Over the past few years, researchers, activists, and policymakers have engaged in debates over how social media companies should respond to extremism on their platforms. One facet of this debate focuses on the consequences – online and offline – of different approaches. Debates about the effectiveness of various approaches have not recognized that there are two different goals: reducing extremist violence and reducing extremism. This article presents a thought experiment that unpacks these goals, thinks through possible relationships between different approaches and different goals, and suggests a number of hypotheses that could be tested to empirically investigate the consequences of banning or tolerating extremists on social media.