Approaches to computational argumentation tasks such as stance detection and aspect detection have largely focused on the text of claims independently, losing out on potentially valuable context from the broader collection of text. We introduce a general approach to these tasks motivated by syntopical reading, a reading process that emphasizes comparing and contrasting viewpoints in order to improve topic understanding. To capture collection-level context, we introduce the syntopical graph, a data structure for linking claims within a collection. A syntopical graph is a typed multi-graph where nodes represent claims and edges represent different possible pairwise relationships, such as entailment, paraphrase, or support. Experiments applying syntopical graphs to the tasks of stance and aspect detection demonstrate state-of-the-art performance in each domain, significantly outperforming approaches that do not utilize collection-level information.