# Predicate Logic and Popular Culture (Part 33): The Eagles

Let $H(x,y,t)$ be the proposition “$x$ hurts $y$ at time $t$.” Translate the logical statement

$\exists x \exists y \exists t (0 \le t \le T \land H(x,y,t))$

into plain English, where the domain for $x$ and $y$ are all people, the domain for $t$ is all times, time $0$ is now, and time $T$ is when the night is through.

The simple way to translate this statement is “There are two people so that the first person will hurt the second person at some time between now and when the night is through.” A somewhat briefer way of expressing this thought is made in the first line of this popular song by The Eagles.

Context: Part of a 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 some time 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.