Cardinal Numerals: Old English from a Cross-Linguistic Perspective 9783110220353, 9783110220346

Table of contents :
Frontmatter
Table of contents
Abbreviations
Introduction
Chapter I. Linguistic numeral systems
Chapter II. The numeral system of Old English
Chapter III. Complex numerals
Chapter IV. Numeral constructions in Old English
Chapter V. The word class ‘cardinal numeral’
Concluding remarks
Backmatter

Citation preview

Cardinal Numerals

Topics in English Linguistics 67

Editors

Elizabeth Closs Traugott Bernd Kortmann

De Gruyter Mouton

Cardinal Numerals Old English from a Cross-Linguistic Perspective

by

Ferdinand von Mengden

De Gruyter Mouton

ISBN 978-3-11-022034-6 e-ISBN 978-3-11-022035-3 ISSN 1434-3452 Library of Congress Cataloging-in-Publication Data Mengden, Ferdinand von. Cardinal Numerals : Old English from a cross-linguistic perspective / by Ferdinand von Mengden. p. cm. ⫺ (Topics in English linguistics ; 67) Includes bibliographical references and index. ISBN 978-3-11-022034-6 (hardcover : alk. paper) 1. English language ⫺ Old English, ca. 450⫺1100 ⫺ Numerals. 2. Cardinal numbers. 3. Numeration. 4. Comparative linguistics. 5. Historical linguistics. I. Title. PE179.M46 2010 4291.5⫺dc22 2009051311

Bibliographic information published by the Deutsche Nationalbibliothek The Deutsche Nationalbibliothek lists this publication in the Deutsche Nationalbibliografie; detailed bibliographic data are available in the Internet at http://dnb.d-nb.de. ” 2010 Walter de Gruyter GmbH & Co. KG, 10785 Berlin/New York Cover image: Brian Stablyk/Photographer’s Choice RF/Getty Images Printing: Hubert & Co. GmbH & Co. KG, Göttingen ⬁ Printed on acid-free paper Printed in Germany www.degruyter.com

Acknowledgements It was Klaus Dietz who initially made the suggestion to me that the linguistic study of numerals would prove to be a rewarding field. I owe him therefore greatest thanks, not only for the initial impetus for this study, but also for the excellent advice and the invaluable criticism which he provided throughout. I would also like to express my gratitude to Elizabeth Traugott, not only for including this study in the series Topics in English Linguistics, but also for her criticism and her most helpful comments and suggestions on the text’s draft versions. Moreover, I am most indebted to Katerina Stathi for her constructive criticism: thanks to her keen eye for detail, a number of flaws and foibles could be prevented from making their way from the pre-final manuscript into the printed version. Numerous other friends and colleagues supported me with fruitful suggestions, encouragement and critical comments and provided their assistance in various other ways throughout the duration of this project. Among them Renate Bauer, Thomas Berg, Guy Deutscher, Volker Gast, Kai Glason, Daniel Hole, Christoph Jehlicka, Andrew James Johnston, Beth Martin, Hans Sauer, Calvin Scott, Casey John Servais, Judith Stemmann, Stefan Thim, and Ellen Westphal all deserve particular mention. I would also like to express my special gratitude to Rosalind Meistermann for her continuous encouragement and her unreserved support. Finally, I would like to thank my parents, Regine and Hans-Jürgen von Mengden, for having so confidently supported my commitment to a field of academic endeavour far beyond the sphere of their own personal and professional interests. My heartfelt thanks go to everyone mentioned above: without their support, this book would have been much less than it is now. All remaining errors and shortcomings that it may contain now remain my sole responsibility.

Ferdinand von Mengden Berlin, November 2009

Table of contents Acknowledgements

v

Abbreviations

xii

Introduction

1

I

Linguistic numeral systems

12

I.1 Cardinal numerals as quantifiers

12

I.2 Cardinal numerals and numbers I.2.1 Preliminaries: cardinal numerals as properties of sets I.2.2 Numbers as ordered sequences I.2.3 Different types of number assignment I.2.4 Numbers are infinite, numerals are not I.2.5 Outlook

16 16 18 20 23 24

I.3 The basic components of numeral systems I.3.1 Simple numerals I.3.2 Complex numerals I.3.3 Arithmetic operands I.3.4 Bases I.3.4.1 Defining a base I.3.4.2 Terminological problem I: bases vs. operands I.3.4.3 Terminological problem II: a mathematician’s base I.3.5 Atoms I.3.6 Complex numerals: a case of syntax or morphology? I.3.7 Summary

25 25 26 30 32 32 34 36 38 39 41

I.4 Systemic and non-systemic cardinality expressions I.4.1 General I.4.2 The counting sequence I.4.2.1 The counting sequence as an ordered sequence of well-distinguished expressions I.4.2.2 The counting sequence of Old English I.4.3 The limited recursive potential of non-systemic expressions I.4.4 Cardinal numerals as the morphological basis of non-cardinal numerals

42 42 46 46 48 49 50

viii

Table of contents I.5 Idiosyncrasies and variant forms in numeral systems I.5.1 ‘Idiosyncratic’ vs. ‘systemic’ I.5.2 Idiosyncratic numerals I.5.3 Variant forms I.5.3.1 Allomorphic variants I.5.3.2 Functional variants

52 52 54 58 59 59

I.6 Summary: Terminological and theoretical basis for the study of numerals I.6.1 Numerals I.6.1.1 Numerically specific vs. numerically unspecific I.6.1.2 Systemic vs. non-systemic number expressions I.6.2 Numbers I.6.2.1 Approaches to defining ‘number’ I.6.2.2 Definition of ‘numeral’ I.6.2.3 Types of number assignment I.6.2.4 Counting words and numerals I.6.3 The elements and properties of numeral systems I.6.3.1 The limit number L I.6.3.2 ‘Simple’ vs. ‘complex’, ‘atoms’ vs. ‘bases’ I.6.3.3 Arithmetic operands I.6.3.4 Idiosyncratic numerals I.6.3.5 Allomorphic and functional variants

62 63 63 63 64 64 65 66 66 67 67 67 68 70 70

II The numeral system of Old English

72

II.1 Overview: the simple forms

73

II.2 The atoms II.2.1 The numerical value ‘1’ II.2.2 The numerical value ‘2’ II.2.3 The numerical value ‘3’ II.2.4 The atomic values from ‘4’ to ‘9’

75 75 76 80 81

II.3 The expressions for ‘11’ and ‘12’

82

II.4 The first base ‘10’ II.4.1 The simple forms for ‘10’ II.4.2 The teens

83 83 83

Table of contents II.4.3

The multiples of ‘10’ II.4.3.1 The expressions up to ‘60’ II.4.3.2 The expressions for ‘70’, ‘80’, and ‘90’ II.4.3.3 The expressions for ‘100’, ‘110’, and ‘120’

ix 84 84 87 90

II.5 The second base ‘100’ II.5.1 The expressions for ‘100’ II.5.2 The distribution of the expressions for ‘100’ II.5.3 The section from ‘100’ to ‘129’

94 94 96 102

II.6 The third base ‘1,000’

105

II.7 The development of the Old English numeral system II.7.1 The pre-history II.7.1.1 The numeral system of proto-Indo-European II.7.1.2 The numeral system of proto-Germanic II.7.2 Changes during the Old English period II.7.2.1 The loss of the overrunning section II.7.2.2 The loss of the circumfix II.7.3 Later modifications of the numeral system

107 108 108 109 112 112 113 115

II.8 Ordinals II.8.1 The expressions for ‘first’ II.8.2 The expressions for ‘second’ II.8.3 The ordinal forms of the simple numerals II.8.4 The ordinal formation of complex forms

117 119 122 124 125

III Complex numerals

129

III.1 The formation of complex numerals III.1.1 1-deletion III.1.2 The use of the third base III.1.3 The coherence of complex numerals III.1.3.1 The position of the quantified NP in complex numerals III.1.3.2 Other splits in complex numerals

130 130 136 139

III.2 The decimal numeral system III.2.1 Recursion and serialisation III.2.2 How to (not) determine a decimal numeral system III.2.3 Old English: a trace of duodecimal counting?

152 152 154 159

139 144

x

Table of contents III.3 Non-systemic expressions for numerical values III.3.1 Preliminaries III.3.2 Non-systemic strategies for expressing numerical values within the scope of the numeral system III.3.2.1 Subtraction III.3.2.2 Extension of the scope of the second base III.3.2.3 Other alternative expressions III.3.3 Strategies for exceeding the scope of the numeral system

IV Numeral constructions in Old English

162 162 164 164 169 171 172 178

IV.1 Preliminaries

178

IV.2 Previous classifications of the syntactic properties of Old English numerals IV.2.1 General overview IV.2.2 Wülfing 1894 IV.2.3 Mitchell 1985 IV.2.4 Conclusion and outlook

180 180 183 185 187

IV.3 Attributive quantification IV.3.1 The Attributive Construction IV.3.2 The Elliptic Construction IV.3.2.1 Elliptic quantification IV.3.2.2 on twa ‘in two parts’ IV.3.2.3 Anaphoric use IV.3.3 Nominalisation of numerals IV.3.4 Conclusion

189 190 192 192 195 197 202 205

IV.4 The Predicative Construction

207

IV.5 The Partitive Construction IV.5.1 General IV.5.2 Constraints on the Partitive Construction IV.5.2.1 Quantification of a subset IV.5.2.2 Quantification by high valued numerals IV.5.3 A uniform account of the Partitive Construction

210 210 215 216 219 222

IV.6 Measure Constructions IV.6.1 The nucleus of a Measure Construction IV.6.2 Measuring predicates IV.6.3 Measuring arguments

227 227 229 230

Table of contents

xi

IV.6.4 Measuring properties IV.6.5 Specifying age IV.6.6 Summary

232 236 237

IV.7 The quantification of mass nouns

239

IV.8 Conclusion

244

V The word class ‘cardinal numeral’

248

V.1 Starting point

248

V.2 Adjectives, nouns, and numerals V.2.1 The numeral – an adjective? V.2.2 The numeral – a noun? V.2.3 Corbett’s generalisation V.2.4 Cardinality-dependent variation of atoms V.2.5 Cardinality-dependent variation of bases V.2.5.1 The emergence of numeral systems V.2.5.2 Rephrasing Corbett V.2.5.3 Another remark on 1-deletion

250 250 253 259 263 265 265 268 272

V.3 Cross-linguistic types of numeral constructions V.3.1 Count and Mass Quantification V.3.2 The Partitive Construction as an intermediate type

273 274 279

V.4 Against the hybridity of cardinal numerals

281

Concluding remarks

286

References

294

Primary sources

294

Studies

301

Subject index

320

Author index

327

Abbreviations General DOE fn. L MEAS

MED ms. n.

Dictionary of Old English footnote Limit number of a numeral system unit of measurement Middle English Dictionary manuscript(s) note

NP NUM

OE OEC OED PDE PIE VP

noun phrase cardinal numeral Old English Old English Corpus Oxford English Dictionary Present-day English proto-Indo-European verb phrase

Key to morpheme-by-morpheme glosses In Chapter I, the morpheme-to-morpheme glosses are usually employed to indicate the underlying arithmetical operations of complex numerals. In order to avoid confusion between the morpheme boundary marker “-” and the arithmetical operator “–”, morpheme boundaries are marked only in the Old English original, but not in the gloss. In Chapters II and III , morpheme boundaries will be marked, according to the convention, in both the original and the gloss. Generally the morpheme-to-morpheme glosses follow the conventions suggested by the Leipzig Glossing Rules. 1 2 3 ACC C CIRC CLF DAT DEM DET DU F GEN IND

first person second person third person accusative common gender form circumfix classifier dative demonstrative pronoun determiner dual feminine genitive indicative

INF INS M N NEG NMLS NOM OBL ORD PL PPRN PREP PRS PST

infinitive instrumental masculine neuter negation nominaliser nominative oblique case ordinal numeral plural personal pronoun preposition present tense past tense

Abbreviations PTCP REL RPRN

participle relative reflexive pronoun

SG SBJV

xiii

singular subjunctive

Manuscript sigla Addit. 47967 CCCC Julius A.x Otho B.xi Tiberius A.iii Tiberius B.i

London, British Library, Cotton collection, ms. Addit. 47967. Cambridge, Corpus Christi College [followed by ms. siglum] London, British Library, Cotton collection, ms. Julius A.x. London, British Library, Cotton collection, ms. Otho B.xi London, British Library, Cotton collection, ms. Tiberius A.iii. London, British Library, Cotton collection, ms. Tiberius B.i.

Introduction Cardinal numerals are not missing in any grammar or textbook of Old English nor in numerous other contributions to the study of the language. Yet, the relevant sections in the handbooks are all short and, it seems, numerals and their system have rarely been examined with closer scrutiny. In this respect, a reference grammar of Old English does not differ much from one of any other language. The scarce attention these expressions seem to receive from grammarians or linguists does not correspond with their frequency in the every-day use of a language. This discrepancy can perhaps be accounted for by the fact that the semantics of cardinal numerals seem quite plain and their use rather natural. As speakers, we probably count or quantify things several times a day without thinking about the mechanisms underlying these activities. Also, from a crosslinguistic perspective, no other class of lexemes is semantically as uniform as that of cardinal numerals. The notion of ‘number’ is independent of the cultural diversity amongst language communities and hence universal. In contrast to any other class of expressions, even to kinship or colour terms, a cardinal numeral always has a one-to-one equivalent in another language. The meaning of a cardinal numeral does not require much explanation in second language teaching and the skills of translators are hardly ever challenged by it. Perhaps the perception of the numerals and the numeral system of one’s own language as an every-day phenomenon, along with the intuition that the semantics of numerals are quite evident, make it appear rather trivial to the (historical) grammarian to take a closer look at the numeral system of a language. Knowing how to count is a capacity which is obviously located on a different level of human comprehension than understanding a Case system or a Tense system. But just as a Case system cannot be reduced to the distinction of agent and patient or a Tense system to the notions ‘past’ and ‘present’, we may well ask for a precise definition of the relation between every-day activities or processes like counting or employing numbers and their linguistic instantiations. This in turn leads us to the question of whether there is a connection between some of the grammatical properties particular to cardinal numerals and the domain of counting and calculating. In the same way as many linguists try to account for linguistic phenomena by (alleged or proven) patterns of human cognition, we may well ask whether a non-linguistic phenomenon (or rather, a model about it) contributes to approaching a linguistic phenomenon. So, if numerals obviously have to do with

2

Introduction

numbers, a very basic question can be employed as a plausible way of entering into the study of numerals: what is (a) number? Being faced with this question, we see that employing a concept ubiquitous in our every-day lives does not necessarily mean that we can explain the concept right away. A possible approach to defining ‘number’ – one of which I think it is most beneficial for studying linguistic numerals – will be presented in § I.2 and will provide a basis for most issues discussed in this study. Several follow-up questions immediately arise from the question about the status of ‘numbers’. What is the relation between ‘numbers’ and ‘numerals’? We will see that numerals are best explained as instantiations of numbers, that is, as a set of tools that we employ if we wish to use numbers for specifying the size of a set. We will see, furthermore, that numerals can only be used in this function if they are elements of a numeral system. That is, one single numeral can only perform its function if it is organised around a larger set of other numerals. The expression four could not denote the property of ‘containing four elements’ if the same language did not also provide neighbouring expressions like three or five; cf. § I.2.2). Thus numerals necessarily constitute a numeral system. But how exactly do we define a numeral system? We know that the notion of a ‘decimal system’ has something to do with the fact that, in many numeral systems, ‘10’ marks something like a turning point. Intuitively, we might say that ‘10’ is the first number to employ two digits and its first power, ‘100’, the first to employ three. This is true only for our written numerals, the Hindu-Arabic symbols that we use for writing numbers, but it is not true for any linguistic numeral system: in English, the expression ten follows nine, but both expressions consist of only one symbol (or of only one morpheme, for that matter). When speaking, we do not say something like one-zero. Likewise, and differing from the written symbol 〈100〉, the expression hundred is a morphologically simple expression and does not contain several digits. Thus linguistic numeral systems are different in some respect and yet they are used for the very same purpose as, say, the Hindu-Arabic notation. (Cf. particularly § I.3.4.3, where this point will be discussed.) Of course, it is not the task of a linguist or a grammarian to explain numbers or mathematics. Yet, if we wish to approach this class of expressions as a linguistic phenomenon, the question of what exactly the relation between a ‘(cardinal) numeral’, a ‘number’ and the size of a set (‘cardinality’) is will have to be raised. This is irrespective of the fact that, as speakers, we use numerals with ease and quite successfully yet never reflect on what exactly we are doing when we quantify a set and, moreover, how we are doing this or by means of which method. This complex of questions will be addressed in Chapter I. It will be shown that clarifying some basics about the status of ‘numbers’

Introduction

3

will bring about a promising basis for understanding many features of numerals – features which have so far led linguists to conceive of numerals as a hybrid class that can be defined semantically but not morphosyntactically. Addressing fundamental questions about quantification by numbers will enable us to define a numeral system as a particular subsystem of a language (with, as we may view it, an internal grammar) and to describe the fundamental characteristics of numeral systems of natural languages. Understanding some general features of linguistic numeral systems will, in turn, help us to account for language-specific peculiarities of numerals. Whereas numerals seem to be approachable more easily with respect to their semantics, difficulties seem to arise if we try to examine cardinal numerals in other domains of linguistic description. With respect to their inflection and their syntactic behaviour, cardinal numerals seem to display the most heterogeneous features. For instance, not only from a cross-linguistic point of view but even within a particular language, some cardinal numerals often follow different inflectional patterns than others; cf. e.g. GREENBERG (2000). With respect to their syntactic properties, cardinal numerals are similarly held to behave inconsistently both across languages and within a given language. They seem to be inscrutable to linguists at times, for instance when it comes to assigning them to a particular word class. The statement that higher valued numerals universally show more noun-like properties than lower valued numerals (CORBETT 1978a, 1978b; cf. § V.2.3) is one of the most frequently quoted generalisations on numerals. But a closer look will reveal that this implicational statement expresses a mere chance coincidence between the numerical value and the morphosyntactic features of an expression. Given that languages, and hence numeral systems of genetically unrelated languages, develop independently, I believe that formulating the implication as such should only be the first step. It should be equally essential to take the consequential second step, which is to find the reason for the apparent connection between the numerical value and the presence or absence of noun-like morphosyntactic features in the use of the respective numeral expression. Accordingly, one question we will have to raise is that of why higher valued numerals seem more noun-like than other numerals. The explanations I will propose (particularly in Chapter V) will be based on the assumption that the more noun-like appearance of higher numerals can be accounted for by properties that are inherently characteristic of numerals (rather than of nouns). I will argue that significant clues to get to the bottom of the problem may be found in the natural way in which numeral systems emerge and, subsequently, develop into a more complex system (cf. §§ II.7 and V.2.5.1). The fact that

4

Introduction

this development, to a considerable extent, runs parallel among genetically unrelated languages – and, accordingly, the resulting properties of numerals show parallels across languages – is, in turn, due to the universally uniform semantic content of cardinal numerals. Thus one general claim of this study is that the difficulties with respect to the morphosyntactic properties of numerals and, as a related question, to the word class character of numerals can be overcome. Hence, the study of the processes that lead to such correlations is equally significant to finding implicational generalisations on numerals in natural languages. And, if we want to learn more about the attested (or reconstructable) long-term changes of numeral systems, cross-linguistic breadth and historical depth will be equally important. While deliberately taking both the dimensions of typology and history into consideration, this study is based on and focuses on historical data of one particular language. One of the advantages of this approach is that both a language-specific description (Old English) can be carried out and, on this basis, a long-term perspective (from proto-IndoEuropean via Old English to Present-day English) can at least be sketched to a sufficient degree. In addition to contributing to the study of the Old English language, a comprehensive language-specific description of a numeral system also serves the purpose of assessing the theoretical model set up in Chapter I. Long-term diachronic considerations – here with a necessary bias towards Indo-European and Germanic – provide evidence for the individual steps in the emergence and the growth of numeral systems (outlined in §§ II.7 and V.2.5.1; cf. also VON MENGDEN 2008), which in turn explains not only the variation in the morphosyntactic properties of numerals (see above), but also the general structure of numeral systems and the existence of such morphemes like -teen and -ty in Present-day English (cf. §§ I.5.3.2, II.4.3, II.7.2, and Chapter V). The Old English language is, in various respects, a perfect candidate for the task of describing a numeral system so that more general, cross-linguistic implications can be made. Generally, Old English is a typical representative of both European and Indo-European languages. Its grammar reflects an intermediate stage between the inflecting Indo-European proto-language and the analytic character of Present-day English. Moreover, of any Early Medieval language of Europe – with the exception of Medieval Latin – Old English has by far the greatest corpus of preserved text documents comprising various genres over a period of several centuries. Finally, and most importantly with respect to numerals, the numeral system of Old English is basically similar to that of other European and Indo-European languages but at the same time shows a number of features which significantly deviate from what we are fa-

Introduction

5

miliar with from the perspective of today’s English. It is surprising, therefore, that Old English numerals have been neglected in the general linguistic literature on numerals and, likewise, that numerals are a rather neglected category in the study of Old English. To give an example of a typologically highly unusual feature of the Old English numeral system: the Anglo-Saxons have an expression for ‘100’ in their language just like any other European language. When counting above ‘100’, however, they do not use it in the first place, but continue to count with multiples of ‘10’, as if we said, ‘eighty’, ‘ninety’, ‘ten-ty’, ‘eleven-ty’, ‘twelve-ty’. Only from ‘130’ onwards do they employ the base ‘100’ and continue with ‘hundred and thirty’, ‘hundred and forty’ and so on (cf. § II.4.3.3). This phenomenon of overrunning a numerical base has been mentioned in some typological studies on numerals with reference to other languages (GREENBERG 1978: 271, referring to Keres; COMRIE 1999: 732, mentioning Polabian), but the same phenomenon in Old English, although stable and wellattested, has gone completely unnoticed in studies on numerals and numeral systems with a cross-linguistic approach. On the other hand, scholars interested in the study of the ancient Germanic languages have made numerous attempts to explain the etymologies of the respective expressions used for counting up to ‘120’ (cf., e.g., SZEMERÉNYI 1960; BAMMESBERGER 1986), but there has never been any attempt to discuss the phenomenon of the Germanic languages in a more general, cross-linguistic context. Indeed, language-specific contributions concerned with these Germanic numerals seem to have completely ignored what typologists say about similar phenomena in other languages. The peculiar way in which the counting-sequence of the Anglo-Saxons is structured between ‘99’ and ‘129’ may serve as one example out of several for the way in which researchers of Germanic or Old English and general linguists have analysed corresponding phenomena completely independently of each other. The grammatical description of Old English has freed itself from traditional approaches influenced by the description of the classical languages only rather recently with the emergence of electronic corpora. Yet much of what we find on numerals of either Old English or the ancient Germanic languages draws, to a large degree, on the framework of classical grammar. Neogrammarian studies on cardinal numerals have, in the tradition of their time, always focused on their phonology and morphology and on the history of particular numerals. Linguists from that earlier period examined the etymologies of numerals (e.g. VAN HELTEN 1905/06) or they provided lists of instances of particular forms and uses of numerals (e.g. FRICKE 1886). But even more recent studies hardly went any further. The very comprehensive contribution by

6

Introduction

ROSS/BERNS (1992) provides a useful overview of the developments of all diatopic and diachronic varieties of the Germanic branch of Indo-European, but their study still focuses primarily on etymological problems, whereas they treat other linguistic aspects, the use of inflection or syntactic constructions for instance, only in the context of the history of particular numeral forms. Yet if we set such a language-specific analysis into a cross-linguistic context, i.e. if, in our description of the numerals of one particular language, we take into account the possible strategies which can be employed for the formation of numeral expressions, we will not only operate on a safer theoretical basis, but we will also be able to gain valuable insights for the reconstruction of pre-historic stages of languages and their respective numeral systems. In my view, this context has been widely ignored in diachronic studies on numerals. I would argue, however, that an understanding of cross-linguistic features of both numeral expressions and numeral systems is in many respects a prerequisite for the historical study of numerals. Eugenio LUJÁN – one of the few historical linguists working on numerals who includes both system and reconstruction (or both typology and history) as equally important – writes (LUJÁN 1999: 203): Traditionally, etymological work on Indo-European numerals lacked general scope, in the sense that it used to deal with each numeral separately, without taking into account what happens to be the most important characteristic of numeral systems: the fact that “the value of each cardinal number corresponds to its order in counting”, as Stampe (1977: 596) stated it. In other words, in order to account for a numeral system we have to bear in mind that the concept of “series” (or “sequence”, as Hurford (1987: 86 ff.), prefers to refer to it) is basic. It is in this sense that most of the work done on Indo-European numerals is insufficient. When concentrating on just one numeral, a given etymology may seem to be possible and the reasoning that has led to it, convincing. The problem is that, when we try to bring together the etymologies proposed for different numerals, in most cases we have to accept that the Indo-Europeans amused themselves by inventing a numeral system with no consistency at all, or else – which is more likely – we begin to suspect that the etymologies are not so convincing as we thought. While arguing that the study of the history and pre-history of a given language requires the study of what is typologically possible and what is unlikely, I do not intend to say that the study of diachronic developments in language (or in

Introduction

7

a particular language) is secondary. In fact, the benefit will certainly be mutual. Especially in the context of numerals and numeral systems, quite a number of substantial contributions have already been made on the origins and the evolution of the number concept in human culture and its representation in language; cf., e.g., IFRAH (1981). It is assumed that human counting was originally carried out by means of gestures. Particular points on the human body, to which somebody pointed when counting, served to refer to particular cardinalities. Originally, the expression for that body part accompanied the gesture until, at a next stage, the linguistic expression became the primary numerical tool (cf. § I.2.2) and, eventually, the accompanying gesture was no longer felt necessary. Not necessary does, however, not mean extinct: whether unconsciously or not, we still often show the relevant number of fingers as an accompanying gesture when we specify numbers. Also, a number of studies have approached numerals from the perspective of the cognitive foundations of number concepts and of numeral systems; cf. e.g. HURFORD (1987), WIESE (2003). Central questions raised in these contributions have been how an individual perceives cardinalities or how an infant acquires the capability of operating with numbers. There are a number of phenomena particular to the word class numeral for which the area of human cognition seems to be the most promising source for explanations, such as for instance the special status that the lowest numeral expressions have in many languages (§ V.2.4; cf. HURFORD 2001) or the sequential ordering of numerals in virtually all languages (§§ I.2.2 and I.4.2). In the times when transformational grammar was most successful, a number of formal models for the description of numeral systems have been suggested; cf. e.g. HURFORD (1975) or the contributions in BRANDT CORSTIUS (1968). Likewise, universal properties of numerals and numeral systems have been identified on the basis of large language samples – most of all by Joseph GREENBERG who provided a list of 54 empirically founded generalisations about numerals (GREENBERG 1978). The present study will try to integrate these approaches – linguistic typology, the connection between human cognition and language, and language history – into one framework for the study of numerals. Each of these areas of study has its value for explaining phenomena related with numerals. Thus in order to understand cardinal numerals in their entirety, all these areas need to be looked at and the ways in which these areas complement each other should be examined and defined.

8

Introduction

In light of the points raised above, the aim of the present study is, first of all, to contribute to the grammatical description of the Old English language by providing a detailed analysis of the Old English numeral system and of the properties of the respective expressions. However, the analyses of this study are at the same time intended to contribute to the linguistic study of numerals in a more general, cross-linguistic context. As a preliminary step, universal features of numeral systems will be discussed in view of the extent to which they are relevant for an analysis of the numeral system of Old English. Chapter I will also provide a definition of what constitutes a numeral system and, hence, what a numeral is. This seems necessary since there are a number of expressions which are classed undisputedly as ‘numerals’, while there are also expressions which sometimes have been treated under the label ‘numeral’ even though this categorisation cannot be maintained once we define ‘cardinal numeral’ in a precise way. For instance, in most grammars or handbooks of Old English, the expression BA ‘both’ has been categorised as a numeral without distinguishing it from the cardinal TWA ‘2’. The two expressions, however, have quite a different distribution. Moreover, while the primary use of a numeral ‘2’ is to specify the cardinality of a set (containing two elements), the use of an expression like ‘both’ requires that the cardinality ‘2’ is a given piece of information in the discourse, i.e. that the cardinality ‘2’ has already been specified. Or, in other studies, not necessarily those concerned with Old English, expressions like dozen are treated in the same way as twelve without any further distinction. GREENBERG (2000: 771) has pointed out that a difference needs to be drawn between genuine numerals and other expressions which specify the cardinality of a set in a likewise unambiguous way. However, a clear definition of this difference, and hence a clear definition of how to draw a line between cardinal numerals and other number expressions, has, to my knowledge, not been provided so far (cf. especially § I.4). The framework thus developed will then allow us to commence the language-specific description of the numeral system of Old English (especially Chapters II and III). In Chapter II, we will discuss the characteristic features of the Old English numeral system and of the morphological (and syntactic) strategies employed to generate numeral expressions in Old English. Chapter III will discuss more detailed phenomena particularly concerning complex numeral expressions in Old English. At the same time, the issues raised in Chapter III will contribute further to the understanding of numeral systems of natural languages. In Chapter IV, we will then examine the morphosyntactic properties of cardinal numerals of Old English. The focus will be on the constructions in

Introduction

9

which cardinal numerals may occur and on the respective functions which they may exhibit in the particular constructions. The underlying assumption is that the key function of numerals is quantification, which, in the context of the morphosyntactic interaction between numeral and noun, I take to be the numerically-specific modification of the extensional reference of the noun phrase. The main point which will be shown in this context is that this function, quantification, can be performed in different types of constructions and that the choice of the relevant construction follows particular, well-identifiable constraints on several linguistic levels. But secondary functions may well arise from this main purpose of numerals as for instance that of anaphoric reference (cf. §§ IV.4.3.2–4). Chapter V will set the results of our analysis into a cross-linguistic context. As already alluded to above, I will basically argue in Chapter V that cardinal numerals can be considered an independent lexical class not only because of their cross-linguistically uniform semantics, but also because their morphosyntactic properties (i.e. inflectional behaviour, syntactic distribution and the underlying constraints) follow relatively consistent patterns within and across languages. The main argument supporting this claim will be that variation in the morphosyntactic properties of numerals should not be viewed as a sign of the hybridity of numerals, but that this variation can be accounted for by the way numeral systems are structured and, as already mentioned, by the way these structures develop. In line with the above assumption – that the study of numerals of an ancient language needs to take cross-linguistic patterns into account – Chapters I and V, but also a few parts of Chapter III – will contain more general discussions on numerals in which Old English does not play a central role. The language-specific description will be in the focus of Chapters II to IV. Another division, although necessarily not a clear-cut one, can be made between the study of the numeral system and the study of the grammatical properties of numerals: Chapters I to III will deal with the numeral system, Chapters IV and V with morphosyntactic properties of numerals. Thus, Chapters I and V correspond largely to what GIL (2001: 1275a) refers to, respectively, as the ‘internal’ and ‘external’ typology of quantification. They will be of particular interest also for those readers whose key interest is not the Old English language but who wish to study numerals from a more general perspective. I have employed a few formal conventions, which I would like to explain briefly. One results from a terminological conflict: the term number may refer to two completely different concepts, both of which are crucial for the study of numerals. It may refer to the number in the sense of a measure for the size of a

10

Introduction

set (cf. § I.2.4), but it may also refer to an inflectional category of many languages, which in Old English comprises the values ‘singular’, ‘dual’, and ‘plural’. As there are no reasonable alternative terms for either concept, they will be distinguished by the capitalisation of grammatical categories. Hence, “number” will refer to the former concept and “Number” to the latter. Accordingly, I generally capitalise the labels for grammatical categories but not for their values. Thus notions like Gender or Case are capitalised, while their values – e.g. nominative or neuter – are not. Generally, this is probably not a necessary practice, but as we need to distinguish the grammatical category ‘Number’ by capitalisation, equivalent categories should, for the sake of consistency, be capitalised too. When discussing Old English expressions, I also distinguish throughout between general types of expressions, i.e. irrespective of variant forms, on the one hand (printed in italicised small caps), and individual attestations (plain italics) on the other. A form such as OE TWEN- in TWEN-TIG ‘20’ (which I analyse as an allomorph of TWA ‘2’; cf. § II.2.2) will be printed in italicised caps whenever the exact spelling or phonetic form of an individual instance is irrelevant. Only their individual realisations are indicated by plain italics, e.g. tuen- or twæn- as different instances of the type TWEN-. Occasionally, it seemed appropriate to explicitly distinguish between the phonological and the graphemic shape of a particular form. The general principle which I have endeavoured to follow is this: where such a distinction seems unnecessary or not helpful, the linguistic expressions are usually rendered in (plain or capitalised) italics. The phonological form is, as is customary, represented by IPA-symbols within slashes. I have marked the graphemic representation of an expression with pointed brackets. However, I do not distinguish between insular 〈h〉 and Carolingian 〈g〉, rendering both as 〈g〉. Likewise, the runic wynn 〈w〉 is rendered as 〈w〉. Moreover, except in particular cases, I generally ignore variant forms and use the most common Classical West Saxon form as the default lexeme for a numeral. As a reference system to the Old English texts, I have used the short titles employed by the Dictionary of Old English.1 Moreover, in the numbered examples I decided to quote an expression together with the immediate context in which it is attested. At these occasions, I have also referred to the most recent (or best) printed edition of the relevant text. When occasionally only short phrases are quoted outside the numbered examples without context, no refer1

For a key to the references see DOE or HEALEY (2000). A printed list is available in HEALEY/VENEZKY (1980), which, however, does not contain later modifications to the system of abbreviations.

Introduction

11

ence to a printed source is given. Yet, whenever it seemed necessary, I have consulted the latest relevant editions as specified in the various publications of the DOE-project. This study is, for the most part, based on the data provided by the Dictionary of Old English Corpus (OEC), the Dictionary of Old English (DOE) and in HEALEY (2000). The OEC basically covers one version of any preserved Old English text. Since many Old English texts are recorded in more than one version, the database does not come close to representing all of the extant linguistic data of the Old English language. If it seemed valuable, I have tried to include deviating readings of analogous texts not captured by the electronic corpus. However, even if one were to scrutinise every accessible text edition in order to gain as much of the material as possible, some part of what is actually preserved of the Old English language would still remain unnoticed as quite a number of extant manuscripts containing parallel versions have never been collated or edited. Therefore, the present study is to some extent based on the choice of base manuscripts selected by the OEC. Moreover, it is also limited by the way in which the linguistic data from those versions not included in the OEC are treated by the respective editors. Bearing these constraints in mind, the results discussed here may, in particular instances, be subject to the disparate ways in which the relevant sources are accessible. On the other hand, the material at my disposal has been rich and varied enough to give a sufficient and representative impression of what may have been the Old English language.

Chapter I Linguistic numeral systems I.1

Cardinal numerals as quantifiers

As a preliminary approach to a discussion of cardinal numerals, their functions and properties and their classification within the range of lexical categories, it is plausible to categorise cardinal numerals as a subclass of quantifiers. That is, cardinal numerals are part of a larger class of expressions which all specify the size of a set. The expression quantified (usually a noun) then denotes the kind of elements that are contained in this set. Quantifiers share a number of semantic and functional as well as formal properties. As for the latter, there is a range of morphosyntactic strategies employed by quantifiers – and in particular cardinal numerals – in interaction with the quantified noun. These will be discussed later in Chapters IV and V. We will first focus on the semantic aspects of quantification because, amongst other reasons, in contrast to their varying morphosyntactic behaviour, cardinal numerals are semantically extremely uniform across languages. One important group of quantifiers comprises the quantificational categories of predicate logic, that is universal quantifiers (‘all’, ‘every’) and existential quantifiers (‘an’, ‘some’). A variety of quantifiers may constitute an intermediate group between these two poles (e.g. ‘few’, ‘several’, ‘many’, ‘most’, etc.). GIL (2001: 1277b–1278a, § 2.3) labels this intermediate category “mid-range quantifiers”. By postulating this subcategory, we take into account the fact that there is a greater semantic diversity of quantifiers in natural languages than entailed by the two prototypes or poles commonly used in quantificational logic, existential and universal. Different perspectives on the particular properties of quantifiers may result in varying sub-categorisations of cardinal numerals within the class of quantifiers. GIL (2001: 1277b–1278a, § 2.3), for instance, groups cardinal numerals as special kinds of ‘mid-range quantifiers’; cf. Figure 1. existential quantifiers → mid-range quantifiers → universal quantifiers ↓ cardinal numerals Figure 1.

Cardinal numerals within the sub-categories of quantifiers according to GIL (2001)

Cardinal numerals as quantifiers

13

Implicitly, GIL ’s main criterion is based on the fact that a quantifier selects a subset of elements from a larger set, which is usually represented by the extensional meaning of the quantified noun. Taking the phrase “x apple(s)” as an example, GIL’s sub-categories can be described as in Table 1: Table 1. Cardinal numerals within the sub-categories of quantifiers according to GIL (2001) phrase

meaning

label of quantifier type

an (apple)

‘at least one element of the class (of apples)’

existential quantifier

many (apples)

‘more than one but not all elements of the class (of apples)’

mid-range quantifier

all (apples)

‘all elements of the class (of apples)’

universal quantifier

Assuming a slightly different perspective, LANGACKER (1991: 81–89) distinguishes between ‘absolute quantifiers’ and ‘relative quantifiers’, the latter specifying a quantity in relation to a “reference mass”, i.e. in relation to the extensional meaning of the quantified expression, thus comprising ‘all’ or ‘most’. ‘Absolute quantifiers’, by contrast, specify a quantity in a more immediate way, that is without such a “reference mass” (LANGACKER 1991: 82). This group would comprise quantifiers like ‘many’ and ‘several’ as well as cardinal numerals. Although LANGACKER’s classification focuses on an important aspect of quantification, it disregards the fact that in most languages there is a choice of different constructions in which quantifier and noun interact, and that the distinction between ‘absolute’ and ‘relative quantification’ is often dependent on the type of construction that is used (cf. §§ IV.3–5).2 In English, for instance, LANGACKER’s classification of cardinal numerals as ‘absolute quantifiers’ is valid for constructions like (1.1)a but not for a partitive construction like (1.1)b. 2

Here and in the following, but particularly further below in Chapter IV, I will use the term ‘construction’ for any type of a use of cardinal numerals that can be distinguished by a correlation of form (syntactic structure) and function, again without committing myself to specific theoretical implications that may be involved in a more technical sense of the term ‘construction’.

14

Linguistic numeral systems

(1.1)a

many / several / three apples

(1.1)b

many / several / three of the apples

Once a construction like the one in (1.1)b is employed, ‘absolute quantifiers’ also quantify a set in relation to a “reference mass”. For English, we may argue that the examples in (1.1)b represent a marked construction and that, therefore, the pattern in (1.1)a is the default case which then justifies LANGACKER’s categorisation. It is questionable, however, as to what extent this would apply cross-linguistically. But even if we ignored this aspect of LANGACKER’s categorisation, cardinal numerals would again share a subclass with some completely different types of quantifiers. Moreover, because a cardinality – be it ‘1’, ‘4’, or ‘27’ – could potentially comprise ‘at least one’, ‘several’, or ‘all’ members of a set, depending on the particular case, for a study like the present one in which cardinal numerals are in the focus, both LANGACKER’s and GIL’s classification are equally unsatisfactory. Without disputing the values of each of the two taxonomies, I would, for our purpose, like to shift the focus to the particular (semantic) feature which makes cardinal numerals stand out of the class of quantifiers most significantly: cardinal numerals specify the size of a set by its ‘cardinality’, that is, by the exact number of elements a set contains. I suggest that the feature [± numerically specific] be employed as a superordinate criterion. In this sense, numerically specific quantifiers specify the exact number of elements of a class. By contrast, numerically unspecific quantifiers determine the size of a class in relation to the extensional meaning of the quantified referential expression. I therefore propose a modification to the position of cardinality expressions within GIL ’s range, taking them as independent of the two poles of numerically unspecific quantification, ‘universal’ and ‘existential’. Accordingly, I suggest the classification shown in Table 2; cf. VON MENGDEN (2008: 291). The same distinction, though in a different context, was made for Modern German by VATER (1984: 29). Table 2 includes a further distinction in addition to the ones drawn so far. In the following sections it will be argued that cardinal numerals form a distinct and cross-linguistically well definable subclass of numerically specific quantifiers. More precisely, I will argue that cardinal numerals are exactly that class of numerically specific quantifiers that constitute a numeral system of a particular language (cf. below § I.4). This implies that there is a group of numerically specific quantifiers which are not part of the numeral system of a given language. I will distinguish between the two by labelling them ‘systemic’ and ‘non-systemic’ cardinality expressions. ‘Systemic’ expressions are

Cardinal numerals as quantifiers

15

at the same time that subclass of quantifiers which are ‘cardinal numerals’; cf. Table 2.

Table 2. Types of quantifiers Quantification Specification of the cardinality of a set

numerically unspecific

universal

“mid-range” (GIL 2001)

few, several, all, every, … many, most, …

numerically specific (cardinality expressions)

existential

systemic

non-systemic

some, a(n)

one, two, three, …. fourteen, twenty-three, one hundred and seventy-six, ….

dozen, score. three twenties, twice a hundred

cardinal numerals

My analysis of the Old English numeral system is based on this distinction. It will become evident that the difference between ‘systemic’ and ‘non-systemic’ expressions is of fundamental importance to the linguistic study of numerals and numeral systems both from a cross-linguistic and a language-specific perspective. I therefore take it as a prerequisite for the description and analysis of cardinal numerals of Old English. (Cf. the summary in § I.6.1.1.) What will remain unconsidered in this study are pragmatic extensions of the numerically specific meaning of cardinal numerals. The use of a cardinal numeral in communication may have implications that go beyond specifying the exact numerical value of a referent set. Referring to a cardinality ‘x’ may imply, depending on the context, both ‘no more than x’ and ‘no less than x’. These ‘scalar implicatures’ are described for Present-day English in HUDDLESTON/PULLUM (2002: 363–364, § 5.2). Part of the reason for not treating these aspects in this study is of a practical nature. Scalar implicatures

16

Linguistic numeral systems

are predominantly a feature of spoken conversation for which we do not have any reliable evidence in Old English. Moreover, it is generally difficult for the modern reader (and interpreter) to identify more subtle pragmatic implications in historical texts without lapsing into speculations. But aside from these merely technical or methodological difficulties, the potential of numerals to be used for scalar implicatures is clearly a secondary feature of their use. It is true, a cardinal numeral may be used in conversation to specify the upper or lower limits of the size of a set. However, if this is done, the numeral nevertheless specifies an exact numerical value. The difference is that the extension of the reference of the quantified expression, say a noun phrase, will be less clearly defined. But the extensional limitation of the reference, albeit less precise, still draws on an exact numerical value. So, if I say four apples in a context that allows the implicature ‘at least four apples’, the lower limits of the size of the set of apples is nevertheless defined by ‘precisely 4’. Thus scalar implicatures operate on numerically specific quantification, however open the pragmatic interpretation of an utterance will be. So far I have suggested isolating cardinal numerals from all other types of quantifiers. While I assume that the distinction between ‘numerically specific’ and ‘numerically unspecific’ quantifiers is intuitively clear, the second distinction I have made, that between ‘systemic’ and ‘non-systemic’ cardinality expressions, requires further explanation and justification. This will be done in due course (§§ I.3–4). Before continuing on this point, another important aspect of a definition of cardinal numerals needs to be discussed: the concept of ‘number’ and the relation to its representatives in human language, the numerals. I.2

Cardinal numerals and numbers

I.2.1

Preliminaries: cardinal numbers as properties of sets

In the previous section, we distinguished cardinality expressions from other quantifiers by their property of specifying the size of a set in a ‘numerically specific’ way. This agrees with the intuitively most natural approach to numerals, i.e. to the fact that cardinal numerals are the linguistic representatives of ‘numbers’. There are, in fact, some fundamental aspects of ‘number’ which will be worth considering when studying numerals as linguistic expressions. As a next step in our discussion, we will therefore try to approach the concept ‘number’ and see which definition or which aspects of existing definitions of this concept will be useful for describing linguistic numerals and numeral

Cardinal numerals and numbers

17

systems. It should be mentioned that there are several ways of defining ‘number’ both in mathematics and in philosophy. It is impossible to treat them all in full detail here. I will restrict myself to a synthesis of these approaches as suggested by Heike WIESE, originally in (1995a) and then, more accessibly, in (2003: particularly 43–93). WIESE’s approach is particularly useful for the linguistic study of numerals and numeral systems. My line of argument in the subsequent sections – including a more precise definition of what a ‘cardinal numeral’ is – therefore owes a great deal to WIESE’s study and its sources. The size of something can be seen as a particular property of it. So, if quantifiers – and, accordingly, cardinal numerals – specify the size of a set we can say that they refer to a particular property of sets. For example, we may at a first glance find absolutely nothing that, say, an apple has in common with a book. There is no property we could think of immediately that the two concepts, ‘apple’ and ‘book’, have in common. However, if we compare the properties of a set of five apples with those of a set of five books, we will be able to find a common property between the two groups of things. A set of five apples shares one common property with a set of five books, namely the property of containing five elements. This particular type of property of a set – the number of elements contained in a set – is called its ‘cardinality’. Now, if we compare two sets of the same cardinality, it may perhaps suffice to say that a given set A (say, a set of five apples) has the same number of elements as a certain set B (say, a set of five books). However, if we would like to refer to this property, for instance when buying apples or books in a shop, we need to specify or label these properties, or, to put it more simply, we need to give a name to each cardinality. For this purpose, it does not suffice to know that a particular group of apples has as many elements as some other set. What we then need is some abstract system for representing these cardinalities without referring to some particular real-world class of concrete objects (such as apples) in the respective context. In short we need a device to specify this property in an abstract way. Bearing in mind that the general aim of this chapter is to find out how such a system, the numeral system, is generated and used, we will now first clarify in what way cardinal numerals are related to numbers. Recall that we said that cardinal numerals are that particular type of quantifiers that specifies the size of a set in a numerically specific way.

18

I.2.2

Linguistic numeral systems

Numbers as ordered sequences

Generally speaking, if we wish to specify the cardinality of a set, we are aware that we employ numbers in some way. WIESE (2003) describes this intuitive relation between ‘numbers’ and the size of sets by saying that, when we specify the cardinality of a set, we assign numbers to sets. Numbers may, therefore, be seen as a kind of device that we need for specifying the cardinality of a set. These devices may occur in various types of manifestations. These different types of manifestations are all different systems of numerals. One type of such a device could be the class of lexical expressions of human language that we are speaking of, numerals as number words. But there are other types of devices that are as familiar to us as number words. We could just as well think of numerals as written characters (such as the Hindu-Arabic notation) as being precisely such a system. Just as plausibly, we could employ the letters of an alphabet for specifying cardinalities, as was done in Ancient Greece where letters were used as numerals. It is also possible to use a salient sequence of parts of the human body as instances of numbers. The most common method of this kind is the use of our ten fingers for indicating cardinalities. In other words, even our ten fingers can be used as numerals, because it is possible to use our fingers for assigning numbers to sets. In this case, we would specify the cardinality of a set by means of a gesture. These systems are more or less all either familiar to us or at least conceivable and any of these systems could easily serve our purpose. From the observation that quite different manifestations of numbers can be used for the same purpose, the question of what all these different devices have in common arises. This question will help us to base the relation between ‘cardinalities’ and ‘numbers’, and between ‘numbers’ and ‘numerals’ on a more solid ground than our intuitive first approach can. Since all the systems mentioned here serve equally well in assigning numbers to (sizes of) sets, we may assume that there is something all these systems have in common which, once we have identified it, would help us to trace the true nature of numbers. One feature which all these systems have in common is that the entities employed in the respective systems are all distinct from each other. It would, for instance, be impossible to use the Hindu-Arabic numerals if two of the characters looked exactly the same, so that the sequence would go, for instance, 〈1, 2, 3, 4, 5, 3, 7, 8, etc.〉. In a similar way, it would be impossible to use number words for specifying cardinalities if there were homonymous cardinality expressions within one variety of a language (cf. HURFORD 1975: 101 and 1987: 28; WIESE 2003: 71).

Cardinal numerals and numbers

19

Another feature common to all the systems listed above is that, in any of them, all the entities have a well-defined place in the way they are arranged. That is, the entities used in systems for cardinal number assignment (of whatever type) do not only form sequences, but each entity also has a fixed place within a sequence. If this were not the case, they could not serve our purpose of assigning cardinalities. If, for instance, there was some variation as to whether the Hindu-Arabic number sign 〈3〉 precedes or follows the symbol 〈4〉, the whole system of numerals would not work. Therefore, the two crucial properties of any system that can be used as numbers are these:  The elements of the system must be well-distinguished from each other.  The elements of the system must form an ordered sequence.

This applies not only to written or spoken numerals, but also just as well, for instance, to finger counting: our ten fingers are well-distinguished from each other and they are arranged in a saliently fixed order. STAMPE (1976: 600) explains the importance of a fixed order of entities for counting: Order is universal in counting. The things counted need not be ordered: each counting imposes an order, but the sum is the same regardless of this order. The numbers we count with are strictly ordered, however, so that the value of each corresponds to its place in the counting order. [Italics original]

If we now conflate the two common properties of any conceivable system of elements which may potentially serve as numbers, we can say that every system for assigning cardinalities to sets must consist of an ordered sequence of well-distinguished elements. This definition, by the way, will help us in delimiting more precisely cardinal numerals from other numerically specific quantifiers in a language; cf. Table 2. Before doing this (§ I.3), a few more important points on ‘numbers’ and ‘numerals’ will be discussed in the following. In accordance with what we have just outlined, WIESE (2003: 64) argues that it is exactly this property – the property of being an ordered sequence of well-distinguished elements – that defines numbers. Any class of entities which matches this description may serve as numbers. We therefore do not need to assume any additional abstract set of entities. Numbers are tools that can be used in ‘number assignment’ and, as such, they may occur in various different forms provided they constitute an ordered sequence of welldistinguished entities. It is in this sense that different forms of numerals are

20

Linguistic numeral systems

simply different possible instantiations of numbers. WIESE further writes (2003: 64): Once we regard numbers as tools in number assignments, we see that there is no need to define properties that pick out one and only one particular progression. What makes numbers so powerful is exactly the fact that they relate to a small set of fundamental features for their tasks, and to no more. … this view acknowledges [numbers] as powerful, efficient, and highly flexible devices with many possible instances. If our number assignment is to be intersubjectively comprehensible, it is merely relevant that the sequence we are using is one that is conventionally acknowledged as a number sequence, such that the relations holding in our numerical relational structure are clear.

The “small set of fundamental features” WIESE refers to are exactly the two properties we have singled out as the common properties of the various kinds of systems for number assignment in human culture. In other words, all that is required for a set of entities to serve as numbers (i.e., to be employed in number assignment) is their being well-distinguished from each other and their having an internal order fixed either by convention or in a sufficiently salient way. What is crucial about this approach to numbers is that we can do well without assuming some prototypical set of ‘numbers’ to which numerals (of any kind) would refer. Such a set of abstract concepts would not have a single property in addition to those of the systems of representation listed above. Once the respective system shares the two definitory features (i.e. once they constitute a conventionalised ordered sequence of well-distinguished entities), numbers can be instantiated in various different forms or, as WIESE puts it, they are “devices with many possible instances”. Accordingly, numerals do not refer to numbers, they are numbers or, more precisely, each numeral system is one of many possible instances of numbers. (Cf. BENACERRAF 1965; WIESE 2003: 68–93. See also the discussion in HURFORD 1987: 86–131 who takes on a more sceptical view on the unified analysis of numbers and numerals. For a summary of this discussion see below §§ I.6.2.1–2.) I.2.3

Different types of number assignment

What are numbers then compared to all these different sorts of numerals or ‘number signs’? There is one important distinction which we have not made explicitly so far. As to linguistic expressions, there is, theoretically, a difference between cardinal numerals and counting words; cf. HURFORD

Cardinal numerals and numbers

21

(2002: 629b). While the former are those expressions that we use for referring to cardinalities, i.e. numerically specific quantifiers, the latter is the set of nonreferential expressions that is used in the conventionalised counting sequence; cf. WIESE (2003: 265–270). As the two types of expressions are homonymous in English and in many other languages, this distinction may perhaps not seem all that obvious at a first glance. But there are some languages in which cardinal numerals can be distinct from the respective counting words. Hungarian, for instance, uses kettő ‘2’ in the counting sequence but két when quantifying a noun. Likewise, German uses eins for ‘1’ in a counting sequence and inflected forms of ein for ‘1’ (none of which is eins) when quantifying a noun. In Japanese there is a native set of numerals from ‘1’ to ‘10’, which is predominantly used as a counting sequence. A fully developed complex numeral system is based on Chinese numerals. Although, according to STORM (2003: 98), there is no clear-cut distinction, the Chinese numerals seem to be used predominantly as cardinal numerals whereas the native set is used as counting words up to ‘10’. For some more examples see GREENBERG (1978: 287) who distinguishes between “absolute forms” (‘counting words’) and “contextual forms” (‘cardinal numerals’); cf. below § I.6.2.4. To be precise, if we specify cardinalities of sets, we use numbers to label the particular properties of sets. Most natural languages have a set of words that meets the requirements for being used as numbers, a conventionalised sequence of counting words. Just like, for instance, the Hindu-Arabic numerals, Roman numerals, or a conventionalised sequence of body parts, the expressions used in the conventionalised counting sequence are (linguistic) instances of numbers. Once we assign them to a particular cardinality, that is, once we employ these tools for specifying a cardinality, they are used as cardinal numerals. While the expressions of the counting sequence are nonreferential and are, just like other instances of numbers, defined only by being in a fixed ordered relation to each other, cardinal numerals are referential expressions because they refer to a particular property of a set, i.e. to its cardinality. Numbers can be assigned in different contexts. While cardinal number assignment specifies the cardinality (the number of elements) of a set, ordinal numerals assign a place within a fixed order to a particular element of a set. STAMPE (1976: 600) considers ordinal number assignment as secondary as compared to cardinal number assignment. This assumption is, however, logically not necessary. The mapping of any ordered sequence of welldistinguished elements onto the elements of a set would be no less immediate if we did this by determining the place in the order of elements (ordinal number assignment) than if we aimed at specifying the cardinality of the set (car-

22

Linguistic numeral systems

dinal number assignment). Yet, in numeral systems (whether linguistic or other) with two distinct sets of forms for cardinal and ordinal number assignment, the ordinals are always the morphologically marked forms, that is, they are always morphological derivatives of cardinals. This may be taken as evidence in support of STAMPE’s claim that cardinal number assignment is cognitively the more basic of the two processes. WIESE (2003: especially 37–42) postulates a third prototypical form of number assignment which she calls ‘nominal number assignment’. This is used for distinguishing elements such as bus lines or the players of a football team. Strictly speaking, what is done in WIESE’s ‘nominal number assignment’ is that a certain order of elements is superimposed on a set of elements which are well-distinguished, but not ordered in a salient way. The use of linguistic numerals in ‘nominal number assignments’ is similar to assigning proper names to the elements of a set (hence the term ‘nominal’). This type of number assignment lacks at least one fundamental aspect of cardinal and ordinal number assignment: in ‘nominal number assignment’ any element of the number sequence may be left out without affecting the efficiency of the system by which numbers label individual entities. For instance, in many cities bus lines or metro train lines are numbered, though not in a consecutive way, i.e. some numbers of the sequence are left out. Or in many sports teams, players may pick any two-digit number although a team has far less than, say, 66 or 99 players. By contrast, both cardinal and ordinal number assignment would be impossible if one element within the sequence were lacking; cf. § I.2.2. Since a tool for ‘nominal number assignment’ does not need to meet the same requirements as tools for cardinal or ordinal number assignment do, other strategies of denomination may equally be employed in these contexts. In some cities, for instance, there are train lines that are not numbered but distinguished by colours, so that the lines are labelled ‘green line’, ‘red line’ and so on. I would therefore argue that WIESE’s ‘nominal number assignment’ is a secondary use of numerals which does not have the same status as cardinal and ordinal number assignment. Cf. also § IV.3.3. In the linguistic literature on numerals, we often encounter several other subcategories of numerals as, for instance, frequentative numerals (‘four times’), multiplicative numerals (‘fourfold’), or distributive numerals (‘four each’). Each of these categories is significant from a morphosyntactic perspective as the respective types of expressions all require very particular types of constructions in their interaction with the quantified expression. Logically however – that is, when it comes to the way in which ‘number’ can be used in language – all these categories are special kinds of cardinal numerals simply because the type of number assignment ultimately determines the cardinality

Cardinal numerals and numbers

23

of a set: frequentatives (‘x times’) determine the cardinality of occasions, multiplicatives (‘x-fold’) determine a size by referring to the cardinality of predefined units of measurement and distributives (‘x each’) specify the cardinalities of several sets of equal size. That is, with respect to the types of number assignment for which numerals are employed, the possible categories are cardinal, ordinal, and perhaps, taking the reservation expressed above into consideration, also nominal number assignment. Morphosyntactic properties of particular expressions (or of their derivates) justify a sub-classification of multiplicative, frequentative and distributive numerals in morphology and syntax, but when it comes to a merely logical distinction of types of number assignment, these categories are not relevant. (Cf. the summary in § I.6.2.3.) Ordinals will find special mention only in § II.8 but since this study focuses on cardinal numerals, both ordinal and nominal number assignment will otherwise be treated only marginally. In the same manner, the aforementioned cardinal subcategories will largely be disregarded; cf. § V.4. For the sake of convenience, when I use the terms ‘numeral’ and ‘number’ from now on without further specification, they refer to cardinal numerals and cardinal numbers.

I.2.4

Numbers are infinite, numerals are not

When defining ‘number’, another necessary property is usually mentioned. In addition to being well-distinguished and forming an ordered sequence, it is often said that the set of (natural) numbers is infinite; cf. WIESE (2003: especially 58). I have left this property out of consideration here because linguistic numeral systems, in spite of their potentially great scope due to their recursive principles (for which see below §§ I.3, I.4.3 and III.2.1), must necessarily remain finite. Every numeral system of a natural language has a highest expressible number. It is impossible for the set of systemic cardinality expressions (which still remains to be defined properly; cf. below § I.4) to exceed a certain ‘limit number’ L; cf. GREENBERG (1978: 253–254, G 1 and G 2).3 To a large extent, the scope of a numeral system is determined by the cultural and scientific needs of a language community. For instance, in the European languages expressions like million, billion, etc., whose introduction 3

There is, in my view, no other account of cross-linguistic constraints on numerals and numeral systems which is as descriptively adequate as that of GREENBERG (1978). GREENBERG’s 39 generalisations on numeral systems are of fundamental relevance for my study, particularly for this chapter. For the sake of simplicity, I will refer to the generalisations in GREENBERG (1978) as “G 1”, “G 2”, etc.

24

Linguistic numeral systems

expanded the scope of the respective numeral systems enormously, did not come into use before the rise of modern science. And even in a scientific register of a contemporary language, the strategies inherent in any numeral system for expressing extremely high numerical values – however flexible and far-reaching – still remain limited. In this respect, the universally limited scope of numeral systems is as such not very remarkable. Moreover, it is often difficult to determine the limit number L for numeral systems with an extremely large scope. Nevertheless, as a theoretical prerequisite of a numeral system, the assumption of a ‘limit number’ L is necessary. (Cf. §§ II.7.3, III.1.1, III.3.3 and V.2.5.1, where extremely high valued numerals such as million and billion will again be at issue.) Thus we postulate a limit number L for every numeral system because only a limited number of numerical values can be expressed by means of the respective numeral system (GREENBERG 1978: 254, G 2). This does not rule out the fact that a language has no means to express numerical values beyond this point (n ≥ L). At the same time any natural language has a number of alternatives, i.e. non-systemic strategies for specifying cardinalities of sets. Such alternative strategies may or may not be capable of expressing a numerical value n ≥ L. (Cf. § III.3.3 for such strategies in Old English.) The whole problem arises because, theoretically, the set of natural numbers is infinite. Since there may be infinitely large sets of discrete elements, the set of cardinalities of sets must necessarily be considered infinite. The tools humans use for number assignment, however, are not infinite if alone for technical reasons. WIESE acknowledges this restriction by saying that natural numbers must only be potentially infinite (2003: 58, n. 5 and 77). With this modification, the property ‘infinity’ (or rather: potential infinity) does apply to any kind of system used in number assignment. This aspect is, however, not ultimately relevant in our context. On the contrary: it is impossible for linguistic numeral systems to achieve infinity simply because no language can possibly have an infinite set of expressions or infinitely complex numeral formations. It is reasonable, therefore, if we restrict ourselves to our two defining features of numbers: within one system, numbers are well-distinguished and form an ordered sequence. (Cf. the short summaries in §§ I.6.3.1–2.) I.2.5

Outlook

Accepting the view on numbers outlined in this section as a theoretical prerequisite will have a great impact on the study of numerals as linguistic expressions and also on linguistic numeral systems. The remaining parts of this chapter will be based on this approach to numbers and numerals. Throughout

Cardinal numerals and numbers

25

the book, we will repeatedly come across instances and phenomena for which exactly this approach proves most helpful both to unambiguously delimit cardinal numerals from other quantifiers – whether numerically specific or unspecific – and, furthermore, to explain quite a number of synchronic and diachronic properties of numerals and numeral systems in natural languages. Let us recall again that the points raised in this section apply to all types of number representations, that is to body parts, written characters, linguistic expressions etc. in more or less the same way. We are soon going to continue our discussion of linguistic numeral systems. Much of what will be outlined in the following will similarly hold true for non-linguistic numerals such as, for instance, the Hindu-Arabic number notation. Naturally, there are also some differences between linguistic and other numerals. One of the more significant differences particularly between the Hindu-Arabic number notation and other systems is the lack of a sign representing the empty set (‘zero’) in linguistic numeral systems. We will briefly discuss this point below in § I.3.4.3. A number of other differences among these systems are often simply due to the fact that they are based on different media (language, writing, gesture, etc.) and to the fact that, as a consequence, these types of systems naturally evolve in different ways cross-culturally. Such differences, however, do not generally affect the way in which linguistic numerals as well as other systems all work as tools in number assignment. We will see in the next section how particularly linguistic numeral systems are composed cross-linguistically. The focus of our discussion will now shift back to linguistic number expressions and it is the ‘numeral’ as a linguistic expression that I generally refer to when I speak of ‘numerals’ or ‘numeral systems’. I.3

The basic components of numeral systems

I.3.1

Simple numerals

Linguistic numeral systems are remarkably uniform cross-linguistically. Overt differences in numeral systems across languages are – in comparison with the properties of other lexical categories – relatively few and moderate. This can be explained by what we discussed in the previous section: both the logical and the cognitive requirements for the internal structure of numeral systems – i.e. to be an ordered sequence of well-distinguished entities – are crossculturally uniform.

26

Linguistic numeral systems

The simplest conceivable set of numerical expressions in a language is a set of simple (i.e. mono-morphemic) forms with an arbitrary phonological shape. In fact, almost every natural language has a certain number of cardinality expressions that are simple arbitrary forms. In Present-day English for instance, the following expressions of the numeral system are simple forms and their phonological shape is, analysed synchronically, arbitrary, as shown in Figure 2.4 ‘1’

‘2’

one

two three

Figure 2.

‘3’

‘4’

‘5’

‘6’

‘7’

four

five

six

seven

‘8’

‘9’

eight nine

‘10’

‘11’ ‘12’

ten

eleven twelve

Arbitrary and mono-morphemic numerals in Present-day English

However, only very few natural languages have a system consisting exclusively of simple and arbitrary numerals; cf. GREENBERG (1978: 255, G 4). The largest attested scope of such a simple numeral system is necessarily small: there are few languages in which the number of cardinal numerals does not exceed four (cf. GREENBERG 1978: 256). Geographically, these languages seem to cluster in Australia. It may be debated whether these expressions can be considered numerals at all. From a morphosyntactic perspective, they are often classified as indefinite pronouns (cf. HALE 1975; DIXON 1980: 107–108; 2002: 67 and the discussion in VON MENGDEN 2008: 305–306). If the focus of an analysis is on the function of quantification, it is actually of secondary importance whether these expressions are used primarily as indefinite pronouns or whether they are etymologically derived from indefinite pronouns. Once these expressions are used for cardinal number assignment, they are at least numerically specific quantifiers in the sense of our initial categorisation in § I.1. (cf. Table 2). The notion of ‘simple numerals’, however, becomes relevant by its contradistinction to ‘complex numerals’. This distinction requires a more complex numeral system to have developed in a language; cf. VON MENGDEN (2008).

4

The way the relation between ‘number’ and its corresponding linguistic expression is graphically represented here and in many other figures, particularly in Chapter II, is adopted from HURFORD (1975) although my theoretical approach to numerals is considerably different from HURFORD’s.

The basic components of numeral systems

I.3.2

27

Complex numerals

The need to memorise every single arbitrary form makes a numeral system that consists only of simple, mono-morphemic expressions as in Figure 2 highly inefficient once the range of expressible cardinalities exceeds a certain size. In order to be able to express higher numerical values, the vast majority of languages have developed numeral systems more complex than those consisting of simple lexical representations only; cf. DETGES (2003: 50–51). In such complex numeral systems, the existing simple numerals are employed as constituents of morphosyntactic combinations.5 For instance, the English numeral six-teen ‘16’ is a combination of six ‘6’ and (a variant of) ten ‘10’. By introducing the possibility of such combinations into the system of a language, the number of linguistically expressible cardinalities multiplies considerably. Hence, most numeral systems consist of a comparatively small set of arbitrary forms – sufficiently small to be memorised easily – which can be combined systematically in order to generate a large number of transparent and analysable linguistic expressions for numerical values. Semantically we can describe these combinations as follows: each simple numeral represents one particular numerical value while the morphological combinations of these expressions represent arithmetic operations. In our example, sixteen is formed as an addition of ‘6’ and ‘10’. The most common types of arithmetic operations employed in numeral systems of natural languages are addition and multiplication but subtraction, division and exponentiation also occur. GREENBERG (1978: 257–258, G 9 and G 10) mentions some implicational generalisations about the occurrence of these different types of operations according to which the use of addition presupposes the use of multiplication and the use of inverse operations (subtraction and division) presupposes the use of both direct types of operations (addition and multiplication). The arithmetic operators involved may or may not be overtly expressed. For instance, in Present-day English the expression twenty-two combines the elements twenty ‘20’ and two ‘2’ without overtly indicating that the result is an addition of the two values. This used to be different in Old English where the corresponding expression twa and twentig ‘2 + 20’ contains the connective and indicating the operator ‘+’. Often the operators do not need to be expressed because other strategies suffice to indicate which type of arithmetic 5

In the context of the formation of complex numerals I use the term ‘morphosyntactic’ in a wide sense, i.e. referring to any strategy that may be interpreted either as morphological, syntactic, or on the interface of the two levels of linguistic description. For the difficulties in unambiguously assigning the formation of complex numerals to either of the two domains, cf. §§ I.3.6 and III.1.3.

28

Linguistic numeral systems

operation is underlying a particular formation. Such strategies may be, for instance, the order of the constituent or specific variants of individual numeral forms (cf. § I.5.3). If the operator is overtly expressed, there are several typical lexical sources for the expression representing the operator across languages, such as ‘and’, ‘with’ for addition, ‘upon’ for multiplication, ‘from’ for subtraction, etc. The different lexical strategies for arithmetic operators are not primarily relevant in our context so that it may suffice here to refer the reader to more detailed typological descriptions of these strategies as for instance in STAMPE (1976), GREENBERG (1978), HANKE (2005), among others. What will be of central importance is that the primary elements of a numeral system are the simple numerals and that these simple numerals are employed as constituents of complex numerals. Thus what basically constitutes a numeral system of a natural language are the following two types of components: (1.2) Components of a numeral system: A numeral system consists of a. a set of mono-morphemic, arbitrarily shaped numeral forms (simple numerals) and of b. a set of syntactic (or morphosyntactic) rules which combine these simple numerals into more complex numerals by means of semantically underlying arithmetic operations.

What this description implies is that a numeral system generates new expressions from an existing stock of elements. The underlying rules are recursive rules in the sense that a numeral system contains elements that are themselves composed of elements of the same system. For instance, in our example above we combined the elements six ‘6’ and ten ‘10’ to six-teen ‘16’ by means of an addition of the two numerical values. The result is a numeral which itself can be employed in the generation of more complex expressions, for instance in hundred and sixteen ‘100 + (6 + 10)’. The recursive principle for the formation of complex numerals implies that every complex systemic numeral has the following structure: NUM

→ NUM + NUM

The basic components of numeral systems

29

The general arrangement of elements of the entire numeral system is determined by the recursive principle. The various strategies and aspects of the recursive principle underlying numeral systems will be described in the remaining parts of this chapter (cf. further § III.2.1). The more general, crosslinguistically valid considerations of features and properties of numeral systems will prepare the ground for a description of the numeral system of Old English provided in Chapters II and III. For the sake of convenience, most examples in the following are taken from Present-day English. The way these complex numerals are generated across languages strongly suggests a subdivision of simple numerals into ‘atoms’ and ‘bases’. Precise and cross-linguistically valid definitions of these notions will be provided further below (§§ I.3.4–5). It makes sense to introduce the two terms at this point in a preliminary manner. Usually, though not always, in a complex numeral, at least one base is combined with at least one atom. For the numeral systems of the Germanic languages we can say that, to the right of the arrow in the above structure of complex numerals, each syntagmatic slot is occupied either by a particular base or by any element of the sequence of atoms. However, a base is never combined with just one atom but always with a paradigmatic choice out of the entire sequence of atoms. In Present-day English, for instance, the atomic numerals represent the numerical values ‘1’, ‘2’, ‘3’, up to ‘9’, and the most common base numerals represent the numerical values ‘10’, ‘100’, and ‘1,000’. (To illustrate this relation of the major two types of simple numerals, we will have to leave idiosyncratic forms like English eleven and twelve out of consideration for the moment; they represent a particularity which will be treated in §§ I.5.2 and II.3). Thus, the Present-day English expressions fourteen, fifteen, and sixteen represent the arithmetic operations ‘4 + 10’, ‘5 + 10’, and ‘6 + 10’ respectively. Both morphosyntactically and arithmetically, all these expressions share the structure ‘n + 10’. In the subsequent decade, the same atoms recur in the same order, constituting the addends to a multiple of the base. The expressions twenty-four, twenty-five, and twenty-six represent the arithmetic operations ‘20 + 4’, ‘20 + 5’, and ‘20 + 6’ respectively. These examples show that the atoms occur in paradigmatic sequences. In other words, whenever one atom occurs (say, five) in a particular combination (say, twenty-five), then all the other atoms from one to nine occur in the same morphosyntactic slot and also (as a consequence of our definition in § I.2) in the same order. This arrangement allows us to (preliminarily) interpret atoms as the variables and bases as the constants in any combination of the two types. What I have shown so far are the following crucial points: complex numerals are based on arithmetic operations that usually contain at least one base

30

Linguistic numeral systems

and at least one atom. Where an atom occurs, the same syntagmatic slot can generally be occupied by every element of the sequence of atoms. Some authors refer to these (sub)sequences as ‘packs’ (HURFORD 1975, 1987; SEILER 1990), but since we are dealing with both the same set of elements and the same order of these elements and since the fixed order of the sequence of atoms is of crucial importance, I prefer to employ the term ‘(sub)sequence’. Recall that in § I.2.2 we already established that the elements of a numeral system as a whole form an ordered sequence. This entails that any subsequence – like the sequence of atoms that we are dealing with at this point – necessarily has a fixed element order itself. In the next section we will briefly examine the arithmetic operations that are the basis from which the complex numerals are formed (§ I.3.3). We will then be in a position to offer a more exact and cross-linguistically valid definition of the central notions ‘atom’ and ‘base’ (§§ I.3.4–5). I.3.3

Arithmetic operands

If, as we just said, the sequential arrangement of some constituents of the combined numeral forms allows us to distinguish between constants and variants in the underlying arithmetic operations, then we might infer from this description that the two elements of an arithmetic operation perform different roles. If we were dealing with the mathematic aspects of the underlying arithmetic operations alone, there would be no difference between the two values of an addition or the two values of a multiplication. Because of the associativity of addition and multiplication, re-arranging the constituent order would not make a difference to the result of the operation. In linguistic numeral systems however, the two constituents of such a combination, in addition to the underlying arithmetic operation, also stand in a morphosyntactic relation to each other. That is, the element order of the two values in addition and in multiplication is potentially, though not necessarily, significant. It therefore makes sense to distinguish between the variables within a sequence of additions – which we call ‘addends’ – and the respective constants – referred to as ‘augends’. Thus, in any sequence formed by an addition (e.g., four-teen ‘4 + 10’, fif-teen ‘5 + 10’, six-teen ‘6 + 10’, etc.) we can say the numerical values represented by the atomic numerals appear as continuously recurring ‘addends’ and the basic numerical value ‘10’ (or any multiple of it) as the respective ‘augend’. The same distinction is necessary for combinations based on multiplication. In the same sense, we will have to employ the terms ‘multiplicand’ and

The basic components of numeral systems

31

‘multiplier’ for sequences of multiplications. Again this distinction implies that, within a multiplication, the ‘multiplicand’ is the constant (a base or one of its multiples) and the ‘multiplier’ will be a variant in the form of the recurring sequence of atoms, as for instance in the sequence one hundred ‘1 × 100’, two hundred ‘2 × 100’, etc. up until nine hundred ‘9 × 100’. The underlying arithmetic operation would then be ‘n × 100’. Both terminological pairs – ‘augend’ / ‘addend’ and ‘multiplicand’ / ‘multiplier’ – were first used by GREENBERG (1978) in the context of linguistic numeral systems. GREENBERG (1978: 266) further distinguishes between ‘sporadic augends’ / ‘sporadic multiplicands’ and ‘serialised augends’ / ‘serialised multiplicands’. What GREENBERG means by ‘serialised’ is that the augends or multiplicands are combined with the same series or sequence of numerals but not sporadically with individual numerals. The way we have just described the notions ‘augend’ and ‘multiplicand’ makes it actually seem unnecessary to introduce the feature ‘serialised’ for arithmetic operands. This is because in English, as well as in most other European languages, any augend and any multiplicand is a serialised augend or multiplicand because every augend or multiplicand is combined with the same (sub)sequence of atomic numerals over and over again. However, there are numeral systems that are not arranged as smoothly as that of, say, Present-day English in this respect. In order to illustrate this point (and at the same time to prepare a more precise and cross-linguistically valid definition of ‘atom’ and ‘base’), let us have a brief look at a particular variety of the numeral system of Modern Welsh. In this system one counts up to ‘15’ in a fairly expectable way, that is, there are simple expressions up to ‘10’ and complex forms based on additions on ‘10’ from ‘11’ onwards. Hence, ‘15’ is expressed as bym-theg, which can be segmented as ‘5 + 10’ just like English fif-teen. The less regular section begins with ‘16’. The expressions for ‘16’, ‘17’, and ‘19’ – un ar bymtheg ‘1 + 15’, dau ar bymtheg ‘2 + 15’, pedwar ar bymtheg ‘4 + 15’ – all employ the expression for ‘15’ as an augend to the atomic addends ‘1’, ‘2’, and ‘4’ with deunaw ‘18’ being an idiosyncratic expression composed as ‘2 × 9’. In the three expressions for ‘16’, ‘17’, and ‘19’, bymtheg ‘15’ is used as a serialised augend, but at no point in the numeral system is bymtheg ‘15’ employed as a multiplicand (cf. KING 1993: 113–114, §§ 164–165 and, for a corresponding sequence in Breton, SEILER 1990: 201). Also, the value ‘9’ in the expression deunaw ‘2 × 9’ serves as a multiplicand; however it serves as a multiplicand to just one multiplier in a somewhat unsystematic way rather than to a sequence of multipliers. The example of Welsh shows us two things: while in English all the augends also serve as multiplicands, in Welsh we have an augend, bymtheg

32

Linguistic numeral systems

‘15’, that is not used as multiplicand anywhere in the counting sequence. Secondly, while in English all augends and all multiplicands are, at the same time, serialised augends and serialised multiplicands and sporadic combinations do not occur, Welsh has a multiplicand which is not a serialised multiplicand: -naw ‘9’. In order to use a terminology that covers cases like these, GREENBERG’S distinction between ‘sporadic augends’ / ‘sporadic multiplicands’ and ‘serialised augends’ / ‘serialised multiplicands’ is generally necessary. (On the notion of ‘serialised’ operands see also § III.2.1 and the summary in § I.6.3.3.) I.3.4

Bases

I.3.4.1

Defining a base

We should now be in a position to define the notions ‘base’ and ‘atom’ in such a way that it also applies to numeral systems like that of Welsh and some other languages in which the counting sequence is arranged somewhat less regularly than in English. In English, we said ‘10’ is the lowest base and at the same time ‘10’ is used as a serialised augend and as a serialised multiplicand. The set of nine atoms continuously recurs either as addends (thir-teen ‘3 + 10’, four-teen ‘4 + 10’, fif-teen ‘5 + 10’, etc.) or as multipliers (twen-ty ‘2 × 10’, thir-ty ‘3 × 10’, for-ty ‘4 × 10’, etc.). Another example which is mentioned quite frequently in the typological literature on numerals is the system of the Sora variety of Munda (AustroAsiatic). This numeral system is basically vigesimal. Within each vigintiad, the expression for ‘12’, miggǝl, is the highest simple expression and is used as an augend, so that the first twelve elements within each higher vigintiad are expressed as ‘(n × 20) + m’, and the 13th to 19th expression of each set of 20 is expressed as ‘(n × 20) + 12 + m’ with the atomic numerals from ‘1’ to ‘7’ used as addends to the augend ‘12’ (STAMPE 1976: 601). So, for example, ‘39’ is expressed as bɔ-koṛi-miggǝl-gulji of which the underlying arithmetic operation is ‘(1 × 20) + 12 + 7’. What is relevant for our point is that, in the Sora numeral system, there is never a sequence of twelve elements immediately followed by another set of twelve. Instead, there are continuously recurring vigintiads, each of which consists of a set of 12 elements plus the remaining eight elements (seven additions on ‘12’ and a multiple of ‘20’). Thus in both Welsh and Sora the continuously recurring sequences are always sets of 20 elements, irrespective of the fact that each vigintiad is separated into two subsets (in Welsh a subset of 15 and one of 5 elements, and in

The basic components of numeral systems

33

Sora, a subset of 12 and a subset of 8 elements). ‘15’ in Welsh and ‘12’ in Sora may, therefore, be used as serialised augends but not as multiplicands. In Welsh, the lowest element that performs the function of a serialised multiplicand is ‘20’. Neither the serialised augend ‘15’ nor the sporadic multiplicand ‘9’ are used as multiplicands for all elements of the continuously recurring ordered subsequence of atoms. The reason why this needs to be made explicit is that it is this very property of an arithmetic operand in a numeral system that defines the base of a system. The crucial typological difference between the numeral systems of Sora and Welsh on the one hand and that of English on the other is that in English, the smallest continuously recurring ordered subsequence (the expressions from ‘1’ to ‘9’) consists of simple (mono-morphemic, arbitrary) elements only, whereas in Welsh and Sora the smallest continuously recurring ordered subsequence contains both simple elements and elements that are combined forms based on arithmetic operations. The fundamental significance of the smallest continuously recurring ordered subsequence has (to my knowledge) first been acknowledged by SALZMANN (1950: 81) who speaks of a “cyclic pattern” in the arrangement of numeral systems. STAMPE (1976: 601) probably has the same idea in mind when he defines the base as “that number from which counting starts over”. It is this feature of numeral systems which is most essential for defining a base. On this assumption, a cross-linguistically valid definition of a ‘base’ of a numeral system is presented in (1.3): (1.3) Definition of ‘base’ In any formation pattern of a numeral system, bases are those elements with which the smallest continuously recurring sequence of numerals is combined.

