Crimes and Punishments

Torrengo, Giuliano; Varzi, Achille C.

John was driving 150 km/h. The law says you cannot exceed 130 km/h, so John got fined. He got fined twice. “Why twice?” Because there were two speed detection devices—one at km 50 and one at km 100—so they caught him twice. “What if the devices were closer to each other, at km 50 and at km 60?” Same story: if they catch you twice, you get fined twice. “What if there was a third device in between, at km 55?” Three devices, three measurements, three infractions—hence three fines. “But they could measure any number of times in between. What if they placed a device every kilometer?” They would fine you for each time a distinct device would measure an infraction. “But that is absurd. By that pattern, I could be fined uncountably many times for speed driving a single meter.”A “pattern” is a mathematical abstraction, and no one will ever risk bankruptcy for a brief infringement of the Traffic Code. But John’s lawyer has a point. How long should the infringement last in order for two or more fines to be applicable? A fine is a punishment in which we incur if we perform a forbidden action—a crime—and there is a strong intuition to the effect that crimes and punishments should go hand in hand: every criminal act ought to be matched by a corresponding punishment, and every punishment ought to reflect a criminal act. We know how to count punishments, especially if they come in the form of a fine. But how do we count crimes?



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November 24, 2014