Trick or Treat? A Logical Approach

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Based on the kind of stuff I post on this blog, you probably think of me as that anime guy. But when I’m not pretending that real life isn’t there to kick my ass, I’m a philosopher that occasionally teaches Math (I say “occasionally” because I’m not exactly working yet).

Now I’m not one to get into the holiday gimmicks very often, but since Halloween is coming up, there has been one thing that puzzles me about this holiday. I am, of course, talking about this thing that kids like to say to neighbors they rarely ever interact with, dressed in their costumes, only to get some candy from them.

What exactly do we mean when we say Trick or Treat?

Yes, I used to dress in costume and go house to house with my siblings on October 31, and the neighbors that were home were nice enough to give us candy. Some neighbors would give the good stuff that will eventually give us all diabetes. Others would provide something a little healthier like a box of raisins (Just kidding. Only I do that). I remember at least one of my neighbors took a clever approach by asking us if we wanted a piece of candy or instructions for a magic trick. That was their way of throwing the question of “Trick or Treat” back at us!

It seems there are a lot of ways to interpret the meaning of this Halloween tradition, whether it is defining what a trick or a treat is, or understanding its rules and ramifications.

But to be honest, I have no idea what “Trick or Treat” means or where it comes from! Given my 21st century point of view, “Trick or Treat” seems to mean “Give me candy, because this is a commercial holiday.” Okay, that’s probably not at all what people mean when they say it. But when I was a child, I was told that it meant something like “Give me a treat, or I will trick you.” How you would come to that conclusion from a simple phrase like “Trick or Treat” is beyond me.

But if that is what we mean by “Trick or Treat,” it doesn’t make any sense! After all, in the purely logical sense, what’s to prevent both from happening?

The logical “or” (as opposed to the common “or”) is a disjunction that entails truth if and only if at least one of its two conjoined statements are true. The only condition that is logically false or impossible would be if both statements are false. If we follow the complete sentence pattern F v G, this is my interpretation:

  • F: I trick you.
  • G: You give me a treat.
  • F v G: I trick you or you give me a treat.

If this is what we mean by “Trick or Treat,” the events that can happen are true for the following:

  1. I trick you and you didn’t give me a treat.
  2. You give me a treat and I don’t trick you.
  3. I trick you even though you gave me a treat.

Not suggesting that anyone abides by these rules at all. I just think that the logic here is absurd, and anyone that thinks that this is how “Trick or Treat” works needs to get their head examined! Besides, the only condition that will prove false (You don’t give me a treat and I don’t trick you) is also possible, not to mention very ordinary. You can’t expect everyone to be at home and provide candy on Halloween night!

But then I remember an alternative to how “Trick or Treat” works. My mother told me once that when she was a child, she learned the phrase as “Treat, no Trick.” Complete, concise, and it departs from the odd disjunctive that comes with a logical or. This phrase is a conditional, and gets closer to my semantic meaning of “Trick or Treat.”

  • G → ~F: If you give me a treat, then I do not trick you.

This actually makes more sense to the origins of pranks on Halloween, for better or worse. If you give me a treat, I cannot trick you (modus ponens). However, if I do trick you, it’s because you didn’t give me a treat (modus tollens). Jerk!

Of course, denying the antecedent and affirming the consequent (If you don’t give me a treat, I still won’t trick you) are still fair, and kids will abide by this if they don’t want their neighbors get revenge in the most terrifying ways (and believe me, neighbors will)! The only time the deal is broken is when the antecedent is true, yet the consequent is false. In other words, if you give me a treat and I still trick you, the Halloween Police can and will arrest me!

So what does this mean for our Halloween tradition? Does this somehow justify the prank side of Halloween? What exactly would we define as a Trick or a Treat? Am I thinking way too deep into this fun tradition?

Whatever the case may be, this is my treat to you. Be safe, enjoy the festivities, and have a happy Halloween!

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