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Quantity evaluations in Yudja: judgements, language and cultural practice

Abstract

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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Notes

  1. 1.

    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.

  2. 2.

    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.

  3. 3.

    For further discussion of crosslinguistic variation in the expression of countability and the count/mass distinction, see Rothstein (to appear).

  4. 4.

    https://pib.socioambiental.org/en/Table_of_Indigenous_Peoples. Accessed 21.11.2018.

  5. 5.

    All data not directly referenced as appearing in published works were collected by Lima on fieldtrips.

  6. 6.

    It is important to highlight that other languages, typologically unrelated to Yudja, present the same pattern (Innu-aimun (Gillon 2010), Inuttut (Gillon 2012), Ojibwe (Mathieu 2012), Halkomelem and Blackfoot (Wiltschko 2012), Nez Perce (Deal 2017)). Cf. Lima (2018b) for an overview.

  7. 7.

    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.

  8. 8.

    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.

  9. 9.

    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).

  10. 10.

    See Davidson et al. (2012).

  11. 11.

    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.

  12. 12.

    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).

  13. 13.

    For example, in terms of ordinality, see Linnebo (2009).

  14. 14.

    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.

  15. 15.

    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.

  16. 16.

    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…”.

  17. 17.

    To our knowledge, we currently have no evidence of a language which has a way of expressing exact measurement but not exact counting.

  18. 18.

    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.

References

  1. Barner, D., & Snedeker, J. (2005). Quantity judgements and individuation: Evidence that mass nouns count. Cognition, 97, 41–66.

  2. Barth, H., La Mont, K., Lipton, J., Dehaene, S., Kanwisher, N., & Spelke, E. (2006). Non-symbolic arithmetic in adults and young children. Cognition, 98(3), 199–222.

  3. Boolos, G. (1990). The standard equality of numbers. In G. Boolos (Ed.), Meaning and method: Essays in Honor of Hilary Putnam (pp. 261–277). Cambridge: Cambridge University Press. (Reprinted in Logic, logic and logic, pp. 202–219, by R. Jeffrey, Ed., 1998, Cambridge, MA: Harvard University Press.).

  4. Brannon, E. M., Abbott, S., & Lutz, D. J. (2004). Number bias for the discrimination of large visual sets in infancy. Cognition, 93(2), B59–B68.

  5. Brannon, E. M., & Terrace, H. S. (1998). Ordering of the numerosities 1 to 9 by monkeys. Science, 282(5389), 746–749.

  6. Buldt, B., Löwe, B., & Müller, T. (2008). Towards a new epistemology of mathematics., 68, 309. https://doi.org/10.1007/s10670-008-9101-6.

  7. Bunt, H. C. (1985). Mass terms and model-theoretic semantics. Cambridge: Cambridge University Press.

  8. Cantlon, J. F., & Brannon, E. M. (2007). How much does number matter to a monkey (Macaca mulatta)? Journal of Experimental Psychology: Animal Behavior Processes, 33(1), 32.

  9. Carey, S. (2001). Evolutionary and ontogenetic foundations of arithmetic. Mind and Language, 16(1), 37–55.

  10. Carey, S. (2009). The origin of concepts. Oxford: Oxford University Press.

  11. Cheng, L. L.-S., & Sybesma, R. (1998). Yi-wan Tang, yi-ge Tang: Classifiers and massifiers. Tsing Hua Journal of Chinese Studies, New Series, 28(3), 385–412.

  12. Chierchia, G. (1998). Plurality of mass nouns and the notion of the semantic parameter. In S. Rothstein (Ed.), Events and grammar (pp. 53–103). Dordrecht: Kluwer.

  13. Chierchia, G. (2010). Mass nouns, vagueness and semantic variation. Synthese, 174, 99–149.

  14. Chierchia, G., & Turner, R. (1988). Semantics and property theory. Linguistics and Philosophy, 11(3), 261–302.

  15. Clearfield, M., & Mix, K. (1999). Number versus contour length in infants’ discrimination of small visual sets. Psychological Science, 10(5), 408–411.

  16. Davidson, K., Eng, K., & Barner, D. (2012). Does learning to count involve a semantic induction? Cognition, 123(1), 162–173. https://doi.org/10.1016/j.cognition.2011.12.01.

  17. Deal, A. R. (2017). Countability distinctions and semantic variation. Natural Language Semantics, 25(2), 125–171.

  18. Dehaene, S., Spelke, E., Pinel, P., Stanescu, R., & Tsivkin, S. (1999). Sources of mathematical thinking: Behavioural and brain-imaging evidence. Science, 284(5416), 97–974. https://doi.org/10.1126/science.284.5416.970.

  19. Doetjes, J. S. (1997). Quantifiers and selection: On the distribution of quantifying expressions in French, Dutch and English. The Hague: HAG.

  20. Doetjes, J. S. (2012). Count/mass distinctions across languages. In C. Maienborn, K. von Heusinger, & P. Portner (Eds.), Semantics: An international handbook of natural language meaning, part III (pp. 2559–2580). Berlin: De Gruyter.

