 Is there a middle ground, then, between the high standard of self-evidence on the one hand and the ‘anything goes’ attitude on the other? One idea, a version of which can be traced back to Bertrand Russell, is to invoke a version of inference to the best explanation. Russell’s view, plausibly enough, is that the propositions of elementary arithmetic—“2 + 2 = 4”, “7 is prime”, etc.—are much more self-evident than the axioms of whatever logical or set-theoretic system one might come up with to ground them. So rather than viewing axioms as maximally self-evident we ought instead to think of them as being chosen on the basis of their (collective) capacity to systematize, derive, and explain the basic arithmetical facts. In other words, the direction of logical implication remains from axioms to arithmetical facts, but the direction of justification may go the other way, at least in the case of very simple, obvious arithmetical facts. Deriving “2 + 2 = 4” from our set-theoretic axioms does not increase our confidence in the truth of “2 + 2 = 4”, but the fact that we can derive this antecedently known fact (and not derive other propositions which we know to be false) does increase our confidence in the truth of the axioms.