. I have outlined a typological theory, or rather, theory fragment, that is a natural extension of the theory of language varieties. B. Typology and classification. Variety structures and typological structures are both classification systems, at different levels of abstrac­ tion. Typological structures are thus subject to some of the objections

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raised against variety structures. The relevant refutations (see Sec. 7) partly carry over to typological structures; in particular, conceiving a typological structure as a classification system is compatible with de­ gree phenomena, prototypicality, similarities and the like. They can all be accounted for by means of linguistic variables, and properties of Svariants, of the right kind; the variables, in particular, may be quantitive (e.g., in the sense of Definition XXIV, (17.17a)). C. The non-uniqueness of typological structures. Typological structures are 'one up' in the hierarchy of sets from variety structures. There is an even more fundamental difference between typological and variety structures than this difference in formal status: for the variety structure of a language, existence and uniqueness are guaranteed by an axiom of the theory of language, which was adopted only after careful consideration of the problems it might give rise to. No such axiom was introduced in connection with typological structures. Typological structures, however trivial from a linguistic point of view, do indeed exist; one such structure was specified in Sec. 19.4. There is, however, no uniqueness assumption. Not only can typology bases be chosen at will, whereas historical languages are, in a sense, given; even for a single typology base that has at least two elements and may therefore have typological structures, there may be different structures, depending on the choice of typological criteria. Postulating uniqueness for variety structures can be defended by the role of external and system-based criteria, which jointly provide a strong anchor for unique variety structures (cf. the correlation theorem, Sec. 11.5). No such anchor has yet been found in language typology, where the choice of typological criteria appears to be governed by considerations of practical or theoretical fruitfulness rather than restrictions imposed by a theory of language. D. Type vs. variety. No uniqueness may be assumed for typologi­ cal structures: it is partly due to this fact that types and typological structures are not related in the same way as varieties and variety structures. Formally, the relations Type (E1 is a type in G) and Varie­ ty (D1 is a variety of D), appear to be analogous; they are both twoplace relations, and we may even be willing to allow not only D and D1 as language-like entities but also E1 and G, in conformity to a ho-

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listic approach. However, D and D1 are of exactly the same type (both are communication complexes) whereas E1 and G are not: E1 is a set of communication complexes whereas G is a set of sets F of sets E of communication complexes. At the level of definitions, the definition of "type" uses "typological structure" (which occurs in the antecedent of (19.11)) whereas "variety structure" is defined by "variety" (Sec. 9.6). In conclusion, typological structures are anchored much less se­ curely in reality than variety structures are. This confronts typology with a serious relevance problem: if typological criteria are badly chosen, the typological structures will be linguistically irrelevant. The present theory, with a clearer conception of typological criteria, allows for a maxim: build your criteria from the most relevant lin­ guistic variables that your theory of language provides — and pray that your theory of language is relevant.

20 Grammars and Their Terminology

20.1 Introduction The theory of linguistic variation developed, or partly developed, in the present essay may further our understanding of grammars written by the linguist, and may be helpful in actual grammar writing. True, the format chosen for a grammar in a specific situation depends on many factors, perhaps most importantly, on the user for whom the grammar is envisaged. I do not intend to give practical advice in the last two chapters of my book. Instead, I will advance a number of claims that concern grammars of various types regardless of degree of formality or practical purpose. These claims are made both for the terminology of grammars (in the present Section) and for grammatical statements (Sec. 21). The claims are on the status of grammatical terms and on the logical form of statements that are characteristic of grammars of different types. There is both a descriptive and a heuristic aspect to these claims. From a descriptive point of view the claims should be by and large correct for the majority of grammars actually written in linguistics ex­ cepting those which insist on being metalinguistic formalisms for enu­ merating sets of sentences or similar entities; i.e. the claims are made for grammars that contain, or can be construed to contain, statements on their objects. To make the descriptive relevance of the claims plau­ sible, I start from statements taken from a recent grammar of English, which will be analysed for their logical form and the status of their terminology. The claims also have a heuristic aspect: it is proposed that future grammars should adhere to formats that actually agree with the claims on grammatical terms and grammatical statements (different formats may still be considered; the claims are not prescriptive of a single for-

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mat). A major reason is this: any format compatible with the claims will lead to grammars that are comparable with one another, and com­ parable with grammars written in a different format that also conforms to the claims. If the claims are correct from a descriptive point of view and ac­ ceptable in their heuristic aspect, they may indeed be used for im­ proved grammar writing, despite the fact that they do not yet offer concrete suggestions to the practising linguist. The claims assign linguistic variables a position at the centre of linguistics. The last two chapters of my book are devoted to a theory of grammars in which my theory of linguistic variables - as part of a theory of language - is presupposed. In this sense, then, the theory of grammars 'extends' the variation theory. The theory of grammars could be expanded, and made much more precise; it might then result in something like the theory of grammars proposed in Integrational Linguistics (Lieb 1983: Part G; forthc. d). The present account is, however, more general and not committed to the integrational version. There are various types of 'grammars' that may be considered. 20.2 Types of ' g r a m m a r s ' Linguistic descriptions of a 'grammar' type, in some traditional sense of "grammar", can be classified roughly as follows: (20.1)

Types of 'grammars' a. Idiolect grammars: the object of the description is a pair of an idiolect and a system of the idiolect. b. Language grammars: the object of the description is a pair consisting of a historical language, or variety of such, and a system for the language or variety (simple language grammar); or the object is a set of such pairs containing more than one element (complex language grammar). c. Comparative grammars: the object of the description is a relation between several pairs that each consist of a historical language, or variety of such, and a system

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for the language or variety; and of the languages or varieties that are first components of different pairs, none is a subset of the other. d. Typologies: the object of the description is a pair con­ sisting of a typology base — a set whose elements are historical languages or language varieties — and a typological structure on the base (a set of classifica­ tions on the base whose classes are 'linguistic types'). "Grammar" occurs also as part of the expression "universal gram­ mar", mostly used in linguistics in the singular and without an article to denote 'the theory of language' as a discipline. I will continue to speak of individual theories of language, avoiding "universal gram­ mar" altogether. The various terms employed in (20.1) in characteriz­ ing types are to be understood in their previous senses (see, in particular, Secs 4, 6, and 19). I am presupposing a broad sense of "grammar" where all aspects of form and meaning may be covered. A grammar may be partial, i.e. deal with its object only to the extent that certain parts or subsystems are involved (of idiolect systems or, derivatively, for systems of sets of idiolects). We may thus speak of phonological, morphological, syntactic, or even semantic grammars. A grammar is complete if it is not partial. Both a partial and a complete grammar may be either exhaustive or non-exhaustive, depending on whether it does or does not specify all relevant properties of its object (to the extent that the object is cov­ ered). No complete and exhaustive grammar may yet exist. A grammar is pure if every name of an idiolect, or a set of idio­ lects, that occurs in the grammar denotes a component of the object of the grammar; it is mixed if it is not pure. The term "grammar" is rarely if ever used for typological de­ scriptions, and will indeed be avoided for descriptions of typological structures; such descriptions may be called typologies, in the plural; "typology" as a count noun is thus restricted to its metalinguistic sense. The distinctions just introduced yield a classification system on the set of all 'grammars' that may be presented as diagram (20,2) (next page). Names of classifications were chosen so as to indicate

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GRAMMATICAL TERMS (20)

207

classification criteria. If two classes belong to a single classification that is based on a subset of the set of partial grammars, these classes may overlap; thus, we may have morphosyntactic grammars, among others, i.e. grammars that are both morphological and syntactic. 2 0 . 3 Comments Idiolect grammars Such grammars appear to be rarely considered in linguistics. They are, however, at the very basis of grammar writing because they provide an ultimate testing-ground for grammars of all other types (a claim that can be made precise and supported, cf. Lieb 1983: Part G; in par­ ticular, the object of an idiolect grammar may be expanded to include specific speakers and utterances). The fundamental role of idiolect grammars clearly appears in the study of endangered languages where generalizations on a language and its varieties must be based on a few remaining idiolects whose systems may already be atypical; some speakers may end up with personal varieties of the language that con­ tain just a single idiolect, determined by a system that has coalesced from systems of different idiolects still kept apart by the speaker at an earlier date. (For the difference between idiolect and personal variety, see Secs 6.4 and 8.3.) Language grammars Such grammars may be devoted either to complete historical languages (a case that should at least be allowed for in view of certain descrip­ tions in historical linguistics), or else to varieties of such, including languages that are periods — i.e. temporal varieties — of historical languages. Introducing complex language grammars in addition to simple ones is to account for the following case: we consider not only a single pair (D, σ) — where D is a historical language or variety of such — but also further pairs ( D 1 , σ 1 ) , ...,(D n , σn) such that each Di is a variety of D and σ i is system for Di; D will be called the primary referent of the grammar.

