According to a passage in Cicero’s Academica, some philosophers considered it legitimate to justify the evidence (or self-evidence). This paper examines the view that Epicurus and his followers were among them. They did not claim to explain evidence, which would be contradictory since evident truth does not require any proof. However, they developed complex strategies to justify the evidence of sensations: not only, as is often said, by the physical description of sensations – which attests that they are reliable perceptions of the external world – but also by indirect and negative arguments. In particular, they used arguments by consequences. Several Epicurean texts state not only that sense-perceptions are irrefutable but also that the consequences of the opposite thesis would be disastrous for knowledge and for action. Thus, avoiding the mistake of trying to explain what is obvious, the Epicureans must be given credit for adopting a consistent theory of the criterion.