Review of Philosophy and Psychology 13 (1):127-149 (2021)
AbstractAccording 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.
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References found in this work
Fixing Language: An Essay on Conceptual Engineering.Herman Cappelen - 2018 - Oxford: Oxford University Press.
Logical Foundations of Probability.Rudolf Carnap - 1950 - Chicago, IL, USA: Chicago University of Chicago Press.
Citations of this work
Situated Counting.Peter Gärdenfors & Paula Quinon - 2020 - Review of Philosophy and Psychology 12 (4):1-24.
Bootstrapping of Integer Concepts: The Stronger Deviant-Interpretation Challenge.Markus Pantsar - 2021 - Synthese 199 (3-4):5791-5814.
Situated Counting.Peter Gärdenfors & Paula Quinon - 2021 - Review of Philosophy and Psychology 12 (4):721-744.
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