The Liars Paradox OR Today Is Not Opposite Day

Today my son Blake started telling me that “Today is Opposite Day!” and then said things like “I love doing my homework. Just kidding. It’s opposite day!”

I told him that he couldn’t possibly be telling me that today is opposite day. If it were opposite day and he was telling me it was opposite day, then it wouldn’t be opposite day. And if it’s not opposite day and he told me that it was opposite day, it would be opposite day. It’s a cycle that never ends. Formally the sentence, “This is opposite day” is neither true nor false and therefore is undefined.

The Infinite Circle of Opposite Day

This, of course, prompted his friend Gabe to try to explain it all to me. “It’s complicated,” he said, “you see, if we say it’s opposite day then we would say that it’s not opposite day to mean that it really is opposite day.” But I didn’t find this line of argument compelling.

Blake tried a different tack, “We can say that Wednesday is opposite day.”

“Yes,” I said, “but you can’t say that on Wednesday.”

This is an ancient logical paradox called the Liar’s Paradox which often takes the form of “I am a liar” or “This sentence is false.” Because the sentence is self-referential and negative.

I figure it’s never to early to teach the kids about logic and paradox. It also makes Blake be more specific about opposite day. The inherent problem with opposite day is that kids randomly choose which items are opposite and which are not (e.g., the sentence “It’s opposite day” is not negated). Now he needs to say “If it were opposite day, I’d say that I love doing my homework.”