Teaching

Courses I have taught in logic, metaphysics, and the philosophy of mathematics, along with open textbook and lecture materials.

MIT (2024–5)

The Modern History of Modal Logic

Spring 2025

A graduate seminar following the origins and development of intensional semantics, from the proof-theoretic systems of strict implication S1–S5 developed by C.I. Lewis and Langford, through the debates over quantified modal logic between Barcan Marcus and Quine, to the semantic theories of Carnap, Kripke, and Prior. After criticizing the two-dimensional theories of Montague and Kaplan, the course defends a novel semantics for a bimodal logic validating the perpetuity principles, then turns to the selection, similarity, and imposition theories of counterfactuals of Stalnaker, D. Lewis, and Fine to motivate a unified hyperintensional framework.

Logic I

Fall 2024

An advanced introduction to propositional and first-order logic, beginning with the subject-matter of logic and its philosophical motivations, and concluding with the soundness and completeness theorems.

MIT (2023–4)

Paradox and Infinity

Spring 2024

Highlights from the philosophy of mathematics, metaphysics, and epistemology, studying a number of puzzles and paradoxes with a focus on the history of type theory and set theory.

Logic I

2023

An advanced introduction to propositional and first-order logic.

Oxford (2015–9)

Introduction to Logic

Propositional and first-order logic, covering regimentation, valid arguments, proofs, and the philosophical consideration of the soundness and completeness theorems.

Philosophical Logic

Non-classical logics, logics for tense and modality, two-dimensional semantics, and counterfactual logics.

Metaphysics

Classic papers on ontology, modality, essence, grounding, the philosophy of time, and the laws of nature.

An Introduction to Formal Logic

I reworked a distant descendant of the open-source logic textbook forall x, replacing the majority of the text to cover propositional and first-order logic through soundness and completeness for Logic I at MIT. This project aims to provide a philosophically and formally rigorous introduction to logic. Here is the PDF I used for the Fall 2024 semester at MIT. You can find the source files for the textbook, syllabus, and lecture notes in the GitHub repository .

Logic Notes

Here are some highly compressed Logic Notes for teaching propositional logic, first-order logic, and propositional modal logic. The aim is to provide a compressed presentation in a uniform notation, not a full exposition of the systems that I include.