Seduction 101 for Logicians and Economists

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.

Seduction by a Logician

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.

A Similar Financial Con Game

Consider now a slight variant of the above story. Suppose an investment con man is talking to a prospective client.

He flatters the client, tells him about the stock newsletter he e-mails to his clients, and asks, "Will you right now solemnly promise to give me your e-mail address if I make a true statement and, conversely, not give it to me it if I make a false statement?"

Feeling that this is a harmless request to consider his newsletter, the prospective client promises. The con man then makes the statement: "You will neither invest all your money with me today nor give me your e-mail address."

As with the seduction above, note that the prospective client can't give the con man his e-mail address since if he were to do so, the con man's statement would be made false, and so he would have broken his promise to give him his e-mail address only if the con man made a true statement. Therefore, he must not give the man his e-mail address under any circumstances.

But if he also refuses to invest all his money with the con man, the latter's statement becomes true, and this would require him to give his e-mail address. The only way the prospective client can keep his promise is to invest all his money with the con man so that the latter's statement becomes false. Again, a seemingly innocuous promise ensnares somebody.

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