Abstract. There is a driving need computationally to interrogate large bodies of text for a range of non-denotative meaning (e.g., to plot chains of reasoning, detect sentiment, diagnose genre, and so forth). But such meaning has always proven computationally allusive. It is often implicit, 'hidden' meaning, evoked by linguistic cues, stylistic arrangement, or conceptual structurefeatures that have hitherto been difficult for Natural Language Processing systems to recognize and use. Non-denotative textual effects are the historical concern of rhetorical studies, and we have turned to rhetoric in order to find new ways to advance NLP, especially for sophisticated tasks like Argument Mining. This paper highlights certain rhetorical devices that encode levels of meaning that have been overlooked in Computational Linguistics generally and Argument Mining particularly, and yet lend themselves to automated detection. These devices are the linguistic configurations known as Rhetorical Figures. We argue for the importance of these devices for Argument Mining, especially in collocations, and we present an XML annotation scheme for Rhetorical Figures to make figuration more tractable for computational approaches, particularly with an eye on the improvements they offer Argument Mining. We also discuss the intellectual and technical challenges involved in figure annotation and the implications for Machine Learning.