Numerals in Grammar and Beyond
Workshop @ Leiden University
17-18 October 2019
Workshop on numeral semantics, morphology, syntax, processing, acquisition, cross-linguistic variation and cognition -- organized by LUCL, Leiden University, as part of NWO VENI project 'Number Words' (PI: Lisa Bylinina, bylinina@gmail.com)

Morning sessions: Lipsius, room 147
Afternoon sessions: Eyckhof 1, room 003C
Thursday, October 17
10:00-10:55
Lisa Bylinina (Leiden University)
The 'Number words' project
12:00-12:55
Marcin Wągiel (Masaryk University Brno)
Doing without atoms:
Evidence from subatomic quantification

13:00-14:00
Lunch break
14:00-14:55
Sjef Barbiers (Leiden University)
ONE is not a number, but is it a numeral?
15:00-15:55
Ljuba Veselinova (Stockholm University)
Cross-linguistic distribution of numeral derivatives
15:55-16:10
Coffee break
16:10-17:05
Maria Spychalska (University of Cologne)
Numerals: ambiguity, processing and truth-value judgment
Friday, October 18
10:00-10:55
11:00-11:55
Stephanie Solt (Leibniz-ZAS)
(joint work with Brandon Waldon – Stanford University)
Bare and approximator-modified numerals under negation
12:00-12:55
Rick Nouwen (Utrecht University)
Numerals and Scope
13:00-14:00
Lunch break
14:00-14:55
Heidi Klockmann (University of Agder)
Decomposing cardinals
15:00-15:55
Ora Matushansky (CNRS, Paris 8)
Numerals and numbers
Who ordered that?!
Ordinal acquisition in Dutch, English and beyond

Caitlin Meyer (UvA)

Thursday October 17 11:00-11:55 / Lipsius 147
Ordinal acquisition turns out to be a process that is unlike anything we have seen in numerical or morphological development before. Data from approximately 250 three-to-five-year-olds, show that irregular ordinals, e.g. English second and Dutch derde 'third', take longer to acquire than regular forms (negende 'ninth') and analytic ordinals (auto drie 'car thee'). I therefore argue that there is no initial lexical learning stage, and that children use morphosyntactic structure to acquire ordinal meaning. Put differently: ordinal acquisition starts out with a rule (informally: cardinal + suffix = ordinal, or for analytic forms: cardinal after a noun = ordinal), rather than following a tiered (cardinals) or u-shaped (e.g., past tense) pathway. By combining insights from both in- (e.g., Yang 2016) and outside (e.g., LeCorre & Carey 2007; Sarnecka 2015, Spelke 2011) linguistics, I propose an account for how linguistic rules can be the driving force behind ordinal acquisition, and for why ordinals are so different in the first place. Time allowing, I will show how this holds up against novel data from 36 'unruly' Russian kindergarteners (4;05–5;10).
Doing without atoms:
Evidence from subatomic quantification

Marcin Wągiel (Masaryk University Brno)

Thursday October 17 12:00-12:55 / Lipsius 147

In standard theories of pluralities and countability, the mass/count distinction is often
formulated in terms of atomicity (e.g., Link 1983, Landman 1991, 2000, Chierchia 1998, 2010, Champollion 2017). Despite significant differences in particular theories, the contrast between count and mass nouns usually boils down to the existence or lack of minimal building blocks in their denotations or, alternativley, to a distinct nature of those building blocks. The approach developed in this paper rejects the view that what counts as one is best represented as an atomic entity. Instead, building on a mereotopological approach to nominal semantics (Grimm 2012, see also Casati & Varzi 1999) I propose that countability is a feature of individuals that constitute non-overlapping and integrated wholes (as opposed to, e.g., scattered entities and arbitrary sums).

The evidence comes from subatomic quantification, i.e., numerical quantification over material parts of referents of concrete count singular NPs, e.g., three parts of the teddy bear. Despite its great significance, so far this phenomenon has been neglected in the study of meaning in natural language. First, I will present the problem such constructions pose for atomicity-based approaches to the mass/count distinction. Next, I will discuss the only two theories attempting to account for that problem I am aware of, i.e., the theories of Chierchia (2010) and Landman (2016), and point what I believe to be their shortcomings. Then, I will argue for two claims, specifically (i) having a notion of atomicity is not enough for a full analysis of quantification of parts and (ii) atomicity is actually not needed to analyze quantification over parts since it can be replaced by topological notions which are required independently. Finally, I will discuss independent cognitive evidence which seems to support my approach.
ONE is not a number, but is it a numeral?

