Predicate Logic and Popular Culture (Part 110): Louis Armstrong

Let L(x,y) be the proposition “x loves y.” Translate the logical statement

\forall x L(x, \hbox{my baby}) \land L(\hbox{mybaby},\hbox{me}) \land \forall y(L(\hbox{my baby}, y) \Rightarrow y = \hbox{me}).

This matches this classic song from the 1930s.

Indeed, the lyrics of this song have some fun implications. If “everybody loves my baby, but my baby don’t love nobody but me,” then who is “my baby”? Suppose, for the sake of contradiction, that “my baby” is someone other than “me.” This is a problem because everyone loves “my baby,” but it’s impossible for “my baby” to love someone else other than “me.” So this can’t happen.

Therefore, we can conclude from the lyrics of the song that “I am my baby.”

Logic is powerful stuff.

green line

Context: 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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