Full Idea
According to Grice, it is the rules that govern conversation beyond the merely logical that account for the counter-intuitiveness of the truth table for the material conditional.
Gist of Idea
The odd truth table for material conditionals is explained by conversational conventions
Source
report of H. Paul Grice (Logic and Conversation [1975]) by Jennifer Fisher - On the Philosophy of Logic 8.I
Book Reference
Fisher,Jennifer: 'On the Philosophy of Logic' [Thomson Wadsworth 2008], p.109
A Reaction
There is a conversational rule which says that replies should normally relevant to context. It would be nice if logical implications were also relevant to context.