Sjef Barbiers (Leiden University)

Thursday October 17 14:00-14:55 / Eyckhof1 003c

Mathematically, ONE is an exceptional number, as multiplication and division by ONE is identity. Philosophers such as Aristotle and Pythagoras have argued that ONE is not a number. This leads to the question whether the linguistic counterpart of the number ONE, the numeral ONE, has an exceptional status among the other numerals. I show in this talk that ONE has a number of exceptional linguistic, i.e. morphological and syntactic properties, indeed. It is distinct from the cardinal numerals and in various respects closer to quantifiers such as MANY. I propose a classification of numerals and quantifiers that does justice to the special linguistic status of ONE. The talk ends with a speculation on the relation between the exceptional status of ONE as a number and ONE as a numeral.
Cross-linguistic distribution of numeral derivatives

Ljuba Veselinova (Stockholm University)

Thursday October 17 15:00-15:55 / Eyckhof1 003c

This study was inspired by the work of Bauer (2000) where this author presents an overview of the semantic categories commonly expressed by derivational morphology and ranks them as regards their cross-linguistic frequency. In a similar fashion, the current paper explores the domain of derived numerals, that is ordinal, multiplicative, distributive, collective and other words which are derived from a numeral base, typically from a cardinal numeral, as for instance in Modern Greek trís 'three' vs. trí-tos 'third', trí-plos 'triples', tri-áδa 'a group of three', apo tris 'three by three', 'three each', trís trís 'three by three' (Joseph and Philipaki-Warburton 1987: 206-9, Alexis Dimitriadis, p.c.). The purpose of this talk is to outline the crosslinguistic distribution of such derivations as well as to give a general description of the strategies used for the expression of derived numeral senses.

Other issues I discuss include the following (i) base of derivation for the derived numeral (ii) the specialization of the morphological strategy used for specific derivatives; (iii) an issue of theoretical and practical importance is what counts as derivation. Specifically, I draw attention to numeral derivatives in languages without classifiers, on the one hand, and on the other hand, to languages with productive classifier systems where one or several classifiers can be used for the formation of some of the series mentioned above.

References

Bauer, Laurie. 2000. What you can do with derivational morphology. In Morphology 2000: Selected Papers from the 9th Morphology Meeting, Vienna, 24-28 February 2000, eds. S. Bendjaballah, W. U. Dressler, O. E. Pfeiffer and M. D. Voeikova, 37-48. Amsterdam: John Benjamins Publishing Company.

Joseph, Brian D., and Philipaki-Warburton, Irene. 1987. Modern Greek. London: Croom Helm.
What degree expressions can tell us about numerals

Jenny Doetjes (Leiden University)

Friday October 18 10:00-10:55 / Lipsius 147

Theories of numerals disagree on whether numerals are compatible with singular complements or not. According to Ionin and Matushansky (2006), numerals always combine with singular predicates and plural in the context of numerals is triggered by agreement: in two books the semantics of the noun books is argued to be be singular (a set of atoms) and the plural marker is the result of the plural reference of the noun phrase as a whole. On the other hand, Bale, Gagnon and Khanjian (2011) claim that numerals are necessarily restrictive modifiers. This means that (except for numeral 'one') they are incompatible with singular predicates. Whenever a noun combines with a noun that is formally singular (i.e. it lacks plural marking), they claim that this noun is a number neutral predicate (i.e. a predicate that includes atoms as well as possible plural individuals corresponding to these atoms). Thus, in Hungarian három gyerek 'three child', the two approaches make different claims about the semantics of the noun: the singular form gyerek 'child' is a singular predicate for Ionin and Matushansky (2006) and a number neutral predicate for Bale, Gagnon and Khanjian (2011).

