*This review appeared originally in the LINGUIST List at http://linguistlist.org/issues/21/21-5213.html*

AUTHOR: von Mengden, Ferdinand

TITLE: Cardinal Numerals

SUBTITLE: Old English from a Cross-Linguistic Perspective

SERIES: Topics in English Linguistics [TiEL] 67

PUBLISHER: De Gruyter Mouton

YEAR: 2010

Stephen Chrisomalis, Department of Anthropology, Wayne State University

SUMMARY

This monograph is a systematic analysis of Old English numerals that goes far

beyond descriptive or historical aims to present a theory of the morphosyntax of

numerals, including both synchronic and diachronic perspectives, and to

contribute to the growing linguistic literature on number concepts and numerical

cognition.

The volume is organized into five chapters and numbered subsections throughout

and for the most part is organized in an exemplary fashion. Chapters II and

III, where the evidence for the structure of the Old English numerals is

presented, will be of greatest interest to specialists in numerals. Chapter IV

will be of greatest interest to specialists in Old English syntax. Chapter V is

a broader contribution to the theory of word classes and should be of interest

to all linguists.

The author begins with an extensive theoretical discussion of number concepts

and numerals, working along the lines suggested by Wiese (2003). Chapter I

distinguishes numerals (i.e., numerically specific quantifiers) from other

quantifiers, and distinguishes systemic cardinal numerals from non-systemic

expressions like ‘four score and seven’. As the book’s title suggests, cardinal

numerals are given theoretical priority over ordinal numerals, and nominal forms

like ‘Track 29′ or ‘867-5309′ are largely ignored. Cardinal numerals exist in

an ordered sequence of well-distinguished elements of expandable but

non-infinite scope. Here the author builds upon the important work of Greenberg

(1978) and Hurford (1975, 1987), without presenting much information about Old

English numerals themselves.

Chapter II introduces the reader to the Old English numerals as a system of

simple forms joined through a set of morphosyntactic principles. It is

abundantly data-rich and relies on the full corpus of Old English to show how

apparent allomorphs (like HUND and HUNDTEONTIG for ‘100’) in fact are almost

completely in complementary distribution, with the former almost always being

used for multiplicands, the latter almost never. This analysis allows the

author to maintain the principle that each numeral has only one systemic

representation, but at the cost of making a sometimes arbitrary distinction

between systemic and non-systemic expressions. This links to a fascinating but

all-too-brief comparative section on the higher numerals in the ancient Germanic

languages, which demonstrates the typological variability demonstrated even

within a closely related subfamily of numeral systems.

Chapter III deals with complex numerals, a sort of hybrid category encompassing

various kinds of complexities. The first sort of complexity, common in Old

English, involves the use of multiple noun phrases to quantify expressions that

use multiple bases (e.g. ‘nine hundred years and ten years’ for ‘910 years’).

The second complexity is the typological complexity of Old English itself; the

author cuts through more than a century of confusion from Grimm onward in

demonstrating conclusively that there is no ‘duodecimal’ (base 12) element to

Old English (or present-day English) — that oddities like ‘twelve’ and

‘hundendleftig’ (= 11×10) can only be understood in relation to the decimal

base. The third is the set of idiosyncratic expressions ranging from the

not-uncommon use of subtractive numerals, to the overrunning of hundreds (as in

modern English ‘nineteen hundred’), to the multiplicative phrases used

sporadically to express numbers higher than one million. Where a traditional

grammar might simply list the common forms of the various numeral words, here we

are presented with numerals in context and in all their variety.

Chapter IV presents a typology of syntactic constructions in which Old English

numerals are found: Attributive, Predicative, Partitive, Measure, and Mass

Quantification. In setting out the range of morphosyntactic features

demonstrated within the Old English corpus, the aim is not simply descriptive,

but rather, assuming that numerals are a word class, to analyze that class in

terms of the variability that any word class exhibits, without making

unwarranted comparisons with other classes.

In Chapter V the author argues against the prevalent view that numerals are

hybrid combinations of nouns and adjectives. While there are similarities,

these ought not to be considered as definitional of the category, but as results

of the particular ways that cardinal numerals are used. Because it is

cross-linguistically true that higher numerals behave more like nouns than lower

ones, this patterned variability justifies our understanding the cardinal

numerals as a single, independent word class. It is regarded as the result of

higher numerals being later additions to the number sequence — rather than

being ‘more nounish’, they are still in the process of becoming full numerals.

They are transformed from other sorts of quantificational nouns (like

‘multitude’) into systemic numerals with specific values, but retain vestiges of

their non-numeral past.

EVALUATION

This is an extremely important volume, one that deserves a readership far beyond

historical linguists interested in Germanic languages. It is not the last word

on the category status of cardinal numerals, cross-linguistic generalizations

about number words, or the linguistic aspects of numerical cognition, but it

represents an exceedingly detailed and well-conceived contribution to all these

areas. While virtually any grammar can be relied upon to present a list of

numerals, virtually none deals with the morphosyntactic complexities and

historical dimensions of this particular domain that exist for almost any

language. Minimal knowledge of Old English is required to understand and

benefit from the volume.

