Reasoning about epistemic possibilities - those based on knowledge - is fundamental in daily life. It is formalized in modal logics, of which there are infinitely many, based on the semantics of 'possible worlds'. An alternative psychological theory postulates that possibilities (and probabilities) in daily life are based on the human ability to construct mental models of finite alternatives, which can each be realized in an indefinite number of different ways. This account leads to three main predictions that diverge from normal modal logics. First, the assertion of an epistemic possibility, A, presupposes the possibility of not-A, in default of knowledge to the contrary. Second, reasoners condense multiple possibilities into one, contravening modal logics, but reducing the load on working memory, e.g.: When knowledge shows that this condensation would be inconsistent, reasoners resist it. Epistemic possibilities are akin to non-numerical probabilities, forming a scale that runs from impossible to certain. In contrast, epistemic necessities state a necessary condition for some other proposition, e.g.: "It is necessary that it rains tomorrow for the plants to survive." The article reports five experiments corroborating these predictions. Their results challenge current conceptions of human reasoning.