In this paper we explore the interpretation of quantity expressions in Yudja, an indigenous language spoken in the Amazonian basin, showing that while the language allows reference to exact cardinalities, it does not generally allow reference to exact measure values. It does, however, allow non-exact comparison along continuous dimensions. We use this data to argue that the grammar of exact measurement is distinct from a grammar allowing the expression of exact cardinalities, and that the grammar of counting and the grammar of measurement may use numerals with different, though related interpretations. As Yudja shows, the language of measurement is not automatically acquired along with the knowledge of exact numeral expressions. We show that the ‘gap’ between prelinguistic intuitions about quantity in terms of numerosity and counting, which is bridged by the learning of language expressing exact cardinality, is paralleled by a similar gap between prelinguistic intuitions about quantity on a continuous dimension and measuring: this gap too must be bridged by language which expresses exact measure values. Our results suggest that the enculturation process by which we develop skills to perform abstract operations in the domain of measurement is (1) language dependent and (2) distinct from the process by which we learn to perform abstract calculations in the cardinal domain.
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Mereological theories of noun and NP denotations favoured by many semanticists (e.g. Krifka 1989, 1992; Landman 1989, 2004; Chierchia 1998, 2010 and many others) treat numerals as denoting properties of plural individuals rather than sets. This property of plural individuals is derived from the definition in terms of sets: a plural individual has the cardinal property n if the set of its atomic parts has n members.
Mass nouns can also be modified by numerals with kind-interpretations. Three coffees can mean three kinds of coffee. This is not relevant to our discussion since this is not a quantity interpretation. On the kind reading, “I bought three coffees” gives no information about the quantity of coffee bought.
For further discussion of crosslinguistic variation in the expression of countability and the count/mass distinction, see Rothstein (to appear).
https://pib.socioambiental.org/en/Table_of_Indigenous_Peoples. Accessed 21.11.2018.
All data not directly referenced as appearing in published works were collected by Lima on fieldtrips.
In fact Barner and Snedeker were most interested in quantity evaluations of object mass nouns, but that is orthogonal to the issues we discuss here.
Quantity judgment tasks with children show that at a particular age range (6–11 years old), children favor a volume interpretation. Crucially, this is not particular to substance nouns: 6–11 year old children consistently favor a volume interpretation for all nouns (no noun effect was found for children). Cf. Lima (2018a) for details.
The fact that cardinality evaluations dropped also with count nouns in Brazilian Portuguese may be due to the fact that bare count nouns (mass syntax) were used in the stimuli and these have been argued to be ambiguous between mass and count interpretations (cf. Pires de Oliveira and Rothstein 2011). Note that the control group in this study (20 Brazilian Portuguese) chose the number response for object nouns in 86% of the trials. Another factor may be that bilingualism can involve different levels of competence in the second language. Thus, while results show a clear difference in the judgments made about count versus mass nouns, the drop in cardinal evaluations with count nouns to 63% suggests that some participants were overgeneralizing in Brazilian Portuguese and using a measure evaluation in all cases. This interpretation is consistent with Lima (2018a) finding that Yudja children in the 6–11 age range who were at the early stages of learning Brazilian Portuguese used comparison in a continuous dimension in both Yudja and Brazilian Portuguese for all stimuli. (See previous note).
See Davidson et al. (2012).
Ferreira (2015: p. 34) describes a series of situations that had caused the knowledge of mathematics to be critical in the communities of the Xingu indigenous populations (in particular the Kisêdjê (Suyá), Yudja (Juruna) and Kawaiwete (Kayabi)). The situations listed by Ferreira include the exchange of goods (sell and buy) with people from outside the communities, and the establishment of local pharmacies, where the indigenous nurses were responsible for, among other things, measuring medicaments). See Ferreira (2015) for details.
The first school in the North of the Xingu Indigenous Territory dates from 1981 (Diauarum Indigenous School). The first group of indigenous teachers were trained in the late 90’s and early 00’s (1994–2005) (Mendonça 2017: p. 15).
For example, in terms of ordinality, see Linnebo (2009).
This predicts, of course, that it would be more difficult for the Yudja to carry out abstract computations in the measure domain. We have not yet had an opportunity to test these predictions, but see Lima (2016) for an initial discussion of the measure interpretation of classifiers such as bottles of in three bottles of water.
We express this tentatively since it is possible that the option of comparing overall measures was conceptually introduced via exposure to Brazilian Portuguese and that this is what leads to the 15% non-cardinal responses. More research is necessary to clarify this.
We are reminded also of an anecdote that we cannot currently trace to source of a child who was asked: “If you have six sweets and give two to your best friend, how many will you have left?” She answered “Two”, and when asked why, she answered “I can’t give two to my best friend without giving two to her sister as well…”.
To our knowledge, we currently have no evidence of a language which has a way of expressing exact measurement but not exact counting.
Hofweber (2005) suggests that two as a predicate and two as a singular domain are related by “cognitive type coercion”, similar in some respects to Rothstein’s account in terms of property theory. But in both cases this is a formal characterization of the relation, rather than an explanation of how the different meanings of the numeral are related.
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First we would like to thank the Yudja people who generously contributed their time and knowledge to this documentation project. We would like to thank two anonymous reviewers for very helpful comments on the first version of this paper, and to Markus Pantsar and Catarina Dutilh Novaes for advice and encouragement in making the revisions. Early versions of this material were presented at the 7th Cambridge conference on Language Endangerment (Cambridge UK, July 2017), at the Workshop on Language and Literacy Development in Multilingual and Multidialectal Contexts (Bar-Ilan University, March 2018) and at the Multilingualism and Multiculturalism Workshop (Bar Ilan University June 2018) We thank the participants at all these events for their helpful comments. We would like to acknowledge the financial support of the American Philosophical Society, and of dissertation grants to Suzi Lima from the Coordenação de Aperfeiçoamento de Pessoal de Nível Superior and the National Science Foundation.
Funding was provided by Capes/Fulbright and NSF Dissertation Grant (Grant No. BCS-1226449).
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Rothstein, S., Lima, S. Quantity evaluations in Yudja: judgements, language and cultural practice. Synthese (2018) doi:10.1007/s11229-018-02016-5
- Mathematical cognition and enculturation
- Quantity judgements
- Mass/count nouns
- Semantics of measurement