1. The Liar 说谎者悖论 英文解析 逻辑学教材(2)

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

that these three situations are genuinely paradoxical, i.e., some statement must be false if it is true, must be true if it is false, and no third option is possible.

In all four variations, the truth of a sentence directly or indirectly implies its own falsehood (which is a contradiction), and the sentence s falsity directly or indirectly implies its own truth (which is a contradiction). By itself, one of these contradictory results merely would constitute a valid reductio ad absurdum/indirect proof for the non-contradictory denial of the assumption (of either truth or falsehood). But, both contradictory results together generate ineliminable contradictoriness: we must hold as true what we cannot hold as true…and the mind boggles. (Such paradoxes are also called . )

II. In the New Testament

In his Epistle to Titus, the Apostle Paul complains of the Cretans adding:2

One of themselves, even a prophet of their own, said, The Cretans are always liars, evil beasts, slow bellies. This witness is true.

According to St. Paul, then, there is a Cretan prophet who asserts that the Cretans always lie, which implies, of course, that the Cretan prophet himself is lying.3 Now, that s fine; but in adding that the Cretan prophet is telling the truth, Paul brutely contradicted himself.

1. Epimenides is a Cretan.

2. Epimenides said, “The Cretans are always liars.”

*3. This witness is true, i.e., what Epimenides said is true.

4. Therefore, “The Cretans are always liars” is true. [by (2) & (3)]

5. Therefore, the Cretans are always liars. [by (4)]

6. Therefore, Epimenides always lies. [by (1) & (5)] when he said, “The Cretans are always liars.” [by (6)]

8. Therefore, what Epimenides said is false, i.e., this witness is false. [by (7)] Contradiction: (3) & (8)! St. Paul s assertion that Epimenides told the truth

implies that Epimenides lied.

Though the Apostle seems not to have realized it, we know that his self-contradiction constitutes a valid reductio ad absurdum (or is it a consequentia mirabilis?) that (3)—his assertion that the witness is true—is false.

Have we just disproven the thesis of Biblical literalism—every statement in the Bible is

2literally true? Titus 1: 12-13. The mentioned Cretan prophet was probably Epimenides, and the Liar Paradox is often called the Epimenidean Paradox. 3 By the way, a Cretan is a person from Crete while a cretin is an idiot. You re bound to insult somebody if you mix the two words up, so get it straight. (Originally, a cretin was someone who suffered the crippling mental and physical results of thyroid disease. The word cretin comes from the Swiss French crestin’ meaning Christian. That is, these unfortunates, though retarded and deformed, are still human beings.)

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