LINGUIST List 21.5213

Wed Dec 22 2010

Review: General Linguistics: von Mengden (2010)

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        1.     Stephen Chrisomalis , Cardinal Numerals: Old English from a Cross-Linguistic Perspective

Message 1: Cardinal Numerals: Old English from a Cross-Linguistic Perspective
Date: 22-Dec-2010
From: Stephen Chrisomalis <>
Subject: Cardinal Numerals: Old English from a Cross-Linguistic Perspective
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Announced at
AUTHOR: von Mengden, FerdinandTITLE: Cardinal NumeralsSUBTITLE: Old English from a Cross-Linguistic PerspectiveSERIES: Topics in English Linguistics [TiEL] 67PUBLISHER: De Gruyter MoutonYEAR: 2010

Stephen Chrisomalis, Department of Anthropology, Wayne State University


This monograph is a systematic analysis of Old English numerals that goes farbeyond descriptive or historical aims to present a theory of the morphosyntax ofnumerals, including both synchronic and diachronic perspectives, and tocontribute to the growing linguistic literature on number concepts and numericalcognition.

The volume is organized into five chapters and numbered subsections throughoutand for the most part is organized in an exemplary fashion. Chapters II andIII, where the evidence for the structure of the Old English numerals ispresented, will be of greatest interest to specialists in numerals. Chapter IVwill be of greatest interest to specialists in Old English syntax. Chapter V isa broader contribution to the theory of word classes and should be of interestto all linguists.

The author begins with an extensive theoretical discussion of number conceptsand numerals, working along the lines suggested by Wiese (2003). Chapter Idistinguishes numerals (i.e., numerically specific quantifiers) from otherquantifiers, and distinguishes systemic cardinal numerals from non-systemicexpressions like 'four score and seven'. As the book's title suggests, cardinalnumerals are given theoretical priority over ordinal numerals, and nominal formslike 'Track 29' or '867-5309' are largely ignored. Cardinal numerals exist inan ordered sequence of well-distinguished elements of expandable butnon-infinite scope. Here the author builds upon the important work of Greenberg(1978) and Hurford (1975, 1987), without presenting much information about OldEnglish numerals themselves.

Chapter II introduces the reader to the Old English numerals as a system ofsimple forms joined through a set of morphosyntactic principles. It isabundantly data-rich and relies on the full corpus of Old English to show howapparent allomorphs (like HUND and HUNDTEONTIG for '100') in fact are almostcompletely in complementary distribution, with the former almost always beingused for multiplicands, the latter almost never. This analysis allows theauthor to maintain the principle that each numeral has only one systemicrepresentation, but at the cost of making a sometimes arbitrary distinctionbetween systemic and non-systemic expressions. This links to a fascinating butall-too-brief comparative section on the higher numerals in the ancient Germaniclanguages, which demonstrates the typological variability demonstrated evenwithin a closely related subfamily of numeral systems.

Chapter III deals with complex numerals, a sort of hybrid category encompassingvarious kinds of complexities. The first sort of complexity, common in OldEnglish, involves the use of multiple noun phrases to quantify expressions thatuse multiple bases (e.g. 'nine hundred years and ten years' for '910 years').The second complexity is the typological complexity of Old English itself; theauthor cuts through more than a century of confusion from Grimm onward indemonstrating conclusively that there is no 'duodecimal' (base 12) element toOld English (or present-day English) -- that oddities like 'twelve' and'hundendleftig' (= 11x10) can only be understood in relation to the decimalbase. The third is the set of idiosyncratic expressions ranging from thenot-uncommon use of subtractive numerals, to the overrunning of hundreds (as inmodern English 'nineteen hundred'), to the multiplicative phrases usedsporadically to express numbers higher than one million. Where a traditionalgrammar might simply list the common forms of the various numeral words, here weare presented with numerals in context and in all their variety.

Chapter IV presents a typology of syntactic constructions in which Old Englishnumerals are found: Attributive, Predicative, Partitive, Measure, and MassQuantification. In setting out the range of morphosyntactic featuresdemonstrated within the Old English corpus, the aim is not simply descriptive,but rather, assuming that numerals are a word class, to analyze that class interms of the variability that any word class exhibits, without makingunwarranted comparisons with other classes.

