Cognitive Structuralism: Explaining the Regularity of the Natural Numbers Progression

Review of Philosophy and Psychology 13 (1):127-149 (2022)
  Copy   BIBTEX


According to one of the most powerful paradigms explaining the meaning of the concept of natural number, natural numbers get a large part of their conceptual content from core cognitive abilities. Carey’s bootstrapping provides a model of the role of core cognition in the creation of mature mathematical concepts. In this paper, I conduct conceptual analyses of various theories within this paradigm, concluding that the theories based on the ability to subitize (i.e., to assess anexactquantity of the elements in a collection without counting them), or on the ability to approximate quantities (i.e., to assess anapproximatequantity of the elements in a collection without counting them), or both, fail to provide a conceptual basis for bootstrapping the concept of an exact natural number. In particular, I argue that none of the existing theories explains one of the key characteristics of the natural number structure: the equidistances between successive elements of the natural numbers progression. I suggest that this regularity could be based on another innate cognitive ability, namely sensitivity to the regularity of rhythm. In the final section, I propose a new position within the core cognition paradigm, inspired by structuralist positions in philosophy of mathematics.



    Upload a copy of this work     Papers currently archived: 93,642

External links

Setup an account with your affiliations in order to access resources via your University's proxy server

Through your library

Similar books and articles

Cognitive Linguistics and the Concept of Number.Rafael Núñez & Tyler Marghetis - 2015 - In Roi Cohen Kadosh & Ann Dowker (eds.), The Oxford Handbook of Numerical Cognition. Oxford University Press UK.
Why cardinalities are the “natural” natural numbers.Mathieu Le Corre - 2008 - Behavioral and Brain Sciences 31 (6):659-659.
Number and natural language.Stephen Laurence & Eric Margolis - 2005 - In Peter Carruthers, Stephen Laurence & Stephen P. Stich (eds.), The Innate Mind: Structure and Contents. New York, US: Oxford University Press USA. pp. 1--216.
Towards a Darwinian approach to mathematics.Helen De Cruz - 2006 - Foundations of Science 11 (1-2):157-196.
An extended mind perspective on natural number representation.Helen De Cruz - 2008 - Philosophical Psychology 21 (4):475 – 490.


Added to PP

21 (#173,985)

6 months
58 (#268,157)

Historical graph of downloads
How can I increase my downloads?

Author's Profile

Paula Quinon
Lund University

Citations of this work

Situated Counting.Peter Gärdenfors & Paula Quinon - 2020 - Review of Philosophy and Psychology 12 (4):1-24.
Situated Counting.Peter Gärdenfors & Paula Quinon - 2020 - Review of Philosophy and Psychology 12 (4):721-744.

Add more citations

References found in this work

Word and Object.Willard Van Orman Quine - 1960 - Cambridge, MA, USA: MIT Press.
Logical foundations of probability.Rudolf Carnap - 1950 - Chicago]: Chicago University of Chicago Press.
The origin of concepts.Susan Carey - 2009 - New York: Oxford University Press.

View all 60 references / Add more references