The series of three lectures will introduce higher-order logics, and will illustrate their importance to philosophical theorising by way of a range of applications and examples.

Lecture 1: Introduction to Higher-Order Logic for Philosophers This lecture will introduce higher-order logic as a framework for logical theorising in general. We will construct the simply typed lambda calculus, the language of higher-order logic, and formulate various higher-order logics of interest. We will then turn to some applications in philosophy, specifically in the metaphysics of properties, modal metaphysics, the foundations of mathematics, and the philosophy of language.

Lecture 2: Modality in Higher-Order Logic Building on Lecture 1, this lecture will explore how notions of possibility and necessity can be analysed in higher-order logic. We’ll derive the modal logic S4 for a logically defined notion of metaphysical necessity within the intensionalist framework of Bacon and Dorr’s 2022 paper “Classicism”, and prove equivalences between principles of modal metaphysics and principles of higher-order logic.

Lecture 3: Mathematics in Higher-Order Logic Next, we will turn to applications of higher-order logic in the foundations of mathematics. We will formulate mathematical theories in higher-order logic, making sure that these theories explain the applicability of mathematics to other domains. Then, we will illustrate how these theories can be reduced to pure logic, thereby vindicating a form of mathematical logicism.

(b) Modelling Awareness

Lecturer Snow Zhang

Time 14:00 to 16:00 from July 4th to 6th

Place Room 109, Lee Shau Kee Humanities Buildings No.3

Description

We are unaware of many things, and unaware that we are unaware of them. But what is (un)awareness, and how does it relate to other epistemic notions such as belief, knowledge and uncertainty? In this lecture series, we will introduce models of awareness that have been developed in philosophy, computer science and economics. The topics that we will discuss include: the problem of logical omniscience, the Dekel-Lipman-Rustichini impossibility result, syntactic vs. semantic models of awareness and their respective sound and complete axiomatizations. If time permits, we will also discuss awareness dynamics, (un)awareness and decision theory and reverse Bayesianism.

https://voidprove.github.io/BISFORM2025/