Predicate Logic and Popular Culture (Part 18): Sleigh Ride


Let H be the home of Farmer Gray, let B(x) be the proposition “x is a birthday party,” let P(x) be the proposition “x is the perfect ending of a perfect day,” let F(x) be the proposition “x is a fireplace,” let S(x) be the proposition “x sings that songs that x knows without a single stop,” and let W(x) be the proposition “x watches the chestnuts pop.” Translate the logical statement

\exists x \in H (B(x) \land P(x) \land \exists y \in H (F(y) \land \exists \epsilon > 0 \forall z \in x

(\parallel y - z \parallel < \epsilon \implies S(z) \land W(z) \, ) \, ),

where the domain for x and y are all places and the domain for z is all people.

I won’t spoil the fun of attempting a direct English translation, but this is one of the closing verses to “Sleigh Ride.”

And while I’m on the topic, I can’t resist also sharing The Three Tenors singing “Sleigh Ride” in perhaps the most delightful waste of immense talent in recorded human history… though the closing note is incredible.

green line

Context: This semester, I taught discrete mathematics for the first time. Part of the discrete mathematics course includes an introduction to predicate and propositional logic for our math majors. As you can probably guess from their names, students tend to think these concepts are dry and uninteresting even though they’re very important for their development as math majors.

In an effort to making these topics more appealing, I spent a few days mining the depths of popular culture in a (likely futile) attempt to make these ideas more interesting to my students. In this series, I’d like to share what I found. Naturally, the sources that I found have varying levels of complexity, which is appropriate for students who are first learning prepositional and predicate logic.

When I actually presented these in class, I either presented the logical statement and had my class guess the statement in actual English, or I gave my students the famous quote and them translate it into predicate logic. However, for the purposes of this series, I’ll just present the statement in predicate logic first.

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