The link between social theory and the production of innovative strategic knowledge in different contexts and eras remains a complex question. Nevertheless, strategic studies being a radically instrumental discipline, the notion of power is at the centre of its relationship with the social world. In line with the Cambridge school of political thought, this article lays out a brief genealogical exercise applied to strategic thinking in the ‘West’ in order to better understand Western leaders’ changing approach toward strategy ‘in their own terms’. This exercise of ideational contextualisation allows for isolating the fluctuating understanding of the very notion of power, and its correlative concept of critique, as the most influential theoretical precondition for strategic innovation in strategic studies. Our analysis retraces a dual tradition competing to inform Western strategy, which is of primordial importance to the problématique of innovation in strategic studies. The first lineage—in line with Machiavelli, Nietzsche and Foucault—advises the subject in terms of technical dynamics of power while the second—in line with Aristotle, Kant and Habermas—enlightens him on the legitimate footings of power. Critical strategic studies cannot integrate the insights of reflexivity—as its distinctive cognitive tool—as long as it encompasses these two distinct perspectives indiscriminately. Their coeval consideration generates an inherent cognitive tension from which arise both the desire for critical strategy to consider power as force and power as legitimacy separately, and the corresponding responsibility for the strategist to balance their implications in practice.