 For Aristotle, an enthymeme is what has the function of a proof or demonstration in the domain of public speech. Since a demonstration is a kind of sullogismos, the enthymeme is said to be a sullogismos too (on the enthymeme and its relation to syllogistic theory see also Raphael 1974). The word ‘enthymeme’ (from ‘enthumeisthai—to consider’) had already been coined by Aristotle’s predecessors and originally designated clever sayings, bon mots, and short arguments involving a paradox or contradiction. The concepts ‘proof’ (apodeixis) and ‘sullogismos’ play a crucial role in Aristotle’s logical-dialectical theory. In applying them to a term of conventional rhetoric, Aristotle appeals to a well-known rhetorical technique, but, at the same time, codifies and redefines the original meaning of ‘enthymeme’: properly understood, what people call ‘enthymeme’ should have the form of a sullogismos, i.e., a deductive argument.