, Volume 191, Issue 17, pp 4201–4229 | Cite as

An empirically feasible approach to the epistemology of arithmetic

  • Markus PantsarEmail author


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.


Arithmetical cognition Philosophy of mathematics Epistemology Empirical study Contextual a priori 1 



This work has been made possible by the generous support of the Academy of Finland and the University of Bucharest. I am in great gratitude to the many colleagues who have provided valuable comments on the manuscript at some point, especially Daniel Cohnitz and Dirk Schlimm.


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© Springer Science+Business Media Dordrecht 2014

Authors and Affiliations

  1. 1.Department of Philosophy, History, Culture and Art StudiesUniversity of HelsinkiHelsinkiFinland

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