We shall best understand Galen’s notion of demonstration in relation to scientific knowledge by considering some examples of what he presents as demonstrative in actual argumentative contexts; but first let us consider the key theoretical features. (See Barnes 1991; Hankinson 1991 and 2008a; Havrda 2015; Morison 2008; Tieleman 1996, Ch. 1; Havrda 2021.) Galen believes that the highest-level, most reliable kind of knowledge (epistēmē) is arrived at through “scientific demonstration” (epistēmonikē apodeixis). A crucial criterion for Galen is that the premisses employed for a demonstration in relation to a subject, X, must be “taken from the essence itself” of X (e.g., PHP II.2, 108; Temp. II.2, 53). Here, the Aristotelian term “essence” (ousia) is closely related to the notion of definition: the requirement is that when attempting a demonstration, any premiss one puts forward which purports to have general validity in relation to Xs must be a proposition which relates to what Xs in their fundamental nature or definition are, not one about Xs’ incidental features (let alone—a recurrent concern—one based on some misunderstanding due to a homonymous usage of the term “X”). Further, the premisses for an epistēmonikē apodeixis must be propositions the truth of which is evident, either to reason or to sense-perception.