Seduction 101 for Logicians and Economists
April 5, 2009 — -- Elementary propositional logic (the logic of "and," "or," "not," and "if... then...") can sometimes give rise to vexing puzzles. Here is one rather whimsical example that occurred to me after reading about Bernard Madoff's Ponzi scheme (and others) and being struck by the word "seductive" appearing in some of the news accounts.
Being a logician, I thought of a kind of seduction that relies on logic rather than psychology to ensnare and entangle its targets.
Let me first state the puzzle in terms of a more standard sort of seduction.
Suppose a man flirts with a woman and then asks her, "Will you solemnly promise to give me right now your telephone number if I make a true statement and, conversely, not give me your number if I make a false statement?"
Maybe he can soften the statement a bit, but let's assume that this is its gist.
Feeling that this is a flattering and benign request, the woman promises to give him her number if and only if he makes a true statement.
The man then makes his statement: "You will neither give me your telephone number now nor will you sleep with me tonight."
What's the trick? Note that she can't give him her number since, if she were to do so, his statement would be made false, and so she would have broken her promise to give him her number only if he made a true statement. (This is the crux of it.) Therefore, she must not give him her number under any circumstances.
But if she also refuses to sleep with him, his statement becomes true, and this would require her to give him her number.
The only way she can keep her promise is to sleep with him so that his statement becomes false. The woman's seemingly innocuous promise ensnares her.
Fortunately or unfortunately, I suspect that the class of people for whom this seduction technique would prove effective is probably rather small. Nevertheless, it might make an interesting premise for a Star Trek episode or perhaps form part of a logicians' dating manual.
