This chapter presents Ockham’s theory of demonstration in Summa Logicae III-2, the syllogism that produces scientific knowledge. He relies on Aristotle’s Posterior Analytics and Grosseteste’s commentary it. Grosseteste, however, founded the necessity of demonstration on necessary relations in the world. For Ockham, the main challenge is to elaborate a theory of science that addresses the singular beings in a contingent world. His theory is characterized by a conception of purely logical necessity, a semiotic conception of cause, and the requirement that subject terms must have reference in order for affirmative propositions to be true. Many propositions about the natural world are not susceptible to demonstration in the strict sense, but Ockham distinguishes different kinds of demonstration. He is not so much trying to limit the field of demonstrable natural knowledge as to relax the meaning of demonstrability so that it includes many dubitable propositions that can be made evident.