In recent years, the full text of papers are increasingly available electronically which opens up the possibility of quantitatively investigating citation contexts in more detail. In this study, we introduce a new form of citation analysis, which we call citation concept analysis (CCA). CCA is intended to reveal the cognitive impact certain concepts—published in a highly-cited landmark publication—have on the citing authors. It counts the number of times the concepts are mentioned (cited) in the citation context of citing publications. We demonstrate the method using three classical highly cited books: (1) The structure of scientific revolutions by Thomas S. Kuhn, (2) The logic of scientific discovery—Logik der Forschung: Zur Erkenntnistheorie der modernen Naturwissenschaft in German—, and (3) Conjectures and refutations: the growth of scientific knowledge by Karl R. Popper. It is not surprising—as our results show—that Kuhn’s “paradigm” concept seems to have had a significant impact. What is surprising is that our results indicate a much larger impact of the concept “paradigm” than Kuhn’s other concepts, e.g., “scientific revolution”. The paradigm concept accounts for about 40% of the concept-related citations to Kuhn’s work, and its impact is resilient across all disciplines and over time. With respect to Popper, “falsification” is the most used concept derived from his books. Falsification is the cornerstone of Popper’s critical rationalism.