Hostname: page-component-8448b6f56d-t5pn6 Total loading time: 0 Render date: 2024-04-19T02:32:02.386Z Has data issue: false hasContentIssue false

Unwarranted philosophical assumptions in research on ANS

Published online by Cambridge University Press:  15 December 2021

John Opfer
Affiliation:
Department of Psychology, The Ohio State University, Columbus, OH43210, USA; opfer.7@osu.edu samuels.58@osu.edu shapiro.4@osu.edu
Richard Samuels
Affiliation:
Department of Psychology, The Ohio State University, Columbus, OH43210, USA; opfer.7@osu.edu samuels.58@osu.edu shapiro.4@osu.edu
Stewart Shapiro
Affiliation:
Department of Psychology, The Ohio State University, Columbus, OH43210, USA; opfer.7@osu.edu samuels.58@osu.edu shapiro.4@osu.edu
Eric Snyder
Affiliation:
Department of Philosophy, Ashoka University, Sonepat, Haryana131029, India. eric.snyder@ashoka.edu.in

Abstract

Clarke and Beck import certain assumptions about the nature of numbers. Although these are widespread within research on number cognition, they are highly contentious among philosophers of mathematics. In this commentary, we isolate and critically evaluate one core assumption: the identity thesis.

Type
Open Peer Commentary
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

Butterworth, B. (2005) The development of arithmetical abilities. Journal of Child Psychology and Psychiatry, 46(1), 318.CrossRefGoogle ScholarPubMed
Chierchia, G. (1985). Formal semantics and the grammar of predication. Linguistic Inquiry, 16(3), 417443.Google Scholar
Frege, G. (1950). The foundations of arithmetic: A logico-mathematical enquiry into the concept of number. Translated by Austin, J. L.. Basil Blackwell & Mott, Ltd.Google Scholar
Hale, B., & Wright, C. (2001). The reason's proper study: Essays towards a neo-fregean philosophy of mathematics. Oxford University Press.CrossRefGoogle Scholar
Kim, J. (1981). The role of perception in a priori knowledge: Some remarks. Philosophical Studies, 40, 339354.CrossRefGoogle Scholar
Linnebo, Ø. (2018). Thin objects. Oxford University Press.CrossRefGoogle Scholar
Maddy, P. (1990). Physicalistic platonism. In A. D. Irvine (Ed.) Physicalism in mathematics (pp. 259289). Springer.CrossRefGoogle Scholar
Moltmann, F. (2013). Reference to numbers in natural language. Philosophical Studies, 162, 499536.CrossRefGoogle Scholar
Russell, B. (1903). The principles of mathematics, Cambridge University Press.Google Scholar
Scontras, G. (2014). The semantics of measurement. Doctoral dissertation, Harvard University.Google Scholar
Shapiro, S. (1997). Philosophy of mathematics: Structure and ontology. Oxford University Press.Google Scholar
Snyder, E. (2017). Numbers and cardinalities: What's really wrong with the easy argument?. Linguistics and Philosophy, 40, 373400.CrossRefGoogle Scholar
Tennant, N. (2009). “Natural logicism.” 10th Midwest PhilMath Workshop, Department of Philosophy, Notre Dame University, USA October. 2009.Google Scholar