Synthese 192 (8):2489-2511 (2015)

Authors
Markus Pantsar
University of Helsinki
Abstract
In this paper I develop a philosophical account of actual mathematical infinity that does not demand ontologically or epistemologically problematic assumptions. The account is based on a simple metaphor in which we think of indefinitely continuing processes as defining objects. It is shown that such a metaphor is valid in terms of mathematical practice, as well as in line with empirical data on arithmetical cognition
Keywords Infinity  Aleph-null  Arithmetical cognition  Metaphor  Process  Object
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DOI 10.1007/s11229-015-0775-4
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References found in this work BETA

The Foundations of Arithmetic.Gottlob Frege - 1953 - Evanston: Ill., Northwestern University Press.
The Nature of Mathematical Knowledge.Philip Kitcher - 1983 - Oxford University Press.
Genetic Epistemology.Jean Piaget - 1970 - New York: Columbia University Press.

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Citations of this work BETA

Early Numerical Cognition and Mathematical Processes.Markus Pantsar - 2018 - Theoria : An International Journal for Theory, History and Fundations of Science 33 (2):285-304.

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