  21. Everett, D. (2005). Cultural constraints on grammar and cognition in Pirahã. Current Anthropology, 46, 621–646.

  22. Fargetti, C. (2001). Estudo fonológico e morfossintático da língua juruna. PhD dissertation, UNICAMP.

  23. Feigenson, L., Carey, S., & Spelke, E. (2002). Infants’ discrimination of number vs. continuous extent. Cognitive Psychology, 44(1), 33–66.

  24. Ferreira, M. L. (1997). When 1 + 1 ≠ 2. Making mathematics in central Brazil. American Ethnologist, 24(1), 132–147.

  25. Ferreira, M. L. (2015). Mapping time, space and the body: Indigenous knowledge and mathematical thinking in Brazil. Netherlands: Sense Publishers.

  26. Flombaum, J. I., Junge, J. A., & Hauser, M. D. (2005). Rhesus monkeys (Macaca mulatta) spontaneously compute addition operations over large numbers. Cognition, 97(3), 315–325.

  27. Frank, M., Everett, D., Fedorenko, E., & Gibson, E. (2008). Number as a cognitive technology: Evidence from Pirahã language and cognition. Cognition, 108(3), 819–824.

  28. Gil, D. (2013). Numeral Classifiers. In Matthew S. Dryer & Martin Haspelmath (Eds.), The World Atlas of language structures online. Leipzig: Max Planck Institute for Evolutionary Anthropology.

  29. Gillon, C. (2010). The mass/count distinction in Innu-aimun: Implications for the meaning of plurality. In WSCLA 15: The fifteenth workshop on structure and constituency in languages of the Americas (pp. 12–29).

  30. Gillon, C. (2012). Evidence for mass and count in Inuttut. Linguistic Variation, 12(2), 211–246.

  31. Gordon, P. (2004). Numerical cognition without words: Evidence from Amazonia. Science, 306, 496–499.

  32. Heck, R. (2011). Frege’s theorem. Oxford: Oxford University Press.

  33. Hofweber, T. (2005). Number determiners, numbers, and arithmetic. The Philosophical Review, 114(2), 179–225.

  34. Khrizman, K., Landman, F., Lima, S., Rothstein, S., & Schvarcz, B. (2015). Portion readings are count readings not measure readings. In T. Brochhagen, F. Roelofsen & N. Theiler (Eds.), Proceedings of the 20th Amsterdam colloquium (pp. 197–206). http://semanticsarchive.net/Archive/mVkOTk2N/AC2015-proceedings.pdf. Accessed 21 Nov 2018.

  35. Krifka, M. (1989). Nominal reference, temporal constitution and quantification in event semantics. In R. Bartsch, J. van Benthem, & P. von Emde Boas (Eds.), Semantics and contextual expression. Dordrecht: Foris Publication.

  36. Krifka, M. (1992). Thematic relations as links between nominal reference and temporal constitution. In I. A. Sag & A. Szabolcsi (Eds.), Lexical matters. Stanford: Center for the Study of Language and Information.

  37. Landman, F. (1989). Groups. Linguistics and Philosophy, 12(5), 559–605.

  38. Landman, F. (2004). Indefinites and the type of sets. Oxford: Blackwell.

  39. Landman, F. (2016). Iceberg semantics for count nouns and mass nouns: The evidence from portions. In The Baltic international yearbook of cognition, logic and communication (Vol. 11). https://doi.org/10.4148/1944-3676.1107.

  40. Li, X. P. (2011). On the semantics of classifiers in Chinese. Ph.D. dissertation, Bar-Ilan University.

  41. Li, X. P. (2013). Numeral classifiers in Chinese. Berlin: De Gruyter Mouton.

  42. Li, X. P., & Rothstein, S. (2012). Measure readings of Mandarin classifier phrases and the particle de. Language and Linguistics, 13(4), 693–741.

  43. Lima, S. (2014). The grammar of individuation and counting. PhD dissertation, UMass Amherst.

  44. Lima, S. (2016). Container constructions in Yudja: Locatives, individuation and measure. In Baltic international yearbook of cognition, logic and communication (Vol. 11). https://doi.org/10.4148/1944-3676.1109.

  45. Lima, S. (2018a). Quantity judgment studies in Yudja (Tupi): Acquisition and interpretation of nouns. Glossa. Special volume: The acquisition of mass-count distinction across languages and populations.

  46. Lima, S. (2018b). New perspectives on the count-mass distinction: Understudied languages and psycholinguistics. Language and Linguistics Compass.

  47. Lima, S., Li, P., & Snedeker, J. (2016). Counting on a count list: what Yudja tells us about number word acquisition. Poster at the 41st CUNY University conference on language development. Boston, Nov 4–6, 2016.

  48. Lima, S., & Rothstein, S. (2017). Borrowing of Brazilian Portuguese measure words in Yudja. Talk presented at Cambridge conference on language endangerment.

  49. Lima, S., & Snedeker, J. (2015). On the acquisition and interpretation of container phrases in English. In 28th Annual CUNY conference on human sentence processing, USC.