By contrast, GREENBERG (1978: 270) simply says that “a serialized multiplicand is a base”. The difference between GREENBERG’s definition and mine is probably only one of perspective. It is conceivable that there are numeral systems in which an element is used as a multiplicand to a small sequence, but not to a continuously recurring sequence. However, judging from GREENBERG’s description, we can infer that there is no language in which this phenomenon occurs. If this holds, then my definition proposed in (1.3) actually covers exactly the same type of elements in the numeral systems of natural languages that GREENBERG’S definition covers. If such a language does exist, then I infer from my reading of GREENBERG (1978) that his definition is

34

Linguistic numeral systems

probably meant to exclude such cases, as he discusses the Sora numeral system in this context (1978: 270). (Cf. the summary in § I.6.3.2.) I.3.4.2

Terminological problem I: bases vs. operands

In defining a ‘base’ of a numeral system in (1.3), I aimed for a definition that is cross-linguistically valid and therefore as precise as possible. Introducing such a definition causes terminological problems in so far as the term ‘base’ has been used in various senses which deviate from GREENBERG’s notion – only slightly when it comes to describing the properties of the notion but with quite a considerable impact for the description of numeral systems. I cannot go into details here, but, if alone in order to justify my insistence on a narrow definition of ‘base’ in the Greenbergian sense, I would like to comment on this problem briefly. Joseph GREENBERG has formulated a couple of generalisations on numeral systems. However, he has done this on the basis of his narrow definition of ‘base’ and also on his distinction between two primitive types of elements in the numeral system, ‘bases’ and ‘atoms’ on the one hand and, on the other, the various types of arithmetic operands we introduced above in § I.3.3. For instance, GREENBERG’s generalisation G 21[b] (1978: 270) states that “[a]ll bases of a numeral system are divisible by the fundamental base”, with a fundamental base being the smallest base of a system (on the notion ‘fundamental base’ cf. below §§ I.3.4.3 and III.2.2). In English for instance, ‘100’, and ‘1,000’ are divisible by the fundamental base ‘10’. This generalisation is valid cross-linguistically as long as we remain faithful to the narrow definition of a base. However, probably because in English the ‘bases’ ‘10’, ‘100’ and ‘1,000’ are all both augends and multiplicands and because all augends and multiplicands are serialised operands, a ‘base’ has occasionally been taken as any augend and any multiplicand. In order to include ‘serialised augends’ as attested in Welsh and Sora, SEILER (1990: 192–193; repeated in 1994: 145–147) explicitly extends GREENBERG’s notion of a ‘base’ and includes cases of serialised augends. Similarly, COMRIE (2005b) defines a ‘base’ simply as “that numerical value to which various arithmetical operations are applied” (2005b: 207). In other words, COMRIE takes any augend and/or any multiplicand as a base. On this basis, COMRIE (2005b: 221–222) tries to reject the universality of GREENBERG’s generalisation, but does not take into account that GREENBERG employs a different notion of ‘base’ than he does. One consequence is that COMRIE (2005b: 211) calls ‘15’ in Welsh and ‘12’ in Sora

The basic components of numeral systems

35

‘bases’. This is of course perfectly in accordance with his, i.e. COMRIE’s, definition but COMRIE’s approach generally deprives us of a way to treat the quite significant difference between the functions which the elements ‘12’ and ‘15’ perform in the two respective numeral systems on the one hand and, on the other, the role that the value ‘20’ plays in these systems. Another consequence is that, for COMRIE , a wide variety of types of numeral systems do exist (such as e.g. a 32-based system in Ngiti; Nilo-Saharan; COMRIE 2005b: 211), whereas for GREENBERG (2000: 773b) only quinary, decimal, duodecimal and vigesimal bases are attested.6 A more useful approach is that by LUJÁN (1999a: 184–187, § 1.2 – which includes a valuable discussion of the problem; see also LUJÁN 2006: 77 and LUJÁN 2007: 43–58). LUJÁN, while basically following SEILER in favouring a looser use of the notion ‘base’ (1999a: 184), generally acknowledges the differences pointed out here. LUJÁN speaks of ‘proper bases’ (serialised multiplicands, i.e. bases in GREENBERG’s sense and in the way I employ the notion here) and ‘improper bases’ (serialised augends). While this distinction would cover the more difficult cases discussed above, LUJÁN’s distinction overlooks one fundamental aspect. LUJÁN’s ‘improper bases’ have a salient function with respect to the arithmetic operations they are involved in. But, other than his ‘proper bases’, they do not play a salient role in the overall arrangement of the entire system. For instance, they do not play a role in determining the type of numeral system and they are not in a complementary relation to the continuously recurring sequences that exist in all complex numeral systems of natural languages. For this reason, I would still consider GREENBERG’s terminology the most beneficial one as it not only covers all elements in more difficult numeral systems like the Welsh or the Sora system, but also draws a clear distinction between types of arithmetic operands (sporadic/serialised augend/multiplicand) on the one hand and landmark-like elements in the arrangement of a system around which the overall recursive principle of a numeral systems is centred (bases) on the other. Further arguments in favour of a narrow, i.e. GREENBERGian notion of ‘base’ will be provided below in § III.2.1.

6

I would like to concede that, in a different publication, COMRIE offers a more precise definition of a base where he writes that a ‘base’ is “the value n such that numeral expressions are constructed according to the pattern …xn + y, i.e. some numeral x multiplied by the base plus some other numeral” (COMRIE 2005a: 530a). However later on in the same text (2005a: 531a), when discussing the “mixed system” of two Niger-Congo languages, he calls any serialised augend a base and thus employs the term ‘base’ in the sense of the wider definition offered in (2005b).

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I.3.4.3

Terminological problem II: a mathematician’s base

According to what we have said so far, the bases of the numeral system of Present-day English are ten, hundred, thousand, and accordingly also million, billion and perhaps – depending on the register – some other simple expressions representing even higher powers of ‘10’ (but cf. the discussion below in § II.7.3 in this respect). A mathematician (or, for that matter, a logician) would probably object by saying that a decimal system has just one base, i.e. ‘10’, in the same way as the binary system has just one base, ‘2’, a quinary system has one base, ‘5’, and so on. The problem here is that much of our mathematical thinking is nowadays – whether consciously or subconsciously – not based on our linguistic expressions, i.e. not on the type of numeral system we are dealing with in this book but on the written number symbols that we use, i.e. the Hindu-Arabic numerals. This intuitive approach to numbers is reflected in COMRIE’s assumption that an “ideal” numeral system “should mirror closely the way numbers are written by means of figures” (COMRIE 2004: 138). This view represents a primacy of one particular written system over all other systems – whether spoken, written, or other – which is unfounded both theoretically and historically. Moreover, it disregards that there is one general typological difference between the Hindu-Arabic written notation and virtually all other common numeral systems of whatever type: the Hindu-Arabic system contains a symbol for the empty place, i.e. 〈0〉.7 In the Hindu-Arabic notation, we may, therefore, use a complex form in which one place has no value, i.e. 〈10〉, once the sequence of atoms is used up. If mathematicians argue that ‘10’ is the base of a decimal system, what they mean is simply that ‘10’ is that number value from which subsequently the sequence of simple and arbitrary symbols – i.e., {〈1〉, 〈2〉, 〈3〉, …, 〈9〉} – is used up and from which subsequently we need to form complex symbols by combining two atoms. The problem for spoken number signs is that – while in a linguistic decimal system the sequence of atoms is likewise used up, i.e. {/wVn/, /tu;/, /θri;/, /fO;r/, /faIv/, …, /naIn/} – there is no insignificant digit to be combined with an atom. We therefore need to employ a different type of simple numeral which, simply because there is no such empty element, again needs to be of a simple and arbitrary shape, for instance

7

I am aware of only two more number notation systems employing a symbol for the empty place: the Incan quipu system – in which different types of knots are employed to represent numbers – and the Mayan notation.

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37

/ten/. This element can then be used – with some formal variation8 – as an augend (thir-teen, four-teen, etc.) and as a multiplicand (twen-ty, thir-ty) in the way we have described it earlier in this section. The same problem arises again when all the possible two-place combinations are used up. In the HinduArabic notation we can simply form a three-place symbol with two empty elements: 〈100〉. Again for want of an empty element, the speaker of a language will have to introduce another simple and arbitrary expression of the same type as the first ‘base’. In Present-day English this would be hundred. What I have tried to point out is that a decimal system of whatever kind always has the base ‘10’. However, the mathematician can operate on the basis of the Hindu-Arabic number symbols and may, therefore, benefit from its major advantage – the insignificant digit expressed by 〈0〉. The speaker of a language can only draw on linguistic numeral systems. Linguistic numeral systems (not languages in general) universally lack a sign for the empty set and therefore employ a sequence of atoms and an additional set of simple expressions. In other words, in the Hindu-Arabic place value notation, which employs the symbol 〈0〉 for the integer ‘zero’, the relevant sign can be used to represent an empty place, as e.g. in 〈10〉, 〈70〉, 〈407〉, etc. Such a device does not exist in any linguistic numeral system (cf. GREENBERG 1978: 255; G 3).9 In the Hindu-Arabic notation it is not only the fundamental base ‘10’, but also any of its powers (〈10〉, 〈100〉, and 〈1000〉) which are expressed by using the same two symbols, 〈1〉 and 〈0〉. By contrast, linguistic numeral systems require individual expressions for these concepts, as e.g. ten, hundred, thousand, million, etc. in Present-day English. As long as we are dealing with linguistic numeral systems (rather than with the Hindu-Arabic written numerals) it is, therefore, perfectly acceptable to call all members of this second category of simple expressions indiscriminately ‘bases’. Following GREENBERG (1978: 270) again, we may call the lowest base of a linguistic numeral system – the one that corresponds most closely with the base of a system written in 8

We will discuss the variation in the various forms of the numerals below in § I.5.3. Let us for the moment accept that variants such as ten and -teen and -ty all represent the same entities of the systems.

9

The Chinese expression lìhng is often mentioned in this context as an exception to this universal. lìngh ‘0’ is indeed used for the empty element, but only in cases where both a higher and a lower constituent is non-empty, as for instance in ‘107’, which is expressed as yāt baak lìhng chāt, i.e. as ‘(1 × 100) + 0 + 7’. It is not used, however, to express bases or their multiples, as in ‘10’ or ‘100’; cf. MATTHEWS/YIP (1994: 385). These are all represented by simple expressions. Therefore, Chinese does not deviate in this respect from what can be observed cross-linguistically. The fact that bases of numeral systems are genuine one-place expressions can thus be seen as a true universal.

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Hindu-Arabic number signs – the ‘fundamental base’. This point will be resumed below in § III.2.1. The terminological difficulty is, therefore, not due to different ideas of numeral systems between mathematicians and linguists. It is due to a particular feature of the nowadays universally used Hindu-Arabic system of written numeral signs, which makes the difference: the symbol for an empty place. In fact, other written numeral systems share this disadvantage with linguistic numeral systems. Roman numerals do not have an empty element with the consequence that, for each power of ‘10’, a new simple symbol needs to be introduced: 〈X〉 for ‘10’, 〈C〉 for ‘100’, 〈M〉 for ‘1,000’. Of course, all this is not to say that no language has an expression for the numerical value ‘zero’. What is meant is that there is no natural language in which a relevant expression is part of the numeral system (GREENBERG 1978: 255; G 3). In other words, while expressions like zero and corresponding expressions in other languages may be part of the lexicon of a language, none of these expressions in any language is used within complex numerals and, hence, none of them takes part in the recursive system that generates complex cardinal numerals (cf. § I.4 below). I.3.5 Atoms As a preliminary description, we said that ‘atoms’ are the variants in arithmetic operations (§ I.3.2). We also said that for a numeral system like that of English, this description is sufficient. Again, our short discussion of the numeral systems of Welsh and Sora in §§ I.3.3 and I.3.4.1 shows us that in some languages the matter is slightly more complicated. While looking at these two numeral systems, we were able to identify a continuously recurring sequence of elements. On the basis of this, we developed a definition of the notion ‘base’. In English and all other Germanic languages, we can say that the expressions constituting this smallest continuously recurring sequence are the atoms from ‘1’ to ‘9’. Taking into account that in some numeral systems the continuously recurring sequence of elements is more complicated than a mere sequence of mono-morphemic expressions, SEILER (1990: 190) defines ‘atoms’ as “that particular set of numerals that has the highest potential of being recursively used in cycles or with bases”. By saying that ‘atoms’ have the highest potential to recur continuously (or, in SEILER’s terms: cyclically), SEILER concedes that in some languages a number of complex expressions need to be added to the sequence of atoms in order to form a continuously recurring sequence.

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39

Two more aspects need to be taken into consideration when adopting SEILER’s approach. One is that atoms are always morphologically simple expressions. If this restriction were not made, then our criteria would apply to virtually any type of addend in the system and the notion would become too unspecific to be of any value. The second point that needs to be modified is that atoms can be combined not only with the bases themselves but also with multiples of bases, as for instance in the sequence from six-ty-one ‘(6 × 10) + 1’ to six-ty-nine ‘(6 × 10) + 9’. With these two additional features in mind, we will be able to slightly rephrase SEILER’s definition and thus arrive at a precise and cross-linguistically valid definition of ‘atom’: (1.4) Definition of ‘atom’ Atoms are those morphologically simple elements of numeral systems that have the highest potential to form a continuously recurring (sub)sequence of numerals in combination with bases or their multiples.

It should be noted at this point that there is some terminological confusion in the relevant literature with respect to the use of the terms ‘atomic numeral’ and ‘simple numeral’. GREENBERG (1978: 256 and 2000: 773a) takes the indivisibility of both elements as the major criterion. He therefore subsumes both bases and our ‘atomic numerals’ under the label ‘atom’. Our ‘atomic numerals’ are referred to by GREENBERG as ‘simple atoms’. The problem is that both types of elements are ‘atomic’ – in the sense that they both cannot be split into smaller morphological (or arithmetic) constituents – and both are, at the same time, ‘simple’ – in the sense that they are (synchronically) mono-morphemic. SEILER (1990: 190, § 4.1), therefore, in the context of his definition quoted above, deviates explicitly from GREENBERG. I follow SEILER and others employing ‘simple numerals’ as a generic term for both types of primitive elements of numeral systems, ‘atoms’ and ‘bases’. Cf. also Tables 3 and 4 below and the discussions in § I.5.2 and in § I.6.3.2. For a comprehensive discussion of the properties of simple numerals cf. SEILER (1990: 190-6). I.3.6 Complex numerals: a case of syntax or morphology? Naturally, the expressions resulting from the combinations of atoms and bases have a more complex morpheme structure than the simple forms on which these combinations are based. Employing the standard categories in the canonical descriptions of word-formation processes, complex numerals can be

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affixations or compounds. The dividing line between affixations and compounds in the context of numerals may vary from language to language and in many cases this line may in fact be difficult to draw (cf. § III.1.3). Also, the question of whether a particular case of a complex numeral is morphologically a genuine compound or rather a phrase is difficult to answer. A potential solution may, for instance, be influenced by the orthographic conventions of a particular language. Although orthographic conventions are not a reliable measure for assigning a structure to the realm of either syntax or morphology, the varying spelling conventions in Present-day English and German for the respective expressions representing the numerical value ‘5,371’ in (1.5)a and (1.5)b may be employed to simply exemplify the problem. (1.5)a

five thousand three hundred and seventy-one

(1.5)b

fünftausenddreihunderteinundsiebzig

Although the same number value is represented by the two expressions, the English expression in (1.5)a is conventionally spelled as a juxtaposition of several phrases forming one superordinate phrase, whereas the German expression in (1.5)b is, by convention, spelled as one single lexeme. Structurally, however, the two complex numerals are formed more or less in the same way (the different element order of the constituents seventy-one ‘70 + 1’ and einundsiebzig ‘1 + 70’ should not bother us in this context) or, in other words, the arithmetic operation underlying the structures of the two expressions is exactly the same. Yet, as STAMPE (1976: 595) notes, the intonation of the English phrase 365 days ('three hundred and sixty-five 'days) is different from that of 300 and 65 days ('three hundred – and sixty-'five days), which shows that the two elements 300 and 65 are linked less tightly in 300 and 65 than they are in 365. For an historical text language like Old English, this test method is unfortunately of no value. In Old English, moreover, the treatment of complex numerals in the manuscripts is anything but uniform. Various scribal conventions can be observed in this context, including the two extremes exemplified in (1.5)a and (1.5)b. Even less complex expressions can be written both as one and as several graphical units; cf. OE 〈an þusend〉 vs. 〈anþusend〉 ‘1,000’; 〈feower hund〉 vs. 〈feowerhund〉 ‘400’; 〈eahta tyne〉 vs. 〈eahtatyne〉 ‘18’. In this study I will ignore such differences because conventional (i.e. graphically realised) word boundaries in complex numerals of a particular language do not affect their internal composition or the systematic arrangement of their individual constituents. In §§ III.1.2–3, we will discuss Old Eng-

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lish cases of complex numeral expressions that can sometimes be discontinuous. These examples suggest that there are some instances of complex numerals, at least in Old English, which are best interpreted as constituting syntactic rather than morphological structures. On the other hand, for the type of structures we will discuss shortly in § I.4, it seems more promising to assign these structures to the domain of morphology rather than to syntax. It will, in most instances, ultimately remain a matter of the underlying theoretical approach whether the rules applied for the formation of complex numeral expressions are taken as morphological rules or as syntactic rules. Moreover, whether a complex numeral is, in the particular case, best analysed as an affixation, a compound or a juxtaposition of co-ordinate syntactic phrases should be a question of locating areas in a continuum of possible structures rather than a categorial decision. The question, rewarding as it may be, will not be pursued further in this study because, as just indicated, the evidence of Old English complex numerals is in any case ambiguous in this respect. Therefore, whichever final decision one wishes to make, none of the possible approaches will be void of disadvantages for the analysis of the complex numerals of Old English (cf. fn. 5 above in § I.3.2). The crucial assumption for the present study in this respect will be that one numerical value is represented by one single linguistic unit, no matter how complex a particular instance of this unit may be. I.3.7 Summary According to what we have said by now, a numeral can be a simple numeral (atomic numeral or base numeral) or a complex numeral which is formed as a combination of several simple numerals. It follows that a complex numeral is not arbitrarily shaped because the numerical value it represents can be inferred from its constituents and from its internal structure, whereas the numerical values represented by simple numerals must be memorised. In the numeral systems of the Germanic languages, as well as in those of many other European languages, the atoms are the expressions from ‘1’ to ‘9’ and the bases represent the numerical values ‘10’, ‘100’, ‘1000’, ‘106’, and perhaps one or two more powers of ‘10’; cf. below §§ II.7.3 and III.3.3). Table 3 summarises the different types of elements of the numeral system of Present-day English (but cf. the modification in Table 4 in § I.5 below.)

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Table 3. Types of expressions in a numeral system; exemplified by the decimal numeral system of Present-day English: simple numerals atoms

expressions

one, two, three, …, nine

bases ten, hundred, thousand

numerical values cardinalities

‘1’, ‘2’, ‘3’, …, ‘9’

‘10’, ‘100’, ‘1,000’

complex numerals affixations four-teen, fif-ty

compounds sixty-one, eight hundred, seven thousand

underlying arithmetic operations ‘4 + 10’ ‘5 × 10’

‘(6 × 10) + 1’ ‘8 × 100’ ‘7 × 1,000’

I.4

Systemic and non-systemic cardinality expressions

I.4.1

General

Let us now resume a question that we have raised already in the very beginning of this chapter and that has repeatedly come to the surface during our discussion. In § I.1 (cf. particularly Table 2), I hypothesised that there are other cardinality expressions in a language apart from cardinal numerals in a narrow sense. The distinction between ‘systemic’ and ‘non-systemic’ expressions that I suggested in the beginning is not made consistently in the literature on numerals and numeral systems and, consequently, many contributions to the subject have treated both types of cardinality expressions indiscriminately. The first who distinguished these two classes was Joseph GREENBERG (1978: 253–254). GREENBERG does not elaborate much on this point, probably because he was mainly interested in formulating generalisations of all kinds in the context of numerals, many of which would apply to a lesser extent to nonsystemic cardinality expressions or even generally to quantifiers. Still, many of his generalisations implicitly depend on this prerequisite. GREENBERG (1978: 253) writes: “It is important to distinguish among numerical expressions in any natural language a special subset, the numerals proper, which constitute the numeral system of the language.” He later repeats this point (GREENBERG 2000: 771ab) and the distinction has more recently also been

Systemic and non-systemic cardinality expressions

43

acknowledged by COMRIE (2005a: 531a). Yet a clear definition of a cardinal numeral proper and a ‘non-systemic cardinality expression’ is still wanting. This section aims at drawing such a clear-cut distinction between cardinal numerals as expressions that are formed in accordance with the numeral system – ‘(systemic) numerals’ – and alternative – or ‘non-systemic’ – strategies for specifying the cardinality of a set. Again, we attempt to find criteria of these notions that are cross-linguistically valid in order to complete our theoretical considerations of numeral systems of natural languages. Later, in § III.3, we will discuss the non-systemic number expressions in Old English and the extent and kind of their usage. I postulate that, although ‘non-systemic’ number expressions may have the same semantic scope (specification of the cardinality of a set) and the same syntactic functions (numerically specific quantification) as ‘systemic’ cardinality expressions, only those expressions which are elements of or are generated by the numeral system should be considered ‘cardinal numerals’. It should be pointed out that non-systemic expressions are not generally unaccepted expressions. Some of them can be used quite frequently, as for instance the type nineteen hundred in specifying a particular year. In a similar context, HURFORD (1975: especially 19–28 and 251–253; cf. also the remark in HURFORD 1999: 15) distinguishes between ‘well-formedness’ and ‘illformedness’. He indiscriminately categorises expressions like nineteen hundred and *two hundred two thousand as ill-formed. I prefer the distinction between ‘systemic’ and ‘non-systemic’ expressions, taking into account that non-systemic expressions are neither “ungrammatical” nor pragmatically unacceptable. In any event, our distinction between a ‘systemic’ and a ‘non-systemic’ expression may so far seem quite trivial, if the definition of what is a ‘systemic’ expression and what is not may even appear to be potentially circular: by now we have only said that cardinal numerals are distinguished from other numerically specific quantifiers by their property of being an element of the numeral system, and at the same time we defined the numeral system as a set of rules for the formation of cardinal numerals. When determining what makes an individual expression systemic or not, some degree of randomness may in fact be involved in the particular case. This applies in the sense that, if there is an alternative between two expressions for one numerical value, there is no structurally motivated reason determining which numerical values are expressed by which simple forms. There is also no language-inherent feature that determines which arithmetic operations are used to combine particular simple forms to create complex numerals. This can be seen by the fact that even grammatically and lexically close varieties of one and the same language may

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have (partially) diverging structures in their respective numeral systems. Take, for instance, the use of the Standard French expression quatre-vingt ‘4 × 20’ for the numerical value ‘80’ and the subsequent vigintiad between ‘81’ and ‘100’ and the use of huitante or octante ‘8 × 10’ and the corresponding sequences of decades in several regional varieties of French. Or take the different uses of the numeral billion in different varieties of Present-day English. However, the type of arbitrariness referred to here applies only if we analyse numeral systems strictly synchronically. Diachronically, there seems to be a rather limited set of lexical sources from which cardinal numerals can evolve; cf. VON MENGDEN (2008: 298–300). Yet, as long as we discuss the numeral systems and their elements, it is more advisable to retain a strictly synchronic perspective. Although the rules employed in a numeral system generally follow arithmetic principles, a perfect numeral system – perfect in the sense that it is void of any idiosyncrasy – does not exist, except perhaps if its scope is extremely small and we accept sets of only very few, low valued cardinal numerals (cf. above § I.3.1) as numeral systems. Taking into consideration this basic arbitrariness of a numeral system, it is absolutely impossible to generally define the numeral system of a particular language without describing it in detail. Thus it is also impossible to generally define a particular cardinal numeral in contrast to a ‘non-systemic’ number expression in a wider context, that is, in a way that would apply more generally than to one particular system. Such a definition would attempt to give a logical explanation for the fact that in some varieties of French the expression for the numerical value ‘80’ is quatre-vingt while in others the expression for the same numerical value is huitante. In any variety of French, the use of either expression would not prevent a successful communication (cf. HURFORD 1987: 28). Similarly, in Present-day English the expression two fifties is as comprehensible as one hundred. These examples may show that the distinction between ‘systemic’ and ‘non-systemic’ expressions is based to some extent on convention. Yet it is possible to define the basic principles of a numeral system as a whole. And on this basis it will be possible to identify one systemic expression out of any pair of synonyms – such as quatre-vingt / huitante, twelve / dozen, one hundred / two fifties – as systemic. In spite of the synonymy of the two expressions of each of these pairs, we will see that there are some criteria which clearly help to adequately distinguish systemic from non-systemic expressions. In contrast to other, non-systemic, numerically specific quantifiers, systemic cardinal numerals show the three defining properties listed in (1.6):

Systemic and non-systemic cardinality expressions

45

(1.6) Defining properties of systemic numerals Systemic numerals…  …correspond to the counting words that occur in the conventionalised counting sequence.  …are used recursively as constituents of more complex (i.e. higher valued) numerals.  …are the morphological basis for the formation of a corresponding form of any other type of numeral (i.e. ordinal, multiplicative, frequentative, etc.).

As an isolated feature, none of these conditions is sufficient for a universally valid distinction of systemic from non-systemic number expressions. Although there are languages in which individual counting words or even a small section of counting words are distinct from the cardinal numerals (cf. § I.2.3), in the majority of languages where this is not the case, the occurrence of a cardinal numeral in the counting sequence is the strongest criterion. However, the use of an expression in a counting sequence is itself a purely conventional feature and, if we had to take it as the sole distinctive feature between systemic and non-systemic expressions, our definition of systemic numerals would, in fact, rely entirely on language-internal convention. With respect to both the second and the third point, there is not always a sharp line separating the possible behaviour of non-systemic expressions from that of systemic expressions. Yet taking all three criteria into consideration, the distinction between systemic and non-systemic number expressions may become sufficiently clear. The three criteria postulated here for the distinction between systemic and non-systemic numeral expressions are, for several reasons, all difficult to verify for Old English. As far as this is possible, some salient Old English examples will be presented in due course. Since this distinction between systemic and non-systemic expressions is generally absolutely essential for a comprehensive description of a numeral system, the three prerequisites will be discussed briefly in the following subsections, predominantly on the basis of examples from Present-day English. (See also the summary in § I.6.1.2.)

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I.4.2

The counting sequence

I.4.2.1

The counting sequence as an ordered sequence of well-distinguished expressions

The most basic defining property of a systemic number expression is its occurrence in a counting sequence. A counting sequence can be seen as a conventionalised ordered sequence of well-distinguished expressions in a language or in a particular variety of a language, as e.g. in Present-day English one, two, three, four, five etc. In § I.2.2 we showed why and in what way the expressions of the conventionalised counting sequence can be employed in number assignment. Theoretically, this entails that the development of the counting sequence precedes its use for counting. Both phylogenetically and ontogenetically this is in fact the case; cf. WIESE (2007). As quite a number of studies suggest – cf. e.g. MENNINGER (1957: 43–49), GREENBERG (1978: 257), MAJEWICZ (1981), IFRAH (1981: 24-29), HEINE (1997: 19–21), and a summary of some language descriptions in RIJKHOFF (2002: 157) – a sequence of salient body parts, most commonly the ten fingers, becomes conventionalised as the most primitive tool for number assignment. While pointing at the body parts that are conventionalised for number assignment, people begin to say the words denoting the respective body parts. Eventually, the accompanying words function as number expressions without the corresponding gesture. In this way, a small counting sequence emerges, which, in turn, serves as a basis for the development of a more complex numeral system. The origin of the conventionalised counting sequence therefore must be seen in the transition from counting by gestures to counting by words; cf. VON MENGDEN (2008: 298-9).10 The conventionalised sequence of non-referential counting words is also the foundation for the acquisition of numeracy by infant language learners. Children are not able to learn to assign numbers until they have learnt to re10 HURFORD (1987: 111) misses this aspect when he argues against the non-referential status of counting words. If the hypothesis (which he refers to as the ‘Ritual Hypothesis’) that it is the sequential status which makes the counting sequence applicable as number words were correct, HURFORD argues, reciting counting words must originally have been an “apparently instinctual activity” or an “uninterpreted activity”. The expressions of the conventionalised counting sequence, he assumes, are not only synchronically but also etymologically arbitrary. The origin of the counting sequence would have to be some arbitrary counting-out rhyme. Although the counting-out rhyme metaphor is extremely useful in the context of the acquisition of the counting sequence by the infant language learner (cf. WIESE 2003: 151– 179), it is now commonly accepted that the etymological origin of most simple numeral expressions lies in the domain of body part expressions (see the references listed above).

Systemic and non-systemic cardinality expressions

47

cite the counting expressions in their correct order. In other words, children learn the counting sequence in the same way as they learn the alphabet or some counting-out rhyme; cf. WIESE (2003: 151–179). The relevance of the counting sequence for the distinction between systemic and non-systemic number expressions can best be exemplified by the English expressions for the numerical value ‘12’. Present-day English has two numerically specific quantifiers for this value, twelve and dozen. Both are arbitrarily shaped and mono-morphemic. Compared with the formation pattern thir-teen ‘3 + 10’, four-teen ‘4 + 10’, etc., both twelve and dozen are idiosyncratic at this point of the counting sequence (cf. below § I.5.2). However, only the expression twelve can occur in the conventionalised counting sequence of Present-day English. To count …ten, eleven, ?dozen, thirteen, fourteen…, would be highly unusual and could only plausibly occur if the speaker deliberately intends to deviate from the convention for a particular pragmatic reason. Otherwise the convention in Present-day English requires the expression twelve at the relevant point of the counting sequence; cf. STAMPE (1976: 596), GREENBERG (1978: 253). Particularly the distinction between twelve and dozen in Present-day English where even the systemic expression twelve formally deviates from the more regular pattern – by analogy with thir-teen ‘3 + 10’, four-teen ‘4 + 10’ we would actually expect *one-teen ‘1 + 10’, *two-teen ‘2 + 10’ rather than eleven and twelve – very conveniently reveals the conventional character of the set of systemic number expressions. The relation between the counting sequence and the systemic status of an expression necessarily follows from the nature of the counting sequence as a cognitive (ontogenetically) and technical (phylogenetically) prerequisite for the development of a numeral system. Theoretically, we may therefore assume that there can be only one systemic expression in any (variety of a) language for any one numerical value. Nevertheless, as we have pointed out already, the choice which expression this would be in the particular case, for instance the choice between twelve, dozen or two-teen as the systemic expression for ‘12’ in Present-day English, is from a synchronic perspective a random one. The few examples of counting words that are distinct – either through some morphological process or completely distinct as suppletive forms – do not generally defy the conventionalised counting sequence as the major criterion for the distinction between systemic and non-systemic number expressions. We have mentioned some of these cases in § I.2.3 and I have referred to GREENBERG (1978: 286–287) for some more examples. Wherever these deviations occur, they are only individual forms or small subsequences where counting word and cardinal numeral deviate from each other. It is only because of those cross-linguistically rare cases in which a counting word differs

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from its cardinal counterpart that it is theoretically difficult to employ the counting sequence as a criterion to distinguish systemic expressions. But in these few cases, the systemic character of the relevant cardinality expression is undisputed with respect to the other two criteria; cf. GREENBERG (2000: 771b) and the summary below in § I.6.2.4. We will shortly move on to the other two criteria for the distinction between systemic and non-systemic expressions. The following section will discuss some methodological consequences of what has been discussed here particularly with respect to the Old English language. While the next short section will be our first approach to the numerals of Old English, in this rather crosslinguistically oriented chapter it forms a digression. Readers who are interested exclusively in the general features of numeral systems may continue below with § I.4.3. I.4.2.2

The counting sequence of Old English

According to what we have said, the most reliable way of discriminating systemic from non-systemic cardinality expressions is to find out whether the relevant expressions occur in the conventionalised counting sequence. In contemporary languages with a more complex numeral system, native speakers will hardly disagree when reciting the counting sequence of their variety. For a historical period of a language, however, it is usually difficult to find instances of a conventionalised counting sequence. A counting sequence only occurs in the spoken language, most often while children are learning their native language. We therefore cannot expect a conventionalised counting sequence to be attested in a written medieval source. As for Old English, I would say, we are extremely lucky in this respect. There is one attested passage, from which it is at least possible to infer with some degree of certainty which lexical elements may have been used in a conventionalised counting sequence in Old English. The following section in Ælfric’s Grammar may not be a genuine counting sequence, but the context of the passage in (1.7) suggests that the lexical items Ælfric uses as equivalents for the Latin cardinal numerals are the default expressions of the conventionalised counting sequence up to ‘21’.

Systemic and non-systemic cardinality expressions

49

(1.7) ÆGram 280.18–281.15 (ZUPITZA 1880 [2001]: 280–281 – my bold type): unus (I) an gebyrað to werlicum hade, una to wiflicum, unum to NEVTRVUM. duo (II) twegen gebyriað to MASCVLINVM and to NEVTRVM, duae twa to FEMININVM. tres (III) ðry gebyriað to MASCVLINVM and FEMININVM, tria þreo to NEVTRVUM. quattuor (IIII) feower gebyriað to eallum þam þrim cynnum and swa forð oð hundteontig. quinque ( V) uiri fif ceorlas. sex litterae (VI) six stafas. septem (VII) uerba seofan word. octo (VIII) eahta to ælcum cynne and to ælcum CASV and swa forð. nouem (VIIII) nigon. decem (X) tyn. undecim (XI) endleofan. duodecim (XII) twelf. tredecim (XIII) þreottyne. quattuordecim (VIIII) feowertyne. quindecim (XV) fiftyne. sedecim (XVI) syxtyne. decem et septem (XVII) seofantyne. decem et octo (XVIII) eahtatyne. decem et nouem (XVIIII) nigontyne. uiginti (XX) twentig. uiginti unum (XXI) an and twentig and swa forð.

Some further indications of an Old English counting sequence can be drawn from a comparison with other modern languages which are genetically closely related to Old English. Since the numeral systems of the Germanic languages (and, to a slightly lesser extent, those of other European languages as well) are very similar, it is generally possible to infer from the analogy with, for example, Present-day English which expressions are systemic and which are not. Yet analogy is not always a safe criterion as can be seen from the example of the Old English numerals from ‘70’ to ‘120’, which are of a different type than the corresponding expressions in the modern Germanic languages (cf. §§ II.4.3.2–3 below). In any case, the comparison with the numerals of modern Germanic languages together with the frequency of particular types of formations in Old English seems to be quite a sufficient basis for determining the default expressions for a particular numerical value and thus for specifying which number expressions are systemic and which are not. I.4.3

The limited recursive potential of non-systemic expressions

Since complex numerals are always morphological combinations of two or more lower valued numerals, any constituent of a complex numeral is itself a numeral which can be used independently. Thus the expression four, itself an independent numeral (i.e. a free morpheme), is a constituent of the expression four-teen. The expression fourteen, in turn, is a constituent of the expression one hundred and fourteen, and so forth. Any other constituent of the expression one hundred and fourteen is likewise a numeral that can be used independently, i.e. one hundred, one, and hundred; cf. GREENBERG (1978: 279– 280, G 37). According to this pattern, a numeral system is an entirely recur-

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sive system in so far as any numeral can be a constituent of a more complex numeral (cf. § I.3). By contrast, non-systemic number expressions cannot generally occur as constituents of more complex number expressions. Where this is possible, the use of a relevant expression is limited compared to the synonymous systemic expression. For instance, in contrast to twelve, the expression dozen cannot occur as addend to one hundred: it is impossible (or, at least, highly unusual) to say *one hundred and a dozen for ‘112’. Likewise, the expression score usually does not occur in such a combination: *one hundred and a score. While the expressions dozen and score may semantically and syntactically share many features with their respective synonyms twelve and twenty, only the latter two can be used in any more complex (i.e. higher valued) combination within the scope of the Present-day English numeral system. In the same way, one hundred can be distinguished from two fifties. The use of both expressions by themselves may be equally successful in a communication, and they may differ only in that the former is more frequent and more conventionalised. However, only the former can be a constituent of a more complex numeral: cf. one hundred and ten vs. *two fifties and ten, or one thousand, one hundred vs. *one thousand, two fifties. Yet simple non-systemic expressions may occur in some standard combinations: it is, for instance, possible to say two dozen, three dozen, or threescore, fourscore. In these expressions, the non-systemic constituent has the same arithmetic function – i.e. that of a multiplicand – as hundred in the numerals two hundred and three hundred. Thus the use of the Modern English expressions dozen and score in arithmetic operations is only strongly constrained but not generally impossible. However, expressions like *seventy-five dozen or *three hundred and thirty-two score are virtually impossible; hence the limited use of non-systemic expressions like dozen and score in arithmetic operations does not challenge our point that only systemic numerals may generally be used in more complex expressions. I.4.4

Cardinal numeral as the morphological basis of non-cardinal numerals

All non-cardinal types of numerals like ordinals, multiplicatives, and frequentatives (cf. § I.2.3) are formed on the basis of the respective cardinal root. This is valid with the exception of suppletive expressions, which are crosslinguistically restricted to the lowest numerical values of each system (cf., e.g., first and second in Present-day English). Forming a non-cardinal numeral

Systemic and non-systemic cardinality expressions

51

is generally possible only on the basis of systemic cardinal numerals. For instance, any non-cardinal numeral can be derived from twelve, e.g. twelfth, twelve times, etc. With non-systemic cardinality expressions, this is possible only in a limited way: affixed forms are impossible (*the dozenth11, *the scoreth), idiomatic constructions of non-cardinal numerals may work with nonsystemic expressions but again, if they do, only to a limited extent. While ?dozenfold is again at least doubtful, a dozen times can well be used. However, the use of an expression like dozen in such a construction changes the semantic character from a numerically specific expression to a numerically unspecific one: usually, the expression a dozen times does not refer to the exact numerical value ‘12’ but is rather understood as ‘a numerically unspecific number of times’, ‘many times’, whereas twelve times always means ‘on exactly 12 occasions’. The only problem with this third criterion for our distinction between systemic and non-systemic number expressions is that it does not take idiosyncratic non-cardinal numerals like first, second or once, twice into account. The fact that the English expressions one and two do not form the morphological basis of their respective ordinals (*oneth, *twoth) may suggest, according to what we have said so far, that one and two are not systemic. However, other formations on the basis of the lowest valued numerals, like e.g. one time, two times, are also in use, although less common or pragmatically more constrained than once, twice. And wherever corresponding formations are genuinely impossible, these idiosyncrasies are cross-linguistically limited to the lowest numerical values. Hence, the impossibility of formations like *oneth, *twoth in Present-day English is due to a cross-linguistic tendency to use suppletive formation patterns of non-cardinal numerals for the lowest numerical values rather than to the fact that the lowest valued cardinal numerals were less systemic than others. While this outline may suffice to draw a clear defining line between systemic numerals and non-systemic number expressions, we will come back to particular aspects of non-systemic expressions below in § III.3 when discussing non-systemic expressions in Old English. As a last major part of these theoretical considerations on linguistic numeral systems, we will now turn to the problem of idiosyncratic numerals and numeral formations.

11 The OED (IV, 1005a) has an entry for dozenth. Of the three quotations given there, the latest is from 1853. Only the oldest one of the three, from 1710, is in fact numerically specific. Today, dozenth is perceived at least by a large number of speakers as non-existent.

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I.5

Idiosyncrasies and variant forms in numeral systems

I.5.1

‘Idiosyncratic’ vs. ‘systemic’

In the previous section we distinguished cardinal numerals from other expressions that likewise represent numerical values. We defined the former type as ‘systemic’ and the latter as ‘non-systemic’ expressions. However, the distinction between systemic numerals and non-systemic cardinality expressions does not entail that the numeral system itself is entirely regular. In §§ I.3.3 and I.4.2.1, we already came across some irregularities of different kinds. In fact, idiosyncrasies in numeral systems of natural languages are very common. However, such irregularities are usually confined to a small number of elements or to a comparatively short section in the counting sequence. Moreover, whenever there is an irregularity in a numeral system, the relevant form still meets the above criteria of systemic elements as postulated in the previous section. Thus ‘irregularity’ and ‘idiosyncrasy’ here only refer to the deviation of a particular element or of a particular sequence of elements in so far as their respective form or formation deviates from what we would expect by analogy with equivalent sequences or with neighbouring elements in the counting sequence. An ‘irregularity’ in our context is a deviation from a major pattern – a “lack of smoothness”, as HURFORD (1987: 51) puts it – rather than a defiance of the rules. The rules of the numeral systems should, therefore, not be taken as being of absolute uniformity. Rather, the rules are defined by the existing elements of the system: if an expression formally deviates from the major part of the numeral system, then this deviation is part of the system and thus in accordance with the rules of the numeral system. Completely excluded from his distinction are expressions which presuppose a particular cardinality rather than specify it. For instance, many traditional descriptions of cardinal numerals include the quantifier ‘both’ into their list (cf. e.g. JESPERSEN 1913: 197, § 7.71; CAMPBELL 1959: 283, § 683; ROSS/BERNS 1992: 571–575, § 15.1.2.11). Similarly, expressions like pair or couple are sometimes treated as numerals and/or quantifiers. The functions of these expressions, although a cardinality ‘2’ may be one aspect of their semantics, are considerably different from those of cardinal numerals. The use of any expression of this kind presupposes a knowledge about the two-ness of the referent among the discourse participants, whereas in many contexts in which cardinal numerals are used, the cardinality of the referent set is previously unknown to the recipient interlocutor; cf. § IV.3. The specifically Germanic expressions for ‘both’ are convincingly analysed by HAWKINS (1978: 161– 165) as dual determiners. Expressions like pair or couple likewise cannot be

Idiosyncrasies and variant forms in numeral systems

53

classified as quantifiers. These expressions do not specify any cardinality but indicate the unity or a particular relation of two entities which has been established previously in the discourse. Most, if not all, of those idiosyncrasies which can be observed within numeral systems of natural languages can be subsumed under the two major groups shown in (1.8). (1.8) Categorisation of idiosyncrasies in numeral systems 1. Some forms of the numeral system can deviate from the formation pattern of the neighbouring forms in the counting sequence. a. They are simple (arbitrary and mono-morphemic) forms at a place in the sequence of numerals where a complex form would be expected, or b. their morphological structure deviates merely on formal grounds from what the analogy with the main part of the numeral system would predict, or c. their morphological structure deviates because the formation is based on an arithmetic operation different from what the analogy with the main part of the numeral system would predict. 2. The phonological shape of a particular simple numeral can vary if used as a constituent in a more complex numeral. a. They are allomorphic variants of their corresponding simple expressions, or b. they are functional variants encoding the type of arithmetic operation underlying the combination.

Since both types will be relevant for the analysis of the Old English numeral system, we will look at them briefly in the following sections. The discussion will show that the distinction between Type 1 and Type 2 in (1.8) is crucial for analysing numeral systems both synchronically and diachronically. Type 1 comprises formal deviations whose occurrence can be seen as arbitrary from a synchronic point of view. The types of deviation described here may render the system somewhat less transparent, but they do not affect the overall arrangement of the system. By contrast, the formal variation of Type 2 is determined by phonological or morphological constraints. Since the constructions represent arithmetic operations, we could just as well say that their occurrence follows arithmetic constraints. In other words, the second type of

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irregularity occurs only if a relevant form performs a particular arithmetic function within the system. It will become clear in the following two sections what exactly this distinction and the short introductory explanation I have given here entail. We will start with Type 1 (and its subtypes) in § I.5.2 and then move on to Type 2 in § I.5.3. I.5.2

Idiosyncratic numerals

Simple idiosyncratic numerals are genuinely suppletive forms. A good example of a simple idiosyncratic form – Type 1a in (1.8) – is the Russian expression for ‘40’, sórok, which, in contrast to all the other multiples of ‘10’, is a simple form and does not represent an arithmetic operation; cf. COMRIE (1992: 776 and 1997b: 50). More relevant in our context will be the example of the Germanic expressions for the numerical values ‘11’ and ‘12’. The English expressions eleven and twelve (and the corresponding forms in the other Germanic languages) do not agree with the formation pattern of the remaining elements in the second decade of the sequence of numerals. All the other teens are formed according to the arithmetic operation ‘n + 10’, i.e. thir-teen ‘3 + 10’ (for the variant thir-, cf. below § I.5.2.1), four-teen ‘4 + 10’, etc. If there were regular expressions for the numerical values ‘11’ and ‘12’, they would have to represent the additions ‘1 + 10’ and ‘2 + 10’ respectively. That is, in Present-day English, regular expressions for ‘11’ and ‘12’ would be *one-teen and *two-teen; cf. § I.4.2.1. PDE eleven and twelve, however, are simple arbitrary forms, which, by analogy with subsequent expressions, cannot be expected to occur at this place of the numeral sequence. (Cf. the section on the corresponding Old English expressions below in § II.3.) We will now have to revise Table 3 above (§ I.1.3) in which we distinguished two types of simple numerals, atoms and bases. We may, therefore, modify Table 3 accordingly as in Table 4. It should be said, however, that atoms and bases have essential functions in the numeral systems and are, with respect to these functions, in a complementary relation to each other (cf. § I.3.4.2). By contrast, there is of course no necessity for idiosyncratic simple forms to occur in the sense that they do not have any specific functions in the system. Idiosyncratic forms are only defined by being formal irregularities. It may nevertheless, at least in the context of the numeral systems of the Germanic languages, be helpful to contrast idiosyncratic simple numerals like eleven and twelve with atoms and bases as in Table 4:

Idiosyncrasies and variant forms in numeral systems

55

simple numerals atoms

idiosyncratic forms

bases

expressions

{one, two, three, …, nine}

{eleven, twelve}

{ten, hundred, thousand, …}

numerical values

‘1’, ‘2’, ‘3’, …, ‘9’

‘11’, ‘12’

‘10’, ‘100’, ‘1,000’, …

continued as in Table 3

Table 4. Possible types of simple numerals (cf. Table 3 above)

Apart from simple forms, there are also idiosyncratic complex numeral forms. These may deviate from the default pattern simply by their different constituent order (Type 1b in (1.8)). This is for instance the case in the Italian expressions for the teens, which are formed as ‘ni + 10’ (se-dici ‘6 + 10’) up to ‘16’ and from ‘17’ onwards are expressed as ’10 + ni’ (dicia-sette ‘7 + 10’). While the Italian expressions for the teens, in spite of a change in the order of elements, all represent the same arithmetic operation – an addition with the base ‘10’ – there may also be sequences in which some expressions deviate not only in their structures, but also in the underlying arithmetic operations (Type 1c in (1.8)). For instance, the sequence of teens in Classical Latin is generally expressed as addition, i.e. un-decim ‘1 + 10’, duo-decim ‘2 + 10’, etc., whereas the systemic expressions for ‘18’ and ‘19’ are expressed as subtractions, i.e. duo-de-viginti ‘20 – 2’, un-de-viginti ‘20 – 1’. (Cf. SIHLER 1995: 417–418, § 390. Also cf. example (1.7) in § I.4.2.2 above for the slightly deviating sequence in Medieval Latin as attested in Ælfric’s Grammar.) One important remark should be made at this point: the categorisation suggested here under Type 1 is a strictly synchronic one. A form may be opaque from a synchronic perspective but its history may nevertheless reveal a formerly transparent structure. It may, therefore, be worth looking at the etymology of the forms. In the case of Russian sórok, the idiosyncratic form has actually entered the numeral system from outside. According to COMRIE (1992: 776), sórok originally denotes a ‘sack of forty sable furs’ and was incorporated into the conventionalised counting sequence, because it specified a culturally salient cardinality. Such a development is, however, rather rare. In other cases, the disruption of the regularity of a system due to foreign influence may also be a feasible explanation for idiosyncrasies. But usually idiosyncrasies arise by system-internal changes. Particularly idiosyncratic simple forms frequently develop out of complex forms independent of whether they used to be regular or irregular at an earlier

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stage of a language’s history. For instance, while eleven and twelve are clearly simple forms, they once were complex numerals representing arithmetic operations (cf. below §§ II.3, II.7.1.2 and III.2.3). Likewise, French vingt ‘20’ is, from a synchronic perspective, an arbitrary simple expression and even its predecessor, Latin viginti, cannot be analysed as ‘2 × 10’ without any knowledge of the pre-history of Latin. Yet its original form in Indo-European is PIE *wī-kṃt-ī < *dwi-dkṃt- which unambiguously represents ‘2 × 10’ (cf. the cognate form in Dorian Greek wí-kati); cf. COLEMAN (1992: 397–398, § 12.1.12); BEEKES (1995: 213, § 13.1.3); and the discussion in SIHLER (1995: 418–419, § 391). The Celtic expressions for ‘20’, Modern Irish fiche, Modern Welsh ugain, etc., go back to the same root as the Latin form. (For an analysis of the Indo-European form slightly deviating from that of COLEMAN 1992, cf. GREENE 1992: 511, § 14.1.1.12 and 540–541, § 14.5.1.7; DETGES 2003: 37–38.) Diachronically, of course, all the forms do represent the ProtoIndo-European system of decimally arranged compounds; i.e. they once transparently represented the arithmetic operation ‘2 × 10’. Finally, DETGES (2003: 36) rightly analyses the Portuguese numerals from ‘11’ to ‘15’ and the French numerals from ‘11’ to ‘16’ as idiosyncratic in the sense discussed here. The relevant forms nevertheless go back to complex structures which were arithmetically transparent in Classical Latin. If we accept the history of a language as an explanatory factor for synchronic systems (and for deviations from a system), the notions ‘idiosyncratic’ versus ‘regular’ and ‘opaque’ versus ‘transparent’ are gradient ones. It is, therefore, ultimately a matter of interpretation whether we analyse the final /-z/ in the French expressions onze, douze, treize, quatorze, quinze, and seize as a regularity, i.e. as a morpheme and, as a consequence, the relevant expressions as morphologically complex and arithmetically transparent. In the case of Latin duodeviginti and undeviginti, the change of the arithmetic pattern within one section only affects particular elements. But once a multiple of a base shows such a deviation, there will be a consequence for a larger sequence within the system. This is because the multiples of bases may form constants to which the sequence of atoms serially combines. In some numeral systems in which this type of idiosyncrasy occurs, entire sections of the system may be affected. For instance in the section of Standard French numerals from ‘61’ to ‘100’, the multiples of ‘10’ display a change in the underlying arithmetic operation. While up to ‘60’, the multiples of ‘10’ are all formed according to the pattern ‘n × 10’, ‘70’, ‘80’, and ‘90’ are formed differently, i.e. as soixante-dix ‘(6 × 10) + 10’, quatre-vingt ‘4 × 20’, and quatre-vingt dix ‘(4 × 20) + 10’, respectively. While, strictly speaking, it is only the arithmetic operations underlying the three expressions for ‘70’, ‘80’,

Idiosyncrasies and variant forms in numeral systems

57

and ‘90’ that deviate, expressions such as the ones for ‘71’ – soixante-onze ‘(6 × 10) + 11’ – or for ‘91’ – quatre-vingt et onze ‘(4 × 20) + 11’ – are likewise affected and, consequently, a larger section is deviant. However, all the idiosyncrasies subsumed under Type 1 recur in more complex expressions in combination with the next higher augend. In Presentday English, ‘112’ is expressed as one hundred and twelve. In Classical Latin, ‘118’ is expressed as centum duo-de-viginti. And in Standard French, ‘179’ is expressed as cent soixante dix-neuf. These cases show how – in spite of the idiosyncratic character of the relevant constituents – such deviations are incorporated into the overall recursive principle of the system. This is the fundamental difference between expressions like twelve or quatre-vingt on the one hand, and dozen or two fifties on the other. It has sometimes been said (e.g. SEILER 1990: 197–198) that such irregularities occur in the vicinity of bases or of their multiples, never in the middle of a particular section. This applies to the first two types of irregularities we have postulated here. The numerals for ‘11’ and ‘12’ in the Germanic languages immediately follow the base ‘10’ and the vigesimal section of the Standard French numeral system immediately precedes the base ‘100’, etc. Yet, Welsh deu-naw ‘2 × 9’ (cf. § I.3.3) shows that this is not universally the case. (Cf. the summary in § I.6.3.4.) An extreme case of idiosyncrasies within a counting sequence can be found in some Indo-Aryan varieties where the forms up to ‘100’ are virtually impossible to analyse from a purely synchronic perspective, while, diachronically the forms all go back to the sufficiently regular decimal pattern of Proto-IndoEuropean. The lack of synchronic transparency of the Modern Indo-Aryan forms is, as BERGER (1992: 243–244) explains, not only due to the rigorous implementation of Modern Indo-Aryan sound laws which have not been following analogical levelling, but also in the peculiar place of numerals within the linguistic system in general. The extremely abstract character of the numerals makes it likely that the series of natural numbers is subject to mechanical repetition more than any other series of words. The consequence of this is not only a tendency to increased phonetic erosion extending beyond the ‘regular’ sound changes, but often also an analogical change in the stem which is not, as with other words, based on an internal semantic relationship, but, rather, exclusively upon the external impetus of the neighbouring items within the series of numerals.”

That is, a once systematic decimal numeral system has become a sequence of arbitrary lexemes because the assimilation to the previous or the anticipation of the subsequent numeral in the counting sequence have caused an extremely

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large number of forms to become synchronically opaque. BERGER’s explanation implicitly provides evidence for the fact that, even at a historical stage when the system is complex enough so that most expressions would have to be formed according to recursive rules and underlying arithmetic operations, the sequential character of the systemic number words is retained. In short, even when it becomes necessary to form complex numerals in order to keep the system sufficient, the system still continues to be a conventionalised sequence. BERGER’s explanation of the large number of idiosyncratic forms is in line with our theoretical considerations given above. It should, however, be pointed out that the situation in Indo-Aryan cannot be taken as representative for linguistic numeral systems, as WINTER (1992: 18) points out: “the situation in Modern Indo-Aryan, with its relegation of all numbers up to ‘one hundred’ to the lexicon as items to be learned separately and not to be derived by palpable rules, is quite exceptional and hard, if not impossible, to explain.” (Cf. BERGER 1992: 245–275, § 7.1, for the relevant forms of Indo-Aryan.) I.5.3

Variant forms

Another type of irregularity does not involve genuinely suppletive forms or deviant sections as the ones just described. As stated in the second item above in (1.8), individual forms may vary according to whether they occur as simple forms or as constituents in particular combinations. The examples discussed in this section all have the fact that variation occurs only if the relevant form is used in a complex numeral in common, but this type of variation does not apply to simple forms. The forms discussed here are all bound forms. Their morphological and functional relation with the corresponding simple form may be of two kinds: some of the relevant numerical values can also be represented either by bound allomorphs – e.g. fif- for five ‘5’ in fif-teen (§ I.5.3.1) – or by functional morphemes – e.g. the suffix -teen for ten ‘10’ in fif-teen (§ I.5.3.2). I will illustrate these types with examples from Present-day English at this point. The situation in Old English is typologically very similar although some remarkable differences can be observed there. These Old English cases will be discussed at the relevant points in the next chapter (§§ II.2–5). (For a short summary of both of the following types see below § I.6.3.5.)

Idiosyncrasies and variant forms in numeral systems

I.5.3.1

59

Allomorphic variants

Allomorphic variants – the type of forms listed under 2a in Table (1.8) above – do not require much comment. The relation between forms like thir- (in thir-teen and thir-ty) or fif- (in fif-teen and fif-ty) and the respective lexical forms three and five is obvious from their phonetic similarity. Likewise – although perhaps a little less transparent but intuitively sufficiently clear – the numerical value ‘2’, if used as a multiplier of ‘10’, is represented by the form twen- for two in twen-ty ‘2 × 10’. The variants of this type do not have any specific function. The distribution of these allomorphs is morphologically conditioned in that they replace their corresponding lexical root whenever they are used in particular combinations in more complex forms. In contrast to the types of variants discussed below, a particular (arithmetic) function cannot be ascribed to them: the same form may be used as an addend (thir-teen ‘3 + 10’; fif-teen ‘5 + 10’) but also as a multiplier (thir-ty ‘3 × 10’; fif-ty ‘5 × 10’). They also do not occur in all cases in which the same numerical value is used in the same arithmetic function: twenin twen-ty ‘2 × 10’ represents ‘2’ as a multiplier but in two hundred ‘2 × 100’, the multiplier ‘2’ is expressed by the default form. Likewise three hundred ‘3 × 100’ and five hundred ‘3 × 100’ have three and five as multipliers but not thir- and fif-. Cf. § II.4.3.1. I.5.3.2

Functional variants

When it comes to cases like -teen and -ty (item 2b in (1.8) above), a different kind of distribution can be observed. These variants are also bound forms and the complementary distribution with the respective simple form, ten in this case, is subject to morphological constraints. However, these forms represent more than mere allomorphic variants of their respective simple forms. The use of these variants for particular numerical values implies a distinct function within the underlying arithmetic operation. If we compare combinations like fif-teen with those of the type fif-ty, the respective arithmetic operators, ‘+’ and ‘×’, are not overtly expressed in both types of formations (cf. §§ I.3.2–3). In both sequences – that of additions to ‘10’ (the teens) and that of multiples of ‘10’ – each atom is represented by the same form in the respective series of combinations, e.g. fif- for ‘5’. The only formal difference between these two sets is the element representing the numerical value ‘10’. We can therefore say that, while ten is the default expression for the numerical value ‘10’, its variant -teen indicates that ‘10’ is used as an augend (and hence stands for ‘+ 10’ ra-

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rather than just for ‘10’) and its other variant -ty indicates that ‘10’ is used as a multiplicand (and hence stands for ‘× 10’ rather than just for ‘10’). In other words, in both types of variants, 2a and 2b of (1.8), the formal deviation of the suffix from the simple form originates in the phonological cross-influence between root and affix. Additionally, the combination of this morphophonemic change in combination with the consistent use of the variant forms in particular arithmetic operations allows the two forms, -teen and -ty – 2b in (1.8) – to become paradigmatically isolated from the simple form ten. In § I.5.2, we have already mentioned the problem that in many languages the morpheme structure of complex numerals needs to be analysed diachronically in order to trace the original numerical meaning of the individual elements or the underlying arithmetic construction. For instance, from a purely synchronic point of view, it is impossible to establish a connection between the suffix -ty and the numeral ten, except perhaps by the fact that they both obviously represent the same numerical value ‘10’. Yet, even in those cases where it is impossible to trace back the etymological origin of such forms in an undisputable way, the most plausible source may still be the simple form (or some ancestor of it). In cases in which we do have some degree of certainty that the functional element is etymologically derived from the simple form, its history plus its morphologically bound character plus its analysis as a functional element (i.e. as an element that determines the (arithmetic) relation between the two numerical values combined) suggests that these elements are the result of a grammaticalisation process (cf. below §§ II.4.2, II.4.3.1, II.7.2 and II.7.3.1 and VON MENGDEN 2008: 303–304).12 The crucial point here being the categorisation of variant forms of numerals, it is still important to note that we find a number of ahistorical descriptions of these affixes. HURFORD (1987: 56), for instance, refers to the general tendency for bases to have variant forms as ‘base suppletion’. HURFORD considers the variants of bases as “phonologically unrelated forms” and compares them to the genuinely suppletive forms of the copula am and is (1987: 56). I believe that such an analysis is difficult to maintain. A clearly suppletive expression like Russian sórok ‘40’ (cf. §§ I.5.2 and III.2.2) stands in a different relation to its paradigmatic neighbours trí-dcat’ ‘3 × 10’ and pjat’-desját ‘5 × 10’ than English -ty and -teen do to ten. Even if the common origin of variant forms for particular numerical values is often synchronically not transparent, the relevant forms are still diachronically related, i.e. derived from the 12 Another possibility – one that is not attested in the history of English – would be that constituents of a complex numeral may undergo univerbation. Recall, for instance, the example of French vingt < Latin viginti < PIE *dui-dḱṃt- ‘2 × 10’).

Idiosyncrasies and variant forms in numeral systems

61

same root. HURFORD himself, in an earlier and strongly generativist (i.e., in those days, purely synchronic) approach assumes that, for instance, /'fIf-/ in fifty and /faIv/ as well as the suffix /'-tI/ and /ten/ are different surface representations of the same element (HURFORD 1975: 37). Similarly in a description of the Danish numerals, HURFORD (1975: 118) assumes that the Danish decades represent arithmetic operations although the respective morpheme structures of the multiples of ‘10’ in Danish are synchronically opaque (see also § III.2.2). In analyses of this kind, the postulation of morphological variation or, for that matter, of varying surface realisations of one and the same underlying form is justified only by the result of an implicit diachronic analysis. In other words, I would strongly argue that a diachronic analysis of these elements has the highest explanatory value with respect to both form and function of these affixes. In any case, as will be seen in detail in §§ II.7.2 and II.7.3.1, the etymological relatedness between the elements -teen and -ty with the simple form ten is a sufficiently safe ground for postulating a relation between the simple form and its functional variants. Having said this, I would concede that, in many cases, we will have to go far back into reconstructed stages of a language – a historical distance which does not always provide safe evidence; also cf. GREENBERG (1978: 263–264.) Interpreting bound forms in numeral systems in this twofold way may not seem necessary in many respects as long as the analysis is restricted to the mere morphological features of the forms. That is, as long as the analysis remains outside the context of the overall systemic arrangement and is limited to the formal aspects of their morphology we do not need to postulate two different kinds of variants. However, it turns out that particularly the postulation of a functional character – in addition to their numerical meaning – bears considerable advantages both for our understanding of the diachronic development of numeral systems and for explaining synchronic generalisations about linguistic numeral systems. While I have illustrated my theoretical discussion using examples from Present-day English, we will see later that Old English provides further evidence for the distinction between functional and allomorphic variants: in Old English, the functional variant -TIG ‘-ty; × 10’ itself has two allomorphic realisations: the suffix -TIG and the circumfix HUND-__-TIG (cf. the more detailed discussion on these two forms below in §§ II.4.3.2–3). This outline of some general features of linguistic numeral systems may suffice as a basis from which we can explore the Old English numeral system. The following chapter will provide a description of the relevant elements and constructions of Old English. There are, of course, a number of crosslinguistic phenomena which could not be included in this first chapter. Some of them – such as for instance ‘1-deletion’ (cf. § III.1.2) or many of the syn-

62

Linguistic numeral systems

tactic properties of numeral constructions (for which cf. Chapters IV and V) – may be treated in a more accessible way when discussed in the context of the relevant phenomena of Old English. Others occur predominantly in languages that are structurally quite distinct from the European languages and will therefore have to be passed over in this book. I.6

Summary: Terminological and theoretical basis for the study of numerals

This section summarises the main points of this chapter and recapitulates the basic notions and the key terminology introduced here. Table 5. Semantic approach: cardinal numerals as quantifiers (as Table 2 in § I.1) Quantification Specification of the cardinality of a set

numerically unspecific

universal

“mid-range” (GIL 2001)

few, several, all, every, … many, most, …

numerically specific (cardinality expressions)

existential

systemic

non-systemic

some, a(n)

one, two, three, …. fourteen, twenty-three, one hundred and seventy-six, ….

dozen, score. three twenties, twice a hundred

cardinal numerals

Summary

I.6.1

Numerals

I.6.1.1

Numerically specific vs. numerically unspecific

63

Semantically, we said numerals are a subtype of quantifiers (which, in turn, are a particular type of noun modifiers). Numerals are numerically specific, which contrasts them with numerically unspecific types of quantifiers, such as universal and existential quantifiers and others. Among the numerically specific quantifiers, we distinguish further between systemic expressions, and non-systemic expressions, of which the former are cardinal numerals. This set of categories and subcategories was discussed in the very beginning of this chapter (§ I.1) and shown in Table 2, which for convenience is repeated above as Table 5. I.6.1.2

Systemic vs. non-systemic number expressions

The term systemic refers to the fact that all cardinal numerals of a language form a numeral system. This is one defining feature of cardinal numerals in contradistinction to all other subcategories of quantifiers. The distinction between systemic and non-systemic cardinality expressions we defined much later in § I.4. The main features we can distinguish cardinal numerals from non-systemic cardinality expressions by are – in addition to the fact that cardinal numerals form a system – their occurrence in the conventionalised counting sequence, their recursive use in more complex numerals and, finally, the fact that they form a morphological basis for derivatives of number expressions, such as multiplicatives, frequentatives, etc. These distinctive properties of cardinal numerals were shown in (1.6) in § I.4.1, which is repeated below as (1.9), albeit with a slight modification. The first bullet point in (1.9) is added, although strictly speaking, the first and the second bullet points can be taken as paraphrases of each other as the sequential character is a prerequisite both for the set of counting words and for the formation of a numeral system. These distinctions may not always be clear-cut. They can best be exemplified by comparing the systemic numeral twelve with the non-systemic expression dozen, both denoting the cardinality ‘12’.

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Linguistic numeral systems

(1.9) Defining properties of systemic numerals Systemic numerals…  …constitute the numeral system of a language.  …correspond to the counting words that occur in the conventionalised counting sequence.  …are used recursively as constituents of more complex (i.e. higher valued) numerals.  …are the morphological basis for the formation of a corresponding form of any other type of numeral (i.e. ordinal, multiplicative, frequentative, etc.).

I.6.2

Numbers

I.6.2.1

Approaches to defining ‘number’

One of the notions that has been employed from the very beginning of our discussion is that cardinal numerals are ‘numerically specific’. Basically, this means that cardinal numerals stand in some semantic relation with natural numbers. Later on (§ I.2.2), we specified that the relation between numerals and numbers is not of semantic nature, but that numerals are in fact instantiations of numbers and that as such – when used in noun modification – can be used for number assignment. The question which therefore needed to be clarified first was: what are numbers? Two approaches to defining numbers are most beneficial for the study of numerals. They are listed in (1.10): (1.10) Defining properties of numbers  Numbers are properties of sets.  The set of (natural) numbers is a set of elements which form an ordered sequence.

We did not go into the details of the logical or mathematical particularities of these two approaches to defining numbers. For the present purpose it was sufficient to say that these two properties of numbers are both crucial to the study of numerals.

Summary

I.6.2.2

65

Definition of ‘numeral’

The question that needed to be approached next is this: what are numerals in relation to numbers? Both defining properties of natural numbers in (1.10) are abstract and hypothesised properties. If we wish to specify the cardinality of a set, we need some more concrete, perceptible items. In § I.2.2 we said that any set of elements forming an ordered sequence can be used as numbers. Every set of elements which form an ordered sequence are, accordingly, instantiations of numbers. Any such set of elements instantiating numbers can be viewed as a (potential) numeral system and the individual elements of a numeral system are called numerals. Accordingly, numerals can have considerably different shapes, for example they can be body parts, graphic symbols, knots, notches, and others, as long as they form, by their physical nature or by convention, an ordered sequence. The physical shape of our object of study, linguistic numerals, is phonetic: as all linguistic expressions they are ultimately sequences of sounds. Yet if a set of elements, which are of the same general physical kind, constitutes an ordered sequence, then all these elements must be distinguished from each other, otherwise the necessary condition that the sequence is ordered could not apply to the entire set in a salient way. Therefore, numerals must be an ordered sequence of well-distinguished elements. Any set of elements which – irrespective of their precise physical properties or shape – meets this condition are instantiations of numbers and can therefore be used for assigning a number (i.e. particular kind of property) to a set. If we view the abstract notion of ‘assigning numbers to sets’ from the perspective of an act of communication, or more precisely in our context, from the perspective of a speaker, we may say that numerals are used to specify the cardinality of a set. As such, numerals are potentially infinite because they represent the set of natural numbers which is defined as infinite. Yet, technically, no numeral system can de facto be infinite. We may say, therefore, that numerals are potentially infinite. Yet, every numeral system is designed such that, by introducing more and more bases, it could theoretically be enlarged ad infinitum. Technically, however, this is not possible and it is probably also not conceivable that the need will arise to regularly specify infinitely large cardinalities. In sum, in order to be numerals, a set of symbols or, in our case, a set of expressions needs to meet the prerequisites listed in (1.11); cf. §§ I.2.2 and I.2.4:

66

Linguistic numeral systems

(1.11) Defining properties of numerals  The elements of a numeral system must be well-distinguished from each other.  The elements of a numeral system must form an ordered sequence.  The numeral system is potentially infinite.

I.6.2.3

Types of number assignment

The elements of a numeral system can be used for number assignment. Number assignment can be of two kinds: cardinal and ordinal. While cardinal number assignment is the type that is relevant to us, ordinal number assignment was (and will be further below) mentioned only briefly. Other paradigms of expressions morphologically derived from cardinal numerals are secondary to these two types and, ultimately, represent special cases of cardinal numerals (cf. § I.2.3). Moreover, what WIESE has introduced as ‘nominal number assignment’ (2003: 37–42) is in fact the use of numerals for a completely different purpose: numerals are often used to label different elements of a group. But this is done in order to distinguish these elements and not for any purpose strictly related with numbers. Numerals used in this way need to be welldistinguished but their sequential order is not relevant. (1.12) Types of number assignment

I.6.2.4

 Cardinal number assignment

– determines the cardinality of a set (i.e. the size of a set measured by the number of its elements)

 Ordinal number assignment

– determines the position within an ordered sequence

Counting words and numerals

With respect to linguistic number expressions, counting words are sometimes distinguished from cardinal numerals proper because they have different (although intimately related) functions and because in a few languages some expression may differ from each other depending on whether they are used as counting words or as numerals proper (§§ I.2.3 and I.4.2.1). Counting words (referred to as ‘absolute’ uses of numerals by GREENBERG 1978: 287) are

Summary

67

those expression that are used when the conventionalised counting sequence is recited. The purpose of this act is either the mere rehearsal of the counting sequence by infants acquiring this set of expressions or the determination of an unknown cardinality of a set. Cardinal numerals, if distinguished from counting words (then referred to as ‘contextual’ uses of numerals by GREENBERG 1978: 287), are used to specify a cardinality of a set already identified by the speaker. I.6.3

The elements and properties of numeral systems

I.6.3.1

The limit number L

The impossibility of infinite numeral systems implies that there must always be a limit number L of a system, which is the largest number that can be expressed by means of a numeral system (§ I.2.4). We may also say that it is the largest number that can be generated by the recursive rules of a numeral system and by the inventory of (simple) expressions of a numeral system. Moreover, there is no numerical value equal to or lower than L which cannot be expressed by means of the numeral system. I.6.3.2

‘Simple’ vs. ‘complex’, ‘atoms’ vs. ‘bases’

If we look at the expressions of a numeral system, one major formal distinction is that of simple and complex expressions. This is primarily a morphological distinction. Simple numerals are mono-morphemic, whereas complex numerals consist of several constituents. Further distinctions, however, are not primarily morphological but functional. The most important of these distinctions is that of ‘atoms’ and ‘bases’. The definitions of atoms and bases are repeated here as (1.13) (cf., respectively, (1.4) in § I.3.5 and (1.3) in § I.3.4.1). (1.13) a

Definition of ‘atom’ Atoms are those morphologically simple elements of numeral systems that have the highest potential to form a continuously recurring (sub)sequence of numerals in combination with bases or their multiples.

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Linguistic numeral systems

(1.13) b

Definition of ‘base’ In any formation pattern of a numeral system, bases are those elements with which the smallest continuously recurring sequence of numerals is combined.

Bases and atoms are both simple expressions. Their complementary relation plays a crucial role in the formation of complex expressions and thus in the overall arrangement of numerals in the system (also cf. below § III.2.1). While there is a comparatively simple and fixed set of simple expressions, complex numerals are those that are potentially infinite. This is because complex expressions are generated recursively, i.e. out of the stock of existing simple forms. Semantically, these combinations of atoms and bases represent arithmetic operations. The distinction (and at the same time the relation) between atoms and bases is therefore situated on the interface between morphological analysis of the forms of numerals on the one hand and, on the other, the underlying arithmetic operations. In other words, the syntagmatic structure of complex numerals is constructed on the basis of arithmetic operations. I.6.3.3

Arithmetic operands

All types of arithmetic operations are attested to be involved in numeral systems of natural languages. In this chapter, we have restricted ourselves to multiplication and addition because these types of operations are far more frequent than the respective inverse operations, subtraction and division, and they are also considerably more frequent than exponentiation. Because both arithmetic and morphology (or, morphosyntax) play a role in the formation of complex numerals, the types of arithmetic operations are crucial for the description of the formation processes. Moreover, while in mathematics in the two positive operations, addition and multiplication, the order of the arguments is irrelevant, it is relevant with respect to the morphology of complex numerals. We therefore distinguished between the respective constant argument in an addition and in a multiplication and the variable argument in both addition and multiplication (§ I.3.3). Augends and multiplicands are the constant elements of the respective operation types, whereas addends and multipliers are the corresponding variables. Basically this implies that in every possible complex structure of a numeral system an augend can be augmented not only by one particular addend, but by every member of a particular (sub)sequence: if twenty can be augmented by four, it can also be augmented

Summary

69

by every member of the sequence from one to nine. Accordingly, every multiplicand is multiplied by every multiplicand in a sequence: if thousand can be multiplied by eighteen, it can also be multiplied by every other member of the sequence from one to ninety-nine. Cf. Table 6: Table 6. Linguistic expressions as arithmetic operands constant

variable

(multiple of) a base

element of a (sub)sequence

multiplication

addition

augend thir-teen twenty-four six hundred and twelve

addend

‘3 + 10’ ‘(2 × 10) + 4’ ‘(6 × 100) + 12’

multiplicand twen-ty six hundred nine thousand

‘2 × 10’ ‘6 × 100’ ‘9 × 1000’

thir-teen twenty-four six hundred and twelve

‘3 + 10’ ‘(2 × 10) + 4’ ‘(6 × 100) + 12’

multiplier twen-ty six hundred nine thousand

‘2 × 10’ ‘6 × 100’ ‘9 × 1000’

When we discussed the numeral systems of Welsh and Sora in §§ I.3.3–4, we saw that there are languages in which this is not always the case. In numeral systems of some languages, operands can also be employed in combination with only one single expression or with only a small number of expressions. For this reason, we distinguished between serialised and sporadic augends and between serialised and sporadic multiplicands. This, for instance, is the case in Welsh where the numerical values ‘16’, ‘17’, and ‘19’ are expressed as un ar bymtheg ‘1 + 15’, dau ar bymtheg ‘2 + 15’, pedwar ar bymtheg ‘4 + 15’. Here, it is still possible to distinguish between an augend (bymtheg ‘15’) and addends (un ‘1’, dau ‘2’, pedwar ‘4’) but we would call the augend bymtheg a ‘sporadic augend’ in contrast to a ‘serialised augend’ which is always combined with an entire subsequence. In the same way, the Welsh expression for ‘18’, deu-naw is expressed as ‘2 × 9’. Because there is no arithmetically parallel construction in the whole counting sequence of Welsh, it is difficult to distinguish between the ‘multiplier’ and the ‘multiplicand’ in this particular expression. In any case, the multiplicand is a sporadic multiplicand and not a serialised one. At any stage of the history of English, sporadic operands are not known to have been part of the numeral system, which is why, for the description of Old English, this distinction will not be relevant.

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Linguistic numeral systems

I.6.3.4

Idiosyncratic numerals

The different forms that are used as constituents in complex numerals can be analysed not only from the point of view of their arithmetic functions, but also with respect to their morphological properties. However, morphology and arithmetic function are often connected. In fact, one can say that at least part of the morphology of linguistic numeral systems encodes functions that are primarily arithmetic. Some numerals (simple or complex) are merely idiosyncratic in their form but in order to describe the idiosyncrasy, we still need to draw on the underlying arithmetic operations. If there are idiosyncratic simple forms, they are usually in a position of the counting sequence in which a complex form should be expected, such as eleven and twelve rather than *one-teen and *two-teen. In our typology proposed in (1.8) in § I.5.1, these cases are listed as Type 1a. There can also be complex forms that deviate in form although they still represent the same arithmetic pattern as the other, regular expressions of the same subsequence. For instance, the teens in the Romance languages all represent additions with the augend ‘10’, but while in most expressions the addend precedes the augend in some – varying from language to language – the addend follows the augend; cf. § I.5.1, Type 1b in (1.8). Additionally, serialised augends such as quatre-vingt ‘4 × 20’ in Standard French form the basis for an entire section in the counting sequence in which the arithmetic pattern deviates from the rest of the system (Type 1c in (1.8)). Finally, recall that the distinction drawn here is a gradual one – ultimately also depending on the degree to which we allow for a diachronic analysis of these structure. Most idiosyncratic forms, particularly the mono-morphemic ones, historically developed out of complex expressions (which may or may not have been idiosyncratic themselves). Cf. further § II.3. I.6.3.5

Allomorphic and functional variants

Other types of morphological variation are more intimately connected with the underlying arithmetic operations. These forms of this type (Type 2 in (1.8); cf. §§ I.5.1 and I.5.3) are all bound forms that occur under particular lexical or arithmetic conditions. Some of these forms are allomorphs of the respective simple numerals. In Present-day English, these are for instance twen- ‘2’ in twenty, thir- ‘3’ in thirteen or in thirty, and fif- ‘5’ in fifteen and fifty. These are lexically conditioned as they occur in particular combinations without that a specific function could be attributed to these variants (Type 2a in (1.8)).

