Paula Quinon
Lund University
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, or on the ability to approximate quantities, 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.
Keywords No keywords specified (fix it)
Categories (categorize this paper)
DOI 10.1007/s13164-021-00524-x
Edit this record
Mark as duplicate
Export citation
Find it on Scholar
Request removal from index
Revision history

Download options

PhilArchive copy

Upload a copy of this paper     Check publisher's policy     Papers currently archived: 60,842
External links

Setup an account with your affiliations in order to access resources via your University's proxy server
Configure custom proxy (use this if your affiliation does not provide a proxy)
Through your library

References found in this work BETA

Logical Foundations of Probability.Rudolf Carnap - 1950 - Chicago]University of Chicago Press.
The Origin of Concepts.Susan Carey - 2009 - Oxford University Press.
Word and Object.Willard Van Orman Quine - 1960 - Les Etudes Philosophiques 17 (2):278-279.

View all 56 references / Add more references

Citations of this work BETA

Situated Counting.Peter Gärdenfors & Paula Quinon - 2020 - Review of Philosophy and Psychology:1-24.

Add more citations

Similar books and articles

From Numerical Concepts to Concepts of Number.Lance J. Rips, Amber Bloomfield & Jennifer Asmuth - 2008 - Behavioral and Brain Sciences 31 (6):623-642.
Why Cardinalities Are the “Natural” Natural Numbers.Mathieu Le Corre - 2008 - Behavioral and Brain Sciences 31 (6):659-659.
Why Numbers Are Sets.Eric Steinhart - 2002 - Synthese 133 (3):343-361.
What is a Natural Number?Noel Balzer - 1988 - Journal of Value Inquiry 22 (2):103-113.
Reference to Numbers in Natural Language.Friederike Moltmann - 2013 - Philosophical Studies 162 (3):499 - 536.


Added to PP index

Total views
6 ( #1,087,533 of 2,438,931 )

Recent downloads (6 months)
6 ( #113,059 of 2,438,931 )

How can I increase my downloads?


My notes