Rationality Without Reasons

Abstract This article is concerned with the question: What makes it rational to believe a mathematical statement? It focuses in particular on philosophical questions concerning rationally believing set theoretic axioms. A distinction is drawn between having mathematical warrant and having philosophical warrant for believing mathematical axioms. I argue that mathematical warrant for believing set theoretic axioms does not consist in having a complex of reasons that constitutes a justification for believing these axioms. “Die Religion befiehlt, Annahmen zu machen (Du sollst glauben), die natürliche Vernunft ebenfalls $$\ldots $$ … ” [10, p. 69]