1. The Liar 说谎者悖论 英文解析 逻辑学教材

全面解析the paradox of the liarfrom the different components of modern logic to the ancient greek philosophical thinking

The Paradoxes of Eubulides of Miletus (4th century B.C.)

1. The Liar

“When I lie and admit that I lie, do I lie or speak the truth?”1

I. The Paradox

A statement that directly or indirectly predicates falsehood of itself is logically

pathological in the worst, most mind-boggling way. Such sentences are called : This sentence is false.

-That sentence, like every other, must be either true or false.

-If the sentence is true, then it follows that what it says is the case. It says that it is false, and, since what it says is the case, it therefore is false. So, if the sentence is true, then it follows that it is false. Contradiction.

-Therefore (by reductio ad absurdum/~I), the sentence This sentence is false cannot be true and, so, must be false.

-But if the proposition is false, then it follows that what it says is not the case. It says that it is false, and, as what it says is not the case, it follows that it is not the case that it is false. Therefore, the sentence is true. So, if the sentence is false, then it follows that it is true. Contradiction.

-Therefore (by reductio ad absurdum), the sentence This sentence is false cannot be false and, so, must be true, which (as we proved) it cannot be…???!!!

As the argument shows, a proposition that directly or indirectly says of itself that it is false must be either true of false (like any other proposition), and, pathologically, cannot be either.

: I am lying.

: The following sentence is false.

The preceding sentence is true.

Hmwk. 1. Show in full and precise detail (on the model of my previous demonstration) 1 Aulus Gellius, Attic Nights, vol. 3, bk. XVIII, ch. II.

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