Analyzing False Arguments

One must be careful not to readily accept the premises and hypothesis of a given argument without first carefully scrutinizing each component of the argument for form and validity. Consider the following apparent conundrum:

Three travelers go into a hotel together and ask to rent a single room for the night for the three of them to share. The desk clerks says “That will be thirty dollars.” Each traveler pays ten dollars and then the three of them are shown to the room that they will share for the night. Later, the desk clerk realizes that since it is a Friday night, the travelers were entitled to a five dollar per night weekend discount making the correct price for the room twenty-five dollars. The desk clerk takes five one-dollar bills out of the till and hands them to the bellhop with instructions to for him to deliver the refund to the travelers who just came in. On the way to the room, the bellhop decides to pocket two of the one-dollar bills. Upon arriving at the travelers’ room, the bellhop returns three of the five dollars to the travelers in the room.

Now the conundrum: The travelers each paid nine dollars. Three travelers times nine dollars is twenty-seven dollars. The bellhop has two dollars in his pocket. The twenty-seven dollars the travelers paid plus the two dollars in the bellhop’s pocket equals twenty-nine dollars. The original price charged for the room was thirty dollars. Thirty dollars minus twenty-nine dollars equals one dollar. What happened to the missing dollar?

The answer is that nothing happened to the missing dollar because there isn’t a dollar missing. The travelers paid twenty-seven dollars for the room. The desk clerk took twenty-five dollars and the bellhop took two dollars. The twenty-five dollars the desk clerk took plus the two dollars the bellhop took plus the three dollars the travelers received back totals the thirty dollars the travelers originally paid for the room.

Whether or not the reader of this apparent conundrum was fooled by it is not crucial to its point being understood. The reason for the apparent conundrum is that, in the recounting of the story, the reader was told how to view the facts and how to reason through them. Upon close scrutiny the facts were found to be true, but the reasoning used was faulty. This is why each component of an argument must be rigorously tested against logic, reason and fact. This is also why the “Argument from Evil” ultimately fails.

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