This paper addresses two methodological issues related to the assessment of teachers' views of science. The first concerns the distinction between the "nature of science" (NOS) and the nature of "scientific inquiry" (SI): should the points related to NOS and those related to SI be analyzed independently? The second concerns the categorization of teachers' views: is it relevant to analyze them according to a grid of predefined epistemological conceptions? Alternatively, does an empirical approach allow the emergence of epistemological profiles with an overall consistency? To investigate these issues, an empirical study has been performed based on a questionnaire on teachers' views of science (called the "VOS questionnaire") which has been submitted to 160 in-service primary teachers. With respect to the first issue, the analysis of the outcomes brings to light implicative relations between teachers' views on NOS-type items and their views on SI-type items. This calls into question the alleged necessity of separating NOS and SI when assessing teachers' epistemology. Concerning the second issue, a multiple correspondence analysis leads us to identify clusters of teachers with various levels of expertise concerning different epistemological points and without an overall consistency from the point of view of philosophy of science. This suggests that teachers' consistency has to be found not in their view of science taken in isolation but considered in combination with other kinds of knowledge (e.g., pedagogical content knowledge) and their practices of science teaching.