I am a philosopher of mathematics, mainly interested in the foundations of mathematics and philosophy of set theory.
I did my PhD at the Philosophy Department of the Cultural and Social Science at Salzburg University (with the support of a DOC-Scholarship of the Austrian Academy of Sciences). My dissertation focussed on the set theoretic multiverse: I developed a new conception of the multiverse (the V-logic Multiverse), by generalising on Friedman's Hyperuniverse. I then argued that my multiverse conception was justified from a naturalistic perspective. My advisor was Prof. Julien Murzi, and my co-advisor Prof. Charlotte Werndl. During the academic year 2018-2018 I was a visiting scholar at the Department of Logic and Philosophy of Science at University of California, Irvine, where I worked on V-logic and the naturalist justification of the multiverse under the supervision of Prof. Toby Meadows and Prof. Penelope Maddy.
After finishing High School in Rome, I studied at the Scuola Normale Superiore in Pisa. During my Bachelor I have been an Erasmus student at the Munich Center for Mathematical Philosophy, where I have worked on my Bachelor Thesis on Second-Order Logic and its application to Graph Theory. Then, during my Master, I was a Visiting Student Researcher at the University of California, Berkeley. In November 2016 I got my MA with a thesis on "The existence of alternative set theoretic universes and the Continuum Hypothesis".
When I am not thinking about the foundations of mathematics, I like to play tennis (badly) and golf (not badly! my EGA handicap is 7.2). If the weather is not the right one, then I play chess (I have an ELO of 1650 on lichess) and wargames.
Disclaimer: as you can really see, this website is still under construction! All the information is up to date, but the layout is stuck in 1989!
I am currently a Visiting Scholar at the University School of Advanced Studies IUSS Pavia, in Silvia De Toffoli's FIS Project "Humanizing Mathematics" (HUMATH).
I am mainly interested in questions regarding the philosophy of set theory (in particular the pluralism/anti-pluralism debate) and the foundations of mathematics (in particular the problem of axiom selection).
Currentyl, I am focussing my research on the problem of pluralism connected to the choice of abstraction principles in neologicism. Moreover, I am broadening my interests in the direction of set-theoretic potentialism and the modal set theories involved. From a more philosophical perspective, I am currently interested in the problem of epistemological disagreement in mathematics and its philosophy (especially in the foundations of mathematics), and the philosophy of mathematical practice more in general.
In addition to my interest in set theory and its philosophy, I have a strong interest in philosophical logic and the philosophy of mathematics more in general.
Since my interests lie in such an interdisciplanary subject, I attach great importance in collaborating with other researchers, to take advantage of their expertise and learn from more experienced philosophers. Currently, I am collaborating with Claudio Ternullo on matters regarding the set-theoretic multiverse and choiceless large cardinals, Simon Schmitt on axiom selection, Guido Tana on a epistemological problem of criterion reading of logical pluralism, and finally with Andrea Sereni on abstraction principles.
Currently, I am working on a paper on the modal logic of forcing and another one on the definition of mathematical problems in Wittgenstein and Feferman.
(Forthcoming) Beyond Naturalism: Neutrality in the foundations of mathematics, in Perez-Escobar, Kant, Sarikaya (eds.) "Mathematicians at work", Springer
(2018) "A naturalistic justification of the Generic multiverse with a core", Contributions of the Austrian Ludwig Wittgenstein Society, 26: 34 - 36.ISSN:1022-3398.
(2024) "The V -logic Multiverse and Benacerraf’s challenge", Report of the Logic Colloquium 2023, Bulletin of Symbolic Logic, 30:1.
(2022) "The V -logic Multiverse and MAXIMIZE", Report of the Logic Colloquium 2021, Bulletin of Symbolic Logic, 28:2.
(2022) "Against the countable transitive model approach to forcing", The Logica 2020 Yearbook, ISBN-13: 978-1848903760.
(2025) "10 years in the multiverse: Reflections and perspectives for the set-theoretic multiverse", Special Issue of Kriterion - Journal of Philosophy (guest editor), Volume 39, Issue 1-2.
(Forthcoming) Review of "A logical foundation for potentialist set theory", by Sharon Berry, 2022, CUP, Bulletin of Symbolic Logic
(2024) Review of "Reflections on the Foundations of Mathematics" (Centrone, S., Kant, D., Sarikaya, D. eds., Springer), Studia Logica. DOI: 10.1007/s11225-024-10097-2.
(Upcoming: February 2026), "How to evaluate good proof presentations", Workshop "Mathematical Knowledge: Philosophical and Sociological Perspectives", Vrije Universiteit Brussel.
(Invited) January 2026: "Defining mathematical open problems with Wittgenstein and Feferman", Workshop "Wittgenstein and Formal Sciences 5", World Logic Day 2026 (online).
(Invited) December 2025: "What is a good proof?", Seminar series on Epistemology and Philosophy of Mathematics, IUSS Pavia.
(Invited) November 2024: "A pluralist perspective on Gödel’s Programme", Workshop "The Limits of Incompleteness", University Babeș Bolyai Cluj.
(Invited) May 2016: "Presentation of the auto-biography 'History of a communist', with Toni Negri", Forum degli Allievi, Scuola Normale Superiore di Pisa.
