# Predicate Logic and Popular Culture: Index

I’m doing something that I should have done a long time ago: collecting a series of posts into one single post. The following links comprised my series on using examples from popular culture to illustrate principles of predicate logic.

Unlike other series that I’ve made, this series didn’t have a natural chronological order. So I’ll list these by concept illustrated from popular logic.

Logical and $\land$: Part 1

• Part 1: “You Belong To Me,” by Taylor Swift
• Part 21: “Do You Hear What I Hear,” covered by Whitney Houston
• Part 31: The Godfather (1972)
• Part 45: The Blues Brothers (1980)
• Part 53: “What Does The Fox Say,” by Ylvis
• Part 54: “Billie Jean,” by Michael Jackson

Logical or $\lor$:

• Part 1: Shawshank Redemption (1994)

Logical negation $\lnot$:

• Part 1: Richard Nixon
• Part 32: “Satisfaction!”, by the Rolling Stones
• Part 39: “We Are Never Ever Getting Back Together,” by Taylor Swift

Logical implication $\Rightarrow$:

• Part 1: Field of Dreams (1989), and also “Roam,” by the B-52s
• Part 2: “Word Crimes,” by Weird Al Yankovic
• Part 7: “I’ll Be There For You,” by The Rembrandts (Theme Song from Friends)
• Part 43: “Kiss,” by Prince
• Part 50: “I’m Still A Guy,” by Brad Paisley

For all $\forall$:

• Part 3: Casablanca (1942)
• Part 4: A Streetcar Named Desire (1951)
• Part 34: “California Girls,” by The Beach Boys
• Part 37: Fellowship of the Ring, by J. R. R. Tolkien
• Part 49: “Buy Me A Boat,” by Chris Janson
• Part 57: “Let It Go,” by Idina Menzel and from Frozen (2013)

For all and implication:

• Part 8 and Part 9: “What Makes You Beautiful,” by One Direction
• Part 13: “Safety Dance,” by Men Without Hats
• Part 16: The Fellowship of the Ring, by J. R. R. Tolkien
• Part 24 : “The Chipmunk Song,” by The Chipmunks
• Part 55: The Quiet Man (1952)

There exists $\exists$:

• Part 10: “Unanswered Prayers,” by Garth Brooks
• Part 15: “Stand by Your Man,” by Tammy Wynette (also from The Blues Brothers)
• Part 36: Hamlet, by William Shakespeare
• Part 57: “Let It Go,” by Idina Menzel and from Frozen (2013)

Existence and uniqueness:

• Part 14: “Girls Just Want To Have Fun,” by Cyndi Lauper
• Part 20: “All I Want for Christmas Is You,” by Mariah Carey
• Part 23: “All I Want for Christmas Is My Two Front Teeth,” covered by The Chipmunks
• Part 29: “You’re The One That I Want,” from Grease
• Part 30: “Only You,” by The Platters
• Part 35: “Hound Dog,” by Elvis Presley

DeMorgan’s Laws:

• Part 5: “Never Gonna Give You Up,” by Rick Astley
• Part 28: “We’re Breaking Free,” from High School Musical (2006)

Simple nested predicates:

• Part 6: “Everybody Loves Somebody Sometime,” by Dean Martin
• Part 25: “Every Valley Shall Be Exalted,” from Handel’s Messiah
• Part 33: “Heartache Tonight,” by The Eagles
• Part 38: “Everybody Needs Somebody To Love,” by Wilson Pickett and covered in The Blues Brothers (1980)
• Part 46: “Mean,” by Taylor Swift
• Part 56: “Turn! Turn! Turn!” by The Byrds

Maximum or minimum of a function:

• Part 12: “For the First Time in Forever,” by Kristen Bell and Idina Menzel and from Frozen (2013)
• Part 19: “Tennessee Christmas,” by Amy Grant
• Part 22: “The Most Wonderful Time of the Year,” by Andy Williams
• Part 48: “I Got The Boy,” by Jana Kramer
• Part 60: “I Loved Her First,” by Heartland

Somewhat complicated examples:

• Part 11 : “Friends in Low Places,” by Garth Brooks
• Part 27 : “There is a Castle on a Cloud,” from Les Miserables
• Part 41: Winston Churchill
• Part 44: Casablanca (1942)
• Part 51: “Everybody Wants to Rule the World,” by Tears For Fears
• Part 58: “Fifteen,” by Taylor Swift
• Part 59: “We Are Never Ever Getting Back Together,” by Taylor Swift
• Part 61: “Style,” by Taylor Swift

Fairly complicated examples:

• Part 17 : Richard Nixon
• Part 47: “Homegrown,” by Zac Brown Band
• Part 52: “If Ever You’re In My Arms Again,” by Peabo Bryson

Really complicated examples:

• Part 18: “Sleigh Ride,” covered by Pentatonix
• Part 26: “All the Gold in California,” by the Gatlin Brothers
• Part 40: “One of These Things Is Not Like the Others,” from Sesame Street
• Part 42: “Take It Easy,” by The Eagles

# Predicate Logic and Popular Culture (Part 61): Taylor Swift

Let $S(t)$ be the proposition “We are in style at time $t$,” let $C(t)$ be the proposition “We crash down at time $t$,” and let $B(t)$ be the proposition “We come back at time $t$.” Translate the logical statement

$\forall t (\lnot S(t)) \Rightarrow (\forall t(C(t) \Rightarrow \exists u>t(B(u)))$.

