 It is not enough merely to pick out the actual extension of knowledge. Even if, in actual fact, all cases of S knowing that p are cases of j, and all cases of the latter are cases of the former, j might fail as an analysis of knowledge. For example, it might be that there are possible cases of knowledge without j, or vice versa. A proper analysis of knowledge should at least be a necessary truth. Consequently, hypothetical thought experiments provide appropriate test cases for various analyses, as we shall see below.