Exact Number Concepts Are Limited to the Verbal Count Range

Abstract

Previous findings suggest that mentally representing exact numbers larger than four depends on a verbal count routine (e.g., “one, two, three . . .”). However, these findings are controversial because they rely on comparisons across radically different languages and cultures. We tested the role of language in number concepts within a single population—the Tsimane’ of Bolivia—in which knowledge of number words varies across individual adults. We used a novel data-analysis model to quantify the point at which participants (N = 30) switched from exact to approximate number representations during a simple numerical matching task. The results show that these behavioral switch points were bounded by participants’ verbal count ranges; their representations of exact cardinalities were limited to the number words they knew. Beyond that range, they resorted to numerical approximation. These results resolve competing accounts of previous findings and provide unambiguous evidence that large exact number concepts are enabled by language.

Keywords

cognition cross-cultural differences language number comprehension open data

Get full access to this article

View all access options for this article.

References

Bender

Beller

(2012). Nature and culture of finger counting: Diversity and representational effects of an embodied cognitive tool. Cognition, 124(2), 156–182.

Bloom

(1994). Generativity within language and other cognitive domains. Cognition, 51(2), 177–189. https://doi.org/10.1016/0010-0277(94)90014-0

Bowerman

Levinson

S. C.

(Eds.) (2001). Language acquisition and conceptual development. Cambridge University Press.

Brannon

E. M.

(2005). What animals know about numbers. In Campbell

J. I. D.

(Ed.), Handbook of mathematical cognition (pp. 85–107). Psychology Press.

Butterworth

Reeve

Reynolds

Lloyd

(2008). Numerical thought with and without words: Evidence from indigenous Australian children. Proceedings of the National Academy of Sciences, USA, 105(35), 13179–13184.

Carey

(2004). Bootstrapping & the origin of concepts. Daedalus, 133(1), 59–68.

Carey

(2009). The origin of concepts. Oxford University Press.

Carey

Barner

(2019). Ontogenetic origins of human integer representations. Trends in Cognitive Sciences, 23(10), 823–835.

Casasanto

(2005). Crying “Whorf.” Science, 307(5716), 1721–1722.

10.

Casasanto

(2016). Linguistic relativity. In Riemer

(Ed.), The Routledge handbook of semantics (pp. 158–174). Routledge.

11.

Cheyette

S. J.

Piantadosi

S. T.

(2020). A unified account of numerosity perception. Nature Human Behaviour, 4(12), 1265–1272.

12.

Chomsky

(1988). Language and problems of knowledge: The Managua lectures. MIT Press.

13.

Cooperrider

Gentner

(2019). The career of measurement. Cognition, 191, Article 103942. https://doi.org/10.1016/j.cognition.2019.04.011

14.

Davidson

Eng

Barner

(2012). Does learning to count involve a semantic induction? Cognition, 123(1), 162–173.

15.

Dehaene

(2011). The number sense: How the mind creates mathematics (2nd edition). Oxford University Press.

16.

Dehaene

Dehaene-Lambertz

Cohen

(1998). Abstract representations of numbers in the animal and human brain. Trends in Neurosciences, 21(8), 355–361.

17.

Diekmann

Smith

Gerbault

Dyble

Page

A. E.

Chaudhary

Migliano

A. B.

Thomas

M. G.

(2017). Accurate age estimation in small-scale societies. Proceedings of the National Academy of Sciences, USA, 114(31), 8205–8210.

18.

Dolscheid

Shayan

Majid

Casasanto

(2013). The thickness of musical pitch: Psychophysical evidence for linguistic relativity. Psychological Science, 24(5), 613–621.

19.

Everett

D. L.

(2009). Don’t sleep, there are snakes: Life and language in the Amazonian jungle. Random House.

20.

Feigenson

Dehaene

Spelke

(2004). Core systems of number. Trends in Cognitive Sciences, 8(7), 307–314.

21.

Fodor

(1975). The language of thought. Harvard University Press.

22.

Forder

Lupyan

(2019). Hearing words changes color perception: Facilitation of color discrimination by verbal and visual cues. Journal of Experimental Psychology: General, 148(7), 1105–1123.

23.

Frank

M. C.

Barner

(2012). Representing exact number visually using mental abacus. Journal of Experimental Psychology: General, 141(1), 134–149.

24.

Frank

M. C.

Everett

D. L.

Fedorenko

Gibson

(2008). Number as a cognitive technology: Evidence from Pirahã language and cognition. Cognition, 108(3), 819–824.

25.

Frank

M. C.

Fedorenko

Lai

Saxe

Gibson

(2012). Verbal interference suppresses exact numerical representation. Cognitive Psychology, 64(1–2), 74–92.

26.

Gallistel

C. R.

Gelman

(1992). Preverbal and verbal counting and computation. Cognition, 44(1–2), 43–74.

27.

Gelman

Carlin

J. B.

Stern

H. S.

Rubin

D. B.

(2014). Bayesian data analysis (Vol. 2). Taylor & Francis.

28.

Gelman

Butterworth

(2005). Number and language: How are they related? Trends in Cognitive Sciences, 9(1), 6–10.

29.

Gelman

Gallistel

C. R.

(2004). Language and the origin of numerical concepts. Science, 306(5695), 441–443.

30.

Gibson

Jara-Ettinger

Levy

Piantadosi

(2017). The use of a computer display exaggerates the connection between education and approximate number ability in remote populations. Open Mind, 2(1), 37–46.

31.

Gijssels

Casasanto

(2017). Conceptualizing time in terms of space: Experimental evidence. In Dancygier

(Ed.), The Cambridge handbook of cognitive linguistics (pp. 651–668). Cambridge University Press.

32.

