Has anyone ever told you, “Today is not opposite day?” Or maybe you’ve told someone a similar sentence? The commonplace phrase that children like to use (usually to annoy their parents) has a deeper, more complex structure. That same structure fuels one of the most complicated, unsolvable paradoxes in the history of the world: The Liar Paradox.

What’s A Paradox?

A paradox is a self-contradictory idea. In other words, it’s an idea that goes against what it itself is saying. While a paradox may appear to be accurate, normal, and possible in the beginning, but when people look deeper into it, it may not be. A common example of a paradox is ‘jumbo shrimp’. It seems regular at first, possible, even accurate. However, shrimp means small, so ‘jumbo shrimp’ is basically saying, ‘jumbo small’. This contradicts itself – it can’t be both jumbo and small.

The Fault Of Opposites

When somebody says, “Today is not opposite day”, what do they really mean? Do they actually mean that today isn’t opposite day? No, they’re attempting to say that ‘today is opposite day’. So “Today is not opposite day” actually translates to “today is opposite day.” But if today is opposite day, just apply the opposite of that sentence. The opposite of “Today is opposite day” is “Today is not opposite day”.. and we’re back at the beginning again. 

So if “today is not opposite day,” it means that “it is opposite day.” But the opposite of “today is opposite day” is “today is not opposite day.” Then, it actually means ‘today is opposite day.” But does it? This loop will just continue forever. A child’s game that tries to convince their parents that they “like homework” – on whichever day of the week is chosen as opposite day – has a much deeper meaning.

The Liar Paradox

The Liar Paradox has a similar baseline as “Today Is Not Opposite Day.” The statement says simply, “This statement is false.” Easy, right? The statement just isn’t true. The thing is, if it’s untrue that “This statement is false,” then it must mean that the statement is true. Well… if it’s true that the statement is false, then it means that the statement is false. If it’s false that the statement is false… then it’s true. So people land themselves back into a loop again.

Another variation is that there are two buttons, a red button and a blue button. The red button says that the blue button is true, and the blue button says that the red button is false. If the red button is true, then it says that the blue button is true. If the blue button is true, it says that the red button is false. Okay, then the red button is false. So it’s false that the blue button is true, meaning that the blue button is false. If it’s false that the red button is false, then it means that the red button is true. And again, people get stuck in a loop.

Is Today Opposite Day?

So, using the same line of thinking, is today actually opposite day? It depends on what you think. The thing is, a simple children’s game turned out to be part of a mind-boggling thought experiment that many famous researchers have been stumped on for ages. Between Opposite Day, the Liar Paradox and the Buttons, there are so many different variations of the paradox. The paradox is going to be very hard to solve, maybe even impossible. But for now, the next time someone tells you that “today is not opposite day,” just remember that there’s a mystery much deeper than what meets the eye.

Citations

Liar Paradox | Internet Encyclopedia of Philosophy. iep.utm.edu/liar-paradox. Accessed 6 Oct. 2022.

“The Liars Paradox OR Today Is Not Opposite Day.” Rob Schlaff’s Website, 8 Sept. 2018, schlaff.com/wp/the-liars-paradox-or-why-there-cant-be-an-opposite-day.

“Paradox.” The Merriam-Webster.com Dictionary, www.merriam-webster.com/dictionary/paradox. Accessed 4 Oct. 2022.

“—.” The Merriam-Webster.com Dictionary, www.merriam-webster.com/dictionary/paradox. Accessed 6 Oct. 2022.

“Jumbo Shrimp Image.” publicdomainvectors.org, publicdomainvectors.org/en/free-clipart/Shrimp-vector-clip-art/70829.html.