Embracing the Crisis in the Foundations of Mathematics
Article [Version of Record]
Is part ofLes Cahiers d'Ithaque ; 2013
Publisher(s)Société Philosophique Ithaque
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.
Friend, M. (2013). Embracing the Crisis in the Foundations of Mathematics. Dans Fradet et Lepage (dir.), "La crise des fondements : quelle crise?". Montréal, Québec : Les Cahiers d'Ithaque.