The large-scale aggregation and analysis of user opinions is becoming increasingly relevant to a variety of applications, from detecting social mood on some political topics to tracking their sentiment changes related to events. The analysis of diverse sentiments is another important application, which becomes possible based on the ability of modern methods to capture sentiment polarity on various topics with high precision and on the ever-growing scale. Therefore, there is a need for a scalable way of sentiment aggregation with respect to the time dimension, which stores enough information to preserve diversity, and which allows statistically accurate analysis of sentiment trends and opinion shifts. In this paper, we are focusing on the novel problem of aggregating diverse sentiments at a large scale, based on data sources that are continuously updated. First, we develop a theoretical framework that models sentiment diversity (contradiction) and defines two types of contradictions, depending on the distribution of sentiments over time. Second, we introduce novel measures that capture sentiment diversity from aggregated sentiment statistics. Third, we develop robust and scalable indexing and storage methods for diverse sentiments. Finally, we propose an adaptive approach for identifying contradictions at different time scales. The experimental evaluation demonstrates the effectiveness of the proposed method of capturing contradictions and its superiority over relational databases in real-world scenarios.