Hostname: page-component-78c5997874-ndw9j Total loading time: 0 Render date: 2024-11-07T22:56:33.078Z Has data issue: false hasContentIssue false
  • English
  • Français

Numbers, numerosities, and new directions

Published online by Cambridge University Press:  15 December 2021

Sam Clarke  and
Jacob Beck Open the ORCID record for Jacob Beck [Opens in a new window]
Sam Clarke
Affiliation:
Department of Philosophy & Centre for Vision Research, York University, Toronto, ONM3J 1P3, [email protected]; http://[email protected]; http://www.jacobbeck.org
Jacob Beck
Affiliation:
Department of Philosophy & Centre for Vision Research, York University, Toronto, ONM3J 1P3, [email protected]; http://[email protected]; http://www.jacobbeck.org
Get access Rights & Permissions [Opens in a new window]

Abstract

In our target article, we argued that the number sense represents natural and rational numbers. Here, we respond to the 26 commentaries we received, highlighting new directions for empirical and theoretical research. We discuss two background assumptions, arguments against the number sense, whether the approximate number system (ANS) represents numbers or numerosities, and why the ANS represents rational (but not irrational) numbers.

Type
Authors’ Response
Information
Behavioral and Brain Sciences , Volume 44 , 2021 , e205
Check for updates
Copyright
Copyright © The Author(s), 2021. Published by Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Alvarez, G. A. (2011). Representing multiple objects as an ensemble enhances visual cognition. Trends in Cognitive Sciences, 15(3), 122–131. doi: 10.1016/j.tics.2011.01.003.CrossRefGoogle ScholarPubMed
Alvarez, G. A., & Cavanagh, P. (2004). The capacity of visual short-term memory is set both by visual information load and by number of objects. Psychological Science, 15(2), 106–111. doi: 10.1111/j.0963-7214.2004.01502006.x.CrossRefGoogle Scholar
Ariely, D. (2001). Seeing sets: Representation by statistical properties. Psychological Science, 12(2), 157–162. doi: 10.1111/1467-9280.00327.CrossRefGoogle ScholarPubMed
Arrighi, R., Togoli, I., & Burr, D. C. (2014). A generalized sense of number. Proceedings of the Royal Society B: Biological Sciences, 281(1797), 20141791–20141791. https://doi.org/10.1098/rspb.2014.1791.CrossRefGoogle ScholarPubMed
Ball, B. (2017). On representational content and format in core numerical cognition. Philosophical Psychology, 30(1–2), 119–139. https://doi.org/10.1080/09515089.2016.1263988.CrossRefGoogle Scholar
Barth, H., La Mont, K., Lipton, J., & Spelke, E. S. (2005). Abstract number and arithmetic in preschool children. Proceedings of the National Academy of Sciences, 102(39), 14116–14121. https://doi.org/10.1073/pnas.0505512102.CrossRefGoogle ScholarPubMed
Beck, J. (2015). Analogue magnitude representations: A philosophical introduction. The British Journal for the Philosophy of Science, 66(4), 829–855. https://doi.org/10.1093/bjps/axu014.CrossRefGoogle Scholar
Benacerraf, P. (1973). Mathematical truth. Journal of Philosophy, 70(19), 661–679. https://doi.org/10.2307/2025075CrossRefGoogle Scholar
Block, N. (2014). Seeing-as in the light of vision science. Philosophy and Phenomenological Research, 89, 560–572. https://doi.org/10.1111/phpr.12135.CrossRefGoogle Scholar
Burge, T. (2010). The origins of objectivity. Oxford University Press.CrossRefGoogle Scholar
Burr, D., & Ross, J. (2008). A visual sense of number. Current Biology, 18(6):425–428. doi: 10.1016/j.cub.2008.02.052.CrossRefGoogle ScholarPubMed
Carey, S. (2009). The origin of concepts. Oxford University Press.CrossRefGoogle Scholar
Carey, S., & Barner, D. (2019). Ontogenetic origins of human integer representations. Trends in Cognitive Sciences, 23(10), 823–835. https://doi.org/10.1016/j.tics.2019.07.004.CrossRefGoogle ScholarPubMed
Cicchini, G. M., Anobile, G., & Burr, D. C. (2016). Spontaneous perception of numerosity in humans. Nature Communications, 7, 12536. https://doi.org/10.1038/ncomms12536.CrossRefGoogle ScholarPubMed
Clarke, S. (2021). Cognitive penetration and informational encapsulation: Have we been failing the module? Philosophical Studies, 178, 2599–2620. https://doi.org/10.1007/s11098-020-01565-1.CrossRefGoogle Scholar
Clarke, S. (forthcoming). Beyond the icon: Core cognition and the bounds of perception. Mind & Language. https://doi.org/10.1111/mila.12315.Google Scholar
DeSimone, K., Kim, M., & Murray, R. F. (2020). Number adaptation can be dissociated from density adaptation. Psychological Science, 31(11), 1470–1474. doi:10.1177/0956797620956986.CrossRefGoogle ScholarPubMed
DeWind, N. K., Adams, G. K., Platt, M. L., & Brannon, E. M. (2015). Modeling the approximate number system to quantify the contribution of visual stimulus features. Cognition, 142, 247–265. https://doi.org/10.1016/j.cognition.2015.05.016.CrossRefGoogle ScholarPubMed
Feigenson, L. (2007). The equality of quantity. Trends in Cognitive Sciences, 11(5), 185–187. https://doi.org/10.1016/j.tics.2007.01.006.CrossRefGoogle Scholar