Summary

71

In other cases, morphology actually encodes arithmetic operations. These forms show that the morphology of numeral systems can be said to be largely independent from the rest of the grammar of a language. It is possible to view these functions (i.e. the arithmetic operations) as crucial parts of an ‘internal grammar’ of numeral systems because the functions encoded by these morphemes are functions that do not occur outside the formation of complex numerals. We called them ‘functional variants’ and listed them as Type 2b in (1.8). Examples of such morphemes are the suffixes -teen and -ty in Presentday English. Both represent the numerical value ‘10’, but both of them at the same time encode whether the value ‘10’ is used as a serialised augend (-teen ‘+ 10’) or as a serialised multiplicand (-ty ‘× 10’). Because they are involved in the formation of complex numeral expressions, suffixes of the type PDE -teen and -ty often appear to be derivational affixes. But, at the same time, by indicating the type of arithmetic operation underlying the respective formation, these morphemes also always encode a ‘grammatical’ function in the sense that the arithmetic operations can be said to constitute the ‘grammar’ of the numeral system. These affixes involved in the formation of complex numerals, therefore, stand outside the derivation/inflection dichotomy. In any case, since both are -teen and -ty are historically derived from an expression representing the numerical value ‘10’, they are the result of a grammaticalization process (cf. § I.5.3.2, II.4.2, II.4.3.1, II.7.2 and II.7.3.1). For convenience, the categorisation of the suffixes discussed here is summarised in Table 7. Table 7. Conditioned variants of simple numerals (Type 2 in (1.8)) allomorphic variants

lexically conditioned

twen- ‘2’ in twenty thir- ‘3’ in thirteen, thirty fif- ‘5’ in fifteen, fifty

Type 2a in (1.8)

functional variants

encode arithmetic operation

-teen ‘+ 10’ -ty ‘× 10’

Type 2b in (1.8)

Chapter II The numeral system of Old English The general introduction to cardinal numerals and numeral systems presented in Chapter I provides a basis for our language-particular description of the numeral system of Old English. This description will comprise Chapters II and III. Although the perspective will not be primarily cross-linguistic in these parts, a comparison of Old English forms and corresponding structures in other languages will of course be drawn whenever it seems appropriate. Moreover, this and the next chapter will contain detailed analyses of those features of the Old English numeral system which are typologically rare and, therefore, particularly interesting to look at from a more general linguistic point of view. The most prominent of these are, as briefly mentioned in the Introduction, the overrunning sequence of multiples of ‘10’, i.e. the method of counting beyond the second base with expressions of the type ‘ten-ty’, ‘eleven-ty’, twelve-ty’, which will be discussed in detail in §§ II.4.3.3, II.5, and II.7.2.1, or the typologically uncommon morphological break between ‘60’ and ‘70’ in the marker for the serialised multiplicand ‘× 10’, which we will discuss in detail in §§ II.4.3.2 and II.7.2.2. In addition to the descriptive parts of this chapter, some of the points raised in the previous chapter will be resumed in the following. For instance, our typology of variant forms proposed in § I.5.3 will not only be applied to the system of Old English, but will also find additional support in another feature that does not exist in Present-day English or in other modern European languages: in addition to the respective affixes -TYNE ‘+ 10’ (cf. § II.4.2) and -TIG / HUND-__-TIG for ‘× 10’ (cf. § II.4.3), which correspond functionally to their respective Present-day English counterparts -teen and -ty, a similar functional distribution can be identified for the different expressions for ‘100’ (cf. § II.5.2). Moreover, Chapters II and III will also introduce additional aspects of numeral systems, which are cross-linguistically highly relevant but have not been included into the theoretical discussion of Chapter I. These are, for instance, phenomena like the ‘Packing Strategy’ (§ II.4.3.3) or ‘1-deletion’ (§ III.1.1). The present Chapter II will deal mainly with the individual numeral forms. The earlier parts of this chapter, in which the simple forms will be presented (§§ II.1–II.4.1), will out of necessity be predominantly descriptive. In the later sections, especially in §§ II.4.2–II.6, the general morphological principles of the formation of complex numerals in Old English will be described and ana-

Overview: the simple forms

73

lysed according to the framework developed in Chapter I. The remaining sections of this Chapter II will complement the descriptions up to § II.6 in two different ways. In § II.7, the predominantly synchronic data presented up to that point will be embedded into a diachronic context by briefly sketching the development of the Old English numeral system. The second addition to the data presented in §§ II.1–6 will be a short overview of the morphological formation of ordinal numerals in § II.8. Both § II.7 and § II.8 may have slightly parenthetical character but both prepare later discussions by providing information which will become important for explaining phenomena presented in later chapters. A more detailed discussion of the internal structure of complex numerals will follow in Chapter III. The general idea is that the basic principles of composition, which are quite unambiguously morphological processes, will be part of Chapter II, whereas Chapter III will deal with aspects of the internal syntax of Old English cardinal numeral constructions. Yet, as briefly discussed in § I.3.6, much of the analysis of complex numerals is located in a grey area between morphology and syntax. A proper distinction between the two domains of linguistic description will, therefore, not always be possible and, more importantly, not useful either. Moreover, as many phenomena and processes presented here are situated in the interface between syntax and morphology, some of the aspects discussed in this chapter will be resumed or analysed in a more detailed way in Chapter III. II.1

Overview: the simple forms

The atomic numerals of Old English constitute the series of lowest valued numerals up to the first (i.e. to the lowest valued) base without any idiosyncrasies disturbing the sequence. In Old English, there are nine atomic numerals for the numerical values from ‘1’ to ‘9’ and the lowest base of the numeral system represents the numerical value ‘10’. In this respect, Old English does not differ typologically from any other Germanic language and from most other languages with a decimal numeral system. Higher base numerals usually represent powers of the lowest base numeral. This is the case in Old English, too, where the second and the third power of ‘10’ are represented by base numerals. As theoretically discussed in § I.3.1, atoms and bases can only be described by simply listing the relevant forms because their shapes are arbitrary and mono-morphemic. The following simple lexical entries are the nine

74

The numeral system of Old English

atomic numerals (Figure 3) and the three base numerals (Figure 4) of Old English.13 ‘1’

‘2’

‘3’

AN

TWA

ÞREO

Figure 3.

‘4’ FEOWER

‘6’

FIF

SYX

‘7’ SEOFON

‘8’ EAHTA

‘9’ NIGON

Atomic numerals of Old English ‘101’

‘102’

103’

HUND(RED)

TYN

Figure 4.

‘5’

ÞUSEND HUNDTEONTIG

Base numerals of Old English

Generally, any numeral valued higher than the lowest base is expressed as a complex numeral unless it is itself a base. In the Germanic languages, however, the expressions for the two numerical values subsequent to the base ‘10’ – i.e. ‘11’ and ‘12’ – are, analysed synchronically, simple and arbitrary forms in the same way as atomic and base numerals. However, because they are neither bases nor atoms, they constitute an idiosyncrasy. In § I.5.2, we categorised expressions of this kind as Type 1a (cf. (1.8)). Consequently, just like atoms and bases in Figures 3 and 4 above, the two expressions can only be described by listing them; cf. Figure 5. See further § II.3 below. ‘11’ ENDLEOFAN

Figure 5.

‘12’ TWELF

Old English expressions for ‘11’ and ‘12’

These lists in Figures 3 – 5 show the unmarked Classical West Saxon forms. It should, however, be borne in mind that, for many of these expressions, there is a considerable variation of actually attested forms. This is caused by many factors such as different scribal conventions, phonological changes during the Old English period and, in most of the cases, dialectal differences. Such dif13 See note 3 in § I.3.1.

Overview: the simple forms

75

ferences cannot be dealt with in detail here and they will be taken into consideration only in relevant cases. I take the forms listed in Figures 3 – 5 as the default forms on which the following discussion will be based, being aware that this is a simplification of what we understand the linguistic reality in Old English times to be. II.2

The atoms

II.2.1

The numerical value ‘1’

A discussion of the forms of OE AN ‘1’ as a numeral in the strict sense is difficult, perhaps impossible. AN is used with a wide range of semantic and functional nuances, of which the strictly numerical sense – i.e. the specification of the cardinality ‘1’ – and the use as a genuine indefinite marker constitute the two extremes. While the morphosyntactic behaviour of AN, if unambiguously used as a numeral, generally corresponds to that of the numerals ‘2’ and ‘3’, other, more pronominal uses allow a wider range of morphosyntactic properties displaying correspondences with those of both adjectives and pronouns. In particular uses, for instance, a distinction between weak and strong adjective inflection is made and there are also examples of plural inflection. To scrutinise the range of attested functional implications of AN and the respective morphosyntactic properties would by far exceed the scope of this study. Since a clear distinction between a numerical and a determiner use of AN is generally difficult, if not impossible, to draw, all we can say here is that the more the specification of the cardinality ‘1’ is implied by a particular use of AN, the more likely its inflection is to be restricted to the paradigm of the strong adjectives. Weak forms of AN are generally not used as consistently as those of genuine adjectives. However, the more AN is used in a particular case solely to mark indefiniteness, the more likely it is that the weak forms will be employed. If used in the sense of ‘sole, exclusive, only’, the weak form for the nominative masculine ANA predominates, and a consistent assignment of a Case or Gender value by the modified NP, i.e. the use of weak forms other than that of the nominative masculine is rare. As a frequentative adverb, the strong genitive singular masculine form ANES is used in the sense ‘once’.14 An overview of the inflectional forms is given in Tables 8 and 9. Of these forms, 14 A detailed and useful examination of the various uses of AN has been provided by SÜSSKAND (1935), RISSANEN (1967), MITCHELL (1985 I: 208–216, §§ 523–547) and, less comprehensively, by RISSANEN (1972) and (1997), finally also in DOE, s.v. “ān”.

76

The numeral system of Old English

the variant /'enn@/ of the masculine accusative forms is limited to the Anglian varieties.

Table 8. Strong forms of AN M

N

Table 9. Weak forms of AN

ān

NOM

M

N

F

āna

āne

āne

F NOM

GEN

ānes

ānes

ānre

GEN

ānan

DAT

ānum

ānum

ānre

DAT

ānan

ACC

ānne, ænne, enne

ān

āne

ACC

ānan

INS

II.2.2

¢ne, āne

The numerical value ‘2’

The most common forms for ‘2’ are TWEGEN (/'twe;j@n/), TWA and TU. All of these are nominative and accusative forms. Genitive forms are TWEG(R )A (/'twej(r)a/), dative forms are TWAM or TWÆM; cf. Table 10. An arithmetic allomorph is TWEN-, which is used if ‘2’ is a multiplier of ‘10’, i.e. in TWENTIG ‘20’ (cf. §§ I.5.3.1 and I.6.3.5 for its Present-day English equivalent). Finally, there is a frequentative form TUWA ‘twice’. For ordinal forms see § II.8.2 below. Table 10. Inflectional paradigm of TWA ‘2’

NOM

M

N

F

twegen

twa, tu

twa

GEN

twegra, twega

DAT

twam, twæm

ACC

twegen

twa, tu

twa

A few remarks will be necessary on the distribution of the nominative/accusative forms. While TWEGEN is generally the form used when masculine

The atoms

77

nouns are quantified and TWA the one used for feminine nouns, the uses of TWA and TU overlap when it comes to the quantification of neuter nouns. In poetry, the distinction between TU for the neuter and TWA for the feminine nouns seems to be kept clearly. If TWA in a poetic text quantifies a non-feminine noun, it is generally used when the referent is a couple as in (2.1) or when there are two quantified nouns of different grammatical Gender, as in (2.2) and (2.3).15 In the few instances in which this does not apply, the numeral does not immediately precede the quantified noun.16 (2.1) GenAB 840 (KRAPP 1931: 28): Hwurfon hie ba twa, togengdon gnorngende oon þone grenan weald They both [i.e. Adam and Eve] left, departing with lament into the green forest. hwurf-on hie leave\PST-PL PPRN:NOM.PL

ba both(NOM)

twa two(NOM)

(2.2) MCharm 2 36 (DOBBIE 1942: 120, 36): Fille and finule, felamihtigu twa, þa wyrte gesceop witig drihten, halig on heofonum, þa he hongode; […] The wise Lord, holy in heaven, created these herbs, thyme and fennel, the powerful two. fille and thyme( F) and

finule fealmihtig-u twa fennel( M) very powerful-NOM.PL two(NOM)

15 In (2.3) it is remarkable that the adjective CEALD ‘cold’ has a feminine ending. This implies that, while the form TWA is employed because the quantified NP is ambiguous with respect to its grammatical Gender (wæter(N) ‘water’ and eorðe(F) ‘earth’), the use of the otherwise feminine TWA as a form unmarked for Gender controls the (feminine) Gender value of the adjective. 16 At this point of the discussion, I will disregard syntactic differences in the way the numeral quantifies the referent. They will be in the focus in Chapter IV. In (2.1)–(2.3), for instance, the numeral never immediately precedes the quantified noun. For an in-depth analysis of constructions of this kind cf. § IV.3.2.

78

The numeral system of Old English

(2.3) Met 20.75 (KRAPP 1932b: 179, 76): Wæter and eorðe wæstmas bringað; þa sint on gecynde cealda ba twa, […]. Water and land bring forth the fruits; both are cold by their nature; wæter and water(N) and

eorðe land(F)

wæstmas bring-að fruit(M)-ACC.PL bring\PRS-3PL

sint be(PRS.3PL)

on

ba both(NOM)

twa two(NOM)

PREP

þa DEM:NOM.PL

gecynd-e cealda kind-DAT.SG cold-NOM.PL.F

In a similar way, the use of TU as an exclusively neuter numeral can expand in poetic texts into contexts in which the referent set consists of two persons (regardless of their sex); cf. (2.4) and (2.5). Again, in deviating instances the numeral does not immediately precede the noun. In (2.6), for instance, the referent is specified by the masculine noun heahengel ‘archangel’ (line 751). (2.4) GenAB 2780 (KRAPP 1931: 83): Þa seo wyrd gewearð þæt þæt wif geseah for Abrahame Ismael plegan, ðær hie æt swæsendum sæton bu tu, halig on hige, […] Then it happened that the woman saw Ismael playing before Abraham as they were both [i.e. Hagar and Abraham] sitting mild-heartedly together at supper, […] hie

æt

PPRN :NOM.PL

PREP

bu both(NOM)

swæsend-um dinner-DAT.PL

sæt-on sit\PST- PST.3PL

tu two(NOM)

(2.5) Rid 63 4 (MUIR 2000: 363, 5): Hwilum mec on cofan cysseð muþe tillic esne, þær wit tu beoþ, […] The good servant sometimes kisses me with his mouth in the chamber where there are the two of us, […] þær there(REL)

wit PPRN(NOM.2DU)

tu two(NOM)

beoþ be(PRS.3PL)

The atoms

79

(2.6) El 751-3 (KRAPP 1932a: 87, 753): “Halig is se halga heahengla god, weoroda wealdend! Is ðæs wuldres ful heofun ond eorðe ond eall heahmægen, tire getacnod.” Syndon tu on þam, sigorcynn on swegle, þe man seraphin be naman hateð. Holy is the God of the holy archangels, the Lord of the hosts. Heaven and earth are full of glory, and all his mighty power is clearly proclaimed. – There are two among them in heaven, a victorious kind, whom we call by the name Seraphim. syndon be:PRS.3PL

tu two(NOM)

Both TWA and (less frequently) TU can be used in the phrase on twa ‘asunder’ (for which cf. § IV.3.2.2). TWEGEN, by contrast, is used in poetry only if it quantifies one masculine noun. In prose, TWEGEN remains the form used exclusively for the quantification of masculine nouns. If compared with TWA and TU, TWEGEN clearly has a marked character. First, it hardly ever occurs as an atomic addend in complex numerals. Second, whenever the Gender value of the quantified noun is ambiguous, either of the other two forms, TU or TWA, is used, but never TWEGEN. The marked use of TWEGEN can be explained by its etymology: the form is apparently originally bi-morphemic; of the two elements, only the first is derived from the proto-Germanic paradigm of the numeral ‘2’.17 In prose, TU and TWA are generally distributed along diachronic lines rather than according to Case/Gender values or types of referents. The type TU is completely absent in all typical representatives of Classical West Saxon, such as Ælfrician texts, Byrhtferth’s Manual, Wulfstanian texts, and the Benedictine Rule. On the other hand, both forms are used in the earlier Alfredian texts18 with the relative frequency of TU in Early West Saxon being clearly 17 The origin of the second element is disputed; it may go back to a pronominal form in protoGermanic, i.e. *yeno-, which survives in the modern (though archaic) form yon (cf. SIEVERS 1885: 495, n. 1; HOLTHAUSEN 1888: 372; PROKOSCH 1939: 273, § 93.4 and 286, § 99). In later contributions, a distributive function (rather than pronominal) of /-jen-/ has been suggested: SEEBOLD (1968: 433) compares the formation with Old Church Slavic dъvojьnъ ‘double’ and trojьnъ ‘triple’, while L ASS (1994: 209–210) refers to Classical Latin bini ‘two each’, terni ‘three each’. 18 Here and in the following, I refer to the group of texts assumed to have been produced under the influence or by instigation of King Alfred’s reign, independent of the degree of the king’s personal involvement as translator or author. These texts are comprised in various sources provided by the DOE-project under the Cameron-number ‘B 9’. Hence, the term ‘Alfredian’ is employed as a convenient cover term in spite of the fact that it has long been assumed that Alfred was not the author (in a narrow sense of the term) of some of the

80

The numeral system of Old English

higher than in the corpus as a whole.19 The fact that – according to the preferences of the respective texts or periods – both types can be used as addends in compound numerals indicates that, diachronically, the form TWA replaces TU as the default expression for the numerical value ‘2’. II.2.3

The numerical value ‘3’

The forms for ÞREO ‘3’ are shown in Table 11. The most frequent nominative/accusative masculine form is ÞRY (/'θri;/), which is also the Classical West Saxon form. ÞRI and, particularly in early texts, ÞRIE (/'θri;@/) are also common. The genitive is ÞREORA, the dative ÞRIM, spelled 〈þrim〉 or 〈þrym〉. Table 11. Inflectional paradigm of ÞREO ‘3’ M NOM

þrȳ, þrī(e)

N

þreo

GEN

þreora

DAT

þrim, þrym

ACC

þrȳ, þrī(e)

þreo

F

þreo

þreo

In Anglian texts, the feminine and the neuter forms ÞREO are also used for the masculine Gender; i.e. there is no form of the type ÞRIE / ÞRI / ÞRY in a northern text (cf. example (4.81)b and fn. 50 in § IV.7). This type is the default expression for the numerical value ‘3’ in Old English. Not only is the type ÞREO used almost exclusively as the addend ‘3 +’ in compound numerals (as in ÞREO-TYNE ‘3 + 10’), but the genitive forms, occasional forms of the dative, and the frequentative numeral are also modelled after ÞREO. Additionally, there is also a frequentative form for the numerical value ‘3’, which is ÞRIWA ‘thrice’. texts (but cf. VON MENGDEN 2006a: 235, fn. 10) and in spite of the fact that some of the relevant texts show more Mercian features than Early West Saxon ones. 19 Moreover, in those Alfredian texts that are preserved only in twelfth-century manuscripts (Soliloquii; Alcuin’s De virtutibus et vitiis), TU is not attested at all but TWA is. Another indicator of the preference for TU in early documents can be found by comparing the various versions of the Anglo-Saxon Chronicle: in the earliest copy, the Parker Chronicle (ms. CCCC 173 – the relevant entries are written around AD 900), the relative frequency of 〈tu〉 and 〈twa〉 is 9 : 4. All other versions use TWA almost throughout.

The atoms

II.2.4

81

The atomic values from ‘4’ to ‘9’

The numerals from ‘4’ onwards were inflected according to the nominal i-stems. Most instances of inflected numerals in Early and Classical West Saxon still reflect the forms of this paradigm. In the eleventh century and even more so in post-Conquest Old English, inflectional endings from the consonantal stems became more frequent (cf. §§ IV.2.1, IV.3.1 and IV.5.2.2). The use of the i-stem-endings is phonologically relevant in so far as most of the numerals in Old English must have been affected by i-umlaut, which can be accounted for only by the regular use of inflected forms at a pre-historic stage. In West Saxon, there is a tendency for the numerals from ‘4’ onwards to show Case distinction only if the numeral does not immediately precede the quantified noun. In such cases, the numerals employ the respective endings of the i-stems, i.e. nominative/accusative -e., genitive -a, and dative -um. This is likely to apply for Kentish too, but the evidence in Kentish texts is too scarce to warrant any definite statements. In any case, even in West Saxon, this must be taken as a tendency rather than a rule; cf. e.g. the impressive list of counterexamples provided by STILES (1986a: 9–11) for the numeral FEOWER alone. In the Northumbrian glosses, numerals are more likely to show inflection but with a more ambiguous marking of syntactic relations. The smaller degree of consistency in the employment of particular Case forms and the generally higher relative frequency of inflected forms in Northumbrian may simply be explained by the fact that the main documents are interlinear glosses in which the inflectional behaviour of an Old English numeral may follow the Latin model rather than the constraints of the vernacular usage. The most commonly used Case endings of numerals in the Northumbrian glosses and in the Mercian Rushworth 1 are -a, -o, and -u for the nominative/accusative. The suffixes -a for the genitive and -um for the dative occur rarely. The expressions for ‘4’ and ‘5’ do not show considerable variation. ‘4’ is expressed as FEOWER (/'fe;ower/) with minor spelling variants in some northern documents. ‘5’ is very consistently expressed as FIF (/'fi;f/). For SYX ‘6’, several spellings, 〈siex〉, 〈six〉, and 〈syx〉, are common. The most frequent form for ‘7’ is SEOFON although the spelling both in the root and in the final syllable varies to a considerable degree. A greater variation of forms is attested for ‘8’. While the most common form, EAHTA, is limited to West Saxon and Kentish, the northern varieties use ÆHTA and, occasionally, ÆHTOWE. All these types vary in spelling. ‘9’ is expressed as NIGON (/'niγon, -@n/) again with varying representations of both vowels.

82

II.3

The numeral system of Old English

The expressions for ‘11’ and ‘12’

While the numerical value ‘12’ is expressed as TWELF very consistently across diachronic and diatopic varieties of Old English, the different dialects of Old English use different, though related forms for ENDLEOFAN ‘11’. The most frequent written forms in West Saxon are 〈endlufan〉 and 〈endleofan〉 – with variation in the representation of the vowels of the final and penultimate syllable – the Northumbrian form is 〈ællef(n)-〉, the Mercian and Kentish use ændle(o)fan. Both ENDLEOFAN and TWELF are idiosyncratic forms (cf. §§ I.5.2 and II.1). The fact that the system employs the numerical value ‘10’ as its smallest and thus fundamental base would require the expressions of the decade following ‘10’ to be expressed as additions with ‘10’ and hence as complex expressions. Yet, while the expressions from ‘13’ to ‘19’ are in fact expressed as additions (as shown below § II.4.2), the two forms appear as simple, non-analysable, expressions. This analysis holds only from a synchronic perspective. If, however, we take a look at the etymologies of ENDLEOFAN and TWELF, we can see that they used to be bi-morphemic in the proto-Germanic period, i.e. *aina-lif- ‘1 remaining [beyond 10]’ and *twa-lif- ‘2 remaining [beyond 10]’ (cf. § II.7.1.2). The diachronic analysis of their respective forms reveals that they used to be irregular even at a stage when their morpheme structure was still transparent because, although complex, it nevertheless deviated from the subsequent elements from ‘13’ onwards (‘x remaining [beyond 10]’ vs. ‘x + 10’). According to the typology of irregularities postulated in § I.5 above (cf. (1.8)), the two expressions belong synchronically to Type 1a, whereas diachronically they belong to Type 1b. Whenever idiosyncratic simple forms interfere with a regularly systematic sequence of numerals, it is possible, if not likely that compound forms are historically underlying. This observation supports the claim made in § I.5.2, i.e. that the existence of idiosyncratic simple forms does not contradict the generally systematic character of a numeral system. In spite of the explanatory force of a diachronic analysis of idiosyncratic forms, an isolated, i.e. noncomparative, analysis of one particular numeral system requires a synchronic analysis of the system and its idiosyncrasies. Therefore, for a grammatical description of Old English, the expressions ENDLEOFAN and TWELF should be considered as idiosyncratic simple forms.

The first base ‘10’

II.4

The first base ‘10’

II.4.1

The simple forms for ‘10’

83

The attested simple forms for the numerical value ‘10’ vary considerably in terms both of spelling and geographical distribution. Token-wise, the most frequently attested spelling is 〈tyn〉 (for /ti;n/), which is predominant in Classical West Saxon texts. Besides this, West Saxon also uses 〈ti(e)n〉 and a diphthongised type 〈tion / teon〉, the latter being also attested in Kentish. The main type in Northumbrian is 〈tea〉. Diatopically, the most widespread variant is 〈ten〉. It is predominant in Mercian, but it also occurs as a minor variant in late West Saxon, Kentish, and Northumbrian. II.4.2

The teens

Except for the higher bases, all numerals of Old English from the numerical value ‘13’ onwards are complex numerals. Arithmetically, the expressions from ‘13’ to ‘19’ are formed as additions with the base as augend and the atomic numerals forming the sequence of addends (from which excluded are the values ‘2’ and ‘3’ in this particular section). The element -TYNE (〈-tyne〉 with the variants, particularly in earlier documents 〈-tine〉 and 〈-tiene〉, and occasionally 〈-tene〉 in Kentish) is used as a suffix attached to the atomic numerals in the sequence from ‘13’ to ‘19’ and represents the augend ‘+ 10’ (cf. § I.5.3.2). Diachronically, the relevant expressions for the numerical values from ‘13’ to ‘19’ consist of the respective atomic numeral and an inflected form of the base numeral TYN with the inflectional suffix *-i > -e; cf. e.g. BRUNNER (1960–62 II: 90). This shows that -TYNE is derived from the simple form for ‘10’. Since the use of inflection in the relevant expressions has been reduced almost completely in Old English, the originally inflected form -TYN-E became fossilised. This allowed for the paradigmatic isolation of the sequence -TYN-E ‘+ 10’ from TYN ‘10’ and for its concomitant reinterpretation as a suffix encoding the arithmetic function ‘augend’, i.e. ‘+ 10’. In other words, -TYNE is the result of a grammaticalisation process by which a simple form comes to be used as a suffix which does not represent the mere numerical value ‘10’ as its source lexeme does, but a specific arithmetic function of it, i.e. ‘+ 10’; cf. VON MENGDEN (2008: 303–304). The distinction that emerged between TYN and -TYNE also allows the operator ‘+’ to not be overtly expressed because the type

84

The numeral system of Old English

of arithmetic operation is inherent in the use of the formally distinct affix -TYNE ‘+ 10’. The resulting complex forms for the sequence of teens are shown in Figure 6. ‘13’

‘14’

‘15’

‘16’

‘17’

‘18’

‘19’

3 + 10

4 + 10

5 + 10

6 + 10

7 + 10

8 + 10

9 + 10

þreo-tyne

feower-tyne

fif-tyne

syx-tyne

seofon-tyne

Figure 6.

II.4.3

eahta-tyne

nigon- tyne

Old English expressions for the teens

The multiples of ‘10’

II.4.3.1 The expressions up to ‘60’ Only nine elements of the second decade were described in the preceding section. The tenth element of the second decade is expressed as the second multiple of the base ‘10’, i.e. TWEN-TIG ‘2 × 10’. Accordingly, all multiples of ‘10’ are expressed by an atomic numeral (or a variant of it) as a multiplier and an element representing ‘10 as a multiplicand’ or ‘× 10’. Up to ‘60’, this element is the suffix -TIG; cf. Figure 7. ‘10’

-tyne Figure 7.

‘20’

‘30’

‘40’

‘50’

‘60’

2 × 10

3 × 10

4 × 10

5 × 10

6 × 10

twen - tig

þri - tig

feower-tig

fif - tig

syx - tig

Old English expressions for the serialised augends from ‘10’ to ‘60’

The sequence of atoms is used cyclically as addends to each multiple of ‘10’. However, opposite to the constituent order in the corresponding formation type in Present-day English, the atomic addends precede the augends, as shown in Figure 8. The following decades are arranged accordingly: the terminal element of any preceding decade is used as augend for the sequence of atomic numerals, i.e. an and twen-tig ‘1 + (2 × 10)’, twa and twen-tig ‘2 + (2 × 10)’, þreo and twen-tig ‘3 + (2 × 10)’, etc. In contrast to the second

The first base ‘10’

85

decade – and also in contrast to the Present-day English usage (cf. § II.7.3 below) – the operator ‘+’ needs to be overtly expressed from ‘21’ onwards. Since the element representing ‘10’, the suffix -TIG, already encodes the function ‘multiplicand’ (i.e. ‘×’, cf. below), the conjunction AND links the atomic numeral with the multiple of the base thus encoding the operator ‘+’ in the addition with the multiple of ‘10’. The final element of the third decade is the expression for the third multiple of ‘10’, i.e. ÞRI-TIG ‘3 × 10’, which in turn serves as an augend in the fourth decade, i.e. an and þritig ‘1 + (3 × 10)’ etc.; cf. Figure 8: ‘21’ 1

+

1

[…] […]

2

+

+ (2 × 10)

[…]

2

+

an and twen - tig

[…]

Figure 8.

20

‘32’

[…] 30

‘67’

[…]

7

+

60

(3 × 10)

[…]

7

+

(6 × 10)

twa and þri - tig

[…]

seofon and

syx - tig

Atomic numerals as addends to the multiples of the base

The element TWEN- in TWEN-TIG ‘2 × 10’ is an allomorph of TWA representing the multiplier ‘2’ (cf. § I.5.3.1). Apart from its phonological form /'twen-/, there are a couple of further aspects which support the assumption that the allomorph TWEN- is a shortened form of TWEGEN. Important evidence in support of this analysis is that there are a few instances of an unshortened twœgentig in northern documents. Other phonological arguments indicating a connection between TWEN-, TWEGEN, and the genitive TWEG(R)A are discussed by VAN HELTEN (1905/06: 117–118), HORN (1923: 106–107, § 103) and, with a slightly different line of argument, SEEBOLD (1968: 430–432). However, the clearest evidence in this case is certainly the correspondence in the diatopic distribution of the graphemic representation of the vowels, which alternates between 〈-a-〉 and 〈-æ-〉. In geographical distribution of the two graphemes, 20 TWEN- corresponds with TWEGEN and TWEG(R)A but differs from TWÆM .

20 Some scholars, most recently ROSS/BERNS (1992: 613, § 15.1.22), have suggested that the element TWEN- is derived from the dative form TWÆM. However, not only is it semantically implausible that the multiplier in the expression ‘2 × 10’ should be a (former) dative form, the typologically uncommon construction would also require an explanation of why dative forms are unattested in the other expressions for multiples of ‘10’.

86

The numeral system of Old English

‘3’ as a multiplier in the sequence of multiples of ‘10’ is also represented by an allomorph, i.e. ÞRI- in ÞRI-TIG ‘3 × 10’ (cf. Figure 7), whereas the elements ‘4’, ‘5’, and ‘6’ if used as multipliers of the base do not differ from the corresponding simple forms as listed in Figure 3 in § II.1. The suffix -TIG represents the base ‘10’ as multiplicand. Thus the operator ‘×’ is not overtly expressed but is encoded by the suffix -TIG ‘× 10’; cf. our analysis of PDE -TY above in § I.5.3.2. If we analyse the suffix -TIG in a way parallel to -TYNE ‘+ 10’ in the previous section, the consequence would be that -TIG is likewise the result of a grammaticalisation process. Thus -TIG (and, accordingly, PDE -ty) would have to be derived from some simple expression for ‘10’, out of which a functional variant must have developed. Unfortunately, direct evidence for this grammaticalisation process does not exist, because the process, and with it the etymological relation between a simple expression for ‘10’ and a suffix for ‘× 10’, dates back to a time long before the earliest written documentation. Generally however, it is undisputed that the affixes representing the multiplicand ‘× 10’ in the Germanic languages go back to an Indo-European form *deḱ-ṃ-, itself based on the root *deḱ- ‘10’. For some of the attested forms of -TIG and its cognates in other Germanic languages, the proto-Germanic suffix *-teγu is held to be underlying; cf. the very comprehensive discussion in SZEMERÉNYI (1960: 27–44 and 148–65). However, the most popular explanation of this form among Indo-Europeanists is that this suffix is derived from an u-stem noun and that the predecessor of the suffix -TIG originally used to denotes ‘decade’; cf. e.g. SZEMERÉNYI (1960: 27–44); BAMMESBERGER (1986); VOYLES (1987: 493–495); JUSTUS (1996: 46). There are a few points which I would put forward against the semantic interpretation underlying this etymology. The formation of multiples of a base by a compound consisting of an atomic numeral plus some abstract noun denoting ‘decade, set of ten’ would be typologically exceptional. The idea of complex numerals formed after the pattern ‘second decade’, ‘third decade’, etc., is highly improbable and without a parallel in natural languages; cf. GREENBERG (1978: particularly 258). Of course, the observation that numeral systems across natural languages overwhelmingly draw on arithmetic operations when forming complex numeral expressions does not rule out the existence of exceptional cases. It is, however, untenable to postulate a crosslinguistically unattested type when reconstructing an undocumented linguistic stage or development. Moreover, to employ the notion ‘decade’ as a constitutive element of complex numerals would imply that the speakers are to some degree conscious of the recursive and sequential arrangement of numerals at a stage when more complex expressions are only about to develop, because the

The first base ‘10’

87

notion ‘decade’ already entails an arrangement in sets. Both the evidence from the reconstruction of proto-Indo-European and cross-linguistic data of numeral systems in natural languages clearly suggest that the expressions for the multiples of ‘10’ were originally mere compounds consisting of the respective simple forms of the atoms and of the simple form for ‘10’, with both representing a multiplication ‘n × 10’.21 (Cf. LUJÁN MARTÍNEZ (1999b: 203) as quoted in the general introduction.) While these statements concern the underlying semantics of the compound of the reconstructed forms, they are not primarily relevant for the morphology of the respective expressions. In other words, the fact that, for instance, ProtoGermanic *-teγu is a nominal u-stem, does not imply that its semantic content must necessarily differ greatly from that of an unmarked form of a cardinal ‘10’. The fact that the respective form deviates morphologically from the simple expression for the base ‘10’ in that it employs inflectional endings of the u-stems may simply reflect a strategy to mark the paradigmatically separate use of the serialised multiplicand ‘× 10’ as against the simple cardinal ‘10’. That this is not a mere hypothetical thought but a plausible scenario can be seen from the process of paradigmatic isolation of the suffix -TYNE ‘+ 10’ from the simple form TYN ‘10’ (cf. § II.4.2). In other words, from all we know about the pre-historic stages of Germanic and Indo-European, it is feasible to assume that the suffix -TIG ‘× 10’ emerged in a grammaticalisation process very similar to the one which brought about -TYNE ‘+ 10’. II.4.3.2 The expressions for ‘70’, ‘80’, and ‘90’ While the numeral system of Old English as described so far is structurally identical to the numeral systems of most of today’s Germanic languages, the expressions for the subsequent multiples of ‘10’ are morphologically diverse. The expressions for ‘70’, ‘80’, and ‘90’ have a different element representing the multiplicand ‘× 10’. Whereas the use of the respective atomic root as multipliers is retained, the suffix -TIG, which has so far served to indicate the multiplicand ‘× 10’, is now replaced by the circumfix HUND-__-TIG. The resulting expressions are those shown in Figure 9: 21 As far as I was able to find out, the theory that the multiples of ‘10’ are derived from a sequence ‘second decade’, ‘third decade’, etc. originates in a mid-19th-century article by Adolf HOLTZMANN; cf. B RUGMANN (1890: 13). Reading the relevant passage, the theory becomes even less likely as HOLTZMANN (1856: 218) claims that the representatives of the atoms in these expressions are not genuine ordinals but older variants of them (“die nämlichen Ordinalzahlen in einer älteren Gestalt”).

88

The numeral system of Old English ‘70’ 7 × 10

hund - seofon - tig Figure 9.

‘80’

‘90’

8 × 10

9 × 10

hund - eahta - tig

hund - nigon - tig

Old English expressions for ‘70’, ‘80’, and ‘90’

The atomic multipliers in these formations generally correspond with the default atomic forms, except in Northumbrian where the multiplier ‘9’ is represented by the allomorph -NEON-. Hence, we have Northumbrian HUND-NEON-TIG but non-Northumbrian HUND-NIGON-TIG ‘90’. The atomic addends are appended to the circumfixed expressions in the same way as they are to the lower valued suffixed expressions. See Figure 10: ‘75’

[…]

‘86’

5

+

70

[…]

6

+

80

5

+

(7 × 10)

[…]

6

+

(8 × 10)

[…]

syx and

fif and Figure 10.

hund - seofon - tig

hund - eahta - tig

Atomic numerals as addends to the multiples of the base

In grammatical descriptions of Old English, this type of formation is traditionally described as a prefixation of the previous augends formed with -TIG. In other words, it is commonly assumed that an additional prefix is added to the type of expressions in Figure 7. Accordingly, the expressions in Figure 9 have been analysed as consisting of three elements constituting the structure HUND-PREFIX + {atomic root} + -TIGSUFFIX; cf. e.g. CAMPBELL (1959: 284, § 686); BRUNNER (1965: 254–255, § 326); LASS (1994: 213). However, if the element HUND- were a morpheme independent of the element -TIG, one would have to determine to what degree its semantic content or its grammatical function is independent of the other two elements. It is true that, by analogy with the lower valued augends, we could analyse the latter two elements (i.e. {atomic root} + -TIG) as representing the structure ‘n × 10’. Superficially, this parallelism suggests that HUND- is an independent addition to the structure attested in the lower valued expressions of Figure 7. This

The first base ‘10’

89

alone, however, does not imply an independent meaning or function of the alleged morpheme HUND-. In fact, in these constructions, it is impossible to attribute either a lexical meaning (a numerical value) or a grammatical function (an arithmetic operation or some derivational function) to the element HUND-. The only candidate for an independent numerical value expressed by an alleged prefix HUND- would be the homophonous base numeral HUND ‘100’ (for which see below § II.5.1). The numerical value ‘100’, however, cannot be involved in the formation of any expression for ‘70’, ‘80’, and ‘90’ for arithmetic reasons. Given this, the respective constituents {atomic root} + -TIG in structures shown in Figure 9 suffice to denote ‘n × 10’. And given further that the attested forms are clearly cardinal numerals and not any other numeral category – ordinals or multiplicatives (which would make the assumption of some derivational morpheme plausible) – it is impossible to determine an independent meaning for the alleged prefix HUND-. I would therefore argue that HUND-__-TIG is one single discontinuous variant of -TIG and should be analysed as a circumfix denoting ‘× 10’. Since the element HUND- – with a meaning clearly different from the numerical value ‘100’ – is attested only in combination with the element -TIG and only affixed to the root of an atomic numeral in expressions for multiples of ‘10’, we have met all necessary criteria for postulating a circumfix. Thus the circumfix HUND-__-TIG represents the base ‘10’ as a serialised multiplicand to the atomic numerals ‘7’, ‘8’, and ‘9’ (and, as we will see below in the next subsection, also to the numerical values ‘10’, ‘11’, and ‘12’). Circumfixation as a morphological process, although rare, does occur in the Germanic languages. For instance, the past participle in Modern German is marked by the circumfix GE-__-T (or GE-__-EN for strong verbs) attached to the verbal stem, a morphological form which should be analysed in exactly the same way. In both cases, the objection may be raised that the final element can occur alone: OE -TIG as suffix to the lower valued multiplicands and German -T as suffix for the past participle of those weak verbs with a lexically motivated prefix to the verbal root. In both cases, however, the paradigmatic distribution of suffix and circumfix is subject to clear morphological or lexical constraints: German -T as a participial marker is limited to prefixed verbs and OE -TIG is limited to the numerals below ‘70’. Old English also uses both circumfixes and suffixes to mark participles, but the distribution between the two participial markers is not as clear-cut as in German. Moreover, in either case, the initial element cannot occur in the same function or with the same

90

The numeral system of Old English

meaning without the corresponding second element; cf. for instance the discussions in BAUER (2003: 28, § 3.1.3) and HALL (2000: 542b–543a).22 It seems clear that the suffix -TIG and the circumfix HUND-__-TIG stand in an allomorphic relation to each other. This is particularly interesting with respect to a point we discussed in § I.5.3. There, we analysed the Present-day English suffix -TY as a functional variant of the simple base numeral TEN while postulating a distinction between such functional variants (§ I.5.3.2) and allomorphic variants of the type PDE FIVE vs. FIF- (§ I.5.3.1). The situation in Old English now provides us with evidence supporting our theoretical categorisation of the two different variant types in numeral systems. The Old English affix -TIG functionally (and etymologically; see below) corresponds with the Present-day English suffix -TY. It is, therefore, a grammaticalised morpheme which – according to our framework outlined in § I.5.3 – is a functional variant of the simple numeral TYN. It may occur in two allomorphic (complementarily distributed) realisations: the suffix -TIG and the circumfix HUND-__-TIG. Accordingly, Old English -TIG, because of its functional relation with TYN and because of the two different allomorphs by which it is realised, would be difficult to account for if we grouped the two classes of numeral variants proposed in § I.5.3 into one category. II.4.3.3 The expressions for ‘100’, ‘110’, and ‘120’ The highest numerical value that can be expressed in a numeral system as we have described it thus far is ‘99’. The base multiplied by the nine atomic numerals results in the highest possible augend HUND-NIGON-TIG representing the multiplication ‘9 × 10’. If we add the highest possible addend ‘9’ we arrive at the numerical value ‘(9 × 10) + 9’, i.e. NIGON AND HUND-NIGON-TIG ‘99’. In order to express higher numerical values , different strategies are generally conceivable. The cross-linguistically most common strategy would be to employ the expression for the second base as an augend for the numerical values 22 It is irrelevant for this analysis that the forms in question are often represented as two distinct graphic units in the manuscripts, i.e. as 〈hund seofontig〉, 〈hund eahtatig〉 etc. The spelling conventions in Anglo-Saxon manuscripts do not generally correspond with our modern intuition of word and morpheme boundaries. For instance, the element GE - in past participle forms is often spelled separately from the rest of the word, but this has never induced anyone to analyse it as a free morpheme. Cf. in this context, for example, the separation in the spelling 〈hundnigon teoða〉 ‘190th’ in the interlinear gloss to the Benedictine Rule (BenRGl 9.38.4; cf. LOGEMAN 1888: 38) where it is the postposed part of a circumfix which is graphically separated, whereas the preposed element is graphically attached to the root.

The first base ‘10’

91

from ‘100’ onwards. But it is likewise conceivable to simply continue the series of multipliers of the base and use an expression for ‘10 × 10’ as the next higher augend in the sequence. In fact, the Old English lexeme HUNDTEONTIG ‘100’ is formed according to the latter pattern. The sequence of augends used in the previous decades (cf. Figures 9 and 10 above) is continued and thus the next higher augend is an equivalent formation, HUND-TEON-TIG ‘10 × 10’. The multiplier ‘10’ is expressed by -TEON-, an allomorph of TYN. Likewise, the expressions representing the numerical values ‘110’ and ‘120’ are formed in the same way: HUND-ENDLEF-TIG ‘11 × 10’ (with the allomorph -ENDLEF- for ENDLEOFAN ‘11’) and HUND-TWELF-TIG ‘12 × 10’ respectively. The sequence of multipliers to the base ‘10’ is extended beyond the range of the nine atomic numerals. Thus the three expressions for ‘100’, ‘110’, and ‘120’ are formed according to the same pattern as the expressions for ‘70’, ‘80’, ‘90’ as shown in Figure 11. (More examples and a discussion of the frequency of HUNDENDLEFTIG and HUNDTWELFTIG will follow below in § II.5.3). ‘100’

‘110’

10 × 10

11 × 10

hund - teon - tig Figure 11.

hund - endlef - tig

‘120’ 12 × 10 hund - twelf - tig

Old English expressions for ‘100’, ‘110’, and ‘120’

The use of these expressions as augends corresponds to the pattern shown in Figure 10; cf. examples (2.7)–(2.9): (2.7) GenAB 1227 (KRAPP 1931: 39): Wintra hæfde twa and hundteontig þa seo tid gewearð þæt se eorl ingan æðele cennan, sunu and dohtor. He was 102 years old when the time had come that the hero began to father nobles, a son and a daughter. twa 2

and +

hund-teon-tig CIRC-(10 × 10)

92

The numeral system of Old English

(2.8) Ch 1444 12 (BIRCH 1885–1899: II, # 619, 282, 13–14): Ðonnæ is þær nu irfæs þæs þæs stranga wintær læfæd hæfð: nigon ealð hriðru and feower and hundændlæftig ealdra swina and fiftig wæþæra […] Then, there is the bequest which the strong winter has left: nine old cattle and 114 elderly swine and 50 ram […] feower 4

and +

hund-ændlæf-tig CIRC-(11 × 10)

(2.9) Bede 5B 17.460.1 (MILLER 1890–1898: 460): On þa sylfan tid se ylca papa þa Agatthón gesomnade sinoð on Rome byrig fif & hund-twelftig byssceopa wið þam gedwolmannum, […] At the same time, the same pope Agathos then assembled a synod [of] 125 bishops against the heretics in the town of Rome. fif & hund-twelf-tig 5 + CIRC-(12 × 10)

From the point of view of Present-day English and of other European languages, the construction type in this section of the counting sequence is rather unusual. Decimal numeral systems usually employ a second base for ‘100’ once the sequence of atomic multipliers of the base is used up. In fact, the arithmetic operation behind the formation pattern of the expressions in Figure 11 defies a general tendency in numeral systems of natural languages. Cross-linguistically, there is a strong tendency for the numerical value of a serialised multiplicand to generally exceed the numerical value of the respective multiplier. This constraint is entailed in what HURFORD refers to as “Packing Strategy”. Rephrasing the Packing Strategy in the terminology employed here, it says that, of two immediate constituents of a complex numeral, the one containing the multiplier must be valued lower than the one containing the serialised multiplicand and the one containing the addend must be valued lower than the one containing the serialised augend (cf. HURFORD 1975: 67– 80; 1987: 242–252). Accordingly, subsequent to the numerical value ‘99’, the base ‘10’ cannot be multiplied by an expression valued ‘10’ or higher. This requires the introduction of a new base for the numerical value ‘100’. “The [packing] strategy states, essentially, that the sister constituent of a NUMBER must have the highest possible value, that is, the highest value that a constituent of its category can have less than or equal to the value of the immediately

The first base ‘10’

93

dominating node” (HURFORD 1975: 67–68).23 What HURFORD’s Packing Strategy predicts theoretically, is formulated as universal generalisations by GREENBERG (1978: 266 and 271; G 18 and G 23) although GREENBERG, mentioning a counterexample (see below), does not assume an absolute universal. Hence, the Old English system is in this respect a counterexample to the absolute universal status of HURFORD’s proposal. Thus the type of expressions like OE HUND-TEON-TIG, HUND-ENDLEF-TIG, HUND-TWELF-TIG, representing a multiplication ‘n × 10’ (where n ≥ 10) is typologically unusual. Instead, most numeral systems introduce a second base – representing the second power of the first base (i.e. ‘10² = 100’). With respect to the arithmetic operation underlying the Old English expressions HUNDTEONTIG, HUNDENDLEFTIG, and HUNDTWELFTIG , the series of multipliers ‘overruns’ the expected second base. Although cross-linguistically rare, there are examples of overrunning sequences in numeral systems in a number of genetically unrelated languages. GREENBERG states that the phenomenon can only occur if the relevant expressions continue a sequence of lower valued – i.e. ‘regular’ – multipliers: “If a serialized multiplicand is a factor in some product in which the multiplier is larger than the multiplicand, it is also a factor in some product in which it is smaller than [the] multiplicand.” (GREENBERG 1978: 271; G 23). The expression for ‘100’ in Keres (isolate / Keresiouan; classification disputed), g’-ats aua g’-ats, transparently represents the multiplication ‘10 × 10’ and continues the formation type of the preceding multiples of ‘10’ (as in Keres tame-aua g’-ats ‘5 × 10’); cf. GATSCHET (1876: 112–115); KLUGE (1939: 468).24 In Polabian (West-Slavic, extinct), the second decade overruns the second multiple of 10. The respective expressions for ‘18’, ‘19’, and ‘20’ in Polabian are visĕm-nocti ‘8 + 10’, divą(t)-nocti ‘9 + 10’, and disą-nocti ’10 + 10’ or ‘ten-teen’ (cf. COMRIE 1999: 89–90; for similar examples from West Slavic cf. COMRIE 1992: 723, § 16.0.7). Hence, this peculiarity is, albeit rare, a typologically possible phenomenon. Some diachronic aspects of the overrunning sequence and of the circumfixed expressions in Old English and particularly their loss in post-Old English times will be addressed briefly below in §§ II.7.2.1 and II.7.2.2, respectively.

23 NUMBER is a category of HURFORD’s (1975) theory which comprises any simple or complex constituent that can be combined with a base. 24 GREENBERG (1978: 271) states that Keres, just like Old English, continues the overrunning sequence up until ‘120’, i.e. expressed as ‘(10 + 2) × 10’. However, I could not find any Keres data containing expressions for ‘110’ or ‘120’.

94

The numeral system of Old English

At this point, we continue with our description of the elements and the structure of the Old English numeral system. II.5

The second base ‘100’

II.5.1

The expressions for ‘100’

What is, from a cross-linguistic perspective, similarly peculiar about the numeral system of Old English is that, in spite of, or in addition to, HUNDTEONTIG and the corresponding formations, there are two other expressions for the numerical value ‘100’ used as a genuine second base: HUND and HUNDRED (cf. above Figure 4 in § II.1). For expressing the numerical value ‘100’ and for the arithmetic operations employing the base ‘100’, there are actually two different strategies in Old English. One strategy is that described in the previous subsection (§ II.4.3.3) – the continuation of the sequence of multiples of the first base ‘10’. The other strategy is the cross-linguistically more common type employed in the modern Germanic languages and many other European languages. It involves the introduction of a new base numeral for the second power of ‘10’ with either of the synonymous expressions HUND and HUNDRED. Hence, up to the numerical value ‘129’, the expressions HUNDTEONTIG, HUNDENDLEFTIG, and HUNDTWELFTIG are the predominant (but not the exclusive) forms for the augends. Only from the numerical value ‘130’ onwards are the numerals formed exclusively with the base ‘100’ as a serialised augend. The base is used as serialised augend to which a lower valued constituent representing the addend can be attached. The entire sequence of expressions from ‘1’ to ‘99’ is cyclically re-used as addends to the second base ‘100’ – thus exposing a second level in the recursion of the numeral system. Within such a construction, the element containing the second base precedes the lower valued elements. Both constituents are linked by the conjunction AND as an overt expression for the operator ‘+’. The general structure of the expressions containing the second base is displayed in Figure 12. For the optional use of AN as multiplier for HUND(RED) cf. below § III.1.1.

The second base ‘100’

95

‘147’ 100

+

47

(1 ×)

100

7

(1 ×)

100

7

(an)

hund and

+

40 4

seofon

and

× 10

feower - tig

Figure 12a. Complex numeral expressions with two bases ‘789’ 700

+

89

7 × 100

9

7 × 100

9

seofon hund and

+

nigon and

80 8 × 10 hund - eahta - tig

Figure 12b. Complex numeral expressions with two bases

In other words, once the series of 99 addends is used up, any base is multiplied by the next higher valued atomic numeral, i.e. TWA HUND(RED), ÞREO HUND(RED), etc. Again, the operator ‘×’ is not overtly expressed, but it is implied by the particular morpheme employed for the respective base. The fact that HUNDRED and HUND are two synonymous expressions used indiscriminately is difficult to explain. Functionally, there does not seem to be any difference, that is, there is no arithmetically or syntactically conditioned distributional pattern between the two expressions. What may perhaps be observed is that the expression HUNDRED becomes more frequent in texts of the eleventh and twelfth centuries although HUND is still in use in post-Conquest Old English. HUNDRED prevails over HUND in Middle English: in the early Middle English period HUND still occurs sporadically, but after the thirteenth century it is no longer in use; cf. MED IV, 1030b-4b, s.v. “hund card.num” and the subsequent entries.

96

The numeral system of Old English

HUNDRED appears to be some compound form based on HUND. The second element is etymologically related to attested words for counting, as e.g. Gothic ga-raþ-jan ‘to count’. The motivation for this formation is obscure as it seems redundant to develop a second expression for the second base ‘100’. A popular explanation used to be that HUNDRED was originally formed in order to distinguish the Great Hundred ‘120’ from the decimal hundred, but the evidence brought forth in favour of this explanation does not withstand closer scrutiny; cf. VON MENGDEN (2005, 2006b) and the discussion in § III.2.2 below. II.5.2

The distribution of the expressions for ‘100’

The mere existence of three different systemic expressions for the numerical value ‘100’ appears to be counterevidential to the claim we raised in §§ I.2.2 and I.4.1 that any one numerical value is represented by exactly one systemic numeral. In order to maintain our claim, we need to identify some distributional pattern of the expressions HUNDTEONTIG, HUND, and HUNDRED in accordance with our categorisation of variant forms postulated in § I.5. The most plausible assumption would be that such a distribution is based on the various arithmetic contexts in which the numerical value ‘100’ can occur. In order to identify such a pattern, we will first summarise the logically possible arithmetic contexts in which an element representing the numerical value ‘100’ may occur in a decimal numeral system (Table 12). Then we will look at whether and, if so, how the instances of the three expressions are distributed over these arithmetic uses (Tables 13 and 14). Let us first categorise the logically possible arithmetic contexts of ‘100’ in Table 12. The use of ‘100’ – or of an element containing ‘100’ – as an addend to the third base ‘1,000’ is rare and hence disregarded in Table 12. It is represented in columns 4 and 5 of Tables 13 and 14 below displaying the distribution of the expressions for ‘100’ over the relevant arithmetic functions. 25 25 In Tables 13, 14, and 15 – as well as in 19 below in § III.1.1 –, b stands for a higher valued base (i.e. actually for ‘1,000’), n and m for any atomic or any lower valued complex numeral. The data are based on the OEC). Consequently, my count only includes those forms attested in the relevant base manuscripts of each Old English text as captured by the OEC. However, whenever an OEC record indicates that the printed edition deviates from the manuscript reading (as is occasionally the case, especially in Byrhtferth’s Manual where the editors generally prefer the “correct” figures to the manuscript reading; cf. BAKER/LAPIDGE 1995: cxxv), I opted for the manuscript reading as the linguistically relevant data. In my count I have included only the most common spellings of the respective lexemes, i.e. 〈hund〉, 〈hundred〉, and 〈hundteontig〉. Variant spellings do occur in all three cases but

The second base ‘100’

97

Table 12. Possible arithmetic context for the base ‘100’ function of the base ‘100’ exact numerical value ‘100’

corresponding arithmetic operation

corresponding numerical values

columns in Tables 13 and 14 below

―

‘100’

1

‘n + 100’

‘200’, ‘300’, …, ‘900’

6

serialised augend (including multiples of ‘100’)

‘(m × 100) + n’

‘101’ – ‘199’, ‘201’ – ‘299’, …, ‘901’ – ‘999’

2, 7

multiplier of the third base (including complex elements containing ‘100’)

‘[(m × 100) + n] × 1,000’

‘100,000’ – ‘999,999’

3, 8

serialised multiplicand

Apparently, the usage of the three forms for ‘100’ differs between those arithmetic operations in which ‘100’ is used as a multiplicand – shown in columns 6, 7, and 8 – and the other possible uses of an element for ‘100’. If we combine the columns of Tables 13 and 14 according to this distinction we get the figures shown in Table 15. It should be noted that the use of the multiplier AN ‘1’ in AN HUND and AN HUNDRED actually turns out to be irrelevant in this context, since AN HUND and AN HUNDRED cannot possibly be used as multiplicands. The instances of AN HUND and AN HUNDRED are, therefore, not included in Table 15. The use of AN HUND and AN HUNDRED will be considered in a different context below (cf. § III.1.1).

are comparatively rare. I have not distinguished whether complex forms are spelled as one or as several words in the manuscripts, i.e. 〈an hund〉 is not distinguished from 〈anhund〉, and 〈hund teontig〉 not from 〈hundteontig〉 (〈anhundred〉 does not occur in the OEC).

Table 13. Distribution of the expressions for ‘100’ by arithmetic conditions (absolute figures) 1

2

3

4

5

6

7

8

alone

augend

multiplier

addend

addend & augend

multiplicand

augend & multiplicand

multiplier & multiplicand

100

hund

∑

100 + n 100 × b b + 100 b + 100 + n n × 100 (n × 100) + m (n × 100) × b

(without an hund)

23

4

4

0

0

342

232

23

628

an hund

27

29

8

2

4

—

—

—

70

(without an hundred)

7

0

2

0

0

49

33

0

91

an hundred

12

1

0

0

0

—

—

—

13

hundteontig

41

22

10

0

1

1

3

0

78

∑

110

56

24

2

5

392

268

23

880

hundred

The second base ‘100’

99

Table 14. Distribution of the expressions for ‘100’ by arithmetic conditions (percentage) 4

5

6

7

8

addend

addend & augend

multiplicand

augend & multiplicand

multiplier & multiplicand

3 multiplier

hund

alone

%

2 augend

1

∑

3.7

0.6

0.6

0

0

54.5

36.9

3.7 100

an hund

38.6

41.4

11.4

2.9

5.7

—

—

— 100

hundred

7.7

0

2.2

0

0

53.8

36.3

0 100

an hundred

92.3

7.7

0

0

0

—

—

— 100

hundteontig

52.6

28.2

12.8

0

1.3

1.3

3.8

0 100

(without an hund)

(without an hundred)

Table 15. Distribution of the expressions for ‘100’ with regard to their use as multiplicand

columns in Tables 13 and 14

other arithmetic functions

multiplicand ‘n × 100’

1–5

6–8

Σ

hund

31 4.9 %

597 95.0 %

628 100 %

hundred

9 9.9 %

82 90.1 %

91 100 %

74 94.9 %

4 5.1 %

78 100 %

hundteontig

The result is now even more obvious: although none of the forms is used exclusively in either of the two contexts, the figures show a clear predominance of particular arithmetic operations for each of the different expressions for ‘100’. The simple expressions HUND and HUNDRED are basically used as multiplicands. In 95.0 % of all the instances of HUND, the form is used as a multiplicand. The predominant use of HUNDRED as a multiplicand is almost as clear with 90.1 % of the total number of instances. HUNDRED seems to be used

100

The numeral system of Old English

slightly more freely than HUND, but the figures do not indicate any striking differences in use between HUND and HUNDRED. In any case, in 94.9 % of its instances, the form HUNDTEONTIG is used in arithmetic functions other than that of a multiplicand. The simple forms HUND and HUNDRED usually do not occur in these contexts (only 3.7 % and 7.7 %, respectively, of the total number of instances). In accordance with our theoretical considerations in Chapter I (cf. § I.4), it follows that HUNDTEONTIG is the default expression for ‘100’ in the Old English counting sequence. This assumption is confirmed by the continuation of that passage in Ælfric’s Grammar, the first part of which we have already quoted in the previous chapter as (1.7). In (2.10) the sequence of multiples of ‘100’ in Old English and Medieval Latin is attested in a context-free list. The expression for ‘100’ here is hundteontig but not hund or hundred. (2.10) ÆGram 281.15–20 (ZUPITZA 1880 [2001]: 281 – my bold type): uiginti (XX) twentig. uiginti unum (XXI) an and twentig and swa forð. triginta (XXX) þrittig. quadraginta (XL) feowertig. quinquaginta ( L) fiftig. sexaginta (LX) syxtig. septuaginta (LXX) hundseofontig. octoginta (LXXX) hundeahtatig. nonaginta (XC) hundnigontig. centum (C) hundteontig.

The default character of HUNDTEONTIG as opposed to HUND(RED) is furthermore confirmed by the fact that the ordinal ‘100th’ is exclusively expressed by HUNDTEONTIGOÞA, i.e. the ordinal suffix can only be attached to HUNDTEONTIG but never to HUND or HUNDRED; cf. § II.8.3. A similar phenomenon is attested in a closely related language: in Old High German zehanzug ‘10 × 10’ is the default expression for ‘100’, whereas if the value ‘100’ is a multiplicand in a complex formation it is mostly expressed by hunt; cf. BRAUNE/REIFFENSTEIN (2004: 237, § 274). Although rather uncommon in European languages, there are parallels to the situation in Old English. There are languages which have a default expression for a base but lexically different expressions for the same value if used as a multiplicand: according to CHARNEY (1993: 160–161) the default expression for ‘10’ in Comanche (Uto-Aztecan) is tokwe. This numeral stands for the value ‘10’ if used outside an arithmetic operation. Within more complex forms, the expression used for ‘10’ is sìmi-matì= which consists of sìmì ‘1’ and the bound form -matì= ‘× 10’. The latter element occurs in the expressions for ‘20’, ‘30’ etc. and sìmì-matì=, therefore, would be morphologically equivalent to an English numeral *one-ty. As a final point in this context, it should be noted that Tables 13 to 15 show a much higher frequency of HUND(RED) than of HUNDTEONTIG. In this case,

The second base ‘100’

101

token frequency cannot be taken as an indicator of the default vs. marked status of two variants. As our discussion has shown, HUNDTEONTIG is nevertheless the unmarked expression for the numerical value ‘100’. The higher number of occurrences for HUND and HUNDRED is simply due to the fact that arithmetically, the numerical value ‘100’ is generally employed much more often as a multiplicand than for the exact numerical value ‘100’ or in other arithmetic contexts. If we now compare the expressions for the second base ‘100’ with those for the first base ‘10’ with respect to the possible arithmetic functions in which a base numeral can occur, we will find that the expressions for the second base are distributed according to a pattern similar to that of the first base: the arithmetic functions of HUNDTEONTIG parallel those of TYN and -TYNE, while the arithmetic functions in which HUND and HUNDRED are employed correspond to those of -TIG and HUND-__-TIG; cf. Table 16. Table 16. Distribution of the variant forms for ‘10’ and ‘100’ with regard to their arithmetic contexts

default lexeme / exact numerical value augend (but not multiplicand) multiplicand

‘10’

‘100’

TYN

HUNDTEONTIG

-TYNE

HUNDTEONTIG

-TIG, HUND-__-TIG

HUND, HUNDRED

In accordance with the different functions of the relevant elements for ‘10’ (cf. § II.4.3.), we may say that the use of the forms HUND and HUNDRED – as opposed to HUNDTEONTIG – implies that the numerical value ‘100’ is used as multiplicand. It should be conceded though that the distribution of the forms for ‘100’ as multiplicands and those for ‘100’ in other arithmetic contexts is not as consistent as that of the respective variants for ‘10’. The tendency, however, is more than obvious. From this observation we may also conclude that, whenever the base ‘100’ is multiplied by an atomic numeral, the operator ‘×’ does not need to be overtly expressed because the use of HUND or HUNDRED generally suffices to encode that the numerical value ‘100’ is used as a multiplicand. In contrast to our findings with respect to HUNDTEONTIG, the forms HUND and HUNDRED are used in free variation with each other; cf. above § II.5.1.

102

II.5.3

The numeral system of Old English

The section from ‘110’ to ‘129’

If we say that HUNDTEONTIG is used predominantly in arithmetic contexts other than that of a multiplicand, we have left one aspect out of consideration. The use of HUNDTEONTIG as an augend cannot be taken as a genuinely baselike use as long as the respective addends are not complex numerals. In other words, if the scope of HUNDTEONTIG as augend were restricted to the numerical values from ‘101’ to ‘109’, it would simply perform functions typical of any multiple of ‘10’. However, as the examples (2.11)–(2.14) show, HUNDTEONTIG can also be used as an augend in the entire sequence up to ‘199’. (2.11) Mart 5 Se 25, A.12 (KOTZOR 1981: 219) – ms. Julius A.x.; ms. CCCC 196 reads: hundteontigum and feowertynum: Æfter hundteontegum daga ond XIIII þæs ðe he of his mynstre ferde, he geleorde on Burgenda mægðe Linguna ceastre. 114 days after he had left the monastery, he passed away in the town of Lyons in Burgundy. hund-teon-teg-um dag-a CIRC-(10 × 10)-DAT.PL day-GEN.PL

and +

XIIII

14

(2.12) ÆLet 4 (Sigeweard Z) 302 (CRAWFORD 1922 [1969]: 28, 311): & se Ioseph leofode on þam lande mærlice hundteontig geara & tin to eacan, & seo boc Genesis geendað þus her. And Joseph lived famously in that land for 110 years and thus the book Genesis ends here. hund-teon-tig CIRC-(10 × 10)

gear-a & tin year-GEN.PL + 10

to eacan thereto

(2.13) Bede 1 5.32.11 (MILLER 1890–1898: 32): Ða wæs ymb hundteontig wintra & nigan & hundeahtatig wintra fram Drihtnes menniscnysse, þæt Seuerus casere, se wæs æffrica cynnes, of þære byrig ðe Lepti hatte, se wæs seofonteogeða fram Agusto, þæt he rice onfeng, & þæt hæfde seofontyne gear. It was 189 years after the incarnation of the Lord that the emperor Severus, who was of African descent from the town that was called Leptis, and who was the seventeenth after Augustus, came to power which he held for 17 years. hund-teon-tig CIRC-(10 × 10)

wintr-a winter-GEN.PL

& nigan & hund-eahta-tig + 9 + CIRC-(8 × 10)

The second base ‘100’

103

(2.14) LS 4 130 (RYPINS 1924: 74, 12): Þæt wæs eaht & feower þusenda manna & hundteontig & fiftyne. There were about 4,115 men. feower 4

At

the

þusend-a × 1,000-PL

mann-a & hund-teon-tig man-GEN.PL + CIRC-(10 × 10)

& fif-tyne + (5+10)

same

time, the expressions HUNDENDLEFTIG ‘110’ and ‘120’ can be employed as augends for the subsequent decades in the same way as all the lower valued multiples of ‘10’ are used; cf. (2.15). HUNDTWELFTIG

(2.15) ÆHomM 14 6 (A SSMANN 1889 [1964]: 92): Hundtwelftig scira he soðlice hæfde and seofon scira, swa swa us secgað bec, on his anwealde ealle him gewylde Verily, as the books tell us, he held 127 provinces under his control, completely subdued to him. hund-twelf-tig CIRC-(12 × 10) and +

seofon 7

scir-a district-GEN.PL

he he

soðlice truly

hæfde have:3 SG.PST

scir-a district-GEN.PL

This means that for the section from ‘110’ up to ‘129’ two different formation types compete: one employing an expression for ‘100’ as augend, resulting in the structure ‘100 + n’, and one with HUNDENDLEFTIG ‘110’ and HUNDTWELFTIG ‘120’ as decadic augends, as described above in § II.1.3.3, i.e. representing the structures ‘(11 × 10) + n’ and ‘(12 × 10) + n’, respectively. Again, we seem to have a problem: according to what we have said about systemic and non-systemic expressions (§§ I.2.2 and I.4.1), there should theoretically be only one default formation type for any one numerical value. This claim would, of course, have to apply to the section from ‘110’ up to ‘129’ as well. Our difficulty at this point is, in fact, due to the limited amount of data. There are simply not enough instances of expressions for the numerical values from ‘101’ to ‘129’ in Old English that would allow for reliable statements on the frequency of the relevant constructions. The evidence is too scarce to determine unambiguously which of the two types is the default expression. There are only five instances of HUNDENDLEFTIG ‘110’ in the entire corpus, of which one is an ordinal. Of the four remaining instances, three are attested in twelfth-century charter copies. By contrast, there are ten instances of complex

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The numeral system of Old English

numerals expressing numerical values from ‘110’ to ‘119’, five of which employ (AN) HUND and another five HUNDTEONTIG. Bearing in mind that the number of instances of ‘110’ do not constitute a sufficiently large sample, we may tentatively conjecture that HUNDENDLEFTIG as an augend seems to have been on the decline if compared to constructions using the second base ‘100’ – whether (AN) HUND or HUNDTEONTIG – as an augend. As for the use of ‘120’, the figures in Table 17 show that the use of the circumfixed form HUNDTWELFTIG ‘120’ prevails over those compounds that express the numerical value ‘120’ as an addition with the base ‘100’.26 Table 17. Distribution of the expressions for ‘120’ by arithmetic conditions alone ‘120’

augend ‘121’ – ‘129’

multiplier ‘120,000’ ff.

∑

hund-twelftig

32

2

3

37

hund twentig

3

0

0

3

anhund & twentig

5

1

0

6

anhundred & twentig

0

1

0

1

hundteontig & twentig

1

1

0

2

41

5

3

49

∑

However, it has been possible to show that the circumfixed lexeme HUNDTEONTIG is, in contrast to HUND and HUNDRED, the default expression for the numerical value ‘100’ unless there is a clearly defined arithmetic constraint. With respect to the possible expressions for ‘110’ and ‘120’, this might suggest that, for ‘110 + n’ and ‘120 + n’, there is also a predominance of the circumfixed expressions over those constructions employing ‘100’ as an augend although, of course, we do not have a definite proof of their default character.

26 The use of ‘120’ as addend (e.g. in ‘1,120’) is not attested. Given the distribution indicated in Table 17, it is remarkable that the 16 ordinals for ‘120th’ attested in the OEC are without exception formed on -TWENTIGEÞAN, i.e. with ‘100’ as augend.

The third base ‘1,000’

II.6

105

The third base ‘1,000’

The set of possible multipliers to the second base ‘100’ is restricted to the sequence of nine atomic numerals. Thus the highest numerical value that can theoretically be expressed by means of the two bases ‘10’ and ‘100’ is ‘999’. The structure of the highest possible expression in a system thus far described represents the arithmetic operation ‘(9 × 100) + (9 × 10) + 9’. To express the next higher numerical value, i.e. ‘1,000’, the introduction of a third base is necessary. The third base of the Old English numeral system, representing the third power of 10, is expressed by the simple form ÞUSEND. The formation patterns of the relevant compound numerals and the arithmetic operations involved are basically the same as for the numerical values below ‘1,000’. Like the two lower valued bases, ÞUSEND is used as a serialised augend to the sequence of the 999 lower valued numerals. The resulting additions express the numerical values from ‘1,001’ to ‘1,999’. When the sequence of addends is used up, the base is multiplied by a preceding atomic numeral, i.e. TWA ÞUSEND ‘2 × 1,000’, ÞREO ÞUSEND ‘3 × 1,000’ etc., which are again used as serialised augends; cf. (2.16)–(2.18). (2.16) ByrM 1 4.2 30 (BAKER/LAPIDGE 1995: 232–234) – as (2.16) above in § II.1.5: Ðæt forme þusend (þæt ys seo forme yld þises middaneardes) stod of þusend wintrum & syx hund wintrum & syx & fiftigum wintrum æfter þære soðfæstnysse þe þa Iudeisce witan heoldon, […] The first thousand (that is, the first age of this world) consisted of 1,656 years according to the verity which Jewish scholars observed […] (transl. BAKER/LAPIDGE 1995: 233) of PREP

& +

þusend 1,000 syx 6

wintr-um winter-DAT.PL & +

& syx + 6

hund × 100

wintr-um winter-DAT.PL

fif-tig-um wintr-um (5 × 10)-DAT.PL winter-DAT.PL

(2.17) ByrM 2.3 61 (BAKER/LAPIDGE 1995: 108): Se dæg hæfð ostenta an þusend & feower hundred & feowertig. A day has 1,440 ostents. an 1

þusend × 1,000

& +

feower 4

hundred × 100

& +

feower -tig (4 × 10)

106

The numeral system of Old English

(2.18) Notes 26.3 16 (NAPIER 1889: 9): Þa wæs fram frymðe ealles a urnen oþþæs temples geweorc. þæt sindon feower þusenda wintra & an hund wintra & seofan & syxtig wintra. Then from the beginning of everything to the construction of the Temple passed by: that are 4,167 years. feower 4

þusend-a × 1,000-PL

& +

seofan 7

& +

wintr-a winter-GEN.PL syx-tig (6 × 10)

& an + 1

hund wintr-a × 100 winter-GEN.PL

wintr-a winter-GEN.PL

If we describe the structure of a compound numeral comprising all three bases as a phrase structure, we would, as a first step, simply have to add another parent node to the structures in Figure 12 (§ II.1.4.1). Figure 13 illustrates the structures of the numerals in (2.16) and (2.18). For an additional specification of the constraints underlying the structures of Figures 13a and 13b cf. § III.1.1 and particularly Figure 17a. ‘1,656’ 1,000

+

656

1 × 1,000

600

1 × 1,000

6 × 100

1 × 1,000

6 × 100

6

1 × 1,000

6 × 100

6

an

+

56 56 +

50 5 × 10

þusend & syx hund & syx & fif-tigum

Figure 13a. Structure of a numeral containing three bases

The third base ‘1,000’

107

‘4,167’ 4,000

+

167

4 × 1,000

100

+

67

4 × 1,000

1 × 100

4 × 1,000

1 × 100

7

4 × 1,000

1 × 100

7

67 +

60 6 × 10

feower þusend & an hund & seofan & syx - tig Figure 13b.

Structure of a numeral containing three bases

The scope of the third base is – in contrast to the two lower valued bases – not restricted to the nine atomic numerals as multipliers. A multiplier of the third base can itself be a complex numeral. This entails that any expression out of the sequence from ‘1’ to ‘999’ can also be used as a multiplier of ‘1,000’. This is in accordance with the constraint that the multiplier should not exceed the respective multiplicand (cf. § II.1.3.3). The highest possible multiplier of the third base is therefore ‘999’. Since ‘1,000’ is the highest base of the Old English numeral system, the highest numerical value that can theoretically be expressed in Old English by a systemic numeral denotes the numerical value 999,999. Or, in the sense of GREENBERG’s first generalisation (1978: 254, G 1; cf. above § I.2.4), the limit number L of the numeral system of Old English is ‘106’ and, accordingly the highest expressible numerical value of the Old English numeral system is ‘999,999’. As we said in § I.2.4, alternative strategies may exist for expressing higher numbers but these expressions are non-systemic. Expressions of this type will be discussed in § III.3.3. II.7

The development of the Old English numeral system

Apart from a few aspects, the previous sections have been primarily descriptive and also primarily synchronic. As some of the phenomena described have shown, a diachronic context sheds some light on some idiosyncrasies within a system and indeed will have some explanatory force for quite a number of

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The numeral system of Old English

phenomena. That this is particularly true for numerals and numeral systems will be shown in detail later in § V.2.5.1. While the phenomena in the previous sections of this chapter have been presented in a systematic (or, systemic, for that matter) order, they will now be revisited with a particular focus on their historical development. This will not only complement much of §§ II.1–6 by looking at the data from a different, i.e. diachronic, angle, but will also provide a crucial basis for general considerations on the word class ‘cardinal numeral’ which will be made as a cross-linguistically oriented conclusion of this study. This will be done first with respect to the pre-history of the Old English numeral system (§ II.7.1), then the changes during the Old English period will be described (§ II.7.2) and, finally, those later changes which mark the systemic differences between Old English and the English of today will be summarised (§ II.7.3). II.7.1

The pre-history

II.7.1.1 The numeral system of proto-Indo-European There is, of course, not much evidence upon which we can base definite statements of what the numeral system was like in proto-Indo-European. To some extent this is a problem which generally applies to all grammatical aspects of reconstructed stages of languages. A reconstruction can only be an approximation of the linguistic reality of a hypothesised speech community. Yet, if we take our knowledge of diachronic and synchronic universals of numeral systems into consideration (for which cf. § I, but also GREENBERG 1978; VON MENGDEN 2008), together, of course, with the results achieved by historical comparison and reconstruction, we will get quite a solid picture of many aspects of the numeral system of proto-Indo-European. In spite of the etymological difficulties that are involved in determining the source expressions of the atomic numerals of proto-Indo-European (cf. e.g. the discussion in LUJÁN MARTÍNEZ 1999b), one of the least debated etymologies is that of the expression for ‘5’, *pénkwe, which is related to the concept ‘finger’ or ‘fist’; cf. e.g. SCHWARTZ (1992); LUJÁN MARTÍNEZ (1999b: 207–208). A second important hint, probably the clearest evidence we have, is the fact that the expressions for ‘10’ and ‘100’ are shared by all languages of the IndoEuropean family, but that almost every branch has a different expression for ‘1,000’. These two points strongly suggest that, at the time of the disintegration of the individual branches of proto-Indo-European, a finger counting method had developed into a pure decimal numeral system and that, further-

The development of the Old English numeral system

109

more, this numeral system must have been complex enough to have fully developed a second base. The numeral system of the Indo-European protolanguage, therefore, must have involved a recursive pattern including addition and multiplication on a decimal basis (cf. §§ III.2.1 and V.2.5.1 where this point will be resumed). II.7.1.2 The numeral system of proto-Germanic Comparing all the ancient Germanic languages with respect to their systemic numerals, we will get quite a clear picture of the developmental stage of the numeral system of proto-Germanic. Since there is a common expression for ‘1,000’ throughout Germanic but not, as we said, in the individual branches of Indo-European, we can date the development of the third base to the time after the separation of the Germanic languages from Indo-European but before the time of the disintegration of the individual Germanic languages. This applies to the idiosyncratic expressions for ‘11’ and ‘12’ in the same way. As already mentioned, the expressions ENDLEOFAN and TWELF go back to the protoGermanic formations *aina-lif- ‘1 remaining [beyond 10]’ and *twa-lif- ‘2 remaining [beyond 10]’ (cf. § II.1.1.2). Remarkably, both the expression for ‘1,000’ and the formation type for ‘11’ and ‘12’ find parallels in the Baltic languages. Balto-Slavic, being the only branch of Indo-European which shares the expression for ‘1,000’ with Germanic (cf. Old Church Slavonic tysęšti, Lithuanian tūkstantis), also has a formation type for the second decade in Lithuanian which exactly parallels that of the Germanic expressions for ‘11’ and ‘12’ (cf. SEILER 1990: 200; SILHER 1995: 417, § 390; see also §§ II.3, III.3.2 and V.2.5.1). Some other idiosyncratic features described above are also to some extent common to the entire Germanic branch but show some variation among the individual Germanic languages at the time of the earliest written records. The allomorphic variation between the multiples of ‘10’ up to and above ‘6 × 10’ (§ II.4.3.2) is very clearly attested throughout the ancient Germanic languages. There can be no doubt that this morphological split must have developed during the common Germanic period; cf. Table 18 in which the split between the two allomorphs is marked by the dotted line.

Table 18. Affixes for ‘× 10’ in the ancient Germanic languages ‘20’ – ‘60’ Gothic x-tigjus Old High German x-zug

‘70’ – ‘90’

‘100’ (default)

‘110’ – ‘120’

x-têhund

x-taíhund, x-têhund

—

x-zō, -zug

x-zō, -zug

—

Old Saxon x-tig

(ant)-x-ta, -da hund(erod)

Old Frisian x-tich

(t)-x-tich

hunderd, hundred x-tich (?)

Old English x-tig

hund-x-tig

hund-x-tig

Old Norse (adj.) x-tøgr

x-tøgr, x-røþr x-røþr

Old Norse x-tigi, x-tiger x tiger

x tiger

‘100’ (multiplicand)

hunt

— hund-x-tig

hund(red)

x-røþr x-tiger ‘110’ hundraþ ‘120’, (‘100’)

The development of the Old English numeral system

111

The second feature which seems to have been widespread in the early varieties of proto-Germanic is the sequence of multiples of ‘10’ overrunning the second base (§ II.4.3.3). It is indicated in Table 18 by the boxes shaded in light grey. Here, however, the evidence is not quite as clear. No statement is possible for Gothic, Old High German and Old Saxon where no expressions for the numerical values from ‘101’ to ‘129’ are attested. However, the existence of a complex form for ‘100’ in Gothic and Old High German plus the lack (Gothic) or the marked character (Old High German) of a simple form for ‘100’ in these two languages suggests that the second base was introduced at a stage at which a complex, but systemic expression at least for the value ‘100’ had existed. While it is therefore feasible that proto-Germanic had multiples of ‘10’ up until ‘120’, the phenomenon is attested only for Old English and, in a slightly deviant manner, for Old Norse. It is uncertain whether tolftich ‘12 × 10’ is attested in Old Frisian, but if it existed, we have evidence for the existence of an overrunning sequence in this closest cognate of Old English, too.27 The emergence of the circumfix hund-__-tig as a marker for the multiples of ‘10’ from ‘70’ onwards (§ II.4.3.2) must have developed at a later stage as traces of it can only be found in Old English, Old Saxon and Old Frisian, i.e. in the subgroup within the Germanic languages traditionally referred to as ‘Ingvaeonic’. The relevant forms are the expressions in the light blue shaded boxes in Table 18. It is remarkable in this context that the suffix for the higher multiples of ‘10’ in Gothic is bi-syllabic, which suggests that it is very likely etymologically bi-morphemic. This allows the assumption that the two parts of the circumfix in the West-Germanic subgroup represent the same components as the suffix in Gothic. The exact kind of relation between the two elements (and the resulting deviation of the two) is difficult to determine; cf. the discussion about the suffix -TIG above in § II.4.3.1 and the literature referred to there.

