Just like like the numerous applications of visualization, there are plenty of theoretical arguments for why visualization can aid in knowledge generation and communication. Meanwhile, to date these arguments have been presented independently, which hinders the exploitation of underlying properties of visualization in practice. We present a network of arguments that explicates not only how different arguments build on each other, but also which arguments demand for trade-offs in the design of visualizations. Furthermore, we call for the extension of our network to the application of visualization in decision-making, as well as visual analytics. We highlight the practical applicability of our theoretical approach with examples, including one from text analysis.