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For example, in a grammar of Modern English (primary referent) we may consistently refer to peculiarities of Modern British English on the one hand and American English on the other. The object of such a grammar may be identified with a set of three suitable pairs. Complex grammars must not be confused with descriptions of (parts of) the variety structure of the grammar's primary referent; (i) the object of the grammar — a set of pairs (D, σ), or relation between en­ tities D and σ — simply isn't the variety structure, which is a classifi­ cation system on the grammar's primary referent; (ii) complex gram­ mars are as a rule non-exhaustive even with respect to the varieties they are meant to cover. From a sufficiently detailed complex gram­ mar we may well be able to extract a description of the variety struc­ ture — or part of the variety structure — of the grammar's primary referent. As a rule, complex grammars appear to have a more modest aim: to supply variety-sensitive descriptions of their primary referent. Complex grammars may be hard to distinguish from simple ones that are mixed; if a certain variety of D is named in the grammar, we must actually be told if this variety is to count as a member of the grammar's object: if so, we are confronted with a complex grammar; if not, with a simple one that is mixed. The role of systems: delimitation vs. characterization A system of an idiolect actually delimits the idiolect. Therefore, if a grammar of (C, S) is exhaustive, then it determines C by specifying S. On the other hand, system σ for a language or variety D may not be sufficient to delimit D, as appears from the following argument. System σ is a set (or a more complex set-theoretical construct) of properties ø of idiolect systems S; each ø in σ is a property shared by the systems of all idiolects that are elements of D. Suppose that D is a variety of a certain historical language D1 and D2 = the set of idiolects C such that C is covered by σ in D1 in the sense of (11.1c); D 2 is the set of idiolects in D1 whose systems share all properties in σ. Now va­ riety D is obviously a subset of D2 but may we also assume that D 2 is a subset of D, i.e. that D = D2? While this is not excluded, it need not be true. There must indeed be a system-based criterion with respect to D l that delimits D (see

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(11.4b) and (11.8)) but this need not be the property of being an idio­ lect C that is covered-by-G in D1 (Sec. 11.3). Whereas a system S of C delimits C, system G for variety D characterizes D but may not actual­ ly delimit it: G specifies, at a certain level of abstraction, properties shared by the systems of all idiolects in D. For actually delimiting D we must specify a property π of idiolects that is an exhaustive systembased criterion with respect to D. We may therefore have an exhaus­ tive grammar of (D, σ) that still doesn't delimit D; this depends on the nature of σ. On the other hand, given the right choice of properties of idiolect systems for inclusion in σ, an exhaustive grammar of (D, G) will indeed delimit D by specifying G. Comparative grammars The term "comparative grammar" is to cover all descriptions written from a comparative point of view; this includes contrastive grammars and historical comparative grammars. (Actually, "grammar" as part of the term may be objectionable, and "comparative theory" may be sug­ gested.) A comparative grammar starts from a set of pairs (D, σ) that each consist of a historical language or language variety D and a system σ for the language or variety. Each pair (D1, σ1) in the set is confronted with at least one other pair (D2, σ2) in the set, in the simplest case as follows: σ1 and σ2 are compared either for properties § (properties of idiolect systems) that occur in both σ1 and σ2 or for properties that, on the contrary, occur only in σ1 or only in σ2. A comparative grammar thus relates pairs (D1, σ1) to pairs (D2, σ 2 ). It is defensible to assume that pairs are related to other pairs only one at a time. We then obtain a set of pairs whose components are themselves pairs (D, σ), e.g. ((D 1 ,σ 1 ), (D 2 ,σ 2 )). The component pairs must differ in their first components: D 1 ≠ D 2 . This set of pairs of pairs may be understood as a two-place relation between pairs (D, σ); and it is this relation that the grammar's object may be identified with. The original set of pairs (D, σ) is now given as the field of the rela­ tion, i.e. as the set of the relation's members. Suppose that (D, σ) belongs to the field of the object of a compara­ tive grammar. (D, σ) may but need not be the object of a language

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grammar: however helpful relevant language grammars may be, com­ parative grammars do not depend on them; two pairs (D 1 ,σ 1 ) and (D 2 , σ2) that are to be 'compared' may be characterized, as far as nec­ essary, in the comparative grammar itself. Typologies The traditional term "grammar" appears defensible in connection with idiolect, language and comparative grammars but should be avoided for typologies. While systems for historical languages or language va­ rieties are involved in setting up linguistic types (see (iii) in (19.10), and (19.9)), the object of a typology is neither a pair (D, a) nor a con­ struct from such pairs. There are obvious consequences for typological description that follow from our account in Sec. 19; these will be briefly indicated below, in Sec. 21.6. Linguistic variables play an essential role in formulating grammat­ ical statements and are especially important in understanding grammat­ ical terminology. For the sake of concreteness I begin by analysing a statement taken from an actual grammar of Modern English. 20.4 A sample grammatical statement Consider the following quotation from Leech and Svartvik (1975:207): (20.3)

Unlike many other languages, English requires an article with singular count nouns as complements [...].

For example, "Mary always wanted to be a scientist", not: "to be scien­ tist". For evaluating (20.3) as a grammatical statement we must first reformulate it in a more precise form. Disregarding "unlike many oth­ er languages", (20.3) may be rendered as (20.4)

For any idiolect system S in English [i.e., Modern Eng­ lish]: for all P, b, f, f1 f2, and f3, if

a. (P,b)  COUNT(--S); b. f is a form of P;

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211

c. f  Sg(-S); d. f1 is a positional variant of f; e. f1 is the head of f2; f. f2 is a complement constituent in f3; then there are P1 b1 f4, and sequences f5 and f6 such that g. (P 1 , b 1 )  ARTICLED, - , S ) ; h. f4 is a form of P 1; i. f2 is a positional variant of f4 + f5 + f + f6 (with "+" for concatenation of sequences). (Remember that COUNT(-, - , S) = the set of all (P, b) such that (P, b) is a COUNT (NOUN) of S; etc.) Less formally, take any English idio­ lect system and any singular form of a count noun paradigm of the system. Assume that the form occurs as the head of a complement constituent in a sentence. Then the complement constituent is obtained as a positional variant of the concatenation of (i) some article-para­ digm form, (ii) possibly, some other unit or units, (iii) the form of the noun paradigm, (iv) possibly, some other unit or units. The following presuppositions were made in reformulating (20.3) as (20.4) (the presuppositions partly derive from the framework of Integrational Linguistics but could in principle be replaced by assump­ tions motivated by other frameworks): (i)

Lexical words are pairs consisting of a paradigm P (possi­ bly, an improper one) and a concept b (possibly, the empty concept b°) that is a meaning of the paradigm.

(ii)

Syntactic units f, in particular, word forms and 'sentenc­ es', are sequences of phonological words, e.g. scientist1 = {(1, scientist)}, a scientist = {(1, a), (2, scientist)}.

(iii)

An occurrence of a syntactic unit in another unit is a 'po­ sitional variant' of the first unit: {(2, scientist)} is a posi­ tional variant of {(1, scientist)} (which is also a positional variant of itself). Variables "f', "f1",... are used for se­ quences and their parts (subsets).

(iv)

Sequences may be concatenated: {(1, a)} + {(1, scientist)}

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= {(l,a), (2,scientist)}; the empty sequence 'does not make a difference' in concatenation. (v)

Articles are lexical words whose meaning is b°.

As an EXAMPLE for (20.4), we have (20.5)

mary wanted to be a scientist,

where (P, b) = {scientistp, -scientist-) (i.e. a certain paradigm/concept pair); f = scientist1 = {(1, scientist)}; f1 = {(6,scientist)}; f2 = {(5,a), (6, scientist)}; f3 = mary wanted to be a scientist; (P 1 ,b 1 ) = (a p ,b o ), where a p is an improper paradigm with three forms (a, á, an) and bo = the empty concept; f4 = a1 = {(1, a)}; f5 = f6 = the empty sequence. In view of subsequent discussion let us take a closer look at the terminology used in (20.4). There is a term in (20.3) that lacks a counterpart in (20.4); this is "require". The term is rendered by logical means: by formulating (20.4) as a universal implication that covers all idiolect systems in English. Disregarding purely logical terms like "for all" or "if ..., then ...", the constants used in (20.4) can be classified as follows: (20.6)

a. Set-theoretical constants  , is a form of, is a positional variant of, +, sequence b. Linguistic constants (i) Variety names English (ii) Names of linguistic variables a. Names of holistic variables is an idiolect system in ß. Names of component variables is a COUNT (NOUN) of, is an ARTICLE of, is a Singular (noun) form of, is a head of, is a complement constituent in

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213

It is not immediately obvious that "is a form of' can be construed as a purely set-theoretical concept; for a demonstration, see Lieb (in press). Similarly, formulation (20.4) is still not explicit enough to bring out the fact that "head" and "complement constituent" denote component variables; as a matter of fact, we can speak of 'head' and 'complement' only with respect to a syntactic unit and its structure in a linguistic system, more specifically, an idiolect system S. The constants "head" and "complement" may therefore be construed as names of functions that take a unit/structure/system triple (f, s, S) (or similar entity) and assign to it the set of pairs (f1 , f2) of constituents of f such that f1 'is a head [complement] of' f2 (for details, see Lieb forthc. a); "complement con­ stituent" is then defined by means of "complement". On this construal, "head" and "complement" denote component variables of the second function type; see (ß1) in (1.12). The classification in (20.6) exemplifies a situation that is charac­ teristic of grammars and, in a modified form, typologies. 20.5 Grammatical terms: non-linguistic constants The terminology of a language grammar may be divided into 'linguis­ tic' and 'non-linguistic' constants roughly as follows: linguistic constants are those whose denotation involves idiolects or their systems, or sets of idiolects, or systems for sets of idiolects, or higher-level settheoretical constructs from such entities; all other constants are nonlinguistic. Linguistic constants may be names of linguistic variables: this ap­ parent terminological clash should be less disturbing when two facts are realized. First, "linguistic" in "linguistic constant" means "belong­ ing to linguistics", whereas "linguistic" in "linguistic variable" would mean "belonging to language" if the term was to be interpreted separa­ tely (it is simply part of an indivisible expression, "linguistic varia­ ble"). Second, "constant" in "linguistic constant" refers to expressions used by the linguist in describing languages whereas "variable", if ana­ lysed separately, would roughly mean "variable entity" and refer to entities in the domain to which linguistic descriptions apply. Among the non-linguistic constants we have, of course, all logical constants in a broad sense where set-theoretical and mathematical con-

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stants are included. The set-theoretical constants in (20.6a) are used to make explicit the formal apparatus that is presupposed in syntactic statement (20.3) (other explications may be considered). Generally, the purely formal aspects of a grammar's object are described by means of logical con­ stants in the broad sense. Rather surprisingly, logical constants are not the only non-linguis­ tic constants that must be allowed in a language grammar, a fact that is not obvious from (20.6a). Suppose that a phoneme is construed as a set of properties of sound events. Define /b/ = {Bilabial, Stop, Voiced}, where Bilabial = the property of being a sound event produced by engaging both lips; etc. In this case, the non-logical constant "/b/" is non-linguistic: it denotes a set of properties of sound events; idiolects, their systems etc. are not involved in this set. Thus, while the term "is a phoneme of' de­ notes a linguistic variable and is a linguistic constant, the term "/b/", which may name a first-place member of the phoneme relation, fails to be a linguistic constant. (It is of course debatable whether entities like phonemes should be construed in a system-independent way; for the sake of the present argument, it is enough that they frequently are.) In the same way, assume that word meanings are taken to be con­ cepts in a psychological sense. A constant denoting a specific concept, say, "-book-" as a name of the concept of being a book, may then be a non-linguistic constant. Again, the term "is a meaning of ... in ... ", as used in "-book- is a meaning of bookp in S1", denotes a linguistic vari­ able, the meaning-of-paradigms relation in idiolect systems, and is a linguistic constant. On the other hand, the constant "-book-" (where raised dots indicate concept status) denotes a first-place member of the meaning relation but is no linguistic constant. (For a conception of word meanings along these lines, see Lieb 1992.) Language grammars aiming at completeness will have to include names of individual phonemes and individual concepts unless no pho­ nemes or concepts are foreseen in the presupposed theory of language. Generally, non-linguistic, non-logical constants are involved in names or descriptions of linguistic units. Such constants may or may not derive from outside the grammar. Indeed, an important role may be assigned to non-linguistic, non-logi-

