No CrossRef data available.
Article contents
Representation of pure magnitudes in ANS
Published online by Cambridge University Press: 15 December 2021
Abstract
According to Clarke and Beck (C&B), the approximate number system (ANS) represents numbers. We argue that the ANS represents pure magnitudes. Considerations of explanatory economy favor the pure magnitudes hypothesis. The considerations C&B direct against the pure magnitudes hypothesis do not have force.
- Type
- Open Peer Commentary
- Information
- Copyright
- Copyright © The Author(s), 2021. Published by Cambridge University Press
References
Burge, T. (1982). Other bodies. In: Thought and object (pp. 97–120), ed. Woodfield, A.. Oxford University Press.Google Scholar
Burge, T. (2005). Truth, thought, reason: Essays on Frege. Oxford University Press.CrossRefGoogle Scholar
Frege, G. (1884). Die Grundlagen der Arithmetik: eine logisch mathematische Untersuchung über den Begriff der Zahl. W. Koebner.Google Scholar
Peacocke, C. (1986). Analogue content. Proceedings of the Aristotelian Society 60:1–17.CrossRefGoogle Scholar
Stein, H. (1990). Eudoxos and Dedekind: On the ancient Greek theory of ratios and its relation to modern mathematics. Synthese 84:163–211.Google Scholar
Sutherland, D. (2006). Kant on arithmetic, algebra, and the theory of proportions. Journal of the History of Philosophy 44:533–558.CrossRefGoogle Scholar
Target article
The number sense represents (rational) numbers
Related commentaries (26)
A rational explanation for links between the ANS and math
Constructing rationals through conjoint measurement of numerator and denominator as approximate integer magnitudes in tradeoff relations
Contents of the approximate number system
Distinguishing the specific from the recognitional and the canonical, and the nature of ratios
Non-symbolic and symbolic number and the approximate number system
Not so rational: A more natural way to understand the ANS
Numbers in action
Numerical cognition needs more and better distinctions, not fewer
Numerical cognition: Unitary or diversified system(s)?
Numerosities are not ersatz numbers
Numerosity, area-osity, object-osity? Oh my
Perceived number is not abstract
Positing numerosities may be metaphysically extravagant; positing representation of numerosities is not
Ratio-based perceptual foundations for rational numbers, and perhaps whole numbers, too?
Real models: The limits of behavioural evidence for understanding the ANS
Representation of pure magnitudes in ANS
Second-order characteristics don't favor a number-representing ANS
Sizes, ratios, approximations: On what and how the ANS represents
The approximate number system represents magnitude and precision
The approximate number system represents rational numbers: The special case of an empty set
The number sense does not represent numbers, but cardinality comparisons
The number sense represents multitudes and magnitudes
The perception of quantity ain't number: Missing the primacy of symbolic reference
Unwarranted philosophical assumptions in research on ANS
Weighted numbers
What are we doing when we perceive numbers?
Author response
Numbers, numerosities, and new directions