 The account of probability explains how one can discriminate among impressions by investigating whether an initially persuasive impression agrees with one’s other impressions or if there is something about the conditions in which it arose that undermines confidence in it. The more such checks it survives, the more confidence one will have in it. Depending on the amount of time available and the importance of the matter in question, it is possible to perform more or fewer of them. Although no amount of checking is sufficient to eliminate any chance of error, it is possible to achieve the degrees of confidence required in different circumstances to make rational action and theoretical inquiry possible (Acad. 2.32, 110). Carneades’ theory is thus an early instance of fallibilism. And he seems to have used it not only to counter the Stoics’ argument that there are no alternatives to their theory, but also to suggest that that theory’s reliance on self-evident perceptual impressions is misplaced, even when viewed as an epistemological ideal. According to Carneades’ theory, the improvement of which our faculties are capable is not a matter of approaching the condition of perfect discrimination of self-evident impressions ever more closely; it consists instead in refining one’s appreciation for the complicated relations between impressions in virtue of which they add to or detract from each other’s value as evidence, which in some cases may lead us to reject apparently self-evident, true impressions.