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215

cal constants that are clearly from outside, say, from psychology, soci­ ology, or neurophysiology; it is such constants that must be available in 'theory integration' as applied to grammars and non-linguistic theo­ ries, an aspect that is elaborated in Lieb (1980a) and (1983: Part G). It may also be argued that reference to speech communities should be allowed within a grammar; and in a complex language grammar, specification of external criteria. This would give rise to additional non-linguistic, non-logical constants in a language grammar. The part played by non-linguistic constants in idiolect grammars and comparative grammars is essentially the same as in language grammars, with one qualification: idiolect grammars, if conceived as suggested above (Sec. 20.3), also have constants to denote individual speakers and utterances. 20.6 Grammatical terms: linguistic constants In (20.3) reference is made to 'many other languages', using the term "language". This part of (20.3) was not reconstructed in (20.4). The terms "language" and "historical language" must, however, be included among the linguistic constants of a language grammar: such a gram­ mar should allow for the statement — seemingly trivial but important from a general point of view — that D is a language (is a historical language, is a variety of a historical language) if D is a component of the grammar's object. These terms are taken over in the grammar from some presupposed theory of language. The linguistic constants that actually occur in (20.6b) function in one of two ways. First, the variety name ("English") together with the name for a holistic variable ("is an idiolect system in") allows to indi­ cate a 'domain' (the set of idiolect systems in English) for the gram­ matical statement. Second, the remaining linguistic constants ("is a COUNT (NOUN) of', etc.) denote component variables that are lin­ guistic variables in this domain (and possibly, in some larger set of idi­ olect systems; cf. "many other languages" in (20.3)). More generally, a simple language grammar will contain names for the two components of the grammar's object, which is a pair (D, σ); in a complex language grammar, there are names for the two components of each pair (D, σ) that is an element of the grammar's ob-

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ject (which is a set of such pairs). We may consider these names to be constants that are specific to the grammar, i.e. are not introduced in any theory that the grammar 'presupposes'. A language grammar may be mixed (Sec. 20.2); in this case, some sets of idiolects — languages or language varieties — that are denoted by constants of the grammar are not components or members of the grammar's object, and the terms that do denote such components or members are supplemented by linguistic constants of the same kind as the terms. In addition to constants for sets of idiolects or their systems, a lan­ guage grammar contains linguistic constants that denote linguistic vari­ ables of one of two types. First, we have a name of a holistic variable, like "is an idiolect system in". Obviously, such constants are not specific to any grammar but are taken from a theory of language that a grammar presupposes. Second, there are names of component variables, which may be either of the relation or the function type. Some of these names denote universal variables, i.e. variables in IDS, the set of all idiolect systems: see "head" and "complement constituent" (or the underlying "com­ plement") in (biiß) of (20.6). Once again, these constants are not spe­ cific to any grammar but are taken from a presupposed theory of lan­ guage. Some constants of the grammar denote component variables but no universal variables', this may be true of the remaining constants listed in (büß) of (20.6a): "is a COUNT (NOUN) of', "is an ARTICLE of', "is a Singular (noun) form of'. It would be easy to jump to the conclu­ sion that such constants cannot be taken from a theory of language, on the grounds that they do not denote universal variables. However, names of non-universal variables must be allowed into a theory of lan­ guage in view of typologies: we may wish to state that for any lan­ guage of a certain type, a certain component variable is vacuous in the set of all S that are idiolect systems in the language; and in doing so, we should be able to denote the variable by a name taken from a pre­ supposed theory of language. Such a name would then be available also for use in language grammars. It is not, of course, excluded that certain names of linguistic varia­ bles that appear in a grammar are introduced 'somewhere in between'

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217

a theory of language and the grammar, or introduced in the grammar itself; as a limiting case we may have a name of a linguistic variable that is defined only in the grammar. It is now defensible to advance the following informal hypothesis for language grammars, be they simple or complex, pure or mixed: (20.7)

Linguistic constant claim. Each linguistic constant in a language grammar belongs to one of the following classes, and each class is represented in the grammar: a. basic terms: constants like "language" and "historical language"; b. names of language-like entities (other than grammars): names of languages or language varieties and names of their systems, in particular, names of the languages or language varieties involved in the grammar's object, and names of their relevant systems; c. names of holistic variables relating, in particular, idio­ lect systems to the grammar's object; d. names of component variables for specifying proper­ ties of idiolect systems that may enter into the systems in the grammar's object.

The linguistic terminology of idiolect grammars is exactly analo­ gous, allowing that an idiolect and one of its systems take the place of a variety and a system for the variety. The linguistic terminology of a comparative grammar is essential­ ly the same as that of a complex language grammar, with the possible addition of a term for the relation that is the grammar's object. The various classes of grammatical terms, both linguistic and nonlinguistic, result from the classification system represented in diagram (20.8) (next page). Names of classifications are chosen so as to indicate relevant criteria. The classes of logical constants are tentative ("nar­ rowly set-theoretical" corresponds to "set-theoretical" in preceding discussion). The non-logical constants can be further classified by cri­ teria such as belonging to a certain discipline other than linguistics.

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21 Grammatical Statements

21.1 Claim on simple grammars Formulation (20.4) explicates part of a statement found in a complex language grammar, a grammar of Modern English that deliberately takes varieties into account. No varieties are mentioned though in ei­ ther (20.3) or (20.4), which allows to take (20.4) as an example of a statement — or explication of a statement — that is typical of simple grammars. It will be argued that (20.4) has a logical form that is char­ acteristic of statements in simple language grammars. Let us use "D", "D 1 " , ... as metalinguistic variables ranging over names or descriptions of sets of idiolects: over expressions such as "English", "American English" etc. Similarly, " ", " ", ... range over names or descriptions of properties ø, in particular, of properties of idiolect systems. We wish to demonstrate that (20.4), the reformula­ tion of (20.3), is logically equivalent to a universal implication of the following form: (21.1)

For all S, if S is an idiolect system in D, then S has .

The first step is straightforward: the "For ... then"-part in (21.1) obvi­ ously corresponds to the initial part of (20.4), "For any idiolect system S in English", with "English" for "D". The second step consists in a demonstration that the rest of (20.4) is logically equivalent to an open sentential formula of the form "S has ", with "S" as its only free variable. The second part of (20.4) is (21.2)

for all P, b, f, f1 f2, and f3, if a. (P,b) COUNT(-, - , S ) ;

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b. f is a form of P; c. f  Sg(-,S); d. f1 is a positional variant of f; e. f1 is the head of f2; f. f2 is a complement constituent in f3; then there are P1, b1, f4, and sequences f5 and f6 such that g. (P1,b1)  ARTICLE ( - , - , S ) ; h. f4 is a form of P1; i. f2 is a positional variant of f4 + f5 + f + f6. (21.2) is an open sentential formula, universally quantified, except for the variable "S". Any open sentential formula whose only free variable is "S" may be understood as a formula attributing a property to entities S, i.e. as being equivalent to a formula of the logical form "S has ". In our example, description of a suitable property ø is obtained from formula (21.2) in two steps: (i) "S" is exchanged for another variable of the same type, say, "S 1 "; (ii) the operator "the property of being an S1 such that:" is prefixed to the new expression. This yields (21.3)

the property of being an S1 such that: for all P, b, f, f1 f2 and f3 [as in (21.2), with "S1" for "S"].

Indeed, (21.2) is logically equivalent to either of the two following formulas: (21.4)

a. S has (21.3). b. S has the property of being an S1 such that: for all P, b, f, f1, f2 and f3 [as in (21.2), with "S1" for "S"].

Statement (20.4) is therefore logically equivalent to (21.5)

For all S, if S is an idiolect system in English, then S has (21.3).

This is a statement of form (21.1): replace "D" in (21.1) by "English", and " " by "(21.3)", or by the property description in (21.3): "the property of being an S1 ...".

GRAMMATICAL STATEMENTS (21)

221

The essential features of this analysis carry over to any typical statement of a simple language grammar. By a typical statement of such a grammar I understand any statement of the grammar that satis­ fies the following conditions: (i) it is a statement on (components of) the grammar's object; (ii) it does not contain 'basic terms' like "lan­ guage"; (iii) it does not — in the case of a mixed grammar — contain names of language-like entities different from the language or variety in the grammar's object. I consider the following claim as defensible: (21.6)

Claim on simple language grammars. All typical state­ ments of simple language grammars are, or can be con­ strued as, universal implications of form (21.1) ["For all S, if S is an idiolect system in D, then S has "] such that, for (D, σ) = the object of the grammar: a. D is a name or description of D; b. the only linguistic constants that occur in (or in the definiens for if is defined) denote component vari­ ables that are linguistic variables in the set of idiolect systems in D; c. the property denoted by is logically implied by σ, i.e. the following is logically true: for all S, if S has every property in σ, then S has the property denoted by .