27 The situation in Frisian is described inconsistently in the relevant literature. KLUGE (1913: 256) mentions the Frisian form tolftich ‘12 × 10’. So do KÖBLER (1983) and HOLTHAUSEN/HOFMANN (1985), but perhaps they only copied from KLUGE because neither STELLER (1928: 50–51, §§ 77–78) nor MARKEY (1981: 130) mention this form. For the data of the other Germanic languages in their oldest stages cf. BRAUNE/EBBINGHAUS (1981: 97, §§ 142–143) for Gothic, BRAUNE /REIFFENSTEIN (2004: 236–237, §§ 273–274) for Old High German, GALLÉE (1910 [1993]: 235, § 259.6) for Old Saxon and NOREEN (1923: 305–306, §§ 449–450 and 308, § 460) for Old Norse. For a more detailed list of the relevant forms in all historical stages of the Germanic languages cf. ROSS/BERNS (1992: 602–620, §§ 15.1.20–30). The particular use of the second base in Old Norse is discussed briefly in VON MENGDEN (2006b: 142–143).

112

The numeral system of Old English

While the circumfix – judged at least from its frequency in the written records (cf. § II.7.2) – seems to be most stable in Old English, its Old Saxon counterpart shows signs of heavy attrition. First, the root-preceding element seems to be used optionally. Moreover, on the assumption that the Old English and the Old Saxon circumfix are exactly cognate, we also observe the loss of the initial aspiration on the continent and, less clearly evidenced, the reduction of the vowel as suggested by the 〈-a-〉-spelling in Old Saxon ant-. In Old Frisian, the loss of the first part of the circumfix is more advanced. In this language only occasional instances with initial /t-/ in the forms (t)ach-tich ‘80’ and (t)niogen-tich ‘90’ can be found. Remnants of the circumfix however can still be seen in Modern Frisian tachtich and Modern Dutch tachtig ‘80’, which both have an initial alveolar stop that does not occur in acht ‘8’, the corresponding atom in both Modern Dutch and Modern Frisian. If we compare the pre-Old English stage with the situation today, the only idiosyncrasy that has survived in all the contemporary Germanic languages is the simple shape of eleven and twelve. We find no traces of the overrunning expressions or of the circumfix in Middle English (but cf. fn. 28 in § II.7.2.2). Evidently, there must have been some pressure on the circumfixed expressions for the numerical values from ‘100’ to ‘129’ by the typologically more common and arithmetically more regular formations employing ‘100’ as an augend. The typological drift to level out these features can also be seen by the fact that none of them has survived in any other contemporary Germanic language (with the exception of the initial stop in one expression of Dutch and Frisian that we have just mentioned). These processes will be discussed in the following section. II.7.2

Changes during the Old English period

II.7.2.1 The loss of the overrunning section The clearest evidence for an ongoing change is the variation in the use of forms for the section between ‘100’ and ‘129’. In § II.5.3, we described the way in which the two different formation types – the augends HUNDTEONTIG, HUNDENDLEFTIG and HUNDTWELFTIG versus the use of HUND(RED) as augend – compete with each other in the Old English period. We also pointed out that the corpus does not provide sufficient data to determine with an absolute degree of certainty which of the two types was the default construction in a certain period or variety of Old English. After all, we can see from the data presented in § II.5.3 that there is some degree of variation during the Old English

The development of the Old English numeral system

113

period. Given that in Middle English no circumfixed expressions of the section from ‘100’ to ‘129’ are attested, it seems that this variation documents an ongoing process of the levelling of the circumfixed forms in this sequence in favour of expressions formed by the augend HUND(RED). This process of levelling must have been completed by the end of the Anglo-Saxon period with the loss of the overrunning sequence. The tendency to level out such an idiosyncrasy necessarily leads to a temporary competition between HUNDTEONTIG and HUND(RED), especially in the function as an augend in the second set of a hundred as exemplified in (2.11)– (2.14) above (§ II.5.3). Although we have shown that the distribution of HUNDTEONTIG and HUND (RED) was sufficiently clear with respect to their arithmetic functions (cf. § II.5.2), example (2.19) – although certainly not representative for the Old English usage – may show that some degree of confusion could possibly arise: (2.19) Notes26.3 7 (NAPIER 1889a: # 10; 9, 9–10): Þonne wæs fram Abrahames acennednesse forð oð Moyses gebyrd-tidu & þara Israhela bearna gefære of Egyptum: þæt wæs ðonne fifhund wintra & fif & hundteontig wintra. Then, from Abraham’s birth to Moses’s birth and to the Exodus of the Children of Israel from Egypt, there were 505 years. fif-hund wintr-a (5 × 100) winter-GEN.PL

& fif & hund-teon-tig + 5 + CIRC-(10 × 10)

wintr-a winter-GEN.PL

Literally, the numeral in this passage would represent ‘(5 × 100) + 5 + (10 × 10)’, hence ‘605’. However, the Latin original of this passage (Chronicon Æthelweardi I, 1; cf. CAMPBELL 1962: 3, lines 18–19) as well as a parallel Old English text (Notes 26.1 5; cf. FÖRSTER 1925: 196a, line 3) both show that the number of years intended by the author of these lines is clearly ‘505’. The fact that ‘100’ is both a serialised multiplicand and a serialised augend in this numeral may account for the erroneous use of two expressions for ‘100’ where only one is arithmetically possible. II.7.2.2 The loss of the circumfix For the numerical values below ‘100’, there is, of course, no such conflict between two types of constructions. There are six decades from ‘70’ to ‘120’ employing the circumfix HUND-__-TIG to mark the multiplicand ‘10’ and five decades from ‘20’ to ‘60’ employing the suffix -TIG in this function. This sug-

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gests that there was a fair balance in the frequency of the two allomorphs so that the variation between the two forms can be assumed to have been relatively stable. However, once the circumfixed expressions for the numerical values ‘100’, ‘110’, and ‘120’ were on the decline (for the reasons discussed in the previous section), the remaining circumfixed expressions HUNDSEOFONTIG, HUNDEAHTATIG, and HUNDNIGONTIG became – both typeand token-wise – a rather small set of morphologically deviating expressions. After the section between ‘101’ and ‘129’ has been levelled out, one might expect the analogy with the lower valued numerals employing the suffix -TIG to exert a stronger pressure on the morphologically more complicated structure with the circumfix. Thus given that the suffix -TIG has completely replaced the circumfix HUND-__-TIG in early Middle English, it would not be surprising if a considerable number of forms with the suffix -TIG were attested to have existed side by side with the circumfixed forms in the numerals for ‘70’, ‘80’, and ‘90’ in Old English.28 There are indeed a few instances of numerals for ‘70’ and ‘80’ of the Modern English type, i.e. using the suffix instead of the circumfix. It is remarkable that they are evidently not used in free variation with the circumfixed forms. The small number of cardinal numerals for ‘70’ and ‘80’ that are formed by the suffix -TIG instead of the circumfix HUND-__-TIG occur almost exclusively in the Old English paraphrase of Orosius’s History, more precisely in the section from Book III.7 to Book V. Since the Old English Orosius is one of the earliest Old English prose texts and since the terminus ante quem for the use of numeral forms for ‘70’ and ‘80’ without circumfix must be the reign of King Alfred the Great (871–899), the circumfix must have been less stable in the spoken language than the almost perfectly consistent distribution of circumfixed and suffixed forms for ‘70’, ‘80’, and ‘90’ in the extant documents of Old English (outside the Orosius) suggests (cf. VON MENGDEN 2006a). The most plausible scenario is this: first, the formation pattern of the expressions from ‘70’ to ‘99’ was entirely clear and there was no pressure on this type of formation to be replaced by a more salient one. But, as the circumfixed expressions for ‘100’, ‘110’, and ‘120’ became increasingly obsolete (cf. 28 Of the circumfixed forms, the MED has entries for hundseventi and hundte(o)ntig only. The instances provided by the MED are very few and for the most part attested in twelfth century versions of Old English texts. The two instances from genuinely Middle English texts – one each in the Trinity Homilies (hund seuenti; 9, 23, cf. MORRIS 1873: 51) and in the Proverbs of Alfred (hunt-seuenti; cf. ARNGART 1955: 83, line 99, § 6) – cannot be dated much later than 1200. Cf. MED IV, 1035a, s.vv. “hundseventi” and “hundtentig”; cf. VON MENGDEN (2006a: 223).

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§ II.7.2.1), the pressure of the analogy with the expressions for ‘20’ to ‘60’ became stronger. In the Old English texts, the type formed on HUND-__-TIG was unquestionably the standard type for numerals from ‘70’ to ‘129’. But the comparatively early date of the Orosius-translation and the occasional occurrence of weakened forms of HUND- in the tenth-century Lindisfarne ms. (unseofontigum in LkHeadGl (Li) 41; cf. SKEAT 1874: 6) suggest that the gradual replacement of the circumfixed forms by the Modern English type was set in motion long before the transition period of the later eleventh and twelfth centuries. In fact, the circumfixed forms are virtually gone in the early Middle English period, while twelfth-century Old English texts still consistently attest to them. Although the evidence is not sufficiently clear to allow definite statements about the change from one type to the other, two important aspects seem to point into the same direction. One of them I have just mentioned: the clear cut in the usage between twelfth-century Old English texts and early Middle English texts. The other is the fact that, as suggested by the evidence of the Orosius-section, the Modern English type must have been in use to some extent as early as the tenth century. Both pieces of evidence can be seen as indications that the circumfixed forms may have been largely retained in the ‘literary’ language of Old English, while at the same time the Modern English type may have been more established in some spoken registers than textual evidence suggests. Only the end of the Late Old English scribal tradition during the twelfth century cleared the way for the suffixed type to enter the written texts. (See VON MENGDEN 2006a for a more detailed discussion.) II.7.3

Later modifications of the numeral system

From the point of view of the system, no significant changes took place from the early Middle English period onwards. The arithmetic and recursive mechanisms were basically those of today’s numeral system after the overrunning section and the circumfixed expressions had been levelled out. Two major differences in comparison with the numeral system of Present-day English should, however, be mentioned briefly: one concerns the internal syntax of complex numerals, the other is a lexeme newly introduced to the system. As shown in § II.4.3.1, the element order between the multiples of ‘10’ and atomic addends was different from the one used today. While in Old English ‘24’ is constructed as feower and twentig throughout (cf. MITCHELL 1985 I: 219, § 555), Present-day English uses the opposite order with the augend preceding the addend: twenty-four. After the Norman Conquest the order addend + multiple of ‘10’ remains in use with the reverse order emerg-

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ing not before the end of the Middle English period; cf. MUSTANOJA (1960: 305). The Old English type still occurs in the literary language of the nineteenth century. The Modern English type is probably the more transparent construction with respect to other types of complex numerals based on addition: both in Old English and in Modern German, the higher valued constituent of a complex numeral always precedes the lower one except for the addition of atom and multiple of ‘10’ as in feower and twentig. In any case, the higher-plus-lower order is cross-linguistically by far the more frequent order between atom and multiple of ‘10’. This can be explained by the cognitive processing of complex numerals: if the constituent with the highest valued base is expressed first, the recipient interlocutor will more immediately have an idea about the approximate value of the cardinality expressed. The lower valued constituents only supply the details; cf. GREENBERG (1978: 274); HEINE (1997: 22–23). In this context, STAMPE (1976: 602–603) points out an interesting crosslinguistic correlation: the reversal of the element order from the crosslinguistically rare type four-and-twenty to the more natural order twenty-four goes parallel with the dropping of the overt expression of the operator ‘+’. Classical Greek , for instance, uses the Old English type plus an overt expression of the operator ‘+’ (téssara kaì eíkosi ‘4 + 20’) and in the modern Germanic languages, this type is the only possible one in German (vier und zwanzig ‘4 + 20’). More significantly, there does not seem to be any instance of an archaic use of the Old English type without overt expression of the operator, i.e. *four-twenty, at any point in the history of English. The underlying hypothesis that the order addend + multiple of ‘10’, being cognitively more difficult to process, cross-linguistically requires a linker between the two constituents is confirmed by the data from a large sample of European languages presented in STOLZ (2002: 373–379; § 4.2). Of the possible combinations of addend preceding/following the multiple of ‘10’ and presence/absence of a connector ‘+’, the combination addend – multiple of ‘10’ without an overt operator ‘+’ does not occur. The other post-Old English modification of the numeral system is formally only slight but apparently has a far-reaching consequence. Through the introduction of one lexical item, the fourth base million in late Middle English, attested since the end of the 14th century (cf. MED VI, 470b-1a, s.v. “miliǒun”), the scope of the numeral system could be extended enormously. Yet a higher base used to be represented by (now archaic) milliard in British English and is now superseded by billion, which, however, is used for varying numerical values. The fact that the use of the fifth base billion for either ‘109’ or ‘1012’ follows a discernible geographical distribution shows that it was not

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introduced until dialectal differences between the English on the British Isles and its overseas varieties had to some degree become conventionalised (cf. the short account in the Oxford English Dictionary; OED II, s.v. “billion”, 195b). I find it questionable whether simple expressions for powers of ‘10’ yet higher than ‘109’ can be taken as genuine bases of the system (cf. GREENBERG 1978: 253). COMRIE (2005b: 217) quotes the following expressions from an internet search: undecillion ‘(106)11’, novemdecillion ‘(106)19’, vigintillion ‘(106)20’, unvigintillion ‘(106)21’, d(u)ovigintillion ‘(106)22’, novagintillion ‘(106)29’, centillion ‘(106)100’. I have no doubt that these expressions are attested in some context, but the crucial question is to what extent their usage can be compared with that of systemic numerals. The main criteria we have employed here for including cardinality expressions into the system are the counting sequence and recursive formation of more complex numerals (cf. § I.4). These criteria are only of theoretical value when it comes to expressions for extremely high cardinalities. First, while these expressions, of course, do fulfil the necessary requirements to be part of the recursive system, we hardly have any instances of extremely high-valued base-like expressions being used as constituents of complex numerals. Second, it would be conceivable that the conventional counting sequence theoretically reaches such expressions but, again, such a case is not attested. Where these expressions are attested, they will hardly ever be used for numerically specific quantification in the strict sense. As long as they are used in the sense of ‘extremely many’, they are not numerals but numerically unspecific quantifiers. The fact that these expressions bear the potential to be systemic bases does not say anything about their (synchronic) status in actual usage. I am, therefore, inclined to take these expressions as non-systemic, or even numerically unspecific quantifiers in the sense of the distinction we have drawn above in § I.1. Cf. the short discussion in the context of non-systemic expressions in Old English below in § III.3.3.

II.8

Ordinals

Before proceeding to more detailed aspects of the internal structure of complex numerals and to some important characteristics of bases in Chapter III, this final section of Chapter II will briefly treat the most important aspects of the formation of ordinal numerals in Old English. Morphologically, ordinal numerals are – with some exceptions (cf. §§ II.2.1–2) – formed as derivations of the respective cardinal root. The mor-

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phological process of forming ordinal numerals generally has no implications for the structure and the constraints of the numeral system. However, ordinal marking is a morphological process which in principle is exerted exclusively on all numerically specific cardinality expressions and thus a central property of cardinal numerals. In this regard, a section on ordinal numerals may well be seen as a necessary complementation of a description of cardinal numerals. Moreover, as we said above (§§ II.2.1–4), most cardinal numerals show inflection only in particular contexts or under certain constraints. Encoding the function ‘ordinal number assignment’ is therefore the only morphological process that is equally exerted on atoms, bases and complex numerals (except the hybrid ordinals ‘first’ and ‘second’; cf. §§ II.8.1–2 below). Describing ordinal numerals thus implicitly reveals properties of cardinal numerals. This may be rather trivial in the case of simple numerals, but once the structures become more complex, it should become rewarding to raise the question of how one morphological process is encoded on a construction consisting of several constituents, indeed on one that may be described as a construction formed as a hierarchically ordered sequence (as we did in Figures 4, 10, 12, 13 above). This section on ordinals therefore not only complements the description of the numeral forms of Old English, it also provides some basic information which will contribute to a number of aspects that will become relevant in Chapter III. We have just indicated that the ordinals for ‘first’ and ‘second’ are excluded from these morphological processes as the relevant expressions are hybrid forms. As will be shown in the next two sections, these forms have no morphological connection with the cardinal forms for ‘1’ and ‘2’. This is in accordance with a universal principle predicting that, if an ordinal numeral is suppletive (i.e. if it is morphologically not derived from the lexical root of the corresponding cardinal), every lower valued ordinal is also suppletive (cf., among many others, GREENBERG 1978: 288; HURFORD 2001: 71; § 1.2.2). More trivially, the generalisation states that if there are hybrid ordinals in a language, they stand for the lowest numerical values.29 29 For a recent attempt at accounting for the hybrid character of ordinals for ‘first’ see BARBIERS (2007). BARBIERS refers to general principles of quantification in which the numerical value ‘1’ plays a different role than higher cardinalities. This is certainly an interesting approach, but there seem to be some methodological problems with the study. BARBIERS’ approach is inductive as it is based on data from Modern Dutch where only eerste ‘first’ is suppletive. It thus leaves unconsidered the fact that in many languages the ordinals ‘second’ and sometimes ‘third’ are also suppletive. Given that the implicational hierarchy mentioned above is undisputed, it seems doubtful whether any type of explanation of the phenomenon may possibly be reduced to ‘first’ and exclude the next higher numerical values.

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119

All other simple ordinal expressions of Old English do stand in some morphological relation to the respective cardinals. Yet morphophonemic crossinfluences between ordinal suffix and root have altered the shape of the numeral roots in most cases so that a uniform derivational pattern may not be transparent without drawing on diachronic knowledge. The following small sections are designed as brief descriptions of the relevant forms and do not attempt at achieving a comprehensive discussion of all relevant aspects. II.8.1

The expressions for ‘first’

As will be shown in more detail below, there is no expression that can be taken as the default ordinal numeral corresponding to PDE first. There is a relatively large number of lexemes in Old English all of which may be used with the ordinal meaning ‘first’. ÆREST is a superlative of the suppletive comparative ÆR ‘before, ere’, but it is often used as an adverb in the sense of ‘at first, for the first time’. In this sense, it can occasionally come close to performing ordinal functions as e.g. in (2.20) and (2.21). The corresponding comparative form ÆR is often used in the sense ‘former, earlier’, in which case it may likewise assign an ordinal number to a referent; cf. (2.22). In none of these instances, however, is the implication ‘temporally prior, earliest’ completely absent. (2.20) Ad 31.2 (CROSS/HILL 1982: 38): Saga me hwilc word wæs ærest. Ic þe secge, drihten cwæð, gewurðe leoht. Tell me, which word was [the] first. – I tell you, the Lord said, “Let there be light!” hwilc which

word word

wæs ærest be(3SG.PST) first/earliest

(2.21) Bede 5 23.488.1 (MILLER 1890–1898: 488): Ða feng Cynegyls Ceolwulfes broðer suna to rice, & hæfde an & þrittig wintra. & he onfeng ærest fulluhte Westseaxna cyninga. Then Cynegyl, Ceolwulf’s son’s brother came to power and he ruled for 31 years. And he was [the] first West-Saxon king to receive baptism. he PPRN .3SG .NOM.M

onfeng ærest fulluht-e receive\PST.3SG first/earliest baptsim-ACC.SG

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The numeral system of Old English

(2.22) ÆLet 6 7 (A SSMANN 1889 [1964]: 3, 50): Nu sæde ic ðe ær þis on þam ærrum gewritum, hu se ælmihtiga drihten ealle þing gesceop, heofonas & eorðan & ealne middaneard […], Now, I told you in the first book, how the Almighty Lord crated all things, heaven and earth, and the whole world, […] on PREP

þam ærr-um gewrit-um DET:DAT.SG first/former-DAT.SG writing-DAT.SG

There is another set of lexemes that can be used as the ordinal ‘first’. The comparative FORMA ‘former’ (cf. (2.23)) can sporadically be found assigning an ordinal number to a referent. More common as an ordinal is the respective superlative FYRMEST (cf. PDE foremost); cf. (2.24). A shortened form of this is 30 FYREST, which is the predecessor of PDE first. (2.23) Or 1 14 (BATELY 1980: 35,26): Her endaþ sio forme boc & onginð sio æfterre. The first book ends here and the second begins. her endaþ sio form-e boc Here end-3SG.PRS DET:3 SG.NOM.F first/former-NOM.SG.F book(F):NOM.SG (2.24) LS 34 642 (MAGENNIS 1994: 53): […] and þæt wæs sona on þam fyrmestan dagan þe Decius se casere to rixianne begann, […] […] and that was soon on the first days when the emperor Decius began to reign […] on

þam PREP DET:DAT.PL.M

fyrmest-an dag-an first-OBL.PL day(M)-OBL.PL

Finally, the form of the cardinal AN is itself quite often used as an ordinal. This is usually the case if the first item of an enumeration or list is specified; cf. (2.25) and (2.26). Cf. RISSANEN (1997: 89–93) for an analysis of these instances with respect to the use of the cardinal form in an ordinal construction.

30 Other forms like FRUM- ‘early, previous’ or FYREST (a superlative formation of the preposition fore ‘before’; hence PDE first) are occasionally mentioned in the literature as ordinals for ‘1st’. Usually, however, these forms are attested in the sense ‘foremost’ rather than with an unambiguously ordinal function.

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(2.25) HomU 46 241 (NAPIER 1883 [1967]: 299, 14): and ðreo þing syndon, þe ne beoð forgifene ne on þissere worulde ne on þam toweardan life: an is, þæt man god to tale habbe, oðer, þæt man ærestes ne gelyfe; þrydde, þæt man ortruwige godes mildheortnysse. And there are three things which will not be forgiven, neither in this world nor in the future life: one is, that one is blasphemous, the second, that one does not believe in the resurrection, and the third, that one has doubts about god’s mercy. (2.26) Or 2 1.36.12 (BATELY 1980: 36, 12): Nu \we/ witon þæt ealle onwealdas from him sindon, […]. An wæs Babylonicum, þær Ninus ricsade. Þæt oðer wæs Creca, þær Alexander ricsade. Þridda wæs Affricanum, þæ[r] Ptolome ricsedon. Se feorða is Romane, þe giet ricsiende sindon. Now, we know that all empires are from him [i.e. from god] […]: The first is the Babylonian [empire], where Ninus reigned. The second was Greece, where Alexander reigned. The third was the African [empire] where the Ptolemies reigned. The fourth is [that of the] Romans who are still reigning.

With respect to the various options the Old English language seems to provide for expressing the ordinal concept ‘first’, the question is whether there was any default term for this concept. Again, we may perhaps infer from Ælfric’s Grammar which expression was perceived as the default expression for the ordinal. However, while example (2.27) uses FYRMEST, in example (2.28) the adjective FYRMEST is contrasted against the ordinal ÆREST, thus contrasting two different types of being ‘outstanding’, i.e. ‘most important’ versus ‘earliest’. (2.27) ÆGram 13.17 (ZUPITZA 1880 [2001]: 13): sume syndon ordinalia, þa geswuteljað endebyrdnysse: primus fyrmest, secundus oðer, tertius ðridda, et cetera. Some [nouns (cf. ÆGram 11.8 ff.)] are ordinals: they specify the order: primus the first, secundus the second, tertius the third and so forth. (2.28) Comp 11.1.1 4 (HENEL 1934: 64): Ðis synd þa þry frigedagas þe man sceal fæstan […] þæt is se æresta frigedæg on kalendis Maius & se oþer æfter PENTECOSTEN, & se þridda on kalenda iulius, þæt is se fyrmesta friedæg. These are the three holidays where we should be fasting […]: That is the first Friday in the kalend of May and the second [Friday] after Pentecost, and the third [Friday ] in the kalend of July which is the most important Friday.

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Given the evidence presented here, it is perhaps justified to question whether an ordinal numeral ‘first’ existed in Old English at all. There is a variety of forms that demonstrate the potential to be employed in contexts in which an ordinal ‘first’ may be appropriate. However, there is hardly an instance in which these forms are used exclusively with ordinal function. It is true that, independently of the particular language under examination, it is generally difficult to distinguish between the ordinal use ‘first’ and related adjectival or adverbial uses. However, the prototypical use of an ordinal ‘first’ is certainly the specification of the first item in an enumeration or a list, and in Old English it is the cardinal form AN which is most commonly used in this prototypical context. II.8.2

The expressions for ‘second’

Like the ordinals for ‘1’, those for the numerical value ‘2’ are all suppletive forms. There are two different lexemes which are employed for ‘second’. OE ÆFTER ‘subsequent, following’ is a comparative formation containing a root which otherwise survives in the adverb OE EFT ‘afterwards, again’. In its weak inflected form æft(e)ra, it is sometimes used as an ordinal. In most instances, the implication ‘following’ cannot be completely interpreted away, and the strictly ordinal sense is implied by the contextual reading rather than by the primary lexical meaning of ÆFTER; cf. (2.29). The use of ÆFTER with an exclusively ordinal function, as in (2.30), is therefore rare. (2.29) ÆCHom II (Pref) 2.33 (GODDEN 1979: 2, 36): Ic gesette on twam bocum þa gereccednyysse ðe ic awende, for ðan ðe ic ðohte þæt hit wære læsse æðryt to gehyrenne, gif man ða ane boc ræt on anes geares ymbryne, and ða oðre on ðam æftran geare. I arranged the treatise which I have translated into two books, because I thought that it were less tedious to listen, if that one book were read in the course of one year, and the other in the following year. on

ðam æftran gear-e PREP DET:DAT.SG subsequent:DAT.SG year-DAT.SG

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(2.30) LawIne 26 (LIEBERMANN 1903: 100, 3): To fund[en]es cildes fostre, ðy forman geare geselle VI scill., ðy æfterran XII, ðy ðriddan XXX, siððan be his wlite. As child benefit for a foundling, give six shillings in the first year, twelve in the second, 30 in the third, [and] afterwards according to their constitution. ðy DET:INS.SG

æfterran second-INS.SG

[gear-e] year-INS.SG

In the passage from Ælfric’s Grammar quoted above as (2.27) (§ II.8.1), we could see that Ælfric uses OÞER as equivalent of Latin secundus. We may take this as a hint that OÞER may be the default lexeme for the ordinal ‘second’. The use of this lexeme for ordinal number assignment is older, since it is attested in other Germanic and in some Indo-European languages, too.31 Like PDE other, the expression is used in a wide variety of senses and implications, such as ‘another’, ‘different’, etc., and instances where OÞER is used clearly and exclusively as an ordinal are again rare; cf. (2.31) and (2.32). (2.31) Met 20.181 (SEDGEFIELD 1899: 183, 186): forðæm ic lytle ær sweotole sæde þæt sio sa[u]l wære þriefald gesceaft þegna gehwilces, forðæm uðwitan ealle seggað ðætte an gecynd ælcre saule irsung sie, oðer wilnung; is sio þridde gecynd þæm twæm betere, sio gesceadwisnes. As I plainly said earlier on, that each man’s soul was a threefold creature, for that reason all scholars say that one nature of every soul is anger, the other is desire; the third nature – of higher value than the two – is reason. (2.32) ÆCHom I.31 439.1 (CLEMOES 1997: 439): Wyrd-writeras secgað þæt ðry leodscipas sind gehatene India. Seo forme India lið to ðæra Silhearwena rice, seo oðer lið to Medas, seo ðridde to ðam micclum garsecge […] Historians say that there are three nations called India: the first India lies towards the Ethiopian empire, the second lies towards the Medes, the third by the great ocean.

31 The Proto-Germanic form */'anθar-az/ goes back to PIE *h2én-ter-os ‘other’ (> preGermanic */'on-ter-o-/), which is also attested in the Baltic and Slavic languages (cf. Lithuanian antràsis) along with its variant *h2él-ter-os, represented by Latin alter; cf. PROKOSCH (1939: 292, § 100); SIHLER (1995: 429, § 398.2); BEEKES (1995: 216, § 16.2).

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II.8.3

The ordinal forms of the simple numerals

The ordinal ÞRIDDE is the first element in the sequence of ordinals that is not a hybrid form. However, it shows a considerable deviation from the cardinal root; its morphophonemic development must have diverged from the other regularly formed ordinals at a very early stage of common Germanic. While the regular suffix of the ordinals in Proto-Germanic was *-þa- (< PIE *-tó-/*-to-), the forms for ‘third’ in all Germanic languages can be accounted for only if we postulate a suffix *-þja- for this numeral. From ‘fourth’ onwards, the ordinal suffix -ÞA is applied in its regular shape. Morphophonemic cross-influences nevertheless occur in many forms. In FEOR-ÞA ‘fourth’, the root FEOWER has been shortened. In FIF-TA ‘fifth’ and SIX-TA ‘sixth’, the stop /-t-/ (rather than /-θ-/) in the suffix still represents the pre-Germanic form, as a preceding fricative usually prevented the Germanic Consonant Shift from taking effect. In SEOFO-ÞA ‘seventh’ and NIGO-ÞA ‘ninth’, the root-final nasal was dropped regularly before fricatives. The same holds for ENDLYF-TA ‘eleventh’ and TWELF-TA ‘twelfth’. Among the atomic numerals, the form EAHTO-ÞA ‘eighth’ (with frequent variants showing 〈-aða〉 and 〈-eða〉) alone shows a relatively regular formation of cardinal root and affix. The most common ordinal form for ‘tenth’ is TEO-ÞA, of which the variant TEG(E)ÞA (/'tej(@)θa/) is predominant in northern texts. Cf. Figure 14 for a summary of the simple ordinals: ÞRIDDE FEOR-ÞA FIF-TA SIX-TA

SEOFO-TA EAHTO- ÞA NIGO-ÞA TEO-ÞA ENDLYF-TA TWELF-TA

Figure 14.

‘3rd’ ‘4th’ ‘5th’ ‘6th’ ‘7th’ ‘8th’ ‘9th’ ‘10th’ ‘11th’ ‘12th’

Ordinal forms of simple numerals

Ordinals

125

The use of the ordinal suffix -ÞA with the higher bases HUND(RED) and ÞUSEND is not attested.32 Expressions for ‘hundredth’, whether as simple forms or as constituents of complex expressions, are formed as circumfixed expressions of the type HUNDTEONTIGOÐA (for which see below). The earliest instance of an ordinal form of HUNDRED in English is not attested before the fourteenth century (cf. MED IV: 1034a, s.v. “hundredethe, ord.num.”) and one of ÞUSEND is even younger as thousandth does not occur before the sixteenth century (cf. OED XVII: 988b, s.v. “thousandth”). II.8.4

The ordinal formation of complex forms

The ordinals from ‘13th’ to ‘19th’ are basically compounds consisting of the atomic cardinal and the ordinal TEOÐA ‘10th’, i.e. typically þreo-teoþa ‘13th’, feower-teoþa ‘14th’, etc. The ordinals of the multiples of ‘10’ use -TIGOÞA up to ‘60th’ and HUND-__-TIGOÞA from ‘70th’ onwards to express the multiplicand ‘× 10th’ (‘-tieth’). Cf. Figures 15 and 16, respectively: ÞREO( T) FEOWER FIF SYX SEOFON

*EAHTA NIGON

Figure 15.

-TEOÞA -TEOÞA -TEOÞA -TEOÞA -TEOÞA TEOÞA

-TEOÞA

‘13th’ ‘14th’ ‘15th’ ‘16th’ ‘17th’ ‘18th’ ‘19th’

Ordinal numerals for the teens

32 Northumbrian documents attest to 〈hundreð-〉 / 〈hundrað-〉. These are cardinal numerals, apparently influenced by (or, borrowed from) Old Norse. There is, however, one instance of 〈hundrað〉 in the Lindisfarne gloss (MtHeadGl (Li) 78; cf. SKEAT 1887: 21) where hundraðes renders Latin centensimi. It appears to be used as an ordinal although the scribe’s motivation to use this particular form is, as is often the case in a word-to-word gloss, difficult to determine. The use of hundrað in this instance may be accounted for by the fact that Latin centesimus is usually rendered by a nominalised form of hundred whenever it refers to a ‘set or unit of a hundred (people)’.

126

The numeral system of Old English TWEN ÞRI FEOWER FIF SYX HUND HUND HUND HUND

*HUND *HUND Figure 16.

-SEOFON -EAHTA -NIGON -TEON -ÆLLEF -TWELF

-TIGOÞA -TIGOÞA -TIGOÞA -TIGOÞA -TIGOÞA -TIGOÞA -TIGOÞA -TIGOÞA -TIGOÞA -TIGOÞA -TIGOÞA

‘20th’ ‘30th’ ‘40th’ ‘50th’ ‘60th’ ‘70th’ ‘80th’ ‘90th’ ‘100th’ ‘110th’ ‘120th’

Ordinal numerals for the multiples of ‘10’

It should be said that the lists in Figures 15 and 16 both form idealised and in part reconstructed sets. The three asterisked forms are indeed not attested in this very spelling. The expression for ‘120th’ listed in Figure 16 is indeed not attested at all.33 Apart from the fact that it is impossible to deal with all aspects of the variation of all relevant morphemes that can be found in Old English documents, the present discussion is intended to focus on the morphological process forming ordinal numerals. For this purpose it is justified, perhaps necessary, to disregard variation. Generally two different structures are conceivable for ordinal forms of complex numerals. One in which an ordinal form representing the base, say, ‘10’ (and the relevant arithmetic operation), is attached to the atomic cardinal form (Type A) and one in which the ordinal marker is attached to the complex cardinal (Type B): Type A: atom – [10 – ORD] Type B: [atom – 10] – ORD The way Figures 15 and 16 present the structures implies that ordinals of both sets, the teens and the multiples of ‘10’, are formed according to Type A, because the expressions are listed without a morpheme boundary between the elements for ‘10’ and what could be identified as the ordinal marker -ÞA. In33 The few instances where complex ordinals with ‘120’ as augend are expressed are forms of the type HUND-TWENTIGOÞA in which hund is not part of a circumfix but represents the augend ‘100’, so that the form does not represent either of the formation patterns discussed below, but the structure ‘100 + (2 × 10)-ORD’.

Ordinals

127

deed, many of the attested forms in the ancient Germanic languages suggest that, diachronically, the formation of the ordinals of the augend ‘+ 10th’ (‘-teenth’) and the ordinals of the multiplicand ‘× 10th’ (‘-tieth’) must have developed according to pattern A, i.e. as a construction consisting of the respective atomic form and the ordinal ‘10th’, as suggested by ROSS/BERNS (1992: 637, § 15.20). It is, of course, difficult to trace the structure that was actually in use in the early stage of the common Germanic period. But the phonological shapes of the West Saxon suffixes -TEOÞA ‘+ 10th; -teenth’ and -TIGOÞA ‘× 10th; -tieth’ allow for the assumption that, in the pre-Germanic period, the difference between the two must have been marked by a different stress position in the compounds consisting of atomic cardinal plus ordinal form of ‘10’. Thus -TEOÞA ‘-teenth’ is derived from ProtoGermanic */-'tiχun-θa/ ‘+ 10th’ with the stress on the element ‘10’, whereas -TIGOÞA is derived from Proto-Germanic */'-tiχun-θa/ ‘× 10th’ with the stress on the atomic constituent. The different stress patterns, then, caused different sequences of sound changes to affect the two forms which resulted in the attested suffixes -TEOÞA ‘+ 10th; -teenth’ and -TIGOÞA ‘× 10th; -tieth’, respectively. The alternative way, Type B, would be to add the ordinal suffix -þa to the complex cardinal forms described in §§ II.4.2–3. In spite of the phonologically sound reconstruction that allows to assume Type A as the underlying type of composition, some aspects of the forms in Figure 16 also clearly speak in favour of Type B. One is that the expressions for ‘20th’, ‘30th’, ‘100th’ and ‘110th’ use the same allomorph for the atomic constituent as the corresponding cardinal forms do. This would clearly suggest that some variant of an ordinal marker – synchronically this would be -OÞA – is attached to the complex cardinals of Figures 7, 9, and 11 (§ II.4.3) as a whole (Type B). Moreover, the use of the circumfixes in the ordinals can only be accounted for if we assume Type B to be underlying. What may look a bit like a dilemma can perhaps be resolved if we accept that the answer does not need to be categorical. I believe it is very likely that both formation types not only interfered with each other at one identifiable point in history, but also that the two types have the potential to constantly interfere during the development of a language (and did so at least during longer periods of the history of English). Whereas the Old English ordinals for the teens, the expressions in Figure 15, are obviously formed according to Type A, nowadays the same set is expressed according to Type B (PDE X-teen-th). Not only are there the two opposing forces of ease of pronunciation (leading to morphophonemic alternations on the syntagmatic level) and of paradigmatic transparency (levelling out such disturbances, however

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The numeral system of Old English

not necessarily in a way uniform across the entire paradigm). Additionally, the latter force may operate on different morpheme boundaries: if the atomic forms should be made transparent, the remaining part consisting of ‘10’ and of the ordinal affix are treated as one unit whose structural opacity will be accepted. If the ordinal function should be made morphologically transparent, the complex cardinal forms will be seen as a whole (irrespective of how transparent its internal structure may be). Thus, theoretically, there are three forces constantly at work: one on the syntagmatic level and two likewise opposing ones on the paradigmatic level. As a final remark it is worth noting in this context that the two elements postulated in Figures 15 and 16, -TEOÞA (/-te;oθa/) and -TIGOÞA (/-tiγoθa/), are phonologically not very distant. Indeed, for the latter form, -TIGOÞA ‘-tieth’, a variant -teoþa is attested which, due to contraction has become homonymous with the former, particularly in copies of the interlinear gloss to the Benedictine Rule. And, vice versa, in Mercian texts, ordinals for the teens often show the form -teogoþa ‘-teenth’, otherwise a common variant of -TIGOÞA ‘-tieth’. For several reasons, confusion is nevertheless hardly ever likely to occur because, in most instances, the context clearly suggests only one of the two numerical values. In other cases, the circumfixed structure, i.e. the addition of the preposed element HUND-, disambiguates. For instance, in the interlinear gloss to the Benedictine Rule in ms. Tiberius A.iii, there is a strikingly clear distinction between contracted forms -teoþa and full forms -tigoþa for ‘-tieth’: the contracted form only occurs as part of the circumfix, i.e. as hund-__-teoða for the ordinals from ‘70th’ onwards, whereas the common full form -teogoða is restricted to ‘-tieth’ in the lower valued multiples of ‘10’ in which the use of the contracted -TEOÞA would indeed cause confusion with ‘-teenth’. The use of the ordinal forms in such a way is indeed exceptional, but, remarkably, these cases show two things. First, there is potentially a constant need for re-arrangements of the two paradigms discussed in these sections. Second, however confusing a paradigm may be that results from such rearrangements, the strongest force that prevails over the principles of economy and transparency is that, as postulated in § I.4.2.1, in one variety (and may it be the variety of only one historical document), there can only be one expression for one numerical value.

Chapter III Complex numerals Up to this point, we have discussed the basic principles according to which simple numerals are combined into complex expressions both from a theoretical and/or cross-linguistic perspective (Chapter I) and from a languageparticular (Chapter II) perspective. In addition to these general principles, there are other characteristics of complex numerals which will be discussed in the present chapter. The focus will be on two closely related aspects. One is the internal syntax of complex expressions which includes constituent order and the possible deletion of constituents. Another aspect closely linked with the internal structure of complex numerals is particular properties of bases. § III.1 will particularly deal with factors which – in addition to the morphological patterns described in Chapter II – determine the actual form of complex numerals in Old English. These properties can be read as syntactic properties in the sense that particular uses of bases (i.e. arithmetic uses) require a particular behaviour of the overall expression. Some of the constraints discussed here, like for instance ‘1-deletion’ (§ III.1.1), do follow cross-linguistic patterns but are instantiated differently in individual languages. Others, like particular properties of higher bases, are language-particular although again, generally, the phenomenon of deviating syntactic behaviour of higher bases is not language-specific (§ III.1.2). Finally, the way other clause constituents, like the quantified NP, interfere with the structure of complex numerals, seems very peculiar to Old English although it may well be that phenomena, like the ones described in § III.1.3, simply failed to catch the typologists’ attention. To some extent, such questions also include the syntactic relation between complex numeral and the quantified NP. This will also be touched upon in § III.1.3.1, but the focus will be on the position of the quantified NP in relation to the internal structure of the complex numeral. More central aspects of the morphosyntactic relation between numerals and NP, such as agreement patterns, different types of Case relations, etc., will be the topic of Chapter IV. In § III.2, again cross-linguistic considerations interact with languagespecific description. At a first glance, it may sound quite trivial to state that the numeral system of a language is a ‘decimal system’ (as is the case in Old English). However, I am not aware that there have ever been attempts to determine the criteria that underlie such a classification. Such an attempt will be made in § III.2. This is a crucial question with respect to Old English, because, as will be shown, there have been many attempts in the history of the linguis-

130

Complex numerals

tic description of the ancient Germanic languages, to account for some particularities of these systems by non-decimal numeral systems – again without specifying criteria for such a classification. A final section of this chapter will be dedicated to non-systemic complex expressions. Although we excluded non-systemic expressions from the object of this study (§§ I.1 and I.4), describing some cases of non-systemic complex expressions is nevertheless relevant. First, as will be seen below in § III.3, the way they are constructed, they often draw on the same or related properties and formation patterns as systemic complex expressions do or they may partly employ systemic numerals as constituents. Second, discussing how these expressions deviate from systemic complex expressions may well contribute to the distinction between the two types of numerically specific expressions – in addition to the criteria we discussed in § I.4 where the focus was on simple expressions. Generally, the three parts of this chapter are more loosely connected with each other than the sections of the other chapters. They all have the fact in common that they deal with complex expressions and their properties, albeit from considerably different angles. III.1

The formation of complex numerals

III.1.1

1-deletion

We described in § I.3.3 how atomic numerals do not only occur as a sequence of addends, but also as a sequence of multipliers to a base. Particularly in §§ II.4.3 and II.5, we illustrated this pattern with the example of Old English. There is an important exception to the use of atoms as multipliers that can be observed across languages, which we did not consider up to this point. There are cases in which the first element in a sequence of atoms is not overtly expressed. For instance, the multipliers of the first base are overtly expressed only from ‘20’ onwards, i.e. TWEN-TIG ‘2 × 10’, ÞRI-TIG ‘3 × 10’, etc. (cf. § II.4.3) but the multiplier ‘1’ in the sequence of teens (cf. § II.4.2) is not. Here, the numerical value alone is expressed as TYN, but not as *AN-TIG ‘1 × 10’. By contrast, an element representing the multiplier ‘1’ may be overtly expressed for the higher bases ‘100’ and ‘1,000’. The use of ‘1’ as a multiplier of the higher bases is, however, optional; compare (3.1) and (3.3) with (3.2) and (3.4), respectively:34 34 All but one instance of AN HUNDRED are attested after the Conquest; the earliest occurrence thus being an interlinear gloss in Byrhtferth’s Manual (mid-eleventh century):

The formation of complex numerals

131

(3.1) Conf 1.1 335 (SPINDLER 1934: 190, 26f.): Gif man husl wyrpe on fyr oððe on stream, þonne hit [man syleð] to ðicgenne, singe he hund sealma. If somebody throws the host into the fire or into a river, then it should be given to him [and] he should sing 100 psalms. sing-e sing-SBJV.SG

he PPRN :3SG .NOM.M

hund 100

sealm-a psalm-GEN.PL

(3.2) Or 4.42.14 (BATELY 1980: 42): Romulus gesette ærest monna senatum: ðæt wæs, an hund monna, þeh heora æfter fyrste wære þreo hund. Romulus first appointed the men of the senate. They were 100 men, although, after some time, they were 300 of them. an 1

hund × 100

monn-a man-GEN.PL

(3.3) Sat 300 (KRAPP 1931: 145): Us ongean cumað þusend engla,[…] A thousand angels come towards us […] þusend 1,000

engl-a angel-GEN.PL

(3.4) Judg 15.16 (CRAWFORD 1922: 411): Ic ofsloh witodlice an þusend wera mid þæs assan cinbane. Verily, I have slain 1,000 men with the chinbone of an ass. an 1

þusend [×] 1,000

The phenomenon of the multiplier ‘1’ being omitted or optional is commonly referred to as ‘1-deletion’ (see the discussion on the terminology further below). Table 19 shows that in Old English there does not seem to be any systematic distribution of instances of the higher bases with and without 1-deletion. The left hand column of Table 19 compares those arithmetic contexts in which an overt expression of the multiplier ‘1’ is logically possible. The middle column lists the figures of those instances of the bases in which a multiplier ‘1’ generally cannot occur. The figures in Table 19 are the same as those of the more detailed Tables 13 and 14 of Chapter II (§ II.5.2). ByrM 3.3.422 (BAKER/LAPIDGE 1995: 194). There is no indication in BAKER/LAPIDGE (1995) that the gloss could be a later addition.

132

Complex numerals

Table 19. Distribution of base numerals with and without preceding expression for the multiplier ‘1’ base not used as multiplicand

base multiplied by a value other than ‘1’

total of instances

hund

54

574

628

an-hund

70

—

70

hundred

9

82

91

anhundred

13

—

13

þusend

63

268

331

anþusend

37

―

37

The figures in Table 19 show that there is neither a general preference for the overt expression of the multiplier ‘1’, nor for its deletion when multiplied with ‘100’ or ‘1,000’. This means that, unless a numerical value other than ‘1’ is used as multiplier to a higher base, there is no difference in use between the expressions AN HUND(RED) and HUND(RED) and between AN ÞUSEND and ÞUSEND. By contrast, the construction *AN HUNDTEONTIG is completely absent in the Old English records, which can be explained by the fact that HUNDTEONTIG itself expresses a multiple of the base ‘10’ (as it represents the arithmetic operation ‘10 × 10’) rather than a simple base numeral as do the multiplicands in Table 19. There seems to be one constraint in Old English which necessarily requires the overt expression of the multiplier ‘1’: if both the third and the second base occur in a complex numeral and the second base is multiplied by 1, then an overt expression of the multiplier ‘1’ is necessary. It should be said, however, that there is no positive evidence for the obligatoriness of overt ‘1’ in this position. It is inferred from negative evidence, i.e. from the absence of instances without ‘1’ in the corpus and supported by corresponding constraints in present-day languages with a similar numeral system, such as English or German. Cf. the constituent for ‘1,000’ in (3.5) as opposed to that for ‘100’ in (3.6).

The formation of complex numerals

133

(3.5) ByrM 1 4.2 30 (BAKER/LAPIDGE 1995: 232–234) – as (2.16) above in § II.1.5: Ðæt forme þusend (þæt ys seo forme yld þises middaneardes) stod of þusend wintrum & syx hund wintrum & syx & fiftigum wintrum æfter þære soðfæstnysse þe þa Iudeisce witan heoldon, […] The first thousand (that is, the first age of this world) consisted of 1,656 years according to the verity which Jewish scholars observed […] (transl. BAKER/LAPIDGE 1995: 233) of PREP

& +

þusend 1,000 syx 6

wintr-um winter-DAT.PL & +

& +

syx 6

hund × 100

wintr-um winter-DAT.PL

fif-tig-um wintr-um (5 × 10)-DAT.PL winter-DAT.PL

(3.6) Notes 26.3 16 (NAPIER 1889: 9) – as (2.18) above in § II.1.5: Þa wæs fram frymðe ealles a urnen oþþæs temples geweorc. þæt sindon feower þusenda wintra & an hund wintra & seofan & syxtig wintra. Then from the beginning of everything to the construction of the Temple passed by: that are 4,167 years. feower 4

þusend × 1,000

& seofan + 7

wintr-a winter-GEN.PL

& syx-tig + 6 × 10

& an + 1

hund × 100

wintr-a winter-GEN.PL

wintr-a winter-GEN.PL

This results in the following overall pattern for the occurrence of 1-deletion in Old English: for the lowest base of the system, there is generally no overt expression of the multiplier ‘1’. If a complex numeral contains the second base, an overt expression for the multiplier ‘1’ is optional. The same applies to the third base. However, if a complex numeral contains the third base, the overt expression of the multiplier ‘1’ for the second base becomes obligatory; cf. Table 20. Table 20. 1-deletion in Old English overt expression of multiplier ‘1’ complex numeral containing:

‘1,000’

‘100’

first base

—

second and first base third, second and first base

‘10’

optional

optional

—

obligatory

—

134

Complex numerals

Consequently, the structures in Figure 13 of Chapter II (§ II.6) will have to be modified through the specification of the optional character of the expression for the multiplier ‘1’, as in Figures 17a and 17b: ‘1,656’ 1,000

+

656

1 × 1,000

600

1 × 1,000

6 × 100

1 × 1,000

6 × 100

6

1 × 1,000

6 × 100

6

an

+

56 56 +

50 5 × 10

þusend & syx hund & syx & fif-tigum

[optional] Figure 17a. Structure of a numeral containing three bases with optional 1-deletion ‘4,167’ 4,000

+

167

4 × 1,000

100

+

67

4 × 1,000

1 × 100

4 × 1,000

1 × 100

7

4 × 1,000

1 × 100

7

67 +

60 6 × 10

feower þusend & an hund & seofan & syx - tig [obligatory] Figure 17b. Structure of a numeral containing three bases without 1-deletion

The formation of complex numerals

135

A number of authors (e.g. HURFORD 1975: 80–86, § 2.6 and 1987: 54–56; CORBETT 1978a – cf. also G 36 in GREENBERG 1978: 278) have referred to this phenomenon as ‘1-deletion’, and, since this expression has apparently become an established term, I have adopted it here. The term ‘deletion’ clearly implies that the overt expression of a multiplier ‘1’ is the default case and that there is a constraint that requires the lack of an element that is actually expected to be there. This is in accordance with the fact that the multiplier/addend of a base is represented by the entire section of atoms. Logically, however, to overtly express the multiplier ‘1’ creates a redundancy. The constituent representing the multiplicand itself denotes the relevant numerical value and arithmetically there is no need to specify that it is multiplied by 1. Two contrary motivations for the formation of numeral expressions with the multiplier ‘1’ seem to compete. It seems as if these motivations are the same as those we have discussed in a completely different context when we tried to explain the diachronic development of the paradigms of complex ordinal numerals (§ II.6.4). One is economy and the other is paradigmatic transparency. The principle of economy in language use is violated if an element (the base numeral) is multiplied by the identity element for multiplication and if both multiplier and multiplicand are overtly expressed. The speaker creates an arithmetic tautology. There is no necessity to express a numerical value by a complex structure if a simple (or, for that matter, a shorter) expression is available for this value. In other words, to express ‘1 × 100’ requires more than the least necessary effort, but, at the same, time it is not any more explicit than to use simply ‘100’. The opposing force to the economy principle is in this case the paradigmatic analogy with the formation of the higher multiples to the base, i.e. with the sequence TWA HUND(RED), ÞREO HUND(RED), etc., and with TWA ÞUSEND, ÞREO ÞUSEND, etc. In these constructions the overt expression of the atomic multiplier is, of course, arithmetically necessary. Particularly in yet more complex numeral expressions, an analogous structure of equivalent constituents becomes crucial for processing the numerical value. (For a similar explanation cf. GREENBERG 1978: 271). If we account for the general phenomenon of 1-deletion by assuming two competing motivations – the morphological structure requires the presence of an overt expression for the multiplier ‘1’, whereas the underlying arithmetic operation does not – we gain at the same time a reasonable explanation for the fact that, in Old English, the multiplier ‘1’ for the lowest base ‘10’ is obligatorily deleted and not only optionally missing. In the second decade, the base ‘10’ is represented by a different element (the suffix -TYNE ‘+ 10’) than in the subsequent decades (the suffix -TIG ‘× 10’); cf. §§ I.5.3.2 and II.4.2-3. The two different morphological representations of what is arithmetically one and

136

Complex numerals

the same element – the base ‘10’ – precludes the analogical formation of an arithmetically redundant expression. In other words, while the expression for the multiplier ‘1’ in AN HUNDRED is arithmetically useless but motivated by the morphological analogy with the subsequent multiples of ‘100’ (i.e. by TWA HUNDRED, ÞREO HUNDRED, etc.), the morphological motivation does not apply to TYN and the suffix -TYNE because the subsequent multiples are formed by the suffix -TIG. Since -TIG is formally different from TYN and -TYNE, an analogous formation is impossible. The multiplier ‘1’ being obligatorily expressed with some base numerals and omitted with others is a common type of variation within numeral systems of natural languages. There is a clear cross-linguistic tendency for the probability of an overt expression of the multiplier ‘1’ to increase with the value of a base numeral. CORBETT (1978a: 362) establishes the connection between these cross-linguistically comparatively uniform principles of 1-deletion and the universally more noun-like syntactic behaviour of higher valued bases (cf. § V.2.5.3). At least with respect to Old English, the explanations we have given may suffice to account for the possibility of 1-deletion with ‘100’ and ‘1,000’ and for the impossibility of 1-deletion with ‘10’ so that a connection with the assumed noun status of cardinal numerals would not be needed to account for the phenomenon. Moreover, the higher frequency of lower bases may also account for the fact that 1-deletion becomes more likely with an increasing value of a base: in a base numeral like, for instance, billion the analogical force of the paradigm may not be as strong because expressions like five billion, six billion, seven billion are hardly ever used. Yet, although these observations may at this point be seen as alternative explanations to Corbett, they do not rule out Corbett’s explanation. In any case, the correlation between 1-deletion and the noun-like properties of higher bases as suggested by Corbett calls for further discussion. We will come back to this point when examining the word class character of cardinal numerals from a more general perspective in § V.2.3-5 and particularly in § V.2.5.3. III.1.2

The use of the third base

According to the description in § II.1, the highest valued expression in the Old English numeral system represents the numerical value ‘999,999’. The most complex structure theoretically possible in the Old English numeral system is one representing a six-digit number, like the one in Figure 18. Unfortunately, there is no numeral attested in Old English which has the most complex structure possible. Any attested systemic numeral expression in Old English with a

The formation of complex numerals

137

numerical value between 100,000 and the limit number L = ‘106’ represents a numerical value with at least one empty digit. The expression displayed in Figure 18 is therefore an unattested construction. 234,567 234,000 200,000

+

+

34,000

200

× 1,000

34

200

× 1,000

4

2 × 100 × 1,000

4

+

567 500

+

67

× 1,000

5 × 100

× 1,000

5 × 100

7

3 × 10 × 1,000

5 × 100

7

30

67 +

60 6 × 10

twa hund þusend and feower and þri - tig þusend and fif hund and seofon and syx - tig Figure 18.

Structure of a numeral representing a six-digit number

We can see that, in one remarkable respect, this structure differs from that of corresponding expressions in related numeral systems like the ones of Presentday English or of other contemporary European languages. The multiplicand representing the third base þusend is not multiplied by the entire constituent for ‘234’, but rather its multiplier is split into two different constituents, each multiplying ‘1,000’ individually. Arithmetically, according to the Distributive Law, there is no difference in whether we say two hundred, and thirty four thousand ‘([2 × 100] + [3 × 10] + 4) × 1,000’, as we do in the English of today, or whether we say twa hund þusend and feower and þritig þusend ‘([2 × 100] × 1,000) + ([4 + (3 × 10)] × 1,000)’, as in Old English. It is noteworthy, however, that the split of the multiplier of ‘1,000’ does not apply to the expression containing the first base, i.e. feower and þritig ‘4 + (3 × 10)’, which could just as well be expressed as *feower þusend and þritig þusend ‘(4 × 1,000) + ([3 × 10] × 1,000)’. We may conclude that the following rule seems to underlie the distribution of overt expressions for bases in complex numerals of Old English:

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Complex numerals

(3.7) Distribution of bases in complex numeral constructions If, in a complex numeral, any constituent containing more than one base is used as a multiplier to a higher valued base, then the multiplicand must be overtly expressed for any phrase of the multiplier which contains a base.

For our example in Figure 18 this means that, because the multiplier of ‘1,000’ – which is ‘234’ – itself contains more than one base – ‘100’ in ‘2 × 100’ and ‘10’ in ‘4 + (3 × 10)’ – the multiplicand ‘1,000’ must be overtly expressed for any constituent of the multiplier that contains a base. Both ‘200’ and ‘34’ must therefore be multiplied by ‘1,000’ individually in the numeral expression. This rule, of course, applies only to expressions for numerical values from ‘101,000’ onwards, since lower valued expressions cannot have a multiplier containing more than one base. Cf. examples (3.8) and (3.9): (3.8) Rec 26.2 19 (BIRCH 1885–1893 I: 415, 3–4): Ðis ealles [is] twa hund þusend & twa & feowertig þusend hyda & syuan hund hyda. All this [amounts to] 242,700 hides. twa 2

hund × 100 & +

þusend × 1,000

syuan 7

& twa + 2

hund × 100

& feower-tig þusend + (4 × 10) × 1,000

hyd-a hide-GEN.PL

hyd-a hide-GEN.PL

(3.9) ByrM 2.3.179 (BAKER/LAPIDGE 1995: 116): & soðlice þæt ger hæfð […] ostenda fif hund þusend & fif & twentig þusend & nigon hund & syxtig […] And truly, the year has […] 525,960 ostents. ostend-a ostent-GEN.PL & nigon + 9

fif 5 hund × 100

hund × 100

þusend × 1,000

& +

syx-tig (6 × 10)

& fif & twen-tig + 5 + (2 × 10)

þusend × 1,000

There is another difference between the third base ‘1,000’ and the two lower valued bases ‘100’ and ‘10’. In §§ II.4.3 and II.5, we said that the operator ‘×’ has no overt expression. The type of arithmetic operation involved is indicated by the use of a particular morph for each base – -TIG for ‘10’ and HUND(RED) for ‘100’ – encoding the additional information ‘multiplicand’. For the third base, there is no such morphological distinction. The form ÞUSEND is used both for the exact numerical value ‘1,000’ and for the base ‘1,000’ as a serial-

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139

ised multiplicand. Whether the lexeme ÞUSEND ‘1,000’ in a complex numeral is used as multiplicand can only be inferred from the entire structure of the complex numeral. Summing up, we may note that there are some differences between the third base on the one hand and the first and the second base on the other with regard to their respective uses in complex numeral structures. These are:  The scope of the third base comprises multipliers up to ‘999’.  If the third base is used as a multiplicand and the respective multiplier is itself a complex expression, the third base is multiplied distributively.  There is no morphological distinction of the possible arithmetic functions in which ÞUSEND can be used.

III.1.3

The coherence of complex numerals

So far in this chapter, we have looked at numerals mostly from within the system. As a subsystem of the much larger linguistic system, its elements interact with other elements outside the system. As we said in § I.1, cardinal numerals are prototypically used for specifying the cardinality of a set. They are, therefore, necessarily in a syntactic relation with the element denoting the set, i.e. with the referential expression of an NP, the head noun. Chapter IV will deal with the general syntactic relation between numeral and quantified noun, and it would be premature to discuss details at this point. Our main interest in this chapter is the internal structure of a numeral expression and how it is embedded into the context of the other clause constituents. When it comes to the position of the quantified noun within complex numeral expressions in Old English, the syntactic relation between the two elements interferes with the internal structure of a numeral, especially with that of complex numerals. The quantified noun will therefore play a certain role in this stage of our discussion, and some of the aspects raised in much more detail later on in Chapter IV will be anticipated here briefly. In the following, however, the main focus will still be on the internal syntax of complex numerals. III.1.3.1 The position of the quantified NP in complex numerals The default position of the quantified NP in a complex numeral in Old English differs from that of many modern European languages. While in most contemporary European languages the quantified noun is generally adjacent to, but outside the complex numeral, the quantified noun in Old English may

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generally follow any base of the numeral construction. That is, the quantified NP may occur between two constituents of the numeral, thus splitting the numeral into two or more discontinuous parts, or it may occur both after a higher base and at the end of the whole expression. In fact, every possible combination of bases followed by the NP and of bases without an NP following is attested. Some combinations are, however, more frequent than others in the corpus. In a complex numeral comprising several bases, the quantified NP is usually repeated after each base, regardless of whether there are two bases involved ((3.10) and (3.11)) or three ((3.12) and (3.13)). (3.10) ÆCHomI.16App 534.34 (CLEMOES 1997: 534): Us secgað eac bec swa swa hit full soð is, þæt ða seofan slæperas þe slepon on ðam timan fram decies dagum ðæs deofollican caseres. oð theodosies timan ðe on crist gelyfde. þreo hund geara fæc & twa & hundseofantig geara,[…] The books tell us, as it is absolutely true, that the Seven Sleepers who slept in the time from the evil emperor Dacius to the time of Theodosius, who believed in Christ, for 372 years […] þreo 3

hund gear-a fæc × 100 year-GEN.PL period of time

and +

twa 2

and +

hund-seofon-tig CIRC-(7 × 10)

gear-a year-GEN.PL

(3.11) Sol I 59 (CROSS/HILL 1982: 34): On XII mo[n]ðum beoð II & L wucena & CCC dagena & V & LX daga; on XII mo[n]ðum beoð ehta þusend tyda & VII hund tyda. In twelve months there are 52 weeks and 365 days. In 12 months there are 8,700 hours. a.

CCC

300 b.

ehta 8

dag-ena day-GEN.PL þusend × 1,000

& V & LX + 5 + 60

tyd-a & VII hour-GEN.PL + 7

dag-a day-GEN.PL hund × 100

tyd-a hour-GEN.PL

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141

(3.12) ByrM 1 4.2 30 (BAKER/LAPIDGE 1995: 232–234) – as (2.16) in § II.1.5 and (3.5) in § II.2.1: Ðæt forme þusend (þæt ys seo forme yld þises middaneardes) stod of þusend wintrum & syx hund wintrum & syx & fiftigum wintrum æfter þære soðfæstnysse þe þa Iudeisce witan heoldon, & æfter þam þe þa hundseofontig witan gesetton se tima wæs standende twa þusend wintra & twa hund & twa & feowertig geara gerimes. The first thousand (that is, the first age of this world) consisted of 1,656 years according to the verity which Jewish scholars observed […] (transl. BAKER/LAPIDGE 1995: 233) of PREP

þusend 1,000

& syx + 6

wintr-um winter-DAT.PL & +

& syx + 6

hund wintr-um × 100 winter-DAT.PL

fif-tig-um wintr-um (5 × 10)-DAT.PL winter-DAT.PL

(3.13) Notes 25.3.2 15 (FÖRSTER 1925: 193, 7): Ðonne fram middan eardes fruman oð Christes akennednysse, þæt is þonne six þusend geara & C geara & XXV geara & IX monðas. Then from the beginning of the world to the birth of Christ, that is then 6,125 years and nine months. six 6

þusend × 1,000

gear-a & C year-GEN.PL + 100

gear-a & XXV year-GEN.PL + 25

gear-a year-GEN.PL

The repetition of the noun after each base is the most frequent type of cooccurrence of base and quantified NP. However, there are many instances of other distributional patterns of one or more quantified NPs within complex numerals. Hence, the type illustrated above in examples (3.10) to (3.13) – although the most frequent – cannot necessarily be considered the default structure. Sometimes, the noun is mentioned only after the highest base; cf. (3.14)–(3.16). (3.14) LS 7 64 (SKEAT 1881-1900: II, 338): Sege me broþor for þære soðan lufan hu fela is eower on þam mynstre? Þa cwæð he þreo hund muneca and twa and fiftig. Tell me, brother, for the true love, how many of you are there in the monastery? – Then he said: 352 monks. þreo 3

hund × 100

munec-a monk-GEN.PL

and +

twa 2

and +

fif-tig (5 × 10)

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Complex numerals

(3.15) Or 1 14.35.22 (BATELY 1980: 35): Nu is hit scortlice ymbe þæt gesægd þætte ær gewearð ær Romeburg getimbred wære, þæt wæs from frymðe middangeardes feower þusand wintra & feower hund & twa & hundeahtatig […] Now it will be shortly reported what had happened before Rome was built, that was 4,482 years after the beginning of the world […]. feower þusand 4 × 1,000 & feower + 4

wintr-a winter-GEN.PL hund & twa × 100 + 2

& hund-eahta-tig + CIRC-(8 × 10)

(3.16) ÆCHomI.1 186.222 (CLEMOES 1997: 186): […] & his sunu hatte arfaxað. se leofode þreo hund geara & þreo & þritti: & his sunu hatte sale se leofode feower hund geara & þreo & þriti. […] and his son was called Arphaxad. He lived for 333 years. And his son was called Shelah who lived for 433 years. a

þreo 3

b

feower 4

hund × 100 hund × 100

gear-a & þreo year-GEN.PL + 3

& þri-tti + (3 × 10)

gear-a & þreo year-GEN.PL + 3

& þri-ti + (3 × 10)

If, however, several bases are comprised in the multiplier of ‘1,000’ – which requires the repetition of ÞUSEND within one numeral (§ III.1.2) – then the quantified noun follows only the highest valued constituent and is not repeated after the second mention of ÞUSEND; cf. (3.17). (3.17) ÆLS (Book of Kings) 402 (SKEAT 1881–1900: 408): Ða asende god his engel to þam syriscan here, and ofsloh on anre nihte an hund þusend manna and hundeahtatig ðusend and sumne eacan ðærto. Then God sent his angel to the Syrian army and he killed 180,000 men and some also more. an 1

hund þusend × 100 × 1,000

mann-a and man-GEN.PL +

hund-eahta-tig CIRC-(8 × 10)

ðusend × 1,000

The structure known from Present-day English complex numerals in which the quantified noun always follows the entire numeral construction, is, although uncommon, occasionally attested; cf. (3.18)–(3.19).

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143

(3.18) HomU 54 23 (PRIEBSCH 1899: 135): Eala, yrmingas, nytege þæt god geworhte heafenas and eorðan, sæ and eal þæt þæron is on syx dagum, and syððan geworhte þone forman man Adam and for his agægednesse fif þusend and twahund and VIII and twentig geara rihtwise and synfulle on helle forlet. Alas, poor souls! Don’t you know that God created the heavens, the earth and the sea and everything that exists therein within six days and [that he] then created the first man, Adam; and [that Adam] for his transgression justifiably and sinfully spent 5,228 years in hell. fif þusend 5 × 1,000

and +

twa-hund and 2 × 100 +

and +

VIII

8

twen-tig (2 × 10)

gear-a year-GEN.PL

(3.19) ByrM 1 2.3.56 (BAKER/LAPIDGE 1995: 108): nu gecyðað we þæt on þam dæge beoð nigon hund & syxtig momenta. Now we announce that there are 960 moments a day. nigon hund & syx-tig 9 × 100 + 6 × 10

moment-a moment-GEN.PL

Finally, in the case of a predicative use of the numeral (cf. § IV.4), the quantified NP precedes the entire numeral structure, independent of whether it is repeated at the end of the numeral (3.20) or not (3.21). (3.20) Comp 13.1.1 1 (HENEL 1934: 67): On twelf monðum bið þreo hund daga & V & syxtig daga; & þæra wucena synt twa & fiftig; & þæra tida eahta þusenda & eahta hund syxtig tida. In twelve months there are 365 days and there are 53 weeks and [there are] 8860 hours. þæra tid-a [synt] DET-GEN .PL hour-GEN.PL [be(3PL.PRS)] & eahta + 8

hund × 100 [+]

syx-tig (6 × 10)

eahta 8 tid-a hour-GEN.PL

þusend-a × 1,000-PL

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Complex numerals

(3.21) Notes 26.3 23 (NAPIER 1889: 9): & þara gerefena wæs þreo ðusenda & eac ðreo hund þeþa men bewiston ætþam temple. There were 3,300 consuls who were watching over the people by the temple. þara DET:GEN.PL þreo 3

geref-ena official person-GEN.PL

ðusend-a × 1,000-PL

& eac + also

wæs be(3SG.PST)

ðreo 3

hund × 100

However, examples of complex numerals with the quantified noun mentioned only once, as in the predicative position ((3.20) and (3.21)) or as in the rather exceptional cases of the noun following the entire numeral construction ((3.18) and (3.19)), are not very common. We can say that usually the quantified noun follows any constituent of the complex numeral that contains a base, but we have to take this statement as a general tendency rather than a rule. III.1.3.2 Other splits in complex numerals Even in those cases in which the quantified NP does not immediately follow every constituent containing a base, the NP still splits the complex numeral because it separates the constituent with the highest base from the rest of the expression; cf. examples (3.14)–(3.16) above. The general tendency of the quantified NP to re-occur after several constituents of a complex numeral suggests that any such constituent is treated as a distinct syntactic unit. The conjunction AND would, in this case, represent more than an arithmetic operator adding up the products. It would also serve as a syntactic link of two or three co-ordinate syntactic phrases. The split in complex numerals is, however, not caused by the quantified NP alone. There is other morphological material that can be interposed between the individual constituents of one and the same complex numeral. One of these instances is the multiple marking of complex ordinal numerals and the fact that there are individual determiners for each of the constituents; cf. the three complex ordinal numerals in (3.22) and that in (3.23). Complex ordinals containing the third base are not attested in Old English.

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145

(3.22) BenR 18.42.20 (SCHRÖER 1885–1888 [1964]: 42): sy þonne þus geendod se hundteontigeþa and se eahtateoða sealm on twam dagum, þæt is on sunnandæge and on monandæge, on tiwesdæge on undern and on middæg and on non syn ðry sealmas to ælcan þæra gesungene of þisum nigum sealmum, þæt is fram ðam hundteontigeðan and nigonteoðan sealme oþ þone hundteontigeðan and þone seofon and twentigeðan; The 118th psalm should be finished within two days, that is on Sunday and on Monday. On Tuesday morning, at midday and noon three psalms each of these nine psalms are to be sung, that is from the 119th psalm to the 127th psalm. a.

se DET:NOM.SG .M

hund-teon-tig-eþa and CIRC-(10 × 10)-ORD +

se DET:NOM.SG .M

b.

ðam DET:DAT.SG.M

DET:DAT.SG.M

oþ until

sealm psalm

hund-teon-tig-eðan CIRC-(10 × 10)-ORD.DAT.SG

se c.

eahta-teo-ða (8 + 10)-ORD

nigon-teo-ðan (9 + 10)-ORD.DAT.SG

þone DET:ACC.SG.M

þone DET:ACC.SG.M

and + sealm psalm

hund-teon-tig-eðan CIRC-(10 × 10)-ORD.ACC.SG

seofon 7

and +

and +

twen-tig-eðan (2 × 10)-ORD.ACC.SG

[psalm]

(3.23) CP 65.465.22 (SWEET 1871: 465): & eft he cwæð on ðæm eahta & hundælleftiogoðan psalme, […] And, again he said in the 118th psalm: […] on PREP

ðæm DET:DAT.SG.M

eahta & hund-ællef-tiog-oðan 8 + CIRC-(11 × 10)-ORD.DAT.SG

psalm-e psalm-DAT.SG

Moreover, in poetry or in rhythmical prose texts, the metre or the alliteration can require that the two (or three) parts of a complex numeral occur in nonadjacent half lines. Syntactically, the constituent numerals are separated not only by the quantified NP, but also by an entire clause; cf. (3.24).

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Complex numerals

(3.24) GenAB 1178 (KRAPP 1931: 37): Wintra hæfde fif and hundnigontig, þa he forð gewat, and eahta hund; eaforan læfde land and leodweard. He was 895 years old when he went away, [when he] left offspring, home and government. wintr-a winter-GEN.PL

hæfde have:3 SG.PST

[þa he forð gewat] [when he went away]

and +

fif and 5 +

hund-nigon-tig CIRC-(9 × 10)

eahta 8

hund × 100

In (3.24), there is, in addition to the split between the two constituents of the numeral, also a change in the constituent order. This shows that the generally greater freedom in the syntax of the metrical language in principle allows for the complete disintegration of the complex numeral into its individual baseheaded constituents. There is obviously sufficient evidence for the fact that each constituent of a numeral containing a base shows properties of a independent syntactical unit in Old English. This can be seen by the repetition of the third base when its multiplier is itself a complex numeral (§ III.1.2), by the general tendency to specify the quantified noun after each element containing a base (§ III.1.3.1), by the possible split in poetical texts (3.24), and by the separate use of determiners and ordinal markers for each element of a complex ordinal numeral containing a base ((3.22) and (3.23)). Other morphosyntactic characteristics confirm this impression. In some quantificational constructions with complex numerals, the quantified NPs show different Case values in spite of the fact that they are quantified by one and the same complex numeral; cf. (3.25)–(3.26). (3.25) ÆLet 2 50 (FEHR 1914 [1966]: 92): Þa coman þær togædere on nycea byrig þreo hund bisceopa & XVIII bisceopas. Then, 318 bishops came together there in the city of Nice. þreo 3

hund bisceop-a × 100 bishop-GEN.PL

and +

XVIII

18

bisceop-as bishop-NOM.PL

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147

(3.26) HomU 44 38 (NAPIER 1883 [1967]: 284, 2): hwæt, we witan, þæt on XII monþum beoð III hund daga and sixtig daga and fif dagas and eac six tida; […] Hwæt, we know that on twelve months, there are 365 days and six hours […] hund dag-a 3 × 100 day-GEN.PL III

and +

six-tig 6 × 10

dag-a day-GEN.PL

and +

fif dag-as 5 day-NOM.PL

Whether a quantified NP requires a partitive genitive or whether its Case value is determined by its syntactic function within the clause, is subject to morphosyntactic constraints which will be described in detail in § IV.5.2. For the moment, it may suffice to say that, in Old English, numerals valued ‘20’ or higher generally require the quantified NP to be formally partitive. That is, if the numerical value is ‘20’ or higher, the quantified noun is generally in the genitive Case. If the numerical value is below ‘20’, the case of the NP is determined by the semantic role of its referent. The crucial point here is that in (3.25) and (3.26), the lowest valued constituent alone is valued below ‘20’ although the entire construction has a far higher value. If the quantified noun occurs both after the lowest constituent and after a higher base, then the Case value may be differ in the individual instances of the (same) NP. That is, both in (3.25) and in (3.26), each NP following the lowest valued constituent is in the nominative Case because both NPs are in the subject position, whereas the NPs following the respective higher base are in the partitive genitive in spite of the subject position of the entire quantificational phrase because the numerical value is ‘20’ or higher. Thus in (3.25) and (3.26), the Case value of the quantified NPs is determined independently by each of the particular numeral constituents to which they are attached, rather than by the complex numeral as a whole. The morphosyntactic behaviour of the quantified NPs in these cases clearly shows that the individual constituents of the numeral (more precisely: those constituents that contain a base) are treated as independent syntactic units. However, the phenomenon described here is not used in an entirely consistent way in Old English. In example (3.27), by contrast, every instance of the quantified noun shows partitive marking in spite of the fact that the lowest valued constituents of the two complex expressions are valued below ‘20’.

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(3.27) Sol I 13.8 (CROSS/HILL 1982: 27): Ða hæfede enos an hund wintra þa gestrinde he chanan & þa lyfde he enos ealles nygon hund wintra & V wintra; & þa hæfede chanan LXX wintra þa gestrinde he malaleh, & canan lyfde þa ealles nygon hund wintra & X wintra. Then Enos was 100 years old when he begot Cainan; and then Enos lived for 905 years all together; and then Cainan was 70 years old when he begot Malaleel; and then Cainan lived for 910 years all together. a. b.

nygon 9

hund × 100

wintr-a winter-GEN.PL

& +

V

nygon 9

hund × 100

wintr-a winter-GEN.PL

& +

X

5 10

wintr-a winter-GEN.PL wintr-a winter-GEN.PL

It turns out to be impossible to determine the degree to which constructions like the ones attested in (3.25) and (3.26) represent the general usage. In order to do this, we would need a sufficiently large set of instances of complex numerals with several bases in which the quantified NP is expressed with the lowest valued constituent and in which this constituent is valued below ‘20’. Unfortunately, the corpus of surviving Old English texts does not contain enough instances of numerals in which all the three phenomena coincide. Another indication of the syntactic disintegration of complex numerals is of a slightly different kind. Occasionally, the lowest valued constituent of a complex numeral is followed by EAC ‘also’ or by a similar expression. (3.28) GenAB 1121 (KRAPP 1931: 36): Us gewritu secgað þæt her eahtahund iecte siððan mægðum and mæcgum mægburg sine Adam on eorðan; ealra hæfde nigenhund wintra and XXX eac, þa he þas woruld þurh gastgedal ofgyfan sceolde. The Scriptures tell us that Adam increased his tribe on earth with women and men for 800 years; all in all he was 930 years old when he was to leave this world due to his death. nigen-hund (9 × 100)

wintr-a winter-GEN.PL

and +

XXX

30

eac too

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149

(3.29) ÆLet 4 (Sigeweard Z) 302 (CRAWFORD 1922 [1969]: 28, 311) – as (2.12) above in § II.1.4.3: & se Ioseph leofode on þam lande mærlice hundteontig geara & tin to eacan, & seo boc Genesis geendað þus her. And Joseph lived famously in that land for 110 years and thus the book Genesis ends here. hundteontig gear-a & tin (10 × 10) year-GEN.PL + 10

to eacan thereto

In (3.28) and (3.29), it seems as if each of the lower valued constituents in the numeral is a mere addition to the respective quantificational construction, i.e. to that part consisting of the base or its multiple. Example (3.21) in the preceding subsection represents a similar case. Literally, the two constructions would have to be rendered as ‘900 years and also 30’ (3.28) or ‘100 years and 10 in addition’ (3.29). A number of instances with split complex numerals also show that, even if the numeral expression is partly or wholly written with Roman numerals, the Roman numerals usually do not represent the entire expression, but they are employed for each individual constituent of a complex numeral. Again, the use of Roman numerals in Anglo-Saxon manuscripts is anything but consistent, however splitting the Roman numeral whenever a quantified noun is part of the phrase, as in (3.13) in § III.1.3.1, or if the split is required for other reasons, as in (3.25), is common practice.35 Strong as the evidence in these examples may be, none of the patterns they illustrate can be taken as a rule without exception. One conclusion we can draw from what has been presented in this section is that any base in a complex numeral is the head of a constituent and that those constituents of complex numerals which contain a base are generally treated as independent syntactic units. With respect to the syntactic coherence of complex numerals and their relationship to other syntactic units of the same clause, there is no default pattern that can be deduced unambiguously from the data provided by the extant Old English texts. There is one aspect, however, which generally – perhaps in a more abstract way – shows how the several constituents of the complex numeral are never35 This practice suggests that, at least in some cases, the Roman numerals are used in Old English manuscripts in order to represent linguistic number expression rather than as an independent system of number signs abstracted away from language. Cf. the first numeral in (3.11) (above, § III.1.3.1) where it reads CCC dagena & V & LX daga rather than CCCLXV dag(en)a. Or cf. the Roman numeral IIIIX for ‘14’ in the Old English Orosius-translation (Or 2 5.45.10); cf. the relevant note in BATELY (1980: 237).

