This paper introduces rhetorical meaning to semantic theory; we use the term by analogy to tropes like metonymy in classical rhetoric, which yields ‘the American president’ from the White House—that is, it substitutes one referential meaning for another. Here we focus on two rhetorical meanings: intensification and attenuation. Intensification is expressed in English and many other languages by total reduplication (an old old man); attenuation is exemplified by Spanish ‘synthetic’ diminutive forms (hombrecito ‘little man’; cf. hombre ‘man’) and English and French ‘analytic’ formations (My Little Chickadee (film); petit caporal ‘Little Corporal’ (Napoléon Bonaparte)). Formally, a rhetorical meaning is a relation with one referential meaning as its domain and, as its codomain, a set of related referential meanings, the particular set specified by the rhetorical meaning at hand. The selection from among elements of the codomain, which can even seem contradictory out of context, is in fact highly context-dependent and indicates a critical role for pragmatics in an overall account of this meaning type.