Semantic externalism and time

Here is a curious thing. Suppose that I’ve been lying in bed trying to fall asleep for a while. I’ve lost track of time. At t₁, I know: “I haven’t fallen asleep yet.” At a later time t₂, I know: “I haven’t fallen asleep yet.” It seems quite possible that my internal mental state at t₁ and at t₂ is exactly the same. Yet what I know at t₂ is logically stronger than what I knew at t₁: for that I haven’t yet fallen asleep by the later time entails that I hadn’t fallen asleep by the earlier time.

So it seems that I gained some information, without any change in my internal mental state. This means is that we need to have some semantic externalism with respect to time.