Pigs would fly

The phrase Pigs would fly is 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 "User:Notorious is a genius" and a person says "If User:Notorious were a genius, pigs would fly", we can see that the person thinks that "User: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_(ja) argument.

Let an improbable assumption be symbolically "Mn". Now, all we need to do is verify whether the proposition "If Mn, then pigs will fly." is true or not.

To prove that the proposition "If Mn, then pigs fly." is true, we prove that its counterpart "If pigs do not fly, then not-Mn." is true.

For the assumption "Pigs do not fly." of the proposition "If pigs do not fly, then not-Mn," it always stands; in this world, no pig flies. And for the conclusion "Not-Mn," it also always stands; Mn is an improbable assumption, and the world is divided only two, Mn or not-Mn. For this proposition, therefore, as the conclusion always stands when the assumption stands, thus it is true.

Then the proposition "If Mn, pigs would fly." is true, as a proposition, where its Contrapositive_(ja) is true, is true.

The answer that has a logical consistency to "Pigs! Would! Fly!" Problem can be proved as such.