Teaching

MIT (2024-5)

  • The Modern History of Modal Logic (Spring 2025) This course follows the development of intensional semantics, beginning with the purely proof theoretic systems of strict implication S1 – S5 developed by C.I. Lewis and Langford as well as the debates over the quantified systems proposed by Barcan Marcus and criticized by Quine. The course will then consider the semantic theories developed by Carnap, Kripke, and Prior. After criticizing the two-dimensional semantic theories proposed by Montague and Kaplan, I will defend a novel semantics for a bimodal logic which validates the perpetuity principles. We will then consider the similarity and imposition theories of counterfactuals developed by D. Lewis and Fine in order to motivate the unified hyperintensional framework that I developed. The course will conclude by considering the structure of bilateral propositions and the logic for the constitutive explanatory operators.
  • Logic I (Fall 2024; Handouts) This course provides an advanced introduction to propositional and first-order logic, beginning with the subject-matter of logic as well as its philosophical motivations, and concluding with the soundness and completeness theorems.

MIT (2023-4)

  • Logic I (2023) This course provides an advanced introduction to propositional and first-order logic as described above.
  • Paradox and Infinity (Spring 2024; Handouts) This course presents highlights from the more technical side of philosophy, studying a cluster of puzzles, paradoxes, and intellectual wonders from the higher infinite to Godel’s Theorem, exploring their philosophical implications.

Oxford (2015-9)

  • Introduction to Logic This course introduces students to propositional and first-order logic, covering regimentation, valid arguments, proofs, and philosophical consideration of the soundness and completeness theorems.
  • Philosophical Logic This course covers non-classical logics, logics for tense and modality, two-dimensional semantics, and counterfactual logics.
  • Metaphysics This course covers a number of 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 ForAllX, 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.