  50. Linnebo, Ø. (2009). The individuation of the natural numbers. In O. Bueno & Ø. Linnebo (Eds.), New waves in philosophy of mathematics. London: Palgrave Macmillan.

  51. Lipton, J., & Spelke, E. (2003). Origins of number sense, large-number discrimination in human infants. Psychological Science, 14(5), 396–401.

  52. Lipton, J., & Spelke, E. (2004). Discrimination of large and small numerosities by human infants. Infancy, 5(3), 271–290.

  53. Mathieu, E. (2012). On the mass/count distinction in Ojibwe. In D. Massam (Ed.), Count and mass across languages. Oxford: Oxford Press.

  54. McCrink, K., & Wynn, K. (2004). Large number addition and subtraction by 9-month old infants. Psychological Science, 15(11), 776–781.

  55. Menary, R. (2015). In T. Metzinger & J. M. Windt (Eds.), Open MIND: 25(T). Frankfurt: MIND Group. https://doi.org/10.15502/9783958570818.

  56. Mendonça, P. (2017). Corpo preparado, alma protegida: jeitos de cuidar e modos de aprender no crescimento da criança Yudja. MA thesis, University of São Paulo.

  57. Pantsar, M. (2014). An empirically feasible approach to the epistemology of arithmetic. Synthese, 191(17), 4201–4229.

  58. Parsons, C. (1995). Frege’s theory of number. In W. Demopolous (Ed.), Frege’s philosophy of mathematics. Cambridge, MA: Harvard University Press.

  59. Pelletier, J. (1975). Non-singular reference: Some preliminaries. Philosophia, 5(4), 451–465. (reprinted in Pelletier 1979).

  60. Pica, P., Lemer, C., Izard, V., & Dehaene, S. (2004). Exact and approximate arithmetic in an Amazonian Indigene Group. Science, 306, 499–503. https://doi.org/10.1126/science.1102085.

  61. Pires de Oliveira, R., & Rothstein, S. (2011). Bare nouns in are mass in Brazilian Portuguese. Lingua, 121(15), 2153–2175.

  62. Rips, L. (2011). Lines of thought. Oxford: Oxford University Press.

  63. Rothstein, S. (2009). Individuating and measure readings of classifier constructions: Evidence from Modern Hebrew. Brill’s Annual of Afroasiatic Languages and Linguistics, 1, 106–145.

  64. Rothstein, S. (2013). A fregean semantics for number words. In M. Aloni, M. Franke & F. Roelofsen (Eds.), Proceedings of the 19th Amsterdam Colloquium (pp. 179–186). https://www.events.illc.uva.nl/AC/AC2013/uploaded_files/inlineitem/23_Rothstein.pdf. Accessed 21 Nov 2018.

  65. Rothstein, S. (2016). Counting and Measuring: A theoretical and crosslinguistic account. In The Baltic international yearbook of cognition, logic and communication (Vol. 11). http://dx.doi.org/10.4148/1944-3676.1106.

  66. Rothstein, S. (2017). Semantics for counting and measuring. Cambridge: Cambridge University Press.

  67. Rothstein, S. (to appear). Count nouns vs. mass nouns. In L. Matthewson, C. Meier, H. Rullman & T. E. Zimmerman (Eds.), Wiley’s companion to semantics (SemCom). Downloadable from https://www.academia.edu/34700872/Count_nouns_vs._Mass_nouns. Accessed 21 Nov 2018.

  68. Sawatzki, C. (2015). Context counts: The potential of realistic problems to expose and extend social and mathematical understandings. In M. Marshman, V. Geiger & A. Bennison (Eds.), Mathematics education in the margins (Proceedings of the 38th annual conference of the Mathematics Education Research Group of Australasia) (pp. 555–562). Sunshine Coast: MERGA.

  69. Scontras, G. (2014). The semantics of measurment. Ph.D. dissertation, Harvard University.

  70. Wilhelm, A. (2008). Bare nouns and number in Dëne Suliné. Natural Language Semantics, 16, 39–68.

  71. Wiltschko, M. (2012). Decomposing the mass/count distinction: Evidence from languages that lack it. In Count and mass across languages. Oxford: Oxford University Press.

  72. Wynn, K. (1990). Children’s understanding of counting. Cognition, 36, 155–193.

  73. Wynn, K. (1992). Children’s acquisition of the number words and the counting system. Cognitive Psychology, 24, 220–251.

  74. Xu, F., & Carey, S. (1996). Infants metaphysics: The case of numerical identity. Cognitive Pyschology, 30, 111–153.

  75. Xu, F., & Spelke, E. S. (2000). Large number discrimination in 6-month-old infants. Cognition, 74(1), B1–B11.

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Acknowledgements

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

Funding was provided by Capes/Fulbright and NSF Dissertation Grant (Grant No. BCS-1226449).

Author information

Correspondence to Susan Rothstein.

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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

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Keywords

  • Mathematical cognition and enculturation
  • Number
  • Quantity judgements
  • Language
  • Mass/count nouns
  • Cardinality
  • Counting
  • Semantics of measurement