The ambigous definition of vacuous truth It is no doubt that the vacuous truth is related to material implication  "$P\Rightarrow Q$". We say the material implication statement is true when $P$ is false. However, seems that this is not the definition for vacuously truth. Do we call it vacuously true only when $P$ can never be true? (Seems that all examples are in this way).
More clearly, suppose we have a statement "$P(x)\Rightarrow Q(x)$", and at some domains of $x$ (we may denote the domain by $T_x$), $P(x)$ is true;  at some other domains of $x$ (denote the domain by $F_x$), $P(x)$ is false. Can we say the statement is vacuously true in the domain $F_x$? Is there any real example?
To make the problem more clear, we may check the statement "For all $x$, $P(x)\Rightarrow Q(x)$". Can we say this statement is vacuously true in the domain $F_x$ ($F_x$ is defined as above)?


Do we call it vacuously true only when P can never be true?

No. In classical logic, for any logical propositions P and Q (it doesn't matter if they are true or false), we have:
$P\implies [\neg P \implies Q]$
This is a tautology. See truth table here.
