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The Small Number System

Published online by Cambridge University Press:  01 January 2022

Eric Margolis
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Abstract

I argue that the human mind includes an innate domain-specific system for representing precise small numerical quantities. This theory contrasts with object-tracking theories and with domain-general theories that only make use of mental models. I argue that there is a good amount of evidence for innate representations of small numerical quantities and that such a domain-specific system has explanatory advantages when infants’ poor working memory is taken into account. I also show that the mental models approach requires previously unnoticed domain-specific structure and consequently that there is no domain-general alternative to an innate domain-specific small number system.

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Articles
Information
Philosophy of Science , Volume 87 , Issue 1 , January 2020 , pp. 113 - 134
Copyright
Copyright © The Philosophy of Science Association

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Footnotes

†

I would like to thank Stephen Laurence, Gerardo Viera, and two anonymous reviewers for valuable comments on earlier drafts of this article. This research was supported by the Social Sciences and Humanities Research Council of Canada.

References

Barner, David. 2017. “Language, Procedures, and the Non-perceptual Origin of Number Word Meanings.” Journal of Child Language 44 (3): 553–90.CrossRefGoogle ScholarPubMed
Carey, Susan. 2009. The Origins of Concepts. New York: Oxford University Press.CrossRefGoogle Scholar
Clearfield, Melissa W., and Mix, Kelly S. 1999. “Number versus Contour Length in Infants’ Discrimination of Small Visual Sets.” Psychological Science 10 (5): 408–11.CrossRefGoogle Scholar
Cordes, Sara, and Brannon, Elizabeth M. 2009. “The Relative Salience of Discrete and Continuous Quantity in Young Infants.” Developmental Science 12 (3): 453–63.CrossRefGoogle ScholarPubMed
Dehaene, Stanislas, and Brannon, Elizabeth, eds. 2011. Space, Time, and Number in the Brain: Searching for the Foundations of Mathematical Thought. New York: Academic Press.Google Scholar
Feigenson, Lisa, and Carey, Susan. 2003. “Tracking Individuals via Object Files: Evidence from Infants’ Manual Search.” Developmental Science 6 (5): 568–84.CrossRefGoogle Scholar
Feigenson, Lisa, Carey, Susan, and Hauser, Marc. 2002. “The Representations Underlying Infants’ Choice of More: Object Files versus Analog Magnitudes.” Psychological Science 13 (2): 150–56.CrossRefGoogle ScholarPubMed
Gross, Hans J., Pahl, Mario, Si, Aung, Zhu, Hong, Tautz, Jürgen, and Zhang, Shaowu. 2009. “Number-Based Visual Generalisation in the Honeybee.” PLoS ONE 4 (1): 4263.CrossRefGoogle ScholarPubMed
Hauser, Marc D., Carey, Susan, and Hauser, Lilan B. 2000. “Spontaneous Number Representation in Semi-Free-Ranging Rhesus Monkeys.” Proceedings of the Royal Society of London B 267 (1445): 829–33.Google Scholar
Hurford, James R. 2001. “Languages Treat 1–4 Specially.” Mind and Language 16 (1): 69–75.CrossRefGoogle Scholar
Káldy, Zsuzsa, and Leslie, Alan M. 2005. “A Memory Span of One? Object Identification in 6.5-Month-Old Infants.” Cognition 97 (2): 153–77.CrossRefGoogle ScholarPubMed
Kobayashi, Tessei, Hiraki, Kazuo, Mugitani, Ryoko, and Hasegawa, Toshikazu. 2004. “Baby Arithmetic: One Object Plus One Tone.” Cognition 91 (2): B23–B34.CrossRefGoogle ScholarPubMed
