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Séminaire
Séminaire Philmath
Nos aurons le plaisir de recevoir : Caroline Antos (Univ. of Konstanz) « The explanatoriness of foundational theories »
Abstract :
This talk aims to answer two main questions: Can foundational theories be explanatory? If yes, can explanatoriness be used as a criterion for the preference of specific foundational theories? This is investigated by bringing together two debates, the one about explanations in mathematics and the other about criteria for preference of foundational theories. To answer the first question, an account of explanatoriness of foundational theories is developed. Two criteria are discussed, namely Explanatory Systematization or Explanatory Reduction, and different accounts of explanation are developed that express these criteria. Finally, we test if set theory is explanatory according to the developed account.