# Predicate Logic and Popular Culture (Part 9): One Direction

Let $S(x,y,t)$ be the proposition “ $x$ sees $y$,” and let $K(x,y)$ be the statement “ $x$ understands why $y$ wants $x$ so desperately.” Translate the logical statement $\forall x (S(\hbox{I},x) \Longrightarrow S(\hbox{you},x)) \Longrightarrow K(\hbox{you},\hbox{I})$,

where the domain is all things.

The clunky way of translating this into English is, If, whenever I see something, you also see it, then you will understand why I want you so desperately.” Of course, this is the second half of the chorus of the following hit by One Direction:

A note in translation: the song actually says “If only you could see what I can see.” In mathematics, of course, the word if and the phrase only if have different meanings, but there is no meaning ascribed to if only. For the purposes of this exercise, I took if only to mean an emphasized version of if, which seems to make the most sense in the song. 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. While I’m marginally on the topic, I should mention the parody song That Makes It Invertible which covers the various equivalent ways of verifying that a matrix has an inverse.

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