International climate negotiations seek to limit warming to an average of two degrees Celsius (2°C). This objective is justified by the claim that scientists have identified two degrees of warming as the point at which climate change becomes dangerous. Climate scientists themselves maintain that while science can provide projections of possible impacts at different levels of warming, determining what constitutes an acceptable level of risk is not a matter to be decided by science alone, but is a value choice to be deliberated upon by societies as a whole. Hence, while climate science can inform debates about how much warming is too much, it cannot provide a definitive answer to that question. In order to fully understand how climate change came to be defined as a phenomenon with a single global dangerous limit of 2°C, it is necessary to incorporate insights from the social sciences. Political economy, culture, economics, sociology, geography, and social psychology have all played a role in defining what constitutes an acceptable level of climate risk. These perspectives can be applied through the framework of institutional analysis to examine reports from the Intergovernmental Panel on Climate Change and other international organizations. This interdisciplinary approach offers the potential to provide a comprehensive history of how climate science has been interpreted in policy making. An interdisciplinary analysis is also essential in order to move beyond historical description to provide a narrative of considerable explanatory power. Such insights offer a valuable framework for considering current debates about whether or not it will be possible to limit warming to 2°C.