More informally, all typical statements of a simple language grammar are, or may be understood as, claims to the effect that every idiolect system in the language or language variety has a certain property that (i) is determined linguistically only by means of appropriate compo­ nent variables and (ii) is logically implied by the system for the lan­ guage or variety (i.e. is logically implied by a certain set of properties of idiolect systems). 21.2 Comments Claim (21.6) is exemplified by our sample statement as follows: - D = "English"

EXTENSIONS (V)

222 -

= "the property of being an S1 such that: for all P, b, f, f1 f2 and f3 [as in (21.2), with "S1" for "S"]"

Inspection of (21.2) shows that only the following linguistic constants occur: "is a COUNT (NOUN) of', "is a Singular (noun) form of', "is the head of", "is a complement constituent in", "is an ARTICLE of". All of these denote component variables that are linguistic variables in the set of English idiolect systems, in conformity to (21.6b). More­ over, to the extent that the Leech/Svartvik grammar is a grammar of English rather than of its varieties, we may assume that the property of idiolect systems specified in (21.3) is implied by the set of proper­ ties that constitute a certain system for English; it is unlikely that prop­ erty (21.3) would be included directly in such a system. Condition (c) in (21.6) does cover statements where the property denoted by is an element of σ itself. Informal grammars do not single out statements of this kind, which explains the fact that σ itself — the second component of the grammar's object — may be hard to identify. Even so, statements that involve properties in the system for the language or variety can frequently be recognized by their form. In (21.1), the property name or description may be based on a sentential formula of arbitrary logical form. The formula may, in par­ ticular, be an identity or an equivalence: it is exactly such statements, where the property expression is obtained from an identity or equiva­ lence, that may involve properties contained in the language or variety system. Consider, for example, (21.7) ø* =df the property of being an S1 such that Phon(-, 01) [the set of phonemes of S1] = {/p/, /b/, /t/, ...}. The definition of "ø*" is based on the open identity formula "Phon (-, S1 = {/p/, /b/, /t/, ...}". Applying (21.1), we obtain: (21.8)

For all S, if S is an idiolect system in D, then S has ø*.

This is a schema for claims that identify — rightly or wrongly — the set of phonemes of any S that is an idiolect system in the language or variety denoted by D: identify this set as {/p/, /b/, /t/, ...}. Surely, property ø* is an excellent candidate for inclusion in a system σ for the denotatum of D.

GRAMMATICAL STATEMENTS (21)

223

It should be emphasized that (21.8) is not a definition in disguise. True, (21.8) is equivalent to (21.9)

For all S, if S is an idiolect system in D, then Phon(-, S1) = {/p/,/b/,/t/, ...}.

A sentence of form (21.9) — or an analogous equivalence — is, how­ ever, no definition, not even a conditional one: the expression "Phon (-, S 1 )" is not a constant but a complex term and therefore does not qualify as the definiendum of anything; and the linguistic constant "Phon(eme)", which names a component variable, is not defined but simply used in (21.9). If a grammar containing a sentence of form (21.9) was to be axiomatized, the sentence would come out as an axiom or theorem not a definition. The term "Phoneme" used in (21.9) should derive from a presupposed theory of language, where it may or may not be defined. In view of this example, the following expansion of the Claim on Simple Language Grammars (21.6) suggests itself (21.10) Expansion of Claim (21.6) d. if the property denoted by is an element of a [the system contained in the grammar's object], then is based on (or defined by) an open sentential (i) formula that is an identity or an equivalence; (ii) the only linguistic constants that occur in (or in the definiens for ) are terms taken from a theo­ ry of language that is presupposed in the gram­ mar. I adopt the expansion, at least heuristically. 21.3 Complex grammars: a sample statement The object of a complex language grammar is a set of pairs (D, a), put differently, a relation whose first-place members are languages or lan­ guage varieties and whose second-place members are relevant systems; there is exactly one first-place member D of the relation such that all other first-place members D 1 are varieties of D; this D is the 'primary referent' of the grammar.

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By a typical statement of a complex language grammar I under­ stand any statement of the grammar that satisfies the following condi­ tions: (i) it is a statement on the relation that is the grammar's object or a statement on its members; (ii) it does not contain 'basic terms' like "language"; (iii) it does not — in the case of a mixed grammar — con­ tain names of language-like entities different from the languages or varieties that are members of the grammar's object; (iv) it contains a name of the grammar's primary referent D and a name of at least one D1 such that D 1 is a variety of D and is a first-place member of the grammar's object. As an example, take the following passage from Leech and Svartvik (1975:130): (21.11) Must+infinitive andhave+to-in-infinitive(or, <esp in BrE>, have got to) can express certainty or logical necessity: There must be some mistake. You have to be joking! <esp AmE> The bombing's got to stop sometime. <esp BrE> The relevant part of (21.11) can be restated as (21.12) For all S, if S is an idiolect system in English, then a. if S is an idiolect system in British English, then cer­ tainty or logical necessity is expressed by have got to rather than have to in S; b. if S is an idiolect system in American English, then certainty or logical necessity is expressed by have to rather than have got to in S. This is a sentence of the following logical form: (21.13) For all S, if S is an idiolect system in D, then a. if S is an idiolect system in D1 then S has b. if S is an idiolect system in D2, then S has

; .

To obtain a sentence from (21.13) that is logically equivalent to (21.12), replace "D" by "English", "D1" by "British English", and

GRAMMATICAL STATEMENTS (21)

"D 2 " by "American English"; and replace descriptions obtained as follows:

225

by property

(21.14) a. Let "Ex" be short for "certainty or logical necessity is expressed by ... rather than ... in ...". b. +got =df the property of being a set that contains (have got to, have to) as an element. c. +have =df the property of being a set that contains (have to, have got to) as an element. 3 d. prop (Ex, +got) ["the property determined by Ex and

+got"] =

the property of being an S1 such that the S1 -vari­ ant of Ex has +got = the property of being an S1 such that (have got to, have to) e Ex(-, - , S1) = the property of being an S1 such that certainty or logical necessity is expressed by have got to rather than have to in S1. e. prop3 (Ex, + have) ["the property determined by Ex and +have"] = ... = ... = the property of being an S1 such that certainty or logical necessity is expressed by have to rather than have got to in S1. Replacing " " in (21.13) by "prop 3 (Ex,+got)" and " " by "prop 3 (Ex, +have)", we obtain: (21.15) For all S, if S is an idiolect system in English, then a. if S is an idiolect system in British English, then S has prop3 (Ex, +got); b. if S is an idiolect system in American English, then S has prop3(Ex, +have). This is logically equivalent to (21.12), which shows that (21.12) has the logical form of (21.13). Reformulation of (21.12) as (21.15) brings out an important point: there is a single component variable (the three-place relation Ex) and

226

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there are two properties that S1-variants of the variable may have (+got and +have) such that all idiolect systems in British English have the property (of idiolect systems) that is determined by the variable (Ex) and the first property (+got), and all idiolect systems in Ameri­ can English have the property determined by the variable and the sec­ ond property (+have). This exemplifies a feature that appears to be characteristic of the typical statements of a complex language gram­ mar. The two properties — prop 3 (Ex,+got) and prop 3 (Ex,+have) — are obviously different and actually incompatible, due to the difference between +got and +have. It would be wrong, though, to require that different properties must be attributed to different varieties by a com­ plex-language-grammar statement; quite on the contrary, such a state­ ment may be a claim that two varieties actually agree in their relation to a given linguistic variable. The underlying properties of variants — such as +got and +have, in our example — must therefore be allowed to be identical for different varieties. We are thus led to adopt the following view. 21.4 Claim on complex grammars Schema (21.13) generalizes as: (21.16) For all S, if S is an idiolect system in D, then a r if S is an idiolect system in D1, then S has

an. if S is an idiolect system in Dn , then S has

;

. (n > 0)

The following claim is analogous to Claim (21.6) on simple grammars: (21.17) Claim on complex language grammars. All typical state­ ments of complex language grammars are, or can be con­ strued as, universal implications of form (21.16) (n > 0) such that: a. D is a name or description of the primary referent of the grammar.

GRAMMATICAL STATEMENTS (21)

227

b. Di (i = 1, ..,n) is a name or description of some D1 such that (i) D1 ≠ the set denoted by D; (ii) D1 is a first-place member of the object of the grammar. c. The denotata of Di. and Dj are different (i, j = 1, ..,n; i ≠ j). d. There are M and a,,.., a such that: 1'

'

n

(i)

M is a linguistic variable in the set of all S that are idiolect systems in the set denoted by D; (ii) M is a component variable; (iii) (α) or (ß): α. for some m > 1, M is an m-place relation and (i = l,..,n) denotes prop m (M,α i ) [the property determined by M and property αi]; ß. for some m > 0, M is an m-place function and (i = 1,.., n) denotes proptm(M, αi.). e. For i = 1,.., n and all (D, σ) e the object of the gram­ mar such that D is denoted by Di., the property de­ noted by is logically implied by σ [see (21.6c)]. More informally, all typical statements of a complex language gram­ mar are, or may be understood as, claims to the effect that every idio­ lect system in the language that is also a system in one of several varie­ ties of the language has one of several properties; these properties — not necessarily different — are determined for the varieties on the ba­ sis of a single component variable and are, in this way, of a single type; and each property is logically implied by the relevant variety system. Claim (21.17) is exemplified by our example as follows, see (21.15): -

D n D1 Dn

= "English" = 2 = "British English" = "American English"

228

EXTENSIONS (V)

- M = Ex = certainty or logical necessity is expressed by ... rather than ... in ... - α1 = +got (see (21.14b)) - αn = +have (see (21.14c)) - m = 3 The two properties determined by Ex and +got and Ex and +have ex­ clude each other given a natural interpretation of "Ex". Both proper­ ties may be too specific to be included directly in systems for British English or American English; in this case, they are only implied by such systems. The linguistic variable Ex may also appear to be pretty ad hoc. True, Ex was motivated mainly by the example itself. On closer analy­ sis, expression of certainty or necessity by one linguistic unit rather than another may have much wider application than would be sus­ pected. Still, Ex may not qualify as a linguistic variable to be named in a theory of language. Thus, we should be rather careful in expanding Claim (21.17) in a way analogous to (21.10), the expansion of Claim (21.6) on simple grammars. The claim on simple grammars is, however, directly relevant for complex grammars. This is due to the fact that many statements of complex grammars are of exactly the same kind as typical statements of simple grammars: if D is the primary referent of a complex gram­ mar, then there is an element (D, a) of the grammar's object, an ele­ ment dealt with in exactly the same way as the object of a simple grammar — what is shared by all English idiolect systems is not stated for British English and American English separately. Claim (21.17) differs from the claim on simple grammars by in­ troducing only a single component variable in connection with the property names . If several variables M1 ..,M. must be admitted, then Claim (21.17) covers only typical statements that are 'elemen­ tary'. A similar proviso may have to apply in connection with compar­ ative grammars, which turn out to be closely related to complex lan­ guage grammars.

