Here you can find some teaching materials for my courses.

General resources

A short guide and tips for writing philosophy papers for my courses: How to write a good philosophy paper.

Oslo Vaerens 2021/2022: Filosofisk logikk og matematikkens filosofi (Philosophical Logic and Mathematical Philosophy)

This course (attended by both advanced undergraduates and masters students) concentrates on the problems posed by mathematics as abstract discipline from both an epistemological and ontological standpoint.


Week 1. Introduction: Mathematics as a philosophical problem. Notes.
Week 2. Frege’s logicism. Notes.
Week 3. Formalism and deductivism. Notes.
Week 4. Hilbert’s formalism. Notes.
Week 5. Intuitionism. Notes.
Week 6. Quine’s empiricist platonism. Notes.
Week 7. Nominalism. Notes.
Week 8. Mathematical intuition. Notes.
Week 9. Abstraction reconsidered. Notes.
Week 10. The iterative conception of sets. Notes.
Week 11. Structuralism. Notes.
Week 12. The quest for new mathematical axioms. Notes.

Konstanz Wintersemester 2020/2021: Computers and Computations

This masters-level course looked at different models of computation, with a focus on the implications of computational difficulty.


Week 1. Outline of the course. Notes. YouTube.
Week 2. The historical role of computation. Notes. YouTube.
Week 3. Turing computability. Notes. YouTube.
Week 4. The Halting Problem. Notes. YouTube.
Week 5. Other Models of Computation. Notes. YouTube.
Week 6. The Church-Turing Thesis (and relatives). Notes. YouTube.
Week 7. The Lucas-Penrose Argument. Notes. YouTube.
Week 8. Computational Functionalism. Notes. YouTube.
Week 9. Computational Complexity. Notes. YouTube.
Week 10. Quantum Computation. Notes. YouTube.
Week 11. Ethics and Computations. Notes. YouTube.
Week 12. Computing and the Standard Model of Arithmetic. Notes. YouTube.
Week 13. Digital and Analog Computation. Notes. YouTube.

Wintersemester 2019/2020: Introduction to the Philosophy of Mathematics

This course for advanced undergraduates and masters students provided an introduction to some of the main views in the philosophy of mathematics, concentrating on the notion of infinity and how different philosophers have understood talk of the (mathematical) infinite.

Week 1. Introduction and outline of the course. Notes.
Week 2. Plato and the Pre-Socratics. Notes.
Week 3. Potential Infinity: Aristotle. Notes.
Week 4. The Calculus: Ghosts of Departed Quantities? Notes.
Week 5. Logicism: Frege. Notes.
Week 6. Logicism: Russell and Whitehead. Notes.
Week 7. Neo-Logicism. Notes.
Week 8. Entfällt.
Week 9. The Cantorian Infinite. Notes.
Week 10. Intuitionism: Brouwer. Notes.
Week 11. Intuitionism and Meaning: Dummett. Notes.
Week 12. Formalism and Hilbert’s Programme. Notes.
Week 13. The Limitative Results I: Gödel and Tarski. Notes.
Week 14. The Limitative Results II: The Halting Problem. Notes.
Week 15. Where Forward? The Continuum Hypothesis and our choice of axioms. Notes.

Research Tutorials: Here are a couple of tutorials I have given at conferences.

The Hyperuniverse. A series of two tutorials (given in June 2017 at the Second  Set Theoretic Pluralism Symposium in Bristol) introducing the Hyperuniverse Programme, some of the mathematical ideas (including Inner Model Hypotheses, V-logic, and #-generation).

Tutorial 1. Maximality Through Absoluteness. Slides.
Tutorial 2. Philosophical Issues Surrounding the Hyperuniverse. Slides.

Maximality and Reflection. A series of three tutorials (given in September 2016 at Entia et Nomina in Warsaw) covering independence and maximality in set theory.

Tutorial 1. Independence and Large Cardinals. Slides.
Tutorial 2. Reflecting Down. Slides.
Tutorial 3. Inner Model Reflection. Slides.