Mathematics and Philosophy Degree:
Upcoming and recent talks:
- "On the methodology of informal rigour: Set theory, semantics, and intuitionism" (with Hidenori Kurokawa), forthcoming in Intuitionism, Computation, and Proof: Selected themes from the research of G. Kreisel, M. Anonutti-Marfori and M. Petrolo (editors), Springer. (Comments welcome, please do not cite without permission.)
- "On consistency and existence in mathematics", Proceedings of the Aristotelian Society, 120 (3), pp. 349–393.
- "Recursive functions" in the Stanford Encyclopedia of Philosophy
- Bernays, Paul Isaak (1888-1977). In The Bloomsbury Encyclopedia of Philosophers
- "Incompleteness via paradox and completeness", Review of Symbolic Logic, 2019, pp. 1-50.
- "Computational complexity theory and the philosophy of mathematics", Philosophia Mathematica, 27(3), pp. 381-439.
- "Strict finitism, feasibility and the sorites", Review of Symbolic Logic, 2018, 11(2), pp.295-346.
- "The Prehistory of the Subsystems of Second-Order Arithmetic" (with Sean Walsh), Review of Symbolic Logic, 10(2), pp. 357-396.
- "Bernays and the completeness theorem", Annals of the Japan Association for Philosophy of Science, 2017, 25, pp. 45-55.
- "Algorithms and the mathematical foundations of computer science", in The Limits of Mathematical Knowledge, L. Horsten and P. Welch (eds.). Oxford University Press, 2016.
- "Squeezing feasibility", in Pursuit of the Universal: 12th Conference on Computability in Europe, CiE 2016, Lecture Notes in Computer Science, pp 78-88.
- "Computational Complexity Theory", Stanford Encyclopedia of Philosophy.
- "Kreisel’s Theory of Constructions, the Kreisel-Goodman paradox, and the second clause" (with Hidenori Kurokawa), Advances in proof theoretic semantics, T. Piecha and P. Schroeder-Heister (eds.), Springer Trends in Logic.
- "Arithmetical reflection and the provability of soundness", Philosophia Mathematica.
- "Explicit modal logic, informal provability and Montague's Paradox", Notre Dame Journal of Formal Logic, 55 (2), 2014.
- "Models and computability", Philosophia Mathematica.
- "The paradox of the Knower revisited" (with Hidenori Kurokawa), Annals of Pure and Applied Logic.
- "From the Knowability Paradox to the existence of proofs" (with Hidenori Kurokawa), Synthese, 176:177–225.
- "Knowledge, proof and the Knower" (with Hidenori Kurokawa), Proceedings of the 12th Conference on Theoretical Aspects of Rationality and Knowledge (Stanford), p. 81-90.
- “Algorithms and Ontology” Proceedings of the Austrian Ludwig Wittgenstein Society, Kirchberg am Wechsel, Austria.
- “The Knower Paradox and the Quantified Logic of Proofs” (with Hidenori Kurokawa), Proceedings of the Austrian Ludwig Wittgenstein Society, Kirchberg am Wechsel, Austria.
- “On Moschovakis’s theory of algorithmic identity”, Proceedings of the 7th Panhellenic Logic Symposium, Volos, Greece.