Laurence, Stephen, and Margolis, Eric. 2005. “Number and Natural Language.” In The Innate Mind, Vol. 1, Structure and Contents, ed. Carruthers, Peter, Laurence, Stephen, and Stich, Stephen, 216–35. New York: Oxford University Press.Google Scholar
Le Corre, M., and Carey, Susan. 2007. “One, Two, Three, Four, Nothing More: An Investigation of the Conceptual Sources of the Verbal Counting Principles.” Cognition 105 (2): 395–438.CrossRefGoogle ScholarPubMed
Leslie, Alan M., Xu, Fei, Tremoulet, Patrice D., and Scholl, Brian J. 1998. “Indexing and the Object Concept: Developing ‘What’ and ‘Where’ Systems.” Trends in Cognitive Sciences 2 (1): 10–18.CrossRefGoogle ScholarPubMed
Margolis, Eric, and Laurence, Stephen. 2008. “How to Learn the Natural Numbers: Inductive Inference and the Acquisition of Number Concepts.” Cognition 106 (2): 924–39.CrossRefGoogle ScholarPubMed
Mix, Kelly S., Huttenlocher, Janellen, and Levine, Susan C. 2002. Quantitative Development in Infancy and Early Childhood. New York: Oxford University Press.CrossRefGoogle Scholar
Oakes, Lisa M., and Luck, Steven J. 2014. “Short-Term Memory in Infancy.” In The Wiley Handbook on the Development of Children’s Memory, ed. Bauer, Patricia J. and Fivush, Robyn, 157–80. Oxford: Wiley.Google Scholar
Pylyshyn, Zenon W., and Storm, Ron W. 1988. “Tracking Multiple Independent Targets: Evidence for a Parallel Tracking Mechanism.” Spatial Vision 3 (3): 179–97.CrossRefGoogle ScholarPubMed
Reznick, S. J. 2014. “Methodological Challenges in the Study of Short-Term Working Memory in Infants.” In The Wiley Handbook on the Development of Children’s Memory, ed. Bauer, Patricia J. and Fivush, Robyn, 181–201. Oxford: Wiley.Google Scholar
Rugani, Rosa, Regolin, Lucia, and Vallortigara, Giorgio. 2008. “Discrimination of Small Numerosities in Young Chicks.” Journal of Experimental Psychology: Animal Behavior Processes 34 (3): 388–99.Google ScholarPubMed
Rugani, Rosa, Regolin, Lucia, and Vallortigara, Giorgio. 2010. “Imprinted Numbers: Newborn Chicks’ Sensitivity to Number vs. Continuous Extent of Objects They Have Been Reared With.” Developmental Science 13 (5): 790–97.CrossRefGoogle Scholar
Scholl, B. J., and Leslie, A. M. 1999. “Explaining the Infant’s Object Concept: Beyond the Perception/Cognition Dichotomy.” In What Is Cognitive Science?, ed. Lepore, Ernest and Pylyshyn, Zenon, 26–73. Oxford: Blackwell.Google Scholar
Simon, Tony J. 1997. “Reconceptualizing the Origins of Number Knowledge: A ‘Non-numerical’ Account.” Cognitive Development 12 (3): 349–72.CrossRefGoogle Scholar
Spelke, E. S. 2003. “What Makes Us Smart? Core Knowledge and Natural Language.” In Language in Mind: Advances in the Study of Language and Thought, ed. Gentner, Dedre and Goldin-Meadow, Susan, 277–311. Cambridge, MA: MIT Press.Google Scholar
vanMarle, Kristy, Chu, Felicia W., Mou, Yi, Seok, Jin H., Rouder, Jeffrey, and Geary, David C. 2016. “Attaching Meaning to the Number Words: Contributions of the Object Tracking and Approximate Number Systems.” Developmental Science 21 (1): e12495.Google Scholar
Wynn, Karen. 1992. “Addition and Subtraction by Human Infants.” Nature 358 (6389): 749.CrossRefGoogle ScholarPubMed
Xu, Fei, and Spelke, Elizabeth S. 2000. “Large Number Discrimination in 6-Month-Old Infants.” Cognition 74 (1): 1–11.CrossRefGoogle ScholarPubMed
Xu, Fei, Spelke, Elizabeth S., and Goddard, Sydney. 2005. “Number Sense in Human Infants.” Developmental Science 8 (1): 88–101.CrossRefGoogle ScholarPubMed