Predicate Logic and Popular Culture (Part 50): Brad Paisley

Let $S(x,y)$ be the proposition “ $x$ sees $y$ , and let $T(x,y)$ be the proposition “ $x$ thinks $y$ .” Translate the logical statement

$(S(\hbox{you}, \hbox{deer}) \Rightarrow S(\hbox{you}, \hbox{Bambi}))$

$\land (S( \hbox{I}, \hbox{deer} ) \Rightarrow S( \hbox{I}, \hbox{antlers up on the wall}))$

$(S(\hbox{you}, \hbox{lake}) \Rightarrow T(\hbox{you}, \hbox{picnic}))$

$\land (S( \hbox{I}, \hbox{lake} ) \Rightarrow S( \hbox{I}, \hbox{a large mouth up under that log}))$

This almost perfectly matches the opening two lines of Brad Paisley’s “I’m Still A Guy.”

And I can’t resist also showing a clip of Tim Tebow singing along to the chorus when Brad Paisley had a concert in Denver and Tebowmania was at an all-time high.

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.

Predicate Logic and Popular Culture (Part 49): Chris Janson

Let $M(x)$ be the proposition “Money can buy me $x$ .” Translate the logical statement

$\lnot(\forall x (M(x))) \land M(\hbox{a boat})$ .

The straightforward way of translating this into English is, “It is false that money can buy me everything, and money can buy me a boat.” These are the closing lines of the chorus of the title song of Chris Janson’s debut country album.

Predicate Logic and Popular Culture (Part 48): Jana Kramer

Let $K(x,t)$ be the proposition “He kisses $x$ at time t.” Translate the logical statement

$\exists t_1 <0 (K(\hbox{I}, t_1) \land \forall t < t_1 \forall x( \lnot K(x,t)))$

$\land \exists t_2 <0 (K(\hbox{she}, t_2) \land \forall t > t_2 \forall x( \lnot K(x,t)))$ ,

where time 0 is now.

The straightforward way of translating this into English is, “There was a time in the past that he kissed me, and no one kissed him before then; and there will be a time in the future that he’ll kiss her, and no one will kiss him after that.” More succinctly, this is the first line of the chorus of one of country music’s biggest hits from 2015.

Predicate Logic and Popular Culture (Part 47): Zac Brown Band

Let $F(x)$ be the proposition “ $x$ is a good friend,” let $S(x)$ be the proposition “ $x$ lives down the street,” let $G(w)$ be the proposition “ $w$ is a good-looking woman,” let $A(w)$ be the proposition “ $w$ has her arms around me,” let $p$ be the proposition “I am in a small town where it feels like home,” let $N(x)$ be the proposition “I have $x$ ,” and let $H(x)$ be the proposition “I need $x$ .” Translate the logical statement

$\exists x_1 \exists x_2(F(x_1) \land F(x_2) \land S(x_1) \land S(x_2) \land x_1 \ne x_2)$

$\land \exists w(G(w) \land A(w)) \land p \land \forall x (N(x) \Leftrightarrow H(x))$ .

I think this is a reasonable translation of the chorus of one of country music’s big hits from 2015.

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.

Predicate Logic and Popular Culture (Part 45): The Blues Brothers

Let $p$ be the proposition “It is dark,” and let $q$ be the proposition “We’re wearing sunglasses.” Translate the logical statement

$p \land q$

Of course, this is one of the many great lines from The Blues Brothers.

Predicate Logic and Popular Culture (Part 44): Casablanca

Let $C(x)$ be the proposition “ $x$ is in Casablanca,” and let $S(x,y)$ be the proposition “ $x$ has less scruples than $y$ .” Translate the logical statement

$C(\hbox{Rick}) \land S(\hbox{Rick}, \hbox{I}) \land \forall x (C(x) \land x \ne \hbox{Rick} \Rightarrow \lnot S(x,\hbox{I})$ ,

where the domain is all people.

The straightforward way of translating this into English is, “Rick is in Casablanca and has less scruples than I, and everyone else in Casablanca who isn’t Rick doesn’t have less scruples than I.” Naturally, this is one of the great lines of the movie Casablanca:

Ricky, I’m going to miss you. Apparently you’re the only one in Casablanca with less scruples than I.

Predicate Logic and Popular Culture (Part 43): Prince

Let $p$ be the proposition “You are rich,” let $q$ be the proposition “You are my girl,” let $r$ be the proposition “You are cool,” and let $s$ be the proposition “You rule my world.” Translate the logical statement

$\lnot(q \Rightarrow p) \land \lnot(s \Rightarrow r)$ .

The straightforward way of translating this into English is, “It is false that if you’re my girl, then you’re rich, and it’s false that if you rule my world, then you’re cool.” This is the chorus of one of Prince’s biggest hits. Unfortunately, I can’t find a good version of Prince’s song on YouTube, so here’s a cover by Tom Jones instead.

More recently, this song was covered near the start of the animated movie Happy Feet.

Predicate Logic and Popular Culture (Part 42): The Eagles

Let $p$ be the proposition “I am running down the road,” let $q$ be the proposition “I am trying to loosen my load,” let $M(x)$ be the proposition “ $x$ is on my mind,” let $W(x)$ be the proposition “ $x$ is a woman,” let $O(x)$ be the proposition “ $x$ wants to own me,” let $S(x)$ be the proposition “ $x$ wants to stone me,” and let $F(x)$ be the proposition “ $x$ says that $x$ is a friend of mine.” Also, let $I$ be the index set $\{1,2,3,4,5,6,7\}$ . Translate the logical statement

$p \land q \land \exists x_1 \exists x_2 \exists x_3 \exists x_4 \exists x_5 \exists x_6 \exists x_7$

$(\forall i \in I (M(x_i) \land W(x_i)) \land \forall i \in I ( i \le 4 \Rightarrow O(x_i))$

$\land \forall i \in I (5 \le i \le 6 \Rightarrow S(x_i)) \land F(x_7)$

$\forall i \in I \forall j \in I(i \ne j \Rightarrow x_i \ne x_j))$

where the domain is all people.

Believe it or not, this forms the opening two lines of the classic song by the Eagles. (The last line of the statement is needed to ensure that the seven women are seven different women.)

Predicate Logic and Popular Culture (Part 41): Winston Churchill

Let $H(x)$ be the proposition “He has $x$ ,” let $L(x)$ be the proposition “I like $x$ ,” let $G(x)$ be the proposition “ $x$ is a virtue,” and let $B(x)$ be the proposition “ $x$ is a vice.” Translate the logical statement

$\forall x((G(x) \land \lnot L(x)) \Longrightarrow H(x)) \land \forall x((B(x) \land L(x)) \Longrightarrow \land \lnot H(x))$ ,

where the domain is all character traits.

After a straightforward translation, this reads, “If a character trait is a virtue that I don’t like, then he has it, and if a character trait is a vice that I like, then he doesn’t have it.”

This logical expression matches one of the most famous quotes by Winston Churchill when describing a political contemporary: “He has all of the virtues I dislike and none of the vices that I admire.”