David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Ezio Di Nucci
Jack Alan Reynolds
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Synthese 92 (3):349 - 370 (1992)
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.
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References found in this work BETA
W. V. Quine (1960). Word and Object. The MIT Press.
W. V. Quine (1986). Philosophy of Logic. Harvard University Press.
Immanuel Kant (2007). Prolegomena to Any Future Metaphysics. In Elizabeth Schmidt Radcliffe, Richard McCarty, Fritz Allhoff & Anand Vaidya (eds.), Journal of Philosophy. Blackwell Pub. Ltd. 507-508.
I. Kant (1787/1998). Critique of Pure Reason. Philosophy 59 (230):555-557.
David Malament (1982). Science Without Numbers by Hartry H. Field. Journal of Philosophy 79 (9):523-534.
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