The Logic and Metaphysics Workshop will meet on May 1st from 4:15-6:15 (NY time) in-person at the Graduate Center (Room 9205) for a talk by Samara Burns (Columbia).
Title: Understanding (and) surveyability
Abstract: In this talk I will discuss the notion of surveyable proof. Discussions of surveyability emerge periodically in recent philosophical literature, but the notion of surveyable proof can be traced back to Descartes. Despite this long history, there is still disagreement about what features a proof must have in order to count as surveyable. This disagreement arises, in part, because there is still significant vagueness regarding the problem that unsurveyability poses for the epistemology of mathematics. I identify three features of justification in mathematics that could be at issue in the surveyability debate: a priority, internalism, and certainty. Each of these features is prima facie troubled by unsurveyable proof. In each case, however, I’ll argue that unsurveyable proof does not pose any real issue. I will suggest that the surveyability debate should not be framed in terms of justification at all, and that the problem is really about mathematical understanding.