The specialist in numerals will be struck by the richness and depth of the

author’s specific insights regarding numerical systems in general, using the Old

English evidence to great effect. Because it is one of very few monographs to

be devoted specifically to a single numeral system, and by far the lengthiest

and theoretically the most sophisticated (cf. Zide 1978, Olsson 1997, Leko

2009), there is time and space to deal with small complexities whose broader

relevance is enormous. The volume thus strikes that fine balance between

empiricism and theoretical breadth required of this sort of cross-linguistic

study rooted in a single language.

With regard to the prehistory of numerals, we are very much working from a

speculative framework, and where the author treads into this territory, of

necessity the argument is more tenuous. It may be true that for most languages,

the hands and fingers are the physical basis for the counting words, but

Hurford’s ritual hypothesis (1987), of which von Mengden does not think highly,

is at the very least plausible for some languages if not for all. These issues

are not key to the argument, which is all the more striking given that they are

presented conclusively in Chapter I.

A potential limitation of the volume is that, by restricting his definition of

numerals to cardinals (by far the most common form in the Old English corpus),

the author is forced into an exceedingly narrow position, so that, ultimately,

ordinals, nominals, frequentatives, and other forms are derived from numerals

but are not numerals as a word class, but something else. But the morphosyntax

of each of these forms has its own complexities — think of the nominal ‘007’ or

the decimal ‘6.042’ – that deserve attention from specialists on numerals.

Numerals may well be neither adjectives nor nouns, but omitting the clearly

numerical is not a useful way to show it. Similarly, the insistence that each

language possesses one and only one systemic set of cardinal numerals is

problematic in light of evidence such as that presented by Bender and Beller

(2006).

When comparing with other sorts of numerical expressions, e.g. numerical

notations, the author is on shakier grounds. It is certainly not the case, as

the author claims that the Inka khipus had a zero symbol, and it is equally the

case that the Babylonian sexagesimal notation and the Chinese rod-numerals did

(Chrisomalis 2010). Similarly, the author seems to suggest that in present-day

English, any number from ‘ten’ to ‘ninety-nine’ can be combined multiplicatively

with ‘hundred’, whereas in fact *ten hundred, *twenty hundred, … *ninety hundred

are well-formed in Old English but not in later varieties.

It is curious that von Mengden does not link the concept of numerical ‘base’ to

that of ‘power’, but rather to the patterned recurrence of sequences of

numerals. Rather than seeing ’10’, ‘100’ and ‘1000’ as powers of the same base

(10), they are conceptualized as representing a series of bases that combine

with the recurring sequence 1-9. But a system that is purely decimal, except

that numbers ending with 5 through 9 are constructed as ‘five’, ‘five plus one’

… ‘five plus four’, would by this definition have a base of 5 even though powers

of 5 have no special structural role and even though 5 never serves as a

multiplicand. This definition is theoretically useful in demonstrating that Old

English does not have a duodecimal (base-12) component, but as a

cross-linguistic definition will likely prove unsatisfactory.

Because the Old English numerals are all Germanic in origin, with no obvious

loanwords, it is perhaps unsurprising that language contact and numerical

borrowing play no major role in this account. Yet on theoretical grounds the

borrowing of numerals, including the wholesale replacement of structures and

atoms for higher powers, is of considerable importance cross-linguistically.

Comparative analysis will need to demonstrate whether morphosyntactically,

numerical loanwords are similar to or different from non-loanwords.

The author has incorporated the work of virtually every major recent theorist on

numerals, and the volume is meticulously referenced. There are a few irrelevant

typos, and a few somewhat more serious errors in tables and text that create

ambiguity or confusion, but no more than might be expected in any volume of this

size.

This monograph is a major contribution to the literature on numerals and

numerical cognition. Its value will be in its rekindling of debates long left

dormant, and its integration of Germanic historical linguistics, syntax,

semantics, and cognitive linguistics within a fascinating study of this

neglected lexical domain.

REFERENCES:

Bender, A., and S. Beller. 2006. Numeral classifiers and counting systems in

Polynesian and Micronesian languages: Common roots and cultural adaptations.

Oceanic Linguistics 45, no. 2: 380-403.

Chrisomalis, Stephen. 2010. Numerical Notation: A Comparative History. New York:

Cambridge University Press.

Greenberg, Joseph H. 1978. Generalizations about numeral systems. In Universals

of Human Language, edited by J. H. Greenberg. Stanford: Stanford University Press.

Hurford, James R. 1975. The Linguistic Theory of Numerals. Cambridge: Cambridge

University Press.

Hurford, James R. 1987. Language and Number. Oxford: Basil Blackwell.

Leko, Nedžad. 2009. The syntax of numerals in Bosnian. Lincom Europa.

Olsson, Magnus. 1997. Swedish numerals: in an international perspective. Lund

University Press.

Wiese, Heike. 2003. Numbers, Language, and the Human Mind. Cambridge: Cambridge

University Press.

Zide, Norman H. 1978. Studies in the Munda numerals. Central Institute of Indian

Languages.