There is a subtlety going on here. You should really parameterize by time. So we have e.g. h(t) - it's raining somewhere in England at time t. Now our empirica

There is a subtlety going on here. You should really parameterize by time. So we have e.g. h(t) - it's raining somewhere in England at time t. Now our empirical theory is forall t e(t) -> h(t). We are told that e(T) for some particular T. This makes us believe that h(T) | ~e(T), but should barely change anything about our belief in the theory. Edit: I noticed you realized the part of higher order in a side thread, but a specific important point to add here. You mentioned that "logically necessary part is sort of trivial (a mere theorem) whereas (h|~e) has actual physical content". Our theory makes predictions about the future - so it's impossible to observe e(t) for all t. We can't just rely on observing all instances of the actual physical thing. We have to make use of logical necessity.