Normative concepts are said to lead to controversial discussions and involve indefinite and valuable elements, unlike other concepts. Although we have to elucidate these concepts (such as justice, equality, and freedom) in the philosophy of law, we do not know how to discuss these matters rationally. In order to solve this problem, legal philosophers, especially those in Japan, have widely accepted the distinction between concept and conception used by John Rawls and Ronald Dworkin. If this distinction applies to the concept of justice, it leads to problems with theories of justice and with the methodology of these theories. Additionally, if this applies to the concept of law, it is connected with problems of jurisprudence. I doubt this distinction is appropriate for addressing these problems. Before extending my argument from this doubt, in this paper, I pay attention to the idea of the "Essentially contested concept," which was introduced by W. B. Gallie in 1956. Many people consider the idea that an "essentially contested concept" has a strong influence on the distinction between concepts and conceptions and often discuss the two of them together. Certainly, these ideas commonly emphasize the contestability of normative concepts. However, rather than the distinction between concept and conception, the seven criteria of the "Essentially contested concept" is complicated, and Gallie also emphasizes the historical influence of the normative concept. In this paper, I examine the issue of the normative concept itself over the discussions of two ideas together. Firstly, I summarize the idea that we divide normative concepts into two elements, and also explain Gallie's original idea of the "essentially contested concept." Secondly, I point out that Jeremy Waldron and Kenneth Ehrenberg apply Gallie's criteria to examples such as the "rule of law" and "law" itself. Thirdly, I consider the problem of both Gallie's idea and the distinction of concept and conception through Christine Swanton's critique. Finally, I conclude that it is difficult to preserve the coherency of the distinction of concept and conception, and if this distinction were collapsed, our discussions about normative concept would not lead to relativism and skepticism. Finally, I introduce David Wiggin's position of "Sensible subjectivism" and present a model of value judgment after the collapse of the distinction of concept and conception.