Fornaciai, M., Cicchini, G. M., & Burr, D. C. (2016). Adaptation to number operates on perceived rather than physical numerosity. Cognition, 151, 63–67. https://doi.org/10.1016/j.cognition.2016.03.006.CrossRefGoogle ScholarPubMed
Fornaciai, M., & Park, J. (2018). Early numerosity encoding in visual cortex is not sufficient for the representation of numerical magnitude. Journal of Cognitive Neuroscience, 30(12), 1788–1802. https://doi.org/10.1162/jocn_a_01320.CrossRefGoogle Scholar
Franconeri, S. L., Bemis, D. K., & Alvarez, G. A. (2009). Number estimation relies on a set of segmented objects. Cognition, 113(1), 1–13. https://doi.org/10.1016/j.cognition.2009.07.002.CrossRefGoogle ScholarPubMed
Gallistel, C. R. (1990). Representations in animal cognition: An introduction. Cognition, 37(1–2), 1–22. https://doi.org/10.1016/0010-0277(90)90016-D.CrossRefGoogle ScholarPubMed
Gebuis, T., Cohen Kadosh, R., & Gevers, W. (2016). Sensory-integration system rather than approximate number system underlies numerosity processing: A critical review. Acta Psychologica, 171, 17–35. https://doi.org/10.1016/j.actpsy.2016.09.003.CrossRefGoogle ScholarPubMed
Green, E. J. (2018). What do object files pick out? Philosophy of Science, 85(2), 177–200.CrossRefGoogle Scholar
Green, E. J. (2019). A theory of perceptual objects. Philosophy and Phenomenological Research, 99(3), 663–693. https://doi.org/10.1111/phpr.12521.CrossRefGoogle Scholar
He, L., Zhang, J., Zhou, T., & Chen, L. (2009). Connectedness affects dot numerosity judgment: Implications for configural processing. Psychonomic Bulletin & Review, 16(3), 509–517. https://doi.org/10.3758/PBR.16.3.509.CrossRefGoogle ScholarPubMed
Kirjakovski, A., & Matsumoto, E. (2016). Numerosity underestimation in sets with illusory contours. Vision Research, 122(34), 42. https://doi.org/10.1016/j.visres.2016.03.005.CrossRefGoogle ScholarPubMed
Lande, K. J. (2020). Mental structures. Noûs, 55, 649–677. https://doi.org/10.1111/nous.12324.CrossRefGoogle Scholar
Marr, D. (1982). Vision: A computational investigation into the human representation and processing of visual information. MIT Press.Google Scholar
Matthews, P. G., & Chesney, D. L. (2015). Fractions as percepts? Exploring cross-format distance effects for fractional magnitudes. Cognitive Psychology, 78, 28–56. https://doi.org/10.1016/j.cogpsych.2015.01.006.CrossRefGoogle ScholarPubMed
Nieder, A. (2016). The neuronal code for number. Nature Reviews Neuroscience, 17(6), 366–382. https://doi.org/10.1038/nrn.2016.40.CrossRefGoogle ScholarPubMed
Núñez, R. E. (2017). Is there really an evolved capacity for number? Trends in Cognitive Sciences, 21(6), 409–424. https://doi.org/10.1016/j.tics.2017.03.005.CrossRefGoogle ScholarPubMed
Odic, D. (2018). Children's intuitive sense of number develops independently of their perception of area, density, length, and time. Developmental Science, 21(2), e12533. https://doi.org/10.1111/desc.12533.CrossRefGoogle ScholarPubMed
Park, J. (In Press). Flawed stimulus design in additive-area heuristic studies. Cognition. doi: 10.1016/j.cognition.2021.104919.Google Scholar
Peacocke, C. (1986). Analogue content. Proceedings of the Aristotelian Society, Supplementary Volumes, 60, 1–17. https://www.jstor.org/stable/4106896.CrossRefGoogle Scholar
Peacocke, C. (2020). The primacy of metaphysics. Oxford: OUP.Google Scholar
Pitt, B., Ferrigno, S., Cantlon, J. F., Casasanto, D., Gibson, E., & Piantadosi, S. T. (2021). Spatial concepts of number, size, and time in an indigenous culture. Science Advances, 7(33), eabg4141. https://doi.org/10.1126/sciadv.abg4141.CrossRefGoogle Scholar
Pylyshyn, Z. W. (2007). Things and places: How the mind connects with the world. MIT Press.CrossRefGoogle Scholar
Szkudlarek, E., & Brannon, E. (2021). First and second graders successfully reason about ratios with both dot arrays and Arabic numerals. Child Development, 92(3), 1011–1027. https://doi.org/10.1111/cdev.13470CrossRefGoogle ScholarPubMed
Spelke, E. S. (1990). Principles of object perception. Cognitive Science, 14(1), 29–56. https://doi.org/10.1207/s15516709cog1401.CrossRefGoogle Scholar
Stevens, S. S. (1939/2006). On the problem of scales for the measurement of psychological magnitudes. In Proceedings of the 22nd annual meeting of the International Society for Psychophysics. St. Albans, England. Retrieved from http://proceedings.fechnerday.com/index.php/proceedings/article/view/330.Google Scholar
Vogel, E. K., Woodman, G. F., & Luck, S. (2001). Storage of features, conjunctions, and objects in visual working memory. Journal of Experimental Psychology: Human Perception and Performance, 27(1), 92–114, doi: 10.1037//0096-1523.27.1.92.Google ScholarPubMed
Walsh, V. (2003). A theory of magnitude: Common cortical metrics of time, space and quantity. Trends in Cognitive Sciences, 7(11), 483–488. doi: 10.1016/j.tics.2003.09.002.CrossRefGoogle ScholarPubMed
Weisberg, M. (2013). Simulation and similarity: Using models to understand the world. Oxford University Press.CrossRefGoogle Scholar