GRAMMATICAL STATEMENTS (21)

229

21.5 Comparative grammars The object of a comparative grammar is a relation between pairs (D, σ). In the simplest case, a pair (D 1 ,σ 1 ) is compared with a pair (D2, σ2) for properties of idiolect systems that occur either in both a1 and σ2, or only in σ1 or only in σ2. More generally, such properties may be implied by, rather than occur in, one of the two systems. Also (D1, σ1) may be compared with more than one other pair. A typical statement of a comparative grammar may be obtained from (21.12) by dropping "if S is an idiolect system in English, then"; this yields: (21.18) For all S, a. if S is an idiolect system in British English, then cer­ tainty or logical necessity is expressed by have got to rather than have to in S; b. if S is an idiolect system in American English, then certainty or logical necessity is expressed by have to rather than have got to in S. Differently from (21.12), the new statement 'compares' British Eng­ lish and American English irrespective of the fact that both are varie­ ties of English. Treating languages or language varieties independently of any D to which they may jointly belong as varieties, is a character­ istic feature of comparative grammars. In dealing with language-inter­ nal variation we have a choice between complex language grammars and comparative grammars, and will as a rule favour the former; in a case of interlanguage variation, only comparative grammars are avail­ able (unless we allow 'grammars' for sets that are obtained by uniting different historical languages, or varieties of such — see (20.1a)). Typical statements of comparative grammars may be characterized by adapting the account previously given for complex language gram­ mars. The following logical form is defensible for such statements:

230

EXTENSIONS (V)

(21.19) For all S, a1. if S is an idiolect system in D1, then S has

a . if S is an idiolect system in Dn, then S has

;

. (n > 1)

This schema is obtained from the schema for complex grammars (21.16) by dropping "if S is an idiolect system in D, then": the denota­ ta of D 1 ..,D1 are considered independently of any D of which they may be varieties. Moreover, the denotata of different IX must not be varieties of each other since they are not allowed to be subsets of one another. The notion of typical comparative statement can be made precise so as to correspond to analogous concepts previously introduced. The following claim is related to the Claim on Complex Language Gram­ mars (remember that the object of a comparative grammar is a rela­ tion whose members are pairs (D, a)): (21.20) Claim on comparative grammars. Any typical statement of a comparative grammar is, or can be construed as, a universally quantified n-place conjunction (n > 1) of im­ plications of form (21.19) such that: a. D.1 is a name or description of some D such that for some a, (D, a) is a first-place member of the object of the grammar. b. Di (i = 2, ..,n) is a name or description of some D such that for some a, (D, a) is a second-place member of the object of the grammar. c. The denotata of D. and D. are different (i,j = 1, ..,n; d. There are M and α1 ..,αn such that: (i) M is a linguistic variable in the set of all S that are idiolect systems in the set denoted by IX (i = l,..,n); (ii) M is a component variable;

GRAMMATICAL STATEMENTS (21)

231

(iii) (α) or (ß): α. for some m > 1, M is an m-place relation and (i = l,..,n) denotes prop m (M,α i ) [the property determined by M and propertyαi.]; ß. for some m > 0, M is an m-place function and (i = 1,.., n) denotes proptm(M, αi). e. For i = l , . . , n and all members (D,σ) of the gram­ mar's object such that D is denoted by Di, the property denoted by is logically implied by σ. More informally, a typical statement of a comparative grammar is, or can be construed as, a claim to the effect that the idiolect systems in the language or variety from which we start share a certain property, and the idiolect systems in any given language or variety used in the com­ parison also share a certain property, which may or may not be differ­ ent from the first; all these properties are determined for the varieties on the basis of a single component variable and are, in this way, of a single type; and each property is logically implied by the relevant lan­ guage system or variety system. Claim (21.20) is exemplified by (21.18), presupposing the analysis of (21.12) in Sec. 21.4: -

n D1 Dn M

= = = =

2 "British English" "American English" Ex = certainty or logical necessity is expressed by ... rather than ... in ... - α1 = +got (see (21.14b)) - αn = +have (see (21.14c)) - m = 3 The comments made in Sec. 21.4 on Claim (21.17) by and large also apply to (21.20).

232

EXTENSIONS (V)

21.6 Grammars, typologies, and linguistic variables The account of grammars given in Secs 20 and 21 is not yet a theory; rather, we have formulated prolegomena to a theory of grammars. Our account does impose conditions on any theory of grammars that accepts the prolegomena. In particular, the relation between individual grammars and a theory of language must be clarified in a theory of grammars: precisely what does it mean to say that a grammar 'presup­ poses' a theory of language? to what extent, and under what condi­ tions, may we assume that names of linguistic variables are taken di­ rectly from a presupposed theory of language so as to serve the de­ scriptive needs of a grammar? how are non-linguistic theories that provide grammatical terminology — such as a set theory or a psycho­ logical theory — related to the grammar itself? how can the distinction of statement vs. definition be made more precise for grammars? — these are some of the more important questions that a theory of gram­ mars is called upon to answer. Providing the answers is a formidable task. One way of tackling it leads to the Integrational Theory of Grammars (esp. Lieb forthc. d): grammars formulated as axiomatic theories are taken to be an ideal reference point for simple language grammars of any form; other types of grammars can also be approached from this angle. There is a second set of problems that may be fruitfully addressed by a theory of grammars that takes the present prolegomena as a start­ ing-point: problems concerning the specific consequences that may be drawn for actual grammar formats, given external factors such as audience or general purpose. Problems of this kind are beyond the scope of the present essay except for a few general considerations that also bring in typologies. An important result of the present essay should be the truly funda­ mental role of linguistic variables that emerges from our discussion, both for grammars of any type and for typologies: it seems not only possible but necessary, for practical as well as theoretical purposes, to construct both grammars and typologies in terms of linguistic varia­ bles. It is frequently suggested that such variables must be 'semantic', or 'functional' in some sense, at least in the case of typologies. Our analy-

GRAMMATICAL STATEMENTS (21)

233

sis does not lend support to this view, which may well be due to lack of an adequate notion of linguistic variable. Variables used in grammar writing or typologies may but need not be universal. If they are, a presupposed theory of language should pro­ vide names for them; these may then be used in both grammars and ty­ pologies. However, even non-universal variables may be denoted by constants of a theory of language. As mentioned before, this is impor­ tant for typologies; they may have to include statements to the effect that for any language variety of a specific type, certain variables are vacuous in the set of all S that are idiolect systems in the variety. There is, however, an important difference between the role of linguistic variables in grammars on the one hand, and in typologies on the other. Variables selected for a grammar must be such that the sys­ tems involved in the grammar's object can be described as systems — put differently, the grammar must still be a grammar even when for­ mulated on the basis of linguistic variables. A typology, on the other hand, may choose its linguistic variables much more freely; it may well be that fruitful typologies — fruitful for practical or theoretical purposes — may be based on linguistic variables that are peripheral to grammars. It would be a major mistake, then, naively to start from ty­ pologies in selecting linguistic variables for grammars. Typologies do not have to account for entire language systems or variety systems; lin­ guistic variables that have proven themselves for typological criteria may constitute a haphazard list when it comes to choosing variables ad­ equate for grammars. I certainly do not wish to deny that there are re­ lations between the two concerns, writing grammars based on linguis­ tic variables and formulating typologies on such a base; some variables may turn up in either case. But this cannot be taken for granted for in­ dividual variables. Typologists and grammarians should closely coop­ erate but not confuse their tasks.

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Weydt, Harald; and Brigitte Schlieben-Lange. 1981. "Wie realistisch sind Variationsgrammatiken?" In: Schlieben-Lange (ed). 1981. 117145. Wiesinger, Peter. 1983. "Die Einteilung der deutschen Dialekte". In: Besch et al. (eds). 1982/1983. 807-900. —. 1987. Bibliographie zur Grammatik der deutschen Dialekte: Laut-, Formen-, Wortbildungs- und Satzlehre 1981 bis 1985 und Nachträge aus früheren Jahren. Bern etc.: Lang. —; Raffin, Elisabeth; and Gertrude Voigt (coll.). 1982. Bibliographie zur Grammatik der deutschen Dialekte: Laut-, Formen-, Wortbildungs- und Satzlehre 1800 bis 1980. Bern etc.: Lang. (Europäische Hochschulschriften, 1. Reihe 509). Wildgen, Wolfgang. 1974. "Versuch einer sprachtheoretischen Fundie­ rung des Variationsbegriffs". Zeitschrift für Dialektologie und Linguistik 41. 129-144. —. 1977. Differentielle Linguistik. Entwurf eines Modells zur Beschreibung und Messung semantischer und pragmatischer Variation. Tübingen: Niemeyer. (Linguistische Arbeiten 42). Wille, Rudolf (ed). 1989. Klassifikation und Ordnung. Tagungsband 12. Jahrestagung der Gesellschaft für Klassifikation, Darmstadt, 17.-19. März 1988. Frankfurt/M.: Indeks Verlag. (Studien zur Klas­ sifikation 19). Wimmer, Rainer (ed). 1987. Sprachtheorie. Jahrbuch 1986 des Instituts für deutsche Sprache. Düsseldorf: Schwann. (Sprache der Ge­ genwart LXXI). Wolf, Herbert. 1984. "Die Periodisierung der deutschen Sprachge­ schichte". In: Besch et al. (eds). 1984/1985. 815-823.

