Explanatory Proofs In Mathematics: Noneism, Someism, And Allism

Falvio Baracco


In recent times philosophers of mathematics have generated great interest in explanations in mathematics. They have focused their attention on mathematical practice and searched for special cases that seem to own some kind of explanatory power. Two main views can be identified, namely noneism and someism: the first is the view that no proof is explanatory, whereas the second is the view that some proofs are explanatory while others are not. The present paper aims to discuss the plausibility of the latter view. I first point out the main dificulties involved in this kind of research and I focus on a recent someist account, namely Frans and Weber’s mechanistic model. Their approach seems promising, but further research is needed before accepting this someist model as a proper one. I then outline a general assessment on someism which doesn’t turn out to be so convincing. I therefore suggest another view that I call allism, i.e. the view that all proofs are explanatory, at least in some sense, and I argue for its plausibility.


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