According to a widely held view in the philosophy of mathematics, direct inferential justification for mathematical propositions (that are not axioms) requires proof.  De Toffoli challenges this view.  De Toffoli argues 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.  De Toffoli suggests that, in order to be successful in transmitting justification, an argument must satisfy specific standards, some of which are social in nature.  Although in this talk De Toffoli will focus on mathematical inferential beliefs, the view on offer generalizes to other inferential beliefs.