Munich Center for Mathematical Philosophy

@lmu-mcmp.bsky.social

News and updates from the Munich Center for Mathematical Philosophy at LMU Munich. Disclaimer: reposts and likes are not endorsements.

I had a good time speaking as an MCMP fellow on metabolism, cognition, and computation. The Summer School Students have things to say about cognition, computation, and computationalism. #philsci, #cogsci, #philsky

Munich Center for Mathematical Philosophy@lmu-mcmp.bsky.social · 2w ago

We had a wonderful 2026 Summer School for Widening Participation in Mathematical Philosophy at @lmu.de! Many thanks to the terrific participants from all over the world and to the fantastic lecturers Dunja Šešelja [Bochum], Xueyin (Snow) Zhang [Berkeley], and @sabinaleonelli.bsky.social [@tum.de]!

Proud to have co-organized our summer school with a dream team again 😊 A big thank you to the lecturers and the participants for making this such a nice event! 🥳

Munich Center for Mathematical Philosophy@lmu-mcmp.bsky.social · 2w ago

We had a wonderful 2026 Summer School for Widening Participation in Mathematical Philosophy at @lmu.de! Many thanks to the terrific participants from all over the world and to the fantastic lecturers Dunja Šešelja [Bochum], Xueyin (Snow) Zhang [Berkeley], and @sabinaleonelli.bsky.social [@tum.de]!

Newly published: "Maximality Axioms and the Principle of Plenitude", by Nicola Bonatti, Erkenntnis, 2026, doi.org/10.1007/s106...

Maximality Axioms and the Principle of Plenitude - Erkenntnis

Hilbert’s (arithmetical) Axiom of Completeness asserts that the structure of the real numbers $$\mathbb {R}$$ R is maximal in the sense of not having a proper extension to an Archimedean ordered field. The more recent works of Ehrlich (2001), McGee (1997) and Aczel (1988) show that certain maximality conditions modeled upon Hilbert’s axiom provide unique characterizations of, respectively, the s-hierarchical ordered field of surreal numbers No, the well-founded hierarchy of pure sets $$\mathbb {V}_{\!k}$$ V k , and the non-well-founded hierarchy of Finsler-extensional sets $$\mathbb {V}_{\scriptscriptstyle \!F\!A\!F\!A}$$ V F A F A . The paper provides a comprehensive historical and theoretical reconstruction of this often overlooked chapter in the history of the axiomatic method. The historical reconstruction suggests that the maximality condition of non-extensibility arises as a natural axiom in the unique characterization of mathematical structures, as illustrated by the theories of (s-hierarchical non-)Archimedean continua and (non-)well-founded sets. The theoretical reconstruction argues that the maximality condition of non-extensibility is the formal explication of the heuristic principle of Plenitude, as usually adopted to describe the intuitive ‘‘fullness” of punctiform continua and the cumulative hierarchy of sets.

doi.org

Newly published: "Maximality Axioms and the Principle of Plenitude", by Nicola Bonatti, Erkenntnis, 2026, doi.org/10.1007/s106...

Maximality Axioms and the Principle of Plenitude - Erkenntnis

Hilbert’s (arithmetical) Axiom of Completeness asserts that the structure of the real numbers $$\mathbb {R}$$ R is maximal in the sense of not having a proper extension to an Archimedean ordered field. The more recent works of Ehrlich (2001), McGee (1997) and Aczel (1988) show that certain maximality conditions modeled upon Hilbert’s axiom provide unique characterizations of, respectively, the s-hierarchical ordered field of surreal numbers No, the well-founded hierarchy of pure sets $$\mathbb {V}_{\!k}$$ V k , and the non-well-founded hierarchy of Finsler-extensional sets $$\mathbb {V}_{\scriptscriptstyle \!F\!A\!F\!A}$$ V F A F A . The paper provides a comprehensive historical and theoretical reconstruction of this often overlooked chapter in the history of the axiomatic method. The historical reconstruction suggests that the maximality condition of non-extensibility arises as a natural axiom in the unique characterization of mathematical structures, as illustrated by the theories of (s-hierarchical non-)Archimedean continua and (non-)well-founded sets. The theoretical reconstruction argues that the maximality condition of non-extensibility is the formal explication of the heuristic principle of Plenitude, as usually adopted to describe the intuitive ‘‘fullness” of punctiform continua and the cumulative hierarchy of sets.

doi.org

Our new DFG-funded project “Procedural Anchors: How Communication Order Shapes Disinformation” is part of the Priority Programme Re:DIS. Prof. Stephan Hartmann and Lilian von Bressensdorf will study how communication order shapes beliefs—and how better deliberation can counter disinformation.

Many thanks to Stephan Hartmann for the invitation to visit LMU Munich. I had a wonderful time meeting colleagues across the university and was honored to give a Philosophy & Physics Colloquium talk, “AI Meets Philosophy of Science: Towards a Foundation of AI.” Link: www.youtube.com/watch?v=aMyk...

Philosophy and Physics Colloquium: Eddy Chen - AI meets Philosophy of Science

YouTube video by Munich Center for Mathematical Philosophy

youtube.com