Index of Names

A Ágel 239 Albrecht 235, 237 Altmann 175,235 Ammon vi, 17, 21, 58, 65, 235-238, 240, 242f Andersen 28, 235 Anderson 28,235 B Bailey 18,236 Ballmer 60, 236 Baur 93, 236 Bernstein 67f, 236 Berruto 12,236 Besch vi, 17, 21, 39, 63, 65, 236, 238f, 242-244 Bierwisch 16f, 53, 236 Bock 61,236 Borsley vii, 236 Brandi 148,237 Bynon 243 C Carnap 82,237 Carr 52, 57, 237 Cheshire 3, 69, 162, 237 Chomsky v, 16f, 19, 52, 57, 135, 147f, 150-153, 155, 172, 182, 237 Cordin 148,237 Coseriu v, 20, 47, 68, 235, 237, 243

D Dittmar v, 20, 235, 237 Domaschnev 68, 237 E Edwards 68,237 E Fisiak 237, 241, 243 Flydal 47, 68, 238 Francis 17,238 Fried 238, 243 G García 172, 175, 238 Goebl 61, 238 Goossens 93,238 Graustein 238,241 Gregory 68,238 Grotjahn 175,235 H Habel 17f, 47, 53, 56, 155, 157, 162f, 166, 238, 240 Haie 238, 240 Harris vii, 236, 239 Heger 4, 20, 33, 67, 239 Henn 67,239 Hessky 239 Holm vi, 239 Horecky 243 Hronek 243 Hudson 45,57,239

246

INDEX OF NAMES

Hyams 147f, 239 J Jacobs 21,29,239,241 Jaeggli 147f, 237, 239f Jones 28,235 Jongen 67,239 Juilland 77, 81f, 240 K Kanngießer 17,49,238,240 Kasher 236, 240 Katz 52, 240 Kenstowicz 147, 240 King 17,240 Klann-Delius 69, 240 Klein v, 17, 160, 162, 240 Knoop 236 Koerner 28, 235 Krauss vi, 240 Krzeszowski 4, 18, 240 Kubczak 67, 129, 240 Kutschera 60, 82, 240 L Labov v, 3, 54f, 136, 162, 172, 241 Leitner 238,241 Lieb vi, vii, 20f, 33, 52-54, 56, 58, 60, 64, 77, 81f, 103, 136, 188, 204, 207, 213-215, 232, 240f Lightfoot 17,242 Lilius 242 Love 236 Lüdtke 235 Ludwig 68,242 M Mattheier 235 Mayerthaler 17,242 O Oksaar 51,242

P Petyt 17,242 Pieper 242f Pinkal 60,236 Poplack 18, 54f,242f Postal 52,240 Putschke 67,93,236,242

R Raffin 244 Reichmann 236 Romaine 162, 172, 242 S Saari 242 Safir 147f, 237, 239f Salomaa 17,242 Sankoff 18, 54f, 172, 242 Saussure 37, 58 Schlieben-Lange 55,243f Schlobinski v, 20, 237 Seiler 4, 19f, 135, 154f, 243 Sgall 17,243 Shibatani 243 Sonderegger 236 Spillner 17,68,243 Stamenov 241,243 Stechow 239 Sternefeld 239 Stickel 242f Suppes 17,243 T Thelander 54,243 Thun 235 V Vachek 17,243 Veith 17,243 Vennemann 184,239,243 Voigt 244

INDEX OF NAMES W Wald 26,243 Westwood 242 Weydt 55, 244 Wheeler 242

Wiesinger 27, 65f,71,244 Wildgen 33,244 Wille 236, 244 Wimmer 241, 244 Wolf 64, 244

247

Index of Subjects and Terms

The entries in this index either refer to subject matter or they are listed as terms; entries that are primarily terminological may also refer to subject matter on individual pages. Entries are either theoretical, i.e. relate to terms, assumptions, theorems or conventions of the theory of language or the theory of grammars that are partly deve­ loped in this book; or they are extra-theoretical, i.e. taken from other contexts in lin­ guistics (and are sometimes marked by inverted commas). Italicized page numbers in­ dicate key passages for a given entry; an additional asterisk identifies a page with a definition or other key occurrence of a term, or the place where an assumption, theo­ rem, claim, or convention is actually found. If there are several occurrences of an as­ terisk for a single term entry, the term may be understood in more than one sense. Page numbers for non-essential occurrences may not be exhaustive. In entries that begin with a variable ("F-set"), the variable is disregarded for alphabetical listing ("Fset" under "S"). — The index conflates, for practical purposes, several indexes that might have been kept apart from a systematic point of view.

A ableitungsbewertende Grammatik 17f Above-Neutral D 68 Above-Neutral German 181 abstract 39f, 103 abstracted from 39* acceptable in 95*, 102 Alemannic 66, 71 Allophone 4,(5,9-12 allophone1 6*, 1Of, 142, 144 allophone2 7*, lOf, 140-142, 145 the Allophone relation: see Allophone ambiguous constant 44* American English 208, 224-226, 228f approaches to linguistic variation 14* appropriate for 168* Arabic numerals 90 architecture de langue 47 architecture of a historical language 47

argument of a function 5 n-ary class 69, 86* n-ary classification 69, 85* n-ary element 85* n-ary variety 69 Assumption 1 of theory of varieties 90*, 92 Assumption 2 of theory of varieties 111* Assumption 3 of theory of varieties 111* Assumption 4 of theory of varieties 115* Assumption 5 of theory of varieties 115* Assumption I of component approach 160* Assumption II of component approach 167*

INDEX OF SUBJECTS AND TERMS Assumption III of component ap­ proach 167* Assumption IV of component ap­ proach 167* assumption on periods and non-tempo­ ral varieties 70 asymmetric 118 axiom 223 B basic dialect 64-68, 70 basic-dialect area 96-98,100 basic dialect division 64-67, 70, 73, 96 basic gender variety division 69 basic interregional dialect 93 basic interregional variety 68 basic medium division 69 basic register 67,68,70 basic register division 68 basic sex variety division 69 basic sociolect 67, 68, 70 basic sociolect division 67 basic terms 217*, 218, 221, 224 basis 47 basis of a division 78* Bavarian 46, 66, 71, 123, 129f Below-Neutral D 68 Below-Neutral German 181 British English 208,224-226, 228f C Central German 66 chain 40*, 103f change 35 characterization by systems 208f Chomskyan Generative Grammar 16, 172 Claim on comparative grammars 230* Claim on complex language grammars 226* Claim on simple language grammars 221*, 228

249

claim on variation studies 15* R-class 191,193* class in 78* classical dialectology 33, 67, 93f classification approach to typology 188 classification criteria 49, 59 classification on 47, 79* classification on M by A 81* classification system 47, 82*, 201 classification system on a language 59 classifications on the set of linguistic variables 8* Class-Neutral D 67 closed interval 159 cluster analysis 61 code 67 code-switching 54f coexistent systems 54 Colloquial 68 communication complex 54*, 99f, 116, 184, 187f, 202 comparative grammar 204*, 206, 209f, 215,217, 229,230 comparative theory 209 complement 213 complement constituent 211,213 complete grammar 205*, 206 complex language grammar 204*, 206, 207f, 215, 217, 223, 226, 228-230 complex term 223 component approach to linguistic vari­ ation 13*, 14, 18f, 22, 104, 131, 135, 177, 184 component of idiolect systems S 127* component of L 9, 11, 127 component variable 8, 10*, 12, 19, 137, 151, 154, 165, 170, 174, 177, 181, 187, 215, 221, 225, 231 concatenation of sequences 211 concatenation product 167 concepts as word meanings 211,214 connotation analysis 17 "constant" 213

250

INDEX OF SUBJECTS AND TERMS

(is) constant 139*, 141*, 145 constant in the logical sense 7 constants of a theory of language 233 constants specific to a grammar 216 contrastive analysis 187f contrastive generative grammars 18 contrastive grammar 26, 28, 209 contrastive linguistics v, 24, 26, 28, 187 Convention for component approach 143* Convention for theory of varieties 90* core 147 correlation between criteria 49 Correlation Theory 112* covary 153 covered by 102* creoles vi, vii, 34, 55 criteria-determining function 97,101f criteria for dialects 66f criteria for varieties 59 criterion in the logical sense: see crite­ rion of a division criterion of a division 82*, 96 cross-classifications on 47, 63, 67, 79* cross-divisions on 79* cross-partitions on 79* cross-section 35 D definition 223,232 degree of abstraction 40,102 degrees in classification 60, 201 delimitation by systems 208f denotatum 167 descriptive aspect 203 descriptive format 21 develop into 41 diachronic 68 diachronic syntax 28 diagrams as names of division systems 83*, 87

Dialect 12, 45f, 64, 72, 93, 95 dialect area 94f dialect division of D1 70f dialect division of D2 71 dialect division of dialect1 73 dialect division of dialect11 73 dialect division of period1 73 dialect geography 93 dialect nucleus 65 dialect of a language period 71 the Dialect relation: see Dialect dialect transition 65 dialectology v, 17, 21, 24, 26-28, 33, 64, 66f, 93f diaphasic 68 diastratic 68 diatopic 68 division of 78* division of M by A 81* division system 82* E Early Modern German 63,122, 181 Early Modern High German 71 elementary evaluation grammar 162* elementary statements 228 empty category 149 empty concept 211 empty sequence 212 endpoint 85*, 92 English 189, 210-212, 222, 224f, 228f English School 68 equivalence (formula) 222f evaluated language 159 evaluated rule 157 evaluation basis 160,163 evaluation basis for CON 173* Evaluation Grammar 7, 17-19, 53, 130, 157-171 evaluation grammars 5, 18, 135f, 157171 evaluation of p 158

INDEX OF SUBJECTS AND TERMS evaluation of s 158 exhaustive grammar 205*, 206, 209 exhaustive system-based criterion 106*, 183, 209 exhaustive system-based point of view 106*, 183 exhaustive system-based set 106*, 111, 183 existence 59 existence of the variety structure 59, 201 existence of typological structures 201 Expansion of claim on simple language grammars 223*, 228 explication problem for component ap­ proach 135*, 175 external criteria for dialects 67, 94, 96, 103 external criterion 48f, 54, 61, 64, 94, 96,100*, 103, 111, 187,201,215 'external languages' 52 external point of view 97, 98*, 105, 187 external set 99*, 187 external structure of a historical lan­ guage 47 F feature values 198 features 188, 198 fifth-level variety 72 first-level class 63 first-level classification 63, 69 first-level variety 63 (is a) form of 213 form system grammar 206* formulated in terms of 136 fourth-level dialect 72 free-order 38*, 108 free-order property 38* frequency of use 175 Frühneuhochdeutsch 71, 122 function in the set-theoretical sense 5

