According to SEP, Lewis's theory of counterfactual conditionals defines truth for counterfactuals as follows:
[...] the truth condition for the counterfactual “If A were (or had been) the case, C would be (or have been) the case” is stated as follows:
(1) “If A were the case, C would be the case” is true in the actual world if and only if either (i) there are no possible A-worlds; or (ii) some A-world where C holds is closer to the actual world than is any A-world where C does not hold.
We shall ignore the first case in which the counterfactual is vacuously true.
I am unable to understand, why the first case is "vacuously true". I could easily explain it by treating the counterfactual conditional as a material conditional, since material conditionals are always true if the antecedent is false. But I have read that counterfactual conditionals shall not be treated as material conditionals. I would appreciate anyone explaining to me why the above mentioned first case is true.
I would also appreciate, if you could use following example (and maybe correct it, if it is wrong) to exemplify your answer:
Real world case: I have eaten fish and my face got swollen.
I think the corresponding counterfactual conditional has to be: If I hadn't eaten fish, my face wouldn't have swollen.
(If I use my example, I would say that A = "I had not eaten fish" and C is = "my face wouldn't have swollen". If I now imagine that in all possible worlds A is false, this would mean that in all worlds [= real world + all possible worlds] I had eaten fish. This is the point, where I am stuck: Why does this mean that the counterfactual conditional is true?)
I thank you very much for any replies.