Predicate Logic and Popular Culture (Part 46): Taylor Swift

Let L(t) be the proposition “I live in a big old city at time t,” and let M(x) be the proposition “You are mean at time t.” Translate the logical statement

(\exists t>0 \forall s \ge t L(s)) \land \forall s \ge 0 (M(s)),

where the domain is all times and time 0 is now.

The straightforward way of translating this into English is, “There exists a time in the future that I will live in a big old city for all times after that time, and you will be always be mean.” More lyrically, this is part of the chorus of one of Taylor Swift’s biggest hits.

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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