Recent years have seen an explosion of empirical data concerning arithmetical cognition.
In this talk 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 proto-arithmetical 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 philosophy of arithmetic. 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.
Markus Pantsar. An empirically feasible approach to the epistemology of arithmetic.
Synthese, forthcoming. DOI 10.1007/s11229-014-0526-y
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