Guillaume Massas

Welcome to my personal website! I am an Assistant Professor of Philosophy at Chapman University. Before, I was a postdoctoral research fellow at the Scuola Normale Superiore in Pisa, working under the supervision of Mario Piazza on the PRIN Project Proof and understanding in mathematics (PUMa). Purity of methods, simplicity, and explanation in mathematical reasoning.

I did my PhD in the Group in Logic and the Methodology of Science at UC Berkeley, working under the supervision of Wes Holliday and Paolo Mancosu. I defended my dissertation Duality and Infinity in October 2023. You can find a recording of the defense and a copy of the slides here. In June 2025, I received the Beth Dissertation Prize, which is awarded every year to "outstanding dissertations in Logic, Language and Information".

My main research interests are in the application of categorical methods broadly construed to problems in logic, and in the history and philosophy of mathematics. I am particularly interested in possibility semantics, an approach to semantics that takes partiality to be a fundamental feature of semantic structures, and in its applications to the philosophy of the infinite and to a foundational framework called semiconstructive mathematics. Recently, I have been working on the following topics:

• Dualities in lattice theory: Dualities use the language of category theory to bring together algebraic and geometric structures, and often provide the robust mathematical machinery behind soundness and completeness proofs for many logics. I am particularly interested in dualities for non-distributive logics and dualities that can be established without the Axiom of Choice. I have developed such results in my papers Choice-free de Vries Duality and Priestley Duality and Bounded Lattices (under review).

• Possibility semantics for non-classical logics: Possibility semantics is an alternative semantic framework in which the fundamental objects are partial possibilities rather than completely determined objects such as possible worlds. My paper B-frame Duality explores the potential of this approach for the semantics of intuitionistic logic, while my paper Orthologic and the Open Future (under review) discusses an application of possibility semantics to an old problem of Aristotle.

• Fundamental logic: Fundamental logic is a non-classical logic that generalizes both constructive and quantum reasoning. As such, its study requires a combination of techniques from intuitionistic logic and from non-distributive logics. Recently, I have been interested in some structural properties of possibility semantics for fundamental logic (Goldblatt-Thomason Theorems for Fundamental (Modal) Logic ), in an extension of fundamental logic that captures exactly the intersection of intuitionistic logic and orthologic (Constructive Quantum Logics, joint work with Juan P. Aguilera, under review), and in translations between fundamental logic and non-classical modal logics (Fundamental Logic through the Lens of Modality, joint work with Wes Holliday, in preparation).

• Infinitesimals: Quantities that are infinitely small yet non-zero have a long and troubled history. Although the modern foundations of analysis avoid any mention of them, infinitesimals were given a rigorous treatment in Robinson's nonstandard analysis, and have played a role in recent debates in the philosophy of probability theory. I have argued for a semiconstructive treatment of infinitesimals in my paper A Semiconstructive Approach to the Hyperreal Line, and my papers Totality, Regularity and Cardinality in Probability Theory  (with Paolo Mancosu) and Infinitesimal Credences without the Axiom of Choice (in preparation) discuss the use of infinitesimals in probability theory.

• Part-whole alternatives to the Cantorian transfinite: The modern notion of cardinality offers a rigorous extension of the concept of size from the finite to the infinite that is based on the intuition that two sets have the same size if and only if there is a one-to-one correspondence between them. Historically, there is however an alternative approach, based on the intuition that a whole is always strictly greater in size than any of its proper parts. My paper Bolzano's Mathematical Infinite (with Anna Bellomo) offers a rigorous formalization of such a view presented by 19th century mathematician Bernard Bolzano, while my paper A New Way out of Galileo's Paradox (under review) offers a new alternative to the Cantorian notion of size that refines a recent proposal called numerosity theory. Together with Mario Piazza and Matteo Tesi, we have also used similar techniques to measure the "quantity of validity" of an infinitary proof, yielding a proof-theoretic semantics for arithmetic (Infinite Proofs and Arithmetical Truth, under review).