Number Concepts Are Constructed through Material Engagement: A Reply to Sutliff, Read, and Everett

I respond to three responses to my 2015 Current Anthropology article, “Numerosity Structures the Expression of Quantity in Lexical Numbers and Grammatical Number.” This study examined the categorical and geographical distribution of lexical numbers, also known as counting numbers, and grammatical number, the ability to linguistically distinguish singular and plural. Both these features of language conform to the perceptual experience of quantity, which consists of subitization, the ability to rapidly and unambiguously identify one, two, and three, and magnitude appreciation, the ability to appreciate bigger and smaller in the numerical quantity of groups when the difference lies above a threshold of noticeability. My reply to Sutliff disagrees with her contention that mathematical ideas are mentally innate on the grounds that this ignores their explicit construction through the interaction of human psychological, physiological, and behavioral abilities with materiality. My reply to Read expands on the idea that language obscures cross-cultural conceptual variability in number concepts because everything that translates as “three” does not necessarily have the same numerical properties. Finally, my reply to Everett notes that investigating numerical origins means discarding the deeply entrenched assumption of linguistic primacy on the grounds that material forms make numerical intuitions tangible, visible, and manipulable in ways that language cannot and, moreover, provide an alinguistic bootstrap mechanism that accounts for the emergence of both concepts of number and words for the concepts.

Numerosity Structures the Expression of Quantity in Lexical Numbers and Grammatical Number

Using data from the World Atlas of Language Structures and other sources, this study analyzed 905 languages for the presence of grammatical number (GN) and lexical numbers (LNs) to investigate what the distribution of these linguistic features might suggest about the relationship between language and numerosity, the perceptual system for quantity. Nearly 7% of the sample had LNs but lacked GN, and GN never occurred without LNs, implying that LNs may develop first and that GN is neither necessary nor sufficient for developing LNs, despite its role in helping children acquire number concepts when present as a feature of language. The geographic-temporal distribution of the two linguistic features additionally supported the idea that LNs may emerge prior to GN. Furthermore, the “one-two-three-many” structure of both LNs and GN, along with the failure of historic artificial intelligence modeling to converge on real-world number system solutions, suggested that numerosity may structure the expression of quantity in both linguistic domains. The role of the hand in numbers (the interaction of numerosity with cognitive processes such as finger gnosia, haptic perception, and neural reactions to tools) implies that LNs may originate in tactile engagement with material structures that may subsequently extend to nontactile domains, such as GN.

CHANGES IN MARI NUMERAL PHRASES UNDER THE INFLUENCE OF MARI-RUSSIAN LANGUAGE CONTACTS

This article presents the results of a study of the Mari numeral phrases in terms of the influence of the Russian language. The aim of this work is to trace the role of Russian borrowings in the formation of Mari numeral phrases, primarily in the expression of their components, and to reveal other changes that have arisen under the influence of similar phrases and structures of the Russian language. The study was conducted on the basis of the lexical card index of the MarNIIYALI (Mari Scientific Research Institute of Language, Literature and History), which is based on written sources of the meadow-eastern literary norm, namely, its electronic part in the amount of about one thousand author's sheets. During the collection and analysis of material, elements and techniques of the following research methods were applied: descriptive and analytical (observation with the identification of the studied facts in sources, their generalization, interpretation and classification, description), comparative (regular comparison of Mari models with Russian ones for identity and non-identity), comparative-historical (in other cases, indications of the origin of the words), quantitative (counting models of various groups containing Russianisms). According to the results of the research, Russian borrowings may play a role of a head word (3 units in 4 models) and a dependent component (mainly substantive case forms and postpositional constructions, numerals, as well as some pronouns and adverbs of degree in 14 models). 3 models with cardinal numbers as a head very rarely can be represented by phrases with Russianisms in both components. As a result the syntactic units in some models and the models of numeral phrases themselves were replenished, the last ones by 3 units. Also the shifts in the forms of grammatical number of dependent nouns in some models appeared.

