Pigs would fly

"Pigs would fly." is a phrase used as a conclusion to show that the corresponding assumption is impossible.

Mainly about

In conditional sentences, it is a kind of wordplay or rhetoric used in the concluding part to show that an assumption is improbable.

For example, considering the case that there is a given assumption "Notorious is a genius" and a person says "If Notorious were a genius, pigs would fly", we can see that the person thinks that "Notorious can't be a genius.

The logical consistency of saying it

The problem if there is any consistency in concluding that "pigs fly" when the assumption is impossible (called "Pigs! Would! Fly!" Problem) has only recently begun to be pointed out, and since ancient times it has continued to trouble the minds of logicians, philosophers, physicists, mathematicians, or cultists who like to fantasize about things that are totally useless in reality. However, it is now known that this "Pigs! Would! Fly!" Problem can be proven by the contrapositive argument.

Let an improbable assumption be symbolically "Mn". Now, we are supposed to determine whether the proposition "If Mn, then pigs will fly." is true or not.

We can prove that the proposition "If Mn, then pigs fly." by proving that its contrapositive "If pigs do not fly, then not-Mn," because the truth values of a proposition P and its contraposition Q are equal.

For the assumption "Pigs do not fly." of the proposition "If pigs do not fly, then not-Mn," it always stands; in this world, a pig would never fly. For the conclusion "Not-Mn," it is always true because Mn is known to be always false. Thus, it is true that, in this contrapostion, the conclusion is true when the assumption is true. Now we have proved this contraposition. Therefore, the proposition "If Mn, pigs would fly." is also true.

Now we have a consistency upon saying "Pigs would fly." as a conclusion of an improbable assumption, and upon expressing the improbabity itself by saying so.