  There are two traditional views concerning the epistemological status of axioms.  On the first view the axioms do not admit further justification since they are self-evident.  On the second view the axioms do not admit further justification since they are definitive of the subject matter.  Each of these views concerning our first question leads to an associated optimistic view concerning our second question—according to the first optimistic view, all mathematical truths are derivable (in first-order logic) from self-evident truths, while according to the second optimistic view, all mathematical truths are derivable (in first-order logic) from statements that are definitive of the subject matter.  Should either of these optimistic views turn out to be correct, then the question of justification in mathematics would take on a particularly simple form: Either a statement would be an axiom (in which case it would be self-evident or definitive of the subject matter (depending on the view under consideration)) or it would be derivable in first-order logic from some such statements.