Mathematical Justification without Proof

In Giovanni Merlo, Giacomo Melis & Crispin Wright (eds.), Self-knowledge and Knowledge A Priori. Oxford University Press (forthcoming)
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According to a widely held view in the philosophy of mathematics, direct inferential justification for mathematical propositions (that are not axioms) requires proof. I challenge this view while accepting that mathematical justification requires arguments that are put forward as proofs. I argue that certain fallacious putative proofs considered by the relevant subjects to be correct can confer mathematical justification. But mathematical justification doesn’t come for cheap: not just any argument will do. I suggest that to successfully transmit justification an argument must satisfy specific standards, some of which are social. I contrast my view with Huemer’s inferential conservatism, which makes mathematical justification too easy to get. Although in this article I focus on mathematical inferential beliefs, the view on offer generalizes to other inferential beliefs.



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Silvia De Toffoli
University School of Advanced Studies IUSS Pavia

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