In this talk I will address this controversy from the perspective of degree modifiers which are compatible with both mass nouns and count nouns (see for instance Doetjes, 1997). I will argue that these modifiers, thanks to their particular distributional properties, form a much more solid test for number neutrality than numerals. When data from degree modifiers and numerals are combined, it turns out that there is evidence that numerals may combine with both singular and number neutral predicates.

References

Bale, Alan, Michaël Gagnon, and Hrayr Khanjian. 2011. Cross-linguistic representations of numerals and number marking. In Proceedings of SALT 20, eds. Nan Li and David Lutz, 109-127: eLanguage.

Doetjes, Jenny. 1997. Quantifiers and selection. On the distribution of quantifying expressions in French, Dutch and English. The Hague: HAG.

Ionin, Tania, and Ora Matushansky. 2006. The composition of complex cardinals. Journal of Semantics 23:315-360.
Bare and approximator-modified numerals under negation

Stephanie Solt (Leibniz-ZAS)
(joint work with Brandon Waldon – Stanford University)

Friday October 18 11:00-11:55 / Lipsius 147

Despite a large literature on the semantics and pragmatics of cardinal numerals, it has gone largely unnoticed that they exhibit a variety of polarity sensitivity, in that they require contextual support to occur felicitously in the scope of negation. I present the results of two experiments that demonstrate that negated cardinals are acceptable when the negated value has been asserted or otherwise explicitly mentioned in the preceding discourse context, but unacceptable when such a value is neither mentioned nor inferable from that context. I propose an account of these findings based on the notion of convexity of linguistic meanings (Gärdenfors 2004), here applied at the level of discourse. I further discuss the differences between bare and approximator-modified numerals, and how the greater polarity sensitivity of the latter can be explained.
Numerals and Scope

Rick Nouwen (Utrecht University)

Friday October 18 12:00-12:55 / Lipsius 147

From a semantic point of view, there are at least three semantic guises of numerals. They sometimes appear to be akin to proper names, referring to specific arithmetic concepts; In some pre-nominal uses they appear to resemble determiners; And, in some other pre-nominal uses they resemble adjectives. In none of these guises, numerals are readily expected to be scope-taking expressions. Kennedy (S&P 8, 2015), however, argues that pre-nominal numerals should be seen as scope-taking degree quantifiers. Such a proposal explains why a sentence like "You are allowed to take six biscuits" may receive a reading on which it is not allowed to take more than six biscuits. In this talk, I will look at a bunch of other phenomena where numerals appear to take scope. However, I will argue that these shouldn't be attributed to quantification, but are rather a consequence of the adjectival guise of numerals. This means that instead of the familiar mechanisms for quantifier scope, it is more likely that a mechanism akin to post-supposition is at play in these cases.
Decomposing cardinals

Heidi Klockmann (University of Agder)

Friday October 18 14:00-14:55 / Eyckhof 1, 003c

Numerals show a wide array of cross-linguistic variation, from patterning morphosyntactically with nouns, verbs, and adjectives (e.g. Corbett 1987, Donohue 2005) to the need for, or lack thereof of classifiers. In this talk, I attempt to capture morphosyntactic variation among simplex numerals by proposing to decompose them. Following Fassi Fahri (2018) and the general direction in my own work (e.g. Klockmann 2017), I analyze numerals as containing a root, which, through embedding under functional structure, acquires its status as a numeral and other language-specific idiosyncratic properties. Decomposing simplex numerals has the advantage that numerals might share a numerosity core, as represented by the root, but can otherwise differ, depending on how the functional structure is realized. This can in principle allow for adjectival, verbal, and nominal morphosyntax, and I explore this with a few case studies. The consequence is that "numeral" does not exist as a universal category, but instead appears to be constructed on a language-by-language basis (cf. Wiltschko 2014).
Numerals and numbers

Ora Matushansky (CNRS, Paris 8)

Friday October 18 15:00-15:55 / Eyckhof 1, 003c

Until Ionin and Matushansky 2006, 2018 the standard take on cardinals has been to regard them as derived from the more basic numerosity concepts: the cardinal two hundred would then mean "to have the cardinality 200", with the number 200 being in some way linguistically and cognitively basic. The aim of this talk is to argue once again against this perspective for both complex and simplex cardinals by showing that the number meaning is derived from the core cardinal predicate.