150

Complex numerals

theless coherent. From a purely syntactic point of view, the cases of complex numerals described here clearly represent several co-ordinate syntactic units rather than parts of a complex compound. Such a formal description, however, does not take into consideration the function of the syntactic structure in which a numeral expression is embedded. While all or some of the constituents may be independently linked with the quantified NP, the referent of the NP is still quantified by the numeral as a whole. To illustrate this, let me refer to two examples which, on the surface, seem to suggest more evidently the disintegration of the different constituents of a complex numeral, that is, instances where the quantified nouns differ. Cf. (3.30) and (3.31): (3.30) LS 34 440 (MAGENNIS 1994: 47): […] þa agane ðreo hund gear[a], and twa and hund-seofontig wintra of ðam dæge þe ða halgan slepon to ðam dæge þe hi eft awocon. […] then 372 years passed by from the day when the Saints fell asleep to the day when they woke up again. ðreo 3

hund × 100

and +

twa 2

gear[-a] year[-GEN.PL] and +

hund-seofon-tig wintr-a CIRC-(7 × 10) winter-GEN.PL

(3.31) ByrM 1 4.2.30 (BAKER/LAPIDGE 1995: 234, 34–35): […] æfter þam þe þa hundseofontig witan gesetton se tima wæs standende twa þusend wintra & twa hund & twa & feowertig geara gerimes. […] according to the [calculation], which the Seventy Scholars did, the age lasted for 2,242 years in number. twa 2

þusend × 1,000 & feower-tig + (4 × 10)

wintr-a winter-GEN.PL

& twa + 2

hund × 100

& +

twa 2

gear-a gerim-es year-GEN.PL number-GEN.SG

Even in those rare instances in which two different lexemes are used in the two quantified NPs within one quantificational construction, the two are synonymous. The two lexemes WINTER ‘winter’ and GEAR ‘year’ are often used interchangeably in Old English if a period of time is specified. In the word-toword gloss, it may be justified to render GEAR and WINTER by the Present-day English expressions year and winter, respectively. In a prose translation, however, there is only one possible idiomatic equivalent: both constructions refer

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151

to a particular number of years. The two separate NPs, therefore, both perform one and the same reference and the numeral constituents are consequently used for the specification of one cardinality of one and the same set (i.e., the number of years). None of the points raised in this section as evidence for the syntactic disintegration of complex numerals can question the fact that the semantic structure underlying such a phrase comprises only one process of quantification – i.e. one cardinality assigned to one referent set – however complex the construction is formally represented. Hence, even if the individual base-headed constituents of a complex numeral can be construed as syntactically independent elements, the semantic function of these constructions is, in fact, the same as that of simple numerals: numerically specific quantification of one set (cf. § I.1). When it comes to the linguistic function of specifying a numerical value (or specifying the cardinality of a referent set), the set of elements which together specify the numerical value must nevertheless be taken as one single – albeit discontinuous – linguistic unit. This can best be seen in those instances in which the syntactic split is most obvious. Whether in the example from poetry (3.24) or in the examples in which two different lexemes are used as quantified NPs – (3.30) and (3.31) – quantification is performed as one single process exerted on only one referent whose cardinality is specified. Irrespective of how many constituents of a complex numeral are represented as independent syntactic units, in none of the instances discussed in this section is there more than one referent quantified by these constituents. If we see quantification as the linguistic process of specifying cardinalities of sets, we may in any case conclude that the syntactic disintegration of complex numerals is, therefore, irrelevant to this linguistic process. In any case, the phenomenon of split complex numerals confirms an important feature of this strategy: split numeral constructions conveniently reveal the compositionality of systemic numeral expressions and, therefore, the recursive character of the numeral system (for which see the next section). This is because, however discontinuous these complex constructions may be, it would not be possible to encode a single linguistic function – quantification of one set – by using syntactically independent units if the numeral in its entirety were not the result of a formation which draws on one and the same set of rules and basic expressions, in other words, if a complex numeral were not composed of several constituents of one and the same subsystem of a language, the numeral system. While we will continue to discuss other syntactic aspects in Chapter IV, the recursion of the Old English numeral system – in fact, of numeral systems in general – will come to the fore in the following section. On the basis of what

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Complex numerals

we have described up to here, we will now make an attempt at a more general classification of the Old English numeral system. III.2

The decimal numeral system

The main purpose of this section will be to establish criteria for defining the notion of a ‘decimal numeral system’ (or any other type of numeral system) and to apply these to the numeral system of Old English (and, in principle, to those of other Germanic languages). We will, moreover, try to explain which features of the composition of complex numerals are linked or interdependent with these defining features of a decimal system and which are not (§ III.2.2). In order to do this, we will first resume the discussion about an essential characteristic of linguistic numeral systems, its internal recursion (III.2.1). A final section will briefly assess the traditional idea that the numeral systems of the ancient Germanic languages are based on, or at least influenced by, duodecimal systems (§ III.2.3), a theory which we will have implicitly falsified in the first two subsections. III.2.1

Recursion and serialisation

The basis for the line of argument brought forth in this section is a notion which we have introduced in § I.3.2: numeral systems are recursive systems. In principle, ‘recursion’ in this context refers to the fact that a system may generate new elements out of existing elements. We employed the example of PDE six-teen ‘6 + 10’, a numeral which consists of two elements that are themselves numerals. At the same time, PDE six-teen may be used as a constituent of higher, i.e. more complex numerals. Accordingly, we represented the structure of any complex numeral as follows (§ I.3.2): NUM

→ NUM + NUM

The representation of complex numerals as phrase structures in Figures 12 (§ II.5.1), 13 (§ II.6), and 18 (§ III.1.2) illustrates this conveniently. Any complex numeral (on the left hand side of the arrow) can be split into several lower valued numerals (to the right of the arrow) which themselves are as much in accordance with the numeral system as the one comprising the parent node. Only simple forms are indivisible and therefore cannot be nodes in the phrase structure. Inversely, any numeral, whether simple or complex, can it-

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self be used recursively as formative of a more complex (i.e. higher valued) numeral. The recursive character of complex expressions – more precisely: of the system behind their formation – is the result of a syntagmatic perspective. That is, the notion of ‘recursion’ describes how the individual constituents of a complex expression are arranged (their order) and, in addition, how in the process of ordering these constituents, a complex form may (under certain conditions or syntactic rules) occupy the same position as a simple form. There is also a paradigmatic counterpart to the ‘recursion’ in numeral systems, which, following GREENBERG’s coinage of ‘serialised operands’ (cf. § I.3), I will refer to as ‘serialisation’. Both these notions – ‘recursion’ and ‘serialisation’ – are closely intertwined with the properties of ‘atoms’ and, particularly, of ‘bases’. Serialisation basically refers to the fact that any slot in a complex structure which can be occupied by an element of a continuously recurring sequence, can also be occupied by any other member of the same sequence. This means that, in principle, any position in a complex numeral is either taken by a base or by any member of a particular continuously recurring (sub)sequence. If this element is a simple expression, it is a member of the smallest continuously recurring sequence, if this constituent is itself complex, it is a member of a larger sequence of continuously recurring elements, for instance a sequence of hundred. We thus established a connection between the sequence of continuously recurring elements in a numeral system and the function of a base. Particularly crucial for the following discussion is the relation between the smallest sequence of continuously recurring elements and the lowest base. Less explicitly, we had mentioned this relation already in § I.3. In §§ I.3.4.2–3, we were discussing several terminological difficulties involved in the notion ‘base’. In this context, we mentioned that the fundamental base plays a key role in the general arrangement of the numeral system. For instance, all higher bases stand in an arithmetic relation to the lowest base, as they are all divisible by it. Moreover, we indicated that the fundamental base and the smallest continuously recurring sequence of elements stand in a complementary relation to each other. We will look at this specific relation in the following, arguing that it plays a crucial role in the overall generation of complex numerals. I will further argue that this phenomenon may allow us to classify numeral systems in types, in a way corresponding to arithmetic numeral systems briefly mentioned in § I.3.4.3. The fundamental base thus becomes an indicator of the type of (linguistic) numeral system. Recall at this point the terminological deviation we have identified between the linguistic notion of a ‘base’ and a mathematic notion of a ‘base’ (§ I.3.4.3).

154

Complex numerals

The point which is at stake here, the relation between the (fundamental) base and the (smallest) recurring sequence of elements, is exactly the point at which the notion of ‘base’ finds a common ground irrespective of whether a numeral system (such as the Hindu-Arabic number notation) employs an empty element (〈0〉) or whether such an element does not exist, as in linguistic numeral systems. This connection once more justifies the preference of GREENBERG’s narrow definition of ‘base’ over wider definitions employed (often implicitly) by other authors. On the one hand, the theoretical considerations of this kind made here and the subsequent conclusion for language-particular phenomena, are dependent on the GREENBERGian narrow definition of ‘base’ which we proposed above in § I.3.4.1. On the other hand, a wider use of a base would not provide a method of determining a decimal (or any other n-based) numeral system and it would be void of any connection with the notion of a ‘base’ as used in mathematics. The point of departure of the following discussion is the observation that the smallest continuously recurring sequence of elements and the fundamental base are two complementary components of any numeral system. In §§ I.3.3– 4, we discussed the examples of the numeral systems of Welsh and Sora in which this continuously recurring sequence is arranged in a complicated way. Nevertheless, in both these languages, the key function of the fundamental base and of the continuously recurring sequence for the recursive principle of a system can be clearly identified. That is, even in numeral systems which contain highly idiosyncratic patterns, there is a complementary relation between the lowest base and the continuously recurring sequence. This relation is inherent in all complex numeral systems of natural languages, that is, in all numeral systems with complex numerals. As a consequence, we can take both the smallest sequence of continuously recurring elements in the system and its fundamental base as the defining feature for the type of numeral system. This connection between the cyclic pattern and the type of numeral system has first been established by SALZMANN (1950: 81). III.2.2

How to (not) determine a decimal numeral system

In Old English as well as in any other Germanic language (see the discussion of Modern Danish below), the smallest sequence of continuously recurring elements is, at the same time, the sequence of atoms. This is different, for instance, in languages like Welsh and Sora in which the smallest sequence of continuously recurring elements may also contain complex expressions. For the sake of simplicity, we may speak of the ‘sequence of atoms’ in the follow-

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ing when we refer to the ‘sequence of continuously recurring elements’ as long as we remain within the context of the Germanic languages. But it should be recalled once again that this simplification can be applied to a large number of numeral systems though not to all systems across natural languages. Thus, accepting what we have said so far, we may state that the Old English numeral system is a decimal system: the smallest sequence of recurring elements – the nine atoms plus a multiple of a base – together form a set of ten elements – a decade. Given the complementary relation between the continuously recurring sequence and the base, this statement is tantamount to saying that the Old English numeral system is a decimal system because the lowest valued base represents the numerical value ‘10’. It is this connection that makes GREENBERG (1978: 270) refer to the lowest valued base as the ‘fundamental base’ of a system. The fact that in more complex expressions of Old English there are larger recurring sequences than the smallest one, i.e. sets of hundred or even of thousand, does not call into question the fundamental character of the lowest base. This is firstly because the recursive arrangement of elements requires that each sequence of a hundred itself consists of sequences of ten, just as each sequence of a thousand in turn consists of sequences of a hundred. And a second reason is that any higher valued base of a numeral system is necessarily a power of the fundamental base. Intermediate augends or intermediate multiplicands, which do exist in some numeral systems (but not in Germanic), cannot call into question the overall arrangement of the respective numeral system. What has often (wrongly, as I argue) been taken as an indicator of the type of numeral system is the constituent structure of a particular complex augend or a particular complex multiplicand – whether morphologically transparent or only diachronically analysable. According to what we have developed above, this criterion is irrelevant in this context. Let me exemplify this with the example of the numeral system of Modern Danish. The Danish numeral system is a decimal system according to the criteria proposed here, but it has often been considered a vigesimal system because some expressions contain morphological idiosyncrasies by showing deviations in the forms of some expressions. However, these morphological idiosyncrasies of some Danish numerals do not affect the recursive arrangement of the numeral system of Danish and therefore cannot be employed in determining the type of numeral system. Cf. the expressions for the multiples of ‘10’ in Modern Danish:

156

Complex numerals

Table 21. Augends in the Modern Danish numeral system expression

numerical value

underlying arithmetic operation

ti

‘10’

simple (fundamental) base

tyve

‘20’

‘2 × 10’

tredive

‘30’

‘3 × 10’

fyrre

‘40’

‘4 × 10’

halftreds

‘50’

‘(3 – ½) × 20’

tres

‘60’

‘3 × 20’

halvjerds

‘70’

‘(4 – ½) × 20’

firs

‘80’

‘4 × 20’

halvfems

‘90’

‘(5 – ½) × 20’

hundrede

‘100’

simple base

If we take the example of the Danish numerals, we will find a discrepancy between the recursive arrangement of elements and the morphological structure of some of the serialised multiplicands in the section between ‘10’ and ‘100’. Synchronically, the relevant expressions in Danish are opaque and do not represent any arithmetic operation, i.e. they are idiosyncratic simple forms (cf. § I.5.2). A diachronic analysis of the morphological structure makes it evident that the arithmetic operations underlying these expressions are based on the multiplicand ‘20’. The corresponding ordinal numerals in Modern Danish, which are morphologically a bit more transparent than the cardinals, also demonstrate this. Diachronically, the constituents can be clearly analysed. The expressions up to ‘40’ and the expression for ‘100’ all follow the Germanic pattern as we have described it for Old English. Ti ‘10’ and hundrede ‘100’ are arbitrarily shaped bases and the expressions for ‘20’, ‘30’ and ‘40’ were once formed expressing the operations ‘2 × 10’, ‘3 × 10’, and ‘4 × 10’, respectively. The original structures of the expressions from ‘50’ to ‘90’, however, do not express multiples of ‘10’. The expressions tres ‘60’ and firs ‘80’ represent multiplications by ‘20’, i.e. ‘3 × 20’ and ‘4 × 20’, respectively. The expressions for ‘50’, ‘70’, and ‘90’, halftreds, halvfjerds, and halvfems, denote the half of each last vigintiad, i.e. arithmetically ‘half the last vigintiad before 3 × 20’,

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‘half the last vigintiad before 4 × 20’, and ‘half the last vigintiad up to ‘5 × 20’ (while the last actually implies the existence of an expression *fems ‘5 × 20’). If we disregard the fact that the original structures of these expressions are synchronically opaque, we can see that the expressions from ‘50’ to ‘99’ contain an element representing the multiplicand ‘20’. Moreover, the multipliers in the expressions for ‘50’, ‘70’, and ‘90’ suggest that the relevant numerical values represent the half of a vigintiad rather than a decade. Based on this evidence, the Danish numeral system looks like a vigesimal system or at least like a numeral system with vigesimal elements. However, such a categorisation is not based on any explicit criteria for a typologisation of numeral systems. It is – implicitly – based on the rather superficial criterion of the morphological shape of some complex expressions. We may perhaps expect that the turning points of the continuously recurring sequence of elements, as for instance the multiples of ‘10’ in Present-day English, which are expressed as X-ty ‘n × 10’, also reveal by their structure that they are involved in a decimal arrangement as is the case in many numeral systems. But this does not necessarily need to be the case. In the extreme case, such an expression may be fully hybrid, as for example Russian sórok ‘40’ which is part of a perfectly decimally arranged system and employs the same functions as its neighbours in the sequence, trí-dcat’ ‘3 × 10’ and pjat’-desját ‘5 × 10’, which by contrast show arithmetic operations with ‘10’ (cf. § I.5.3.2). With respect to the Danish numeral system, (wrongly) interpreting it as a vigesimal system thus ignores two essential aspects. One is that the sequence of numerals is still arranged entirely in decades. Apart from the fact that some of the expressions – tyve ‘20’, tredive ‘30’, and fyrre ‘40’– do not express multiplications by ‘20’ but use ‘10’ as multiplicand anyway (cf. Table 21) – all of the expressions in Table 21 represent the tenth element following the recurring sequence of nine atomic numerals. No matter how we analyse the morpheme structures of the crucial expressions in Table 21 – whether we take them as idiosyncratic forms (synchronic analysis) or as multiplications by ‘20’ (diachronic analysis) – the sequence of numerals is entirely arranged in sets of ten and not in sets of 20. The numerical value ‘20’ may be involved in the morpheme structures of the expressions from ‘50’ to ‘90’, but once the nine atomic numerals are used up as addend, a new augend is required. This holds both from a synchronic and from a diachronic perspective. In fact, if there had ever been a vigesimal arrangement of the numerals in the history of Danish, an expression marking the half of the vigintiad would not only be unnecessary, but also inappropriate.

158

Complex numerals

If we compare the Danish expressions with the vigesimal sequence in Standard French, we find that after soixante-neuf ‘(6 × 10) + 9’, there is no new augend, but that the sequence of addends continues up until ‘19’, i.e. until soixante-dix-neuf ‘(6 × 10) + (10 + 9)’. In French, the series of addends from ‘60’ to ‘99’ indeed has vigesimal elements, because the sequence of the first 19 elements of the numeral system plus a new augend constitute a vigintiad, although even this vigintiad in fact consists of two decades as its smallest continuing sequence contains ten elements. Therefore, the French system is ultimately decimal, too, even in the idiosyncratic section from ‘60’ to ‘99’. In Danish, in any case, it is always the sequence of the lowest valued nine elements of the numeral system plus an augend, which together constitute a continuously recurring sequence. This means that, once the arrangement of the recurring sequences is clear and regular, it is irrelevant whether the morpheme structure of an expression represents that arithmetic operation by which the sequence of numerals is arranged (Old English), whether it is completely arbitrary (Danish, synchronic analysis) or whether it implies an arithmetic operation other than that is actually not employed for the arrangement of numerals (Danish, diachronic analysis). The arithmetic operations represented in the morpheme structure of complex numerals indeed often correspond with the recurring sequences and hence often do indicate the type of the numeral system. In Old English, there is such an agreement between morpheme structure and recursive arrangement of elements. Once there is a discrepancy between the sets of recurring elements and the arithmetic operations underlying the morpheme structure, it is exclusively the arrangement of the sequences and not the morphological structure of particular expressions which is of relevance for determining the type of numeral system. To sum this up, the Danish numeral system is often wrongly referred to as a vigesimal system. The respective addends in Danish always cyclically recur in decades: in spite of the fact that the relevant expressions (etymologically) represent multiples of ‘20’, all of these augends terminate a sequence of ten elements. The only feature in which the Danish numerals differ from those of other Germanic languages is the constituent morphemes of the multiples of ‘10’, or for that matter, the etymology of the relevant expressions; cf. VON MENGDEN (2006b: 144).

The decimal numeral system

III.2.3

159

Old English: a trace of duodecimal counting?

If it is the cyclical recurrence of atoms that determines the type of the numeral system, then the numeral system of Old English is unambiguously and purely decimal. However, the attempt to explain some of the idiosyncrasies of the Old English numeral system that have been described in § II.4.3 has led many scholars of the nineteenth and twentieth centuries to believe that the numeral systems of the ancient Germanic languages once were a duodecimal system or at least influenced by a duodecimal system. This categorisation has had a long tradition and occasionally we find corresponding statements in quite recent publications (cf., for instance, JUSTUS 1996: 66–67). The theory of a duodecimal system in Germanic goes back to a rather tentative statement by Jacob GRIMM (1819: 265), which had not been substantially questioned for a long time, particularly not on the basis of a theory of numeral systems; cf. VON MENGDEN (2005). In VON MENGDEN (2005) and (2006b), I have argued in detail that there is no evidence for duodecimal influence whatsoever on the Old English numeral system. In the following, I will briefly summarise the main points of my line of argument. What has from time to time been taken as evidence of some historically underlying non-decimal counting method, generally in the (pre-)history of the Indo-European languages, is the fact that metrical measuring is a very recent invention, whereas many older measuring systems are based on values other than ‘10’, frequently on ‘12’ or ‘60’. While it is no doubt true that metrical measuring is comparatively young, the fatal misunderstanding at this point is that, quite often, systems of measuring and numeral systems have been treated as one and the same phenomenon (see e.g. the rather misleading statements in JUSTUS 1988: 529 or in COMRIE 2005b: 211 and 222–223). Yet there is no immediate connection between measuring systems and systems of counting. A system in which 12- and 60-based units are used in virtually all parts of the world is, for instance, the measuring of time. If I add up 60 minutes to an hour, the unit of measure may be 60-based, but the linguistic expressions I use to name these units are the same that I use for naming metrical measures of length or volume. In other words, if we refer to ‘59 minutes’, we still use a linguistic expression, fif-ty nine, which is constructed in an exclusively decimal way, i.e. as ‘(5 × 10) + 9’. It is actually quite natural that by far the most languages have a decimal numeral system given that the most archaic method of counting is the use of one’s fingers as a kind of abacus (cf. § I.2.2 and see DETGES 2003: 52–54; VON MENGDEN 2008: 301–302). Although very old themselves, measuring systems based on 12, 60 or other numbers other than 10 were invented at a much later phylogenetic stage than decimal numeral

160

Complex numerals

systems, because numbers like 12 or 60 are arithmetically much more convenient than 10. For instance, 12 is divisible by the factors 2, 3, 4, and 6, whereas 10 is only divisible by 2 and 5. In short, metrical measuring systems may be very young in the history of human civilisation but they have been invented for one main reason: they are compatible with those number signs that are cross-culturally by far most archaic and also most common: decimally arranged systems of number words (cf. §§ I.4.2.1 and V.2.5.1). However, some features, particularly of the Old English and/or ancient Germanic numeral systems themselves, have also been accounted for by the assumption of non-decimal influence on the Germanic numeral systems. Some of the idiosyncrasies of the system that we have described in Chapter II seem to be somehow connected with the numerical value ‘12’: the fact that the allomorphic variation between -tig and hund-__-tig has its turning point after ‘60’ (§ II.4.3.2), the overrunning sequence of multiples of ‘10’ (§§ II.4.3.3 and II.1.5.3) that goes as far as to the twelfth multiple of ‘10’, and, finally the suppletive forms for ‘11’ and ‘12’ in the Germanic languages (§ II.3). All these features are both typologically uncommon and, with some modifications, attested in all ancient Germanic languages. The fact that the paradigmatic split between the suffixed forms with -tig and the circumfixed forms with hund-__-tig is between ‘60’ and ‘70’ is indeed difficult to explain. There may well be a historical reason that could explain the position of this split, but if there is one, it is no longer traceable. Whatever its ultimate reason, a non-decimal counting system cannot serve as an explanation for this point of demarcation. The point in the sequence after ‘6 × 10’ marks the borderline for the distribution of two allomorphs which both encode the multiplicand ‘× 10’. I do not see how a non-decimal system can possibly influence the distribution of two purely formal variants of a morpheme which, in both of its realisations, has an unambiguously decimal character. Likewise the overrunning sequence of multiples of ‘10’ cannot serve as evidence for duodecimal or sexagesimal influence. Again, first of all, the overrunning section in Old English is still a sequence of multiples of ‘10’ (and not one of multiples of ‘12’) and it is, from this point of view, nothing but decadic. Moreover, its last section is formed by the nine atoms and the expression HUNDTWELFTIG as their augend. It runs up until nigon and hundtwelftig ‘9 + (12 × 10)’, i.e. ‘129’. The turning point – that is, the point in the overall counting sequence where this method ends and the ‘regular’ use of the decimal base HUNDRED begins – is, therefore, the numerical value ‘130’ expressed in Old English as (an) hund and þritig. If this idiosyncrasy were due to the influence of a non-decimal counting method, this could only be a 13-based

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161

system. However, such a system is, to the best of my knowledge, unattested across the world’s languages. Finally, the idiosyncratic use of the expressions for ‘11’ and ‘12’ in Germanic cannot serve as evidence for duodecimal counting either. While synchronically opaque and therefore simple and idiosyncratic forms even in the earliest attested stages of the Germanic languages, their undisputed etymology shows that they are connected with decimal counting. As mentioned several times above, the proto-Germanic of Old English forms are postulated as *aina-lif and *twa-lif-, and they originally meant ‘one-remaining’ and ‘tworemaining’, respectively. Hence, even though an element explicitly representing the base ‘10’ is not contained in these reconstructed forms, their morphological structure without any doubt refers to the base value ‘10’. The decimal character of these expressions also becomes evident if we consider the etymologically corresponding formations in Lithuanian, where the entire sequence from ‘11’ to ‘19’ is expressed according to the same pattern: vienú-lika ‘1 remaining’, dvý-lika ‘2 remaining’, trý-lika ‘3 remaining’ etc. up until devynió-lika ‘9 remaining’; cf. COMRIE (1992: 763, § 16.1.11.1). Thus, in Lithuanian, the corresponding formation type constitutes a decadic sequence. I do not have an explanation for why the turning point between the idiosyncratic formation and the ‘regular’ formation of the type þreo-tyne ‘3 + 10’ follows after the expression for ‘12’. But, again, such a morphological turning point in a sequence of number expressions (which formally all refer to the base ‘10’) as such cannot possibly be taken as evidence for non-decimal influence (as conjectured for instance by JUSTUS 1996: 69). SEILER (1990: 199–203) describes quite a number of irregularities, in morphological structures around bases, none of which defies the overall arrangement of the system. Two of the examples stated by SEILER (1990: 200), Basque and Yucatec Maya, have a deviating formation type in the expressions for ‘11’ and ‘12’. A more detailed discussion for the duodecimal/sexagesimal-theory and its rejection can be found in VON MENGDEN (2005) and (2006b). The next section will deal with the history of the Old English numeral system. In part, the following diachronic sketch will shed more light on the emergence of the idiosyncrasies we have discussed here.

162

Complex numerals

III.3

Non-systemic expressions for numerical values

III.3.1

Preliminaries

In § I.4 we distinguished systemic and non-systemic expressions for numerical values. We also defined the distinctive features of systemic numerals in contrast to non-systemic number expressions. We said that non-systemic expressions do not occur in a conventionalised counting sequence (§ I.4.2) and that their ability to be used as a constituent in a more complex number expression is very limited (§ I.4.3). Structurally, alternative strategies for expressing numerical values do not differ much from systemic numerals in so far as both can be simple forms, like PDE dozen or score, or complex expressions, like e.g. two fifties (cf. § I.4.3). More often than not, non-systemic complex expressions, partly or entirely, consist of elements which themselves are systemic numerals, and it is only the internal constituent structure that deviates from the system, for instance in the way arithmetic operations are represented. Non-systemic expressions are not necessarily uncommon. For instance, the Present-day English expression nineteen hundred is often as common as the corresponding systemic expression one thousand, nine hundred. In a particular context, e.g. when referring to a particular year, the former type is even strongly preferred to the latter. However, the occasional preference of nonsystemic expressions is always limited to special contexts. Whenever nineteen hundred can be used side by side with one thousand, nine hundred, the latter expression is considered the default expression for the numerical value ‘1,900’. Apparently, this is a matter of convention and differences in usage are often difficult to define. While it is generally possible to draw a clear dividing line between systemic and non-systemic expressions – as we did in § I.4 – there is a hierarchy among non-systemic expressions in terms of conventionality and frequency. From the fact that a particular number expression is non-systemic, a statement about its distribution, about its frequency of use, about stylistic preferences, or about other constraints or implications of its use cannot necessarily be inferred. In Old English, for instance, a generally greater freedom of expression in metrical texts (cf. example (3.24) in § III.1.3.2 above) results in a higher number of non-systemic number expressions in this category of texts. But the higher frequency of (often rather slight) deviations from the system in Old English poetry compared to prose can be accounted for by the requirements of the metre or by stylistic adornments that generally characterise poetic language in contrast to prose.

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163

In Old English, only one simple non-systemic number expression is attested: OE scoru ‘20’ is attested twice in a list of goods from Bury St Edmunds dating from the eleventh century. Otherwise the predecessor of PDE score only occurs in Middle English texts; cf. (3.32). (3.32) Rec 5.4 60 (ROBERTSON 1956: 196, 15): Her onstent gewriten hwæt man funde æt Eggemere syððan Cole hit let Ðæt is VII oxen & VIII cy & IIII feldhryþera & II stottas & V scora scæp & XV scæp under ealde & iunge & VIII score æcere gesawen & I flicce & I swin & XXIIII cesen. Here is written what was found at Egmere after Cole had left it: that is 7 oxen, 8 cows, 4 field-oxen, 2 horses, 115 old and young ones, 160 sown acres, one flitch of bacon, one pig and 24 cheeses. a. b.

scor-a 5 (× 20)-PL V

VIII

8

score (× 20).PL

scæp sheep æcere acre

& +

XV

15

scæp sheep

ge-saw-en CIRC-sow-PTC

There are, however, a number of common strategies for the formation of complex non-systemic expressions. As we have just said, particular types of nonsystemic compounds can be more or less conventionalised. It is impossible to cover all instances of non-systemic formations that occur in Old English texts. Therefore, only the most common types of non-systemic expressions can be discussed in the following. A major distinction between two types of non-systemic expressions can be drawn according to the numerical value to which the relevant expressions refer. There are some formations referring to numerical values for which a systemic numeral can be used just as well, i.e. referring to numerical values below the limit number L of the system (cf. above §§ I.2.4 and II.6). These formations will be described below in § III.3.2. Other non-systemic expressions refer to numerical values which exceed the limit number of the numeral system. An outline of this type as attested in Old English will follow in § III.3.3. The distinction drawn here generally applies to any language. However, the latter group is perhaps more noticeable in a numeral system, for instance, of one of the medieval European languages which have a more limited scope than that of contemporary languages where the use of more than three decimal bases allows the formation of systemic expressions for numerical values far above ‘106’ (cf. § III.3.3).

164

III.3.2

Complex numerals

Non-systemic strategies for expressing numerical values within the scope of the numeral system

III.3.2.1 Subtraction One of the more common ways of forming non-systemic number expressions in Old English employs subtraction as the underlying arithmetic operation. While in Old English subtraction is generally a non-systemic strategy for forming number expressions, it is generally possible to employ subtraction (and division) as a systemic formation type in numeral systems of natural languages. GREENBERG (1978: 258–260) lists the following five constraints for subtraction in numeral systems: 36 G 11 “Subtraction is never expressed by the mere sequence of the subtrahend and the minuend.” (1978: 258) G 12 “When a number is expressed by subtraction, or when a subtraction occurs as a constituent of a complex expression, the subtrahend is never larger than the remainder.” (1978: 259) G 13 “A subtrahend is always a simple lexical expression.” (1978: 260) G 14 “If a number n is expressed by subtraction as y – x, then every number [z (y > z > n)] is also expressed subtractively and with y as the minuend.” (1978: 260) G 15 “Every minuend is a base of the system or a multiple of the base.” (1978: 260)

It is noteworthy that the Old English constructions described in this section – although not systemic – nevertheless submit to the universal constraints of complex number expressions employing subtraction as described by GREENBERG’s generalisations.37 36 I have corrected what is apparently a typo in G 14 (GREENBERG 1978: 260). The original reads: “z (z > y > n)”. GREENBERG’s subsequent reference to n representing Latin duodeviginti, y representing ‘20’ and z representing ‘19’ shows that y is intended to refer to the highest of the three values. 37 HURFORD (1987: 86–88; 1999: 15) considers subtraction as a trace of temporary gaps in a numeral system in the pre-history of a language. A numeral system with gaps, i.e. a system in which not every numerical value between ‘0’ and the limit number L can be represented by a systemic expression, would not be in accordance with the definition of the numeral system that is employed here (cf. § I.2). If we define a numeral system in such a way that it would allow gaps, then the notion of a ‘numeral system’ becomes random and it would, ultimately, make no sense to speak of a ‘numeral system’ at all. In short, where gaps seem to

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In the relevant expressions attested in Old English, the operator ‘–’ is generally overtly expressed (G 11). In most instances, the lexeme LÆS ‘less’ is used. The subtrahend is restricted to the numerical values ‘1’ and ‘2’ and as minuends only ‘20’, ‘30’, and ‘40’ occur; cf. (3.33)–(3.36). (3.33) ÆGram 287.6 (ZUPITZA 1880 [2001]: 287): Man cweð eac undeuiginti an læs twentig, duodeuiginti twam læs twentig, duodetriginta twam læs þrittig ET CETERA. One also says: undeuiginti ‘one less than twenty’, duodeuiginti ‘two less than twenty’, duodetriginta ‘two less than thirty’, etc. a.

an 1

læs less than

twen-tig 20

b.

twam 2:DAT

læs less than

twen-tig 20

c.

twam 2:DAT

læs less than

þri-ttig 30

(3.34) LS 17.1 90 (MORRIS 1874–1880: 215): Ða he þa hæfde twæm læs þe twentig wintra, þa gefullode hine mon on ðære ciricean endebyrdnesse; [...] When he was 18 years old, he was baptised according to the rule of the church; [...] twæm læs two:DAT less

þe than

twen-tig (2 × 10)

wintr-a winter-GEN.PL

(3.35) ÆHom 2 146 (POPE 1967–1968: 236): Lege [þas twa beb]oda to þam twam læs feowertigum þæs langs[uman legere]s þæs laman beddrydan, þonne bið þær fullice [feowertig-g]etel. Place the two commandments to the 38 [years] of the long-lasting disease of the bed-ridden lame, then there is the complete number of forty. to PREP

þam DET:DAT.SG.M

twam læs feower-tig-um two:DAT less than (4 × 10)-DAT

appear, L necessarily represents the highest numerical value before the gap. In this light, I am inclined to take the discussions in COMRIE (1997b: 45 and 2005b: 216–217) and the alleged counter-evidence listed there as based on a misunderstanding of GREENBERG’s generalisation G 2 (1978: 254). Any expression beyond the gap is by definition non-systemic. Or, in other words, gaps only exist if we do not distinguish between ‘systemic’ and ‘nonsystemic’ numerals. See also above § II.7.3.

166

Complex numerals

(3.36) ÆLS (Book of Kings) 393: He rixode on Iudea lande an leas ðryttig geara, […] He ruled in the Land of Judea for 29 years […] an 1

leas ðry-ttig less than (3 × 10)

gear-a year-GEN.PL

As (3.33) conveniently shows, the same strategy is attested for Medieval Latin (duodeviginti ‘20 – 2’, undeviginti ‘20 – 1’). Both expressions seem to have been used parallel to octodecim ‘10 + 8’ and novodecim ‘10 + 9’ (cf. example (1.7) above in § I.4.2.2) but seem to have been the systemic variants in the classical period. Similarly, optional expressions in Classical Greek (duoîn dékonta eíkosi ‘20 – 2’, henòs déonta eíkosi ‘20 – 1’) suggest that this type is inherited from Proto-Indo-European; cf. SIHLER (1995: 417–418, § 390). Otherwise, the operator ‘–’ is expressed in Old English by WAN ÞE or WANA ‘wanting’. Here only ‘1’ is attested as a subtrahend. Of the six instances I could find in which WAN ÞE or WANA functions as an operator, two expressions denote ‘19’ and ‘29’ respectively, one denotes ‘49’ and one ‘59’; cf. (3.37)– (3.39). According to RISSANEN (1967: 32–33), example (3.37) and the parallel passage in the Peterborough Chronicle (ChronE 972.1; cf. IRVINE 2004: 59) are the only instances of this construction in which AN is not in the genitive. (3.37) ChronD 972.1 (CUBBIN 1996: 46): Her wæs Eadgar æþeling gehalgod to cyninge on pentecoste mæssedæg on V idus Mai, þy XIII geare þe he to rice feng, æt Hatabaþum, & he wæs þa ane wana XXX wintre. In this year, Prince Edgar was ordained King at Pentecost on 11 May at the Hot Baths, 13 years after he came to power; and he was then 29 years old. ana 1:GEN.PL

wana wanting from

XXX

30

wintr-e winter-GEN[?].PL

Non-systemic expressions for numerical values

167

(3.38) And 1029 (KRAPP 1932a: 32): […] ond þa gelædde of leoðobendum fram þam fæstenne on frið dryhtnes tu ond hundteontig geteled rime, swylce feowertig, generede fram niðe, (þær he nænigne forlet under burglican bennum fæstne), ond þær wifa þa gyt, weorodes to eacan anes wana þe fiftig forhte gefreoðode. […] and then he led likewise 240 in number from the bonds out of the fortress into the Lord’s safety, rescued from strife. He did not leave one in wounds in the town’s stronghold. And there, the 49 frightened women of the multitude he also set free. to eacan anes thereto 1:GEN.SG.M

wana þe fif-tig except (5 × 10)

(3.39) Bede 3 16.236.31 (MILLER 1890–1898: 238): […] ond eft æfter þon wæs magister & lareow þæs mynstres, oð þæt heora daga rim gefylled wæs, þæt is anes wonþe syxtig wintra. […] and then, after that, [she] was a teacher of this monastery until the number of her days was complete, which is 59 years. anes 1:GEN.SG

wonþe wanting from

syx-tig (6 × 10)

wintr-a winter-GEN.PL

Finally, there are spurious instances in which the use of BUTAN ‘without, except’ looks as if it is employed as an operator ‘–’ for subtraction. The least doubtful of them is in the Will of Ælfwold, Bishop of Crediton, written in the 11th century; cf. (3.40). (3.40) Ch 1492 29 (NAPIER/STEVENSON 1895: 23): & [he geann] in-to wiltune calic & disc on CXX manc goldes butan þrim manc And [he bestowed] to Wilton a chalice and a paten [in the value of] 117 gold mancuses. on

CXX

PREP

120

manc[us-a] gold-es butan mancus[-GEN.PL] gold-GEN.SG except

þrim manc[us-a] 3:DAT mancus[-GEN.PL]

Usually, however, BUTAN is used in the sense of ‘except’. It often occurs when two quantities of different measures or categories are compared, as in (3.41) and (3.42).

168

Complex numerals

(3.41) Ch 493 7 (BIRCH 1885–1893 II: 547, 37): Þonne is hit þær feower furlanga brad butan feower gyrdan. Then, it is four furlongs wide less four yards. feower 4

furlang-a furlong-PL

brad butan wide less

feower 4

gyrd-an yard-PL

(3.42) Men 15 (DOBBIE 1942: 49): Swylce emb feower wucan þætte Solmonað sigeð to tune butan twam nihtum, [...] Likewise, for after four weeks less two days, Salomon came to the town [...] emb after

feower 4

wuc-an […] week-ACC.PL […]

butan except

twam 2:DAT

niht-um night-DAT.PL

The examples in (3.41) and (3.42) logically both represent subtractions, because in both instances the two numerals quantify one and the same category – area in (3.41) and time in (3.42) – and in both examples the lower value is subtracted from the higher value. Linguistically, however, each numeral in these quotations refers to a different measure and therefore quantifies a different referent.38 (For a discussion and additional data of constructions representing subtractions, cf., among others, FRICKE 1886: 27; HIRT 1927: 311, § 218; RISSANEN 1967: 32–34; MITCHELL 1985 I: 224–225, §§ 573 and 576–577. RISSANEN also provides a list of all instances of subtraction, except the rather unusual one in (3.40) above). There is no evidence that the relevant formations employing subtraction have ever been systemic expressions. Those numerical values for which a subtraction is attested are much more frequently represented by the standard 38 There is one more instance of a genuine subtraction with BUTAN. In the Burghal Hidage, four constructions of this kind occur: & to Tweoneam hyrþ V hund hida buton XXX hidan […] (‘[…] 500 hides less 30 hides […]’) – Rec 26.1 7; cf. ROBERTSON 1956: 246, lines 8– 9); […] & to Brydian hyrþ eahta hund hida butan feowertigan hidan. (‘[…] and to Bridport belong 800 hides less 40 hides’. – Rec 26.1 9; cf. ROBERTSON 1956: 246). The constructions here contradict our criteria in so far as both the respective minuends and the subtrahends are valued higher than expected. However, the text cannot be taken as reliable linguistic evidence. Not only does it survive only in a sixteenth century transcript, but its ultimate textual history is also obscure. Although the document was originally written in the early tenth century, the only copy traceable from Anglo-Saxon times (ms. Otho B.xi; c.1025) was destroyed in the Cottonian fire of 1731. Its content has survived only in the transcript made by Laurence Nowell in 1562. All other extant copies of the charter are from the twelfth or the thirteenth century; cf. ROBERTSON (1956: 495–496). Moreover, ROBERTSON (1956: 495–496) states that the figures in Nowell’s transcript occasionally differ from those in the younger manuscripts. Cf. the following note.

Non-systemic expressions for numerical values

169

expressions formed by addition. Also, the expressions employing subtraction listed in Ælfric’s Grammar are clearly specified as ‘alternatives’ to the default type of formation employing addition. Immediately before the passage quoted here as (3.33), Ælfric lists various kinds of formations of cardinal and noncardinal numerals. Our quotation begins with the words Man cweð eac… ‘One also says…’, which clearly suggests that the use of these expressions is secondary. There is, moreover, no instance of an expression formed by subtraction which is used as a constituent of a more complex expression, e.g. as an addend to a higher base (§ I.4.3). Finally, no ordinal or multiplicative numeral attested is formed on the basis of an expression employing subtraction (§ I.4.4). III.3.2.2 Extension of the scope of the second base In systemic numeral expressions, the scope of multipliers of the base ‘100’ ranges from ‘1’ to ‘9’. In Old English, as in Present-day English and in many other modern European languages, there are non-systemic expressions in which the multiplier of the base ‘100’ exceeds the numerical value ‘9’. The type of PDE eleven-hundred, twelve-hundred, thirteen-hundred, etc. is attested in Old English as well although predominantly in charters; cf. (3.43)–(3.44). The highest valued expression of this type in a pre-Conquest manuscript is that in (3.44) denoting a numerical value ‘20 × 100’. (3.43) Ch 1482 36 (HARMER 1914: 4, 10): & Freoðomund foe to minum sweorde & agefe ðeræt feower ðusenda, & him mon forgefe ðeran ðreotene hund pending. And Freothomund [shall have] my sword, and he give 4,000 [mancusses] for it, and he should be given 1,300 pence of it. ðreo-tene (3 + 10)

hund × 100

(3.44) Ch 1497 61 (WHITELOCK 1968: 15): Þa lædde heo að to Hyccan, xx hund aða. Then she took an oath at Hitchin, 2,000 oaths. XX

20

hund × 100

að-a oath-GEN.PL

170

Complex numerals

Outside charters, this type of formation is restricted to the multipliers ‘10’, ‘11’, and ‘12’; cf. (3.45)–(3.47). Most of the instances are in poetic texts; cf. (3.46) and (3.47).39 (3.45) LawMirce 1.1 (LIEBERMANN 1903: 462): Ðegnes wergild is syx swa micel, þæt bið twelf hund scillinga. The wergeld of a servant is six times as much, that is 1,200 shillings. twelf hund 12 × 100

scill’ shilling[-GEN.PL]

(3.46) Ex 232 (LUCAS 1994: 109): [...] hæfde cista gehwilc cuðes werodes garberendra, guðfremmendra, X hund geteled, tireadigra. [...] each selection of the renowned army had glorious warriors, 100 in number X

10

hund × 100

ge-tel-ed CIRC-count- PTC

(3.47) CEdg 10 (DOBBIE 1942: 21): And ða agangen wæs tyn hund wintra geteled rimes fram gebyrdtide bremes cyninges, […] And then 1,000 years have passed by from the birth of the noble king, […] tyn 10

hund × 100

The reason why this type of non-systemic expression is so widespread in the Germanic languages is obvious: there is neither an arithmetic nor a grammatical reason for a numeral system to employ only nine multipliers to the second base. The numerical value of the multiplier does not come close to exceeding that of the multiplicand. Arithmetically, it would be sufficient if, in a decimal system, the third base were introduced for the second power of ‘100’. In other words, to meet the constraint that the multiplier cannot exceed the multiplicand (cf. § II.4.3.3), the limit of the potential multipliers would have to end 39 Again, the Burghal Hidage (Rec 26.1) and the subsequent Hidage for Defence (Rec 26.3; cf. ROBERTSON 1956: 246–248) contain a remarkably high number of constructions of this type. Moreover, there are two expressions in the Burghal Hidage denoting ‘24 × 100’ (Rec 26.1 6 shows feower & twentig hund hida and Rec 26.1 18 has XXIIII hund hida; cf. ROBERTSON 1956: 246, lines 6 and 19 respectively). For the problems related to the text, particularly as a reliable source for linguistic data, cf. the previous note.

Non-systemic expressions for numerical values

171

only with ‘99’, but not, as it does, with ‘9’. The introduction of the third power of ‘10’, i.e. of ‘1,000’, as the third base is, therefore, arithmetically premature. The reason why European languages still introduce a third base at the numerical value ‘1,000’ is probably the analogy with the set of multipliers of the first base: in contrast to ‘100’, the multiplicand ‘10’ must necessarily be limited to nine multipliers. The scope of the sequence of nine multipliers was simply transferred to the second base in the course of the development of the numeral system. In any case, it is the lack of an arithmetic constraint on the extension of the second base up to ‘99 × 100’ which makes the type nineteen-hundred comparatively common in the Germanic languages. III.3.2.3 Other alternative expressions The expressions we have described in the previous two subsections should be considered conventionalised to some extent. There is, however, some freedom in any language to circumscribe concepts for which there is a ‘default expression’ in the lexicon. This applies especially to cardinalities. This freedom to paraphrase numerical values generally allows the speaker to avoid the expressions of a conventionalised system such as the numeral system. Examples (3.48)–(3.50) illustrate that, occasionally, alternative strategies for expressing numerical values do not necessarily have to be conventionalised in the way that the types described in the previous two subsections are; cf. also MITCHELL (1985 I: 224, §§ 570–571). (3.48) Or 6 1.132.28 (BATELY 1980: 132–133): Sio gestod tuwa seofon hund wintra on hiere onwealde ær hio gefeolle, from Ninuse hiora ærestan cyninge oþ Sardanopolim heora nihstan: þæt is [I]III C wintra & I M. It [i.e. the city of Babylon] stood for twice 700 years in her might before it fell, from Ninus its first king to Sardanapallus the last one: that are 1,400 years. a.

tuwa seofon twice 7

hund × 100

wintr-a winter-GEN.PL

b.

IIII

C

4

× 100

wintr-a winter-GEN.PL

& +

I

M

1 × 1,000

172

Complex numerals

(3.49) Or 5 12.127.13 (BATELY 1980: 127): He hæfde eahta & eahtatig coortana, þæt we nu truman hatað, þæt wæs on þæm dagum V hund monna & an M. He had 88 cohorts, which we now call troops, that was in those days 1,500 men. hund 5 × 100 V

monn-a man-GEN.PL

& an + 1

M

× 1,000

(3.50) Bede 1 9.44.3 (MILLER 1890–1898: 44): Hæfdon hi Breotona rice feower hund wintra & þæs fiftan hundseofontig, ðæs ðe Gaius, oðre naman Iulius, se casere þæt ylce ealond gesohte. They had been ruling Britain in the 475th year when Gaius, by another name Julius, the emperor visited the same island. feower hund wintr-a 4 × 100 winter-GEN.P & þæs + DET:GEN.SG.M

III.3.3

fif-tan 5-ORD.GEN.SG

hund-seofon-tig CIRC-(7 × 10)

Strategies for exceeding the scope of the numeral system

The highest base numeral in the Old English numeral system is ÞUSEND ‘1,000’. Unlike in Present-day English, which has even higher base numerals (million ‘106’ and billion ‘109’/ ‘1012’, etc.), numerical values above ‘999,999’ cannot be expressed by systemic number expressions in Old English. Generally, natural languages employ alternative strategies to express numerical values exceeding the scope of the system. The most common strategy for specifying a numerical value n ≥ L, is to combine two different systemic numeral expressions by means of an arithmetic operation. Basically, this is, of course, the same strategy employed for the formation of systemic expressions. The only difference between a systemic and a non-systemic expression would be that there is no conventionalised or standard way to represent a particular numerical value n ≥ L. However, any paraphrase that unambiguously specifies an exact numerical value falls into this category of non-systemic number expressions. For instance, in order to express the numerical value ‘1028’ in Present-day English, one would use phrases as for instance the twenty-eighth power of ten or twenty eight to the power of ten. A different, non-arithmetic strategy to specify the same numerical value would be a paraphrase like a one with twenty-eight zeroes.

Non-systemic expressions for numerical values

173

In the numeral system of Old English, the limit number L is unambiguously ‘106’. Numerical values from this value onwards may still be expressed, but not by conventionalised expressions. Conventionalised here means that the recursive numeral system does not cover these numerical values and that, in this sense, there is no default expression for the respective numerical values. Yet some constructions are clearly more frequent for particular numerical values than others. In Old English texts, the most frequently attested number expression for a numerical value outside the scope of the system represents the numerical value L = ‘106’. It is usually expressed as a multiplication ‘1,000 × 1,000’. This can be done either with or without overt expression of the operator ‘×’; cf. (3.51)– (3.52) and (3.53) respectively. (3.51) HomS 44 68 (BAZIRE/CROSS 1982: 51): Þær ætstandað þusend þusend engla and micel mægen heahengla and ealle halige and soðfæste Godes witegan and heahfæderas and apostolas. There, one million angels withstood and a great host of archangels and all saints and the righteous prophets of God and the high fathers and apostles. þusend 1,000

þusend × 1,000

engl-a angel-GEN.PL

(3.52) HomM 1 111 (HEALEY 1978: 69): & Paulus ða gehyrde æfter ðan ðusend ðusendo ængle lofigendra, & God wuldrigenda, & herigenda, […] And then, afterwards, Paul heard the one million angels praising and glorifying and commending God […] ðusend 1,000

ðusend-o × 1,000-PL

ængl-e angel-GEN[?].PL

lofig-end-ra praise- PTC.PRS-GEN.PL

(3.53) OccGl 91.4 18 (FÖRSTER 1914: 329): Lacna þusend wunda, þa stinceð wiðinnan me, & forgif nu me þusend siðan þusend synna. – ‹Sana milia uulnera, quę fetent intus me, & ignosce nunc mihi milies mille crimina› Heal thousand wounds that smell inside me and forgive me now one million sins. þusend 1,000

siðan þusend times 1,000

synn-a sin-GEN.PL

The strategy applied in (3.51) and (3.52) is actually the most plausible formation with respect to the attested strategies of the numeral system. Since there is

174

Complex numerals

no available expression for the second power of ‘1,000’ – as there is in Present-day English with the expression million – it seems plausible if speakers simply ignore the constraint that the multiplicand exceeds the multiplier in value. One could say that, due to the lack of a simple base numeral for ‘106’, the expected but non-existent base is simply overrun. However, this strategy is not inherent in the Old English numeral system. If the expression þusend þusend were systemic, the overt expression of the arithmetic operator ‘×’, siðan ‘times’ in instances like (3.53), would generally not occur. Moreover, higher numerical values could be expressed with þusend þusend as an augend. However, the formation þusend þusend is attested only for the exact numerical value ‘106’, but not as an augend or as a multiplicand in a more complex number expression. A genuinely systemic expression would require a simple expression as a fourth base for ‘106’. We can infer from the later history of the English language, and also from related numeral systems, that as soon as the need to express higher numerical values arises more frequently, new terms for higher bases are introduced. This happens either through internal word-formation (e.g. Italian milli-one ‘great thousand’) or by borrowing (Late Middle English million as a loanword from Italian via French; see DIETZ 2005: 580). Conversely, the fact that there is no higher base than ‘1,000’ in the Old English numeral system suggests that a context requiring the reference to a numerical value ‘106’ or higher hardly ever occurred for Anglo-Saxon scribes. An astronomic treatise like Byrhtferth’s Manual, which contains by far the largest number of expressions for numerical values above L, is certainly an exceptional text in this respect. Higher numerical values are usually expressed by multiplication with SIÞ-AN ‘time, occasion-DAT/INS.PL’ (realised most frequently as 〈siþan〉, 〈siþon〉, or 〈siþum〉) as an overt expression for the operator ‘×’; cf. (3.54)– (3.57). The frequent use of SIÞAN shows that these constructions must be analysed as two systemic numerals combined in a non-systemic way in order to form a non-systemic number expression. (3.54) HomU 46 155 (NAPIER 1883 [1967]: 296, 26): ðæt wæs, þæt Titus and Uespasianus tobræcon þa burh and ofslogon þær hund þusend manna, and XI siðan hund þusenda hi læddon þanon ealle gebende. […] that was when Titus and Vespasian destroyed the city and killed there 100,000 men and they brought 1.1 million thither, all fettered. siðan hund þusend-a 11 times 100 × 1,000-PLΑ XI

Non-systemic expressions for numerical values

175

(3.55) HomS 21 238 (MORRIS 1874–1880 [1967]: 79, 18–23): Wæs þara manna eallra þe þær ofslegene wæron & hungre swultan, mid wifmannum & wæpnedmannum, endleofan siþum hund[-teontig] þusenda; & þa hi gýt genaman þæs folces þe þær to lafe wæs, & him selost licodan, hund-teontig þusenda, and mid him læddon on hæftned; & ehtatyne syþum hund-teontig þusenda hi tosendon, & wið feo sealdon wide into leodscipas. Of all the men that were slain there or starved to death, including men and women, there were 1.1 million. And then they also took 100,000 who they liked best of those who remained, and took them with them into captivity; and they sent 1.8 million away and sold them into distant countries. a.

endleofan 11

siþum times

hund-teon-tig CIRC-(10 × 10)

þusend-a × 1,000-PL

b.

eahta-tyne (10 + 8)

syþum times

hund-teon-tig CIRC-(10 × 10)

þusend-a × 1,000-PL

(3.56) Or 6 7.138.15 (BOSWORTH 1859: 119, 42) – Reading of ms. Tiberius B.i (cf. (3.60) below): & he fordyde þara Iudea endlufon siþon hund M: sume he ofslog, sume on oðer land gesealde, sume he mid hungre acwealde. And he killed 1.1 million of the Jews, some he killed, some he sold to another country, and some he let starve to death. endlufon siþon 11 times

M

1,000

(3.57) HomU 34 221 (NAPIER 1883 [1967]: 200, 22-3): and he asent geond middaneard ridendne here, to ðan þæt hy scylon þriddan dæl mancynnes ofslean, þæt syndon þonne twentig þusend siðan tyn þusenda. And he sent a riding army through the world so that they should kill a third of mankind, that are then two hundred million. twen-tig (2 × 10)

þusend × 1,000

siðan tyn times 10

þusend-a × 1,000-PL

If SIÞAN is not used, the multiplier of one of the bases usually overruns its systemic scope, as in ÞUSEND ÞUSEND. It is also possible to overrun the second base ‘100’ in a constituent used as a multiplier of ‘1,000’, i.e. by an expression representing ‘(ni × 100) × 1,000’ with n > 9. In this type, it is basically the formation of the type fourteen hundred (§ III.3.2.2) used as a multiplier of the third base. Again, this can be done either with an overt expression for the op-

176

Complex numerals

erator ‘×’ – cf. (3.54)–(3.56) – or without overtly expressing it; cf. (3.58)– (3.60). (3.58) Or 3 9.70.19 (BATELY 1980: 70, 18): Þæt wæron fieftiene hund þusend monna þæt binnan þæm forwurdon, & of þæm ilcan folcum forwurdon lytle ær, swa hit her beforan sægð, nigantiene hund M monna, […] That were 1.5 million men who perished therein and of the same nation died shortly before, according to what he told her earlier, 1.9 million men. a.

fief-tiene (5 + 10)

hund × 100

þusend × 1,000

monn-a man-GEN.PL

b.

nigan-tiene (9 + 10)

hund × 100

M

monn-a man-GEN.PL

× 1,000

(3.59) Or 2 5.48.26 (BATELY 1980: 48): […] þa swa micel folc on swa lytlan firste æt þrim folcgefeohtum forwurdon, þæt wæs nigon x hund þusenda of Persa anra anwealde buton hiera wiþerwinnum, ægþer ge of Sciþþium ge of Crecum. […] when so many people fell in two battles, that was 1.9 million alone from the Persian kingdom apart from their enemies, both of the Scythians and of the Greeks. nigan X hund (9 + 10) × 100

þusend-a × 1,000-PL

(3.60) Or 6 7.138.15 (BATELY 1980: 138) – Reading of ms. Addit. 47967 (cf. (3.56) above): & he fordyde þara Iudena XI hund M: sume he ofslog, sume on oþer land gesealde, sume he mid hungre acwealde. And he killed 1.1 million of the Jews, some he killed, some he sold to another country, and some he let starve to death. XI

11

hund × 100

M

× 1,000

The relatively frequent use of ÞUSEND ÞUSEND for ‘10 6’ and the otherwise more common strategy for combining two numerals by SIÞAN shows that some non-systemic formations are more in accordance with the rules of the numeral system than others. The borderline between systemic and non-systemic expressions can be drawn sharply only if it is possible to determine a formation type which is by convention the default one and which, at least potentially, takes part in the recursive system for the generation of other expressions.

Non-systemic expressions for numerical values

177

In any case, in contrast to numerical values within the scope of the system, i.e. n ≤ L, none of the logically possible ways of forming a number expression is by convention the default usage for a particular numerical value. Having said this, we should be aware that, if we are dealing with historical text languages like Old English, we might face some difficulties in identifying the default expression for a particular numerical value. In a text language, we are dependent on the evidence provided by documents with supposedly normative contents, like, in Old English for instance, Ælfric’s Grammar. In particular cases, however, it is impossible to make statements about the degree of conventionalisation of a particular usage of a non-systemic expression. In many cases, the higher frequency of one expression over the other and the comparison with the related numeral systems of contemporary languages provide the only available evidence. While it is more difficult to identify a default numerical value in historical languages like Old English unless we have the evidence of a quasi-counting sequence like the one in (1.7) (§ I.4.2.2) and (2.10) (§ II.5.2), it is more difficult to determine the limit number L for contemporary languages. While all the bases up to million ‘106’ are in common use in Present-day English, it may be disputed to what extent higher bases form part of the system. A borderline case may be represented by some specialised registers, for instance in some scientific disciplines, say, among astronomers who regularly deal with extremely high numerical values, it is likely that the particular register used in these communities conventionally employs expressions like ten thousand quadrillions (British English) or ten octillions (American English) for ‘1028’. It may perhaps be possible to consider such expressions as systemic within a particular, specialised register. While mentioning these difficulties, I maintain that the assumption of an upper limit of a numeral system in the Greenbergian sense is, although sometimes difficult to define (cf. GREENBERG 1978: 254, G 1 and § I.2.4 above), essential for an appropriate use of the notion ‘numeral system’ (also cf. § II.7.3).

Chapter IV Numeral constructions in Old English IV.1

Preliminaries

After the detailed description of the systemic character of numerals and of the internal constituent structure of numeral expressions provided in the previous chapters, we will now turn to the syntactic constructions in which the cardinal numeral interacts with other constituents in a clause.40 The basic assumption, which we have already outlined in § I.1, is that the default function of a cardinal numeral is the specification of the cardinality of a set. By exerting this function, the cardinal numeral refers to a particular cardinality while the quantified noun refers to the respective set. In § III.1.3.1, we have already touched upon particular aspects of the relation between numeral and quantified noun. This has been done only in the special context of very complex numerals in which the position of the quantified noun within the numeral constituents was of interest. In the present chapter, the focus will be on the general relationship between these two elements. Since any systemic numeral, however complex, represents one cardinality, a distinction between simple and complex numerals will not be relevant anymore. Even if the internal structure of a complex numeral is discontinuous (cf. § III.1.3), it will necessarily be treated as one expression, i.e. as one element assigning one cardinality to the respective referent. What we will focus on here will be the morphosyntactic relation of quantifier and quantified NP when this process of numerically specific quantification is carried out. Hence, I will use the term ‘quantification’ in the following to refer to that particular linguistic function which specifies the extension of a referent in a numerically specific way or, in other words, which specifies the cardinality of a referent. Accordingly – and in line with what we said in § I.1 – I will use the term ‘quantifier’ for that particular element in a syntactic construction which exerts this function. It is likely that the constructions discussed in the present chapter and the cross-linguistic conclusions that will be drawn in the subsequent Chapter V generally apply to numerically unspecific quantifiers as well. However, the data on which this discussion is based are instances of cardinal 40 Once again, I would like to remind the reader that I do not intend to make theoretical implications when using the term ‘construction’, but that I simply refer to a conventionalised correlation of syntagmatic form and a particular meaning or function; cf. fn 1 in § I.1.

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numerals. Accordingly, the claims derived from the interpretation of the data are claims for cardinal numerals. In the respective constructions, the referent, i.e. the set of which the cardinality is specified, may be represented by a simple noun, by a pronoun, or by a more complex noun phrase (NP). In the following, I will generally refer to this element as the ‘quantified NP’. I will employ the notion of a ‘noun phrase (NP)’ without specific theoretical implication, in a general sense of a construction used as an argument of a predication or as a complement of an adposition. Alternative expressions such as ‘term’, ‘argument’, or ‘DP’ may probably be used interchangeably in the particular case. It may also be the case that the referent of which the cardinality is specified is not represented at all in the respective construction or phrase, but that it is only implied by the context. Not for this reason alone does ‘quantification’ as a particular linguistic function exerted by the numeral always mean quantification of the respective referent. In other words, I assume that a numeral does not necessarily quantify the NP as a linguistic expression, but the referent set or the concept which is either overtly expressed by an NP or which is implied and which potentially can be referred to by an NP. The present chapter will contain a description and an analysis of the morphosyntactic constructions of Old English in which numerals operate as numerically specific quantifiers. It will also serve as a basis for a more general discussion on numeral constructions and on the word-class character of cardinal numerals in Chapter V. While this chapter will remain largely languagespecific, Chapter V will embed the results of this analysis into a wider crosslinguistic context. Before proceeding to the syntactic properties of the Old English numerals themselves, it may be helpful to give a short overview of previous studies dealing with the syntax of cardinal numerals in Old English – an overview which deliberately focuses on the research history of Old English syntax (and the syntax of other ancient Germanic languages) rather than on descriptions of numerals and/or of quantifiers in the general linguistic literature. In crosslinguistically oriented contributions, the focus has always been on constructions with numerically unspecific quantifiers – most of all of partitive constructions (of various types). A large share of these contributions have been committed to one of the various versions of Chomskyan syntax. Numerically specific expressions have been treated implicitly as marginal in these contexts. Most remarks on the syntax of Old English numerals and its implications for the process of quantification have been influenced by the general tendency of grammarians of Old English to focus on morphology and phonology. Many accounts have, so far, been motivated by a desire to explain the use of inflec-

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tional morphology. This tradition has had a strong effect not only on descriptions of syntactic features of numerals, but also on the terminology employed. In descriptions of numerals in historical grammars of Old English or ProtoGermanic, it is not uncommon to simply label cardinal numerals as adjectives in some instances and as nouns in others. However careful or comprehensive an account of Old English numerals may have been, the notions ‘noun’ and ‘adjective’ have always been employed for the description in one way or the other. So far, the question of whether, when, or to what extent the cardinal numeral is, or is used as, a noun or an adjective has, at least implicitly, always been an issue. We will see that, albeit from quite a different perspective and with a more profound theoretical basis, typological and generative syntacticians have also referred to these categories when describing properties of numerals. There will be an underlying line of argument in this and the next chapter according to which these properties are more adequately described without general reference to the (alleged) noun/adjective dichotomy. We will see in Chapter V that this dichotomy is not only characteristic of the more traditionally minded grammatical description of Old English, but also of a more general linguistic discourse on cardinal numerals. As already mentioned, the actual discussion will be preceded by a brief review of the history of the syntactic descriptions of Old English numerals (§ IV.2). Especially relevant for this introductory overview will be the respective sections in WÜLFING (1894) (§ IV.2.2) and, more comprehensively, in Bruce MITCHELL’s Old English Syntax (1985) (§ IV.2.3). These summaries will provide a starting point for a discussion leading to a categorisation, which I will propose in the subsequent sections (§§ IV.3–6) and which I will try to develop further in a more general context in Chapter V. Underlying this discussion will be the general claim that it is in many respects difficult to employ the dichotomy of the notions ‘noun’ and ‘adjective’ as a general reference system for the description of syntactic properties of numerals. IV.2

Previous classifications of the syntactic properties of Old English numerals

IV.2.1

General overview

Not a single detailed remark on syntactic properties of numerals can be found in any of the early studies on Old English or Germanic numerals. FRICKE (1886), for instance, does not say a word about syntax. VAN HELTEN

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(1905/06: 86) refers to the nominal (“substantivisch”) and attributive functions of numerals, but he does so only in order to distinguish between the inflected and uninflected use of numerals (cf. § II.2.4), and his remarks lack an explanation of what his terms “substantivisch” and “attributivisch” actually imply. This reflects the general approach not only of the Neogrammarian period, but a similar tendency is also present in the vast majority of more recent descriptive contributions of the ancient Germanic languages. According to the conventional descriptions – whether in specialised studies on numerals or in the relevant paragraphs of reference grammars – the numeral is said to be used ‘adjectivally’ or ‘attributively’ when the numeral is adjacent to a noun with which the numeral agrees in Case and Gender. All other uses are generally referred to as the ‘nominal’ or ‘substantival’ uses of the numeral. As we will see below, this bipartite categorisation does not reflect the actually attested set of construction types in Old English and its constraints. A more severe problem is perhaps that definitions of the notions ‘adjectival’ and ‘nominal’ are hard to find and that therefore, these descriptions are often based on rather implicit ideas of the categories ‘adjective’ and ‘noun’. While I will demonstrate this briefly for the study of Old English, I would like to point out that the following brief discussion is not intended to criticise studies from several decades ago for not being up to date from our present perspective of linguistic theory. Rather, it should serve as a good starting point for both a description of the syntactic constructions in which numerals quantify nouns in Old English and for a line of argument which involves more general, cross-linguistic considerations. It will be shown later – cf. particularly the discussion in Chapter V – that more recent and more general linguistic descriptions of morphosyntactic properties of cardinal numerals basically employ the same or comparable assumptions and thus potentially bear the same difficulties in categorising cardinal numerals. In any case, the following should be taken as a discussion of selected (because, perhaps, prototypical) examples but not as a criticism of general attitudes. Some basic characteristics in the approach of the Neogrammarians and their contemporaries mentioned above has been maintained in the course of the twentieth century. Apart from a remark on the distribution of inflected and uninflected numerals from ‘4’ to ‘12’, CAMPBELL (1959: 284, § 683) describes the various forms of numerals comprehensively but takes no notice of their syntactic uses. BRUNNER (1960–1962 II: 84; 1965: 253, § 325), while dealing with the general inflectional behaviour of numerals, mentions the ‘attributive’ use of numerals but does not provide any further explanation. One of the more recent handbooks, Roger LASS’s Old English, does not comment on the syntax of numerals at all. In the section on numerals, LASS refers to Indo-

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European where numerals are “a kind of hybrid category” (LASS 1994: 208, § 8.4.3). However, his description probably refers to their morphological properties only, as the relevant section is placed in the chapter on “Vocabulary and word-formation” (LASS 1994: 208–215). The term ‘partitive’ is explained only in the overall context of the functions of Cases (LASS 1994: 127, n. 6). STILES (1986a: 9–11), whose study is restricted to the numeral ‘4’ in the ancient Germanic languages, also distinguishes between the “adjectival” and “substantival” use. The “adjectival” use is “regular” when the numeral is uninflected and immediately precedes the noun. The “substantivally” used numeral is “regular” if inflected. If we take STILES’ terminology literally, it follows that any other use of the numeral is irregular or exceptional. STILES’ categorisation differs from that of all others in one interesting point. He includes the use of a numeral with a partitive NP into his “adjectival” use. As if following a tradition, STILES does not provide a proper definition of his terminology. But from what he lists as “regular adjectival” use and “regular substantival” use, we may infer that, according to STILES, “adjectival” implies that numeral and quantified noun are adjacent elements of one construction, while “substantival” means that the numeral is a single constituent of a phrase. The most recent study providing a comprehensive account of numerals in all Germanic languages (and their respective historical periods) is that by ROSS/BERNS (1992). Their contribution to the syntactic features of numerals is again only marginal (1992: 557-8, § 15.1.0). ROSS/BERNS employ the terms “adjective” and “noun” only in connection with expressions for ‘1’ and with higher valued base numerals, i.e. ‘100’ or ‘1,000’. They distinguish between declinable and indeclinable numerals for Proto-Germanic. Numerals may have an “attributive” and a “non-attributive function”. Most of the relevant studies, however, focus on the morphology and phonology of Old English or Proto-Germanic. It would, therefore, be unfair to overstate their lack of syntactic analysis. What we may emphasise at the beginning of this discussion, however, is that the relevant studies or grammars – whether Neogrammarian or recent – are confined in their descriptions of the syntactic properties of numerals to a comparison with nouns and adjectives. Furthermore, there is often no explicit definition of what exactly is ‘noun-like’ or ‘adjective-like’ about the use of a numeral in a given instance. Finally, and perhaps most importantly, the means of comparison, ‘noun-like’ and ‘adjective-like’ are not always used consistently across the various contributions. The most comprehensive studies of the syntax of Old English – i.e. WÜLFING (1894) and MITCHELL (1985) – contain a more detailed treatment of the syntactic properties of Old English numerals. For this reason, the following two sections will contain brief overviews of the relevant sections on nu-

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merals in WÜLFING 1894 (§ IV.2.2) and MITCHELL 1985 (§ IV.2.3). An account of numerals in a study focusing on syntax is, of course, more promising in our context than more general descriptions focussing on the phonology and/or inflectional paradigms of the expressions. It will turn out, however, that the syntactic treatises shift the problems alluded to above rather than solve them. IV.2.2

WÜLFING 1894

One of the relevant early studies on Old English syntax is WÜLFING’s work on the syntax of the texts generated in the circle of Alfred the Great. Judged from the context of his time, WÜLFING’s exhaustive contribution has been of high value, particularly because in the nineteenth century exploring syntax and syntactic functions was not in the focus of linguistics and philology. It may, therefore, seem unfair to take WÜLFING’s categorisation as an example from which to develop ex negativo a categorisation of (morpho-)syntactic properties of cardinal numerals. If I still place WÜLFING’s categorisation at the beginning of this discussion, it is because much of what we find in later descriptions of the syntactic properties of Old English numerals has already been present in WÜLFING’s approach, and because most of these later contributions are less comprehensive (necessarily so, being usually sections in handbooks or grammars). Given this, it may perhaps be justified to take a description from more than a century ago as a starting point for our discussion. WÜLFING (1894: 302–311, §§ 171–196) distinguishes the following four syntactic uses of numerals: (4.1) WÜLFING’s categorisation of syntactic uses of Old English cardinal numerals a.

the numeral as an adjective – “als Eigenschaftswort”

b. the numeral with pronoun or article – “mit einem Fürwort oder mit dem Artikel” c.

the numeral as a noun without article – “als Hauptwort (ohne Artikel)”

d. the numeral with a partitive genitive – “mit partitivem Genitiv”

One basic characteristic of WÜLFING’s categories is that the labels for the particular categories do not include any functional implications of the respective uses. This is, of course, legitimate but, as I will argue, a fruitless delimitation in the context of cardinal numerals. A more essential problem is that the

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definitions of his categories are not mutually exclusive. It is, for instance, not clear whether numerals in categories b and d can be both adjectives and nouns or neither. Also, WÜLFING’s category b defines the numeral in terms of its cooccurrence with other parts of speech. Categories a and d, by contrast, focus on the syntactic relation between numeral and quantified noun. Category c does both. WÜLFING’s description seems to be confined to the co-occurrence of words in a clause. He does not take into account the syntactic function of a numeral in a given instance, i.e. whether the numeral is used to quantify the referent or whether its function is not, or not primarily, the quantification of the referent. In WÜLFING’s list, categories a and d must be understood in such a way that they contain numerals in a syntactic relation to an NP. This in turn suggests that they are used for quantification. In some constructions listed under b and c, however, quantification is not necessarily the main function of the numeral and in some others, the numeral is not used for quantification at all. For instance, example (4.2) shows a numeral whose use is subsumed by WÜLFING under b. (4.2) Bede 1 16.70.15 (MILLER 1890–1898: 70): Ac forðon þe awriten is: Erunt duo in carne una: wer & wiif, heo tu beoð in anum lichoman “And as it is written, ‘Erunt duo in carne una,’ ‘Man and wife, they two shall be in one body.” (transl. MILLER 1890–1898: 71) wer man

& and

in PREP

wif wife

heo PPRN :NOM.PL

an-um one-DAT.SG.M

tu 2(NOM)

beoð be(3PL.PRS)

lichoman body(M)

Is the main characteristic of the numeral in (4.2) its co-occurrence with a pronoun, as the definition of category b suggests? Or is its predominant feature the absence of a quantified noun, as WÜLFING’s examples and the contrast to a and d suggest? Does the adjacency of pronoun and numeral necessarily mean that a numeral must not have a quantified noun? If this is the case, is it still used for quantification or does it have any other function? These remarks are not meant to dispute the value of WÜLFING’s exhaustive study judged in the context of his time. Nonetheless, his categorisation shows that a purely descriptive analysis without applying an adequate analytical framework cannot lead to sufficient results which would stand up against closer scrutiny. We will see that this type of disadvantage – while obvious in a

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late-nineteenth-century study – is underlying to almost any later contribution to the study of Old English numerals. IV.2.3

MITCHELL 1985

The only slightly more comprehensive account of the syntactic properties of Old English numerals since WÜLFING (1894) has been the relevant section in MITCHELL’s Old English Syntax (1985 I: 216–219, §§ 548–554). Although MITCHELL’s account seems to be more differentiated and is based on a much larger corpus of data, the point of criticism raised in the previous section applies here equally well. MITCHELL differs from his predecessors in so far as he generally employs a different terminology (following MUSTANOJA 1960: 291) – although he, too, refers to numerals as nouns and adjectives at the beginning: “The cardinal numbers may be used independently as nouns or dependently as adjectives” (MITCHELL 1985 I: 216, § 548). After this introductory statement, MITCHELL uses the terms ‘independent use’ and ‘dependent use’ throughout. Although potentially a step in the right direction, MITCHELL’s shift of terminology suffers from the fact that, in the defining passage, he merely replaces one pair of descriptive labels by another pair of equally undefined labels, i.e. ‘as noun’ by ‘independent’ and ‘as adjective’ by ‘dependent’. MITCHELL’s ‘independent use’ comprises WÜLFING’s categories b, c and d. MITCHELL suggests a further subdivision of the ‘independent use’ into the following nine subtypes (1985 I: 217–218, § 550) of the syntactic uses of numerals. Cf. (4.3): (4.3) Subtypes of MITCHELL’s “independent use” of cardinal numerals (my additions in square brackets) 1. [the numeral stands] alone, either declined or undeclined 2. [the numeral co-occurs] with an adjective 3. [the numeral co-occurs] with a demonstrative 4. [the numeral co-occurs] with an 5. [the numeral co-occurs] with sum 6. [the numeral co-occurs] with oþer 7. [the numeral is used] in apposition with a noun 8. [the numeral is used] with [the quantified noun in] a partitive genitive 9. [the numeral is used] with [the quantified NP following] the preposition of

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Numeral constructions in Old English

Although apparently proposing a more fine-grained list of uses than WÜLFING, MITCHELL’s classification generally faces the same problems. MITCHELL does not explain the criteria he employs for setting up his list of descriptive labels. Only from the labels themselves and from the respective examples can the reader infer what kind of properties MITCHELL’s subtypes of the ‘independent use’ imply. Generally, one could assume that, according to his list MITCHELL’s term ‘independent use’ implies ‘not adjacent to a quantified NP’. But even his subtypes of ‘independent uses’ as listed here do not apply to equal levels of syntactic description. For instance, MITCHELL’s types 1 to 6 describe the general co-occurrence of numerals with other elements, i.e. the numeral as a single-word constituent, the numeral with a demonstrative, the numeral with an adjective, etc. By contrast, types 7 to 9 describe the syntactic relation between the numeral and the quantified element. Either the numeral is in an apposition to the quantified NP, or the quantified NP is in a partitive genitive, or the quantified NP is the complement of an of-phrase. Like WÜLFING, MITCHELL sets up a list of syntactic uses employing distinctive features that are orthogonal. The result is a list of (sub)types that are not mutually exclusive. A numeral in types 1 to 6 could theoretically also appear in types 7 to 9 (and, as we will see, does so in one of MITCHELL’s examples). Moreover, numerals in some of the nine types – which are explicitly subtypes of the ‘independent use’ – could just as well be analysed as ‘used as adjective’ and therefore be subsumed under the ‘dependent use’. A closer look at one of MITCHELL’s examples will help to illustrate this problem. Example (4.4) is given by MITCHELL as an example of category 2 – the independently used numeral adjacent to an adjective. MITCHELL apparently analyses monig ‘many’ as an “adjective” modifying the numeral ðusend ‘1,000’. (4.4) Or 3 7.61.22 (BATELY 1980: 61): His forme gefeoht wæs wið Atheniense, & hie oferwonn; & æfter þæm wið Hiliricos, þe we Pulgare hatað, & heora monig ðusend ofslog, & heora mæstan burg geeode, Larisan. His first battle was against the Athenians and [he] defeated them; and after that against the Illyrians whom we call Bulgarians; and [he] killed many thousands of them, and [he] conquered their greatest city, Larissa. heora PPRN .GEN .PL

monig many

ðusend 1,000

ofslog kill\PST.3SG

The phrase monig ðusend thus quantifies the pronoun heora. Since heora is a partitive genitive, the passage quoted in (4.4) could just as well be classed under MITCHELL’s category 8. In fact, MITCHELL’s only example of his type 2

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– our example (4.4) – reappears in the list of instances for the partitive genitive. Additionally, there is good reason to argue that categories 4 and 5 actually refer to exactly the same syntactic use or co-occurrence and should be considered one type, perhaps also comprising type 3. Types 2 and 6 may also well be treated as one syntactic use.41 IV.2.4

Conclusion and outlook

The preceding discussion may suffice to show that MITCHELL’s types, like those proposed in earlier descriptions, do not provide a classification covering and delimiting sufficiently the syntactic properties of numerals in Old English. Basically, but not exclusively, this is due to the orthogonality of the criteria distinguishing the postulated types, as a consequence of which the proposed categories are not mutually exclusive. While discussing these approaches, we could see that there are generally three parameters of features according to which Old English numerals are categorised in syntax-based descriptions. Cf. (4.5): (4.5) Distinctive parameters for the classification of syntactic uses of (Old English) cardinal numerals  the general co-occurrence of numerals with other parts of speech,  the syntagmatic / inflectional / agreement relation between the numeral and the quantified NP, and  the morphosyntactic analogies of numerals with other parts of speech (usually adjective and noun).

Any of these sets of features listed in (4.5) is, of course, in itself an important aspect of the syntactic properties of numerals. As we have pointed out in the preceding section, the problem is that these three levels of criteria have always 41 There are also a number of doubtful or ambiguous cases in MITCHELL’s examples. To mention only two: ða oðre twegen (ÆCHom II.22 193.109 – cf. (4.17) below in § IV.3.2.3) constitutes the prototype of category 6 (with oþer), but at the same time it contains a demonstrative and could therefore just as well be grouped under category 3. – In þæs oþres folces XXV M [ofslog] (Or 4 8.100.19), the immediately quantified element is not þæs oðres folces. This would perhaps be more obvious had MITCHELL included the verb ofslog in his quotation. The genitive Case of FOLC has, it is true, a partitive function, but the syntactic construction is entirely different from all other examples given by MITCHELL. Cf. below the discussion of example (4.83) in § IV.7.

