Central and East European
Society for Phenomenology

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Apriority and applied mathematics

Robert A. Holland

pp. 349-370

Abstract

I argue that we need not accept Quine's holistic conception of mathematics and empirical science. Specifically, I argue that we should reject Quine's holism for two reasons. One, his argument for this position fails to appreciate that the revision of the mathematics employed in scientific theories is often related to an ‘expansion’ of the possibilities of describing the empirical world, and that this reveals that mathematics serves as a kind of rational framework for empirical theorizing. Two, this holistic conception does not clearly demarcate pure mathematics from applied mathematics. In arguing against Quine, I present a formal account of applied mathematics in which the mathematics employed in an empirical theory plays a role that is analogous to the epistemological role Kant assigned synthetic a priori propositions. According to this account, it is possible to insulate pure mathematics from empirical falsification, and there is a sense in which applied mathematics can also be labeled as ‘a priori’.

Publication details

Published in:

(1992) Synthese 92 (3).

Pages: 349-370

DOI: 10.1007/BF00414287

Full citation:

Holland Robert A. (1992) „Apriority and applied mathematics“. Synthese 92 (3), 349–370.