A paradox .

Many years ago, a man, Paul the Publican, opens a pub. To get customers, he puts up a large sign in front of his establishment: “Cheaper than all bars in Oldtown.” For a few years, it worked: his bar is packed most nights. In fact, his prices are so cheap that all of the other bars in Newton close for a lack of business.

However, Paul gets tired of Oldtown and moves the pub to the nearby Newtown. Not wanting to pay for a new sign, he keeps the sign in this new location. His bar in Newtown is even more successful, since there are still no bars in Oldtown.

However, one former patron, Grumpy Joe, hates the location and wants the bar to be moved back to Oldtown. Joe comes up with a perfect plan to accomplish this: in Newtown, consumer protections are tough, and there is a law that states all business signs must be true, or the business must be shut down. Joe sues Paul under this law, and the arguments in court get contentious.

“Name one bar in Oldtown that is cheaper than mine,” Paul asks rhetorically. Paul is confident he will win, since his sign is only false if there exists a bar in Oldtown with less expensive beer than his; since there are no more bars in Oldtown, his sign must be true.

“Yes, all the bars in Oldtown are cheaper than yours,” Joe retorts, “precisely because there are no more bars here!” Joe is also confident he will win, because since there are no bars in Oldtown, one cannot find a bar in Oldtown that has higher prices than Paul’s.

The judge in the case did not know what to do. Both parties in the case have argued a true claim. The judge decides to make a compromise. He will not order a shutdown of the bar if Paul puts another sign in front of his bar. Begrudgingly, Paul acquiesces to the judge’s request. Thus, today Paul’s bar has two signs in front:

“Cheaper than all bars in Oldtown.”

“More expensive than all bars in Oldtown.”

Most patrons who enter the bar seem unbothered by this, because there are no better deals around (there are, of course, no worse deals around either).