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been used for one and the same range or list of syntactic uses of numerals. The possible patterns in which a numeral co-occurs with other elements should, for instance, be described and analysed independently of the syntactic relation between the numeral and the quantified NP. In other words, if it is stated that a numeral in a particular construction shares a characteristic feature with, say, an adjective or a noun, which level of syntactic analysis this analogy can be observed on should be explained. For instance, is a numeral like an adjective, because it seems to occur, in particular cases, in the same syntactic position as an adjective? Or is a numeral like a noun because a quantified NP in the partitive genitive behaves like a genitive attribute to a noun? As a first superficial approach to the different syntactic constructions in which cardinal numerals (of Old English) may occur, I have just made a case for the mutual exclusiveness of the criteria employed. Of the three parameters of criteria drawn from the categorisations proposed by WÜLFING and MITCHELL (cf. (4.5)), any one may well be justified as long as the analysis of numerals is strictly confined to a purely syntactic level. However, as a next step towards a more in-depth description and analysis of numeral constructions, it is important to recognise that – beyond the orthogonality of the parameters of description in (4.5) – the syntactic properties of numerals are multi-layered and cannot be reduced to the co-occurrence of the numeral with other parts of speech. To examine the fundamental question – namely, under which circumstances a numeral is used with a partitive phrase, or under which circumstances the Gender and Case value of the numeral is dependent on the respective value of the quantified NP – more than a purely distributionalist typology of attested co-occurrences will be required. Consequently, the syntactic properties of Old English numerals should be described in the context of their functional and (if possible in a historical text language) discourse and information structural implications. Accordingly, the following sections §§ IV.3–7 contain quantificational constructions that are generally more complex than the ones discussed here. In the constructions discussed in § IV.3 under the label ‘Attributive Quantification’, the morphosyntactic relation between numeral and quantified referent is more immediate than in the following. This applies formally either in that the numeral is an immediate attribute to the quantified noun (§ IV.3.1) or in that the numeral itself replaces the referential expression (§§ IV.3.2–3). In the Predicative Construction discussed in § IV.4, the two elements are linked by a copula. In this respect – and only in this respect – there are parallels in the ways in which adjectives and numerals can be linked to the phrasal heads. Morphologically, if the numeral is inflected (cf. § II.2.4), numeral and quantified expression agree with each other: while Case and Gender value are as-

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signed by the quantified head on the numeral, the Number value of the phrase is determined by the cardinality of the referent set. By contrast, the following constructions presented in §§ IV.5–7 are morphosyntactically more complex. The numeral does not show prototypical properties of a modifier to a head. Agreement relations are also less plain. IV.3

Attributive quantification

In this section, I will propose several constructions in which the numeral resembles an attributive modifier. The degree to which it is attached to the modified expression varies across the different constructions postulated here. So does the degree to which the quantified noun is the referential expression of the construction. The order in which the constructions are presented in this section corresponds with both the increasing degree of referentiality carried by the numeral and, at the same time, or rather, as a consequence of this, with the decreasing quantificational force that the numeral exerts. Thus, in the Attributive Construction (§ IV.3.1), the quantified noun is the referential expression and the numeral is solely used as a quantifier. In the Elliptic Construction (§ IV.3.2.1) the numeral is used for quantification in the same way as in the Attributive Construction, but the quantified noun is not overtly expressed so that the numeral quantifies a contextually given referent. In the Anaphoric Use (§ IV.3.2.3), the numeral is, strictly speaking, no longer used as a quantifier, but its main function is to exert the reference of the phrase. Finally, in (§ IV.3.3), we will briefly discuss cases in which the numeral has been lexicalised as a noun – i.e., instances of a conversion from numeral to noun – and thus is no longer used as a quantifier at all. Although the expressions in this last case are synchronically not numerals, I would like to discuss them briefly for two reasons. First I will argue that the series of constructions presented in this section form a continuum. We will see below what exactly this implies. Another reason for including a short section on nouns derived from numerals is because they have often been subsumed under the same label, i.e. as genuine numeral constructions that, for other reasons, were taken as ‘nominal uses’ of numerals. It should be pointed out, however, that the expressions discussed in § IV.3.3 are not numerals but the result of a word-formation process of which the source category is a numeral, whereas all other cases (whether or not designated as ‘nominal’ numerals) are instances of numerals as defined in Chapter I.

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IV.3.1

The Attributive Construction

The Attributive Construction is the most common type of quantification, not only in Old English but also in other modern Germanic and Western European languages. In Old English the Attributive Construction is both the most frequent and the unmarked type in the sense that any other type discussed below involves some additional functional and/or morphosyntactic constraints. In an Attributive Construction, the numeral is a constituent of a phrase in which the quantified noun is the head. This type corresponds in many respects to what GIL (2001: 1281b, § 3.3) and many others refer to as “attributive position” of quantifiers. Examples of this type of construction are given in (4.6)42 – (4.9). (4.6) Beo 2163 (MITCHELL/ROBINSON 1998: 122): Hyrde ic þæt þam frætwum feower mearas lungre, gelice, last weardode, æppelfealuwe I heard that four steeds, bay horses, all swiftly followed the treasures. feower 4

mear-as horse-NOM.PL

(4.7) Beo 574 (MITCHELL/ROBINSON 1998: 67): Hwæþere me gesælde þæt ic mid sweorde ofsloh niceras nigene. Nevertheless, it happened to me that I killed nine sea-monsters with my sword. ic […] I […]

ofsloh kill\PST.1SG

nicer-as sea.monster-ACC.PL

nigen-e 9-ACC.PL

(4.8) ÆCHom I.6 225.33 (CLEMOES 1997: 225): Abrahames nama wæs æt fruman mid fif stafum gecweden abram, þæt is hælic fæder, ac god geihte his naman mid twam stafum & gehet hine abraham þæt is manegra þeoda fæder; ‘Abraham’s name was at first spelled with five letters: Abram; which means: “Great Father”, but God extended the name by two letters and called him Abraham, which means: “Father of Many Nations”.’ a.

mid PREP

b.

mid PREP

fif 5

staf-um letter-DAT.PL

twam staf-um two:DAT letter-DAT.PL

42 On the plural of weardode in (4.6) cf. MITCHELL (1985 I: 10, § 19).

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(4.9) BedeHead 5.10 (MILLER 1890–1898: 22, 30): Ðæt Wilbrord on Frysena lande bodiende monega to Drihtne gecyrde: & þæt his geferan twegen healicne martyrdom wæron þrowiende. That Willibrord, when he was preaching in Frisia, converted many to the Lord and that his two comrades suffered glorious martyrdom. his PPRN :GEN .SG .M

gefer-an comrade-NOM.PL

twegen two:NOM.PL

In examples (4.6) and (4.7), the Case value of the whole NP is determined by the syntactic roles of the phrase, i.e. roughly, nominative for the subject in (4.6), accusative for the direct object in (4.7). In (4.8), the quantified noun STÆF is in the dative Case as required by the preposition mid. In (4.9), the quantified noun GEFERA is the subject of the clause and hence in the nominative Case. The inflection of the numeral both in (4.8) and in (4.9) is, in turn, dependent on that of the corresponding quantified noun. If the numeral shows inflection (cf. § II.2.4)–(4.7), (4.8)b, and (4.9) – the quantified noun assigns Gender and Case to the numeral and the Number value of the noun is determined by the number of elements of the referent set. The relation between numeral and quantified element is that of an attribute to the noun. With respect to Gender and Case assignment, the relation may resemble that of an adjective to the noun, but, as will be shown below (cf. § V.1.1), there are clear differences between the relation of a numeral to the quantified noun and that of an adjective to the modified noun at all levels – syntactic, semantic, and morphological. In the Attributive Construction, both the referent and its cardinality are overtly expressed, each by an individual constituent within the same phrase. The cardinality is defined by the numeral and the set of which the cardinality is specified is represented by the quantified NP. Generally, the numeral precedes the quantified NP in Old English far more often than it follows it. Yet the comparatively free word order in Old English generally allows the inverse order just as well; cf. (4.7). What matters here is that both numeral and quantified NP are two adjacent constituents of one and the same phrase; cf. (4.6)– (4.9). Since non-universal quantifiers are inherently indefinite, so are cardinal numerals. Although they do not function as markers of indefiniteness, the unmarked type of a non-universal quantificational construction is an indefinite noun phrase. This means that the noun phrase refers to at least one, but not all members of a set which is shared by speaker and hearer of a discourse; cf. HAWKINS (1978: 186). In other words, a noun phrase is indefinite if it refers to

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less than all potential referents provided by the context. Thus if cardinal numerals quantify an NP, they always identify a subset out of a potentially larger set. Where the larger set has not been mentioned previously, the shared set in the discourse is the set of all potential referents that exist in the discourse universe. IV.3.2

The Elliptic Construction

IV.3.2.1 Elliptic quantification In the Elliptic Construction, the numeral basically has the same function as in the Attributive Construction: it quantifies the referent. However, while in the Attributive Construction the quantified noun specifies the referent, this quantified element is dropped in the Elliptic Construction. That is, of the two adjacent elements, numeral and quantified NP, only one, the numeral, is overtly expressed. This is possible because the referent has already been introduced – explicitly or implicitly – previously in the discourse, i.e., because, in contrast to the quantified NP in the Attributive Construction, the referent is thematic. The lack of an overt expression denoting the referent in this particular clause may, for instance, be due to the requirements of the metre or it may be stylistically more elegant to avoid the repetition of the same noun; cf. (4.10)–(4.12). (4.10) ÆCHomII.17 164.108 (GODDEN 1979: 164): Se hælend hine geswutelode æfter his æriste æt ðære sǽ tyberiadis. his seofon leorningcnihtum on fixnoðe; Þær fixode Petrus. and Thomas. and Nathanael. Iacobus. and Iohannes. and oðre twegen. þæra naman ne némde se godspellere. There were Peter, Thomas, Nathaniel, Jacob, and John fishing and another two whose names the evangelist did not mention. oðre other:NOM.PL

twegen two:NOM.M

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(4.11) ÆCHom II.14.1 140.95-8 (GODDEN 1979: 140): Cwæð þæt he mihte ða. ma ðonne twelf eoroda heofenlicra engla. æt his fæder abiddan. […] Wise men tealdon an eorod to six ðusendum. and twelf eorod sind. twa and hundseofontig ðusend. He said that he could ask his father for more than twelve hosts of heavenly angels. […] Wise men divided a host [of angels] into 6,000 and twelve hosts are 72,000. an eorod to six one.NOM host PREP 6 sind be:3PL.PRS

twa (2

and +

ðusend-um [×] 1,000-DAT

and and

twelf eorod 12 host[NOM.PL]

hundseofontig 70)

ðusend [×] 1,000

(4.12) ByrM 1.2 94 (BAKER/LAPIDGE 1995: 30): On hwylcum dæge man ræt IX kalendas Aprilis, swa fela beoð concurrentes, swylce ic þus cweðe: gif man ræt þæne datarum on Sunnandæg, þænne beoð an; gif on Sæterndæg, þonne beoð seofon. “On whatever day one reads 24 Mar., there are so many concurrents, as if I were to speak thus: if one reads that date on Sunday there is one; if on Saturday there are seven.” (transl. BAKER/LAPIDGE 1995: 31).

What is crucial in the analysis of these instances is that it is impossible to replace the numeral by a co-referential noun or by an anaphoric element (pronoun, determiner). Or, if the numeral were replaced, the meaning of the clause would change, in some cases only through the missing specification of the cardinality (in (4.10)) but in others more significantly (in (4.11) and in (4.12)). This suggests that the function of the numeral is the same as in the Attributive Construction – quantification in the sense that the numeral specifies the cardinality of the set – a point which will become relevant below in § IV.3.2.3. Our analysis requires that, in both the Attributive Construction and in the Elliptic Quantification, the cardinality of the set is a piece of information newly introduced in the discourse. A closer look at examples (4.10)–(4.12) may help to illustrate this. In (4.11) and (4.12), there is explicit mention of each referent in the respective previous sentence. In (4.11), it is clear from the preceding sentence that a ‘band’ or a ‘host’ (eorod) consists of angels and that the second part of the quotation is only intended to specify the precise number of angels in one host and in twelve hosts respectively. In (4.12), seofon quantifies concurrentes in a very similar way.

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In (4.10), there is no element representing the referent previously in the text (Ælfric’s paraphrase of St John’s Gospel only begins at this point; cf. GODDEN 1979: 164 and 2000: 504). However, it seems obvious, if only from naming the fishermen immediately before, that twegen specifies the cardinality of the set of fishermen. The semantic content of the referent (‘fishermen’) is only implied by the context, i.e. by the fact that, at the beginning of the sentence, a number of persons are listed as subject to the verb FISCIAN ‘to fish’. The reason why instances of this type have often been taken as ‘noun-like’ (cf. above § IV.2) is quite obvious: since the prototypical referential expression of a noun phrase, the head noun, is dropped, it is the numeral which is perceived as the referring expression of that phrase. The resulting uncertainty is manifested in remarks like that of FOX (2005: 175) who comments on a similar construction in German: “[The numeral in this construction] is ambivalent: it could be considered to be a noun or an adjective with the noun elided.” The association of elliptically used numerals with nouns is, however, superficial: although nouns can be taken as the default referential expression of an argument, the fact that the numeral takes over this function is not, in any rate, typical of a noun. To the contrary, it is typical of a nominal modifier and thus finds its closest parallel in the properties of adjectives, but also in those of determiners. In fact, any satellite of a noun, be it a quantifier, an adjective or a determiner, is capable of becoming the syntactic head once the referent has been introduced by the noun. So what has traditionally been taken as noun-like would, if we do wish to compare with other word classes, actually be typical of an adjective. Yet it is as typical of other elements of the noun phrase, such as quantifiers and other determiners, as it is of adjectives. Accordingly, LANGACKER (1991: 85) labels numerals in these constructions as ‘pronominal’. But while I think that the label ‘pronominal’ describes the properties of the Elliptic Construction more adequately than ‘nominal’ (in the sense of ‘noun-like’ or ‘substantival’, not in the sense of ‘part of the noun phrase’), I would generally doubt whether a comparison with any one particular noun modifying word class is a sufficient label for the numeral in the constructions discussed in this section. We may, therefore, prefer to say that in the Elliptic Construction, the numeral behaves more or less the way a noun modifier normally behaves under the condition that the noun has been elided – it takes over the referential function of the head. Perhaps GIL’s (2001: 1281b, Table 92.1) label “referential use” gets much more to the heart of the phenomenon under discussion than any analogy with non-numeral word classes. The following section may be seen as a parenthesis in which we briefly discuss a special idiomatic expression, which is derived from the use of TWA in

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an Elliptic Construction. After this, we will resume some of the points discussed here in § IV.3.2.3 when we analyse another subtype of the Attributive Quantification of numerals, which I will assume has developed on the basis of the Elliptic Quantification. IV.3.2.2 on twa ‘in two parts’ There is a lexicalised expression in Old English which has sometimes been discussed along the lines of constructions like those in (4.10)–(4.12), but which should be kept apart from a quantificational construction in the proper sense. Examples of this idiom are shown in (4.13)–(4.15). (4.13) HomS 18 229 (K.G. SCHAEFER 1972: 31, 186): & þa þæt templ wearð todæled on twa [...] and then, the temple was torn into pieces […] þæt DET.NOM.SG.N

templ temple(N)

wearð todæled become.3SG.PST divide.PTC

on PREP

twa two

(4.14) ÆCHom II.12.1 112.89 (GODDEN 1979: 112): And moyses ða sloh þære sæ ofer mid his gyrde, and seo sæ toeode on twa, […] And then, Moses stroke there over the sea with his staff and the sea went into two [halves] […] seo DET:NOM.SG .F

sæ sea( F)

to-eo-de apart-go(PST)-3SG.PST

on

twa PREP two

(4.15) Or 1 1.11.15 (BATELY 1980: 11, 16): Þonne of þæm æwielme mon hæt wæter Nilus þa ea, & þonne forþ þonan west irnende heo toliþ on twa ymb an igland þe mon hæt Meroen [...] Then, from this source, the water is called Nile River; and it runs from there to the west and, near an island that is called Meroe, it splits into two. toliþ split.3 SG.PRS

on PREP

twa two

Both WÜLFING (1894: 303–304, § 173) and STILES (1986a: 10) include the phrasal expression ON TWA ‘in(to) (two) pieces / parts’, ‘asunder’ in their list of “substantival” uses of numerals – probably because the numeral is used without a quantified element. I would hold against this analysis that the ex-

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tremely frequent use of the verb TODÆLAN ‘divide’ (or semantically related verbs as in (4.14) and (4.15)) with ON TWA and the rare use of numerals other than TWA in this construction suggest that ON TWA is a lexicalised idiom. This becomes particularly obvious by the fact that, in (4.13)–(4.15), the translations into Present-day English prefer an additional noun such as pieces or halves but that the numeral two could, at the same time, be easily dropped. The conventionalised character of the construction in Old English is thus evident by the fact that the preposition does not require a nominal complement any more, but that what used to be preposition and numeral are now one lexeme. The idiom ON TWA, therefore, cannot be subsumed in any typology of syntactic uses of numerals but should rather be taken as an adverbial adjunct. Yet WÜLFING’S and STILES’s categorisation is, of course, motivated by the fact that the origin of the idiom was a construction of the shape TODÆLAN X ON TWA (HEALFA) ‘divide X into two (parts)’ and that the first step in the process of idiomatisation was the ellipsis of the quantified noun HEALF ‘side, part’. In this case, the underlying noun would clearly be the feminine noun HEALF ‘part, side’. The fact that it is predominantly the feminine form TWA which occurs in this idiomatic construction with the preposition ON (cf. § II.2.2.) further suggests that the source construction is (TODÆLAN) ON TWA HEALFA ‘(divide) into two parts’. A considerable frequency in use allowed for a conventionalised elliptic use as (TODEALAN) ON TWA ‘(divide) into two’ from which the construction ON TWA ‘apart’ was transferred to other, semantically similar verbs and thus became an autonomous unit. In spite of instances like (4.16) in which the autonomy of the idiomatic expression ON TWA is attested, a verbal notion related to ‘divide’ underlies the construction in most cases. (4.16) Jn(WSCp) 19.18 (SKEAT 1878: 168): þær hi hyne ahengon. & twegen oðre mid him on twa healfa & þæne hælend on middan. They crucified him there and with him two others on each side and the Saviour between them. on

twa PREP two:ACC.F

healf-a side( F)-ACC.PL

While the motivation for an analysis of TWA as a noun is unfortunate, the motivation behind this analysis will be of some relevance further below. We will, therefore, resume this point in § IV.3.3.

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IV.3.2.3 Anaphoric use In this subsection, I will postulate another variant of the Attributive Quantification. The crucial aspect is that it does not differ formally from the Elliptic Construction as discussed in § IV.3.2.1. However, since one of the main presuppositions of this chapter is that quantification is the key function of cardinal numerals, the categorisation I would like to argue for here is based on the distinction between two considerably different uses of the Elliptic Construction – Elliptic Quantification (§ IV.3.2.1) and the Anaphoric Use. In what I refer to as the ‘Anaphoric Use’, the referent is again not overtly expressed but can generally be inferred from the context. In contrast to the Elliptic Quantification, the numeral here is reduced to an anaphoric element. That is, it is no longer used for quantification and its sole function is that of anaphoric reference. While inherently indefinite numerals on their own cannot single out a predefined referent (cf. § IV.3.2.1), an anaphoric element does exactly this. By being co-referential with an element that has occurred previously in the context, the referent is assumed by the speaker/writer to be known by the listener/reader. This entails the respective phrase as a whole, i.e. including the numeral, being definite. It therefore usually requires a definite marker. Examples (4.17)–(4.19) will illustrate this. As will be explained below in more detail, in all three examples, the referents are explicitly mentioned earlier in the respective texts: in (4.17), a group of three angels, in (4.18), Jesus’s twelve disciples, and in (4.19), the first two humans of creation according to Genesis, Adam and Eve. (4.17) ÆCHom II.22 193.109 (GODDEN 1979: 193): Se gewæpnoda engel ða fleah him ætforan todælende ðine lig. and ða oðre twegen him flugon on twa healfa. and hine wið þæs fyres frecednysse gescyldon The armed angel then flew in front of him separating the flame; and the other two flew on either side of him and protected him against the danger of the fire. ða DET:NOM.PL

oðre other:NOM.PL

twegen two:NOM.M

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Numeral constructions in Old English

(4.18) Mt(WSCp) 10.5 (SKEAT 1887: 82): Ðas twelf se Hælynd sende him bebeodende & cweþende, ne fare ge on þeoda weg & ne ga ge innan Samaritana ceastre. The Saviour sent forth these twelve instructing them and saying: “Do not travel on a Gentile road and do not enter into a Samaritan town. ðas DEM:ACC.PL

twelf 12

se DET:NOM.M.SG

Hælynd saviour(M)

send-e send\PST-1/3SG

(4.19) GenA 194 (KRAPP 1931: 8): Þa gebletsode bliðheort cyning, / metod alwihta, monna cynnes / ða forman twa, fæder and moder, / wif and wæpned. Then the merciful king, the almighty creator of mankind, blessed the first two, father and mother, woman and man. ða DET:NOM.PL

form-an twa first-NOM.PL two:NOM.C

One might argue now that whether a phrase is definite or not does not justify the postulation of a distinct type of construction. I would hold against this objection that the feature [+ definite] is only the superficial consequence of a more crucial difference between the Elliptic Quantification and the Anaphoric Use of the numeral. The essential characteristic of the Anaphoric Use is that the cardinality of the referent is thematic, i.e. that the cardinality is familiar to the recipient interlocutor. The numeral in its default function as a quantifier, that is, as an element that defines or specifies the cardinality of a set (cf. § I.1), is therefore not necessary in the context of an Anaphoric Use. In contrast to the Elliptic Quantification, the numeral could well be replaced by a coreferential noun or by some other anaphoric element. In § IV.3.2.1, we said that, if the numeral in the Elliptic Quantification were dropped or replaced by a different element, then the meaning of the clause would change at least in so far as the cardinality would not be specified. In (4.10) for instance, the number of anonymous fishermen would not be specified as ‘2’. That is, the extensional reference of the noun phrase would be less precisely specified. By contrast, for the Anaphoric Use it is a necessary prerequisite that the cardinality of the referent set has already been specified sufficiently previously in the discourse. More simply: in the actual case of an Anaphoric Use of a numeral, the cardinality of a set is already known and therefore does not need to be specified again.43 43 I have not come across an instance of a cataphorically used numeral in Old English, but I would not want to rule out that such an instance exists. Generally, cataphoric reference by

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199

The crucial point now is that, because the numeral is no longer required for quantification in the Anaphoric Use, the construction makes use of the prototypical property of the numeral – i.e. its reference to the cardinality – for a different, new purpose. Since the referent is – for whatever reason – not overtly represented by a head noun, reference is made to the cardinality as a particular feature of the referent assumed to be sufficiently familiar to the discourse participants. For instance, in (4.19), the cardinality ‘2’ is mentioned merely to enforce the association with the referent – Adam and Eve – but not to provide any new piece of information. If twa were replaced by a different element or if it were completely dropped, the referential meaning of the phrase and of the entire clause would not change at all. In (4.17) (cf. above, fn. 41 for this), the two unarmed angels and the third, armed angel of the same group have already been mentioned several times before in the text (cf. the relevant passages in Ælfric’s Homily for the Wednesday in Ascension Week; ÆCHom II.22 191.27-28 and 192.58; GODDEN 1979: 191–192). From the context, it is therefore entirely clear to the recipient interlocutor that the cardinality of the set of angels in the relevant clause is ‘2’. It is, therefore, not necessary to specify the number of angels at this particular point in the text. What is crucial is that, because the cardinality is assumed to be known, the phrase ða oðre twegen can refer to the concept ‘angels’ without overtly using a relevant noun. The same analysis can be applied to example (4.19), which has already been discussed briefly. The phrase ða forman twa ‘the first two’ refers to Adam and Eve. The feminine/neuter form twa (cf. § II.2.2) cannot possibly refer back to masculine monna ‘man(M)-GEN.PL’. In this instance, the numeral twa has therefore an exclusively anaphoric function and could – if the metre allowed it – be replaced by ‘both’ or by any word for ‘person’, ‘man’, ‘creature’, etc., without changing the reference. It would, however, be odd to imply that the author had intended to specify the cardinality ‘2’ at this point in the text. Recall again that in § IV.3.2.1 we said that in the Elliptic Quantification, the numeral could not be replaced by a noun or by another anaphoric element. a numeral is, of course, possible. This would however imply that the referent is unknown up to this point in the discourse and, consequently, that its cardinality is unknown. This, in turn, means that the numeral – in spite of its additional pronominal functions – specifies the cardinality of the referent at least on its first occurrence. It could, therefore, not be replaced by a pronoun in the same way as we have postulated for the Anaphoric Use, because, if the pronoun replaced the numeral, the cardinality would not be specified at this point. Since, as we said above, both possible replacement by a pronoun and lack of quantification are features of the Anaphoric Use by which it contrasts with the Elliptic Quantification, it would be generally difficult to group a cataphoric of a numeral into either of the two subcategories postulated here.

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Numeral constructions in Old English

We now know why: as long as the cardinality of the set is a new piece of information in the context, no other expression than the numeral can assume the head position of a phrase once the noun is elided. If the cardinality of the set is known – as in the cases discussed here – then any other potentially referential expression that is semantically appropriate could assume the head position. Compared to the Elliptic Quantification, the cardinality of the set shifts from the foreground to the background in the Anaphoric Use of a numeral while the referential force moves from the background to the foreground. The difference will perhaps become more obvious if we compare the numeral twelf in (4.18) with similar uses of the same numeral. Whenever the expression ða twelf refers to ‘the Apostles’, the specification of the number of Apostles is, although encoded by the numeral, irrelevant in the respective context. In our example (4.18), the Apostles have been mentioned immediately before the quoted passage (Mt(WSCp) 10.2: “þæra twelf apostola naman” – ‘the names of the twelve apostles’). There are, however, instances of the expression ÐA TWELF for ‘the Apostles’ where the Apostles have not been mentioned before or only at a very remote point of the text; cf. (4.20), which is a quotation of verse 16.14 of the West Saxon version of the Gospel of St Mark. What is important in this context is that the previous occurrence of TWELF is in verse 14.43 and the last instance where TWELF is adjacent to a noun is in verse 11.11 (“he ferde to Bethaniam mid his twelf leorningcnihtum” – ‘he went to Bethany with his twelve disciples’). (4.20) Mk(WSCp) 16.14 (SKEAT 1871: 132): Ða æt nehstan he ætywde him twelfum þar hi æt-gædere sæton & tælde hyra ungeleaffulnesse & hyra heortan heardnesse [...] Then after this he appeared to the twelve while they were sitting together and he reproached them for their incredulity and for the hardness of their hearts [...]. he PPRN :NOM.SG.M

ætyw-de him show-1/3SG.PST REFL:DAT.SG.M

twelf-um 12-DAT.PL

One might be inclined to conclude that ÞA TWELF is a conventionalised expression for ‘the Apostles’. This would, in turn, suggest that ÞA TWELF in these instances is a former numeral now lexicalised as a noun. However, the expression ÞA TWELF may perhaps be conventionalised in a special context – i.e. in a translation or a paraphrase of the Gospels. It is debatable, however, whether the reference to the apostles by a lexeme denoting ‘12’ (in whatever language) would still have the same connotation outside a New Testament context. Thus,

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although we probably cannot speak of a lexicalised noun TWELF meaning ‘Apostles’ in the sense discussed below (§ IV.3.3), the example of ÐA TWELF for ‘the Apostles’ again shows that the Anaphoric Use is clearly distinct from the Elliptic Quantification. Admittedly, as the discussion of ÐA TWELF in these instances shows, it would be extremely difficult to establish precise criteria as to which contextual distance is necessary to distinguish between the two types. However, as I said in the introductory section of § IV.3, the types proposed here should be seen as a continuum and the discussion is meant to point at the distinctive features of the (sub)types rather than to the borderline between them. In any case, in contrast to the Elliptic Quantification, the cardinality of the referent is only a secondary semantic feature in the Anaphoric Use whereas the main function of the numeral in cases like (4.17)–(4.19) and (4.20) is that of anaphoric reference. On purely formal grounds, the difference between the Elliptic Quantification and the Anaphoric Use may be considered irrelevant. Given that the core function of cardinal numerals is quantification, it is, of course, of key relevance whether or not an element actually quantifies a referent. I would argue, therefore, that in the two constructions discussed here, Elliptic Quantification and Anaphoric Use, there are different grammatical processes at work – quantification and anaphoric reference – which makes it necessary to keep the two constructions apart. There is another interesting aspect of the relation between the Elliptic Quantification and the Anaphoric Use. Only the possibility of Elliptic Quantification allows for the Anaphoric Use of a numeral. In other words, the numeral assumes a new function – that of an anaphoric, ultimately pronoun-like expression. This shift or expansion of the function of the numeral is possible only on the condition that the quantified noun can be dropped and only because the numeral can quantify a referent without the referent being overtly expressed. We may therefore conclude that the three constructions discussed so far, the Attributive Construction (§ IV.3.1), then the Elliptic Quantification (§ IV.3.2.1) and finally the Anaphoric Use (§ IV.3.2.3), form a chain or a continuum. An attributive modifier (of whatever kind) has the potential to assume the referential function of the usually modified head if this head is dropped (Attributive > Elliptic). Once this step is conventionalised, the weight of the modifier may shift from its original semantic value (in the case of numerals it is the specification of the cardinality of a set) to a mere anaphoric element (Elliptic > Anaphoric). The functional differences between the Elliptic Quantification and the Anaphoric Use as discussed here could never be captured by the traditional reference to the categories ‘noun’ and ‘adjective’. In fact, instances like those

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given in these two subsections (i.e., §§ IV.3.2.1 and IV.3.2.3) have often been referred to as ‘noun-like use’ of the numeral simply because the quantified NP is not overtly expressed and because, in Old English, the higher valued numerals from ‘4’ onwards are more likely to show inflection in these constructions. But again, the core functional difference between the two subtypes – i.e. that between quantification (Elliptic Quantification) and anaphoric reference (Anaphoric Use) – and the way these functions are encoded (presence / absence of the noun, [± definite]) has much more obvious parallels with possible uses of adjectives or other noun satellites than with those of nouns. IV.3.3

Nominalisation of numerals

MITCHELL (1985: 217; § 550.1) takes the numeral in the following passage (4.21) from Ælfric’s Grammar as an instance of an ‘independently used’ numeral that stands ‘alone’ (cf. (4.3) above in § IV.2.3): (4.21) ÆGram 283.9 (ZUPITZA 1880[2001]: 283): Genoh bið, þæt we awriton þa CARDINALES NVMEROS, þæt synd þa heafodgetel; tyn and twentig and swa fram tyn to tynum. It is sufficient that we wrote down the Cardinales Numeros; they are the cardinal numerals: ten and twenty and so [forth] from decade to decade. fram tyn from 10

to tyn-um to 10-DAT.PL

This example has been quoted by various other authors as an instance of the ‘nominal’/ ‘independent’ category – thus assigning the same status to these expressions as the numerals used in an Elliptic Construction. The lexeme TYN employed in this passage, however, cannot be taken as a numeral the way we defined it in Chapter I. Rather, it is a genuine noun referring to a mathematical notion ‘decade, subsection of ten numbers in a decimal system’. It clearly cannot be used to specify the cardinality of a set. The only relation to a cardinal numeral is that the numeral TYN for ‘10’ provides the lexical source for the noun TYN ‘decade’. There are languages that employ a different lexeme in such contexts as e.g. in my translation of (4.21) into Present-day English provided above, ‘from decade to decade’. Other languages may use derivations of the numeral for similar notions, as for instance Modern German Zehn-er ‘10-NMLS’.

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203

The forms of TYN in (4.21) do not only behave like nouns or have functions of a noun. They are nouns – resulting from a conversion of a numeral into a noun. For any categorisation of syntactic properties of numerals, these instances are therefore irrelevant. In the previous section, we repeatedly noted that there is no advantage in comparing numerals in particular constructions (especially those without a referential head) with nouns and thus we implicitly rejected the noun status of cardinal numerals in both instantiations of the Elliptic Construction. The implicit reason why numerals have often been assigned a noun status in the Elliptic Construction is that they, once the quantified referential expression is not overtly expressed, are more likely to show inflection in Old English (as in other languages) than numerals do when they are adjacent to the quantified noun. We argued above that these are superficial parallels between numerals and nouns and that these parallels do not outnumber the parallels that numerals in these constructions share with other word classes, such as adjectives or pronouns. By contrast, to assign noun status to expressions derived from numerals and denoting something else than a cardinality, as in (4.21), is entirely justified. But to label expressions like TYN in (4.21) a noun does not tell us anything about cardinal numerals. However, instances of nominalised numerals other than (4.21) may be closer to those categorised as Elliptic Quantification, for instance numerals used in a purely arithmetic discourse, as in (4.22)–(4.23). In such arithmetic contexts, the numerals do refer to cardinalities in general, though not to cardinalities of specific sets. The difference between a numeral in (4.22) and (4.23) and a numeral in the cases discussed in the previous sections is similar to that drawn in § I.2.3 between counting words with a potential to be used as numerical tools on the one hand and, on the other, cardinal numerals which refer to cardinalities. (4.22) ByrM 1.2.123 (BAKER/LAPIDGE 1995: 30): feower siðon seofon beoð eahta & twentig; ‘Four times seven equals 28.’ (4.23) ByrM 1.2 264 (BAKER/LAPIDGE 1995: 38): Þrittig siðon twelf oððe twelf siðon þrittig beoð þreo hund & syxtig. ‘30 times twelve or twelve times 30 equals 360.’

Yet this comparison does not completely solve the problem. In an arithmetic use, numerals do refer to cardinalities but not to the cardinality of a particular set, i.e. not to a set which has been referred to in the discourse. Accordingly,

204

Numeral constructions in Old English

they do not seem to quantify a referent. They do refer to a cardinality in a general way, i.e. to a general property all possible sets may potentially have. WIESE (2003: 233) describes the difference by distinguishing between ‘abstract cardinalities’ and ‘individualised numbers’. Linguistically, there is however a fuzzy borderline between the respective expressions, i.e. between numerals used in an isolated arithmetic context and numerals quantifying a specific set. The distinction is valid as long as, in an arithmetic discourse, there is clearly no potential referent, no quantified set even in the wider context. For instance, we might think of the context of a maths class in which arithmetic operations are discussed for the mere purpose of an exercise. However, in most instances of an arithmetic discourse, the presence of a non-overt referent is actually likely. Usually, if we do calculations, we always calculate something. This means that, even if the quantified referent is not explicitly mentioned at all, it may be contextually given. For instance, the mathematical operation carried out in the example from Byrhtferth’s Manual in (4.22) is part of a schema for the determination of concurring dates in the 28-year cycle of solar years. Likewise, if we look at the wider context of (4.23), we will find that the calculation is about the lunar regulars, i.e. particular dates in the one-month circle of the moon. That is, in the wider context of both (4.22) and (4.23), the referent whose cardinality is to be specified is a set of ‘days’. Accordingly, the numerals in (4.22) and (4.23) may just as well be interpreted as numerals in an Elliptic Quantification.44 Summing up, the nominalisation of a numeral is not an instance of a numeral in a particular morphosyntactic construction but the result of a wordformation process (conversion) whose source is a cardinal numeral. In contrast to all the instances discussed in § IV.3.2, the resulting nouns do not specify the cardinality of a set. They may, as in (4.21), refer to a linguistic expression, i.e. a number word of a language, but theoretically they can refer to anything that is in any way associated with a number (cf. the discussion of OE TWELF for ‘the Apostles’ in (4.20) in the previous section and also the remarks below in § IV.3.4). Finally, numerals may be used to simply label or mark different elements of a group or set in order to distinguish them. We mentioned such cases in § I.2.3 and they are discussed in detail e.g. by WIESE (2003: 37–40) where the

44 HURFORD (2002: 629a) and WIESE (2003: 233) analyse numerals in an arithmetic context as proper names. But cf. HURFORD (1987: 159–161), who relates a numeral in an arithmetic discourse to an elliptically used numeral on psychological grounds. Cf. further GREENBERG (1978: 287–288).

Attributive quantification

205

prototypical examples are numbers of bus lines or football players. In Old English, instances of this type are, as far as I am aware, unattested. IV.3.4

Conclusion

As the discussion in the previous section has shown, nouns derived from numerals may either refer to concepts that are closely related with arithmetic concepts, such as a particular well-defined sequence, like ‘decade’, or they may simply be used to refer to numbers as mathematical concepts rather than to specify the cardinality of a set, as for instance in (4.24) and (4.25). (4.24)

Seventeen is a prime number.

(4.25)

Fifty is represented in Roman numerals by the symbol L.

Another kind of noun derived from numerals has been potentially discussed in § IV.3.2.3 in the context of example (4.20). Although we rejected the idea (of a widespread use) of an Old English noun TWELF for ‘the Apostles’, such a coinage would, of course, not be implausible. In the case of such derivations, i.e. in the case of nouns derived from numerals but with a denotation outside a mathematical or quantificational sphere, they would most probably result from the Anaphoric Use of numerals. Thus, although not representing numerals as defined in § I.1, we may well include these nominalisations into the continuum suggested in the beginning of § IV.3. We may, therefore, postulate a cline of Attributive Quantification, with adnominal modifiers (i.e. quantifiers) on one end and with nouns derived from numerals on the other. In between, several uses of numerals are attested, which vary in their degree of referential and quantificational force, as summarised in Table 22. It is important to note that this cline has been described here as a synchronic continuum of constructions, but that it may potentially also be regarded as a diachronic continuum. Its implication for a synchronic perspective is that the different construction types postulated here have smooth transitions rather than clear-cut category boundaries. Diachronically, the continuum may be seen as a possible pathway of change.

206

Numeral constructions in Old English

Table 22. Continuum of Attributive Quantification Type of attributive quantification

Attributive Construction

Elliptic Construction Elliptic Quantification

Anaphoric Use

Nominalisation

Section

IV.3.1

IV.3.2.1

IV.3.2.3

IV.3.3

quantification

+

+

—

—

information structural status of cardinality

new

new

given

(—)

information structural status of quantified referent

new

given

given

(—)

quantified referent expressed by

quantified NP

context, (numeral)

(context), numeral?

nominalised numeral

Directionality / Hierarchy

The prototypical construction for the numerically specific quantification consists of a noun representing the referent which is to be quantified and the numeral as the quantifying expression. In this case, the cardinality is a piece of information newly introduced by the construction. Whether the quantified referent is itself given or new, is secondary, but in contrast to all the other constructional variants, it can be new (Attributive Construction; § IV.3.1). If the quantified referent is not new then it is possible to drop the noun. The numeral is still required because the cardinality needs to be specified, i.e. it has not been introduced previously (Elliptic Quantification; § IV.3.2.1). What is formally the same construction may also be used if both cardinality and quantified referent are contextually given. We simply say, in such cases, that the referent is provided by the context. However, to assume that the referent is represented by a non-overt noun, at least in this type of an ellipsis, obscures the fact that it is the semantic content of the numeral, i.e. the cardinality of the referent set, which contributes the key information for the recipient interlocutor to tracking the referent. In other words, although the cardinality is known, reference to it is needed in order to evoke an association with the referent of

Attributive quantification

207

the entire NP. The main function of a numeral is no longer to specify the cardinality but, by means of association with a contextually given cardinality as a salient feature of the referent, to track the (contextually given) referent (Anaphoric Use; § IV.3.2.3). Again, numerals in the Anaphoric Use are far from being nouns. Yet, because the numeral in the Anaphoric Use is that expression most explicitly employed for reference tracking, it substitutes the quantified noun in its function as a referential expression. This, I believe, makes it liable to be used as a noun if conventionalised in a particular context, such as for instance the numeral TWELF representing ‘the Apostles’ in a Biblical context. Only then, only if this particular reference has become sufficiently conventionalised, may a numeral be turned into a noun. Then, however, this new noun is no longer a numeral. IV.4

The Predicative Construction

In what I refer to as the Predicative Construction, the numeral quantifies the NP, i.e. it specifies the cardinality of the set represented by the NP. Both numeral and quantified NP are overtly expressed. However, in contrast to the cases subsumed under the label Attributive Quantification, numeral and quantified NP are not constituents of the same phrase. In the Predicative Construction, the quantified NP is in the subject position while the numeral is generally in the predicate position or, more precisely, a subject complement. The predicate is usually headed syntactically by the copula, i.e. in Old English a form of BEON ‘be’; cf. (4.26)–(4.28). VISSER (1963–1973 I: 226–227, § 250) notes that Predicative Construction often occurs with the quantified subject represented by the demonstrative ÞA in the genitive plural, as for instance in (4.28). (4.26) ÆCHom I.25 385.170 (CLEMOES 1997: 385, 170): Twa forhæfednysse cynn sindon, an lichamlic, oðer gastlic. There are two kinds of abstinence, one physical and one spiritual. Twa forhæfednyss-a 2.NOM.N abstinence-GEN.SG

cynn kind(N).NOM

sindon be.3PL.PRS

208

Numeral constructions in Old English

(4.27) Ch 1403 11 (ROBERTSON 1956: 202, 24, #107): Þissa gewrita syndan þreo an is on ealdan mynstre and oþer is on Wiltune and þridde æfed Wlfric. There are three of these documents: one is at the Old Minster, the second is at Wilton and Wulfric holds the third. Þissa gewrit-a DEM.GEN.PL document-GEN.PL

syndan COP.PRS.3P.PL

þreo 3

(4.28) ÆGram 105.21: (ZUPITZA 1880[2001]: 105): FIGVRA is gecweden on englisc hiw oððe gefegednyss. þara synt twa: SIMPLEX anfeald ET COMPOSITA and gefeged. Figura is called shape or figure in English. There are two of them. simplex single et composita and connected. þara DET:GEN.PL

synt be:3PL.PRS

twa two:NOM.F

It is difficult to identify constraints on the use of this construction most of all because Predicative Constructions are rare. It seems, we can only identify a very general property of the Predicative Construction, which is derived from its morphosyntactic features rather than from its distribution across the corpus. In contrast to all other instances of quantificational constructions, in this type, the specification of the cardinality is an independent proposition and thus syntactically a full clause. Semantically, the specification of the cardinality is the only piece of information attributed to the referent, whereas in other, more frequent quantificational constructions the quantified set is itself an argument of a more complex proposition. Thus, in other types of quantificational constructions, the quantifier modifies a noun phrase, which itself is only an argument of a predication, whereas in the Predicative Construction the predication as a whole consists of the specification of the cardinality. We may, therefore, conjecture that this construction is preferred if a set is quantified in a more generic way. With respect to these considerations, it is noteworthy that most translations into Present-day English prefer an existential there isconstruction. Cf. also examples (3.20) and (3.21) in § III.1.3.1. In examples (4.26)–(4.28), the quantified NP is in the subject position and the numeral is a part of the predicate. There is an interesting modification to this order, which is not uncommon. Examples (4.29), (4.30)a, and (4.31) show the numeral in the first position.

The Predicative Construction

209

(4.29) HomU 38 68 (NAPIER 1883[1967]: 245, 12): hit is gecweden and on halgum gewritum geræd, þæt ehta synd heafodgyltas. It is said and explained in the Holy Scriptures that there are eight capital sins. ehta 8

synd be:3PL.PRS

heafodgylt-as capital sin-NOM.PL

(4.30) BenRApp 134.3 (SCHRÖER 1885–1888: 134): Syx synt muneca cynerena, þara synt þreo þa selestan, þa oþere þreo þa forcuþestan and eallum gemete to forbugenne. There are six kinds of monks. Three of them are the best. The other three are the most reproved and to be avoided by all means. a.

syx 6

synt be:3PL.PRS

munec-a monk-GEN.PL

b.

þara synt DEM:GEN .PL be:3PL.PRS

cyneren-a kind-GEN.PL

þreo three(NOM.PL)

þa DET:NOM.PL

selest-an best-NOM.PL

(4.31) BenR 1.9.3 (SCHRÖER 1885–1888: 9, 3): Feower synt muneca cyn. Ðæt forme is mynstermonna, þæt is þara þe under regule and abbodes tæcinge on gecampe wuniað. There are four types of monks: the first is the man in a monastery; this is the one who lives under the rule, and in a struggle under the instruction of the abbot. feower 4

synt COP.PRS.3PL

munec-a monk-GEN.PL

cyn kind

It seems that this alternation is basically driven by information structure. The numeral stands in the clause-initial position if the cardinality is in the focus of the predication. Unfortunately, the number of instances of Predicative Constructions is far too small to test this by a reliable quantitative analysis. Information structural reasons for the alternation would, however, be the most plausible area to look for possible constraints if more data were available. (Cf. FISCHER 2001 for a similar claim on the position of attributive adjectives.) It is also noteworthy that in some of the above examples the quantified NP is in the genitive Case – (4.27), (4.28), and (4.30) – whereas in others, the quantified NP in a Predicative Construction is in the nominative, as in (4.26), (4.29) and (4.31). Anticipating what we will discuss in greater detail in the next major section of this chapter, we may say already here that the quantified NPs with genitive value cannot be considered ‘partitives’ in the sense we will

210

Numeral constructions in Old English

define them below. First of all, the genitive NPs in the Predicative Construction are syntactically not attributes to the numeral, whereas in Partitive Constructions they are; cf. below § IV.5.1. Moreover, later in §§ IV.5.2–3 we will identify clear constraints for encoding the genitive Case on the quantified NP. These constraints do not operate in the few instances of a Predicative Construction with quantified NP in the genitive: neither do the constructions in examples (4.27), (4.28), or (4.30) specify a subset of a larger set (§ IV.5.2.1) nor is its value ’20’ or higher (§ IV.5.2.2). Due to the very small number of instances of a Predicative Construction with the quantified NP in the genitive Case, we cannot but speculate about the status of these genitive NPs, but they may perhaps be best analysed as genitive subjects. We will now proceed to the third major type of quantificational construction, the Partitive Construction, which has just received a mention already. IV.5

The Partitive Construction

In the following, I will first introduce what I refer to as ‘Partitive Construction’ as a morphosyntactic pattern, without referring to the constraints or conditions which require its use (§ IV.5.1). The term partitive should be seen as a label. When we discuss the constraints for the Partitive Construction (§ IV.5.2), we will see that the term partitive, referring to a part of a whole, is motivated, strictly speaking, by one possible use of this construction, the quantification of a subset (§ IV.5.2.1) but not by all of its uses. We will see that the conditions requiring the use of the Partitive Construction operate on different levels and are thus not immediately linked. An attempt to account for the use of one construction under different, at least superficially quite unrelated constraints, will be made in (§ IV.5.3). IV.5.1

General

In contrast to both the various types of Attributive Quantification and the Predicative Construction, it is characteristic of the Partitive Construction that the quantified element is syntactically an attribute of the quantifier. The quantified element is generally in the plural and it is almost always in the partitive genitive, but occasionally it can also be an argument of an of-phrase. The Partitive Construction in Old English is illustrated by examples (4.32)–(4.35). Examples (4.32) and (4.33) are used by MITCHELL (1985 I: 217–218, § 550) to exemplify his ‘independent use’.

The Partitive Construction

211

(4.32) ÆCHom I.16 126 (CLEMOES 1997: 311): Se apostol paulus cwæð þæt we sceolon arisan of deaðe: on þære ylde þe crist wæs þa ða he þrowade: þæt is ymbe þreo & þrittig geara. The apostle Paul says that we will rise from death at the [same] age at which Christ was when he was suffering: that is at [the age of] thirty-three years. ymbe PREP

þreo (3

& +

þrittig 30)

gear-a year-GEN.PL

(4.33) Or4 9.101.10 (BATELY 1980: 101): [...] & on Romanum swa micel wæl geslog swa heora næfre næs ne ær ne siþþan æt anum gefeohte, þæt wæs feower & feowertig M, & þara consula twegen ofslog, & þone þriddan gefeng; [...] and [Hannibal] made such a great slaughter of the Romans as never had been made of them in one battle – neither before nor after this. There were 44.000, and [he] killed two of the consuls and captured the third. þara DET:GEN.PL

consul-a consul-GEN.PL

twegen two:ACC.M

(4.34) GenA 1335 (KRAPP 1931: 42): Ond ðu seofene genim on þæt sundreced tudra gehwilces geteled rimes, þara þe to mete mannum lifige, and þara oðerra ælces twa. And you take seven of each race on the ark, of those that live to feed men, and of the others two each. þara oðer-ra DEM:GEN .PL other-GEN.PL

ælc-es each-GEN.SG.N

twa two(ACC.N)

(4.35) ÆHom 24 37 (POPE 1967–1968: 738): He wearð ða gefullod æt ðam foresædan papan mid wife and mid cildum and mid gesibbum mannum and mid æhtemannum, ealles twelf hundred manna and fifti, [...] Then he was baptised with [his] wife, with [his] children, with [his] kinsmen, with [his] serfs, 1,250 people all together [...] twelf (12

hundred × 100)

mann-a and man-GEN.PL +

fifti 50

In (4.32), the relevant phrase is a complement of the preposition ymbe. The preposition assigns the accusative Case to the numeral but, in contrast to the prepositional phrase in (4.8) above (§ IV.3.1) it does not determine the Case value of the quantified noun, which is in the genitive. This genitive is, in turn, governed by the numeral in this construction type. In (4.33), the entire quan-

212

Numeral constructions in Old English

tificational construction is the direct object of the verb ofslog ‘kill\PST.3SG’ while only the numeral and not the noun is in the accusative, which is the Case required for the patient of a transitive predication. Example (4.32) differs from (4.33) and (4.35) only in so far as in (4.32), it is the preposition which assigns the Case value of the numeral while in (4.33) and (4.35), it is determined by the syntactic relation between subject and object. The main characteristic of the Partitive Construction is the lack of agreement in the syntactic and the semantic relationship between numeral and quantified noun. Semantically, the whole phrase in (4.33) denotes the patient, i.e. the victim of the killing. The element representing the victim, consula ‘consul-GEN.PL’, is the quantified noun. The numeral only modifies this noun the way an attribute does in that it provides additional information about the concept ‘consul’, thus narrowing down the extension of the referent. On the semantic level, the relation between numeral and quantified NP is generally the same as in the Attributive Construction (but cf. below § IV.5.2.1). As the phrase constituent denoting the patient of a transitive event, the quantified noun should syntactically be the direct object, which we would expect to be in the accusative in Old English (as in many other accusative languages). The quantified noun is, however, not in the accusative but in the genitive Case. It is the numeral which is in the accusative instead. Interpreting the relations indicated by the Case value of the two elements, the noun only provides a semantic link to the referent, while it is the inflection of the numeral which specifies the syntactic relation in the overall clause (direct object) and hence the semantic role of the relevant phrase (patient, victim of the killing). This relation – displayed in Table 23 (for which cf. KATZ 1982: 113 in a slightly different context) – seems to be a paradox. We will come back to this alleged paradox below in § IV.5.2.1. What is crucial at this point of the discussion is that in cases like the one exemplified in (4.33), it is the accusative value of the numeral which encodes that the referent of the noun, ‘consul’ in (4.33), is not the agent but the patient of the predication. The only function that remains for the quantified noun CONSUL is to denote the quantified set.

The Partitive Construction

213

Table 23. Paradox of semantic and syntactic structure of numeral and quantified NP in (4.33)

head of phrase

adjacent attribute

syntax

twegen

consul

semantics

consul

twegen

In a Partitive Construction, the quantified noun does not show any Number distinction in Old English as it is always marked for plural. Cf. (4.36) and (4.37) where the cardinality is ‘1’. In (4.36), for instance, the cardinality ‘1’ of the set of ‘birds’ would require the singular value. The noun FUGEL-A ‘birdGEN.PL’, however, is in the plural. Therefore, if quantification is encoded by means of a Partitive Construction, the quantified noun alone only refers to an abstract concept (i.e., a type) but not to the referent itself. Syntactically, it is the numeral that provides any additional information required for inferring a specific, context-dependent reference from a general concept (‘bird’, ‘consul’). The Case value of the numeral specifies the syntactic relation to the other elements of the predication. The Case value of the quantified NP, therefore, only needs to encode the (syntactically) attributive character of the NP to the numeral. The lack of a formal Number distinction in the NP is possible, because the semantic contribution of the numeral (the specification of a cardinality) is a sufficient indicator of the Number value, i.e. of the feature [± plural]. (4.36) ÆCHom II.10 86.194 (GODDEN 1979: 86): Ac an ðæra fugela eft fleogende com ymbe ðry dagas [...] But one of the birds came flying back after three days [...]. an one

þæra DET:GEN.PL

fugel-a bird-GEN.PL

(4.37) ÆCHom I.1 188.266 (CLEMOES 1997: 188): Ða wearð an þæra twelfa cristes þegena se wæs Iudas gehaten þurh deofles tyhttingge beswicen & he eode to ðam Iudeiscan folce & smeade wið hi hu he crist him belæwen mihte. Then, one of the twelve servants of Christ, who was called Judas, was seduced by the enticement of the devil; and he went to the Jewish people and considered with them how he could betray Christ to them. an one

þæra DET:GEN.PL

twelf-a 12-GEN.PL

crist-es Christ-GEN.SG

þegen-a servant-GEN.PL

214

Numeral constructions in Old English

In Old English, the partitive relation between numeral and noun does not necessarily have to be encoded by the Case value of the noun (genitive). As in many modern European languages – where a prepositional phrase has replaced most functions of the genitive Case – an of-phrase sometimes encodes the functions of the genitive in Old English; cf. (4.38). (4.38) Mk(WSCp) 14.13 (SKEAT 1871: 112): Ða sende he twegen of his leorningcnihtū & sæde hī; Gað on þa ceastre & inc agen yrnð, sū man berende sume wæterflaxan; Folgiað him. Then he dispatched two of his disciples and spoke to them: “Go to that town and a man will approach you carrying a jar of water. Follow him.” twegen of two(ACC.M) of

his PPRN :GEN .SG .M

leorningcniht-um disciple(M)-DAT.PL

Example (4.38) shows a Partitive Construction in which this is the case: the quantified element is not in the genitive Case ((4.32), (4.33), and (4.35)) but a complement of an of-phrase. While the Case value of the numeral twegen ‘2:ACC.M’ depends on the syntactic role of the entire quantificational construction, the quantified noun (LEORNINGCNIHT ‘disciple’) shows partitive marking (as in (4.32)–(4.35)). The beginning of the gradual replacement of the genitive by the of-phrase is usually dated to the twelfth century. There are, however, earlier instances of of-phrases in contexts in which the genitive would be common in Old English. Partitive Constructions with the quantified noun in an of-phrase are not only far less frequent than genitive nouns, but also rare in absolute terms before the twelfth century. Most of them are attested in the West Saxon Gospels. Some scholars have proposed the construction with a quantified noun in an of-phrase as a type of construction distinct from the Partitive Construction with a genitive; cf., e.g., MITCHELL (1985 I: 218, § 550); YEAGER (1993: 180). Formally, there are, of course, good reasons to distinguish between the two. I would argue, however, that the differences are superficial. What is crucial for the Partitive Construction is that a particular value or feature ‘partitive’ is encoded on the noun – irrespective of how this is formally realised. As we will see in the following sections (§§ IV.5.2–3), both formal variants of the Partitive Construction, the genitive NP and the of-phrase, are subject to the same constraints and should, therefore, be subsumed under one and the same category of quantificational constructions.

The Partitive Construction

IV.5.2

215

Constraints on the Partitive Construction

In § IV.3.1, we said that the Attributive Construction is the unmarked construction for numerically specific quantification. In the Partitive Construction, the syntactic and semantic relations of the two elements, numeral and quantified NP, do not correspond (cf. Table 23). The Number value is not relevant and the information otherwise provided by it is encoded alone by the semantic content of the numeral. To attribute a marked character to the Partitive Construction entails that its use is contingent on particular pragmatic, semantic, or syntactic conditions. The main difficulty in identifying these constraints lies in the syncretism of inflectional endings in Old English, especially in later texts. If we have the Case value of the two constituents of a quantificational construction – numeral and quantified NP – as the only evidence of whether a numeral is in an Attributive or in a Partitive Construction, a decision is in many instances difficult, if not impossible. The overall inflectional suffix marking the genitive plural in all noun classes and in all types of noun modifiers of Old English is -a. For a number of nominal stems, however, the suffix for the nominative/accusative plural is also -a and thus homophonous (and homographic) with this universal genitive plural marker. In fact, this is true of all feminine noun classes and of the masculine u-stems. Moreover, especially in later manuscripts, the suffix -a is generally employed for the nominative/accusative plural in noun classes other than the feminine and the u-stems. This applies particularly to r-stem nouns where in later texts forms like gebroðra ‘brethren’ are frequently nominative or accusative plural. In such potentially doubtful cases, only an adjacent determiner would allow for an unambiguous identification of the Case value. In the remaining instances in which the quantified NP can unambiguously be said to be in the genitive Case, the following two contexts can be observed. The Partitive Construction can be used if the cardinality specified by the numeral is ‘20’ or higher. Otherwise, there is a particular constraint which requires the Partitive Construction irrespective of the numerical value of the numeral. That is, if – in addition to the mere specification of the cardinality – the set denoted by the quantified element is a subset of a previously specified or contextually implied larger set, then the Partitive Construction is used. These two contexts in which the Partitive Construction is required will be discussed in the following subsections – the part-whole relation in § IV.5.2.1 and the high valued numerals in § IV.5.2.2.

216

Numeral constructions in Old English

IV.5.2.1 Quantification of a subset Whenever a context clearly suggests that the quantified referent constitutes a subset selected from a contextually given larger set, there is a part-whole relation between the two constituents of the quantificational construction. Usually the referent of the larger set, of which the quantified subset forms a part, is familiar to the recipient interlocutor. This normally requires the numeral to remain indefinite while the quantified noun should be definite. Examples (4.39)–(4.41) will illustrate this. (4.39) ÆLS (Maccabees) 490 (SKEAT 1881-1900 II: 98): Hwæt ða færlice comon fif englas of heofonum, and twægen þæra engla on twa healfe iudan feohtende wæron, and hine eac bewerodon. Then five angels came suddenly from heaven and two of these angels fought on both sides of Judas and [they] also protected him. a.

fif 5

engl-as angel( M)-NOM.PL

b.

twægen two:NOM.M

þæra DET:GEN.PL

engl-a angel(M)-GEN.PL

(4.40) ÆLS (Maur) 362 (SKEAT 1881-1900 I: 168): Twegen þæra muneca ðe mid him þyder comon forð-ferdon þær on þam fore sædan cwealme and twegen cyrdon ongean [...] Two of the monks who had come with him thither passed away in the aforesaid pestilence and two returned again [...]. twegen two:NOM.M

þæra DET:GEN.PL

munec-a monk(M)-GEN.PL

(4.41) ÆLS(Maur) 192 (SKEAT 1881-1900 I: 158): Ac ða þa hi swiþost tældon þone soðfæstan maurum þa wurdon afyllede mid ðam fulan gaste þry þæra wyrhtena [...] But while they were most fiercely insulting the righteous Maur, then three of the workers were filled by the foul spirit [...] þry three:NOM.M

þæra DET:GEN.PL

wyrht-ena worker(M)-GEN.PL

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The part-whole relation between the two elements is most obvious in example (4.39) because it allows us to compare two quantificational constructions in the same context. The first quantificational construction of this passage, fif englas in (4.39)a, is a prototypical Attributive Construction as discussed above in § IV.3.1. The ‘five angels’ constitute the set out of which two angels are selected as a subset in the second quantificational construction in (4.39)b (twægen þæra engla). Consequently, the second instance of a quantificational construction requires the Partitive Construction. Example (4.33) in § IV.5.1 – here repeated as (4.42) – shows that sometimes the part-whole relation becomes evident only through the wider context. The very beginning of chapter 9 in the fourth book of the Old English version of Orosius’ History gives an account of three consuls who attack Hannibal. 45 Later on in the chapter, the text reports on Hannibal’s counter-attack; cf. (4.42). In the course of this battle, Hannibal kills two consuls. These consuls are not any two consuls, but they belong to the group of three consuls mentioned at the beginning of the account. (4.42) Or 4 9.101.10 (BATELY 1980: 101, 14): [...] & on Romanum swa micel wæl geslog swa heora næfre næs ne ær ne siþþan æt anum gefeohte, þæt wæs feower & feowertig M, & þara consula twegen ofslog, & þone þriddan gefeng; [...] and [Hannibal] made such a great slaughter of the Romans as never had been made of them in one battle – neither before nor after this. There were 44.000, and [he] killed two of the consuls and captured the third. þara DET:GEN.PL

consul-a consul(M)-GEN.PL

twegen two:ACC.M

The use of the Partitive Construction in examples (4.34)–(4.42) must be accounted for by the part-whole relation between the quantified referent (subset) and the extension of the quantified NP (larger set). The larger set is known to the interlocutors and as such pre-established in the discourse. This means that the quantified NP is always definite. In (4.42), the respective phrase does not refer to any two consuls but to two consuls out of those three consuls who are already familiar to the recipient of the text. The numeral therefore always quantifies a subset of the extensional concept of the quantified NP. By contrast, in the Attributive Construction the numeral immediately specifies the extension of the quantified NP. In other words, while in the Attributive Con45 For an explanation of the unusual number of three consuls cf. the commentary to the respective passage in BATELY (1980: 287).

218

Numeral constructions in Old English

struction a subset of a potentially larger set is referred to (§ IV.3.1), in (this use of) the Partitive Construction, the construction refers to a subset of a contextually given larger set. Although these considerations suggest that the combination of a nondefinite numeral and a definite NP may suffice to encode a part-whole relation, there is no evidence that such an implication is conventional. In Old English, there are occasionally constructions – such as those in (4.43) and (4.44) – in which there is a combination of a non-definite numeral and a definite quantified noun but no partitive marking of the quantified NP. In spite of their low frequency in the existing Old English texts, these constructions might suggest that definiteness is a necessary prerequisite for encoding a part-whole relation but not the inverse, i.e. that the definiteness of the quantified noun generally requires a Partitive Construction. (4.43) Or 1 1.14.30 (BATELY 1980: 14–15): Swiþost he for ðider, toeacan þæs landes sceawunge, for þæm horshwælum, for ðæm hie habbað swiþe æþele ban on hiora toþum þa teð hie brohton sume þæm cyninge [...]. He travelled thither very fast, because of – in addition to the inspection of the country – the walruses, because they have very valuable bone in their teeth. They brought one [of] the teeth to the king [...]. þa

teð tooth(M)\ACC.PL

DET:ACC.PL

sum-e one-ACC.SG.M

hie PPRN :NOM.PL

þæm DET:DAT.SG.M

broht-on bring\PST-PL

cyning-e king(M).DAT.SG

(4.44) ÆLS (Julian&Basilissa) 65 (SKEAT 1881–1900 I: 94): [...] and twegen his halgan mid twam cynehelmum, arærdan hi þa upp and heton hi rædan. […] and two [of] his saints with two crowns then raised them up and told them to read twegen two:NOM.M

his PPRN :GEN .SG .M

halg-an saint(M)-NOM.PL

The constructions in (4.43) and (4.44) are extremely rare and it is impossible to find an adequate explanation for them. To say the least, their number is too small to question our general analysis of the part-whole relation as one use of the Partitive Construction. It is noteworthy, in any case, that (4.43) and (4.44) represent exactly that type of quantificational construction which HAWKINS (1983: 161–162; examples 3.181 and 3.183) rules out for Present-day English

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219

and on the basis of which he explains the conditions of a Partitive Construction (in Present-day English): definite reference is used when the set of objects referred to is known or can be implied by the hearer. Indefinite reference does not do the opposite but is indifferent to this parameter. If the reference is indefinite but, at the same time, the speaker wants to specify that the set denoted is part of a previously known set, then the indefinite numeral must be combined with a definite quantified NP; cf. HAWKINS (1978: 175). Bearing this in mind, let us briefly return to the alleged paradox between the semantic and the syntactic structure of Partitive Constructions, which we discussed in § IV.5.1 above (cf. Table 23). From what we said about the Partitive Construction, it is clear that in examples like (4.33)/(4.42), the cardinality is the only piece of information within the respective phrase which is newly introduced in the discourse. From this perspective, the numeral – although semantically a modifier to the noun – contributes the most relevant piece of information. IV.5.2.2 Quantification by high valued numerals Numerals valued ‘20’ or higher often have a quantified element in the partitive genitive. Example (4.45) conveniently shows how all multiples of ‘10’ and all multiples of a higher base ((4.45)a and all the following quantificational constructions) are in a Partitive Construction while the only numeral in an Attributive Construction ((4.45)b) has a value below ‘20’. The same can be observed with regard to the simple base numerals HUND(RED) (4.46) and ÞUSAND (4.47) and for other complex numerals as in (4.48). (4.45) Gen 32.13 (CRAWFORD 1922[1969]: 165): He asyndrode ða lac of þam ðe he hæfde Esauwe hys breðer, Twahund gata & twentig buccena, & twahund ewena & twentig rammena. Þrittig geflora olfendmyrena mid heora coltum, & feowertig cuna, & twentig fearra, & twentig asmyrena mid hyra tyn coltum. He separated the gift that he had [for] Esau, his brother: 200 she-goats, 20 hegoats, 200 ewes, 20 rams, 30 milch-camels with their young, 40 cows and 20 bulls and 20 she-asses with their ten young. a.

twa-hund 2 × 100

b.

tyn 10

gat-a goat(F)-GEN.PL

colt-um colt-DAT.PL

220

Numeral constructions in Old English

(4.46) Ruin 6 (KRAPP/DOBBIE 1936: 227): Eorðgrap hafað waldend wyrhtan forweorone, geleorene, heardgripe hrusan, oþ hund cnea werþeoda gewitan. The earth’s embrace has the rulers [and] builders, who have perished [and] are lost, by strong seizure, until 100 generations of men have passed away. hund 100

cne-a generation-GEN.PL

werþeod-a people-GEN.PL

(4.47) ÆCHom I.31 446.205 (CLEMOES 1997: 446): Þa wearð se cyning Astriges gehathyrt, and sende ðusend gewæpnodra cempena, þæt hi ðone apostol gebundenne to him bringan sceoldon. Then, King Astryges was enraged and sent a thousand armed warriors that they bring the apostle bound to him. ðusend 1,000

ge-wæpn-od-ra CIRC-arm- PTCP-GEN .PL

cemp-ena fighter-GEN.PL

(4.48) ByrM 3.2.252 (BAKER/LAPIDGE 1995: 158): Tellað þreo and twentig daga fram æfterweardum Martium upweard and hawiað mid hluttre gesihðe hwær beo VII idus Martii. Count 23 days from the end of March, and observe clearly where the 7th ide of March is. þreo (3

and +

twentig 20)

dag-a day-GEN.PL

This generalisation describes a strong tendency but does not apply categorically. It is generally impossible to find a regular pattern for quantificational constructions with numerals valued ‘20’ or higher. All we can say about these constructions is that the Attributive Construction is rare with high numerical values and that the Partitive Construction can be taken as the regular case for numerical values above ‘19’. Apart from this statement, we can only observe that Attributive Constructions – where they do occur with high valued numerals – are generally much more common with multiples of ‘10’, less common with other complex numerals, and extremely rare with the higher bases. However, if the numeral above ‘19’ and the quantified noun form the complement of a preposition and the preposition requires the dative Case, the relation between the two is usually attributive; cf. (4.49) and (4.50).

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221

(4.49) ÆLS (Maccabees) 620 (SKEAT 1881–1900 II: 108): Nicanor þa eft genam oðre fyrde of Sirian, wolde his gebeot mid weorcum gefremman; and Iudas him com to mid þrim ðusend cempum, and gebæd hine to Gode gebigedum limum þus, [...] Then Nicanor again took another troop from Syria; he wanted to suit the action to the words, and Judas came to him with 3,000 warriors, and prayed thus to God with bent limbs: [...] mid PREP

þrim 3:DAT

ðusend [×] 1,000

cemp-um fighter-DAT.PL

(4.50) Judg 4.6 (CRAWFORD 1922[1969]: 404): Ða asende him God sumne heretogan to, Barac gehaten, & he þa ferde mid tyn þusend mannum to þære burnan Cison,[...] Then God sent them a commander, who was called Barak, and then he went with 10,000 men to the torrent of Kishon [...] mid PREP

tyn 10

ðusend [×] 1,000

mann-um man-DAT.PL

Attributive Constructions are also more likely to be found in late charter copies or other texts in which the apparent decline of the inflectional system often causes a less accurate distinction of inflectional endings than we may find, for instance, in manuscripts of the Classical Old English period. However, since according to BRUGMANN (1911: 43, § 36) the base ‘100’ was obligatorily used in the Partitive Construction in Proto-Indo-European – as were both ‘100’ and ‘1,000’ in Proto-Germanic (cf. BRUGMANN 1911: 49, § 43) – we can assume that this constraint is old but in the process of being weakened during the Old English period. The situation is similarly vague when it comes to the inflection of the particular constituents of the complex numeral. Not only are inflectional endings of the numerals from ‘4’ onwards used inconsistently, but there are also various combinations of inflected and uninflected constituents in complex numerals. Cf. § II.2.4 and see further CAMPBELL (1959: 285, §§ 686–691). Examples are shown in (4.51) and (4.52), which we discussed already in § III.1.3.2 as (3.25) and (3.26). There, we took these complex numerals as evidence for the syntactic independence of the individual constituents in a complex numeral.

222

Numeral constructions in Old English

(4.51) ÆLet 2 50 (FEHR 1914 [1966]: 92) – as (3.25) above in § II.2.3.2: Þa coman þær togædere on nycea byrig þreo hund bisceopa & XVIII bisceopas. Then, 318 bishops came together there in the city of Nice. þreo 3

hund × 100

bisceop-a bishop-GEN.PL

and +

XVIII

18

bisceop-as bishop-NOM.PL

(4.52) HomU 44 38 (NAPIER 1883 [1967]: 284, 2) – as (3.26) above in § III.1.3.2: hwæt, we witan, þæt on XII monþum beoð III hund daga and sixtig daga and fif dagas and eac six tida; […] Hwæt, we know that on twelve months, there are 365 days and six hours […] hund dag-a 3 × 100 day-GEN.PL III

and +

six-tig 6 × 10

dag-a day-GEN.PL

and +

fif dag-as 5 day-NOM.PL

There are cross-linguistic parallels of similar constraints on related construction types. HURFORD (2002: 53, § 5.3.3.2) mentions a case in a non-cognate language. In Finnish, whenever the quantified NP is in the nominative or accusative, the base numerals kymmenen ‘10’, sata ‘100’, tuhat ‘1,000’, and miljoona ‘106’ are in the partitive Case while the other constituents of a complex numeral agree in Case with the quantified noun. If the quantified noun is in a Case other than the nominative or accusative, each constituent of the complex numeral takes the same Case. NELSON/TOIVONEN (2000: 182–186) report a similar case in Inari Sami (Uralic) where a lexically/semantically motivated Case marking overrules the Cases usually assigned by the numeral. Romanian even seems to have exactly the same constraint as Old English: if the cardinality is ‘20’ or higher, Romanian requires the quantified noun to be a complement of the preposition de ‘of’; cf. STOLZ (2002: 356). IV.5.3

A uniform account of the Partitive Construction

While the Partitive Construction, as shown in § IV.5.2.1, is required under certain discourse or information structural conditions (quantification of a subset), the other constraint on the use of the Partitive Construction depends on the cardinality of the quantified referent, irrespective of the context (§ IV.5.2.2). Therefore, although requiring a common morphosyntactic strategy, these two constraints operate independently. Superficially, this reduces the Partitive Construction to a morphosyntactic pattern, i.e. to a merely formal device without having any inherent function per se.

The Partitive Construction

223

What may, however, give us a clue to a uniform account of the Partitive Construction is the fact that the quantified noun lacks a distinction of both the Case value (its Case is always genitive or, in rare cases, is a complement of an of-phrase which, in our context, can be taken as functionally equivalent to the genitive) and the Number value (which is always plural). Lack of Number distinction becomes obvious when the cardinality is ‘1’ because in these cases, the quantified NP is still in the plural; cf. (4.36) above in § IV.5.1. In a number of instances, however, high valued numerals show a lack of Number agreement in yet a different way, i.e. their Number value does not agree with that of the verb. MITCHELL (1985 I: 221–222, §§ 562–564) provides examples of quantificational constructions with high valued numerals in which there is no Number agreement between the verb and the respective quantificational construction. In (4.53)–(4.55), the verb is singular even though the cardinality of the subject is not ‘1’. According to the morphosyntactic features of these passages, it seems as if the referent in each of the respective quantificational constructions is ‘de-individualised’, which means that it is taken as an aggregate or an abstract concept rather than as a set of individuals. If this is the case, then the plural value of the quantified NP is an inherent feature of the Partitive Construction and thus independent of the semantic plurality of the referent – even with cardinalities above ‘20’. (4.53) Or 1 1.9.31 (BATELY 1980: 9): On Indea londe is XLIIII þeoda buton þæm iglande Taprabane, þæt hæfð on him x byrg, buton oðerum monegum gesetenum iglondum. In India, there are 44 nations except on the island of Taprobane which has 10 towns in it, [and] besides many other inhabited islands. on PREP

Inde-a Indian-GEN.PL

lond-e is land-DAT.SG be:3SG.PRS

XLIIII

44

þeod-a nation-GEN.PL

224

Numeral constructions in Old English

(4.54) Or 3 9.72.26 (BATELY 1980: 72): Þa he com on India eastgemæra, þa com him þær ongean twa hund þusenda monna gehorsades folces When he came to the eastern confines of India, 200,000 men of a riding tribe were coming towards him. þa com him þær ongean then come\3SG.PST PPRN:DAT.SG.M there against twa hund þusend-a 2 × 100 [×] 1,000-GEN.PL) ge-hors-ed-a CIRC-horse-PTCP-GEN.PL

monn-a man-GEN.PL

folces tribe.GEN.SG

(4.55) Bede 3 17.232.30 (MILLER 1890–1898: 232): Mid þy þa broðor þa gehyrdon, þa þe in his mynstre wæron in Eastseaxna mægðe, heora biscop forðferendne & bebyrgedne in Norðanhymbrum, þa eode heora þritig of þam mynstre & þider cwomon. [...] then thirty of them came there from the monastery þa then

eo-de go(PST)-PST.SG

heora PPRN :GEN .PL

þritig 30

There are similar cases which differ from the cases shown in (4.53)–(4.55). These are constructions with forms of the verbs BEON ‘be’ or WEORÐAN ‘become’ plus a past participle as, for instance, in (4.56) and (4.57). (4.56) Or 1 8.27.1 (BATELY 1980: 27): Ær ðæm ðe Romeburh getimbred wære syx hund wintran & fif, in Egyptum wearð on anre niht fiftig manna ofslegen, ealle fram hiora agnum sunum; & ealle ða men comon fram twam gebroðran. 605 years before Rome was built, there were 50 men killed on one night in Egypt, all by their own sons, and all the men descended from two brothers. wear-ð [...] become\PRS-3 SG […]

fiftig mann-a ofsleg-en 50 man-GEN.PL slay\PTCP- PTCP

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225

(4.57) Or 3 9.69.2 (BATELY 1980: 69): Þær wæs Persa X M ofslægen gehorsedra, & eahtatig M feþena, & eahtatig M gefangenra There were 10,000 mounted Persians killed and 80,000 infantrymen and 80,000 [were] prisoners. a. b.

þær wæs Pers-a there be(PST.3SG) Persian-GEN.PL & and

eahtatig M 80,000

& and

XM

10,000

ofslæg-en slay\PTCP- PTCP

feþ-ena infantryman-GEN.PL

eahtatig M 80,000

ge-fang-en-ra CIRC-capture- PTCP-GEN .PL

(4.58) CP 13.77.15 (SWEET 1871: 77): On ðæm selfan hrægle, ðe he on his breostum wæg, wæs eac awriten ða naman ðara twelf heahfædera. On the same vestment that he wore on his breast, there were also written the names of the twelve patriarchs. wæs eac be(PST.3SG) also ðara DET:GEN.PL

awrit-en ða nam-an write\PTCP-PTCP DET:NOM.PL name-NOM.PL

twelf heahfæder-a 12 patriarch-GEN.PL

These are all passive constructions without an overt agent. Whether, or to what degree the singular value of the verb is enforced by the agentless passive structure may be speculated. In any case, from the evidence of (4.56)–(4.58), we may generally note that the combination of singular verb and plural quantified NP – although extremely rare – further illustrates the absence of Number distinction with numerals valued ‘20’ or higher and with the Partitive Construction in general. Lack of Number agreement is occasionally attested in a particular kind of Measure Construction, which involves the genitive Case, but is distinct from the Partitive Construction. The relevant examples will be discussed below in § IV.6.46 As a preliminary summary, we may say at this point that the Partitive Construction in Old English is primarily a morphosyntactic pattern. Where there is a part-whole relation between a quantified subset and a contextually pre46 BAUCH (1912: 51–52) and STOELKE (1916: 13–17 and 33) provide a considerable number of Old English examples in which the quantificational construction and the verb do not agree in their Number values. Some of their instances can, however, be accounted for as Partitive Constructions. The others are all agentless passive constructions as in (4.56)– (4.58).