251

M-function is a linguistic variable in T 143* M-function is constant in M1 141* M-function is general in M1 142* M-function is local in M1 142* M-function is vacuous in M1. 142* function variant 141* M-function varies in M1 141* functional style 68 'functional' variable 232 G (is) general 139*, 142*, 145 generalized variable rule approach 172, 175 Generative Grammar 16-18, 21, 53, 136, 148 German 27, 33, 36f, 39, 41f, 53, 63, 65f, 70, 91, 108-110, 121, 123, 129f 'grammars' 204-206 grammars 53, 136, 184, 203-205, 206*, 207-233 grammar approach to linguistic varia­ tion 75*, 16f, 21f, 184 grammar-independent variables 173175 grammar variable 8, 166, 170f grammar-writing 233 grammars for code-switching 18, 55 grammatical statement: see typical statement, and: claims on grammars grammatical terms 213-217,218*, 232 groups of varieties 66 H head 213 heuristic 223 heuristic aspect 203 High German 33, 63, 66, 70f historical comparative grammar 209 historical language 33*, 34, 37, 40, 42, 45-47, 53, 57f, 63f, 73, 90-92,

252

INDEX OF SUBJECTS AND TERMS

96, 111, 115-117, 121, 123, 125, 127, 129, 131, 189, 192, 201, 204f, 207, 209, 275 historical linguistics v, 17, 21, 24, 26, 28, 42, 64, 207 historical period 33*, 35, 37, 40, 42, 45, 46, 47, 64, 68, 69f, 189, 207 historical period division 63, 73 holistic approach to linguistic variation 13*, 14, 19f, 22, 131, 184,201 holistic variable 8, 72*, 187 'homogeneous' 54f homogeneous 56* homogeneous set of non-language en­ tities 97 Mn-of-x-hyphen 747* I 'ideal speaker' 53 identity (formula) 222f idiolect 34, 51-60, 64, 69, 123, 191, 207 idiolect grammar 204*, 206,207, 215, 277 idiolect in a language 34 idiolect system 36*, 52, 57f, 193 idiolect system in 725*, 188 IDS 143* immediate dialect of D1 70 implicational scale analysis v, 20 improper paradigm 211f informant in 98* integration of component approach 183* integration problem for component ap­ proach 755*, 175 Integrational Linguistics vii, 7, 20f, 136,204,211 Integrational Theory of Grammars 232 interlanguage variation vii, 184, 187, 229 interlanguages 188 intermediate entities 53f

'internal languages' 52, 147, 152 interpretation of proper rules 168 interpretation of proper sentences 168 interpretation of rules 166-168 interregional variety 65f irreflexive 118 Italian 149 L 'language' 117 language 33*, 45, 99, 191, 275 language acquisition vii, 26, 34, 147, 187,188 language approach to linguistic varia­ tion 75*, 16f, 19, 21f language development 41f language grammar 204*, 206, 207f, 210,214-216,277 language use 69 language variable 8,166 language type 188, 190, 191, 194, 198 language typology v, vii, 22, 24, 26, 28, 147, 184, 188f, 200-202 language-internal variation vii, 229 language-like entity 4*, 165, 188, 201, 221, 224 langue 59 n-th level class 69,86* n-th level classification 69, 85* n-th level cross-classifications on 86* n-th level cross-divisions on 86* n-th level cross-partitions on 86* n-th level element 85* n-th level subclassification on 86* n-th level subdivision of 86* n-th level subpartition of 86* n-th level variety 69 lexical criterion 67 lexical word 211 lexicology 130 "linguistic" 213 linguistic communication 52

INDEX OF SUBJECTS AND TERMS linguistic constant 212, 273*, 214, 275,216,275 Linguistic constant claim 217* linguistic descriptions 184 linguistic type 190, 795*, 198-200, 205 linguistic variable 5*, 95, 111, 136, 151, 154, 165, 170, 7 77, 184, 187, 189, 190, 193, 198, 204, 210, 214-217, 228, 232, 233 linguistic variable in 136, 138, 743*, 144f, 170, 174 (is) local 739*, 742*, 145 location of C in D 727* location of C in D1 and D 723* location of S in D 725* location of S in D1 and D 126* logical concepts 77 logical constant in a broad sense 273*, 218 logically implied by 227* Low German 33, 63, 66, 122 Lower Class D 67 Lower Class German 67 Lower Saxonian 66 lowest system 103 M mathematical constants 213,275 means of communication 34, 35*, 51, 69, 99, 188 means of communication for S 725* measurement by variable rules 175 Medieval Bavarian 46 Medieval German 46, 63, 91 metalinguistic 166 metalinguistic variables 279* methodology 21, 50, 58, 60-62, 96 Middle Class D 67 Middle High German 63,71 Middle Low German 63 Mitteldeutsch 66 mixed grammar 205*, 206, 208, 216,

253

221, 224 Modern British English 208 Modern English 195, 208, 210 Modern French 195 Modern German 41f, 63, 122 Modern High German 71, 195 Modern Standard German 66, 102 morphological criterion 67 morphological grammar 205*, 206 morphological variable 77* morphology 67 morphosemantic grammar 206* morphosyntactic grammar 207 N names of component variables 215, 27(5, 217*, 218 names of concepts 214 names of holistic variables 215, 216, 217*,218 names of language-like entities 217*, 218, 221, 224 names of linguistic variables 212f, 218 names of non-universal variables 216 names of phonemes 214 narrowly logical constants 218 narrowly set-theoretical constants 217f Neuhochdeutsch 71 neurophysiology 215 Neutral D 68 Neutral German 181 Niederdeutsch 122 noematic linguistics 20 non-basic dialect 64, 67 non-basic register 68 non-exhaustive grammar 205*, 206, 208 non-exhaustive system-based point of view 105 non-grammar variable 8 non-language entities 49, 97, 103, 105 non-linguistic constant 273*, 214f, 275

254

INDEX OF SUBJECTS AND TERMS

non-linguistic theories 215, 232 non-logical constants 214f, 217f non-temporal immediate varieties of D1 70 non-temporal variety 46, 72, 122 non-universal variable 216, 233 Noun Group 136-138, 144 nuclear dialect 65 null subject parameter 147f numerical taxonomy 60 O Oberdeutsch 66, 71 object of a grammar 204f obligatory pronoun-subject sentence 749 Old German 33, 41f, 63 Old High German 33,71 Old Low German 33 optional pronoun-subject sentence 149 other variable 8, 12,95 P paradigm 211 'parameter' v, vi, 16, 19, 147, 152 parameter in T 150*, 151f parameter set 153 'parameter value' 19; see also: value Parent Language 12 parole 59 M1-part of O 86* partial grammar 205*, 206f partition of 79* partition of M by A 81* partition system 82* partly specified in terms of 179, 757*, 182, 187 period: see historical period Period 64*, 72 period division of D1. 69f, 71 period division of D2 71 period division of dialect1 73 period division of dialect11 73

period division of period1 73 period of a basic dialect 71 the Period relation: see Period periphery 147 permissible type of non-language enti­ ties 97,187 permissible type of systems 103*, 104,183*, 187 person 97 personal variety 53-55, 69, 70, 123, 207 personal variety division 69, 70, 73 personal variety division of D1 70 personal variety division of period1 73 phoneme 141, 214 Phoneme 189, 191, 195, 214, 223 the Phoneme relation: see Phoneme phonetic criterion 67 phonetic grammar 206* phonetic variable 77*, 22 phonetics 67 phonological critierion 67 phonological grammar 205*, 206 phonological variable 11*, 22 phonological word 211 phonology 67 pidgins vi, vii, 34 place assignment 89* place of x in O 89*, 90 polylectal grammars 18 position of c in D 727* position of c in D1 and D 727* positional variant 277 potential dialect informant 94*, 95, 97 pragmatic variable 77* Prague School 17,68 precedence between cross-sections 35 precedence between stages 35, 41 precedence between states 41* presuppose 204, 214-216, 223, 232 primary class 63 primary classification 63 primary dialect 71

INDEX OF SUBJECTS AND TERMS primary referent 207*, 208, 223f, 228 primary variety 63f 'principle' 147, 152 principle 150*,151f Principles and Parameters 19, 135, 147 probability in G of p 159 probability of use 159 pro-drop parameter 147f pronoun-subject sentence 149 proper language 158 proper part 158 proper rule 157 proper sentence 158 properties of variants 184,190,198 property determined by [function] M and α 178* property determined by [relation] M and α 178* prototype 60, 201 psycholinguistics v, 24, 26 psychological reality 53 psychology 215, 232 pure grammar 205*, 206 purely + criterion 107* purely + point of view 107* purely + set 107* purely logical terms 212 purely morphological criterion 106, 707* purely morphological point of view 107* purely morphological set 107* purely phonetic criterion 106,107* purely phonetic point of view 107* purely phonetic set 107* purely phonological criterion 106, 107* purely phonological point of view 107* purely phonological set 107* purely qualitative (evaluation grammar) 162*

255

purely quantitative (evaluation gram­ mar) 162* purely semantic criterion 106,107* purely semantic point of view 107* purely semantic set 107* purely syntactic criterion 106,107* purely syntactic point of view 107* purely syntactic set 107* Q qualitative at i (evaluation grammar) 162* qualitative at i given δ 174* qualitative variable in T [I"] 171* qualitative variable in T [CON] 174* quantitative at i (evaluation grammar) 162* quantitative at i given δ 173* quantitative variable in T [Γ] 171* quantitative variable in T [CON] 174*, 175 quasi-idiolect 188 quasi-linguistic communication com­ plex 34f R regional dialect 64f, 67, 69, 93 regional variety 66 register 54, 56, 68 relation associated with a permissible type 9T relation in the set-theoretical sense 6 M-relation is a linguistic variable in T 143* M-relation is constant in M1 139* M-relation is general in M1 139* M-relation is local in M1 139* M-relation is vacuous in M1 139* relation of belonging 97 M-relation varies in M1 139* relevant system of 35* representation 154 representation in S 154

