Chapter 5 begins by analyzing the transition from Neo-Kantian Ideensgeschichte to Reinhart Koselleck’s Begriffsgeschichte. The latter intended to break the ahistorical assumptions behind the former tradition. It was closely associated to the postulate of the radical indefinability of concepts, given the contextual transposition they undergo. For Koselleck, the capacity of concepts to transcend their contexts of origin make of them to serve as the articulators of the structural connections in history. It permits conceptual history transcending social history. Yet, conversely, social history would transcend conceptual history because only the former could explain how structural connections eventually become broken. The postulate was at the basis of his polemic with Gadamer. However, as the chapter shows, Koselleck’s argument is founded on a fallacy. Lastly, the reintroduction of the opposition between “conceptual history” and “social history” breaks the tenets of his own historical-conceptual theory.