Related papers: Ren{\'e} Thom: From mathematics to philosophy
In this paper, I present a critical discussion of mathematical arguments employed in the philosophy of event of Alain Badiou. On the basis of "Being and Event" as well as his other writings, I analyze the main notions of his philosophy such…
The mathematical analysis was conceived in XVII century in Newton and Leibniz works. The problem of logical rigor in definitions was considered by Arnauld and Nicole in "Logique ou l'art de penser". They were the first, who distinguished…
The science of complexity is based on a new way of thinking that stands in sharp contrast to the philosophy underlying Newtonian science, which is based on reductionism, determinism, and objective knowledge. This paper reviews the…
This article reviews and develops an epistemological tradition in the philosophy of science, known as convergentism, which holds that inference methods should be assessed based on their ability to converge to the truth across a range of…
Isaac Newton, in popular imagination the Ur-scientist, was an outstanding humanist scholar. His researches on, among others, ancient philosophy, are thorough and appear to be connected to and fit within his larger philosophical and…
This paper explores the ethical implications of integrating Artificial Intelligence (AI) in educational settings, from primary schools to universities, while drawing insights from ancient Greek philosophy to address emerging concerns. As AI…
Mathematics and its relation to the physical universe have been the topic of speculation since the days of Pythagoras. Several different views of the nature of mathematics have been considered: Realism - mathematics exists and is…
Aristotle is generally accepted as the father of logic. The ideas that he raised in his study of logical reasoning carried the development of science over the centuries. Today, in the era of AI, this title of the fatherhood of logic has a…
Stephen Toulmin once observed that `it has never been customary for philosophers to pay much attention to the rhetoric of mathematical debate'. Might the application of Toulmin's layout of arguments to mathematics remedy this oversight?…
This paper has been withdrawn by the author. In this article I review W\"ust's recent handbook on mathematical physics from a philosophical standpoint. It emerges a structural approach to mathematics which evidences the utility of logic in…
Mathematics has become inescapable in modern, digitized societies: there is hardly any area of life left that isn't affected by it, and we as mathematicians play a central role in this. Our actions affect what others, in particular our…
This article offers a critical engagement with J\"urgen Renn's historiographical approach, with particular focus on "The Evolution of Knowledge" and "The Einsteinian Revolution" (co-authored with Hanoch Gutfreund). It explores how Renn…
This is an exposition of facts about Arithmetic with an approach via mathematical logic. In Section 1 we present Peano Arithmetic, PA, and the complete theory of $\mathbb{N}$, and we show that $\mathbb{N}$ is a prime model of the theory of…
Mathematical Theory of Evidence (MTE) is known as a foundation for reasoning when knowledge is expressed at various levels of detail. Though much research effort has been committed to this theory since its foundation, many questions remain…
This article proposes a fresh and direct reading of foundational texts of philosophy and aims at bringing back the inflamed debates that are contemporaneous with the birth of Greek axiomatics, and indeed at understanding what is timeless in…
We state the defining characteristic of mathematics as a type of symmetry where one can change the connotation of a mathematical statement in a certain way when the statement's truth value remains the same. This view of mathematics as…
This text is based on an invited talk at the Dedekind Symposium at Braunschweig in October 2016. It summarizes views from my recent commented edition of Dedekinds two books on the foundations of mathematics.
The learning of mathematics starts early but remains far from any theoretical considerations: pupils' mathematical knowledge is first rooted in pragmatic evidence or conforms to procedures taught. However, learners develop a knowledge which…
This text summarizes and expands the content of a general audience talk given in 2018 at the University of Mainz. Motivated by recent developments in dependent type theory and infinity category theory, it presents a history of ideas around…
We give a general overview of the influence of William Thurston on the French mathematical school and we show how some of the major problems he solved are rooted in the French mathematical tradition. At the same time, we survey some of…