Opposite Day

What the day is

Opposite Day is observed on January 25. Everything said is to be taken as meaning its reverse, which collapses the moment anyone announces it.

Origin and background

The origin of the observance is not documented. The trap in it is real and well studied.

Saying today is Opposite Day is self-defeating. If the statement is true, then by its own rule it means the reverse, so it is not Opposite Day. If it is false, then statements are not reversed, so the sentence means what it says, and it is. The claim cannot settle into either value. Children work this out quickly and enjoy it, which is most of the appeal.

It belongs to the family of self-referential paradoxes that gave philosophers and mathematicians serious trouble. The oldest is the liar, a sentence asserting its own falsity, known to ancient Greek logicians. The version with real consequences arrived in 1901, when Bertrand Russell asked whether the set of all sets that do not contain themselves contains itself. Either answer contradicts the other, and the question was not a game: it undermined the foundations being built for mathematics at the time, and forced a substantial rebuilding of set theory to exclude self-reference of that kind.

The same structure turns up in computing, where the question of whether a program can decide in advance whether another program will ever stop is answered no, by constructing a program that does the opposite of whatever the decider predicts for it.

So a playground joke shares its machinery with one of the genuine limits on what can be known.

How to take part

• Declare it and watch the argument that follows. That argument is the point.
• Ask a child to explain why the announcement breaks. Many can.
• Read the liar paradox, which takes one sentence and a long time.
• Look up Russell's paradox and what it did to mathematics.
• Do not use it to get out of anything. That is the one move everybody tries.