Philosophy of Mathematics Seminar (Monday - Week 4, TT26)

Abstract: While paradoxes play a prominent role within philosophical logic, epistemologies of logic have so far paid insufficient attention to how and why they inform our logics. This talk begins the project of attempting to provide such an explanation of why paradoxes inform logics. By drawing on an analogy with the role of paradoxes in the sciences, I propose that logico-semantic, deontic, and epistemic paradoxes serve to highlight putative incompatibilities between our established logics and other well-evidenced commitments; a hypothesis I call Paradoxes as Incompatibility Recognition Mechanisms (or PIRM, for short). If correct, PIRM would have quite significant consequences for how we think about logic’s methodology. To assess the proposal, we consider a range of case studies, including the liar, sorites and knowability paradox.

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