Introduced by Aristotle in his Rhetoric an enthymeme is a kind of inference. Characteristically an enthymeme involves the fact that something has been left unsaid. The essay is intended to elucidate this and to uncover some similarities and differences existing between the two most prominent 20th century accounts of explaining the unsaid of what is said: the one presented by Grice, the other presented by Brandom. Though being conceptualized to characterize those aspects of our verbal behavior that are closely akin to the phenomenon Aristotle has introduced, both accounts do not take any notice of this relationship. Brandom is concerned with the phenomenon of making explicit what has not been said explicitly; regarding it as a kind of implicature, Grice is concerned with the phenomenon of letting been unsaid what is intended to be communicated. Taking it as a point of departure, Grice and Brandom differ in their attitudes with regard to formal logic: Grice’s attitude is a positive one, Brandom’s is negative in its spirit. Grice and Brandom both are primarily interested in inferentialism, but they locate it within different realms: Brandom is interested in inferential semantics, Grice pleads for something that could be called inferential pragmatics.