Invariances and the Number Concept
(2026) In Journal of Cognitive Science 27(1). p.1-23- Abstract
Cognitive scientists Spelke and Kintzler (2007) and Carey (2009) identify objects, actions, space and numbers as “core domains of knowledge” that are essential for conceptualizing the world. Gärdenfors (2019, 2020) argues that objects, actions and space are characterized by invariances in sensory signals. In this paper, we extend the analysis of invariances to the domain of numbers (understood as positive integers). As a theoretical background, we assume that numbers, as studied in cognitive science, are properties of collections. We claim that the domain of numbers is determined by two types of invariances: (i) the invariance under the location of its objects; (ii) the unconstrained fungibility of objects, which is the determinant... (More)
Cognitive scientists Spelke and Kintzler (2007) and Carey (2009) identify objects, actions, space and numbers as “core domains of knowledge” that are essential for conceptualizing the world. Gärdenfors (2019, 2020) argues that objects, actions and space are characterized by invariances in sensory signals. In this paper, we extend the analysis of invariances to the domain of numbers (understood as positive integers). As a theoretical background, we assume that numbers, as studied in cognitive science, are properties of collections. We claim that the domain of numbers is determined by two types of invariances: (i) the invariance under the location of its objects; (ii) the unconstrained fungibility of objects, which is the determinant invariance of the number concept: If an object in a collection is exchanged for another object, the collection will still contain the same number of objects. We show that invariance under fungibility closely maps onto one-to-one correspondences between collections. Our theoretical analysis is supported by empirical material.
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- author
- Quinon, Paula and Gärdenfors, Peter LU
- organization
- publishing date
- 2026-03
- type
- Contribution to journal
- publication status
- published
- subject
- keywords
- fungibility, invariance, number properties, numerical cognition, one-to-one mapping
- in
- Journal of Cognitive Science
- volume
- 27
- issue
- 1
- pages
- 23 pages
- publisher
- Seoul National University, Institute for Cognitive Science
- external identifiers
-
- scopus:105037326017
- ISSN
- 1598-2327
- project
- Cognitive modeling
- language
- English
- LU publication?
- yes
- id
- 86278c47-f720-4130-864d-ecd6489aadd7
- date added to LUP
- 2026-05-19 15:27:00
- date last changed
- 2026-05-26 06:44:04
@article{86278c47-f720-4130-864d-ecd6489aadd7,
abstract = {{<p>Cognitive scientists Spelke and Kintzler (2007) and Carey (2009) identify objects, actions, space and numbers as “core domains of knowledge” that are essential for conceptualizing the world. Gärdenfors (2019, 2020) argues that objects, actions and space are characterized by invariances in sensory signals. In this paper, we extend the analysis of invariances to the domain of numbers (understood as positive integers). As a theoretical background, we assume that numbers, as studied in cognitive science, are properties of collections. We claim that the domain of numbers is determined by two types of invariances: (i) the invariance under the location of its objects; (ii) the unconstrained fungibility of objects, which is the determinant invariance of the number concept: If an object in a collection is exchanged for another object, the collection will still contain the same number of objects. We show that invariance under fungibility closely maps onto one-to-one correspondences between collections. Our theoretical analysis is supported by empirical material.</p>}},
author = {{Quinon, Paula and Gärdenfors, Peter}},
issn = {{1598-2327}},
keywords = {{fungibility; invariance; number properties; numerical cognition; one-to-one mapping}},
language = {{eng}},
number = {{1}},
pages = {{1--23}},
publisher = {{Seoul National University, Institute for Cognitive Science}},
series = {{Journal of Cognitive Science}},
title = {{Invariances and the Number Concept}},
volume = {{27}},
year = {{2026}},
}