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, 1:12, and identified as such by Clement of Alexandria:
The logical inconsistency of a Cretan asserting all Cretans are always liars may not have occurred to Epimenides, nor to Callimachus, or 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 and 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.
Several interpretations and analyses are available, if the statement is considered false. It might be contended that the truth-value "false" can be consistently assigned to the simple proposition that "All Cretans are liars," so that this statement by itself, when deemed false, is not, strictly speaking, paradoxical. Thus, if there ever existed a Cretan (not Epimenides in this instance) who even once spoke the truth, the categorical statement "All Cretans are (always) liars," would be false, and Epimenides might be simply regarded as having made a false statement himself. But if Epimenides' statement is understood as in essence asserting its own falsehood, then the statement cannot consistently be false, either, because its falsehood would imply the truth of its self-asserted falsehood.
An interesting asymmetry is possible under one interpretation: the statement's truth clearly implies its falsehood, but, unless the statement is interpreted to refer specifically to itself (rather than referring categorically to all statements by Cretans), the statement could be contingently false without implying its own truth.
Paradoxical versions of the Epimenides problem are closely related to a class of more difficult logical problems, including the liar paradox, Russell's paradox, and the Burali-Forti paradox, all of which have self-reference in common with Epimenides. Indeed, the Epimenides paradox is usually classified as a variation on the liar paradox, and sometimes the two are not distinguished. The study of self-reference led to important developments in logic and mathematics in the twentieth century.
An oblique reference to Epimenides in the context of logic appears in "The Logical Calculus" by W. E. Johnson, Mind (New Series), volume 1, number 2 (April, 1892), pages 235-250. Johnson writes in a footnote,
The Epimenides paradox appears explicitly in "Mathematical Logic as Based on the Theory of Types", by Bertrand Russell, in the American Journal of Mathematics, volume 30, number 3 (July, 1908), pages 222-262, which opens with the following:
In that article, Russell uses the Epimenides paradox as the point of departure for discussions of other problems, including the Burali-Forti paradox and the paradox now called Russell's paradox. Since Russell, the Epimenides paradox has been referenced repeatedly in logic. Typical of these references is Gödel, Escher, Bach by Douglas Hofstadter, which accords the paradox a prominent place in a discussion of self-reference.
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Oct 01, 2006; The next sentence is true. But the previous sentence is false. Epimenides of Knossos (Crete) was a semi-mythical philosopher-poet...