226

Numeral constructions in Old English

defined larger set denoted by the NP, the use of the Partitive Construction hardly requires any further explanation because morphosyntactic strategies encoding ‘possession’ such as the genitive Case and the of-phrase are common devices for expressing a part-whole relation with or without the context of quantification. By contrast, an attempt at an explanation of the use of the Partitive Construction with high valued numerals appears to be more complex and also perhaps more speculative: it may be that, in these cases, larger quantities are treated as a collective rather than as a set of individuals. This is suggested by the lack of Number distinction on the quantified NP and, in a few cases, also on the verb. It is generally conceivable that – perhaps as a remainder from a stage when the scope of the numeral system did not exceed the numerical value ‘20’ – any referent with a higher cardinality is treated as an aggregate rather than as a set of individuals. TRAUGOTT (1992: 180), for instance, explaining the singular value of the verb in (4.56) (TRAUGOTT’s example (30)) as triggered by a base numeral or by a multiple of it, concludes that these higher cardinalities may be perceived as collectives. The postulate of an extinct Number value ‘collective’ in Proto-IndoEuropean – proposed, among others by EICHNER (1985), but going back to an old discussion in Indo-European linguistics; cf. SCHMIDT (1889: 1–37) – might perhaps point in the same direction. EICHNER (1985: 136) assumes a morphological Number value ‘collective’ in addition to ‘singular’ and ‘plural’ at least for some Proto-Indo-European nouns. He discusses the semantic implications of the use of different plural forms for the same noun in Homeric Greek, Classical Latin and Hittite and refers to a regular lack of agreement in Number between verb and noun in Hittite (EICHNER 1985: 139–150). What is particularly interesting in our context is that one of the nouns that may show the postulated ‘collective’-forms is PIE *(d)kṃtóm-h2 ‘100’ (EICHNER 1985: 166–167). Although, synchronically, the use of the Partitive Construction with high valued numerals is clearly primarily a formal feature and not necessitated by semantics, it is feasible to draw a connection between traces of a ‘collective’ Number value for nouns in the proto-language and some inconsistencies in Number agreement in the daughter languages. Generally, nouns denoting aggregates are always more difficult to categorise within a ‘singular’/‘plural’dichotomy. Cf. the variety of systems for ‘singular’/‘plural’/‘mass’distinctions sketched by GIL (1996: 61–62). It is, in any case, feasible to draw a connection between a lack of discreteness, higher cardinalities and a lack of Number distinction. CORBETT raised this point in the context of the integration of new, higher bases into the numeral system. He writes that “it is easier to view, say, a group of four as individuals than a group of 100. Thus individua-

The Partitive Construction

227

tion (which favours semantically justified agreement forms) is inversely proportional to numerical value.” (CORBETT 1983: 246) While it has been our main concern here to describe the Partitive Construction and the two constraints that require it in Old English, we will resume the connection between the countability of nouns and the features of particular quantificational constructions at later points. It will be relevant for the quantification of mass nouns (§ IV.7). The morphosyntactic features of the Partitive Construction will also become relevant again in § V.3.2 when we re-examine the quantificational constructions of Old English in a cross-linguistic context. IV.6

Measure Constructions

Measure constructions are, strictly speaking, not a distinct type of quantificational constructions in the sense we have distinguished them by in the foregoing sections. The relation between numeral and quantified NP in a Measure Construction can be classified as either Attributive or Partitive. The very particular application of the numeral in measuring and its possible syntactic and morphosyntactic formal instantiations requires a treatment of the Measure Construction separate from the typology proposed in §§ IV.3–5. It will, moreover, provide the basis for the discussion of another major type of quantificational construction – the quantification of mass terms – which we will discuss in § IV.7. For the quantification of non-discrete entities, the particular properties of Measure Constructions are essential prerequisites. IV.6.1

The nucleus of a Measure Construction

The notion of ‘measuring’ is used here in a general sense in contradistinction to numerical quantification. Numerical quantification and measuring are the two possible applications of cardinal number assignment; cf. BENACERRAF (1965: 49); WIESE (1995b: 213–215). While in numerical quantification the size of a set of individual items is specified (cf. § I.2), in measuring, a property of the measured entity is characterised by the cardinality of a conventionalised unit of measurement. In other words, while numerical quantification specifies the cardinality of a set, measuring specifies the extent or the amount of a particular property of the referent. The extent of a property of a set is usually referred to by means of more or less conventionalised units (e.g. OE PUND

228

Numeral constructions in Old English

‘pound’, FOT ‘foot’, DÆG ‘day’, WINTER ‘winter, year’, etc.).47 These units, in turn, are quantified by cardinal numbers. Measurement, therefore, mediates between the relevant property of the set – typically length, time, weight, etc. – and cardinalities; cf. WIESE (1995b: 185–189 and 202–203). It should be noted that both measuring and numerical quantification are numerically specific in the sense we have defined it in § I.1 and are thus distinct from numerically unspecific quantification by means of notions like ‘many’, ‘all’, etc. Like any other quantificational construction, a Measure Construction generally consists of two elements, a numeral and a quantified element. In Measure Constructions, the element modified by the numeral is the appropriate unit of measurement. Numeral and unit of measurement form the nucleus of a Measure Construction. The syntactic relation between numeral and unit of measurement is subject to the same constraints as the relation between numeral and quantified NP in any other quantificational construction: the numeral is an adjacent attribute to the unit of measurement unless it is a high numeral, in which case the unit of the two are in a partitive relation as described in § IV.5. Accordingly, the nucleus of a Measure Construction has the following structure: [NUM → MEAS] In this and the following formal representations, the arrows indicate ‘x modifies (i.e. quantifies or measures) y’. The order of the elements does not necessarily correspond to the element order of every instance of a particular construction or clause, but it represents the most common element order of the relevant type in Old English. NUM stands for ‘cardinal numeral’ and MEAS for ‘unit of measurement’. As we will see in the following sections, some Measure Constructions are quite complex, which means that the process of quantification/measuring is carried out in several steps. In all Measure constructions, the numeral quantifying the unit of measurement ([NUM → MEAS]) forms the first step in the quantification process while the thus formed nucleus in turn quantifies/measures further elements until the ultimate target of quantification is reached. The hierarchy of these steps is indicated by the square brackets and the arrows.

47 I do not distinguish between conventionalised units of measurement like ‘metre’, ‘inch’ etc. and culturally salient objects of comparison like ‘glass’, ‘handful’ etc. The use of salient objects like ‘foot’, ‘stone’, or ‘cup’ as standardised units shows that this distinction is fuzzy anyway.

Measure Constructions

IV.6.2

229

Measuring predicates

The simplest form of a Measure Construction quantifies predicates. Almost every instance of this construction is a temporal adverbial. Thus, while the numeral quantifies the unit of measurement and thereby forms a Measure Construction, the Measure Construction as a whole modifies the predicate (here indicated, without any intended theoretical implication, as “VP”). Accordingly, in (4.59)–(4.61) we find the following construction: [[NUM → MEAS] → VP] (4.59) ÆCHom II.30 237.75 (GODDEN 1979: 237): Efne nu ðreo gear ic sohte wæstm on ðisum fictreowe. and nænne ne funde; “Behold now, for three years I have sought fruit on this fig tree and found none.” (transl. THORPE 1846: 409) ðreo three:NOM/ACC.N

gear year(N)[NOM/ACC.SG]

ic I

soht-e seek\PST-1SG

(4.60) LS 8 163 (SKEAT 1881–1900 II: 200): Þa on niht genamon heora twægen suna, and ferdon to egypta lande, soðlice æfter þam þe hi ferdon twegen dagas, þa comon hi to sæ, and þær gemetton hi scip standan and hi on þæt eodon and mid him reowan. Then, at night, they took their two sons and travelled to Egypt. Truly, after they had been travelling for two days, they came to the sea and found a ship standing there and they went on it and rowed [away] with it. hi PPRN :NOM.PL

fer-d-on travel-PST- PL

twegen two:NOM.M

dag-as day(M)-NOM.PL

(4.61) ÆCHom II.33 249.10 (GODDEN 1979: 249): Ic fæste twegen dagas on þære wucan and ic teoðige ealle mine æhta. I fast two days a week and I tithe all my belongings. ic I

fæst-e twegen fast-1SG.PRS two:NOM.M

dag-as day(M)-NOM.PL

We can see that in this type of Measure Construction, the relation between numeral and unit of measurement follows the same constraints as in all other quantificational constructions. The relation between the two constituents is

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Numeral constructions in Old English

generally attributive; cf. (4.59)–(4.61). Only high numerals require a Partitive Construction; cf. (4.62). The types of Measure Constructions discussed in the following sections, by contrast, show morphosyntactic strategies that diverge from those of the main types discussed so far in §§ IV.3–5. (4.62) ÆGram 285.11 (ZUPITZA 1880 [2001]: 285): [...] millenarius þusendfeald getel oððe se ðe leofað þusend geara, swaswa dyde MATVSALAM buton an and þrittig geara. millenarius : thousandfold number or the one who lives for thousand years, as did Methuselah minus 31 years. leof-að þusend live- PRS.3SG 1,000

IV.6.3

gear-a year-GEN.PL

Measuring arguments

If the target of measuring is in an argument position, then the nucleus of the Measure Construction forms an immediate attribute of the measured element. Prototypically, the measured element is a simple noun or a noun phrase (here interchangeably referred to as ‘measured NP’); cf. (4.63) and (4.64). [[NUM → MEAS]GEN.PL → measured NP] (4.63) MSol 406 (DOBBIE 1942: 45): Swilc bið seo an snæd æghwylcum men selre micle, gif heo gesegnod bið, to ðycgganne, gif he hit geðencan cann, ðonne him sie seofon daga symbelgereordu. Likewise the one piece [of the host] is much more honourable for any man to receive, if it is blessed so that he can remember it, than a carousal [lasting] seven days may be granted to him [lit.: ‘be to him’]. seofon 7(GEN)

dag-a day-GEN.PL

symbelgereord-u carousal-NOM.PL

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231

(4.64) HomS 16 29 (A SSMANN 1889[1964]: 145): And he eac on anum dæge mid ungesceade and mid micelre synne forspilð þreora daga oððe feowera andlifene [...] And he also unreasonably and very sinfully wasted the ration of three or four days on one day [...] þreo-ra three-GEN.PL

daga day-GEN.PL

oððe feower-a or 4-GEN.PL

andlifen-e food/money-ACC.SG

If the Measure Construction has a structure like that displayed in these examples, i.e. if it alone modifies a noun, the construction generally has a temporal implication. In (4.63), it is the duration of the carousal which is indicated by the Measure Construction. In (4.64), the Measure Construction indicates the length time which a certain ration of food will last. (For a syntactically similar instance that exceptionally does not refer to a concept of ‘duration’, cf. example (4.74) below in § IV.6.4.) This type requires that the nucleus (numeral + unit of measurement) as a whole be in the genitive plural if it modifies an argument and not a predicate. The problem is that, since most numerals are generally not inflected, the respective nuclei usually look like Partitive Constructions. Because the genitive numeral does not show inflection, it looks like a nominative or accusative form. And since the quantified noun, the unit of measurement, is in the genitive Case, the construction looks as if the morphosyntactic relation between the two elements of the nucleus is the same as in the Partitive Construction. However, this genitive has an attributive function rather than a partitive one. In his description of equivalent constructions in Old Norse, FAARLUND (2004: 61) calls these nuclei ‘descriptive genitives’. If there were not a small number of instances with regularly inflected numerals, it would be impossible to tell that both elements of the nucleus, numeral and unit of measurement, are in the genitive. While (4.63) resembles a Partitive Construction because the numeral is uninflected and therefore could have any Case value, (4.64), owing to the overt inflection of the two numerals þreor-a ‘3-GEN.PL’ and feower-a ‘4-GEN.PL’, shows that the nucleus as a whole is in the genitive Case. Cf. § IV.6.6 where this point will be discussed further. A fossilised variant of this construction is the following, very common method for measuring time. In this construction, a noun, itself modified by the nucleus like in (4.63) and (4.64), modifies a verb. The two nouns usually employed in this type are FÆC (4.65) and FYRST (4.66). They both mean ‘period of time’.

232

Numeral constructions in Old English

(4.65) Nic(A) 15.1.12 (CROSS 1996: 185, 1): And hig sona eond þa muntas foron þreora daga fæc ac hig hyne nahwær fyndan ne myhton And then they travelled throughout the mountains for three days but they could not find him anywhere. for-on travel\PST-PST.PL

þreo-ra three-GEN

dag-a day-GEN.PL

fæc period

(4.66) GD 3 16.211.21 (HECHT 1900: 211): & hit þa þus seo nædre & se halga wer singallice heoldon þreora gæra fyrst betweoh heom. And then, the serpent and the holy man both continued to do this between each other for three years. heold-on hold\PST-PST.PL

þreo-ra three-GEN

dag-a day-GEN.PL

fyrst period

Examples (4.65) and (4.66) show constructions with the following structure: [measured verb ← [[NUM → MEAS]GEN.PL → FÆC / FYRST]] Note that, as stated above, the order of elements in these formalisations represents the most common (but not necessarily the exclusive order) in Old English. The arrow pointing to the left is a consequence of this. In accordance with what we said in § 6.1, it indicates that the ultimate target of the measuring process is the verb, which is (most commonly) followed by nucleus and FÆC / FYRST. The structure suggests that this construction is derived from the one displayed in (4.63) and (4.64) with FÆC or FYRST being the former target of the measuring. This construction as a whole now measures the duration of events expressed by verbs. Hence, the ultimate target of the Measure Construction in (4.65) and in (4.66) is a verb. The relative frequency of this type suggests that it is idiomatic. This construction will also play a role in the quantification of mass terms discussed in § IV.7. IV.6.4

Measuring properties

If a referent is modified by a measure other than time, an adjective indicating the type of measurement is required. These adjectives are predominantly adjectives of distance (i.e., WID ‘wide’, SCEORT ‘short’, DEOP ‘deep’, BRAD

Measure Constructions

233

‘broad’, HEAH ‘high’, LANG ‘long’), as in (4.67) and (4.68), less frequently of age (EALD ‘old’), as in (4.69), or value (WEORÐ ‘worth’), as in (4.70). The inflection of the adjective and, if present, of the determiner is dependent on the measured noun. [[[NUM → MEAS]GEN.PL → measured NP] → adjective] These measured adjectives can be used attributively, as in (4.67), (4.69) and (4.70) or predicatively, as in (4.68). If they are used predicatively, their structure is the following: [measured NP ← [COP + [[NUM → MEAS]GEN.PL → adjective]]] (4.67) Bede 1 9.46.2 (MILLER 1890–1898: 46): & hi him ða eac to ræde & to frofre fundon, þæt hi gemænelice fæsten geworhten him to gescyldnesse, stænene weal rihtre stige fram eastsæ oð westsæ [...]: ðone man nu to dæg sceawian mæg eahta fota bradne & twelf fota heanne. “They also thought it advisable and helpful, that they should construct a general line of fortification for their protection, that is a stone wall in a straight line from the sea on the east to the sea on the west [...]: this may still be seen, and is eight feet broad and twelve feet high.” (transl. MILLER 1890– 1898: 47). a.

eahta 8(GEN)

fot-a brad-ne foot(M)-GEN.PL broad-ACC.SG.M

b.

twelf fot-a hea-nne 12(GEN) foot(M)-GEN.PL high-ACC.SG.M

(4.68) Or 1 1.15.26 (BATELY 1980: 15): [...] he cwæð, þær hit smalost wære, þæt hit mihte beon þreora mila brad to þæm more [...] [...] he said that where it [the land] was narrowest, it might be three miles broad to the wasteland [...] hit PPRN :NOM.SG.N

þreo-ra three-GEN

miht-e be able\PST- SG.SBJV mil-a mile(F)-GEN.PL

beon be(INF)

brad broad[NOM.SG.N]

234

Numeral constructions in Old English

(4.69) Comp 8 2 (NAPIER 1889: 6): On ðreora nihta ealdne monan wanað se sæflod oþþæt se mona bið XI nihta eald oþþe XII. At the three-day-old moon, the tide is waning until the moon will be eleven or twelve years old. on PREP

ðreo-ra three-GEN.PL

niht-a eald-ne night(F)-GEN.PL old-ACC.SG.M

mon-an moon(M)-DAT.SG

(4.70) Rec 9.1 26 (ROBERTSON 1956: 254, 13): Þæt is þo[nne] ealles geseald of Elig to ðornige butun hyra scrudfeo þe [...] lste, on golde & on s[eolfre] syxtena punda wyrþ butun feowertigum penegun. “The value of the total amount given by Ely to Thorney (apart from the money of their clothes which [...] is 16 pounds in gold and [silver] less 40 pence).” (transl. ROBERTSON 1956: 255). hyra PPR:GEN .PL syxten-a 16-GEN.PL

scrudfeo money for clothes(N) pund-a pound-GEN.PL

[…] […] wyrþ worth[NOM.SG.N]

We can see that in (4.67), (4.69), and (4.70), the nucleus and the adjective together modify the measured NP. In (4.67), the adjectives BRAD ‘broad’ and HEAH ‘high’ are both marked for accusative masculine and hence agree with the demonstrative ðone ‘DEM:ACC.M’, which in turn modifies the masculine noun WEAL ‘wall’ mentioned in the previous clause. The adjectives and the determiner all constitute the object complement of the verb SCEAWIAN ‘see, observe’. A more literal rendering of (4.67) would therefore be: ‘This eight feet wide and twelve feet high one [i.e. the wall] may still be seen’. In (4.67) and in (4.70), the difference in the use between Old and Present-day English can be seen in the translation of the respective editors who add a copula and thus transfer the nucleus and the adjective into the predicate position.48 Whereas, as we said, the nucleus of a Measure Construction is as a whole in the genitive plural, there are a few instances of this particular type of Meas48 For this particular type cf. the short treatise On the Length of Shadow in ms. Tiberius A.iii (Comp 12.2; COCKAYNE 1864–1866 III: 218–222). It is a short text on the varying length of shade during the year. It consists of a number of parallel sentences, all containing the sequence [numeral + fota]. They generally specify that, on a particular occasion, the shade has a particular length measured in feet. In only very few cases is the adjective lang adjacent to the nucleus consisting of numeral + fota. In most cases, the construction is used elliptically, consisting only of the numeral and the unit of measurement fota.

Measure Constructions

235

ure Construction in which the numeral is in the genitive singular. Whereas in (4.67)–(4.70) both numeral and the quantified unit of measurement are in the plural, in (4.71)–(4.73) both parts of the nucleus are in the genitive Case, but the immediately quantified noun, the unit of measurement, shows the genitive plural while the numeral has a genitive singular ending. (4.71) CP 49.385.13 (SWEET 1871: 385): For ðissum ilcan ðingum wæs ðætte ure Aliesend, ðeah he on hefenum sie Scieppend & engla lareow, nolde he ðeah on eorðan bion monna lareow, ær he wæs ðritiges geara eald [...] For the same reasons it was that our Saviour – although he was the Creator and master of the angels in heaven – did not want to be the master of mankind on earth before he was thirty years old [...] ðritig-es 30-GEN.SG

gear-a eald year-GEN.PL old

(4.72) Or 4 6.93.31 (BATELY 1980: 93, 33): Þa hio gefylled wæs, he het hie behyldan, & þa hyde to Rome bringan, & hie ðær to mærðe aðenian, for þon heo wæs hund-twelftiges fota lang. When it [i.e. a reptile] was killed, he commanded to flay it and to bring the skin to Rome; and to exhibit it there as a miracle, because it was 120 feet long. hundtwelftig-es 120-GEN.SG

fot-a foot-GEN.PL

lang long

(4.73) ChronA 892 (BATELY 1986: 55, 8): Se wudu is eastlang & westlang hund twelftiges mila lang oþþe lengra & þritiges mila brad. The forest is 120 miles long from east to west or longer and 30 miles broad. a.

hund-twelftig-es 120-GEN.SG

b.

þritig-es 30-GEN.SG

mil-a lang mile-GEN.PL long

mil-a brad mile-GEN.PL broad

Almost all instances with lack of Number agreement between numeral and noun that I was able to find are Measure Constructions modifying adjectives. However, I could find two exceptions: example (4.74) from the Beowulf-poem belongs syntactically to the previous Measure Construction discussed as argument measuring (§ IV.6.3). The difference is, however, that in (4.74) the nucleus XXXtig-es mann-a ‘30-GEN.SG man-GEN.PL’ modifies mægencræft

236

Numeral constructions in Old English

‘strength, power’, a noun which, in contrast to the cases discussed in § IV.6.3, does not denote duration. Example (4.75) shows a case with the same lack of Number agreement as in (4.71)–(4.74), but in (4.75) the numeral is apparently not part of a Measure Construction at all. (4.74) Beo 377 (MITCHELL/ROBINSON 1998: 60): Ðonne sægdon þæt sæliþende, þa ðe gifsceattas Geata fyredon þyder to þance, þæt he XXXtiges manna mægencræft on his mundgripe heaþorof hæbbe. Then the sailors – who gratefully brought thither valuable gifts to the Geats – said that he, the brave, has in his hand-grasp the strength of thirty men. XXXtig-es

30-GEN.SG

mann-a mægencræft man-GEN.PL great strength

(4.75) Mart 5 Ma 22, A.4 (KOTZOR 1981: 41, 3): Woroldsnottre men secgað þæt þa fiscas sýn on sæ hundteontiges cynna ond ðreo ond fiftiges; Wise men say that the fish are in the sea of 153 kinds. hundteontig-es 100-GEN.SG

cynn-a ond kind-GEN.PL +

ðreo 3

ond +

fiftig-es 50-GEN.SG

This combination of singular numeral and plural quantified NP is extremely rare, but these cases may be interesting to note, particularly in the light of the discussion on the lack of Number agreement in the context of the Partitive Construction in § IV.5.3. IV.6.5

Specifying age

Finally, there is a particular Measure Construction in Old English which is used exclusively for specifying age. In these cases, the measured NP always refers to a person and the nucleus indicates the age of a person. The copula can be a form of either BEON ‘be’ or of HABBAN ‘have’, as in the following structure; cf. (4.76) and (4.77). [measured NP ← [COP (BEON/HABBAN) + [NUM → MEAS]GEN.PL]]

Measure Constructions

237

(4.76) LS 17.2 82 (SCRAGG 1992: 296): Ða he ða hæfde eahtatyne wintra, ða gefullade hine man æfter cirican endebyrdnesse. Then, when he was 18 years old, he was baptised according to the rule of the church. he PPRN :NOM.SG.M

ða then

hæf-de have-PST.3 SG

eahtatyne 18

wintr-a winter-GEN.PL

(4.77) Mart 5 My 12, A.1 (KOTZOR 1981: 102, 3): On ðone twelftan dæg þæs monðes bið Sancte Pancrates ðrowung þæs æþelan cnihtes, se wæs fiftene geara ða he for Cristes geleafan deað geðrowade. On the 12th day of the month is the passion of the noble servant Saint Pancras, who was 15-year-old when he suffered to death for the belief in Christ. se DET:NOM.SG .M

IV.6.6

wæs fiftene be(PST.3SG) 15

gear-a year- GEN.PL

Summary

We have shown three general types of Measure Constructions in §§ IV.6.3–5 which differ in the relation between nucleus, measured element and the ultimate target of the quantification. There are those constructions shown in (4.76) and (4.77) in which the nucleus of the Measure Construction itself forms the predicate of the measured element (§ IV.6.5). Then there is the construction in (4.68) in which the nucleus of the Measure Construction modifies an adjective, which in turn forms the predicate of the measured element (§ IV.6.4). And finally, there are those instances in (4.63)–(4.67), (4.69) and (4.70) in which the thus measured adjective forms an attribute of the measured element (§§ IV.6.3–4). What all these Measure Constructions (except for the ones presented in § 6.2) have in common is that both the numeral and the unit of measurement are in the genitive. We have already mentioned the difficulty of identifying whether or not the genitive Case is encoded on the numeral in these Measure Constructions (§ IV.6.3). While there is only a small number of instances in which generally uninflected numerals do have a genitive suffix (as e.g. in (4.70) above in § IV.6.4), there are also sporadic examples in which usually inflected numerals are unmarked, or more precisely, occur in their nominative/accusative form. Such cases are clearly exceptional and some of them are not unlikely to be scribal errors. For instance, (4.78), as it is quoted below, represents the reading of the OEC. Ms. Julius A.x, as the base manuscript of the OEC for the

238

Numeral constructions in Old English

relevant section of the Martyrology, reads þreo geara eald. The parallel version in ms. CCCC 196, however, reads þreora geara eald, i.e. with þreora in the genitive Case. This comparison suggests that the construction exemplified in (4.78) is more likely to be erroneous than to represent a counterexample to the genitive value of both constituents of the nucleus in a Measure Construction. (4.78) Mart 5 Se 8, A10 (KOTZOR 1981: 202, 9): Ond þa hio wæs þreo geara eald, ða læddon hi fæder ond modor to Hierusalem ond sealdon hi þer in þara fæmnena gemænnesse. And when she was three years old, [her] father and mother brought her to Jerusalem and gave her to the community of the women. hio PPRN :NOM.SG.F

wæs þreo gear-a be(PST.1SG) three(NOM.N) year(N)-GEN.PL

eald old[NOM.SG.F]

If, in spite of these cases, further evidence for the regular character of the attributive (rather than partitive) genitive in Measure Constructions is needed (cf. § IV.6.3), we may once again heed a renowned Anglo-Saxon grammarian. In Ælfric’s Grammar, there is a passage containing 14 of the relevant constructions in one paragraph, predominantly employing the numerals for ‘2’ and ‘3’. Here, the inflected numerals twegra ‘2:GEN.PL’ and þreora ‘3:GEN.PL’ are without exception in the genitive Case, while all higher numerals – feower ‘4’ and fif ‘5’ – are unmarked for Case but, by analogy with the first two constructions, should nevertheless be taken as constituents of constructions which, as a whole are in the genitive Case; cf. (4.79). (4.79) ÆGram 287.15–288.9 (ZUPITZA 1880 [2001]: 287–288): biennium for twam gearum oððe twegra geara fyrst, triennium þreora geara fyrst, quadriennium feower geara fyrst, quinquennium fif geara fæc ET CETERA. [...] Biduum twegra daga fæc, triduum þreora daga fæc, quatriduum feower daga fæc. biduanum ieiunium twegra daga fæsten, triduanum þreora. binoctium twegra nihta fæc, trinoctium ðreora nihta fæc, quadrinoctium feower nihta [fæc]. [...] Eft biuium twegra wega gelætu, triuium þreora.

Relying on Ælfric’s authority, it seems clear that the genitive value of the measured units encodes an attributive or an adverbial function but does not represent a partitive genitive. This means that not only the measured unit, but also both constituents of the nucleus of a Measure Construction, i.e. numeral and unit of measurement, must be in the genitive. It is noteworthy that, at one

Measure Constructions

239

point in his passage, Ælfric gives a variable as shown in (4.79)a and (4.79)b. Cf. also (4.62) above in § IV.6.2. (4.79)a.

for for

(4.79)b.

twegra 2:GEN

twam 2:DAT

gear-um year-DAT.PL

gear-a fyrst year-GEN.PL period

Table 24 summarises the Measure Constructions attested in Old English as discussed in this section: Table 24. Measure constructions in Old English

section

structure

ultimate syntactic target of measurement

IV.6.2

[[NUM → MEAS] → verb]

verb

duration

IV.6.3

[[NUM → MEAS] GEN. PL → noun]

noun

duration

IV.6.3

[verb ← [[NUM → MEAS] GEN.PL → FÆC / FYRST]]

verb

duration

IV.6.4

[[[NUM → MEAS] GEN. PL → noun] → adj.]

adjective

distance, age, value

IV.6.5

[noun ← [COP + [NUM → MEAS] GEN.PL]]

noun

age

IV.7

type of measurement

The quantification of mass nouns

Mass nouns cannot immediately be quantified. Therefore, a Measure Construction is needed in order to quantify the mass term. In Old English, quantifying a mass term by means of a Measure Construction requires that the mass term be in a partitive relation to the Measure Construction by which it is quantified. The mass term is therefore in the genitive and, since mass nouns do not show plural marking, it is always in the genitive singular; cf. (4.80) and (4.81).

240

Numeral constructions in Old English

Accordingly, the general shape of the type of construction quantifying a mass term, which I label ‘Mass Quantification’, is this: 49 [[NUM → MEAS] → mass noun GEN.SG.] Again, the partitive relation between the mass term and the Measure Construction in these constructions can be encoded either by the genitive Case or, as (4.82) (although a later addition to the text) conveniently shows, by an of-phrase. (4.80) Lch I (Herb) 80.1 (DE VRIEND 1984: 120): Wið blædran sare & wið þæt man gemigan ne mæge genim þysse wyrte wyrttruman utewearde ðe man gladiolum & oþrum naman glædene nemneþ, drige hyne þonne & cnuca & gemengc ðærto twegean scenceas wines & þry wæteres, syle drincan. Against a sore bladder and against the inability to urinate, take the outer root of the herb that is called gladiolus and by another name gladdon, dry it then, pound [it] and add to it two cupful of wine and three [cups] of water [and] give it to drink. a.

gemencg ðærto mix[IMP] to it

b.

& and

twegean two:ACC.M

scence-as win-es draught-ACC.PL wine-GEN.SG

þry wæteres three:ACC.M water-GEN.SG

49 For the sake of simplicity, I refer, unless a more precise distinction is needed, to any type of non-count nouns as mass nouns or mass terms, irrespective of whether the relevant expression denotes a mass or rather an aggregate (collective nouns).

The quantification of mass nouns

241

(4.81) Lch I (Herb) 90.10 (DE VRIEND 1984: 130): Eft wið þæra ðearma ece & wið ealles þæs innoðes nim þas ylcan wyrte, dryg hy þonne & gegnid to duste swyþe smale, do ðonne þæs dustes fif cuculeras fulle & ðreo full godes wines, syle hym ðonne drincan þæt. Again against pain of the bowels and against [pain of] all intestines, take the same herb, dry it then, grind it very finely to dust and then add five spoonful of the dust and three [spoonful] of good wine [and] then give him this to drink. a.

do do[IMP]

ðonne then

þæs DET:GEN.SG.N

fif cuculer-as 5 spoon(M)-ACC.PL b.

& and

ðreo full three[ACC] 50 full

dust-es dust(N)-GEN.SG

full-e full-ACC.PL.M god-es win-es good-GEN.SG.M wine(M)-GEN.SG

(4.82) Lch II (1) 58.4.1 (COCKAYNE 1864–1866 II: 128): Wiþ þa blacan blegene syle þam men etan twegen croppas oððe þry of þære wyrte þe man on þreo wisan hateð myxenplante. Against the black blain, give to the man to eat two or three sprouts of this herb which is called in three ways the nightshade plant. twegen two:ACC.M

croppas sprout(M).ACC

þry three[ACC.M]

of of

oððe or

þære DET:DAT.SG.F

wyrt-e herb(F)-DAT.SG

Since the quantification of mass terms requires a construction in which the referent is not represented by the immediately quantified element (the unit of measurement), an elliptically used numeral can well occur in this context – similarly to the cases discussed in § IV.3.2.1. In (4.83), the two quantifiers ma ‘more’ and nigon ‘9’ both quantify the set of people who fell in a battle.

50 The use of the feminine/neuter form ÞREO quantifying the masculine nouns ‘spoonfull’ in (4.81)b is an Anglian feature; § II.2.3.

CUCULER

242

Numeral constructions in Old English

(4.83) Or 4 1.84.27 (BATELY 1980: 84): Þær næs his folces na ma ofslagen þonne nigon. There were no more than nine of his people killed. þær næs his there NEG.be( PST.SG) PPRN:GEN.SG na NEG

ma ofslag-en more slay\PTCP- PTCP

þonne than

folc-es nation-GEN.SG nigon 9

In (4.83), the nucleus of a Measure Construction – cf. the prototypical structure shown above for Mass Quantification – is reduced to an Elliptic Construction as described in § IV.3.2.1. The unit of measurement as the immediately quantified element is dropped and syntactically represented by the numeral. Its semantic content ‘men, soldiers’ can be inferred from the mass term FOLC ‘people, nation’.51 The structure of this reduced construction is: [[NUM → (MEAS)ellipsis] → mass noun GEN.SG.] Another completely different variant of the Mass Quantification is interesting. Similar to the method for measuring time discussed in § IV.6.3 (cf. examples (4.65) and (4.66)), the quantification of mass terms may involve an additional lexeme in the construction. This additional noun denotes the relevant type of measurement, usually ‘weight’. The most common lexemes employed here are GEWÆGE and GEWIHTE (both meaning ‘weight’); cf. (4.84) and (4.85). In contrast to FÆC and FYRST above in (4.65) and (4.66) (§ IV.6.3), their function is that of a genuine numeral classifier (cf. below § V.3.1). The nucleus and the classifier together form a Measure Construction as described in the previous section. Not only does the nucleus modify a nominal element, the classifier, but the entire nucleus also shows genitive marking as in most Measure Constructions. [[[NUM → MEAS]GEN.PL → CLF] → mass noun GEN.SG.]

51 MITCHELL (1985 I: 217, § 550.8) quotes a similar example as partitive genitive (Or 4 8.100.19: [...] þæs oþres folces XXV M, & VI gefengon; cf. BATELY 1980: 100, 25). However, the phrase þæs oþres folces is not an immediately quantified noun. Here and in (4.83), respectively, the numeral quantifies ‘people’, not ‘peoples’.

The quantification of mass nouns

243

(4.84) LchI (Herb) 20.5 (DE VRIEND 1984: 66): Wið nædran slite genim þysse ylcan wyrte wyrttruman tyn penega gewæge & healfne sester wines, gewesc tosomne, syle drincan gelomlice. Against snakebite, take from the root of this same herb the weight of ten coins and half a pitcher of wine, and soak [it] together, and give generously to drink. genim take[IMP]

þysse DEM:GEN .SG .F

wyrttrum-an root-GEN.SG

tyn 10

ylc-an same-GEN.SG.F

wyrt-e herb(F)-ACC.SG

peneg-a gewæg-e coin-GEN.PL weight(CLF)-ACC.SG

(4.85) PeridD 63.47.3 (LÖWENECK 1896: 47): Nim eft dyles sædes twelf penega gewiht and piperes ælswa fela and cimenes swa fela and gnid hit to duste; Take again the weight of twelve coins of dill seed and as much of pepper and as much of cinnamon and grind it to dust; [...] nim take[IMP]

eft again

dyl-es dill-GEN.SG

sæd-es seed-GEN.SG

twelf peneg-a gewiht 12 coin-GEN.PL weight(CLF)[ACC.SG]

Some instances of these constructions seem to suggest now that the adjacency of the measure expression and the classifier has become conventionalised to such an extent that both elements are written together as a compound; cf. (4.86)a, (4.87). (4.86) Comp 12.1.1 4 (HENEL 1934: 60): To underne and to none XI fotgemetu and to middæges fif fota gemetu. In the morning and in the afternoon [the length of the shadow is] the measure of eleven foot and at noon it is the measure of five foot. a. b.

11

fot-gemet-u foot-measure-NOM.PL

fif 5

fot-a gemet-u foot-GEN.PL measure(CLF)-NOM.PL

XI

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Numeral constructions in Old English

(4.87) LawIne 70.1 (LIEBERMANN 1903: 118): Æt X hidum to fostre X fata hunies, CCC hlafa, XII ambra Wilisc ealað, XXX hluttres, tu eald hriðeru oððe X weðeras, X gees, XX henna, X cesas, amber fulne buteran, V leaxas, XX pundwæga foðres & hundteontig æla. Of the ten hides [pay] ten barrels of honey, 300 loafs, twelve vessels of British beer, 30 [vessels] of light beer, two old cattle or ten rams, ten gees, 20 hens, ten cheeses, a vessel full of butter, five salmons, and 20 pound-weights of fodder and 100 eels. XX

20

pund-gewæg-a pound-weight-GEN.PL

foðr-es fodder-GEN.SG

This implies that the above structure, as attested in examples (4.84), (4.85) and (4.86)b, has been reanalysed as follows: [[NUM → [MEAS + CLF]] → mass noun GEN.SG.] Since the numeral now quantifies the compound consisting of unit of measurement and classifier as one nominal expression, there is no nucleus of a Measure Construction anymore. As a consequence of this, the constraint requiring both constituents of the nucleus to be in the genitive does not apply anymore. Hence, the same constraints which we discussed in § IV.5.2 for the relation between numeral and quantified NP are underlying to the relation between numeral and the new classifier, i.e., the classifier pundgewæga in (4.87) is in the genitive Case because the numerical value is above ‘20’, whereas the classifier in (4.86), fotgemetu, is in the nominative Case because the numerical value is below ‘20’. The motivation behind the reanalysis is obvious: both classifier and unit of measurement are elements individuating the mass noun. The use of two individuating elements, however, was felt to be redundant and, thus, the two elements have been analysed as one. This point will be discussed further in § V.3.1 when the parallels between units of measurement and classifiers are discussed from a more general, cross-linguistic perspective. IV.8

Conclusion

I have proposed that there are five different types of quantificational constructions in Old English: the Attributive Construction (§ IV.3), the Predicative Construction (§ IV.4), the Partitive Construction (§ IV.5), Measure Construc-

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tions (§ IV.6), and Mass Quantification (§ IV.7). What Attributive, Predicative and Partitive Quantification all have in common is that the target of the quantification is a countable entity whereas the target of the quantification in Measure Construction and in Mass Quantification is not immediately countable. Measure Constructions are used to quantify properties. These can be properties of nominal concepts like duration, weight, age, etc., or they can be properties of events, i.e. particularly duration. Finally, Mass Quantification is used to measure uncountable substances. In order to make them countable, a unit of measurement is needed as a standard of comparison. Therefore, Measure Constructions are constituents of the constructions employed for Mass Quantification. On a strictly syntactic level, the immediately quantified element in Mass Quantification is the unit of measurement. From such a perspective, the modified (measured) mass noun is irrelevant for the relation between the numeral and the immediately quantified element. However, this does not hold once we consider the functional aspects of quantification in our analysis. The ultimate target of the function ‘quantification’ is not the unit of measurement but the mass term. For example, in a phrase like three glasses of wine, it is the quantity of wine that is supposed to be encoded. The number of drinking vessels would be completely irrelevant without the context of the notion ‘wine’. Only because the mass term wine cannot be quantified alone by means of a cardinality, is an additional element required to relate the mass noun to the numerically specific quantifier. In the Attributive Construction, the numeral immediately quantifies the NP, which in turn represents the referent. Whether or not the numeral immediately quantifies the NP in the Partitive Construction is less obvious. The adjacency of the two elements suggests so. Yet we saw in § IV.5.3 that there is no Case agreement between numeral and noun and that the Number value of the quantified noun is independent of the cardinality expressed by the numeral. The quantified element can be analysed as a dependent constituent of the larger quantificational construction in both formal instantiations of the Partitive Construction – quantified element in the genitive or in an of-phrase. These aspects seem to indicate that the two elements, numeral and quantified NP, are not as tightly connected as in the Attributive Construction. The required marker for the partitive relation (irrespective of which of the two instantiations is chosen) could be read as a necessary link between the two elements. This, in turn, would suggest that the numeral in a Partitive Construction does not quantify the noun as immediately as it does in the Attributive Construction. At this point, this remark may be of a mere hypothetical value but it will contribute to a later discussion below in § V.3.2.

246

Numeral constructions in Old English

Mass Quantification is, however, quite clear in this respect: it unambiguously requires an additional lexical item as a link between the numeral and the element representing the quantified referent. The unit of measurement is syntactically quantified by the numeral, and the numeral and the unit of measurement together modify (or measure) the mass noun (cf. § IV.7). It is due to this larger morphosyntactic independence that in many traditional descriptions the numeral has been read as a more ‘noun-like’ element than the numeral in an Attributive Construction (cf. § IV.2). But, superficially, the numeral is also morphosyntactically independent in the two instances of the Elliptic Construction, which we have categorised as a modification of the Attributive Quantification. From this perspective, we can explain MITCHELL’s (1985) distinction between ‘dependent’ and ‘independent’ use of numerals which roughly runs parallel to the line between our Attributive Construction (‘dependent’) and all other constructions, particularly Elliptic and Partitive (‘independent’). The finer distinctions, however, which we could identify for those Old English constructions in which count nouns are quantified, all seem to be triggered by information structural constraints – basically by the thematic status of both cardinality and quantified referent. Moreover, we have seen that the type of reference ([± definite]) may also be involved in the choice of a particular construction. Recall that in § IV.5.2.1 we argued that what is superficially a part-whole distinction between a subset and a larger set requires that the larger set is contextually given and that, consequently, the definite reference of the quantified NP is a necessary prerequisite for the Partitive Construction. Similarly, our distinction between the Elliptic Quantification and the Anaphoric Use was superficially accompanied by the distinction of whether the reference is definite or indefinite. And this very distinction proved to be crucial for the question of whether the numeral was used predominantly as a quantifier or as an anaphoric element. In this respect, our working hypothesis for the present chapter expressed above in § IV.2.4, that a categorisation along the lines of the traditional word classes should be replaced by one that analyses the main types of quantificational constructions with respect to their morphosyntactic features (agreement patterns between numeral, quantified NP, and, if present, intermediate elements such as unit of measurement or classifier) and to the functional and pragmatic implications (such as information structure, type of reference, etc.) seems to be endorsed. In § IV.2, I alluded to the fact that the comparison of numerals with nouns and adjectives is not limited to descriptions of ancient languages, which often seem to adhere to more traditional terminologies and approaches, but that a similar tendency can be found in the general linguistic literature on numerals.

Conclusion

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Although the way numerals are compared with nouns and adjectives differs in cross-linguistically oriented studies, nouns and adjectives still constitute the main standard of comparison for the description of the morphosyntactic features of numerals. This observation will be our starting point in the next chapter. Some of the findings presented here for Old English will be developed further in Chapter V. The aim will then be to show that, from a cross-linguistic perspective, too, there may be a more rewarding approach to classifying cardinal numerals. Accordingly, our main concern in Chapter V will be the question of the word-class character of cardinal numerals. If a numeral is not ‘either noun or adjective’ where should its position in the categorisation of word classes be? We will employ both synchronic and diachronic arguments for a hypothesis that postulates numerals as a largely independent category and that explains their similarities with other word classes. We will argue, furthermore, that such an account can go beyond the limits of the description of a single language and will generally hold cross-linguistically.

Chapter V The word class ‘cardinal numeral’ V.1

Starting point

The morphosyntactic properties of cardinal numerals can vary in three ways. First, they vary within the counting sequence. That is, in a given language, some elements of the counting sequence may show a different inflectional or syntactic behaviour than others. For instance, we mentioned that simple numerals above ‘4’ in Old English (at least in West Saxon) show Case/Number inflection only if the numeral immediately precedes the quantified noun (§ II.2.4), whereas the lowest three numerals show Case/Number inflection in any syntactic position. Also, higher bases (but not TYN ‘10’) may or may not show inflection. That is, irrespective of the syntactic construction in which a numeral interacts with the quantified expression, the inflectional behaviour of numerals in Old English is not uniform. There are different rules concerning the same phenomenon that apply to different members of one class. The inflectional behaviour of cardinal numerals in Old English varies depending on the numerical value. I will refer to this type of variation of properties as ‘cardinality-dependent variation’. GREENBERG (1966: 42) lists a couple of instances of cardinality-dependent variation within numeral systems. He considers the lowest members of a system generally to be the unmarked ones. We will suggest an alternative view to this approach below in § V.2.3. Second, one element of the counting sequence of one and the same language may vary in its inflectional and syntactic behaviour depending on the context (information structure) and on some properties of the quantified noun, most of all its countability. We discussed his type of variation in the previous chapter for Old English and I will refer to it as ‘context-dependent variation’; cf. GIL (2001: 1282a–1284a, § 3.3.1). Finally, the morphosyntactic properties of cardinal numerals vary across languages; cf. GIL (2001: 1284a–1287b, § 3.3.2). This can, of course, be said of any lexical category and it is, therefore, not a phenomenon which immediately calls for an explanation. However, in the present chapter, I will argue that there are certain patterns in this third type, the ‘cross-linguistic variation’, and that it is therefore possible not only to define a cross-linguistic category ‘cardinal numeral’ on semantic grounds, as we did in Chapter I, but also to assign at least a certain pattern of morphosyntactic features to such a crosslinguistic category. It will be the task of the present Chapter V to substantiate

Starting point

249

this claim. After a few more preliminary remarks, we will discuss the cardinality-dependent variation in § V.2 and the context-dependent variation in § V.3. In the previous chapter, I continuously argued that any attempt to associate the morphosyntactic properties of the cardinal numerals of Old English with those of other word classes, predominantly with nouns and/or adjectives, is ultimately insufficient for describing and explaining their morphological and syntactic behaviour. Recall that in § IV.2, we said that even those few studies that employ a terminology other than the dichotomy ‘nominal/substantival’ vs. ‘adjectival’ – e.g. MITCHELL (1985), ROSS/BERNS (1992) – do, nevertheless, refer indirectly to nouns and adjectives. To some extent, this is justified by a number of syntactic and morphosyntactic properties of nouns or adjectives that are shared by numerals. But each of these parallels is confined to either a particular number of syntactic uses of numerals or to a particular type of quantification. Another problem is that the attribution of numerals to the ‘noun’ and to the ‘adjective’ class is always motivated by completely different criteria (which, moreover, are usually left implicit). Recall the discussion in § IV.2.1 in which we mentioned the following discrepancy: while STILES (1986a: 10) categorises the Partitive Construction as ‘adjectival’ use – justified (though STILES does not make this explicit) by the adjacency of the numeral and the quantified element in the Partitive Construction – MITCHELL (1985 I: 217–218, § 550), by contrast, lists the Partitive Construction as one of the ‘independent’, i.e. nominal uses – justified (though MITCHELL does not make this explicit) by the analysis of the genitive attribute as a subordinate constituent of a phrase with the numeral as its head. We will resume this criticism in this chapter in order to develop an alternative approach to the word class character of cardinal numerals. We will argue that cardinal numerals form a class of their own and we will try to explain some of the features that numerals potentially share with other word classes. These parallels, I believe, actually support the claim of an independent category ‘cardinal numeral’ rather than question it or contradict it. The line of argument will operate on the basis of the findings of the previous chapters. Our point of departure is thus the situation in Old English. However, I think that, to a considerable degree, the claim made in this chapter generally holds across languages. As far as possible, given the limited scope of this study, we will include cross-linguistic considerations in the discussion in this chapter although they must necessarily remain tentative to some degree. In the first main section of this chapter, we will deal with what we referred to above as ‘cardinality-dependent variation’. We will first discuss adjectivelike features of cardinal numerals (§ V.2.1), then noun-like features (§ V.2.2) and then proceed to a discussion of those approaches that compare numerals

250

The word class ‘cardinal numeral’

with both (§ V.2.3). Finally, §§ V.2.4-5 will offer possible explanations for some patterns of cardinality-dependent variation. In particular, our discussion of the Anaphoric Use has shown that there can also be essential analogies with pronouns. Although it may be valuable to discuss these parallels with pronouns a little more thoroughly, I will leave this point largely unconsidered. V.2

Adjectives, nouns, and numerals

V.2.1

The numeral – an adjective?

It has already been mentioned that, in contrast to the Partitive Construction, the numeral in an Attributive Construction does not only stand semantically in an attributive relation to the quantified NP – i.e. as a quantifying modifier – but also syntactically – i.e. agreeing with and adjacent to the quantified NP. This constitutes an essential parallel to the morphosyntactic properties of an adjective. Moreover, in § IV.3.2.1 we pointed out that even in the Elliptic Construction – although traditionally taken as an instantiation of the numeral as a noun – the morphosyntactic behaviour of numerals corresponds to that of adjectives in many respects. The immediate and more superficial question resulting from these observations is whether or in which cases these parallels suggest that a numeral is an adjective. Whether explicitly or implicitly, especially in Indo-European and traditional Historical Linguistics, numerals have often been associated with adjectives; cf., for instance, W.P. LEHMANN (1974: 208, § 5.4.6) and the literature cited there. This is because in Indo-European languages, at least in their earliest attested stages, both numeral and adjective show inflection for Case and Gender and, if used attributively, the modified noun assigns its Case and Gender value to both modifying numerals and adjectives (cf. e.g. STILES 1985: 82–83 for the ancient Germanic languages; FOX 2005: 175 for Presentday German). Such a comparison disregards several aspects; for instance that – not only in Old English – the observed correspondences apply only to bases and to the lowest valued atomic numerals, or that – in Old English – the inflectional suffixes are those of the nominal i-stems and not of the adjectival paradigm. On the morphosyntactic level, a numeral in an Attributive Construction and an adjective differ in a significant respect: numeral and adjective – if the numeral is inflected at all – both agree in Case and Gender with the noun. Yet, while the adjective is the target of Number agreement, the numeral does not show Number marking. The Number value of the quantificational construction is determined by the cardinality of the referent set, and thus, one

Adjectives, nouns, and numerals

251

could say that, although the numeral does not assign the Number value to the quantified noun (as claimed by GIL 2001: 1285b for Present-day English), it semantically further specifies its Number value. In any case, this point leads us to another, more essential difference between a numeral and an adjective. Semantic differences may not be considered relevant in a discussion in which the main line of argument is based on morphosyntactic properties. Nevertheless, as we will see, crucial semantic differences between adjectives and numerals (or, for that matter, quantifiers) have quite substantial syntactic consequences. Semantically, the crucial difference between the modification with an adjective and the modification with a quantifier is that the numeral modifies the extension of the reference of the NP while the adjective primarily modifies its intension. In other words, modifying the noun book with an adjective, say small, alters the concept irrespective of the number of elements of the class book refers to. So, without any further context, small book refers to the class of objects which is defined by all properties that are inherent in the concept ‘book’ (i.e. a bound pile of usually printed paper sheets) and, in addition, by the property ‘small’, i.e. by the fact that each individual of these objects is relatively limited in its size. By narrowing the intension of the expression by means of the adjective small, we can exclude a folio, an encyclopaedia, or any other type of large volume as referent. The reference is however unspecific with respect to how large the class is, i.e. how many elements the referent set contains. A quantifier, by contrast, alters the references in a different way. It is the extension of the reference rather than its intension which is specified. By modifying book for example with the numeral three, we specify the size of the set of books irrespective of what kind of ‘book’ is referred to, i.e. irrespective of which further properties the individual members of the class ‘book’ may possibly have. Without any further context, three books refers to a class of objects which is defined by all properties that are inherent in the concept ‘book’, but the properties of the objects are not specified any more narrowly. It could comprise any type of ‘bound pile of usually printed paper sheets’. The same would hold if we used a numerically unspecific quantifier, like ‘many’ or ‘few’. It would be the extension of the referent (the size of the set) which is narrowed down, albeit not as precisely as with a numeral: the set of possible objects referred to is smaller than the class of all existing books. In short, to modify a noun with an adjective specifies the properties of the individual members of the set referred to but it does not modify the set as a whole. Cf. in this context the various discussions from different backgrounds, e.g. FREGE (1884 [1934]: 68–69; § 57);

252

The word class ‘cardinal numeral’

BENACERRAF (1965: 59–60); SCRIBA (1968: 2–4); HURFORD (1987: 218); REINHARDT (1991: 199).52 There are a number of syntactic consequences of this semantic distinction. STAMPE (1976: 599), for instance, notes that, while adjectives may well modify several nouns distributively as in (5.1), the same syntactic structure with a numeral as modifier, as in (5.2), will at least be ambiguous (examples from STAMPE). Another syntactic consequence of the distinction between extensional and intensional modification is that numerals, in contrast to adjectives, cannot be modified by adverbs or degree adverbs; cf. BLOOM (2000: 222). (5.1) old women and men (5.2) three apples and oranges

On a purely syntactic level, there may in fact be few distinctive features between adjective and numeral in an Attributive Construction. The most essential difference is that, cross-linguistically, numerals hardly ever follow the nouns, while no predominant type exists for the element order between adjectives and the modified noun; cf. HURFORD (2002: 630a).53 We may therefore conclude that, although an adjective and a numeral may in fact share a number of more or less similar morphological and syntactic features, there is also a considerable number of differences between these to classes of expressions. These differences make a comparison difficult and – more importantly – do not allow a categorisation of the numeral as an adjective, if only in a particular type of quantificational construction. In § I.1, we (preliminarily) defined cardinal numerals as a subtype of quantifiers drawing exclusively on semantic criteria. Cardinal numerals also share 52 It should be noted, though, that I use the term ‘modification’ to refer to all types of specification of the reference of an NP. It makes sense to speak of ‘qualification’ if we refer to a specification of the intension of a reference and to contrast this with ‘quantification’ which we use if we speak of an extensional specification of a reference. REINHARDT, in the given quotation, seems to use modification in the sense of intensional modification. – For the question whether a numeral modifies a noun or whether modification is restricted to adjectives cf. also the discussions in FREGE (1884 [1934]: 27–33; §§ 21–25) and in HURFORD (1987: 132–141). 53 HURFORD (1987: 191–193) calls for a strict of between morphology and syntax. It is true that we have to remain conscious of the different levels of purely syntactic and purely morphological features. However, the syntactic relations among the different word classes, especially the relation between numeral and quantified noun – as HURFORD himself implies (1987: 190) – often appears overtly only in agreement patterns, that is, at the interface of syntax and morphology.

Adjectives, nouns, and numerals

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a number of distributional properties with other, numerically unspecific quantifiers. Both types of expressions occupy the same syntagmatic position within a complex noun phrase as in three / many expensive red cars. In the same way as described for the Old English numerals in § IV.5, numerically unspecific quantifiers can head a Partitive Construction.54 Finally, quantifier floating is possible for numerals as it is for all types of quantifiers. All these distributional properties are not shared by adjectives; cf. WIESE (2003: 274–277). The fact that these points generally apply cross-linguistically has been shown by GIL (2001: 1284a–1287b; § 3.3.2) who compares (attributive) numeral-noun constructions with adjective-noun constructions across typologically different languages and concludes that, in spite of the similarities, there are crosslinguistically significant differences between (attributive) quantifiers and adjectives. V.2.2

The numeral – a noun?

Except perhaps early generativists (cf. JACKENDOFF 1977: 128–130, § 5.5.2 and the short section in REINHARDT 1991: 197), most linguists nowadays do not propose a rigid categorisation of the form “numerals are nouns”. Yet, in many contributions, numerals are described as noun-like in several but not all respects. There seems to be an interesting distinction: while both traditional Historical Linguists (of Indo-European and Germanic) seem to focus on the context-dependent variation of their inflectional behaviour when providing evidence for the noun-like status of (some) numerals, typologists and General Linguists prefer to discuss cardinality-dependent variation. It is the Partitive Construction and the Elliptic Construction (and equivalent constructions in other languages) which are focussed on when traditional descriptions classify numerals (at least in these uses) as nouns. What seems to suggest the categorisation of a numeral in a Partitive Construction as a noun is the fact that the genitive attribute makes the numeral appear as the head of the respective phrase. This analogy, however, will not resist closer scrutiny. First of all, the head status of the numeral is not as unambiguous as that of a head noun in an NP. While the numeral does assign the Case value to the quantified elements of the phrase (genitive), the Number value is independent of the nu54 Note, however, that Partitive Constructions are possible with superlatives. Superlative adjectives, however, are semantically distinct from positive adjectives in that they single out one object of a pre-defined set and thus modify the extension rather than the intension of the reference. Superlatives are, therefore, closely related – both semantically and syntactically – to ordinal numerals.

254

The word class ‘cardinal numeral’

meral and the Gender value of the numeral is controlled by the quantified noun. Therefore, with respect to agreement patterns between numeral and noun, a clear distinction between ‘head’ and ‘dependent’ is obscured in any type of numeral-noun construction; cf. STOLZ (2002: 387, § 6). Secondly, the fact that there is a genitive attribute adjacent to the numeral is again not an exclusively nominal feature. The Measure Constructions in (4.67)–(4.70) above in § IV.6.4, for example, show that a genitive attribute can just as well be used as a modifier of adjectives. In addition to these points, on a purely semantic level, we have already shown that it is not the quantified noun that modifies the numeral, but, instead, the numeral that – in spite of its relative morphosyntactic independence – quantifies the noun; cf. Table 23 in § IV.5.1. We also pointed out that in cases in which the quantified noun is elided and the numeral is the only constituent of a phrase, assigning a noun status to the numeral results from a superficial analysis. In § IV.3.2, we even argued that the numeral’s potential to function syntactically as the head of a phrase (or as its sole constituent) when the referential expression is not overt is a typical property of modifiers. Drawing on alleged analogies between numerals and nouns, therefore, does not seem useful in any grammatical domain. We have shown that this applies to Old English and I conjecture that this would not be considerably different in any other language. Yet there also seems to be a tendency of higher base numerals to be more noun-like. FAARLUND (2004: 61), for instance, says that in Old Norse high base numerals “are nouns”, because they generally require the Partitive Construction (in a way similar to the constraints discussed for Old English in § IV.5.2.2). Similar tendencies – i.e. that high valued numerals are morphosyntactically less immediately linked with the quantified NP than lower numerals – can be observed for many languages. In addition to language-specific constraints barring higher numerals from constructions in which numerals quantify the referent immediately (like the Attributive Construction), there are a number of other morphosyntactic features which distinguish high numerals from lower ones in many languages, all of which resemble typical features of nouns in the respective languages. HURFORD, for instance, defines bases and multiples of bases as nouns. He writes (HURFORD 1975: 51): “Finally, it is convenient to introduce at this stage a mechanism for expressing the fact that items belonging to the category M [which corresponds to any base or multiple of a base in our terminology, i.e. to any serialised augend; cf. HURFORD (1975: 19–26, §§ 2.1–2); FvM] also possess properties of nouns.” Thus HURFORD proposes a rule which converts any M, i.e. any (multiple of a) base into a noun. The motivation for this is the observation that serialised augends “also possess properties of nouns”

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(HURFORD 1975: 51; my italics). This clearly means that serialised augends possess other properties, too, which are explicitly not noun-like. Even within the framework of HURFORD’s theory, it is, therefore, not justified to postulate a device that generally labels serialised augends as nouns. Cf. also CORBETT’s (1978a: 362) objection to HURFORD’s definition and HURFORD’s (1987: 187) discussion of CORBETT (1978a, 1978b). In her study of Present-day English numerals, REINHARDT (1991: 196) observes three “strongly noun-like features” for high valued numerals: the potential to show Number marking (cf. PDE *threes/*tens/hundreds/thousands of people), their frequent use with an of-phrase and their “countability”. REINHARDT uses the term countability to refer to the possibility of quantifying numerals like HUNDRED and THOUSAND with atomic numerals. She therefore suggests labelling such numerals as “peripheral nouns” (1991: 196). Although REINHARDT examines the situation in Present-day English, her discussion generally applies to Old English as well. REINHARDT herself (1991: 196) remarks that “[i]t should be pointed out that the [Present-day] English position on higher cardinals holds true for many other languages – it might even be universal as posited by CORBETT (1978).” Before coming back to CORBETT’s generalisation (§ V.2.3), which REINHARDT refers to and which will become a central point of orientation for the present discussion, I would briefly like to discuss the three criteria postulated by REINHARDT as indicators of the noun status of an expression. The problem with the first two of REINHARDT’s criteria, pluralisation and the frequent use in an of-phrase, is that they apply to expressions like PDE hundred and thousand only in instances in which they denote ‘a large, numerically unspecific multitude’. REINHARDT’s suggestions are valid as long as these expressions do not specify exact numerical values. Her nominality criteria apply to the use of base numerals in sentences like those in (5.3) and (5.4). The crucial point here is that numerals in these examples are numerically unspecific in the sense discussed in § I.1. In (5.3) and (5.4), these expressions are (both!) best paraphrased as ‘a great multitude / masses (of people)…’ but clearly not as ‘(an integral multiple of) 100 / 1,000…’. (5.3) Hundreds / Thousands have gathered in the streets. (5.4) Hundreds / Thousands of people have gathered in the streets.

Once the Present-day English expressions hundred and thousand specify a cardinality, i.e. once they are used for numerically specific quantification, neither of the two nominality criteria applies. Neither hundred nor thousand

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can be pluralised when denoting precisely ‘102’ and ‘103’, respectively. Finally, particularly in Present-day English, an of-phrase in a quantificational construction is only possible if there is a part-whole relation, i.e. in contexts similar to those described for Old English in § IV.5.2.1. These contexts, however, require an of-phrase for low numerals just as well – in both Old English and Present-day English. Thus high valued numerals, when specifying a cardinality, retain all features of lower valued numerals as opposed to those of genuine nouns. What about the third of REINHARDT’s nominality criteria, the ‘countability’ of high numerals? In a complex numeral like five hundred and thirty-two, an atomistic analysis of the elements five and hundred could well result in the statement that five quantifies hundred in this structure. But this analysis is based on a very superficial comparison of a multiplier-multiplicand construction with a quantifier-noun construction (as in five flowers) and is therefore misleading. There is no substantial morphosyntactic or semantic property that the two constructions have in common (see the previous section for some of the salient differences). The relation between five and hundred is that of two constituents of a complex numeral with the former being the multiplier and the latter the multiplicand. The whole point is even more difficult to support if we consider a complex numeral with more than two hierarchically ordered constituents: in five hundred thousand, the constituent hundred could be analysed as both modifier and modified head at the same time; cf. STAMPE (1976: 599). What REINHARDT refers to as ‘countability’ are two quite different processes: one is the necessity and/or capability of numeral systems to form complex expressions, the other is simply quantification. Only the result of the former process, i.e. the entire complex form, can be employed for quantification. The criticism of REINHARDT’s nominality criteria applies, of course, to Old English, too. The Old English expressions HUND(RED) and ÞUSAND comprise the same syntactic functions as other, lower valued numerals do. More often than other numerals, high bases appear in contexts in which they do not specify an exact numerical value. The possibility of combining higher bases with other non-numerical quantifiers like OE MONIG or FELA ‘many’ has often been taken as evidence for the nominal status of high valued bases as opposed to low valued numerals. It is true that, once higher bases are combined with nonnumerical quantifiers, they do adopt noun-like features. At the same time, however, the combination of a high valued base numeral with a non-numerical quantifier attests to their lack of numerical specificity. In other words, once a high base numeral is used together with a non-numerical quantifier, it does not denote a cardinality but more generally ‘a great, numerically unspecific

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amount’. Again, in these contexts, the expressions are no longer used as systemic numerals but rather as numerically unspecific quantifiers. The only difference between higher base numerals in Old English and those in Present-day English is that OE HUND(RED) and ÞUSAND can in fact be pluralised when used for numerically specific quantification, whereas PDE HUNDRED and THOUSAND cannot. The inconsistent use of the plural form þusenda in sequences like the ones in (5.5)–(5.7) shows, however, that the pluralisation does not follow any regular pattern.55 In instances in which Old English high base numerals both show plural marking and are used for numerically specific quantification, they are still distinct from nouns in so far as they cannot stand alone but need a quantified element specifying the referent. (5.5) ByrM 2.3.170 (BAKER/LAPIDGE 1995: 116): An ælpig monð æfter þære sunnan ryne hæfð seofon hundred tida & twentig, & twa þusend & eahta hundred & hundeahtatig prica, & minuta seofon þusend & twa hund, & momenta twentig þusend & eahta þusend & eahta hundred & ostenta þreo & feowertig þusenda & twa hundred, & atomos an hund þusenda & hundteontig siðon syxtig þusenda. “According to the sun’s course, a single month has 720 hours, and 2,880 points, and 7,200 minutes, and 28,800 moments, and 43,200 ostents, and ‘100,100 × 60,000’ atoms.” (transl. BAKER/LAPIDGE 1995: 117). (5.6) ByrM 2.3.179 (BAKER/LAPIDGE 1995: 116): & soðlice þæt ger hæfð nigon þusend tida & seofon hund tida & syx & syxtig, & fif & þrittig þusend prican & an hundred & hundnigontig, & minuta hundeahtatig þusend & seofon þusenda & syx hundred & syxtig, & momenta þreo hund þusenda & fiftig & syx hund & feowertig, & ostenda fif hund þusend & fif & twentig þusend & nigon hund & syxtig, & atomos an hund þusend & hundteontig siðon tyn þusend & nigon siðon hundteontig þusend & þusend siðon þusend & nigon hund þusenda & an & þrittig þusend & syxtig. “And truly, the year has 9,766 hours, and 35,064 points, and 87,660 minutes, and 35,190 moments, and 525, 960 ostents, and 100,100 × 10,009 × 1,001,000 × 1,931,060 atoms” (transl. BAKER/LAPIDGE 1995: 117).

55 In (5.5)–(5.7), each non-pluralised ÞUSEND is underlined and each pluralised ÞUSEND is highlighted by bold face. In (5.5) and (5.6), I did not follow the editors in replacing the figures of the manuscript by those of Byrhtferth’s source (De computo by Hrabanus Maurus). In (5.6), Hrabanus gives astronomically incorrect figures for the atoms of the year which are again rendered incorrectly by Byrhtferth; cf. the discussion of these passages in BAKER/LAPIDGE (1995: 309–310).

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(5.7) ByrM 1 2.3.279 (BAKER/LAPIDGE 1995: 116): & soðlice þæt ger hæfð […] minuta hundeahtatig þusend & seofon þusenda & syx hundred & syxtig, […] And truly, the year has […] 87,660 minutes. minut-a minute-GEN.PL & syx + 6

hund-eahta-tig CIRC-(8 × 10)

þusend × 1,000

& seofon + 7

þusend-a × 1,000-PL

hundred & syx-tig × 100 + (6 × 10)

While it seems that the pluralisation of high bases does not follow any regular pattern in Old English, it can generally be observed that ÞUSEND as a multiplicand is pluralised more often than HUND or HUNDRED as multiplicands. We can conclude that, at least in Old English, not all the noun-like features of the third base ÞUSEND apply to the second base HUND(RED), and that hardly any noun-like feature is shared by the fundamental base TYN and its variants. Moreover, as (5.5)–(5.7) show, the distribution of instances of ÞUSEND with and without plural marking seems to be arbitrary. The crucial point is that, if high base numerals (whether in Old or Presentday English) stand alone – i.e. if there is neither a quantified element nor a contextually implied referent – they unambiguously refer to nothing else but ‘people’ (cf. (5.8) and, for Present-day English, (5.3) above). It seems as if their numerically specific meaning in these constructions expands from ‘100’ and ‘1,000’ to ‘a great (i.e. numerically unspecific) mass of people’. Note that the term expand here is not meant to imply a diachronic directionality between the two notions ‘unspecific large quantity’ and ‘numerically specific base value’. In any case, as a consequence of this semantic difference, we may conclude at this point that the syntactic properties and functions of base expressions are different when used as numerically unspecific expressions and thus cannot be taken as properties of numerals. (5.8) ÆLS (Lucy) 111 (SKEAT 1881–1900 I: 216): Lucia him cwæð to, þeah þu clypige tyn þusend manna, hi sceolan ealle gehyran þone halgan gast þus cweðende, Cadent a latere tuo mille, et decem milia a dextris tuis, tibi autem non adpropinquabit malum, þusend feallað fram þinre sidan, and tyn þusend fram þinre swyðran, þe sylf soðlice ne genealecæð nan yfel. Lucy said to him, although you call 10,000 men, they will all hear the Holy Spirit, speaking thus: “Cadent a latere tuo mille, et decem milia a dextris tuis, tibi autem non adpropinquabit malum. 1,000 fall from your side, and 10,000 from your right [side], truly, no evil will approach yourself”.

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More generally, we cannot necessarily deduce any categorisation of the syntactic properties of cardinal numerals from the fact that high base numerals cross-linguistically have more noun-like features than other numerals. Once a high valued numeral does not denote an exact numerical value, its function has become different from that of a systemic numeral. Once it stands alone, or once it is used in a Partitive Construction, it displays all the properties of lower valued numerals. The fact that in Old English high base numerals may (or may not!) be pluralised when used for numerically specific quantification does not suffice to generally treat them as a category different from other numerals. In this respect, the potentially more noun-like behaviour of high valued bases is irrelevant to an overall categorisation of cardinal numerals. Finally – and with respect to the overall discussion of this section – the fact that high valued bases may adopt noun-like features does not imply that other numerals consequently have adjective-like features. V.2.3

Corbett’s generalisation

While it is undisputed that across languages high base numerals share more features with nouns than lower numerals do – in this respect Old English does not deviate from a universal tendency – even if high numerals do not specify an exact numerical value, their morphosyntactic properties only approximate those of nouns. REINHARDT (1991: 196), in a way, admits this by saying that “[t]he fact that [high numerals] meet essential requirements of a noun does not mean, however, that higher cardinals are true nouns. While thousand in a thousand flowers is more noun-like than five in five flowers it is less noun-like than bunch in bunch of flowers.” A formula which has taken these difficulties into consideration is a generalisation put forward by Greville CORBETT. He proposes the following bipartite universal generalisation (CORBETT 1978a: 355 and 368, 1978b: 70) reproduced in (5.9): 56

56 CORBETT states his generalisation at three different points (1978a: 355 and 368, 1978b: 70), each time with a slightly different wording. The way I reproduced it in (5.9) is not a literal quotation in the strict sense. Instead, I included all crucial aspects even if they do not occur in each of the three instances. For example, at one point (1978a: 355), CORBETT does not state that he speaks of simple numerals – a crucial point, because he only takes bases into consideration, but never high valued complex expressions. He is also inconsistent in referring to the “behaviour” of numerals or to their “syntactic behaviour”. At one point he only writes “cardinal numerals fall between adjectives and nouns” (1978a: 368). The only specification that is entirely mine is the addition “morpho-“ in “morphosyn-

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(5.9) CORBETT’s generalisation on the morphosyntactic properties of cardinal numerals 1 The [morpho-]syntactic behaviour of simple cardinal numerals falls between that of adjectives and nouns. 2 If numerals vary in their [morpho-]syntactic behaviour, then the higher will be nounier.

This generalisation has been quoted frequently in the linguistic literature on numerals. It takes into consideration both the parallels between higher numerals and nouns, which doubtlessly exist, and the difficulties that immediately arise when a comparison with nouns (or other word classes) becomes too strict. The advantage of CORBETT’s generalisation is that it does not rigidly equate numerals with other categories like nouns or adjectives. But there is also an aspect in which CORBETT does not differ considerably from the classifications discussed above: CORBETT, too, draws on the analogies of numerals with other word classes. By employing nouns and adjectives as the means of comparison, he assumes in principle the same perspective as the more traditional categorisations do. The generalisation, therefore, does not say anything specific about the inherent properties of numerals. It, and all previous classifications, says more about nouns and adjectives than about numerals. There is only one property of numerals that is implicitly described in all these approaches to a comparison, namely that the morphosyntactic behaviour of simple numerals is likely to vary within one language. CORBETT mentions this, but this property is not in the focus of his statement. In the following, I will propose a shift in the focus. I will argue that, whatever similarities there are in the morphosyntactic behaviour between numerals and other word classes in a language, these are not the crucial properties of cardinal numerals. What I take as crucial is the mere fact that cardinal numerals vary in their morphosyntactic behaviour (cf. § V.1, where I have entered the discussion on the basis of this very assumption). I will argue later (§ V.2.5) that this perspective will also allow us to explain why some properties of cardinal numerals look noun-like. Thus, as an alternative approach, it is possible to take the fact that the morphosyntactic behaviour of cardinal numerals is prone to variation as an inherent property of numerals. It is certainly this variation which has, to some extactic”. Since most of CORBETT’s line of argument is based on inflectional properties, I consider this addition as justified.

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tent, complicated the categorisation of numerals within the parts-of-speechsystem (which is, in a way, surprising, as there is no class of expressions that does not show some variation in the morphosyntactic behaviour of its members). But I would like to go a step further. The point here is not about acknowledging that members of a category may vary (a point, which is rather trivial and which is probably difficult to bring in line only with rigidly formalist concepts of stable categories). In addition to merely stating that there is variation, it is also possible to conceive of this variation itself as a property of a class. In other words, if we can identify patterns of variation within one class, the variation may even be seen as a potentially defining property of that class. In the case of numerals this means that it is a property of cardinal numerals that they necessarily vary in their morphosyntactic behaviour. Moreover, it is the way in which the morphosyntactic properties of numerals vary cardinalitydependently – depending on their numerical value – and context-dependently – from one possible construction type to the next – which is in fact wellidentifiable and thus becomes a defining property of numerals. While this is certainly true for a particular language, I would take it as likely that this also holds to a large extent cross-linguistically. By accepting the variation in morphosyntactic behaviour as a class-defining property, numerals can be taken as an independent word class not only by semantic criteria (§ I.1), but in principle also on morphosyntactic grounds. Cf. WINTER (1992: 26–27) for a similar point in the context of the reconstruction of numeral forms in proto-languages. A step in this direction is the conclusion STOLZ (2002) draws in his paper on numerals in European languages. He writes (STOLZ: 2002: 387; § 6): A lot of numerals combine head and modifier functions because they govern [N]umber on nouns and at the same time agree with the noun in a variety of categories. There is no easy way out of this dilemma because neither of the two properties can be said to dominate one. An idea that comes to mind is that numerals of this kind form a separate word-class whose members are ambiguous as to head-hood and modifier status.

STOLZ is, I believe, on the right path, but he focuses too strongly on the head/modifier-status of an expression. What we also need to take into account is that in many languages (as shown for Old English in the previous chapter), one and the same numeral may display varying government/agreement behaviour in its interaction with the quantified NP depending on the construction type in which the two interact with each other. STOLZ ’s very last sentence (2002: 388; § 6) reads: “It is a task for the future to investigate whether cardi-

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The word class ‘cardinal numeral’

nal numerals are a serious challenge to the concepts of word-class, head, and modifier.” I would respond: a challenge to the concept of word class? – probably not; a challenge to the concepts of head and modifier? – only if we assume that all members of one word class can generally only be either heads or modifiers (by whatever criteria). It should be noted in this context that such an exclusive assignment to either head or modifier status has never been suggested for adjectives and nouns, both of which can appear as both heads and modifiers at least in most European languages. Why, then, should it be required of numerals? Before proceeding with a closer analysis of the variation in the morphosyntactic behaviour of numerals, one crucial aspect about Corbett’s universal should be noted: CORBETT (1978a: 368; 1978b: 70) speaks of simple numerals. The class of expressions that Corbett makes a statement about is thus actually very limited. He analyses the syntactic behaviour of atoms and bases, but he does not make a statement about complex numerals. Complex numerals – type-wise the vast majority of high valued numerals – do not play a role here. Yet CORBETT and other typologists do not draw on GREENBERG’s (more precisely: on SEILER’s; cf. the final remark in § I.3.5) distinction between atoms and bases when focusing on the syntax of numerals. Although the internal grammar of numeral systems (cf. Chapters I-III) and their interrelation with the quantified expression (Chapter IV) are two different issues, we will show in the next subsection that there is some connection between the two areas. In fact, I believe, at least in one respect, that CORBETT’s generalisation may well be explained by taking into consideration that numerals form an own system, the numeral system, and that the individual expressions perform particular functions within this system as set out in Chapter I. Since CORBETT does not focus on the notions of ‘atoms’ and ‘bases’, what can be deduced from his generalisation is a continuum from most adjectivelike lowest numerals to the most noun-like highest base. Let us assume that there is a set of simple numerals in between the two poles that is neither most adjective-like nor most noun-like. These numerals can be seen as the expressions with the prototypical morphosyntactic behaviour of the category ‘cardinal numeral’ in a given language. It is interesting that this set of, say, default numerals potentially includes both higher atoms and lower bases. Figure 19 shows a hypothetical decimal numeral system in which the atoms numerals from ‘5’ onwards and the lowest base all show the same morphosyntactic properties and thus constitute the set of prototypical numerals in that language. The lowest atoms potentially deviate from these properties, with ‘1’ showing the highest degree of deviation and a decreasing number of deviating features in proportion to the increasing numerical value. Similarly, higher bases devi-

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263

ate in more features than lower bases with the fundamental base usually behaving like higher atoms. Generally, the lowest atoms deviate from prototypical numerals in a different way than higher bases do.

‘1’

‘2’

‘3’

Figure 19.

‘4’

‘5’

‘6’

‘7’

‘8’

‘9’

‘10’

‘100’

‘1,000’

‘106’

‘109’

Deviation versus prototypicality in the morphosyntactic behaviour of simple numerals

For the reasons given in §§ V.2.1-2, I argue that variation among atoms does not have much to do with adjectives. On the other end of the scale, however, I believe that there is a conceivable connection between the variation among bases and nouns. Let us first look at the cardinality-dependent variation among atoms (§ V.2.4) and then proceed to the bases (§ V.2.5). V.2.4

Cardinality-dependent variation of atoms

In many languages, the lowest elements of the counting sequence (on the left hand end of the scale in Figure 19) exhibit morphosyntactic properties distinct from those of the other atomic expressions, as e.g. their inflectional behaviour or their varying Case assignment on the quantified noun; cf. HURFORD (2001). As we have seen, it is generally difficult to compare the lowest simple numerals with adjectives. As shown for Old English (§ IV.3.2.3), numerals do not share less features with determiners than they do with adjectives. These commonalities may be simply due to the fact that all these classes can be subsumed as noun modifiers. This alone suffices to explain most of the parallels with adjectives observed by many linguists. However, it is doubtful whether these parallels are significant in any way beyond the fact that all noun modifiers may to a certain degree display a similar morphosyntactic behaviour in relation to the head noun, i.e. with respect to agreement in and assignment of morphological categories such as Case, Gender and Number. As these properties are concerned, numerals (and, in fact, all types of quantifiers) are not generally more distant from determiners than they are from adjectives. Accordingly, REINHARDT actually modifies CORBETT’s generalisation in this respect: “[...] [Present-day English] numerals form a transitional class, sharing at the same time characteristics of different word classes.” (REINHARDT 1991: 196). And: “[...] [T]he grammatical behaviour of [Present-Day] English numerals falls between that of determiners, adjectives and nouns [...]” (REINHARDT

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The word class ‘cardinal numeral’

1991: 201). In short, there is no reason to take the adjective as that category by which morphosyntactic features of noun modifiers should be measured. Yet the question remains as to why there is cardinality-dependent variation of morphosyntactic properties at all within the sequence of atoms. The two studies by CORBETT (1978a; 1978b) show that, for Slavic, there are a number of differences between the lowest numerals and the higher atoms as displayed in Figure 19. Again, phenomena like these can be observed across languages (see, e.g., HURFORD (2003) for examples). Some suggest a connection between the morphosyntactic deviant behaviour of the lowest atoms and the way in which these lowest cardinalities are cognitively processed: humans can perceive the lowest cardinalities up to ‘3’ or ‘4’ at once, i.e. without counting – a cognitive capacity referred to as ‘subitising’. If we see three apples on a table, we recognise at once that there are three. If there are five apples, by contrast, we have to count them in order to determine the size of the set; cf. HURFORD (2001). (For a more general description of the phenomenon, cf. HURFORD 1987: 93–94; WIESE 2003: 95–98). However, although the morphosyntactically deviating atoms often comprise the set of subitising cardinalities, i.e. the numerals from ‘1’ to ‘3’ or ‘4’, there is no necessary connection between the morphosyntactic features of a set of linguistic expressions (i.e. of lexemes) and subitising as a cognitive phenomenon concerning the denotations of these expressions (i.e. cardinalities). Recall that numerals instantiate numbers and that, if used in the counting sequence proper, numerals are all uninflected anyway. There may or may not be a connection but this explanation will ultimately remain speculative. Moreover, while the range of subitisible cardinalities is universally the set from ‘1’ to ‘3’ or ‘4’, the set of morphosyntactically deviating lowest members of the counting sequence may not always be limited to this set. SEILER (1990: 191) offers a linguistic explanation, with which this last point can be resolved more easily. He points out that the range of low cardinalities constitutes an “area of convergence between the dimensions of numeration and determination […]” (SEILER 1990: 191). The extreme case in many languages is that the numeral ‘1’ and the indefinite pronoun are one and the same expression or at least have the same historical source. SEILER’s explanation does not contradict HURFORD’s but it operates with genuinely linguistic notions – ‘quantification’ and ‘determination’ – rather than with phenomena of cognitive psychology. This obviously has an equally strong explanatory force because it is more feasible to link different reference types (e.g. indefiniteness) – rather than cognitive processes – with constraints for the use or absence of linguistic markers such as inflectional affixes. Nevertheless,

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265

the cognitively special status of these low cardinalities may have some impact on the grammatical properties of the respective linguistic expressions. Although I consider SEILER’s explanation to be plausible, there is, admittedly, no way to prove that the conceptual connection between quantification of low cardinalities and (indefinite) determination is the ultimate reason for the phenomenon that the lowest numerals may deviate in their morphosyntactic behaviour. However, the fact that it will probably not be possible to find an ultimate, logically necessary reason for this phenomenon does not defy our general assumptions that morphosyntactic variation among simple numerals can be seen as an inherent property of this class. Let us now look at the morphosyntactic properties of higher bases. Here, I believe, we will be able to find a sufficient explanation for why the highest bases deviate. A clue to this question lies in the way numeral systems emerge historically. Although this is an extremely long-term process, there is crosslinguistic evidence that most numeral systems unfold and develop in a more or less uniform way. And it is this development – basically the diachronic side of what we discussed theoretically about numerals and numeral systems in Chapter I – which offers an explanation of the fact that numerals synchronically display varying inflectional and syntactic properties. V.2.5

Cardinality-dependent variation of bases

V.2.5.1

The emergence of numeral systems

The clue for the variation in the morphosyntactic behaviour of high base numerals can be found in the way numeral systems emerge. This process is cross-linguistically relatively uniform because the connection between the concept ‘number’ and the tools to assign numbers to sets (cf. § I.2) is not specific to a particular culture but to general cognitive capacities of humans. Hence, the way numeral systems come into being and develop is cultureindependent and thus largely language-independent. Recall that the conventionalisation / acquisition of an ordered sequence of well-distinguished elements (that is, in the case of linguistic numeral expressions, the counting sequence) is both phylogenetically and ontogenetically a prerequisite for the development of numeracy and not vice versa; cf. § I.4.2.1 and WIESE (2007). And since the concept ‘cardinality’ is generally the same, not only within a particular community, but also across different human cultures, the technical device that is required in order to employ this concept must also meet the same criteria across cultures.