The straightforward way of translating this into English is, “If we never go out of style, then whenever we crash down we come back at a later time. This approximately matches the second half of the chorus of one of Taylor Swift’s hit songs.

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 60): Heartland

Let $L(x,t)$ be the proposition “$x$ loves her at time $t$.” Translate the logical statement

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

where $t = 0$ is now.

The clunky translation is “There was a time that I loved her, and nobody loved her before that time.” More succinctly, this is the title of the song that’s been played for countless father-daughter dances at wedding receptions since 2006. (I cannot tell a lie: I always turn into a sobbing and amorphous pile of mush whenever I hear this song.)

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 59): Taylor Swift

Let $T(x)$ be the proposition “You go talk to $x$,” and let $G(x)$ be the proposition “We are getting back together at time $t$.” Translate the logical statement

$T(\hbox{your friends}) \land T(\hbox{my friends}) \land T(\hbox{me}) \land \forall t\ge 0 (\lnot G(t))$,

where time 0 is now.

Of course, this is the ending part of the chorus to “We Are Never Ever Getting Back Together.”

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 58): Taylor Swift

Let $Y(x)$ be the proposition “You are $x$ years old,” and let $L(x)$ be the proposition “$x$ tell you that $x$ loves you,” and let $B(x)$ be the proposition “You believe $x$.” Translate the logical statement

$(Y(15) \land \exists x(L(x))) \Rightarrow B(x)$,

where the domain is all people.

The straightforward way of translating this into English is, “If you are 15 years old and there exists someone who says that he/she loves you, then you believe him/her.” This approximately matches the chorus of one of Taylor Swift’s earliest hits.

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 57): Frozen

Let $C(t)$ be the proposition “The cold bothers me at time $t$.” Translate the logical statement

$\lnot(\exists t\le 0 (C(t)))$,

where the domain is all times and $t=0$ is now.

The straightforward way of translating this into English is, “It is false that there exists a time in the past that the cold bothered me.” Also, DeMorgan’s Laws could be applied:

$\forall t\le 0(\lnot C(t))$,

which can be read “For all times in the past, the cold did not bother me.” Of course, this is the closing line of the chorus of the signature tune from Frozen.

Of course, I can’t mention Frozen without mentioning its parodies; this is the best one that I’ve seen.

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 56): The Byrds

Let $S(x,t)$ be the proposition “$t$ is the season for $x$.” Translate the logical statement

$\forall x \exists t (S(x,t))$.

This pretty much matches the opening line of the 1960s hit song by The Byrds from Ecclesiastes 3.

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 55): The Quiet Man

Let $L(x)$ be the proposition “$x$ is a lock,” let $B(x)$ be the proposition “$x$ is a bolt,” and let $H(x)$ be the proposition “$x$ is in your own mercenary little heart.” Translate the logical statement

$\forall x ( (L(x) \lor B(x)) \Rightarrow H(x))$,

where the domain is all people.

The straightforward way of translating this into English is, “If it’s a lock or a bolt, then it’s in your own mercenary little heart.” With a little more emphasis, this is one of the great lines uttered by John Wayne in the 1952 film The Quiet Man (a wonderful movie which really needs to be digitized and restored to its original brilliance).

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 54): Michael Jackson

Let $p$ be the proposition “Billie Jean is my lover,” let $q$ be the proposition “Billie Jean is a girl,” let $r$ be the proposition “Billie Jean claims I am the one,” and let $s$ be the proposition “The kid is my son.” Translate the logical statement $\lnot p \land q \land r \land \lnot s$.

Naturally, the translation is the chorus of one of Michael Jackson’s iconic hits.

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 53): Ylvis

Let $G(x,y)$ be the proposition “$x$ goes $y$.” Translate the logical statement

$G(\hbox{dog},\hbox{woof}) \land G(\hbox{cat},\hbox{meow}) \land G(\hbox{bird}, \hbox{tweet}) \land G(\hbox{mouse}, \hbox{squeak})$

$\land G(\hbox{cow},\hbox{moo}) \land G(\hbox{frog}, \hbox{croak}) \land G(\hbox{elephant}, \hbox{toot})$

$\land G(\hbox{duck},\hbox{quack}) \land G(\hbox{fish},\hbox{blub}) \land G(\hbox{seal}, \hbox{ow ow ow})$

With the slight exception of one line (“Ducks say quack”), this is the opening verse of perhaps the most head-scratching hit song in modern memory.

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.