Predicate Logic and Popular Culture (Part 250): Marvin Gaye

Let $T$ be the set of all things, let $M(x)$ be the statement “$x$ is a mountain,” let $V(x)$ be the statement “$x$ is a valley,” let $R(x)$ be the statement “$x$ is a river,” let $H(x)$ be the statement “$x$ is high enough to keep me from getting to you, baby,” let $L(x)$ be the statement “$x$ is low enough to keep me from getting to you, baby,” and let $W(x)$ be the statement “$x$ is wide enough to keep me from getting to you, baby.” Translate the logical statement

$\sim \exists x \in T ((M(x) \land H(x)) \land (V(x) \land L(x)) \land (R(x) \land W(x)))$

This matches the chorus of the timeless “Ain’t No Mountain High Enough” by Marvin Gaye, which has increased in popularity in recent years thanks to the Marvel Cinematic Universe.

Context: 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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