Oxford University Press's
Academic Insights for the Thinking World

The paradoxes of Christmas

While most of you probably don’t believe in Santa Claus (and some of you of course never did!), you might not be aware that Santa Claus isn’t just imaginary, he is impossible!

In order to show that the very concept of Santa Claus is riddled with incoherence, we first need to consult the canonical sources to determine what properties and powers this mystical man in red is supposed to have. John Frederick Coots and Haven Gillespie tell us, in the 1934 classic “Santa Claus is Coming to Town,” that:

He sees you when you’re sleeping.
He knows when you’re awake.
He knows if you’ve been bad or good.
So be good for goodness sake!

But can Santa always know if you’ve been naughty or nice?

First of all, it is worth making a rather simple observation: If one tells a lie, then one is being naughty, and if one is telling the truth, then one is being nice (unless one is doing something else naughty at the same time, a possibility we shall explicitly rule out below). After all, my mother, an expert on the subject, told me many times that lying is naughty and truth-telling is nice, by both her own lights and by Santa’s. You wouldn’t call my mother a liar, would you?

Weihnachtsmann in Annaberg-Buchholz, by Kora27. CC-BY-SA-4.0 via Wikimedia Commons.
Weihnachtsmann in Annaberg-Buchholz, by Kora27. CC-BY-SA-4.0 via Wikimedia Commons.

Now, consider Paranoid Paul. Paul, who is constantly worried about whether he has been nice enough to get presents from Santa, at some point utters:

Santa knows I’m being naughty right now!

Assume, further, that Paul is not doing anything else that could be legitimately assessed as naughty or nice. Now, the questions are these: Is Paul being naughty or nice? And can Santa know which?

Clearly, Paul isn’t being naughty: If he is being naughty, then Santa would know that he is being naughty, via the magical powers attributed to Santa in the aforementioned carol. But if Santa knows that Paul is being naughty, then what Paul said is true, so Paul isn’t lying. But since he isn’t doing anything else that could be assessed as naughty, Paul isn’t being naughty after all.

But equally clearly, Paranoid Paul isn’t being nice: If he is being nice, then Santa would know he is being nice. But that would imply that Santa doesn’t know that Paul is being naughty, by the Principle of Christmas Non-Contradiction:

PCNC:  No single action is simultaneously naughty and nice.

But then Paul is lying, since he said that Santa does know that he’s being naughty. And lying is naughty, so Paul isn’t being nice after all.

Of course, there is nothing to prevent Paranoid Paul from uttering the utterance in question. And, if he does so, then surely he is either being naughty or being nice – what other Christmas-relevant moral categories are there? (We might call this the Principle of Christmas Bivalence!) So the problem must lie in the mysterious magical powers attributed to Santa Claus in the song. Thus, Santa Claus can’t exist.

This Christmas revelation is probably shocking enough to most of you. But I’m afraid it gets worse.

It is well-known that Santa Claus gives presents to children on Christmas night. What is most important for our purposes are the two strict rules that govern Santa Claus’s Christmas gift-giving. The first of these we might call the Niceness Rule:

Nice: If a child has been nice (overall), then he or she will receive the toys and gifts he or she desires (within reason).

And the second we can call the Naughtiness Rule:

Naughty: If a child has been naughty (overall), then he or she will receive coal (and nothing else).

Following these rules is an essential part of what it is to be Santa Claus – these rules codify his place and purpose in the universe. Thus, they are non-negotiable: Santa does not, and cannot, break them.

This Christmas revelation is probably shocking enough to most of you. But I’m afraid it gets worse.

Let’s again consider Paranoid Paul, who as usual is worrying about his status with respect to the naughtiness/niceness metric. Assume further that, at one minute before midnight on December 24th (the well-known deadline for Santa’s final yearly naughty/nice judgments) Paul’s actions over the past year have, unbeknownst to him, fallen precisely on the line separating the overall naughty and the overall nice. He only has time for one more action, and if it is nice, then he will get the presents he want, and if it is naughty then he will only get coal. Paul, who is aware that his behavior over the past year has been less than exemplary, utters:

I’m going to get coal for Christmas this year!

Such an utterance prevents Santa Claus from giving anything – coal or goodies – to Paranoid Paul.

Santa can’t give Paranoid Paul toys and gifts. If Santa gives Paul toys and gifts, then he can’t give him coal. But this means that Paul told a lie, which would push him over into overall naughtiness. But then Santa should have given him coal, not goodies.

But Santa also can’t give Paul coal. If he gives Paul coal, then Paul was telling the truth. This would push Paul into overall niceness. But then Santa should have given him toys and presents, not coal.

Thus, we once again see that the very concept of Santa Claus is outright inconsistent. And since Santa Claus is an integral part of Christmas, this means that Christmas itself is incoherent, and hence must not exist.

And that’s how the Grinch proved that there’s no Christmas!

I hope everyone who reads this column (regardless of which, if any, winter holiday you celebrate) has a wonderful month and a safe winter holiday! See everyone next year, and thanks!

Featured image credit: Christmas present. Public domain via Pixabay.

Recent Comments

  1. Steve Reilly

    Unfortunately for you, Paranoid Paul also said “If this sentence is true, then Santa Claus exists”. Which proves that Santa Claus does exist after all! I asked a Priest about this seeming contradiction, and he told me he disagreed with the Principle of Christmas Non-Contradiction.

  2. Roy T Cook

    For those who might not have gotten the reference, Graham Priest is a famous philosopher of logic who defends dialetheism – the view that sentences (including paradoxical, Liar-like sentences) can be both true and false at the same time. Thus, Steve’s priest, who denies a similar principle for Santa Claus, is a reference to Graham (and an incredibly clever one!) Thanks Steve!

  3. oliverio

    Unfortunately, “Santa knows I am being naughty right now!” clearly expresses a belief about the world. Having a mistaken belief about the world (i.e. leprechauns exist, or “the earth accelerates things at 50 m/s/s”) is very clearly not “naughty” in any respect and should carry no more weight than Paranoid Paul sneezing.

    If Paranoid Paul went about telling other people, and making it clear, that it was the factual case that Santa stood in knowledge of Paul’s naughtiness, it would be a statement of perfect coherence (he would be telling a lie that would at the time of telling be factually false– afterwards it would have become true, but that does not mean it was not a lie; if Santa is naughty-omniscient, he knows that Paul is naughty before the lie even leaves his lips).

  4. Luc Baudouin

    By uttering “Santa knows I’m being naughty right now!”, Paranoid Paul is being illogical, which is neither nice nor naughty (at least under a certain age). His thought will simply wheight nothing on Santa’s balance. The same applies to the “coal” case. Santa’s existance is not unproven.

    Regarding the paradox proposed by Steve Reilly, it is not reasonable to undertake a logical inference if you dont admit (at least provisionally) the premises. I’m saying “at least provisionally” in case you intend to make a reductio ad absurdum. but in that case, “If this sentence is true, then Santa Claus exists AND the previous sentence is true ” immediately reduces to “Santa exists”, which may be true or false. Santa’s existance is not proven.

    Santa’s mystery is here to stay…

  5. asdf

    “If I wanted coal for Christmas would I have to be bad and if I were bad and I still wanted coal would you give it to me? Because then you’d be rewarding me for bad behavior and that would throw off the whole naughty/nice thing”

Leave a Comment

Your email address will not be published. Required fields are marked *