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A l’occasion de réflexions sur l’axiome du choix, Zermelo et Poincaré sont amenés à préciser ce qui doit être au fondement des mathématiques et peut servir à justifier un axiome. Défendant l’autonomie des mathématiques, chacun d’eux invoque une intuition mathématique spécifique visible dans la pratique du mathématicien. D’abord, nous explicitons ce qui distingue l’attitude du mathématicien de celle logicien, en prenant l’exemple de Zermelo. Puis, pour déterminer la nature réelle de l’intuition invoquée...
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