Paradoxes of Material Implication - Paradox of Entailment

Paradox of Entailment

As the most well known of the paradoxes, and most formally simple, the paradox of entailment makes the best introduction.

In natural language, an instance of the paradox of entailment arises:

It is raining

And

It is not raining

Therefore

George Washington was a zombie.

This arises from the principle of explosion, a law of classical logic stating that inconsistent premises always make an argument valid; that is, inconsistent premises imply any conclusion at all. This seems paradoxical, as it suggests that the above is a valid argument.