Related papers: Constructive mathematics
In contrast to other constructivist schools, for Brouwer, the notion of "constructive object" is not restricted to be presented as `words' in some finite alphabet of symbols, and choice sequences which are non-predetermined and unfinished…
The ability to read, write, and speak mathematics is critical to students becoming comfortable with statistical models and skills. Faster development of those skills may act as encouragement to further engage with the discipline. Vocabulary…
Nous rappelons des versions constructives de la th\'eorie de la dimension de Krull dans les anneaux commutatifs et dans les treillis distributifs, dont les bases ont \'et\'e pos\'ees par Joyal, Espan\~ol et les deux auteurs. Nous montrons…
Pure type systems arise as a generalisation of simply typed lambda calculus. The contemporary development of mathematics has renewed the interest in type theories, as they are not just the object of mere historical research, but have an…
This text is my thesis, defended in June 2007, in the status it was at this time. The most important results are contained in the article "Foncteur de Picard d'un champ alg\'ebrique" to appear in "Mathematische Annalen" (see the preprint…
This article gives an account of a teaching experience carried out from 2008 to 2021 at the university of Franche-Comt{\'e} as an answer to the ministerial command of proposing cross-disciplinary courses in the curricula. The goal of the…
In this paper, I argue, contrary to the prevailing opinion in the linguistics and philosophy literature, that a sortal approach to aspectual composition can indeed be explanatory. In support of this view, I develop a synthesis of competing…
In this paper we use theoretical frameworks from mathematics education and cognitive psychology to analyse Cauchy's ideas of function, continuity, limit and infinitesimal expressed in his Cours D'Analyse. Our analysis focuses on the…
Discussion of the necessity to use the constructive mathematics as the formalism of quantum theory for systems with many particles.
I have merged the lecture notes (in french) of two 24 hour courses I taught at the university Pierre-et-Marie Curie (Paris 6) during the first semester of the academic year 2013-2014. The first one was devoted to the general material that…
There are several classical characterisations of the valuative dimension of a commutative ring. Constructive versions of this dimension have been given and proven to be equivalent to the classical notion within classical mathematics, and…
This is a draft of my textbook on mathematical analysis and the areas of mathematics on which it is based. The idea is to fill the gaps in the existing textbooks. Any remarks from readers are welcome.
This essay contains three parts. The first part of essay focuses on the hypothesis of the functional semantic constructions (FSC-Hypothesis). This hypothesis explains that a language, a number, a money are the functional semantic…
This a free translation with additional explanations of {\em Processus \`a Accroissement Independants Chapitre I: La D\'ecomposition de Paul L\'evy}, by J.L. Bretagnolle, in {\em Ecole d'Et\'e de Probabilit\'es}, Lecture Notes in…
We propose a constructive interpretation of truth which resolves the standard semantic paradoxes.
We offer a view of mathematics as an experimental science where axioms play the role of foundational theories like general relativity and quantum mechanics in physics. Under this view, axioms are provisional and inferred from experience…
In this essay, I argue that mathematics is a natural science---just like physics, chemistry, or biology---and that this can explain the alleged "unreasonable" effectiveness of mathematics in the physical sciences. The main challenge for…
We introduce seven foundational principles for creating a culture of constructive criticism in computational legal studies. Beginning by challenging the current perception of papers as the primary scholarly output, we call for a more…
Cantor's ordinal numbers, a powerful extension of the natural numbers, are a cornerstone of set theory. They can be used to reason about the termination of processes, prove the consistency of logical systems, and justify some of the core…
Linear logic was conceived in 1987 by Girard and, in contrast to classical logic, restricts the usage of the structural inference rules of weakening and contraction. With this, atoms of the logic are no longer interpreted as truth, but as…