In Chapter V the author argues against the prevalent view that numerals arehybrid combinations of nouns and adjectives. While there are similarities,these ought not to be considered as definitional of the category, but as resultsof the particular ways that cardinal numerals are used. Because it iscross-linguistically true that higher numerals behave more like nouns than lowerones, this patterned variability justifies our understanding the cardinalnumerals as a single, independent word class. It is regarded as the result ofhigher numerals being later additions to the number sequence -- rather thanbeing '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 oftheir non-numeral past.


This is an extremely important volume, one that deserves a readership far beyondhistorical linguists interested in Germanic languages. It is not the last wordon the category status of cardinal numerals, cross-linguistic generalizationsabout number words, or the linguistic aspects of numerical cognition, but itrepresents an exceedingly detailed and well-conceived contribution to all theseareas. While virtually any grammar can be relied upon to present a list ofnumerals, virtually none deals with the morphosyntactic complexities andhistorical dimensions of this particular domain that exist for almost anylanguage. Minimal knowledge of Old English is required to understand andbenefit from the volume.

The specialist in numerals will be struck by the richness and depth of theauthor's specific insights regarding numerical systems in general, using the OldEnglish evidence to great effect. Because it is one of very few monographs tobe devoted specifically to a single numeral system, and by far the lengthiestand theoretically the most sophisticated (cf. Zide 1978, Olsson 1997, Leko2009), there is time and space to deal with small complexities whose broaderrelevance is enormous. The volume thus strikes that fine balance betweenempiricism and theoretical breadth required of this sort of cross-linguisticstudy rooted in a single language.

With regard to the prehistory of numerals, we are very much working from aspeculative framework, and where the author treads into this territory, ofnecessity 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, butHurford'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 issuesare not key to the argument, which is all the more striking given that they arepresented conclusively in Chapter I.

A potential limitation of the volume is that, by restricting his definition ofnumerals 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 numeralsbut are not numerals as a word class, but something else. But the morphosyntaxof each of these forms has its own complexities -- think of the nominal '007' orthe decimal '6.042' - that deserve attention from specialists on numerals.Numerals may well be neither adjectives nor nouns, but omitting the clearlynumerical is not a useful way to show it. Similarly, the insistence that eachlanguage possesses one and only one systemic set of cardinal numerals isproblematic in light of evidence such as that presented by Bender and Beller(2006).

When comparing with other sorts of numerical expressions, e.g. numericalnotations, the author is on shakier grounds. It is certainly not the case, asthe author claims that the Inka khipus had a zero symbol, and it is equally thecase that the Babylonian sexagesimal notation and the Chinese rod-numerals did(Chrisomalis 2010). Similarly, the author seems to suggest that in present-dayEnglish, any number from 'ten' to 'ninety-nine' can be combined multiplicativelywith 'hundred', whereas in fact *ten hundred, *twenty hundred, … *ninety hundredare well-formed in Old English but not in later varieties.

It is curious that von Mengden does not link the concept of numerical 'base' tothat of 'power', but rather to the patterned recurrence of sequences ofnumerals. Rather than seeing '10', '100' and '1000' as powers of the same base(10), they are conceptualized as representing a series of bases that combinewith the recurring sequence 1-9. But a system that is purely decimal, exceptthat 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 powersof 5 have no special structural role and even though 5 never serves as amultiplicand. This definition is theoretically useful in demonstrating that OldEnglish does not have a duodecimal (base-12) component, but as across-linguistic definition will likely prove unsatisfactory.

Because the Old English numerals are all Germanic in origin, with no obviousloanwords, it is perhaps unsurprising that language contact and numericalborrowing play no major role in this account. Yet on theoretical grounds theborrowing of numerals, including the wholesale replacement of structures andatoms 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 onnumerals, and the volume is meticulously referenced. There are a few irrelevanttypos, and a few somewhat more serious errors in tables and text that createambiguity or confusion, but no more than might be expected in any volume of thissize.

This monograph is a major contribution to the literature on numerals andnumerical cognition. Its value will be in its rekindling of debates long leftdormant, and its integration of Germanic historical linguistics, syntax,semantics, and cognitive linguistics within a fascinating study of thisneglected lexical domain.


Bender, A., and S. Beller. 2006. Numeral classifiers and counting systems inPolynesian 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 Universalsof Human Language, edited by J. H. Greenberg. Stanford: Stanford University Press.

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

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

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


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.

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