Philosophy of Mathematics Seminar (Tuesday - Week 8, MT25)

Abstract: Shapiro (1997) proposes that we take mathematics at face-value and uses this to partially motivate his version of mathematical structuralism. That is, our philosophy of mathematics should not contradict mathematical practice. We will call this the faithfulness constraint. Stebbing (1932) proposes a system of analysis that takes common-sense truths and reasoning at face value. On the face of it, these systems have a lot in common, in particular in how they consider the data which motivates their theories. But at their cores they are very different. In this paper, using a modern version of directional analysis, I will show that if we take mathematics at face value in the way directional analysis requires, we wind up with a very different type of philosophy of mathematics from the articulated by Shapiro.

Please note: A notice will be sent out by the convenors for each talk with the Zoom link.