How do individuals detect inconsistencies? According to the theory described in this article, they search for a possibility represented in a mental model, in which each proposition in a description is true. If they find such a possibility, the description is consistent; otherwise, it is inconsistent. Evidence corroborates the theory. The evaluation of consistency is easy when the first possibility generated from the start of a description fits later propositions in the description; it is harder when this possibility does not fit later propositions, and individuals have to look for an alternative possibility. The theory postulates that models represent what is true, not what is false. As a result, individuals succumb to systematic illusions of consistency and of inconsistency.