But before we get to the unicorns, we need to talk about some logic.

When we say “[claim 1] OR [claim 2],” we mean that at least one of the claims is true. If both claims are false, then the entire statement is false. If one claim is true, then the entire statement is true. Let’s try some examples:

“The ukulele is a stringed instrument OR basketball is a sport” (True)

“Bears are reptiles OR my pencil is a cat” (False)

“I am human, OR today is Friday” (True)

That last one is a little interesting. This blog will be posted on a Friday, but I have no idea what day you are reading this. Still, I confidently tell you that the statement is true. Why? Going back to the definition of “OR,” if one claim is true then the entire statement is true. The first claim, “I am human” is certainly true, so it doesn’t matter what the second claim is.

This means I can substitute any proposition in for the second claim, and the statement is still holds:

“I am human, OR I am a cat” (True)

“I am human, OR the Earth is flat” (True)

This process of starting with a true statement then adding “...OR [any other statement]” is called a “Disjunction introduction,” which is just a fancy of saying “add an OR.”

Wikipedia’s example of this trick illustrates it quite nicely:

“Socrates is a man. Therefore, Socrates is a man or pigs are flying in formation over the English Channel.”