Gleitman

Papafragou

(2013). Relations between language and thought. In Reisberg

(Ed.), The Oxford handbook of cognitive psychology (pp. 504–523). Oxford University Press.

33.

Gordon

(2004). Numerical cognition without words: Evidence from Amazonia. Science, 306(5695), 496–499.

34.

Henrich

Heine

S. J.

Norenzayan

(2010). The weirdest people in the world? Behavioral & Brain Sciences, 33(2–3), 61–83.

35.

Huanca

(2008). Tsimane oral tradition, landscape, and identity in tropical forest. South-South Exchange Programme for Research on the History of Development.

36.

Hume

(1978). A treatise of human nature. In Raphael

D. D.

(Ed.), British moralists: 1650–1800. (Original work published 1739)

37.

Hume

(2000). An enquiry concerning human understanding. Prentice Hall. (Original work published 1748)

38.

Jara-Ettinger

Piantadosi

Spelke

E. S.

Levy

Gibson

(2017). Mastery of the logic of natural numbers is not the result of mastery of counting: Evidence from late counters. Developmental Science, 20(6), Article e12459. https://doi.org/10.1111/desc.12459

39.

Kay

Kempton

(1984). What is the Sapir-Whorf hypothesis? American Anthropologist, 86(1), 65–79.

40.

Landy

Silbert

Goldin

(2013). Estimating large numbers. Cognitive Science, 37(5), 775–799.

41.

Laurence

Margolis

(2007). Linguistic determinism and the innate basis of number. In Carruthers

Laurence

Stich

(Eds.), The innate mind: Vol. 3. Foundations and the future (pp. 139–169). Oxford University Press.

42.

Le Corre

Carey

. (2007). One, two, three, four, nothing more: An investigation of the conceptual sources of the verbal counting principles. Cognition, 105(2), 395–438.

43.

Leslie

A. M.

Gallistel

Gelman

(2007). Where integers come from. In Carruthers

Laurence

Stich

(Eds.), The innate mind: Vol. 3. Foundations and the future (pp. 109–149). Oxford University Press.

44.

Leslie

A. M.

Gelman

Gallistel

(2008). The generative basis of natural number concepts. Trends in Cognitive Sciences, 12(6), 213–218.

45.

Lupyan

(2016). The centrality of language in human cognition. Language Learning, 66(3), 516–553.

46.

Majid

Bowerman

Kita

Haun

D. B.

Levinson

S. C.

(2004). Can language restructure cognition? The case for space. Trends in Cognitive Sciences, 8(3), 108–114.

47.

McWhorter

J. H.

(2014). The language hoax: Why the world looks the same in any language. Oxford University Press.

48.

Overmann

K. A.

(2018). Constructing a concept of number. Journal of Numerical Cognition, 4(2), 464–493.

49.

Pahl

Zhang

(2013). Numerical cognition in bees and other insects. Frontiers in Psychology, 4, Article 162. https://doi.org/10.3389/fpsyg.2013.00162

50.

Piantadosi

S. T.

Tenenbaum

J. B.

Goodman

N. D.

(2012). Bootstrapping in a language of thought: A formal model of numerical concept learning. Cognition, 123(2), 199–217.

51.

Piazza

Izard

Pinel

Le Bihan

Dehaene

(2004). Tuning curves for approximate numerosity in the human intraparietal sulcus. Neuron, 44(3), 547–555.

52.

Pica

Lemer

Izard

Dehaene

(2004). Exact and approximate arithmetic in an Amazonian indigene group. Science, 306(5695), 499–503.

53.

Pinker

(1994). The language instinct. William Morrow.

54.

Regier

Kay

(2009). Language, thought, and color: Whorf was half right. Trends in Cognitive Sciences, 13(10), 439–446.

55.

Sapir

(1929). The status of linguistics as a science. Language, 5(4), 207–214.

56.

Sarnecka

B. W.

Goldman

M. C.

Slusser

E. B.

(2015). How counting leads to children’s first representations of exact, large numbers. In Cohen Kadosh

Dowker

(Eds.), The Oxford handbook of numerical cognition (pp. 291–309). Oxford University Press.

57.

Saxe

G. B.

(1981). Body parts as numerals: A developmental analysis of numeration among the Oksapmin in Papua New Guinea. Child Development, 52, 306–316.

58.

Schneider

R. M.

Barner

(2020, July). Children use one-to-one correspondence to establish equality after learning to count. In CogSci 2020 Proceedings (pp. 515–521). Cognitive Science Society.

59.

Spaepen

Coppola

Spelke

E. S.

Carey

S. E.

Goldin-Meadow

(2011). Number without a language model. Proceedings of the National Academy of Sciences, USA, 108(8), 3163–3168.

60.

Spelke

E. S.

(2003). What makes us smart? Core knowledge and natural language. In Gentner

Goldin-Meadow

(Eds.), Language in mind: Advances in the study of language and thought (pp. 277–311). MIT Press.

61.

Whorf

B. L.

(2012). Language, thought, and reality: Selected writings of Benjamin Lee Whorf. MIT Press.

62.

Wiese

(2003). Iconic and non-iconic stages in number development: The role of language. Trends in Cognitive Sciences, 7(9), 385–390.

63.

Wynn

(1992). Children’s acquisition of the number words and the counting system. Cognitive Psychology, 24(2), 220–251.

Supplementary Material

Please find the following supplemental material available below.

For Open Access articles published under a Creative Commons License, all supplemental material carries the same license as the article it is associated with.

For non-Open Access articles published, all supplemental material carries a non-exclusive license, and permission requests for re-use of supplemental material or any part of supplemental material shall be sent directly to the copyright owner as specified in the copyright notice associated with the article.

0.00 MB

0.41 MB