Smullyan’s Ham Sandwich Argument

Many, if not most, attacks on free markets take the form of the Straw Man logical fallacy. Instead of stating the views or your opponent in fair terms that the other party would accept  you create a “straw man” attack in its place. This straw man is easy to defeat and you pound Mr. Strawman unmercifully.  Irrelevant to the actual argument as the strawman might be; you declare victory and move on. The Straw Man fallacy is well known and fairly easy to spot.

A more subtle and sophisticated version of the Strawman fallacy was presented by Raymond Smullyan  in his book What Is the Name of This Book? (1978), He called it the Ham Sandwich Argument. Dr. Smullyan is a famous logician. (and a magician, a musician, and a mathematician) He claimed he could prove that a ham sandwich was better than eternal happiness.

“Certainly you would agree,” he said, “that nothing is better than eternal happiness.”

“Of course.”

“But you have to admit that a ham sandwich is better than nothing!”

“But…”

“And by the transitive property, therefore, we see beyond a doubt that a ham sandwich is better than eternal happiness. Q.E.D.”

Funny and very clever, and it shows that to change definitions mid-argument leads to fallacy. That is, the ‘nothing’ in the first statement means, “there is no thing” whereas the ‘nothing’ in the second statement means, “not having anything”. Don’t let anyone do that to you!


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