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Honest Oscar was a cruel criminal, but he always spoke the truth.

After being swindled by Lying Larry (another cruel criminal, and a much less honest one), Oscar confronted Larry on the roof of a tall building.

"You've lied to me," said Oscar, lifting his handgun. "And I am going to kill you now. But first, I want you to talk."

There was a dramatic pause.

"If what you say is true," said Oscar, "I will shoot you. If you lie or remain silent, I will push you off the roof."

A sly grin spread across Larry's face. "You are going to push me off the roof."

Oscar considered this.

And then, true to his word, Honest Oscar killed Lying Larry.

How?

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He shot him and pushed him off.

He never said he would push him only if he lied or remain silent.

Actually, he said I am going to kill you now., so killing him, pushing him off the roof and shooting him was the only way to keep his promises.

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  • $\begingroup$ Ah, you're too quick! :) I can't even mark the answer as accepted yet. $\endgroup$ – Yehuda Shapira Mar 15 '16 at 8:27
  • $\begingroup$ Hahahaha. Too often I think about this when people, like Larry, "create" this kind of logical paradoxes. $\endgroup$ – Masclins Mar 15 '16 at 8:32
  • $\begingroup$ Once shot, he will lie still on the rooftop and remain silent forevermore... $\endgroup$ – feelinferrety Mar 15 '16 at 17:56
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Are all false answers lies? If I tell you "you're going to do X" it's less a statement of fact than a prediction. So if upon hearing these words you proceed to do Y instead of X, even though my statement was false, it's not that I've lied so much as that I was merely incorrect, especially since the chief factor in the outcome of my prediction is your behavior and not my own.

Oscar's threat only covers the conditions that Larry's statement is (a) true or (b) dishonest; he is silent on how he will kill Larry if his statement is false but sincere. In this case, Oscar is free to kill Larry any way he chooses (although if Oscar decides to push Larry off the roof, Larry's prediction becomes true, and Oscar must also shoot him to fulfill his promise).

But we might also take that a prediction is an expression of personal belief, i.e., that when Larry says "You are going to push me off the roof", it should be understood as "I believe that you are going to push me off the roof". In this case, Larry's statement is honest if he does believe Oscar will push him off the roof, and a lie if Larry believes that he won't. Taken this way, Oscar can now evaluate Larry's statement in both relevant dimensions (true/false and sincere/lie), giving us four possible outcomes:

True and sincere prediction: Oscar must shoot Larry False and sincere prediction: Oscar may kill Larry by any means he chooses False and insincere prediction: Oscar must push Larry off the roof True and insincere prediction: Oscar must shoot Larry and push him off the roof

Since Oscar can't know for sure whether Larry really believes in his stated prediction, his best course of action is to push him off the roof and shoot him, which fulfills Oscar's promise in every eventuality.

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  • $\begingroup$ This is a good point - Oscar did specify in his phrasing that the first was "if what you say is true" rather than if he wasn't lying, but the second was based on the subjective non-factual state of lying. $\endgroup$ – Samthere Mar 16 '16 at 11:02

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