Silvia de Toffoli: Mathematical Justification without Proof

Tuesday April 14 2026 @11:30 (CET)
Sala B, Edificio de Humanidades, UNED & online

Abstract
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. I argue that certain fallacious mathematical arguments 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, in order to be successful in transmitting justification, an argument must satisfy specific standards, some of which are social.  The picture I delineate is a hybrid form of phenomenal conservatism.  Although in this talk I focus on mathematical inferential beliefs, the view on offer generalizes to other inferential beliefs.

Bio
Silvia De Toffoli is Associate Professor of Philosophy at the Department of Humanities and Life Sciences of Scuola Universitaria Superiore IUSS Pavia. Before that, she was an Assistant Professor at Linköping University and a Postdoc in the Philosophy Department at Princeton University.  She received a Ph.D. in Philosophy from Stanford in 2019 and a Ph.D. in Mathematics from the Technical University of Berlin in 2013.  Her work focuses on the philosophy of mathematics and epistemology.  She has written extensively on the epistemology of diagrams in mathematics and on issues related to mathematical fallibilism.