256

INDEX OF SUBJECTS AND TERMS

representation of Possession 154 require 212 Roman numerals 143 Romance 149 rule evaluation 158, 160, 165 rule interpretation 166-168 Γ-rule status 161* rule-weight 18 rule-weight 1 165*, 166, 169, 171f, 174 rule-weight, 169*, 170-172, 174 S secondary classification 69 second-level dialect 70 section 35* semantic 4 semantic grammar 205*, 206 semantic variable 11*, 155, 232 sentence 34, 58 sentence evaluation 158,160,165 sentence- weight1 165 sequence 211 α-set 81* F-set 191, 192* Σ-set 180* set-theoretical concepts 77 set-theoretical constants 212f, 214, 217 set-theoretical entities 192 set-theoretical variation concepts 187 set theory 232 similarities 60,201 similarity-based property 60f similiarity relation 60 simple language grammar 204*, 206, 208,215,219,227,225,228 social aspects 52 social class 67, 97 social dialect 67 Sociolect 12,67 sociolinguistics v, 21, 24, 26 sociology 215

sound system grammar 206* source 47,85* Southern Bavarian 46, 71f Spanish 149 speaker 64,97,207,215 'speaker-specific' 52f specific to D1 in E and D (of compo­ nents) 729*, 130 specific to D1 in E and D (of proper­ ties) 131*, 182 specific to in the logical sense: see spe­ cific to M1 in N specific to M1 in N 80*, 130f specifically D1 in E and D (of compo­ nents) 129 , 130 specifically D1 in E and D (of proper­ ties) 131* speech 59 speech community 35, 49, 215 Spoken D 69 Sprachepoche 64 stage 35, 187 Stammesdialekt 66 standard clause 36* standard clause property 36* standard language 65 standard variety 64-66 state 37,47*, 187 statement vs. definition 232 stronger component approach 14*, 19 stronger holistic approach 14* stronger variety approach 14* structural dialectology 67 Structuralism 17, 67 style 55f, 68 style-shifting 54f stylistic s 68 subclassification 47, 86* subdivision 86* subgrammar sequence 158, 160, 163, 165 subpartition 86* subsystem of a system for 37

INDEX OF SUBJECTS AND TERMS syntactic criterion 67 syntactic grammar 205*, 206 syntactic unit 211 syntactic variable 77*, 22 syntactic variation studies 23-29 syntactic-semantic grammar 206* syntax vi, vii, 7, 22-29, 67, 135, 172 syntax in dialectology 27f system-based criteria for dialects 67, 96 system-based criterion 48f, 64, 96, 106*, 111, 183, 187,201,208 system-based point of view 705*, 183, 187 system-based set 105*, 183, 187 system class 36*, 103f system for 36, 37*, 39, 166, 180, 187, 192, 208, 221 system of 34, 35, 166, 180, 192, 208 system variable 8, 166, 170f T t-criterion 191,193* t-criterion relative to F 193* temporal immediate varieties of D1. 70 temporal variety 46, 207 terminal element 85* tertiary classification 71 tertium comparationis 4 theorem 223 theorem on division systems 87* theory integration 215 theory of grammars 204,232 theory of language 22, 92, 136, 184, 201f, 204f, 214-217, 223, 228, 232 theory of language change 41 theory of linguistics 22, 184 theory of speech 55 third-level dialect 71 third-level classification 71 third level variety 71 time 97

257

time relation 64 total grammar 163 transitional dialect 65 transitive 118 tribal dialect 66 Type: see type in R-type 194*, 198-200 type and typological structure: defini­ tions 202 type in 194*, 198-200,201 types of entities in typology 191f types of 'grammars' 204-205, 206*, 207 types of grammatical terms 277,218* types of language-like entities 5 types of linguistic variables 8, 187 typical statement of a comparative grammar 229, 230*, 231 typical statement of a complex lan­ guage grammar 224*, 226, 227 typical statement of a simple language grammar 227*, 228 typological criterion 191, 193*, 197f, 201f, 233 typological criterion relative to F 193* typological structure 188-191, 194*, 197f, 200-202, 205 typology: see language typology (a) typology 205*, 206, 210, 216, 232f typology base 189, 191, 792*, 197, 200f, 205 U überregionale Varietäten 65 Umgangssprache 68 uniqueness 59 uniqueness of the variety structure 61, 62, 201 uniqueness of typological structures 201 unit sequence 166 UNITYP 20, 135, 154f

258

INDEX OF SUBJECTS AND TERMS

universal grammar 205 universal variable 752*, 181, 191, 196, 216, 233 Upper Class D 67 Upper German 66, 71 user community 35 utterance 58, 64, 97, 207, 215 V (is) vacuous 139*, 142*, 145, 216, 233 vagueness 59f, 66 value of a function 9 value of a parameter 150*, 151f value of a variable 7 "variable" 213 + variable 77* variable entity 213 variable followed by an asterisk 44* variable in: see linguistic variable in variable italicized 44* variable rule approach 16, 18, 136, 155, 162, 171f variable rules 136, 162, 175 variables from set theory 43* variables in the logical sense 4*, gener­ ally, see List of Variables and Ab­ breviations variables not from set theory 43* variables related to grammars 155, generally, see List of Variables and Abbreviations S-variant 139, 142 variant 7 x-variant of the M-function 747* variant of the M-function 747*

x-variant of the M-relation 138* variant of the M-relation 138* varies 759*, 141*, 145 varieties of historical languages 46, 48,58 Variety 11f, 45f, 72, 90f, 775, 116, 118-120, 123, 127, 189, 191f, 2OO,201,2O4f, 209, 224 variety and variety structure: defini­ tions 92 variety approach 13*, 14, 104, 175, 177,184 variety concept 48, 92 variety grammars v, 17, 160, 162 variety names 212,215 the Variety relation: see Variety variety-sensitive description vi, 208 (a) variety specific to 118* variety structure of a historical lan­ guage 48, 51, 57-72, 73, 74, 97*, 92, 111, 116, 129, 131, 183,200202, 208 variety structure of a variety 48, 97*, 92, 115f, 127 variety with respect to F 61 verb-final 38*, 108 verb-final property 38* W weaker component approach 14*, 19f weaker holistic approach 14*, 20f weaker variety approach 14*, 21 weight 174* Word Order Pattern 181 Written D 69

List of Symbols and Abbreviations

There are three sublists A, B, and C. — Sublist A identifies the pages where variables or ambiguous constants used anywhere in the book are first introduced or where they are interpreted. Variables from set theory, other variables not specific to grammars, and variables specific to grammars are listed separately. — Sublist B collects the more important special symbols used in the book and either explains them or gives relevant page numbers; several numbers are given in cases of ambiguity. Symbols and nota­ tions from set theory are kept separate from mathematical and other symbols. — Sublist C gives page numbers for abbreviations (mostly, a single number) that are intro­ duced in the book.

A. Variables and ambiguous constants From the variables and ambiguous constants listed, additional ones are formed by ad­ ding number subscripts. 1. Variables from set theory A a M N O R x: 43; y: 6; 2. Other variables not specific to grammars b: 211 c C: 44 con CON: 173 D: 44 δ: 173 E: 44 f: 211 F G (cf. (3a)): 44

i j : 43 K: 168 L: 4 m n: 43 p (cf. (3a)): 94 P: 211 π  ø (cf. (3a)): 44 Q: 42

r: 95 r: 159 t: 43 T: 44(152) V: 43 w: 169

3. Variables specific to grammars 3a. Evaluation grammars ß: 166 G: 159 γ Γ: 160

p(cf.(2)): 159 ø (cf. (2)): 160 (see 158)

Φ: 1 6 0

3b. Other grammars D ø: 219 4. Ambiguous constants Ambiguous constants are formed for use in a specific context by italicizing a variable or adding one or more asterisks. The same constant may be used differently in different contexts, as indicated by more than one page number. (No ambiguous con­ stants, despite asterisk: IT* 110; ß* 167.) α*: 178 D*: 93, 119 D**: 119

M*: 109 *: 96 ø*: 130, 178, 222

S S1: 137 σ1* σ2*: 108 Σ*: 108

B. Special symbols 1. Symbols from set theory 

  Ø: 77

: 78 (N: union of a set N of sets; different from "": Ml  M2, i.e. M l united with M2) : 89 (N: intersection of a set N of sets; different from "": M1  M2, i.e. M1 intersected with M2) x1: the unit sequence of x = {(1, x)} +: 167 (concatenation product); 211 (concatenation) (cf. also (2) and (3)) Braces "{x |...}" reads "the set of all x such that:..." "{...}" reads "the set whose elements are:..." Parentheses -

tuple-notation: "(xl, ...,x n )" reads "the n-tuple whose first component is x 1 ,..., and whose n-th component is xn";

261

LIST OF SYMBOLS AND ABBREVIATIONS

function notation: "M(x l ,..., xn)" reads "the x such that (x1, ..., xn, x)  M" or "the value of M for (x l ,..., xn)", where M is an n-place function, n > 0, and (x 1 ,..., xn) is an argument of M.

-

Hyphen notation M n ( - , . . . , - , x): 137 (Mn-of-x) M n [- . . . , - , x , - ] : 141 (Mn-of-x-hyphen) 2. Mathematical symbols < : smaller than > : greater than + : plus sign (cf. also (1) and (3)) 3. Other symbols * : see (A4) =df

:

6

+ : metalinguistic variable in definitions 11, 107 (cf. also (1) and (2)) / / : phoneme notation + / / : 189 - / / : 189 +got (etc.): 225 b°: 211 •book-(raised dots): 214

C. Abbreviations Bav 121 Coll 121 con: see (Al) CON: see (Al) EG 157 EMG 122 Ex 225,228 G 41 +got 225 +have 225 IDS 143

iff 5 LAN 157 mc [mc(S)] 125 ME 195 MF 195 MG1 121 MHG 195 ModG 41 MSG 102 NGr 136, 144 OG 41

Per 121 post 157 prae 157 prob 159 propn 178 propn 178 PS 149 PS0 149 PS1 149 PV 121 Rom-IDS 149

r-rs 161 +/s/ 199 SCI 36 Suab 122 +/ / 199 +/w/ 189 -/w/ 189 WOP 181 +/ / 199