Let $P$ = "Pigs can fly" and $Q$ = "I'm king".
Apparently, there's a rule stating that $P \implies Q$ is true, if $P$ is false.
In this example, $P$ is indeed false, because pigs cannot fly. But how does this make the implication true?
The way I see it, pigs learning to fly will not cause me to be crowned king.
What am I missing here?
Any help appreciated?
On
Taking this back to natural language, this says "Assume pigs fly. Since pigs fly, I am king". It reads completely ridiculus because it is, but it doesn't make it wrong. You're starting from a false assumption.
For example, if you wanted to discover the properties of a hypothetical object, but didn't know one exists or not. You'd start with "If [OBJECT] exists, we should expect to see..." Which would have reaonable conclusions but without knowing the thing exists to begin with! That make the statement "If [OBJECT], then ..." a true statement.
One way you could interpret your implication would be "every time a pig has been able to fly, I have been king." In order to show this was not true, you would have to demonstrate a time when (a) pigs have flown ($P$ is true), and (b) you have not been king ($Q$ is false). But, $P$ is never true, so you can't do this. Thus, the implication is valid.