The liar's Paradox
is sometimes called the Cretan Paradox
because it was first thought to be expressed by a Cretan, Epimenides as:
"Cretans always lie."
This (slightly paraphrased) statement, made by a Cretan, demonstrates the paradox. If the statement is true then the statement is necessarily a lie, and can't be true. Strangely, the statement is not a very good example of what has come to be known as the Cretan Paradox. A more generalized version of this statement, and a much better representation of the paradox, can be expressed as:
"This sentence is false."
In this more generalized form, the paradox is fully exposed. Here, the statement can't be true (since it asserts its own falseness), but it can't be false, either (since it would then be a true statement, which it would not be). This demonstrates the shortcomings of our current understanding of logic, or at least points up that more work may need to be done.
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More recent interpretations of Godel's incompleteness theorem, (circa. 1930s) and attempts to informally state it, have led to an interesting twist on the paradox, i.e.,:
"This sentence is not provable."
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Saint Paul (formerly Saul of Tarsus), mentioned the original statement about Cretans in the New Testament of the Bible:
Even one of their own men, a prophet from Crete, has said about them, "The people of Crete are all liars, cruel animals, and lazy gluttons." — Titus 1:12: