I just think of it as P->Q only says something about Q when P is true; no information is given about Q when P is false, so Q can be whatever it wants in that ca

I just think of it as P->Q only says something about Q when P is true; no information is given about Q when P is false, so Q can be whatever it wants in that case. And since any value of Q is acceptable, then the statememt holds regardless of Q's value (when P is false). We only have the chance to return false when P is true, because thats the only time P says something about Q (that its true)