Bruno Jacinto (Universidade de Lisboa, Portugal)

Higher-order modal logic and the philosophy of mathematics

Abstract: Modality has been influential in addressing a number of perennial philosophical questions, and there has recently been a resurgence of philosophical interest in higher-order logic, especially in so-called higher-order metaphysics. In this tutorial we present and address important technical-cum-philosophical questions concerning the interaction of modality with higher-order quantification. Moreover, we show how the appeal to higher-order modal resources paves the way to Upper Logicism, a novel form of logicism based on the Russellian view that mathematical entities are logically definable entities at higher-orders.