The paradoxes of material implication show that the usual interpretation of implication as "if ... then" statements leads to counter-intuitive results. For example, from
(P & Q) -> R we can derive
(P -> R) v (Q -> R), which doesn't make much sense if we consider them as "if ... then" statements. Quoth wikipedia:
(P & Q -> R) |- (P -> R) v (Q -> R)] can be read "If both switch A and switch B are closed, then the light is on. Therefore, it is either true that if switch A is closed, the light is on, or if switch B is closed, the light is on." If the two switches are in series, then the premise is true but the conclusion is false. Thus, using classical logic and taking material implication to mean if-then is an unsafe method of reasoning which can give erroneous results
I know that there are methods like relevance logic and connexive logic which try to make logic fit the mold of our intuition. But are there any ways in which we can restate implication as a different intuition which would work better with the laws of classic logic?