 From this observation, it would appear that there is a gap between what is true of inferences, and what is true of “reason why” relations. There is an inferential sense in which the truth of S is both a necessary and sufficient condition for the occurrence of the sea battle. However, there is an explanatory sense in which the occurrence of the sea battle is necessary and sufficient for the truth of S, but not vice versa. It would appear that in cases like (vii) and (viii) the inferences run in both directions, while explanatory reasons run only one way. Whether we read (vii) as equivalent to (viii) seems to depend on the sense in which the notions of necessary and sufficient conditions are being deployed.