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Liar Paradox

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The Liar Paradox

By James Donahue

"This sentence is false."

The sentence is known as the liar paradox. This is because the statement can be neither true nor false. If you think about it long enough, it could drive you nuts. It has had world philosophers scratching their heads without anyone finding a way out of the paradox built within.

The paradox here is that if the sentence is really false, then it is true. Thus the sentence cannot be false. But if we argue that the sentence is true, then saying that it is false is not true.

Do you see how befuddled a paradox like this can get your brain?

There is another similar puzzle linked to what is called the card paradox. The card has statements printed on both sides. On the front it says: "The sentence on the other side of this card is true." On the back it reads: "The sentence on the other side of this card is false."

Thus it is impossible to assign a truth value to either statement. Thus we find ourselves caught up in another paradox, similar to saying "This statement is false."

If we try to reason the card paradox, we find ourselves wrapped in the same dilemma. If the first statement is true, then so is the second statement. But if the statement on the back of the card is true, then the statement on the front is false. Thus if the first statement is true, then the second statement has to be false. And if the first statement is false, then the second statement also must be false. But in this dilemma, can either statement be true?

We can debate such paradoxical issues until the cows come home, but other than coming up with a complex philosophical or mathematical equation that tries to assess a possible solution, there really cannot be a good answer. This is the ultimate paradox.

In the old Star Trek television dramas, Captain Kirk and Harry Mudd used the liar paradox to confuse and disable an android that was holding them captive. The machine operated on a computerized brain that was unable to solve such a strange riddle. That is because there can be no rational answer.