Reasoners succumb to predictable illusions in evaluating whether sets of assertions are consistent. We report two studies of this computationally intractable task of ``satisfiability.'' The results show that as the number of possibilities compatible with the assertions increases, the difficulty of the task increases, and that reasoners represent what is true according to assertions, not what is false. This procedure avoids overloading memory, but it yields illusions of consistency and of inconsistency. These illusions modify our picture of human rationality.