Mathematics is either inconsistent or incomplete.
What is your philosophical interpretation of Gödel’s incompleteness theorems?
#math #mathematics #maths #logic #MathematicalLogic #gödel #kurtgödel #godel #KurtGodel #Philosophy #PhilosophyOfMathematics #PhilosophicalLogic #philosophyoflogic #logic
The conference “Mathematics as an artistic experience”, organized by the Grothendieck Institute in collaboration with the Henri Poincaré Institute in Paris and the MICS Laboratory of Centrale Supélec (Paris-Saclay University), will be held on Friday 11 July 2025, at the Hermite Amphitheater of the Henri Poincaré Institute, 11 Rue Pierre et Marie Curie, 75005 Paris, from 2:00 p.m. to 8:00 p.m.
The conference will feature talks by Charles Alunni, Coordinator of the Centre for Grothendieckian Studies (CSG), Olivia Caramello, President of the Institute, Mateo Carmona, Archivist of the CSG, and Francesco La Mantia, language philosopher at the University of Palermo.
On the occasion of the conference, an exhibition of mathematically inspired works by Dominique Lepetz, a former student of Alexander Grothendieck, will be inaugurated in the presence of the artist.
#Grothendieck #PhilosophyOfMathematics #ToposTheory #Mathematics #PhilosophyOfScience #IHP #artnet
On June 20th, José Ferreirós (University of Seville) will give a talk at the Centre Gilles-Gaston Granger (Aix-en-Provence), titled:
“Dedekind and the Axiomatic Method”
https://www.cggg.fr/agenda/seminaire-avec-jose-ferreiros
🕤 9:30–11:30 (CEST)
📍 Maison de la Recherche, Room 2.44
This session will include a discussion on Dedekind’s role in the emergence of the axiomatic approach, with further reflections on mathematical practice.
(Feel free to contact [email protected] to confirm attendance.)
#philosophy #mathematics #philosophyOfMathematics #seminar #Dedekind #cggg
What does it mean (to you) to understand a piece of mathematics?
📍 Paris, October 15–17, 2025
FPMW–ESPM 2025
The 17th French Philosophy of Mathematics Workshop (FPMW 17) and the 2nd conference of the European Society for the Philosophy of Mathematics (ESPM) will be held jointly in Paris, at Université Paris Cité and Université Paris 1 Panthéon-Sorbonne.
Five invited speakers:
• Timothy Gowers (Collège de France)
• Elaine Landry (UC Davis)
• Georg Schiemer (University of Vienna)
• David Rabouin (CNRS, SPHERE, Paris)
• Andrea Sereni (IUSS Pavia)
Five additional talks will be selected through open submission.
Proposals in philosophy of mathematics are welcome, including philosophical work on mathematics beyond the field’s traditional scope.
Submission period: April 15 – May 15, 2025
Notification: July 1, 2025
Talks: 1h presentation + 30 min discussion
Languages: French and English (French talks must include English slides)
Proposals (10k–15k characters, anonymized) in PDF:
📧 [email protected]
cc: [email protected]
Subject: “FPMW-ESPM2025”
This Topos Institute seminar (Kevin Carlson presenting) is an interesting topic -- do we actually need infinite sets to do mathematics? But, I think he takes a long and questionable route to the meat of the topic.
The fallacy here is that the answer to "why is there so much consensus in modern mathematics" cannot be a mathematical answer! It has to be grounded in something else: sociology, history, or psychology. It's all very well to point at the structural approach as a unifying point of agreement, but that by itself does not answer "why"?
It could be: humans have some set-sense like they have a language-sense, and so building things on sense connects to a lot of people. That might be JP Mayberry's point, in his appeal to "Euclidean set theory." But that's not a mathematical claim!
It could be: people who do not get on board with the structuralist approach don't succeed at being modern mathematicians.
It could be: we are living in an era that encourages that consensus instead of discouraging it, for reasons that will be evident only in retrospect.
I think part of the answer is that modern mathematics has achieved consensus by successfully eliminating "truth" as a topic of debate and instead making it a topic of study, in a very postmodernist way. You can insist to your dying day that you're a intuitionist or an ultrafinitist or whatever, and the only response you can get is mathematicians studying what is or isn't provable in your version of logic! It is no longer possible to disagree what mathematics is, because the modern conception swallows any such disagreement into a mathematical object.
Philosophy of maths questions:
Say I want to ask for an explanation of some mathematical phenomenon (that is, to ask "Why is it true that <X>?"). You might offer a formal proof of <X>, but that doesn't feel like an explanation to me because a proof is essentially a statement that <X> is logically implied by the assumptions. So the proof, as an explanation, is equivalent to "because I chose these assumptions".
Are proofs the only explanations that pure maths has to offer?
Are there other forms of mathematical explanation (e.g. involving reference to assumptions outside the minimal axioms required for a formal proof)?
Is it even sensible to ask these questions in the context of pure maths?
Is it different when we shift to applied maths and have to recognise that the maths is a model of the system of interest (so there's a possibly fallible mapping between the maths and the system of interest and the mathematical axioms presumably correspond to assumed truths in the system of interest)?
#math #maths #mathematics #philosophy #explanation #PhilosophyOfMathematics
Next week, I’m heading off to North America for a few talks. (I’d committed to these talks before last year’s election and I have mixed feelings about the trip, but I’m going, nonetheless.)
If you're in the LA area, in or around Calgary, or New York, and you’re into philosophical logic, why not drop by? Details of the talks are here https://consequently.org/presentation/
J Lou
David Grayless
Frédéric Jaëck
Petra Schwer
Mark Gritter
Ross Gayler
Greg Restall