# Why is the implication “If pigs could fly, I'd be king” a true implication? [duplicate]

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?

## marked as duplicate by Zev Chonoles, Joffan, Community♦May 25 '15 at 18:37

• this is the principle of explosion. It's unintuitive – man and laptop May 25 '15 at 18:23
• Well they say that one could deduce anything based on false knowledge – alkabary May 25 '15 at 18:23
• if $1=2$ then $2 =3$, you see now how it might work ? – alkabary May 25 '15 at 18:24
• This is a duplicate of many previous questions... – anon May 25 '15 at 18:25
• In another system of logic-of your own making-it sure can be true,even a truism.. – MathematicianByMistake May 25 '15 at 18:26

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.