Kant and Finitism

Journal of Philosophy 113 (5/6):261-273 (2016)
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Abstract

An observation and a thesis: The observation is that, whatever the connection between Kant’s philosophy and Hilbert’s conception of finitism, Kant’s account of geometric reasoning shares an essential idea with the account of finitist number theory in “Finitism”, namely the idea of constructions f from ‘arbitrary’ or ‘generic’ objects of various types. The thesis is that, contrary to a substantial part of contemporary literature on the subject, when Kant referred to number and arithmetic, he was not referring to the natural or whole numbers and their arithmetic, but rather to the real numbers and their arithmetic.

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William W. Tait
University of Chicago

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