An Empirically feasible approach to the epistemology of arithmetic

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Recent years have seen an explosion of empirical data concerning arithmetical cognition. In this paper that data is taken to be philosophically important and an outline for an empirically feasible epistemological theory of arithmetic is presented. The epistemological theory is based on the empirically well-supported hypothesis that our arithmetical ability is built on a protoarithmetical ability to categorize observations in terms of quantities that we have already as infants and share with many nonhuman animals. It is argued here that arithmetical knowledge developed in such a way cannot be totally conceptual in the sense relevant to the philosophy of arithmetic, but neither can arithmetic understood to be empirical. Rather, we need to develop a contextual a priori notion of arithmetical knowledge that preserves the special mathematical characteristics without ignoring the roots of arithmetical cognition. Such a contextual a priori theory is shown not to require any ontologically problematic assumptions, in addition to fitting well within a standard framework of general epistemology.
Originalspråkengelska
TidskriftSynthese
Volym191
Utgåva17
Sidor (från-till)4201-4229
Antal sidor29
ISSN0039-7857
DOI
StatusPublicerad - 2014
MoE-publikationstypA1 Tidskriftsartikel-refererad

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  • 611 Filosofi

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An Empirically feasible approach to the epistemology of arithmetic. / Pantsar, Markus.

I: Synthese, Vol. 191, Nr. 17, 2014, s. 4201-4229.

Forskningsoutput: TidskriftsbidragArtikelVetenskapligPeer review

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AB - Recent years have seen an explosion of empirical data concerning arithmetical cognition. In this paper that data is taken to be philosophically important and an outline for an empirically feasible epistemological theory of arithmetic is presented. The epistemological theory is based on the empirically well-supported hypothesis that our arithmetical ability is built on a protoarithmetical ability to categorize observations in terms of quantities that we have already as infants and share with many nonhuman animals. It is argued here that arithmetical knowledge developed in such a way cannot be totally conceptual in the sense relevant to the philosophy of arithmetic, but neither can arithmetic understood to be empirical. Rather, we need to develop a contextual a priori notion of arithmetical knowledge that preserves the special mathematical characteristics without ignoring the roots of arithmetical cognition. Such a contextual a priori theory is shown not to require any ontologically problematic assumptions, in addition to fitting well within a standard framework of general epistemology.

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