Logique, langage, philosophie des mathématiques

HYPOTHESES Le raisonnement hypothétique dans la théorie de la démonstration - HYPO 2

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Ce programme est consacré à différentes formes et modélisations du raisonnement par hypothèse. Le thème général du projet précédent est conservé. Nous nous proposons de préciser de qu'est le raisonnement hypothétique, comment le représenter de façon spécifique et de déterminer ses lois primitives. Cependant il y a un changement d'orientation dans la mesure où le nouveau projet se place uniquement dans la perspective de la théorie de la démonstration. La structure choisie pour organiser le projet précédent ayant été profitable, le projet actuel est aussi divisé entre un projet Maître et plusieurs projets individuels. 

Mathematics : Objectivity by reprensentation - MathObRe

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As far as the physical world is concerned, the standard realist attitude which conceives of objects as existing independently of our representations of them might be (prima facie) plausible: if things go well, we represent physical objects in the way we do because they are so-and-so.In contrast, as we want to argue, in the mathematical world the situation is reversed: if things go well, mathematical objects are so-and-so because we represent them as we do. This does not mean that mathematics could not be objective: mathematical representations might be subject to constraints that impose objectivity on what they constitute. If this is right, in order to understand the nature of mathematical objects we should first understand how mathematical representations work. In the words of Kreisel’s famous dictum: “the problem is not the existence of mathematical objects but the objectivity of mathematical statements” (Dummett 1978, p. xxxviii).

The problem we tackle concerns the philosophical question of clarifying the role of representations in mathematical reasoning and proofs and the way they contribute to mathematical ontology and understanding. This is a fresh inquiry concerning a classical problem in philosophy of mathematics connecting understanding to proofs and to the way the ontology of mathematic is conceived. But our starting point is neither classical proof theory nor classical metaphysics. We are rather looking at the problem by opening the door to the practical turn in science.

athematical objects. We rather wonder how appropriate domains of mathematical (abstract) objects are constituted, by appealing to different sorts of representations, and how appropriate reasoning on them are licensed.

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