September 2025 "Problems in the application of Maximize", G.A.P. 12 Conference, University of Düsseldorf.
August 2025 "Logical Pluralism as Skepticism", SIFA 2025 Conference, University of Turin.
April 2025 "The Problem of Axiom Selection via Maximize" (with Simon Schmitt), Realism and Anti-realism Workshop, University of Tübingen.
February 2025, "The Problem of Axiom Selection" (with Simon Schmitt), FilMat Workshop 2025, University of Turin.
February 2025 "Axiom disagreement and set-theoretic pluralism", Zagreb Logic Conference 2025, University of Zagreb.
October 2024, "Hierarchical pluralism is monist universism" (with Simon Schmitt), Colloquium Logicum 2024, Austrian Academy of Sciences.
September 2024, "The Good Company Problem, Pluralism, and the Foundations of Mathematics", Roots and new trends in Logicism, Universidad Lisbon.
September 2024, "The Good Company Problem, Pluralism, and the Foundations of Mathematics", British Logic Colloquium 2024, Birmingham University.
July 2024, "The Modal logic of forcing and the Free Choice Principle", FoMoLo Seminar.
June 2024: "What is a good mathematical proof", 7th APMP, IUSS Pavia.
August 2023: "The V -logic multiverse and Benacerraf’s challenge", ECAP 11, Universität Wien.
June 2023: "The set-theoretic multiverse and Benacerraf’s challenge", Logic Colloquium 2023, Università di Milano.
March 2023: "Mathematical practice and set-theoretic pluralism", Wittgenstein Meets Philosophy of Mathematical Practice, Vrije Universiteit Brussel.
October 2022: "Defining multiverses as relations on a collection of models", Midwest Philosophy of Mathematics Workshop, University of Notre Dame.
October 2022: "Set-theoretic multiverses as a paritioning of a collection of models", 14th FMPW, Nantes University.
September 2022: "What is a multiverse?", Colloquium Logicum 2022, Universität Konstanz.
September 2022: "Generalising on the notion of set-theoretic multiverse", Masterclass on Hamkins’ Multiverse, Universität Konstanz.
September 2022: "The multiverse operator and Hamkins’ multiverse", DMV Annual Meeting 2022, FU Berlin.
August 2022: "A general theory of the set-theoretic multiverse", BLAST2022 (online).
July 2022: "The V-logic multiverse maximizes over ZFC + LCs", 13th Panhellenic Logic Colloquium (video recording).
June 2022: "A universal theory for the set-theoretic multiverse", AAL 2022 (online).
September 2021: "A Tableaux System for V -logic", PhDs in Logic XII, FU Berlin.
July 2021: "The V-logic Multiverse and restrictiveness", Logic Colloquium 2021 (online).
June 2021: "The V-logic Multiverse and MAXIMIZE", BLAST2021 (online).
March 2021: "V-logic Incompleteness", 22nd Annual Graduate Conference in Mathematical Logic (online).
July 2020: "Against Categoricity", 2020 Joint Session of the Mind Association and Aristotelean Society (online).
July 2019: "The V-logic Multiverse", with Claudio Ternullo, Konstanz, 2nd Forcing Project Networking Conference.
September 2018: "A case in favour of the generic multiverse with a core", Konstanz, 1s t Forcing Project Networking Conference.
August 2018: "A naturalistic justification of the generic multiverse with a core", Kirchberg am Wechsel, 41s t International Wittgenstein Symposium.
May 2018: "A naturalistic account of the generic multiverse with a core", Prague, PhD in Logic X.99
Spring Semester 2026: "Logic, Paradoxes, and Set Theory", IUSS Pavia
MA Seminar, "Topics in the Philosophy of Logic", MA Program in Philosophy, Winter Semester 2022-2023, Department of Philosophy (Faculty of Social Sciences), Salzburg University
MA Course, "Mathematics for Philosophers", MA Program in Philosophy, Summer Semester 2022, Department of Philosophy (Faculty of Social Sciences), Salzburg University
MA Course, "Logic III: Metalogic and Modal Logic", MA Program in Philosophy, Winter Semester 2021-2022, Department of Philosophy (Faculty of Social Sciences), Salzburg University
MA Seminar, "Topics in the Philosophy of Mathematics", MA Program in Philosophy, Winter Semester 2021-2022, Department of Philosophy (Faculty of Social Sciences), Salzburg University
MA Seminar, "Assessment sensitivity: relative truth and its applications", MA Program in Philosophy, Summer Semester 2021, Department of Philosophy (Faculty of Social Sciences), Salzburg University
MA Course, "Introduction to Logic", MA Program in Philosophy, Summer Semester 2020, Department of Philosophy (Faculty of Social Sciences), Salzburg University
Guest Lecture, May 2025, "The problem of axiom selection in the foundations of mathematics", IUSS Pavia
Guest Lecture, June 2023, "The Russell-Myhill Paradox", Department of Philosophy (Faculty of Social Sciences), Salzburg University
Paride Brogiolo (Bachelor Thesis), Giacomo Giugni (Bachelor Thesis), Davide Daniele Ripari (Bachelor Thesis)
If you have any questions, an idea to share (and maybe start a collaboration!), a student to supervise (or you are a student in search of a supervisor), don't hesitate to contact me at decegliematteo[at]gmail[dot]com.