This is the “paradox of the material conditional”, which is one of the primary motivations of relevance logic—to provide a sentential connective that corresponds to how we actually use “implies”, as opposed to the material (truth-functional) implication.
This is the “paradox of the material conditional”, which is one of the primary motivations of relevance logic—to provide a sentential connective that corresponds to how we actually use “implies”, as opposed to the material (truth-functional) implication.
http://plato.stanford.edu/entries/logic-relevance/
Good point! Perhaps you won’t be surprised, though, if I say that my own preferred account of the conditional is the probabilistic conditional.