Embracing the Crisis in the Foundations of Mathematics



March 11, 2016


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Math mathématiques

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Michèle Friend, « Embracing the Crisis in the Foundations of Mathematics », Papyrus : le dépôt institutionnel de l'Université de Montréal, ID : 10670/1.ogtz9a


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Abstract 0

The crisis in the foundations of mathematics is a conceptual crisis. I suggest that we embrace the crisis and adopt a pluralist position towards foundations. There are many foundations in mathematics. However, ‘many foundations’ (for one building) is an oxymoron. Therefore, we shift vocabulary to say that mathematics, as one discipline, is composed of many different theories. This entails that there are no absolute mathematical truths, only truths within a theory. There is no unified, consistent ontology, only ontology within a theory.

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