Epistemic possibility

In philosophy and modal logic, epistemic possibility relates a statement under consideration to the current state of our knowledge about the actual world: a statement is said to be:
Epistemic possibility is often contrasted with subjunctive possibility (or alethic possibility), and although epistemic and subjunctive possibilities are often expressed using the same modal terms (such as "possibly", "could be", "must be") or similar modal terms that are sometimes confused (such as "may be" and "might be"), statements that are qualified in terms of epistemic possibility and statements that are qualified in terms of subjunctive possibility have importantly different meanings.
The contrast is best explained by example. Consider the two statements:
Although these two statements are often confused with one another, they mean two different things: the first says something "true" about the vagaries of war; the second says something that is certainly "false". The difference comes from the fact that the first statement—a statement of "subjunctive" possibility—says something about how things "might have been" under counterfactual conditions, whereas the second—a statement of "epistemic" possibility—says something about the relation between a particular outcome (a victory by Japan) and "our knowledge about the actual world" (since, as it happens, we know perfectly well that that particular outcome did "not" actually obtain, we know that what it says is false).
The parallel distinction arises between types of conditionals (if-then statements). Consider the difference between the epistemic connection expressed by an indicative conditional and the causal or metaphysical relation expressed by a subjunctive conditional:
The first statement says something that is certainly true, and will be accepted as such by anyone who is convinced that somebody shot Kennedy. It's clearly true because it expresses this epistemic relation between its antecedent (the "if"-clause) and its consequent (the "then"-clause): The antecedent, if we came to know it was true, would provide us with excellent evidence that the consequent is true. The second statement, on the other hand, expresses a causal or metaphysical relation: It says that the world was set up so that the consequent would have been made true if the antecedent were true. One will accept that second statement to the extent that one thinks the world was set up in that way. (Conspiracy theorists who think there was a back-up shooter, for instance, may accept the second statement.) 
Because of these differences, epistemic possibility bears on the actual world in ways that subjunctive possibility does not. Suppose, for example, that one wants to know whether or not to take an umbrella before going outside. If one is told "It's "possible that" it is raining outside"—in the sense of epistemic possibility—then that would weigh on whether or not I take the umbrella. But if one is told that "It's "possible for" it to rain outside"—in the sense of "metaphysical possibility"—then one is no better off for this bit of modal enlightenment.