Université Sorbonne-Nouvelle
  •  86
    Are there arguments in mathematics? Are there explanations in mathematics? Are there any connections between argument, proof and explanation? Highly controversial answers and arguments are reviewed. The main point is that in the case of a mathematical proof, the pragmatic criterion used to make a distinction between argument and explanation is likely to be insufficient for you may grant the conclusion of a proof but keep on thinking that the proof is not explanatory.
  •  49
    Argument or Explanation: Who is to Decide?
    Informal Logic 37 (1): 23-41. 2017.
    Granting that arguments and explanations that answer a why-question are the products of two species of the activity of reason-giving, do they make an exclusive and exhaustive classification? The orthodox distinction between argument and explanation already faces some tough cases, which are discussed. This paper shows that most of the criteria used to distinguish argument and explanation on the basis of the status of their conclusions cause tough cases to proliferate unless a debatable decision i…Read more
  •  12
    Old and New Fallacies in Port-Royal Logic
    Argumentation 33 (2): 241-267. 2019.
    The paper discusses the place and the status of fallacies in Arnauld and Nicole’s Port-Royal Logic, which seems to be the first book to introduce a radical change from the traditional Aristotelian account of fallacies. The most striking innovation is not in the definition of a fallacy but in the publication of a new list of fallacies, dropping some Aristotelian ones and adding more than ten new ones. The first part of the paper deals with the context of the book’s publication. We then show the i…Read more
  •  7
    The translation into French of the English word “fallacy” opens a discussion on the difference between fallacy and sophism in English. The two words are sometimes synonyms, but a difference is sometimes made on the ground that a sophism is deliberate and a fallacy is non-deliberate. In a second part of the paper this distinctive criterion is taken seriously to discuss the relative frequency of sophisms and of fallacies for a typical kind of fallacious argument. I claim that this aspect should be…Read more
  •  5
    Arguing Around Mathematical Proofs
    In Andrew Aberdein & Ian J. Dove (eds.), The Argument of Mathematics, Springer. pp. 61-76. 2013.
    More or less explicitly inspired by the Aristotelian classification of arguments, a wide tradition makes a sharp distinction between argument and proof. Ch. Perelman and R. Johnson, among others, share this view based on the principle that the conclusion of an argument is uncertain while the conclusion of a proof is certain. Producing proof is certainly a major part of mathematical activity. Yet, in practice, mathematicians, expert or beginner, argue about mathematical proofs. This happens durin…Read more
  •  5
    Inferential communities are communities using specific substantial argumentative schemes. The religious or scientific communities are examples. I discuss the status of the mathematical community as it appears through the position held by the French mathematician Henri Poincaré during his famous ar-guments with Russell, Hilbert, Peano and Cantor. The paper focuses on the status of complete induction and how logic and psychology shape the community of mathematicians and the teaching of mathematics…Read more
  •  3
    This paper is a survey of Father Mersenne’s views about the classification of sciences, its reasons and its practical consequences. Some emphasis is put on the interconnection between Mersenne’s two majors ideas about the practice of science : scientific research is an activity mostly devoted to religious apology and to the edification of the people. This religious concern allows him to resist two of the most influential philosophical streams of his time, scepticism and alchemy, which provide so…Read more
  • There is a French saying to the effect that scientific popularization is a kind of translation. This is sometimes associated with the claim that popularization downgrades science. From a literary point of view it has even been said that popularization can be characterized by the mere production of metaphors in sharp contrast to science that ought to be a literal language. ;We claim that the statements about translation and downgrading appear around the first third of the nineteenth century and a…Read more
  • L'émergence de la probabilité (edited book)
    with Ian Hacking
    Editions du Seuil. 2004.