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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
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' (= 11x10) 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.
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.
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.
ABOUT THE REVIEWER
ABOUT THE REVIEWER:
Stephen Chrisomalis is an assistant professor in the Department of
Anthropology and the Linguistics Program at Wayne State University. His
research interests include numerals, linguistic anthropology, and writing
systems / literacy.