Paolo Mancosu

Researcher in residence at the Maison Suger | May–June 2026

Paolo Mancosu is Willis S. and Marion Slusser Professor of Philosophy at the University of California at Berkeley. He is the author of numerous articles and books in logic and philosophy of mathematics. He has also extensively published on the editorial history of Pasternak’s Doctor Zhivago. During his career he has taught at Stanford, Oxford, and Yale. In 2021-2022 he was a visting professor at the Université de Paris 1 Panthéon-Sorbonne as Chaire d’excellence internationale Blaise Pascal.

The project

Title: Mathematical Infinity

"The investigations to be described find their roots in my studies in mathematical logic (see my 1989 article on recent incompleteness results and rapidly growing functions, my Ph.D. dissertation, my recent book on proof theory (forthcoming book co-authored with S. Galvan and R. Zach), Mancosu-Siskind 2019 and Siskind-Mancosu-Shapiro 2023. The key theme I am after here is the surprising role that infinitary considerations play in establishing results about the finite. This is a topic that also intersects with the philosophy of mathematical practice, for the role of appealing to infinitary principles for establishing results about the finite is key in discussions of purity (why should infinity enter into the proof of statements that are apparently only about finite entities?) and explanation (does infinity play an explanatory role in proving results about the finite?). The logical issue first emerges in connection to Peano Arithmetic. In order to understand the conceptual distinctions required let us grant, an assumption granted by most logicians, that all finitistic modes of reasoning are included in first-order Peano Arithmetic (henceforth PA). The language of PA is given by {0, s, +, x} and within it one can express ordinary arithmetical claims such as the commutativity of addition and the infinitude of prime numbers. The axioms of PA tell us that s is one-one; that 0 is not the successor of any number; that+ and x satisfy the usual recursive definitions; and finally we have a schema of induction for every formula A(x) expressible in the language, i.e. if A(0) and for all x, A(x) à A(s(x)), then for all x, A(x). Gödel’s first incompleteness theorem shows that under the assumption that PA is consistent (and minimally sound) one can find a statement such that neither it nor its negation is provable in PA. While perfectly fine for the logician’s needs, the Gödel sentence, call it G, appears concocted from the point of view of the practicing mathematician."

Selected Publications

2021, with Sergio Galvan and Richard Zach, An Introduction to Proof Theory. Normalization, Cut-Elimination, and Consistency Proofs, Oxford University Press, Oxford. [432 pp.]
2022, Le voyage secret du Docteur Jivago. Le roman du roman, Éditions de la Maison des Sciences de l’Homme, Paris. [458 pp.]
2023, with Massimo Mugnai, Syllogistic Logic and Mathematical Proof, Oxford University Press, Oxford. [227 pp.]
2024, In the KGB’s Crosshairs. New Soviet documents on the Pasternak and Ivinskaya cases, WriteUp, Rome. [252 pp.]
2026, The Wilderness of the Infinite. Robert Grosseteste, William of Auvergne and mathematical infinity in the 13th century, Oxford University Press, Oxford, [360 pp.].