Epimenides paradox

The Epimenides paradox is a problem in logic. This problem is named after the Cretan philosopher Epimenides of Knossos (flourished circa 600 BC), who stated Κρῆτες ἀεί ψεύσται, "Cretans, always liars". There is no single statement of the problem; a typical variation is given in the book Gödel, Escher, Bach (page 17), by Douglas R. Hofstadter.

History

The Epimenides paradox, as a problem in logic, appears to have a relatively recent origin, although the statement "Cretans, always liars" has quite a history itself.

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Epimenides was philosopher and religious prophet who, against the general sentiment of Crete, proposed that Zeus was immortal. As he wrote in his poem Cretica,

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:They fashioned a tomb for thee, O holy and high one-

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:The Cretans, always liars, evil beasts, idle bellies!

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:But thou art not dead: thou livest and abidest forever,

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:For in thee we live and move and have our being.

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Denying the immortality of Zeus, then, is the lie of the Cretans. It appears that by "Cretans", Epimenides intended "Cretans other than myself". The phrase "Cretans, always liars" was quoted by the poet Callimachus in his Hymn to Zeus, with the same theological intent as Epimenides. The entire second line is quoted in the Epistle to Titus, chapter 1, verse 12, and identified as such by Clement of Alexandria. In the Epistle to Titus, the phrase has no theological import, and appears to be solely intended to defame the Cretans.

Related Topics:
Callimachus - Epistle to Titus - Clement of Alexandria

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The inconsistency of a Cretan asserting all Cretans are liars does not seem to have occurred to Epimenides, nor to Callimachus, the author of Titus, and Clement. In the original context, Epimenides necessarily meant "Cretans other than myself", so there is no self-reference and thus no logical problem to speak of. The liar paradox was known in antiquity, but it was not associated with Epimenides then. (Saint Augustine restates the liar paradox, without mentioning Epimenides or Titus, in Against the Academicians III.13.29.) Many variations of the liar paradox (called insolubilia) were studied in the Middle Ages, but none of the extant medieval works on insolubilia refer to Epimenides, neither directly nor through the Epistle to Titus. The earliest appearance of Epimenides in the context of a logical problem dates only to the nineteenth century. Since that time, the Epimenides paradox has been commonly employed in discussions of logic.

Related Topics:
Saint Augustine - Against the Academicians - Insolubilia

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