Predicate Logic and Popular Culture (Part 17): Richard Nixon


Let H(x,y) be the proposition “x hates y,” let W(x) be the proposition “x wins,” and let $D(x,y)$ be the proposition “x destroys y.” Translate the logical statement

\forall x (H(x,\hbox{you}) \Longrightarrow (H(\hbox{you},x) \Longleftrightarrow W(x) \land D(\hbox{you},\hbox{you}))),

where the domain is all people.

The clunky way of translating this into English is, “If anyone hates you, they win and you destroy yourself exactly when you hate them too.” When rewritten, this is one the remarkably poignant final remarks of Richard Nixon’s farewell address to the White House staff before resigning the presidency in 1974.

A technical note: this famous address of Nixon did not explicitly say “Others don’t win when you don’t hate them,” but this inverse implication was certainly implied.

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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