 Boethius’ theory of scientific knowledge and science is fundamentally Aristotelian. Any particular science is an axiomatic system with its own primitive terms, primitive propositions (axioms, “principles” in medieval terminology), and deduced theorems (“conclusions”). All of a science’s propositions are universal and necessary, and thus can only be grasped by the intellect. Yet, the primitive terms and propositions have their origin in sense-perception, and the truth of an affirmative proposition of the form “Every S is P” depends on the instantiation in reality of the composition of subject and predicate that it signifies, and thus requires that the subject term have at least one individual referent. Several particular sciences may form a cluster subordinated to a superior science, whose primitive terms and propositions they may use, but they each add their own set of primitives.