Polarity is not what states make of it. Most policy-makers have no concept of polarity. They typically have a sense of what power is and of its contemporary distribution. In neorealism, polarity is a structural feature of the international system: changes of polarity are the most important structural changes we observe. Polarity is not something we do, but something the system does to us. However, it does not do so independently of how we approach power. Polarities only have their distinct, systematic effects in systems where the main actors have specific conceptions of power and its distribution, but not conditioned on their conceptions of polarity. What concepts does polarity theory presume to be socially active for the mechanisms to unfold? I examine three concepts: ‘power’, ‘balance of power’ and ‘polarity’. The surprising conclusion is that most of the dynamics posited in polarity theory—from Waltz (1979) to Hansen (2011)—demand the conceptual emergence of ‘abstract’ or ‘aggregate’ power and of ‘balance of power’ as abstraction, but only for some secondary features do polarity dynamics depend on actors thinking in terms of ‘polarity’. Conceptual history meets IR realism is the basic plot of this article. To what extent does power need to recognize itself as such, for it to have effects?