When one is singular: Notes on zero-person constructions in Latvian

Axel Holvoet has demonstrated that Latvian has two types of zero-person constructions which formally differ in grammatical number, and that the singular type has a parallel in Finnic, but not in Lithuanian. This paper shows that the meanings covered by the two types are distinct and do not overlap. Using the framework proposed by Gast and van der Auwera for the description of human impersonal pronouns, it is shown that the singular type is characterized by non-veridicality and an internal perspective. As in Finnish, but not Estonian, it is used in conditional sentences with all kinds of verbs. The plural type is used in Latvian as well as in Lithuanian with veridical propositions and an external perspective.

Dependent plurals and three levels of multiplicity

The paper focuses on the semantics of distributivity, grammatical number, and cardinality predicates (numerals and modifiers like several). I argue that constructions involving so-called ‘dependent plurals’, i.e. plurals lacking cardinality predicates occurring in the scope of certain quantificational items such as all and most (e.g. All the girls were wearing hats), pose a challenge to familiar semantic frameworks that distinguish between two sources of multiplicity: mereological plurality and distributive quantification. I argue that dependent plural readings should be analysed as distinct both from cumulative readings and distributive readings, in the classical sense. I demonstrate how this can be accomplished in a semantic framework where expressions are evaluated relative to sets of assignments, or plural info states (van den Berg, in Stokhof and Torenvliet (eds) Proceedings of the 7th Amsterdam Colloquium, ILLC, University of Amsterdam, Amsterdam, 1990, in Dekker and Stokhof (eds) Proceedings of the 9th Amsterdam Colloquium, ILLC, University of Amsterdam, Amsterdam, 1994, Some aspects of the Internal Structure of Discourse. The Dynamics of Nominal Anaphora. PhD thesis, University of Amsterdam, 1996). The specific formal implementation is based on a modified version of Brasoveanu’s (Structured nominal and modal reference. PhD thesis, Rutgers, The State University of New Jersey, 2007, Linguist Philos 31(2):129–209. 10.1007/s10988-008-9035-0, 2008) Plural Compositional DRT. In this framework we are able to distinguish between two types of distributivity: weak distributivity across the assignments in a single plural info state and strong distributivity across multiple info states. I argue that both of these types of distributivity play a role in the semantics of natural language, accounting for the contrasting properties of ‘singular quantifiers’, such as each and every, and ‘plural quantifiers’, such as all and most. The contrasting properties of bare plurals and plurals involving cardinality modifiers are analysed in terms of the distinction between state-level and assignment-level (mereological) plurality.

Nominal Number and Language Pathologies

This chapter provides an overview of the evidence on grammatical number processing taken from cognitive neuropsychology, including developmental delays and impairments of language (e.g. developmental language disorder, and Williams syndrome) and aphasia, an acquired language impairment after brain injury. These types of language impairment can give insight into the functional architecture of nominal number processing by looking at error patterns that arise in each of the aforementioned populations. By classifying observed responses in language production tasks into non-number and number errors, we are able to reveal underlying mechanisms of syntactic rules and their representations when they develop, but also learn about processes and representation of number when this information breaks down.

The Oxford Handbook of Grammatical Number

This volume offers an overview of current research on grammatical number in language. The chapters Part i of the handbook present foundational notions in the study of grammatical number covering the semantic analyses of plurality, the mass–count distinction, the relationship between number and quantity expressions and the mental representation of number and individuation. The core instance of grammatical number is marking for number distinctions in nominal expressions as in English the book/the books and the chapters in Part ii, Number in the nominal domain, explore morphological, semantic, and syntactic aspects of number marking within noun phrases. The contributions examine morphological marking of number the relationship between syntax and nominal number marking, and the interactions between numeral classifiers with semantic number and number marking. They also address cases of mismatches in form and meaning with respect to number displayed by lexical plurals and collective nouns. The final chapter reviews nominal number processing from the perspective of language pathologies. While number marking on nouns has been the focus of most research on number, number distinctions can also be found in the event domain. Part iii, Number in the event domain, presents an overview of different linguistic means of expressing plurality in the event domain, covering verbal plurality marking, pluractional modifiers of the form Noun preposition Noun, frequency adjectives and dependent indefinites. Part iv provides fifteen case studies examining different aspects of grammatical number marking in a range of typologically diverse languages.

Introduction

This introduction gives an outline of the major issues in the research on grammatical number, covering different types of nominal number marking, the relation between number and individuation, and number in the event domain. The second part of the chapter provides a summary of the chapters of the book, which is divided into four parts: foundations, nominal number, event number, and case studies.