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What are we doing when we perceive numbers?
Published online by Cambridge University Press: 15 December 2021
Abstract
Clarke and Beck rightly contend that the number sense allows us to directly perceive number. However, they unnecessarily assume a representationalist approach and incur a heavy theoretical cost by invoking “modes of presentation.” We suggest that the relevant evidence is better explained by adopting a radical enactivist approach that avoids characterizing the approximate number system (ANS) as a system for representing number.
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References
Anderson, M. L. (2014). After phrenology: Neural reuse and the interactive brain. MIT Press.CrossRefGoogle Scholar
Anobile, G., Arrighi, R., Castaldi, E., & Burr, D. C. (2021). A sensorimotor numerosity system. Trends in Cognitive Sciences, 25(1), 24–36.CrossRefGoogle ScholarPubMed
Anobile, G., Cicchini, G. M., & Burr, D. C. (2016). Number as a primary perceptual attribute: A review. Perception, 45(1–2), 5–31.CrossRefGoogle ScholarPubMed
Culham, J. C., & Kanwisher, N. G. (2001). Neuroimaging of cognitive functions in human parietal cortex. Current Opinion in Neurobiology, 11(2), 157–163.CrossRefGoogle ScholarPubMed
Frege, G. (1950). The foundations of arithmetic (1884), trans. JL Austin. Evanston, 111, 1893–1903.Google Scholar
Gibson, J. J. (1979). The ecological approach to visual perception. Houghton Mifflin Comp.Google Scholar
Gillebert, C. R., Mantini, D., Thijs, V., Sunaert, S., Dupont, P., & Vandenberghe, R. (2011). Lesion evidence for the critical role of the intraparietal sulcus in spatial attention. Brain, 134(6), 1694–1709.CrossRefGoogle ScholarPubMed
Grefkes, C., & Fink, G. (2005). The functional organization of the intraparietal sulcus in humans and monkeys. Journal of Anatomy, 207(1), 3–17.CrossRefGoogle ScholarPubMed
Hutto, D. D. (2019). Re-doing the math: Making enactivism add up. Philosophical Studies, 176(3), 827–837.CrossRefGoogle Scholar
Hutto, D. D., & Myin, E. (2012). Radicalizing enactivism: Basic minds without content. MIT Press.CrossRefGoogle Scholar
Hutto, D. D., & Myin, E. (2017). Evolving enactivism: Basic minds meet content. MIT Press.CrossRefGoogle Scholar
Jones, M. (2016). Number concepts for the concept empiricist. Philosophical Psychology, 29(3), 334–348.CrossRefGoogle Scholar
Jones, M. (2018). Seeing numbers as affordances. In Bangu, S. (Ed.) Naturalizing logico-mathematical knowledge (pp. 148–163). Routledge.CrossRefGoogle Scholar
Kitcher, P. (1984). The nature of mathematical knowledge. Oxford University Press on Demand.Google Scholar
Penner-Wilger, M., & Anderson, M. L. (2013). The relation between finger gnosis and mathematical ability: Why redeployment of neural circuits best explains the finding. Frontiers in Psychology, 4, 877.CrossRefGoogle ScholarPubMed
Simon, O., Mangin, J. F., Cohen, L., Le Bihan, D., & Dehaene, S. (2002). Topographical layout of hand, eye, calculation, and language-related areas in the human parietal lobe. Neuron, 33(3), 475–487.CrossRefGoogle ScholarPubMed
Zahidi, K. (2021). Radicalizing numerical cognition. Synthese, 198(1), 529–545.CrossRefGoogle Scholar
Zahidi, K., & Myin, E. (2016). Radically enactive numerical cognition. In Etzelmüller, G. & Tewes, C. (Eds.), Embodiment in evolution and culture (pp. 57–71). Mohr Siebeck.Google Scholar
Target article
The number sense represents (rational) numbers
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What are we doing when we perceive numbers?
Author response
Numbers, numerosities, and new directions