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Constructing rationals through conjoint measurement of numerator and denominator as approximate integer magnitudes in tradeoff relations

Published online by Cambridge University Press:  15 December 2021

Jun Zhang Open the ORCID record for Jun Zhang [Opens in a new window]
Jun Zhang*
Affiliation:
Department of Psychology, The University of Michigan, Ann Arbor, MI 48109, USA. junz@umich.edu www.lsa.umich.edu/psych/junz
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Abstract

To investigate mechanisms of rational representation, I consider (1) construction of an ordered continuum of psychophysical scale of magnitude of sensation; (2) counting mechanism leading to an approximate numerosity scale for integers; and (3) conjoint measurement structure pitting the denominator against the numerator in tradeoff positions. Number sense of resulting rationals is neither intuitive nor expedient in their manipulation.

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Type
Open Peer Commentary
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Behavioral and Brain Sciences , Volume 44 , 2021 , e204
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Copyright © The Author(s), 2021. Published by Cambridge University Press

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References

Carey, S. (2001). Cognitive foundations of arithmetic: Evolution and ontogenisis. Mind & Language 16(1): 37–55.CrossRefGoogle Scholar
Carey, S. (2009). Where our number concepts come from. The Journal of Philosophy 106(4): 220.CrossRefGoogle Scholar
Carey, S., & Barner, D. (2019). Ontogenetic origins of human integer representations. Trends in Cognitive Sciences 23(10): 823–835.CrossRefGoogle ScholarPubMed
Cohen, M., & Narens, L. (1979). Fundamental unit structures: A theory of ratio scalability. Journal of Mathematical Psychology 20(3): 193–232.CrossRefGoogle Scholar
Dehaene, S., Izard, V., Spelke, E., & Pica, P. (2008). Log or linear? Distinct intuitions of the number scale in Western and Amazonian indigene cultures. Science (New York, N.Y.) 320(5880): 1217–1220.CrossRefGoogle ScholarPubMed
Feigenson, L., Carey, S., & Spelke, E. (2002). Infants’ discrimination of number vs. continuous extent. Cognitive Psychology 44(1): 33–66.CrossRefGoogle ScholarPubMed
Feigenson, L., Dehaene, S., & Spelke, E. (2004). Core systems of number. Trends in Cognitive Sciences 8(7): 307–314.CrossRefGoogle ScholarPubMed
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.CrossRefGoogle ScholarPubMed
Krantz, D., Luce, D., Suppes, P., & Tversky, A. (1971). Foundations of measurement, Vol. I: Additive and polynomial representations.Google Scholar
Le Corre, M., & Carey, S. (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
Lemer, C., Dehaene, S., Spelke, E., & Cohen, L. (2003). Approximate quantities and exact number words: Dissociable systems. Neuropsychologia 41(14): 1942–1958.CrossRefGoogle ScholarPubMed
Luce, R. D., & Narens, L. (1987). Measurement scales on the continuum. Science (New York, N.Y.) 236(4808): 1527–1532.CrossRefGoogle ScholarPubMed
Narens, L. (1981). A general theory of ratio scalability with remarks about the measurement-theoretic concept of meaningfulness. Theory and Decision 13(1): 1–70.CrossRefGoogle Scholar
Narens, L., & Luce, R. D. (1986). Measurement: The theory of numerical assignments. Psychological Bulletin 99(2): 166.CrossRefGoogle Scholar
Núñez, R., Cooperrider, K., & Wassmann, J. (2012). Number concepts without number lines in an indigenous group of Papua New Guinea. PLoS One 7(4): e35662.CrossRefGoogle Scholar
Sarnecka, B. W., & Carey, S. (2008). How counting represents number: What children must learn and when they learn it. Cognition 108(3): 662–674.CrossRefGoogle Scholar
Stevens, S. S. (1936). A scale for the measurement of a psychological magnitude: Loudness. Psychological Review 43(5): 405.CrossRefGoogle Scholar
Stevens, S. S. (1956). The direct estimation of sensory magnitudes: Loudness. The American journal of Psychology 69(1): 1–25.CrossRefGoogle ScholarPubMed
Stevens, S. S. (1957). On the psychophysical law. Psychological Review 64(3): 153.CrossRefGoogle ScholarPubMed
Stevens, S. S., & Galanter, E. H. (1957). Ratio scales and category scales for a dozen perceptual continua. Journal of Experimental Psychology 54(6): 377.CrossRefGoogle ScholarPubMed
Xu, F., Spelke, E. S., & Goddard, S. (2005). Number sense in human infants. Developmental Science 8(1): 88–101.CrossRefGoogle ScholarPubMed