What's Illogical? There is a point in time identified as "midnight" and marks a transition from one day to the next. The point (since it is infinitesimally small like all other points) does not lie on either side of the timeline. Everything else is just semantics. You can define that point however you want: "Midnight" = "00:00 tuesday" = "24:00 monday" = "moment Cinderella turns into a pumpkin" = "??" ... We are discussing a communication issue, not a logic issue. We can choose anything but to avoid confusion, it's best to choose a standard definition for that specific (logical)point.