Review: von Mengden, Cardinal Numerals

This review appeared originally in the LINGUIST List at

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

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.


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

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

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

Deutscher, Through the Language Glass

Deutscher, Guy. 2010. Through the Language Glass: Why the World Looks Different in Other Languages. New York: Metropolitan Books.

Guy Deutscher’s new book has attracted a great deal of attention among linguistic anthropologists, not least because anthropology is virtually made invisible throughout. It has a few very serious flaws; nonetheless, it is nonetheless the best presentation of a wide range of specialist literature on linguistic relativity for laypeople and introductory students. It should be read widely and critically.

Deutscher begins with four chapters on a particular theme in linguistic relativity, colour terminology, and ends with a fifth chapter on that subject. His approach is historical – many linguists and anthropologists, even ones who know this field well, will find surprising historical tidbits in his narrative. Deutscher takes us from the classical speculations of Gladstone (yes, the same one) through the seminal work of Berlin and Kay, through modern refinements and interpretations. It is not quite an alternate history, but one that notes rightly that interest in the language-cognition interface with respect to colour is a longstanding part of the history of our disciplines, not one emergent from the cognitive sciences in the past half-century. Deutscher’s correct answer is that both perceptual and cognitive constraints are at play – biology does not determine how we categorize the colour spectrum, but neither are we completely free to divide it however we wish. This is not an especially innovative answer, but it is a well-presented one that will appeal to people who are new to this subject.

Chapter 5, ‘Plato and the Macedonian Swineherd’ is both the weakest chapter and the most out-of-place. Deutscher sets up a straw man in claiming that “For decades, linguists have elevated the hollow slogan that ‘all languages are equally complex’ to a fundamental tenet of their discipline, zealously suppressing as heresy any suggestion that the complexity of any areas of grammar could reflect aspects of society” (125). Deutscher tries to resuscitate the idea of different levels of linguistic complexity by rephrasing the question in terms of complexity within specific domains of language. But we’ve known for a very long time that different languages have different numbers of phonemes, or that there are correlations between social complexity and domains like colour terms and number words (a topic sadly neglected in the book), and Deutscher is wrong to imagine an inquisition against the subject. Worse, Deutscher links these ideas to statements such as, “If you are a member of an isolated tribe that numbers a few dozen people, you hardly ever come across any strangers, and if you do you will probably spear them or they will spear you before you get a chance to chat” (115). In so doing he will doubtless reinforce the pervasive myths of primitivity: that small-scale societies are more isolated, more xenophobic, and more violent than larger-scale ones. It is very interesting that smaller-scale societies have smaller colour lexicons than larger ones, but this doesn’t provide an answer. For this reason alone I suspect that I will not give this book to introductory students. Moreover, it is poorly linked to the general theme of the book – it neither advances any particular claim between the relation between language and cognition nor supports the other chapters’ claims. The whole chapter would have been better omitted.

In Part II, ‘The Language Lens’, Deutscher begins by lambasting Benjamin Whorf’s ‘language prison’ model of linguistic relativity in favour of the model proposed by Franz Boas and Roman Jakobson, which emphasized what languages require their speakers to say, rather than the Whorfian question of what they allow or prohibit their speakers from saying. The fact that some languages require one to specify the gender of inanimate objects, or that others require you to note evidentiality when making factual statements (how you know what you know), develops habits of thought that, over time, lead individuals to favour particular modes of cognition over others. He supports this through two newer themes of research – the effects of spatial language on the cognition of the relationships between physical objects, and the role of gender categories in affecting the semantic connotations of inanimate objects. These are well-known fields among specialists, but are presented here in an engaging fashion, allowing novices to experience radically different modes of spatial cognition through the eyes of Guugu Yimithirr speakers of Australia, for instance.

Perhaps the most striking absence for linguistic anthropologists is the complete absence of discussion of a number of central figures in the field, from the early work of Lucien Levy-Bruhl to modern scholars such as John Lucy, Eve Danziger or Anna Wierzbicka, who are neither mentioned nor cited. Through the Language Glass is not, and is apparently not intended as, a full recounting of the history of linguistic relativity concepts, which is fine except insofar as it sometimes claims to be one. Because Deutscher is not, and has no plans to be, a scholar doing original research in this field, he is perceived, rightly or wrongly, as an interloper whose contribution is to summarize the work of others without consulting them. While this is not a mortal sin, one can question his judgement in failing to work with the body of scholars whose work he intends to present to a general audience.

Despite these failings, Through the Language Glass is an engaging presentation of an important theme in linguistics and anthropology. With the exception of one chapter I found it very enjoyable to read and a good presentation of important past and present research, and in particular on the field of colour studies I learned much of the history of the field that I had not previously known. It would be highly suitable for use in undergraduate courses with the caveat that it should be discussed critically.

