Abstract

This article aims to evaluate the purported empirical character of computer-assisted proof, as suggested by Thomas Tymoczko and others. Tymoczko famously argued that the proof of the Four-Color Theorem introduced a new, empirical method of proof, forcing us to modify the traditional conception of mathematical argument as a priori reasoning. Detlefsen and Luker contended that Tymoczko’s suggestion entailed that typically mathematical proofs were empirical. My chief interest is to raise some objections to a line of thought common to both of these arguments, with a view to outlining an account of the a priori which allows thepossibility of a priori knowledge obtained by appeal to computers or through testimony. Drawing on some recent discussions by Tyler Burge, this account gives a broad construal of the non-justificatory, ‘enabling’ role that experience is held to play in knowledge and cognition, allowing us to argue that the purported empirical character of the appeal to computers pertains only to the role experience plays in enabling our access to the a priori warrant provided by computer proof.