Research in the area of human information interaction (HII) typically represents viewpoints on debated topics in a binary fashion, as either against or in favor of a given topic (e.g., the feminist movement). This simple taxonomy, however, greatly reduces the latent richness of viewpoints and thereby limits the potential of research and practical applications in this field. Work in the communication sciences has already demonstrated that viewpoints can be represented in much more comprehensive ways, which could enable a deeper understanding of users' interactions with debated topics online. For instance, a viewpoint's stance usually has a degree of strength (e.g., mild or strong), and, even if two viewpoints support or oppose something to the same degree, they may use different logics of evaluation (i.e., underlying reasons). In this paper, we draw from communication science practice to propose a novel, two-dimensional way of representing viewpoints that incorporates a viewpoint's stance degree as well as its logic of evaluation. We show in a case study of tweets on debated topics how our proposed viewpoint label can be obtained via crowdsourcing with acceptable reliability. By analyzing the resulting data set and conducting a user study, we further show that the two-dimensional viewpoint representation we propose allows for more meaningful analyses and diversification interventions compared to current approaches. Finally, we discuss what this novel viewpoint label implies for HII research and how obtaining it may be made cheaper in the future.