Philosophy Colloquium: Jeremy Heis’s “Kant on Parallel Lines”

By the turn of the twentieth century, many philosophers claimed that Kant’s philosophy of mathematics (and, indeed, his entire philosophy) was undermined by the real possibility of geometries in which Euclid’s axiom of parallels is false. It is surprisingly not well known that Kant – though never discussing parallel lines in his published work – did write a series of unpublished notes on the philosophical problems posed by parallel lines. This paper presents the argument and chief issues of these notes. Kant’s main point in these notes is that neither Euclid’s definition of parallel lines, nor the alternative definition proposed by Leibniz and Christian Wolff, fulfills the requirements on mathematical definitions that Kant explicates in the Critique of Pure Reason. Thus, these notes show that Kant did reflect on the problems posed by the theory of parallel lines and recognized that it was uniquely problematic. Moreover, these reflections, Heis argues, connect in interesting ways with Kant’s wider philosophy of mathematics and (especially) with the new critical theory of concepts laid out in the first Critique.

All are welcome to attend! The Department of Philosophy at California State University, Long Beach, hopes to establish a forum where southern California philosophers can gather to discuss new work by young scholars.