266

The word class ‘cardinal numeral’

These criteria we described in detail in Chapter I. This section therefore rephrases much of what we said in §§ I.2-4, albeit from a diachronic perspective. In § I.4.2.1, we have already touched upon the issue of how a sequence of conventionalised number words emerges. The crucial step in the development of a numeral system is the evolution of an ordered sequence of simple expressions for numerical values. The most likely lexical source for a numeral is an expression denoting a body part; cf., for instance, RIJKHOFF (2002: 157); DETGES (2003: 52–54); VON MENGDEN (2008). This is because body parts are the best available set of culturally salient and constantly available items that meet the necessary criteria to serve as tools for number assignment in that they form by nature ordered sequences of well-distinguished elements (§ I.2). At some stage, the expressions denoting those body parts which are used for counting are themselves used for counting. The body parts become obsolete as a numerical tool and the respective expressions undergo a semantic split: while they retain their original body-part meaning, some variants of these expressions become a small set of systemic numerals: a sequence of simple numerals. This is not to say that the lexical source of an atomic numeral is necessarily a body-part expression. But expressions for body parts are certainly the most frequent and the most natural sources for numerals – simply because a sequence of body parts is the only potential numerical tool which is salient and constantly available for human cultures in early developmental stages. Once the set of simple expressions used for number assignment becomes too large – to be easily memorised by an individual or also to retain its conventional character across a larger community – combinations of such simple expressions occur on the basis of arithmetic operations: complex numerals. At first, such combinations may be used sporadically (§ I.3.2). If this system needs to go beyond a small number of sporadic combinations of this kind, a base expression is needed in order to form serialisations of arithmetic operations (§§ I.3.3 and III.2.1). From this point onwards, a numeral system is much more efficient than a mere sequence of simple expressions. However, the cultural development of a society may require, at some much later point in history, the further expansion of the numeral system by the introduction of another base (§§ I.3.4 and II.7.3). Up to the introduction of the next higher base, again an extremely long time passes. (We disregard here the possibility of a sudden introduction of an entire new system due to language contact). Evidence both for the process itself and for its duration can be seen by the age of the bases of, say, the numeral system of English: the expression for ‘100’ is shared by all Indo-European branches; cf., e.g., SZEMERÉNYI (1960: 1). By contrast, the expression for ‘1,000’ is only shared by Germanic,

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Baltic, and Slavic (cf. below fn. 57 and § II.7.1.2). It follows that ‘1,000’ must have been introduced at a later point in history, long after the disintegration of the Indo-European daughter languages. ‘1,000’ must have been the highest base of the numeral system from at least before the emigration of the Goths to the Balkan up to the late fourteenth century when MILLION is first attested in English (cf. § II.7.3 and the description in § III.3.3). Given this scenario, we can state with certainty that the higher a base, the later it became integrated into the numeral system. Where do the bases come from? There is a widespread assumption that higher bases are derived from numerically unspecific quantifiers that denote high quantities. CORBETT (1983: 245), for instance, refers to Old Church Slavic t'ma ‘10,000’, which originally used to mean simply ‘multitude’. There may well be cases of expressions denoting high, numerically unspecific quantities which become fully integrated into a numeral system as numerically specific bases. Most of the etymologies of high base numerals that I am aware of, however, are intensifications of lower bases. If PIE *(d)ḱṃtóm ‘100’ is derived from *déḱṃt ‘10’ (cf. BRUGMANN 1890: 15–16, § 5 and 1911: 35, § 29), then it must mean something like ‘a great ten’. More certain is the etymology of the next higher base: Proto-Germanic *þus-hund-, which can be construed as a ‘strong hundred’.57 Higher bases are otherwise likely to be borrowed, as for instance PDE million, which is borrowed from Italian. However, the Italian expression is again an intensification of the next lower base: Italian milli-one means ‘a great thousand’. If more evidence is needed, the fact that the varieties of Present-day English differ in their ways to express the next higher base – both the outdated milliard and billion being neo-classical intensifications of million – shows that these expressions were integrated into the

57 The ultimate etymology of Proto-Germanic *þushund- is difficult to determine. It is probable that the Proto-Indo-European expression for ‘100’ is a constituent of the compound. SZEMERÉNYI (1990: 241, § VIII.5.5) suggests a pre-Germanic *tūso-ḱṃt-ī, a compound consisting of an adjective ‘strong’ and of the word for ‘100’. The exact relation between the Germanic forms and the corresponding expressions in the Balto-Slavic languages still needs to be explained. PIJNENBURG (1989: 101–105) offers an explanation slightly different to SZEMERÉNYI’s, according to which neither of the two groups borrowed the expression from the other. Typologically, the etymology suggested by SZEMERÉNYI is confirmed by the semantically parallel formation of Italian millione ‘106’, formed by Latin mille ‘1,000’ and the suffix -one ‘great’; cf. §§ II.4.1.2 and IV.1.5.1. However, with respect to Finnish tuhat ‘1,000’, the numeral may also be a substrate word of the Baltic area. The resulting Proto-Germanic form is *þus-hund-, whence OE /'θu;s@nd/.

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The word class ‘cardinal numeral’

system at a yet later stage. Cf. VON MENGDEN (2008) for a more detailed discussion.58 In any case, and this is crucial for our discussion, the most likely lexical sources for numerals of all types are nouns – whether they were originally expressions for body parts, for high numerically unspecific quantities or intensifications of higher bases. However, since atoms (and usually the first base) are so old, their original nominal properties have long been worn out. The morphological properties of these expressions are those which we postulated above in § V.2.3 to be prototypical for cardinal numerals in a given language. We may now assume that the degree to which the morphosyntactic behaviour of a higher base resembles that of the prototypical set of numerals (usually the lowest base and the atoms, but not the lowest atoms; cf. Figure 19 above) depends on the time that has passed since this base was integrated into the numeral system. The later the time of integration into the system, the less time there has been for it to adapt to the morphosyntactic characteristics of the word class it now belongs to. The length of this time is, of course, inversely proportional to the numerical value of the base. In other words: higher base numerals are former nouns which are still in a (long-lasting) process of full integration into the system and, thus, into the word class ‘cardinal numeral’.59 V.2.5.2

Rephrasing Corbett

In § V.2.3, I argued that what should be altered about CORBETT’s generalisation is not the generalisation itself but the perspective of the arguments in the comparison. When explaining the properties of numerals, the numerals themselves should be the standard of comparison, not other word classes. According to this perspective, higher base numerals are ‘less numeral-like’ rather ‘than more noun-like’. In § V.2.5.1, we looked at the way numeral systems grow. This diachronic scenario, of which I hypothesise that it has a universal status, clearly shows why higher bases necessarily have more properties in common with nouns than lower simple numerals do. But, once again, this does by no means imply that they are nouns, nor does the statement that something 58 See also WIESE (2007) for an account that focuses on the first steps in the emergence of numeracy and of numeral systems. The details of these early steps are not crucial for our line of argument and are therefore disregarded here. 59 Cf. the remark by ROSS/BERNS (1992: 557–558, § 15.1.0; my highlight) which points into the same direction: “The decads ‘hundred’, ‘thousand’, million’, etc., are, by origin, nouns, but for the most part these numerals have, in attributive function, become indeclinable adjectives, though they decline – as nouns – in non-attributive function.”

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about numerals is like nouns say anything about the properties of numerals. Higher base numerals are, more than anything else, numerals. We will find evidence for this explanation if we look at other word class changes, some of which are often described as grammaticalisation processes. For instance, there are old prepositions which are usually mono-morphemic and which all share, in principle, the same grammatical properties. They are often called ‘primary prepositions’ and constitute the prototypical members of the class ‘preposition’. There are also ‘secondary prepositions’ which are often complex and which still reveal their lexical sources – either nouns (because of < by the cause of) or verbs (during); cf. C. LEHMANN (2002: 120). In Present-day English, we can analyse these changes basically by looking at the etymologies of these expressions. In German, which has retained a Case system, we can also observe a change in the morphosyntactic properties of some younger prepositions: the preposition während ‘during’ requires the genitive Case of the following noun phrase in literary German. This is because it is derived from a present participle of the verb währen ‘last, endure’. This, together with a following noun, could be used as a time adverbial if the whole construction was in the genitive Case; cf. (5.10). After the participle came to be used conventionally as a preposition, the noun still needed to take the genitive Case, as in (5.11) – a remainder from the adverbial use of the entire construction. In literary German and in normative grammatical descriptions, the genitive is the rule for the prepositional complement, but in spoken German, the noun takes the dative because the dative is more common for prepositional complements (5.12). (5.10) Archaic German währen-d-en Essens last-PTC-GEN supper-GEN.SG ‘during supper’ (5.11) Literary German während des Essen-s during DET:GEN.SG supper-GEN.SG ‘during supper’

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The word class ‘cardinal numeral’

(5.12) Colloquial German während dem Essen-Ø during DET:DAT.SG supper-DAT.SG ‘during supper’

The example from German does not exactly match with the development of numerals. However, it conveniently shows that a shift of word class does not take place from one day to the next. An expression undergoing such a change sheds the properties of the old class only gradually. Nevertheless, it would not occur to any linguist to say that German während or PDE during are verbs, or are “more verb-like” because they still show some features which they do not share with prototypical prepositions – features which can be explained by the fact that these prepositions have developed out of verbs. What matters in our context is that linguistic expressions in an ongoing process of shift from one class to another generally show a hybridity in their morphosyntactic features similar to that of higher bases. In the context of grammaticalisation studies, this phenomenon comprises in HOPPER’s notions ‘persistence’ (1991: 28–30) and ‘de-categorialisation’ (1991: 30–31). These notions can well be transferred to types of category change which, in the case of higher base numerals, are not grammaticalisation processes in the strict sense: when describing the individual steps in the shift of an expression, from one class to another he says that “details of its lexical history may be reflected in constraints on its grammatical distribution” and that “[f]orms undergoing grammatic[al]isation tend to lose or neutralise the morphological markers and syntactic privileges characteristic of the full categories Noun and Verb, and to assume attributes characteristic of secondary categories such as Adjective, Participle, Preposition, etc.” (HOPPER 1991: 22). We may also add ‘numeral’ to HOPPER’s list. Therefore, rather than calling some numerals “noun-like”, we may explain those properties which are different from the prototypical members of the word class ‘numeral’ by the fact that they have developed out of nouns. Thus, if we look at the cardinality-dependent morphosyntactic variation of numerals from the perspective of what we assumed to be prototypical numerals (in a given language), we can retain CORBETT’s generalisation but rephrase it by assuming the opposite perspective; see (5.13):

Adjectives, nouns, and numerals

271

(5.13) CORBETT’s generalisation revised Cardinal numerals constitute a distinct word class. If the morphosyntactic behaviour among numerals of one language varies, then the higher the numerical value of a simple numeral, the less it has adapted to the morphosyntactic behaviour of that class and the more it still displays morphosyntactic properties of its source category, i.e. of nouns.

This generalisation disregards the lowest set of numerals which may likewise deviate in their morphosyntactic behaviour. As we have discussed in § V.1.4, they deviate for different reasons than higher bases do. And, more crucially, if they deviate, their properties are distinct from prototypical numerals but they do not necessarily match or resemble significantly those of a particular other word class. The degree of similarity with other word classes does not expand the morphosyntactic similarities that usually exist among noun modifiers of one language. It is both the diachronic perspective that we assume here and the theoretical basis for the analysis of numeral systems we set out in Chapter I which together enabled us to provide sufficient evidence for explaining CORBETT’s universal. CORBETT himself has suggested that the historical development of numeral systems may provide the clue to an explanation of his generalisation. CORBETT (1983: 245) writes: It is less easy to see why numerical value should correlate with nouniness, though the beginnings of a solution can be suggested. In the course of history the need has arisen for successively higher numerals; nouns referring to a vague large number have then taken on a specific numerical value, larger than that of the previously largest numeral. Thus the higher numerals are nouns pressed into the service as numerals. … As in the course of cultural development new numerals are introduced, naturally at the top of the earlier system, the previously highest numeral may be further integrated into the system and lose some noun-like features.

Whether or not CORBETT is correct with his claim that numerically unspecific expressions are the main source for higher bases (see the previous section for an alternative suggestion) it is their history that explains the properties of higher bases. But a category change is not a forceful process, as CORBETT’s

272

The word class ‘cardinal numeral’

metaphor implies. It is a very common phenomenon in human languages (see also HEINE 1997: 29–31; § 2.3).60 V.2.5.3

Another remark on 1-deletion

At this point, it will be rewarding to briefly recall another characteristic of higher bases which we discussed earlier. In § III.1.1, we discussed 1-deletion – the phenomenon that higher bases require an arithmetically redundant multiplier ‘1’. The degree to which 1-deletion applies to the individual bases of a numeral system is also proportional to the numerical value of a base; cf. Table 20 in § III.1.1. There, we said that the term ‘1-deletion’ implies that something is deleted which should actually be there. This can be accounted for by the arithmetically redundancy of an overt expression of the multiplier ‘1’. We can now conjecture that, if 1-deletion stands in proportion to the value of a base in a given language, it may also be an indicator of the degree of integration of an expression into the system. This perspective allows us to say that the probability of 1-deletion decreases the longer the expression has been part of the numeral system rather than that it increases with the numerical value of the base. Since, as we said, higher (or younger) bases have retained more of their nominal properties, we can interpret the overt expression of the multiplier ‘1’ as a nominal feature rather than as a numeral feature. Evidence for this may be seen in a similar property which increases with the numerical value to the base. The higher a base numeral, the more likely it is to replace the multiplier ‘1’ by an indefinite determiner. This is true at least for those languages that have indefinite determiners which are both etymologically related with and formally distinct from the numeral ‘1’. The possibility to say a million, a thousand, and a hundred instead of one million, one thousand, one hundred has already existed in Middle English. In other words, it has been there ever since the indefinite determiner developed out of the cardinal numeral OE AN; cf. RISSANEN (1967: 29–30). Evidence for this also comes from Modern German where bases from ‘100’ onwards can have an overt expression for the multiplier ‘1’. With very high bases like e.g. million ‘106’, this expression can occur in its unstressed form (‘ne Million ‘a million’; ‘ne Milliarde ‘1012’). While the indefinite determiner and the numeral ‘1’ are homophonous in their basic forms, i.e. ein, the reduced form is only possible 60 This process does not only account for the noun-like features of higher bases, but also explains the fact that lower bases have functional variants – e.g. the affixes described in §§ I.5 and II.4.2-3 – than higher bases do. For a more detailed description including the development of these affixes cf. VON MENGDEN (2008).

Adjectives, nouns, and numerals

273

for the indefinite article but not for the numeral. By contrast, the lower valued bases in German, hundert and tausend, always require the full form (einhundert ‘one hundred’, but not *’n hundert ‘a hundred’, eintausend ‘one thousand’, but not *’n tausend ‘a thousand’). Given this, we may even say that 1-deletion is in fact ‘an-deletion’ – the loss of the capacity to be marked by an indefinite determiner with an increasing integration of a base into the numeral system. Only through the paradigmatic pressure exerted by the sequence of higher multipliers (i.e. two/three/four [etc.] hundred; cf. § III.1.1) does the determiner become reinterpreted as a multiplier, which results in the possibility of using one rather than a(n). While these considerations must remain to some degree hypothetical at this point, we can say with certainty that 1-deletion and the related phenomenon of the replacement of the multiplier ‘1’ by an indefinite determiner both show once more that numeral-like features are gradually adopted by expressions which once used to be nouns. V.3

Cross-linguistic types of numeral constructions

The morphosyntactic properties of numerals do not only vary among the different members of the counting sequence. There is also variation in their external properties, i.e. in their relation with the quantified NP in terms of syntactic and inflectional behaviour. For Old English, this variation has been described in detail in Chapter IV. In § V.2, we have argued that the cardinalitydependent variation – the fact that different numerals of the counting sequence show different inflectional behaviour under the same morphosyntactic constraints – can be interpreted as an inherent property of numerals rather than as an indicator of their hybridity. On the basis of this hypothesis, we could explain to a large degree why variation occurs and also why this is likely to be a cross-linguistic rather than a language-specific phenomenon. A similar approach will now be employed for the context-dependent variation. This will be based on our analysis in Chapter IV, but again we will take cross-linguistic aspects into consideration. Of course, such a typological comparison cannot be on a safe ground unless it is based on data from a representative language sample. Since the present study deals with the numerals of one particular language, a representative cross-linguistic comparison cannot be provided. However, the following considerations are based on undisputed data and the conclusions I will draw may at least be taken as a confirmation of the categorisation proposed here for Old English. The claim will be that, while the construction types described in Chapter IV are language-specific, certain patterns of these constructions are, in

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The word class ‘cardinal numeral’

principle, universal. Consequently, their context-dependent variation, too, constitutes a typical and in some way a necessary feature of numerals or of numerically specific quantification. We will therefore argue that – just like the cardinality-dependent variation discussed in § V.2 – some features of the variation in the morphosyntactic relation of numerals and their quantified NPs are inherent, defining features of numerals rather than a sign of their hybridity. V.3.1

Count and Mass Quantification

In Chapter IV, one of the fundamental aspects with respect to the distinction between the different construction types was mentioned in a rather passing manner. In § IV.8, we said that the key distinction between the use of a numeral in the Attributive and the Partitive Constructions on the one hand and in the Mass Quantification on the other, is due to features of the quantified noun rather than to syntactic constraints or to grammatical properties of numerals. The former two construction types are used with count nouns, the latter with uncountable nouns. Although this classification is to some degree superficial – as is the distinction between count and mass nouns (cf. ALLAN 1980 for a valuable discussion) – it will suffice for our purpose to use this distinction without discussing the details underlying it. These two constructions have more or less close parallels in most languages in which nominal quantification (rather than verbal quantification) is the unmarked type of specifying cardinalities. However, while Old English (like Present-day English and most other European languages) uses the Attributive Construction as a default construction, in other languages, quantification with numeral classifiers is the unmarked case. In these languages, there is generally no or only a limited degree of plural marking on nouns. In classifier languages, nouns unmarked for Number have collective meaning; cf. GREENBERG (1972: 17–18). As with collective nouns and mass nouns in Western European languages, it is not possible to use a noun to immediately refer to an individual representative of a concept. In order to refer to an individual member of a class, the noun must be individualised by an additional element – the classifier. The functional domains in which this process of individuation of a nominal concept by a classifier is most likely to be carried out are determination, interrogation, and quantification.61 Cf. the examples from Thai in (5.14)–(5.16) (taken from GREENBERG 1972: 10). 61 The following description will necessarily be a little simplified. It summarises only those aspects of numeral-classifier-noun constructions that are most relevant for our discussion. For a detailed study of classifiers cf. AIKHENVALD (2003). For classifiers in the particular

Cross-linguistic types of numeral constructions (5.14) bùrì cigarettes

sǑŋ sO•ŋ two packs

(5.15) bùrì cigarettes

sǑŋ lǒ two dozen

(5.16) bùrì cigarettes

sǑŋ muan two long-object

275

Whenever a particular amount or quantity – and this may be expressed by a unit of measurement (5.14) or by a conventionalised quantity (5.15) – is employed for quantification, the same kinds of lexical items as in Western European languages are employed for such a construction. If, however, the cardinality of individuals in a set is to be expressed, then the classifier must take the place of the unit of measurement (5.16). In European languages, similar constraints hold for non-count nouns. If, for instance, we wish to quantify ‘gold’, this cannot be done attributively; cf. (5.20). Instead, we basically have the same options as classifier languages do; cf. (5.17)–(5.19). (5.17) There are

five ounces of gold

(5.18)

five bars of gold

(5.19)

five pieces of gold

in the safe.

But: (5.20)

*five golds.

One option would be to use a particular unit of measurement, as for instance ounce in (5.17). We could also employ an expression which refers to some characteristic of the mass, for instance, to a typical shape in which it appears: context of quantification cf. also GREENBERG (1972: 17–18), SEILER (1986: 96–97, § 4.6.3), BISANG (1999: 113, § 1.1), and RIJKHOFF (2002: 162–166, § 5.2.2.1.3), among others. There is also some variety of individuating constructions within and across languages, which will not be covered by the present discussion. There can be, for instance, a morphological element which turns the collective noun into a singulative derivate (similar to PDE *two police but two policemen). Another method is a compound consisting of the classifier and the quantified mass term (similar to PDE *three ices but three ice cubes, i.e. three cubes of ice); GREENBERG (1972: 22–23 and n. 25). Also cf. KRIFKA (1991: 400b– 401a, § 1.3) in this context.

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The word class ‘cardinal numeral’

(5.18). In this case, we would actually individuate the mass term. Hence, the use of the word bar in our Present-day English example (5.18) may be compared with that of the Thai classifier muan ‘long object’ (5.16). A third way of quantifying ‘gold’ would be simply to employ a completely neutral expression that does not refer to any particular property of the mass. This would be an expression like e.g. piece (5.19). While bar may be used for other kinds of precious metal (like ‘silver’) or for other masses (like ‘chocolate’), it is not conventionally used for any solid substance. For instance, while in Presentday English a/three wooden bar(s) is always conceivable, individuation of the notion ‘wood’ by the expression bar (?a/three bar(s) of wood) would not be idiomatic. By contrast, piece may be employed to individuate expressions for any solid substance. Likewise, if in a classifier language a term needs to be quantified which does not lend itself to conventionalised classifications like [± animate], [± long] etc., a more neutral lexeme like one for ‘piece’ is employed. Syntactically, quantification in classifier languages corresponds with quantification of mass terms in Old English and in other Western European languages in many respects. In both types of constructions, an additional lexical element is necessary for assigning a particular cardinality to the referent of the mass term. Disregarding the constituent order, the prototype construction we have described for Mass Quantification in Old English in § IV.7 differs from the Classifier Constructions in Thai ((5.14)–(5.16)) only with respect to the semantic content of the respective lexeme. In Mass Quantification of Old English, it is a unit of measurement and in classifier languages, it is a classifier: Mass Quantification:

[[NUM → MEAS ] → non-count NPGEN.SG.]

classifier languages:

[[NUM → CLF] → non-count NP]62

There are numerous remarks in the literature on the parallels and differences between classifiers in classifier languages and units of measurement used in these constructions in non-classifier languages. Some linguists seem to prefer to keep the two constructions apart, particularly the two constituents that are 62 It is equally possible to analyse the hierarchy in a Classifier Construction such that the numeral quantifies a phrase consisting of the classifier and an NP denoting the referent; i.e. [NUM → [classifier → NP]]. Cf. the varying interpretations of this structure in GREENBERG (1972: 28); SEILER (1986: 99; § 4.6.4.2); LINK (1991: 134–137); KRIFKA (1991: 401b– 402a, § 2.2); HURFORD (2003: 570–572, § 3.1.2). For our line of argument, the hierarchy among the three expressions is irrelevant.

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277

used for individualising the referent. AIKHENVALD (2003: 114–121) distinguishes mensural and sortal ‘quantifying expressions’ in non-classifier languages from genuine classifiers in classifier languages. Similar distinctions are made, among others, by SEILER (1986: 99–100; §§ 4.6.4.2–3); KOPTJEVSKAJA-TAMM (2001: 530).63 Without denying the differences among these expressions both within classifier languages and between classifier and non-classifier languages, our comparison reveals that there are obvious parallels. The main argument brought forth in favour of a separate account of the two is a semantic and/or etymological one: while most of the relevant expressions in languages with the majority of nouns being countable represent a more or less conventionalised unit of measurement, the lexical source of classifiers actually represents concepts which, in the literal sense, ‘classify’ denotations according to the type of concept the nouns denote, e.g. ‘human’, ‘animate’, ‘long’, ‘flat’, etc. By contrast, the equivalent expressions in non-classifier languages tend to denote more or less conventionalised units of measurement, or at least objects that may contain certain amounts of non-discrete masses and that may therefore serve for quantifying these masses. For a more detailed picture of the semantics of noun classification I refer here, among others, to CROFT (1994); BISANG (1999: 124–142, § 2.2); AIKHENVALD (2003: 270– 306.) Most formal differences between the relevant expressions in classifier and non-classifier languages, such as possibly different inflectional behaviour or possible fusion of classifier and quantifier (an Old English example of which we discussed above in § IV.7; cf. examples (4.84), (4.85), and (4.86)b), are marginal with respect to the parallels that do exist between the set of constructions in (5.14)–(5.16) and that in (5.17)–(5.19). These and other differences do not play a role for the present discussion and I will disregard them here (cf. LANGACKER 1991: 167; WIESE 2003: 277). The main syntactic difference between the two types lies in the inherent grammatical features of nouns in the respective languages rather than in the use of the individuating expressions themselves: since nouns in classifier languages require a classifying element by default, these elements naturally acquire a higher degree of grammaticalisation than they do in non-classifier languages. What matters in our context is 63 The terminology employed in this context for the respective expressions is anything but consistent. GREENBERG (1972: 12) and others distinguish ‘unit counters’ as a subcategory of ‘classifiers’. ‘Unit counters’ are classifiers that do not denote conventional units like bunch or cup in a bunch of flowers and a cup of tea. Instead, they refer to terms that denote individual items, like PDE piece. For other sets of labels see K RIFKA (1991: 401b–402a, § 2.2); KOPTJEVSKAJA-TAMM (2001: 530); GRINEVALD (2004: 1020a); GIL (2005: 226a).

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The word class ‘cardinal numeral’

that both types of expressions occupy the same position in a parallel quantificational construction. The crucial typological difference between classifier languages and nonclassifier languages is not primarily the choice of default quantificational construction – Attributive Construction or Mass Quantification. The fundamental distinction between the two language types is whether the default kind of nominal expression is countable or uncountable in the respective language. This choice implies that the inverse type would exist as a marginal or at least as a non-prototypical class of nouns in the same language. Whether an Attributive Construction (or the equivalent thereof) or Mass Quantification (or the equivalent thereof) is the default type of quantification in a language is only a consequence of the default noun status in that language. Likewise, other evident differences between the expressions that serve as individualising elements ultimately depend on whether the language primarily uses count or noncount nouns: if a language hardly uses count nouns, nominal concepts are necessarily individuated according to their semantic classes whereas in languages in which the class of non-count nouns is largely limited to nouns denoting non-discrete aggregates, the respective referents are necessarily individuated by expressions that denote objects which may serve for measuring these aggregates. To put it simply: it is impossible to quantify ‘trees’ or ‘men’ by means of ‘cups’ or ‘barrels’ and at the same time it is not a culture-specific phenomenon that non-discrete masses cannot be perceived in terms of [± human], [± animate], or [± long object] etc. CROFT’s (1994: 151–152) remark that “if measure terms are included [i.e. if they are categorised as classifiers; FvM], then all languages are classifier languages, […]” bypasses the reason for the semantic differences of these expressions (or rather, of their lexical sources). In this context, it is more than a side remark to mention that classifier languages, too, may have a marginal set of count nouns that do not require classifiers for quantification. Even in those languages in which a classifier is obligatory, it may only be so with particular nouns, in particular contexts or in particular registers; cf. KRIFKA (1989a: 10); GIL (2005: 226b– 227a). In short, although classifiers and units of measurement are, of course, distinct with respect to their lexical sources, in the function they perform in quantificational constructions, they are not significantly distinct from each other – and nor are the respective construction types themselves. These parallels suffice to postulate that quantification in classifier languages and Mass Quantification in non-classifier languages represent the same type of quantificational construction in a cross-linguistic comparison.

Cross-linguistic types of numeral constructions

V.3.2

279

The Partitive Construction as an intermediate type

We have argued so far that two of the quantificational constructions we have postulated for Old English, Attributive Construction and Mass Quantification, have equivalents across languages, cognate and non-cognate. In principle, the Attributive Construction is cross-linguistically possible only with count nouns and the quantifier immediately quantifies the NP. By contrast, Mass Quantification requires the impossibility of morphological Number distinction on the quantified NP and that an intermediate element between quantifier and quantified NP be employed, the classifier. What about the Partitive Construction? The Partitive Construction shares a number of features with the Attributive Construction as opposed to the quantification of non-count NPs: numeral and quantified element are (or can be) adjacent, and both constructions are restricted to count nouns. Yet the Partitive Construction shares a number of other characteristics with Mass Quantification. In Old English, both Partitive Construction and Mass Quantification are confined to a certain class of nouns or to certain contextual constraints. In contrast to the Attributive Construction, they are both marked types of quantification in the sense that their use is constrained to particular conditions. I would also argue that, in spite of the fact that the numeral and the quantified element in a Partitive Construction are adjacent, the numeral does not quantify the noun as immediately as it does in the Attributive Construction because the partitive relation must be encoded by morphological (genitive) or syntactic (of-phrase) means; cf. § IV.8. The most important characteristic which Partitive Construction and Mass Quantification have in common is that in both types of quantification, Number values are not distinguished. In classifier languages, the concept is not encoded grammatically on nouns (or, if it is, it occurs in a limited way). A noun quantified in a Partitive Construction can be used as a count noun, but it still lacks Number distinction in this particular construction (cf. § IV.5.3). We can therefore state that the Partitive Construction requires the countability of nouns without taking advantage of the defining property of count nouns, i.e. Number distinction. In the Partitive Construction, the inherent discreteness of the referent of count nouns is suspended and the count noun is (morphosyntactically) used in a collective sense. In this case, the morphological value [+ plural] does not provide any information about the cardinality of the referent (‘more than 1’). Instead, it encodes de-individualisation, i.e. the semantic feature [+ collective], or rather [– discrete]. Considering the two constraints we identified for the use of the Partitive Construction in Old English, this interpretation makes sense. In the first case, the quantification of a subset

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The word class ‘cardinal numeral’

(§ IV.5.2.1), the (discrete) referent is the subset and the discreteness of the larger set, out of which the quantified set is extracted, becomes irrelevant for the underlying grammatical process (no Number distinction). In the second case, the quantification by high numbers (§ IV.5.2.2), the constraint follows a general tendency of languages to encode higher quantities as non-discrete aggregates, which, in turn, can easily be explained by the way human cognition treats larger sets in contrast to smaller ones. Only the numerical value which respectively marks the point from which the constraint takes effect – ‘20’ in Old English (cf. § IV.5.2.2) – remains arbitrary. We have just listed a number of morphosyntactic and/or semantic features of the Partitive Construction, shared by either the Attributive Construction or Mass Quantification. The way these features are distributed over the two other constructions strongly suggests that the key to a typology of quantificational constructions is not primarily the morphosyntactic properties of the numeral but rather may be found in the countability of the quantified nouns. The two prototype constructions, Attributive Construction and Mass Quantification, respectively require Number distinction and the impossibility of Number distinction on the quantified NP. The Partitive Construction requires count nouns but – in contrast to the Attributive Construction – the quantified NP lacks Number distinction since it is always plural even if the cardinality is ‘1’. The conclusion I would like to draw from these parallels and differences is this: there can be quantificational constructions in languages intermediate between the two cross-linguistic poles, Attributive Construction and Mass Quantification. We discussed the Partitive Construction here because it can be seen as such an intermediate type in Old English. Whether intermediate quantificational constructions of other languages are close or comparable to the Partitive Construction of Old English in their morphosyntactic properties, is largely irrelevant in our context.64 The crucial point here is that there are, crosslinguistically, two poles of quantification, two types of constructions which are dependent on the count or non-count status of the quantified nouns, and that, for Old English, the Partitive Construction can be interpreted as having an intermediate status between these two poles. 64 For instance, some Uralic languages have constructions in which the numeral from a certain numerical value onwards assigns partitive Case to the quantified noun, whereas the lowest valued expressions assign nominative or accusative according to the syntactic role of the argument; cf. HURFORD (2003: 576–590, § 3.3) for a typological survey of quantificational constructions in European languages. It should be noted that the label ‘partitive’ is used for different phenomena in the context of different languages. For instance, what is called ‘Partitive Case’ in Fennic languages does not fully correspond with what is referred to as ‘partitive’ in Western European languages; cf. e.g. NELSON/T OIVONEN (2000) for Inari Sami.

Against the hybridity of cardinal numerals

V.4

281

Against the hybridity of cardinal numerals

The aim of this chapter has been to show that the semantic categorisation of numerals in § I.1, upon which we have based our descriptions so far, may also hold for a morphosyntactic and distributional categorisation of a lexical category ‘cardinal numeral’. In their morphosyntactic behaviour, Cardinal numerals potentially vary in two ways. They may vary according to the position of the numeral in the numeral system. This is the cardinality-dependent variation discussed in § V.2. The type-wise most frequent group of numerals displays the prototypical behaviour of that class. The other, non-prototypical members of the class ‘numeral’ – the very lowest atoms and the higher bases – are not only peripheral members when it comes to their morphosyntactic behaviour, but they are also located at the periphery of the counting sequence and, accordingly, of the numeral system. As to the context-dependent variation, a cross-linguistic comparison of quantificational constructions suggests that the use of numerals in different types of constructions should not be seen as evidence of a hybrid morphosyntactic behaviour – neither from a cross-linguistic nor from a language-particular perspective. Rather, it should be seen as their adaptation to the varying degrees of countability of the quantified NP, or, semantically speaking, to the varying degree of discreteness of the quantified referent – again, in both perspectives, language-particular and cross-linguistic. The more Number distinction is relevant to a noun (either according to its grammatical properties or according to contextual constraints), the more immediate the syntactic relation between the quantifier and the quantified noun is. GREENBERG (1972: 23) makes a generalisation along these lines. It is based on languages like Arabic or Russian, which both have a class of collective nouns that require singulative marking for quantification (cf. also fn. 61 above): [...] where there is a system of collectives, the direct construction of the numeral with a collective is avoided. Among the alternatives is the use of one or more non-collectives in a construction with the numeral and more loosely joined syntactically to the collective which is in apposition or is a dependent (partitive) genitive.

The fact that I focused on the parallels of quantificational constructions across languages is not meant to explain away or to ignore the differences that exist in each of the constructions that I postulated as cross-linguistic equivalents. But the observable parallels suggest that both the context-dependent variation and the cardinality-dependent variation of numerals cross-linguistically follow

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identifiable patterns. These patterns are constrained not that much by inherent properties of numerals but by factors such as countability of the quantified nouns, human perception of high quantities as non-discrete masses, and also by information structural constraints. If we see the variation in the morphosyntactic properties of numerals from this perspective, it seems that this variability is characterised by kinds of constraints which we would easily accept if we were to account for the – language-internal and cross-linguistic – variability of, say, nouns or verbs. As I have repeatedly argued in this chapter, there is no necessity to describe and classify the morphosyntactic properties of numerals measured against the standard of other word classes. As a consequence, if we wish to explain the constraints on the varying morphosyntactic behaviour of numerals, the point of departure should be the question of how numerals behave rather than what is similar to other word classes in the behaviour of numerals. As we could see, we will gain a clear picture of how numerals in one language may or may not behave in terms of distribution and inflectional properties. In principle, we will not find more idiosyncrasies and marginal phenomena than we do if we examine the morphosyntactic properties of nouns, verbs or adjectives as a whole class. Thus, whatever is transitional or hybrid about numerals is not more transitional or hybrid than those idiosyncrasies are which we would also observe in other word classes. We can therefore say that numerals can be taken as a word class that may be sufficiently defined on its own, not only on semantic grounds (as we did in § I.1), but also on morphosyntactic grounds. The question as to how far these properties of numerals may or may not match with nouns, adjectives or with whatever else, is irrelevant for most research questions concerning numerals and is in any case potentially misleading. The morphosyntactic variation of numerals has always been interpreted as an indicator of the hybridity of that class or sometimes even as a sufficient reason to reject the existence of this class. To take one example, FOX says (for German) (2005: 175): “Some grammarians also establish a class of ‘numerals’, one of whose functions is to qualify a noun. However, ‘numeral’ is a purely semantic class, since numbers may have a variety of syntactic roles.” This line of argument is characteristic of the way numerals have been treated in the literature, not only in the traditional descriptions of ancient languages. This reasoning should be rejected. Nouns and adjectives, too, can occur in a variety of syntactic roles. Nouns can be in the subject position, in the object position, they can be predicates (if used with a copula) and they can be complements or adjuncts of a proposition (with an adposition). We have already mentioned the way nouns may have varying inflectional properties, for in-

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stance (but not exclusively), depending on their countability (§ V.3.1). I do not think there is one linguist who would reject the existence of a word class ‘noun’ because of this variability. So why treat the word class ‘numeral’ differently? Again, once we compare numerals with, say, prototypical nouns, the variation among numerals may appear striking. If we did it the other way, that is, if we compared the variety of syntactic roles and of the morphosyntactic behaviour of, say, nouns in a given language with that of prototypical numerals, we may find ‘nouns’ strikingly instable and the properties of numerals nice and plain. Cf., in this context, the valuable discussion in PLANCK (1984). The later part of this chapter aimed at indicating a path to explore crosslinguistic patterns of morphosyntactic behaviour of cardinal numerals. The patterns, along which numerals vary in their morphosyntactic properties across languages, could only be alluded to since cross-linguistically valid claims should ideally be substantiated by a representative sample of languages. Nevertheless, I think that those cross-linguistic parallels that have been mentioned (particularly in § V.3) suffice to show that the ways in which numerals vary in their morphosyntactic behaviour is to some degree universal. In any case, to say that the behaviour of numerals is ‘hybrid’ would mean that there is no connection between the different types of properties and that the crosslinguistic variation of numeral-noun constructions is arbitrary. This is not the case. The fact that there are certain patterns of variation (rather than just variation) in the morphosyntactic behaviour of numerals is a phenomenon we also observe for nouns, verbs and adjectives. I therefore believe that, if it is possible at all to define word classes from a cross-linguistic perspective, cardinal numerals are one of them. Cardinal numerals are still more plainly defined on semantic grounds (Chapter I). But they share morphosyntactic and distributional properties to a sufficient extent. Variation in these properties can be explained and is not more extensive than the morphosyntactic and distributional variation that many other traditionally undisputed classes display. If a subcategorisation is wanted, it is most reasonable to classify numerals as a subclass of quantifiers not only for semantic reasons (cf. § I.1, esp. Table 2), but also on the basis of their morphosyntactic and distributional properties. This does not mean that all types of quantifiers share all inflectional and all distributional properties – such a total agreement in properties is generally not necessary for whatever classification. Quantifiers can, in turn, be taken as one of several groups of noun modifiers which would also include all adjectives and determiners, and also pronouns. It is perhaps even more promising to view these classes in a continuum of noun modification rather than as discrete subclasses, but I am not going to elaborate this point here. (Cf., for instance, REICH 2001: 86–104;

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§ 4.3 for a valuable discussion for Present-day English.) Parallels between numerals and adjectives exist only on this level. So, if we take numerals as ‘adjectives’, determiners and (some) pronouns would also have to be taken as adjectives. Such a classification was suggested, for instance, by BLOOMFIELD (1933: 202–204) who labels all noun modifiers as ‘adjectives’ and subdivides them into ‘descriptive’ and ‘limiting’ adjectives (in principle matching our ‘intensional’/‘extensional’ distinction in §§ I.1 and IV.1.1), the latter being ‘numeratives’ (corresponding to our ‘quantifiers’) and ‘determiners’. There are no significant differences in the classification, only in the terminological labels assigned to the subclasses. To label numerals ‘adjectives’ the way BLOOMFIELD does would, therefore, extend the notion of ‘adjective’ to a degree that would allow no statement about the individual members except that they are noun modifiers. 65 Although generally using the term ‘numeral’, we have only referred to cardinal numerals. Most languages have modifying expressions that are morphologically derived from cardinal numerals, such as ordinals (‘forth’), multiplicatives (‘fourfold’), frequentatives (‘four times’), and distributives (‘four each’). These sets of expressions have often been subsumed under the label ‘numeral’. Although these expressions, in addition to their morphological basis, do draw on the notion of ‘cardinality’ in the specific kinds of modification that they perform, neither their morphological nor their distributional properties lend support to such a classification. Not only with respect to their morphosyntactic properties, but also in some crucial semantic and/or functional respects, ‘four’ stands closer to ‘many’ than it does to ‘four times’ or to ‘fourth’. Numerals as a class in a parts-of-speech categorisation are, therefore, always and exclusively ‘cardinal numerals’. Other types of expressions that draw on the notion of ‘cardinality’ such as ordinals, multiplicatives, frequentatives, and distributives are expressions formally and semantically derived from cardinal numerals but otherwise clearly distinct from them. HURFORD (2002: 628b) remarks that any language with the category ‘numerals’ has the subcategory ‘cardinal’ but not necessarily one of the other subcategories listed here. This statement consists of a typological generalisation and of a presupposed (sub-)categorisation. Yet the generalisation is obviously evidence against the presupposed categorisation: cardinal numerals are not a subcate65 Subsuming numerals under a larger category ‘noun modifiers’ would perhaps facilitate the inclusion of verbal quantification into the discussion, i.e. of languages in which numerals are by default in a Predicative Construction. That verbal quantification only occurs in languages in which other typical argument modifiers are also restricted to the predicate position is indicated by the data in AHN (2003). However, AHN’s language sample is too poor to make statements that go beyond speculation.

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gory of numerals, cardinal numerals are numerals proper and all other sets of expressions traditionally also labelled ‘numerals’ are derived from them.

Concluding remarks We have looked at cardinal numerals from various angles and brought forth a number of novel suggestions on how numerals are to be categorised on several levels. If numerals have been “from a linguistic point of view, […] a mystical category per se”, as KOPTJEVSKAJA-TAMM (2001: 565, n. 2) has perceived them, I hope that the present study could relieve them of some of their mysticism and at the same time retain (or even increase) some of the fascination about this class of expressions. Much of what has been achieved in the discussions of the five Chapters could be achieved by combining different perspectives. The language-particular description of cardinal numerals (predominant in Chapters II, III and IV) was embedded into a more general, cross-linguistic context, comprising a theoretical framework (Chapter I) and a revision of the common approaches to a categorisation of cardinal numerals within the range of word classes (Chapter V). Additionally, two different areas in the study of numerals have been combined. One is the numeral system, that is, the way systemic numerals interact with each other, their arrangement in relation to each other, as well as the internal structure and the logical foundations of numeral systems. We could say that these aspects comprise the ‘internal grammar’ of numeral systems. The other area covers the way numerals interact with other expressions in the actual linguistic usage, that is, basically, when they quantify nouns, including the morphosyntactic properties numerals display in this process. In contradistinction to the ‘internal grammar’ of the numeral system, we could refer to this area as the ‘external grammar’ of numerals. What could be shown in the present study, among other things, is that the description and the analysis of the morphosyntactic properties of numerals profits from an in-depth analysis of the relevant numeral system. One of the key points which have been made evident is that the study of numerals does require a framework both delimiting the class ‘numeral’ from neighbouring noun modifiers, such as numerically unspecific quantifiers and non-systemic number expressions (cf. § I.1; particularly Table 1.2), and setting the category ‘numeral’ in a relation with the abstract concept of ‘number’. Numerals, I have argued as a first step, need to be defined as expressions comprising, and generated by a numeral system. We have briefly mentioned previous theoretical frameworks on cardinal numerals in the Introduction. The early ones, BRANDT CORSTIUS (1968) and HURFORD (1975) are – in the spirit of their time – formal and deductive approaches but in several respects difficult to apply to language-specific descrip-

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tions. GREENBERG’s (1978) contribution, by contrast, provides empirically founded ‘generalisations’ on numerals. HURFORD (1987) and WIESE (2003) focus in different ways on the cognitive foundations of numeracy. Some valuable theoretical aspects have also been contributed by SEILER (1990). The present study has been based particularly on those by GREENBERG (1987) and by WIESE (2003), but, because these two studies approach numerals from two quite different angles, the idea of the present study has been to unite the two approaches and thus provide a more integrated basis for the study of numerals. Chapter I has provided a theoretical framework aiming at a precise definition of the essential notions for both describing and explaining linguistic numeral systems. Although a semantic definition of cardinal numerals intuitively seems unproblematic, the relation between numerals and the concepts of ‘number’ and of ‘cardinality’ needs to be defined and set into a relation with the notion of ‘numeral’. Numerals, we said, are instantiations of numbers and thus employed in a process which, on a general, abstract level, we can describe as ‘number assignment’. Numbers are properties of sets in that they are measures for the potency or cardinality of sets of discrete elements. Accordingly, numerals are tools for assigning numbers to sets. In this abstract sense, numerals may occur in various forms, written symbols of different kinds, knots, notches, body parts – and linguistic expressions. The present study has been concerned with this last type, i.e. with the way numbers are assigned to sets by means of linguistic expressions. If we focus on this particular type of number assignment, we may basically say that, when a numeral modifies a noun, it assigns a number to the referent of the noun phrase, i.e. to the set referred to by the noun phrase. In the context of noun modification, numerals are a type of quantifiers. Numerals proper, in addition, form a numeral system and are thus distinguished from non-systemic cardinality expressions; cf. § I.1; Table 2 in Chapter I. Only systemic numerals occur in the counting sequence of a given (variety of a) language. Similarly, other expressions which may also specify the cardinality of a set – whether simple or complex – are clearly distinct from genuine (i.e. ‘systemic’) numerals in such that they can serve only to a limited extent as constituents in more complex number expressions and as formatives for other numeral categories like for instance ordinals. The crucial distinctions within the class of numerals which provide the basis for the analysis of the numeral system, are, first, that between simple and complex expressions and, further, the division of simple numerals into atoms and bases. Atoms, we said, are those simple expressions with the highest potential to form a continuously recurring (sub)sequence of numerals in combination with bases or their multiples (cf. (1.4) in § I.3.5) whereas bases are

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those elements with which this smallest continuously recurring sequence of numerals is combined (cf. (1.3) in § I.3.4.1). The way the two definitions depend on each other shows that the two types of numeral expressions perform complementary functions in the numeral systems. Once a numeral system employs complex expressions systematically (i.e. not only occasional, sporadic complex forms), we referred to the principles underlying these formations as ‘serialisation’ and ‘recursion’. The most crucial feature of a complex numeral system is the continuously recurring sequence of elements. This feature is not only essential for efficiently generating complex expressions and thus for providing a language with a device for referring to a large range of cardinalities. It also constitutes the link between what we labelled above the ‘internal grammar’ of numeral systems and the very essential properties of numbers. Numbers, we said, can be seen as any ordered sequence of welldistinguished elements. Systemic numerals, being instantiations of numbers, must necessarily display the defining properties of numbers and constitute such an ordered sequence of well-distinguished elements; cf. § I.2.2. Recursion and serialisation are another pair of complementary notions in numeral systems. In § III.2.1, we noted that they represent, respectively, the syntagmatic and the paradigmatic dimension in the formation of complex numerals. While ‘recursion’ describes the fact that any constituent of a complex numeral is itself a numeral (whether simple or complex). Each syntagmatic position in a complex numeral can be occupied either by an atom or by a base. The notion of ‘serialisation’ describes this phenomenon from a different angle: if a syntagmatic position is taken by the base in a particular structure, the position is always taken by the same base. There is thus, in contrast to the atoms, no paradigmatic exchangeability among the bases with respect to one particular syntagmatic slot. If a position within a complex numeral is occupied by an atom, then it can necessarily also be occupied by any other expression of the sequence of atoms. This paradigmatic exchangeability of atoms is, however, only one aspect. What is crucial here is that these atoms form an ordered sequence. This property stands in contrast to other linguistic paradigms such as, for instance, a set of affixes encoding different values of an inflectional category. While a particular function is assigned to each Case or Number marker (which makes the morpheme meaningful), atoms in complex numerals draw their function from their order in the sequence. For instance, if four, as in twenty-four or in four hundred, were not defined by being the fourth element of the sequence of atoms (or, in other words, if it were not defined by being that element following three and preceding five), the expression could not possibly carry any numerical meaning and thus could not exert any function in the numeral system. It is this aspect which makes serialisation (the property of

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being used in ordered sequences) a crucial property of numeral systems because it allows them to be recursive systems. These are the key categories and notions from which numeral systems will have to be described. This approach allows us to deal with both universal properties of numeral systems and various types of possible idiosyncrasies in numeral systems of individual languages. A crucial point in this respect is the definition of the notion ‘base’. In most contributions dealing with numeral systems, this notion has been used in a looser sense than we defined it here. However, at several points, a narrow definition of ‘base’ has proved to be fruitful and, indeed, essential. To give only one example, when we try to identify precise criteria for determining the type of numeral system, i.e., whether it is decimal or quinary or other (cf. § III.2.2), the principles of the composition of complex numerals and, thus, for the overall arrangement of the system, recursion and serialisation, are fundamental. And again, ultimately, these notions and, consequently, the findings drawing on these notions depend on the narrow definition of the notion ‘base’ as proposed in § I.3.4. Both the theoretical basis and the integration of a language-specific description into a cross-linguistic context seem to have been advantageous for the description and the analysis of the Old English numerals, particular in the context of those features of the Old English numeral system, which can be regarded as peculiar from a cross-linguistic perspective. These features have hitherto been described in isolation or, at the most, in the context of same or similar phenomena in the closest cognate languages. However, to the best of my knowledge, they have never been subject to a typological comparison. There is, for instance, the fact that the multiples of ‘10’ from ‘70’ onwards express the multiplicand ‘× 10’ by a circumfix, i.e. HUND-__-TIG ‘× 10’, and one might think of the speculations we find related to the history and the character of this circumfix. The first element of this circumfix has often been interpreted to represent the second base ‘100’ – an assumption which exclusively draws on the phonological shape of the element but does not take into account how numeral systems of human languages are arranged (§ II.4.3.2). Another case in point is the fact that in Old English the sequence of multiples of ‘10’ continues up to ‘120’ and thus overruns the second decimal base ‘100’ (§§ II.4.3.2–3). Speculations on the influence of a duodecimal system in Old English and/or Germanic underlying this phenomenon have been popular but never made reference to descriptions of attested linguistic numeral systems; cf. VON MENGDEN (2005). Yet a framework on numerals which includes sufficiently precise and descriptively adequate definitions of the relevant notions

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will necessarily lead these discussions into a different direction (the circumfix) or bring them to a halt (duodecimal system). Yet it is not only the fact that a cross-linguistic perspective provides promising pathways for explaining these peculiarities which seems to have gone unnoticed, but also the significance of these phenomena in the ancient Germanic languages for a more general linguistic context has been overlooked. It may be worth recalling another peculiarity of Old English numerals: the (possible) syntactic discontinuity of complex numerals (§§ III.1.3.1–2). A complex numeral comprising more than one base can be construed as consisting of several phrases which are all headed by the respective multiplicand. This can be observed particularly well when these individual constituents of the complex numeral are interrupted by other morphological or lexical material. For instance in complex ordinals where each of these constituents can be marked independently by a determiner and by an ordinal suffix. The quantified NP also may be overtly expressed individually for each (or some) of these phrases. Yet the fact that these expressions, no matter how discontinuous they may be, can only as a whole specify the cardinality of a referent, suggests that even discontinuous complex numerals should, in spite of their discontinuity, be taken as one syntactic unit (cf. § III.1.3.2, but also § I.3.6). Again, the (to the best of my knowledge) complete absence of descriptions of similar phenomena in unrelated languages from the literature on numerals seems remarkable. Finally, in regard to the peculiarities of the Old English numeral system, it has been possible to identify patterns in the distribution of the expressions for ‘100’, HUNDTEONTIG and HUND(RED). They are not synonyms but variants representing the same numerical value in different ways. The Old English expressions HUNDTEONTIG and HUND(RED) were shown to be distributed along the lines of arithmetic functions connected with the overall arrangement of the numeral system – HUNDTEONTIG is used as a multiplicand, whereas HUND(RED) is used in all other arithmetic functions. Hence, the distribution of the expressions HUNDTEONTIG and HUND(RED) for the base ‘100’ follows, respectively, the same patterns as the distribution of -TIG ‘× 10; -ty’ versus TYN ‘10’ / -TYNE ‘+ 10; -teen’. The basis for identifying these parallels in the distributional pattern has been the postulate that numerical values can be represented by functional variants to the simple numerals, which, in addition to the numerical value, encode a particular arithmetic operation in which the numerical value is used (§ I.5.3). In (Old) English and in many other languages, some of these functional variants, as we have mentioned at several points, have undergone a grammaticalisation process from a simple numeral to a functional affix encoding arithmetical information.

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As to the relation between numeral and quantified NP, we showed that the different constructions, in which numerals and quantified nouns interact, are basically constrained by two different parameters. One is the thematicity of both the cardinality and the quantified referent. The other is whether the quantified referent is expressed by a countable or by a non-countable expression in a given language. The choice of the appropriate subtype of Attributive Quantification in the particular context depends on the givenness both of the quantified referent and of the cardinality in the discourse. The Partitive Construction is conditioned by two constraints, one a partwhole relation between the quantified set and a larger set previously introduced in the discourse, the other a numerical value above ‘20’ (§ IV.5.2). Interestingly, these two constraints for the use of the Partitive Construction operate on different levels. The part-whole relation is determined by a particular correlation between cardinality and the (thematic) extension of the referent and thus is ultimately based (again) on information structural or discourserelated factors. The other, the quantification of high numerical values, may best be explained, as we suggested in § IV.8, by the cognitive perception (or processing) of large quantities as uncountable aggregates. Thus one constraint of the Partitive Construction is related to the conditions underlying the variants of Attributive Quantification, whereas the other constraint of the Partitive Construction is related to the count/non-count distinction, which, in turn, is the primary factor in Mass Quantification. This consideration supports the classification that has been suggested in § V.3.2, i.e., that the Partitive Construction constitutes an intermediate type of quantificational construction, sharing features with Attributive Quantification and others with Mass Quantification and thus forming a link between the two in a typology of quantificational constructions. The parallels between the Mass Quantification in Old English (and in many other European languages) and classifier constructions in classifier languages suggest that the typology of quantificational constructions, proposed here for Old English, may, to some extent, be applied in a wider, cross-linguistic context. For Old English, we could determine a correlation between the use of a particular type of quantificational construction and the irrelevance (Partitive Construction) or impossibility (Mass Quantification) of Number distinction in the quantified NP. Similarly, an essential difference in the grammatical properties of nouns between a classifier language and, say, European languages, is the way in which the category Number may or may not be encoded on the noun. The analogies in the quantificational constructions of different language types suggest a general correlation between the range of quantificational constructions and the (grammatically obligatory or pragmatically adequate) possi-

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bility or impossibility of Number distinction on the quantified NP – whether within a given language or cross-linguistically (cf. Chapter V). An important conclusion we can draw from this consideration is that cross-linguistic variation in the morphosyntactic behaviour of numerals may, to a considerable extent, not be owed to the variation in inherent properties of numerals, but to the way in which languages vary in encoding the mass/count distinction. Both parameters relevant to a typology of quantificational constructions, givenness and countability, I have argued, can in principle be observed to condition the morphosyntactic variation not only in Old English, but generally across languages. This study could not give a substantial cross-linguistic account and had to draw on a selection of descriptions in the literature, but one of the tasks for future studies in this field will be to assess this claim on the basis of a more representative cross-linguistic sample. If the correlations we have observed generally hold, it would strengthen one of the main points proposed in this study, i.e. that the variation in the morphosyntactic behaviour of numerals generally follows specific, non-arbitrary patterns. So too does the cardinality-dependent variation of morphosyntactic properties within one language. Rather than adhering to the traditional classifications of numerals as a hybrid class, definable merely on semantic grounds and as being located somewhere between nouns and adjectives, we argued that numerals have independent well-definable properties in each language. Just like in any other word class, the class ‘numeral’ has peripheral members which deviate in these properties. These deviating members can be found on both ends of the counting sequence, that is, among the smallest atoms and the higher bases (§ V.2.3). For the lowest valued numerals we could make out a functional proximity to determination and also differences in the cognitive processing of small cardinalities by humans as possible approaches to explaining their deviation. In the case of higher bases, we could be much more specific. They deviate because the category shift from nouns to numerals has not been entirely completed. Rather than saying that higher bases are more nounlike (as suggested in CORBETT’s generalisation; cf. CORBETT (1978a: 355 and 368, 1978b: 70), it is more appropriate to say that higher bases are (as yet) less numeral-like than the core numerals. Thus particularly these aspects discussed in Chapter V form a promising agenda for cross-linguistic and language-specific research. What had to remain unconsidered here is the question as to what extent the findings of this study can be applied to their closest neighbours in the range of categories. To what extent do the constraints identified for quantificational constructions proposed in Chapter IV apply to numerically unspecific quantifiers, too? A different, but related matter is the interface of numerically specific quantifica-

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tion and of (indefinite) determination. What is the exact relation between low valued numerals and indefinite pronouns or determiners? That a relation exists can be seen not only from the universally common (diachronic) identity of numeral ‘1’ and indefinite marker, but also by the fact that languages which have expressions only for the lowest cardinalities up to about ‘4’ use the same expressions also as indefinite determiners; cf. HALE (1975: 296–297) for some Australian languages and the brief discussion in VON MENGDEN (2008: 305– 306). We have concluded our last chapter by rejecting the alleged hybrid character of numerals. A class is hybrid if it consists of members from different other classes. That numerals form a hybrid class according to their morphosyntactic properties can therefore safely be denied. The members of the class ‘numeral’ may be heterogeneous but, much more than members of other lexical classes, they are so in a regular, definable way. This makes them in fact much less mystical than they may sometimes appear at a first glance.

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Subject index Ælfric of Eynsham, 79, 194, 199 Grammar, 48, 55, 100, 121, 123, 169, 177, 202, 238, 239 addend → arithmetic operands addition, 27, 28, 30–32, 54, 55, 59, 68, 70, 82, 83, 85, 104, 109, 149, 169 adjective, numeral as, 75, 180–188, 191, 194, 201–203, 246, 247, 249– 253, 259, 259 n. 56, 260, 262–264, 282–284, 292 anaphoric reference, 9, 193, 197– 202, 246 Anaphoric Use, 189, 197–202, 205– 207, 246, 250 Anglian, 76, 80, 241 n. 50 Anglo-Saxon Chronicle Parker Chronicle, 80 n. 19 Peterborough Chronicle, 166 Arabic, 281 arithmetic operands, 29–35, 68, 69 addend, 29–32, 39, 50, 59, 68–70, 79, 90, 83–85, 88, 90, 92, 94– 96, 98, 102, 104 n. 26, 105, 115, 116, 130, 135, 157, 158, 169 augend, 30–35, 37, 57, 59, 68–71, 83–85, 88, 90–92, 94, 97, 101– 105, 112, 113, 115, 126 n. 33, 127, 155–158, 160, 174, 254, 255 minuend, 164, 165, 168 n. 38

multiplicand, 30–35, 37, 50, 60, 68, 69, 71, 72, 84–87, 89, 92, 93, 97–102, 107, 113, 125, 127, 132, 135, 137–139, 155–157, 160, 170, 171, 174, 256, 258, 289, 290 multiplier, 31, 32, 59, 68, 69, 76, 84–86, 88, 91–94, 97, 98, 104, 105, 107, 130–139, 142, 146, 157, 169–171, 174, 175, 256, 272, 273 subtrahend, 164–166 arithmetic operations in the formation of complex numerals, 27–33, 35, 40, 43, 50, 53–55, 58–61, 68, 70, 71, 84, 86, 89, 92–94, 97–100, 105, 126, 132, 138, 156–158, 162, 164, 172, 204, 266, 290 numerals used in calculating, 96, 203, 204, 204 n. 44 arithmetic operators, 28, 144, 174 atom, 29–34, 36–39, 41, 42, 54–56, 59, 67, 68, 108, 112, 115, 116, 118, 130, 135, 153–155, 157, 159, 250, 255–257, 262–264, 266, 268, 281, 287, 288, 292 definition of, 39, 67 of Old English, 73–92, 95, 96 n. 25, 101, 105, 107, 124–128, 130, 135, 154, 155, 159, 160 Attributive Construction, 189–193, 201, 206, 212, 215, 217, 220, 221, 227, 244–246, 250, 252–254, 274, 278–280

Subject index

321

Attributive Quantification, 181, 182, 188, 190–207, 210, 213, 220, 230, 245, 246, 250, 253, 268 n. 59, 278, 291

Byrhtferth of Ramsey Manual, 79, 96 n. 25, 130 n. 34, 174, 204, 257 n. 55

augend → arithmetic operands

cardinality, 2, 8, 14–18, 21–23, 43, 52, 53, 55, 62, 63, 65–67, 75, 116, 139, 151, 178, 178, 189, 191, 193, 198–209, 213, 215, 219, 222, 223, 226, 227, 245, 246, 248–250, 253, 255, 261, 263–265, 270, 273, 274, 276, 279–281, 284, 287, 290–292

Australian languages, 26, 293 Austro-Asiatic, 32 Baltic, 109, 123 n. 31, 267 Balto-Slavic, 109, 267 n. 57 base, 5, 29–39, 41, 42, 54–57, 60, 65, 67–69, 72, 73, 109, 111, 116– 118, 129, 130, 135, 136, 153, 154, 156, 159–161, 163, 164, 169–171, 177, 182, 221, 222, 250, 254–259, 262, 263, 265–273, 281, 287–290, 292 definition of, 32, 68, 153 fundamental base, 34, 37, 83, 82, 153–156, 258, 263 of Old English, 73, 74, 82–107, 109, 111, 125, 126, 129, 130– 142, 144, 146–149, 151, 155, 160, 161, 169, 170, 172, 174, 175, 219, 220, 226, 248, 250, 256–259, 289, 290 proper / improper base, 35 Basque, 161

Celtic, 56 Chinese, 21, 37 n. 9 classifier, 242–244, 246, 274–279, 291 collective, 226, 274, 278, 279 collective nouns, 240 n. 49, 274, 275 n. 61, 281 Comanche, 100 copula, 60, 188, 207, 234, 236, 282 count nouns, 246, 274, 278–280 counting sequence, 21, 32, 45–49, 52, 53, 55, 57, 64, 67, 69, 70, 92, 100, 117, 160, 162, 249, 263, 264, 273, 281, 287, 292 counting words, 20, 21, 45–47, 63, 64, 66, 67, 203

Beowulf, 235 billion, 23, 24, 36, 44, 116, 117, 136, 172 body part counting, 7, 18, 19, 21, 25, 46, 65, 108, 159, 266, 268, 287 Breton, 31 Burghal Hidage, 168 n. 38, 170 n. 39 Bury St Edmunds, 163

Danish, 61, 154–158 decimal system, 2, 35–37, 42, 56, 57, 73, 92, 96, 108, 129, 130, 152– 161, 163, 170, 202, 262, 289, 290 definite(ness), 197, 198, 202, 216– 219, 246 1-deletion, 61, 72, 129–136, 272, 273

322

Subject index

determiner, determination, 52, 75, 144, 193, 194, 215, 233, 234, 263– 265, 272–274, 283, 284, 290, 292, 293 distributive numerals → numerals division (as an arithmetic operation), 27, 68, 164

Fennic, 280 n. 64 Finnish, 222, 267 n. 57 finger counting → body part counting French, 44, 56, 57, 60, 70, 158, 174 frequentative numerals → numerals

dual, 10, 52

Frisian Modern Frisian, 111 n. 27, 112 Old Frisian, 110, 111

duodecimal system, 35, 159–161, 289, 290

gaps (in numeral systems), 164 n. 37

dozen, 8, 15, 44, 47, 50, 51, 57, 62, 63, 162

Dutch, 112, 118 n. 29 Elliptic Construction, 189, 192–203, 206, 234 n. 48, 241, 242, 246, 250, 253 Elliptic Quantification, 192–204, 206, 246 English Modern → Present-day Middle, 95, 112–116, 163, 174, 272 Present-day, 4, 15, , 26, 27, 29, 31, 36, 37, 40–42, 44, 45, 46, 47, 49–51, 54, 58, 61, 70, 72, 76, 84, 85, 90, 92, 114–116, 142, 150, 157, 162, 169, 172, 177, 196, 202, 208, 218, 219, 234, 251, 255–258, 263, 267, 269, 274, 276, 284 European languages, 4, 5, 31, 41, 49, 62, 72, 92, 94, 100, 116, 137, 139, 163, 171, 190, 214, 261, 262, 274– 276, 280 n. 64, 291 exponentiation, 27, 68

genitive attributive, 231, 238, 249, 253, 254 forms of numerals, 76, 80, 81, 85, 166 partitive, 147, 183, 185–188, 209– 215, 219, 223, 238, 242 n. 51, 245, 253, 279, 281 quantified element in genitive, 207, 209, 210, 215, 225, 226, 231, 234, 235, 237–242, 244, 254 German Present-day, 14, 21, 40, 89, 116, 132, 194, 202, 250, 269, 270, 272, 273, 282 Old High German, 100, 110, 111 Germanic contemporary languages, 4–6, 29, 38, 41, 49, 52, 54, 57, 73, 74, 86, 87, 89, 94, 111, 112, 123, 154–158, 160, 170, 171, 180, 182, 190 ancient languages, 5, 86, 109–111, 127, 130, 152, 159–161, 179– 182

Subject index pre-, proto-, 79, 82, 86, 87, 109– 111, 123 n. 31, 124, 127, 159, 161, 180, 182, 221 Gothic, 96, 110, 111, 267 grammaticalisation, 60, 71, 83, 86, 87, 90, 269, 270, 277, 290 Greek Classical, 116, 166 Dorian, 56 Homeric, 226 Greenberg’s generalizations G 1, 23, 107, 177 G 2, 23, 24, 165 n. 37 G 3, 37, 38, 49 G 4, 26 G 9, 27 G 10, 27 G 11, 164, 165 G 12, 164 G 13, 164 G 14, 164 G 15, 164 G 18, 93 G 21[b], 34 G 23, 93 G 36, 135 G 37, 49

323

Indo-Aryan, 57, 58 (proto-)Indo-European, 4. 6, 56, 57, 86, 87, 108, 109, 123, 159, 166, 221, 226, 250, 253, 266, 267 inflection, 3, 6, 9, 10, 71, 75, 76, 80, 81, 83, 87, 122, 181–183, 188, 191, 202, 203, 212, 215, 221, 231, 233, 237, 248, 250, 253, 260, 263– 265, 273, 277, 282, 283, 288 information structure, 188, 209, 222, 246, 248, 282, 291 Irish, 56 Italian, 55, 174, 267 Japanese, 21 Kentish, 81–83 Keres, 5, 93 Latin Classical, 55–57, 60, 79, 123, 164 n. 36, 226, 267 n. 57 Medieval, 4, 48, 55, 81, 100, 113, 123, 125 n. 32, 166 lexicalisation, 195, 196, 200, 201 limit number, 24, 67, 107, 137, 163, 164, 173, 177 Lithuanian, 109, 123, 161

Hittite, 226 Hrabanus Maurus, 257 n. 55

Martyrology, 238

Hungarian, 21

mass nouns, 227, 232, 239–246, 274–278, 292

Inari Sami, 222, 280 n. 64

mathematics, 17, 30, 36–38, 68, 153, 154, 202, 204, 205

Incan indefinite(ness), 26, 75, 191, 197, 216, 219, 246, 264, 265, 272, 273, 293

Mayan numerals, 36 n. 7 Measure Construction, 225, 227– 245, 254, 275

324

Subject index

Mercian, 80, 82, 83, 128 Middle English, 95, 112–116, 163, 174, 272

Number (grammatical category), 189, 191, 213, 215, 223, 225, 226, 235, 236, 245, 248, 250, 251, 253, 255, 263, 274, 279–281, 288, 291, 292

milliard, 116, 267

numeracy, 46, 265, 268, 287

million, 23, 24, 36, 116, 172–177, 267, 268 n. 59, 272

numerals absolute vs. contextual, 21, 66, 67 vs. counting words, 20, 21, 45–47, 63, 64, 66, 67, 203 distributive, 22, 23, 284 frequentative, 22, 23, 45, 50, 63, 80, 284 Greek, 18 Hindu-Arabic, 2, 18, 19, 21, 25, 36–37, 154 multiplicative, 22, 45, 50, 63, 64, 169, 284 Roman, 21, 38, 149 ordinal, 21–23, 45, 50, 51, 64, 66, 73, 76, 87 n. 21, 89, 100, 103, 117–128, 144, 146, 156, 169, 253 n. 54, 284, 287, 290 written, 2, 18–20, 25, 36–38, 149 n. 35, 287

Metrical Texts → Poetry

multiplication, 27, 28, 30, 31, 68, 87, 90, 93, 109, 135, 157, 174 multiplicative numerals → numerals. multiplicand → arithmetic operands multiplier → arithmetic operands Munda, 32 Ngiti, 35 Niger-Congo, 35 n. 6 Nilo-Saharan, 35 nominalisation, 125 n. 32, 202–206 (Old) Norse, 110, 111, 125 n. 32, 231, 254 Northumbrian, 81–83, 88, 125 n. 32 noun numeral as, 3, 86, 136, 180–185, 187, 188, 194, 196, 201–203, 207, 246, 247, 249, 250, 253– 263, 268–270, 272 n. 60, 273, 282, 283, 292 nominal number assignment number (cardinal), 1–3, 6, 7, 9, 10, 14, 16–26, 36, 57, 64, 65, 204, 205, 228, 265, 271, 282, 286–288 number assignment, 20–23, 25, 26, 46, 64–66, 118, 119, 123, 227, 265, 266, 287

of-phrase, 186, 210, 214, 223, 226, 240, 245, 255, 256, 279 Old Church Slavonic, 79 n. 17, 109, 267 operands → arithmetic operands ordinal numerals → numerals Packing Strategy, 72, 92, 93 partitive, 147, 182, 183, 185–188, 209, 210, 214, 218, 219, 222, 228, 231, 238–240, 242 n. 51, 245, 279–281

Subject index Partitive Construction, 179, 210– 227, 230, 231, 236, 244–246, 249, 250, 253, 254, 259, 274, 279, 280, 291

See also: Attributive Construction, Predicative Construction, Partitive Construction, Measure Construction, mass nouns

Parts-of-speech → Word Class

quinary system, 35, 36, 289

plural, 190 n. 42, 215, 226, 257, 258, of numerals, 75, 231, 234, 235, 255–259 of (quantified) nouns, 207, 210, 213, 223, 225, 231, 234–236, 274, 279, 280

quipu system, 36 n. 7

Poetry Old English, 77, 79, 146, 245, 151, 162, 192, 199

Ritual Hypothesis, 46 n. 10

Portuguese, 56 Predicative Construction, 188, 207– 210, 244, 245, 284 n. 65 pronouns, 26, 75, 179, 183, 184, 186, 199 n. 43, 201, 203, 250, 264, 283, 284, 293 proto-Germanic → Germanic proto-Indo-European → IndoEuropean quantification / quantifiers, 1–3, 9, 12–16, 26, 42, 52, 53, 62, 118 n. 29, 151, 178, 179, 263, 264, 265 absolute, 13, 14 existential, 12, 13, 62, 63 numerically specific, 14–16, 17, 21, 26, 43, 44, 47, 62, 63, 117, 151, 168, 178, 179, 187–247, 257, 259, 265, 274 numerically unspecific, 14–16, 62, 63, 117, 178, 257, 267 relative, 13 universal, 12, 13, 62, 63, 191

325

recursion, 23, 28, 29, 35, 38, 45, 49, 50, 57, 58, 63, 64, 67, 68, 86, 94, 109, 115, 117, 151–156, 158, 173, 176, 288, 289 Romanian, 222 Russian, 54, 55, 60, 157, 281 (Old) Saxon, 110–112 scalar implicatures, 15, 16 score, 15, 50, 62, 162, 163 serialisation serialised augends, 31–35, 69, 71, 84, 92, 97, 105, 113, 254, 255 serialised multiplicands, 31, 32, 35, 69, 71, 72, 87, 89, 92, 93, 97, 113, 139, 156 sexagesimal system, 160, 161 singular, 10, 223, 225, 226 of numerals, 235, 236 of (quantified) nouns, 213, 239 singulative, 275, 281 Slavic, 93, 123, 264, 267 Sora, 32–35, 38, 69, 154 subitising, 264 subtraction, 27, 68, 164–169 Thai, 274, 276 theme / thematic, 192, 198, 291

326

Subject index

Uralic, 222, 280 n. 64

West Saxon Gospels, 200, 214

Uto-Aztecan, 100

Will of Ælfwold, 176

vigesimal system, 32, 35, 44, 57, 155–158

word class, 3, 4, 9, 136, 179, 184, 187, 188, 194, 203, 247–249, 252 n. 53, 260–265, 268–271, 282– 284, 286, 292, 293

Welsh, 31–35, 38, 56, 57, 69, 154

Yucatec Maya, 161

verbal quantification, 274, 284

West Saxon, 10, 74, 79–83, 127, 248

zero, 2, 25, 37, 38, 172

Author index This section lists modern authors of linguistic works. Medieval authors and other historical persons are listed in the subject index.

Ahn, Miran, 284 n. 65 Aikhenvald, Alexandra Y., 274 n. 61, 277 Allan, Keith, 274 Bammesberger, Alfred, 5, 86 Barbiers, Sjef, 118 n. 29 Bauch, Heinrich, 225 n. 46 Bauer, Laurie, 90 Beekes, Robert S. P., 56, 123 n. 31 Benacerraf, Paul, 20, 227, 252 Berger, Hermann, 57, 58 Berns, Jan, 6, 52, 85, 111, 127, 182, 249, 268 n. 59

Comrie, Bernard, 5, 34–36, 43, 54, 55, 93, 117, 159, 161, 165 n. 37 Corbett, Greville G., 3. 135, 136, 226, 227, 255, 259–264, 267–271, 292 Croft, William, 277, 278 Detges, Ulrich, 27, 56, 159, 266 Dietz, Klaus, 174 Dixon, Robert Malcom Ward, 26 Eichner, Heiner, 226 Faarlund, Jan Terje, 231, 254 Fischer, Olga, 209

Bisang, Walter, 275 n. 61, 277

Fox, Anthony, 194, 250, 282

Bloom, Paul, 252

Frege, Gottlob, 251, 252 n. 52

Bloomfield, Leonard, 284

Fricke, Richard, 5, 168, 180

Brandt Corstius, Hugo, 7, 286 Braune, Wilhelm, 100, 111 n. 27 Brugmann, Karl, 87 n. 21, 221, 267 Brunner, Karl, 83, 88, 181 Campbell, Alistair, 52, 88, 113, 181, 221 Charney, Jean Ormsbee, 100 Coleman, Robert, 56

Gallée, Johann H., 111 n. 27 Gatschet, Albert S., 93 Gil, David, 9, 12–15, 62, 190, 194, 226, 248, 251, 253, 277, 278 Greenberg, Joseph Harold, 3, 5, 7, 8, 21, 23, 24, 26–28, 31–35, 37–39, 42, 46–49, 61, 66, 67, 86, 93, 107, 108, 116–118, 135, 153–155, 164, 165, 177, 204 n. 44, 248, 262, 274–277, 281, 287

328

Author index

Greene, David, 56

Kluge, Theodor, 39

Grimm, Jacob, 159

Koptjevskaja-Tamm, Maria, 277, 286

Grinevald, Colette, 277 n. 63 Hale, Kenneth L., 26, 293 Hall, Christopher John, 90

Krifka, Manfred, 275 n. 61, 276 n. 62, 277 n. 63, 278

Hawkins, John A., 52, 191, 218, 219

Langacker, Ronald W., 13, 14, 194, 277

Healey, Antonette diPaolo, 10 n. 1, 11

Lass, Roger, 79 n. 17, 88, 181, 182

Heine, Bernd, 46, 116, 272 van Helten, Willem Lodewijk, 5, 85, 180 Hirt, Hermann, 168 Hofmann, Dietrich, 111 n. 27 Holthausen, Ferdinand, 79 n. 17, 111 n. 27 Holtzmann, Adolf, 87 n. 21 Hopper, Paul John, 270 Horn, Wilhelm, 85 Huddleston, Rodney, 15 Hurford, James R., 6, 7, 18, 20, 26 n. 4, 30, 43, 44, 46 n. 10, 52, 60, 61, 92, 93, 118, 135, 164 n. 37, 204 n. 44, 222, 252, 254, 255, 263, 264, 276, 280 n. 64, 284, 286, 287

Lehmann, Christian, 269 Lehmann, Winfred P., 250 Link, Godehard, 276 n. 62 Luján Martínez, Eugenio R., 6, 35, 87, 108 Majewicz, Alfred F., 46 Markey, Thomas L., 111 n. 27 von Mengden, Ferdinand, 4, 14, 26, 44, 46, 60, 80 n. 18, 83, 96, 108, 111 n. 27, 114, 115, 158, 159, 161, 266, 268, 272 n. 60, 289, 293 Menninger, Karl, 46 Mitchell, Bruce, 75 n. 14, 115, 168, 171, 180, 182, 183, 185–188, 190 n. 42, 202, 210, 214, 223, 242 n. 51, 246, 249 Mustanoja, Tauno F., 116, 185

Ifrah, Georges, 7, 46 Nelson, Diane, 222, 280 n. 64 Jackendoff, Ray Saul, 253

Noreen, Adolf, 111 n. 27

Jespersen, Otto, 52 Justus, Carol F., 86, 159, 161

Pijnenburg Wilhelmus Johannes Juliana, 267 n. 57

Katz, Elisabeth, 212

Planck, Frans, 283

King, Gareth, 31

Prokosch, Eduard, 79 n. 17, 123 n. 31

Kluge, Friedrich, 111 n. 27

Author index

329

Pullum, Rodney, 15

Stiles, Patrick Valentine, 81, 182, 195, 196, 249, 250

Reich, Sabine, 283

Stoelke, Hans, 225 n. 46

Reiffenstein, Ingo, 100, 111 n. 27

Stolz, Thomas, 116, 222, 254, 261

Reinhardt, Mechthild, 252, 253, 255, 256, 259, 263

Storm, Hiroko, 21

Rijkhoff, Jan, 46, 266, 275 n. 61 Rissanen, Matti, 75 n. 14, 120, 166, 168, 272 Ross, Alan S. C., 6, 52, 85 n. 20, 111 n. 27, 127, 182, 249, 268 n. 59 Salzmann, Zdeněk, 33, 154 Schmidt, Johannes, 226 Schwartz, Martin, 108 Scriba, Christoph Joachim, 252

Süsskand, Peter, 75 n. 14 Szemerényi, Oswald, 5, 86, 266, ko7 n. 57 Toivonen, Ida, 222, 280 n. 64 Traugott, Elizabeth Closs, 226 Vater, Heinz, 14 Venezky, Richard Lawrence, 10 n. 1 Visser, Fredericus Theodorus, 207 Voyles, Joseph Bartle, 86

Seebold, Elmar, 79 n. 17, 85 Seiler, Hansjakob, 30, 31, 34, 35, 38, 39, 57, 109, 161, 262, 264, 265, 275 n. 61, 276 n. 62, 277, 287

Wiese, Heike, 7, 17–24, 46, 47, 66, 204, 227, 228, 253, 264, 265, 268 n. 58, 277, 287

Sievers, Eduard, 79 n. 17

Winter, Werner, 58, 261

Sihler, Andrew Littleton, 55, 56, 123 n. 31, 166

Wülfing, Johann Ernst, 180, 182– 186, 188, 195, 196

Stampe, David, 6, 19, 21, 22, 28, 32, 33, 40, 47, 116, 252, 256

Yeager, Deborah, 214

Steller, Walther, 111 n. 27