Review: Archaeoastronomy

Archaeoastronomy, the subdiscipline, is the study of the relationship between ancient material culture and ancient beliefs and behaviours with respect to phenomena in the sky. Archaeoastronomy, the blog, is the web presence of Ph.D candidate Alun Salt, who is a classical archaeoastronomer (Salt and Boutsikas 2005) and in my opinion, one of today’s finest public thinkers on matters related to ancient science. I’ve never met him nor even corresponded with him, but the Archaeoastronomy blog (in its various incarnations over the years) has been a regular source of interest for me for some time.

The trick about archaeoastronomy is that it is really an effort to reconstruct prehistoric cognition, which is a very tricky task given the limitations of the archaeological record. It is thus generally a part of the broader subfield of cognitive archaeology (Renfrew and Zubrow 1994) and cognitive anthropology (d’Andrade 1995), of which I consider myself to be a part. It is practically self-evident that the cross-cultural study of astronomy and the cross-cultural study of mathematics have much in common. The central issues of cognitive archaeology are epistemological in nature. How do we reliably obtain knowledge of ancient astronomical concepts given only the record of megalithic architecture, pictographic star-charts, and (if we are very fortunate) ancient (but easily misinterpreted) texts? And how do we, as fallible scientists, distinguish patterns that were meaningful to ancient peoples from the archaeological equivalent of Rorshach tests, patterns constructed by the archaeologist out of random noise? Establishing that the alignment of a particular archaeological feature with a particular astronomical event was intentional and meaningful is exceptionally difficult, which is one of the reasons why archaeoastronomy is more heavily burdened with pseudoscientific nonsense than practically any other endeavour.

This, I think, is why the Archaeoastronomy blog is so timely: it doesn’t retreat from this challenge, but instead helps the reader to see how the act of interpretation is fraught with peril, and yet it can be done. Alun Salt’s description of the field is perhaps the clearest I’ve ever read. Beyond this, it illustrates the political and social dimensions of interpretation in a field where attributing great works to one’s putative ancestors is part of keeping the public’s interest. And beyond that still, it’s a well-written and sometimes hilarious blog that neither sinks to the lowest common denominator nor appeals only to the specialist. It hasn’t been as active lately as one would like (something about finishing a dissertation, I hear …) but it is an extraordinary and fascinating resource.

Posts of interest
Monet the astronomer
The Antikythera Mechanism
Inspired by Nebra

Works cited
Aveni, A. F. 2001. Skywatchers. University of Texas Press.
D’Andrade, R. 1995. The Development of Cognitive Anthropology. Cambridge University Press.
Renfrew, C., and E. B. W. Zubrow. 1994. The Ancient Mind: Elements of Cognitive Archaeology. Cambridge University Press.
Salt, A., and E. Boutsikas. 2005. Knowing when to consult the oracle at Delphi. Antiquity 79, no. 305: 564-572.

Review: Omniglot

Omniglot is an encyclopedic web site detailing the structure and history of the world’s writing systems.  Created in 1998 by Simon Ager, a web developer who is both polyglot (a learner of many languages) and linguist (scholar of language), it reminds me in so many ways of the Phrontistery – a site that began as one young man’s obsession and has turned into something more over the past decade.   I consider it to be the best online information source for writing systems; sure, you could go to Wikipedia, whose page on the topic is currently very good, but why bother?  If you can’t afford The World’s Writing Systems (Daniels and Bright 1996), the best print volume out there, then Omniglot is a good place to start.   I don’t know Ager personally, but I think when my book comes out that I’ll see what can be done about improving his numerals page, which really isn’t as informative as it could be.

Simon Ager also runs an Omniglot blog, which is primarily about second-language acquisition and topics related to multilingualism, particularly discussions of specific differences among words in different languages, but digresses into all sorts of other topics of interest to lingustically-minded anthropologists, such as literacy studies, animal communication, and language evolution.  It’s all written in a very accessible and engaging style, and requires virtually no background knowledge of the subjects in order to be enjoyed.  Refreshingly, he is always happy to admit when his knowledge of a topic is imperfect and to use his readers to learn more.

Recent posts of interest

Txtng nt bd 4 U

Television and stinky badgers

Writing systems and manuscripts

Works cited

Daniels, Peter T. and William Bright, eds. 1996. The World’s Writing Systems. New York: Oxford University Press.

News: The supernatural and natural selection

A recent book by anthropologists Craig Palmer and Lyle Steadman, The Supernatural and Natural Selection: Religion and Evolutionary Success (Steadman and Palmer 2008) attempts to account for the evolution of religion in a novel way, linking sociality, communicative practice, and reproductive fitness.   I will be very interested to see the book (whose publication date is this week) and may give it a more thorough review then; for now, I am relying on a recent report in ScienceDaily.

