Research on students´ concepts based on conceptual change theory is being conducted in relation to more and more different subject content. CONCEPT, the concept of a concept, however, has very different meanings and functions in different contexts of subject-matter teaching and learning. In this study tools of analytic philosophy of science and philosophy of cognition are applied to examine the recent process of a research transfer from science education to philosophy education. Transmutations of CONCEPT are evident in empirical studies in philosophy education. However, such a transfer process can reveal problems of CONCEPT that affect any subject- matter research on student´s concepts. Three main problems are shown: a problem that is new to philosophy education, one that is a legacy of science education, and another, future problem that is emerging with conceptual engineering. The solution to these problems could lie in an integrated interdisciplinary project, the theoretical determination of subject-matter CONCEPT.