In philosophy and political theory, the term paradox is often used synonymously with antinomy, contradiction and aporia. This article clarifies the meaning of these terms through tracing their respective etymology. We see that antinomy denotes a deep-seated conceptual opposition, whereas contradiction and aporia represent alternative responses to antinomy. The former presents the antinomy as potentially resolvable at some future time, and the latter sees the antinomy instead as a constitutive impasse. By way of contrast, para doxa originally referred to a (...) statement that is ‘contrary to received opinion’, but this idea has generally been subsumed – both in philosophy and more common place understandings – under the notion of aporia. This conceptual recovery enables a better understanding of key traditions in social and political theory, notably post-structuralism and Habermasian critical theory, which can be demarcated through their respective responses to the emergence of ‘paradoxes’. However, the article also demonstrates the material significance of these philosophical categories through their application to contemporary democratic politics. I analyse the constitutive tension between liberalism and democracy as well as the emergence of populism and show how these conceptual tools provide new insights for understanding these most pressing political developments of our time. (shrink)