The claim that interests me most is the assertion that religion does not primarily serve an individual, cognitive function – that its evolutionary basis is not that it explains the unexplainable or gives comfort in times of need.  Rather, they argue, religious belief serves to increase social cohesion and cooperative behavior among non-kin because of the kin-like model of society it creates.  This, so far, is not a novel claim, and can be found in anthropologists as far back as Edward Tylor (1920 [1871]).

Palmer and Steadman go further, however, using observable instances of communication of the acceptance of supernatural claims as analogues to the way that children accept their parents’ influence.  Rather than focusing about what people say about what they believe as evidence for what they believe, they treat what people say as communicative acts and observe what consequences these acts have on other human beings. In other words, they assert, religion creates kin-like social ties through the mutual acceptance of otherwise unobservable social realities.  Further evidence for this position, they assert, is found in the widespread use of basic kin terms (especially for parents, siblings, and children) in religions throughout the world.  This is an interesting combination of linguistic, anthropological, and evolutionary-psychological insights that deserves

Now, this theory is bound to cause controversy.  I don’t even want to address whether I think it is correct until I have a look at the book.  I’ve been interested in the rather different theory espoused by Pascal Boyer in his The Naturalness of Religious Ideas (Boyer 1994), which focuses on the evidence from child development and is essentially a cognitive account rather than a social one.   I’ll be particularly interested to see how Palmer and Steadman have handled the cross-cultural evidence, and the extent to which they are able to deal with differences as well as similarities among the world’s religious systems.

Works cited

Boyer, Pascal. 1994. The naturalness of religious ideas. Berkeley: University of California Press.

Steadman, Lyle B. and Craig T. Palmer. 2008. The supernatural and natural selection: religion and evolutionary success. Boulder, CO: Paradigm.

Tylor, Edward B. 1920 [1871]. Primitive culture. New York: Putnam.

Review: A Very Remote Period Indeed

[Since one of the things that makes academic blogging so fascinating to me is the opportunity to be part of a network of interesting people working on interrelated subjects, from time to time I will post little reviews of blogs that I think might be of interest to my readership -- SC]

A Very Remote Period Indeed is the brainchild of my friend Julien Riel-Salvatore, a Paleolithic archaeologist who is currently a postdoctoral fellow at our mutual alma mater, McGill University.   Julien is one of those sorts of people whose career path should make one envious or infuriated, by all rights.  I first met him in 1996 when he was a wide-eyed freshman in the undergraduate Prehistoric Archaeology course I was TAing, and by 2001, two years before I had published anything, he had a major article in Current Anthropology (Riel-Salvatore and Clark 2001).   Nothing like being lapped to instil a little humility in you.

But anyway, the fact is that Julien is one of the humblest, nicest, and funniest future academic superstars you will ever meet, and his blog reflects that fact.  His academic posts largely focus on Middle and Upper Paleolithic Europe, his area of specialty, on topics such as the relationship (or lack thereof) between Neandertals and anatomically modern humans, the nuances of Paleolithic lithic technology in Italy, or the recent controversies over the Liang Bua ‘hobbit’ hominin.  He’s quite hooked into the rather specialized network of paleoanthropologists and has an uncanny ability to extract useful information from media reports and preprints, and to present it in a fascinating way to an educated but nonspecialist audience.

But like all us McGillians, Julien has the soul of a theorist, and you will find some pretty significant insights at AVRPI about why Paleolithic archaeology is important, and how it relates to our knowledge of human behavior, and more generally the advantages and disadvantages of working in an area whose database is both vital for our understanding of human biology and culture and also depressingly sparse.   From my own perspective, his work leads me to think about the evidence for the evolution of mathematical capacities in relation to the early (and contradictory) evidence for Paleolithic symbolic behavior (d’Errico et al. 2003), a subject I and my students investigated last term in our bibliographic research project on Paleolithic notations.  Archaeological research is at times maddeningly detail-oriented, but it is only through those details, rather than the idle speculations of armchair philosophers (not to mention evolutionary psychologists) that big questions about the evolution of human language and cognition can be addressed.

Recent posts of interest:

Surveying Surveys

The unbearable lightness of the Paleolithic record

Mad Neanderthal disease

Archaeology and the public: a complicated relationship?

Neanderthals, now in color!

Works Cited

d’Errico, F., C. Henshilwood, G. Lawson, M. Vanhaeren, A.-M. Tillier, M. Soressi, F . Bresson, B. Maureille, A. Nowell, J. Lakarra, L. Backwell, and M. Julien. 2003. Archaeological evidence for the emergence of language, symbolism, and music: an alternative multidisciplinary perspective. Journal of World Prehistory 17:1–70.

Riel-Salvatore, Julien and Geoffrey A. Clark. 2001. Grave markers: Middle and early Upper Paleolithic burials and the use of chronotypology in contemporary Paleolithic research. Current Anthropology 42(4): 449-479.