Epimenides's paradox

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Epimenides

The paradox of Epimenides is the first known pre-form of the liar's paradox and is in the popular version: "Epimenides the Cretans said: All Cretans are liars."

Historical background

The paradox is passed down through the New Testament. In Paul's letter to Titus , the apostle writes about the Cretans, quoting and commenting on a verse by an unnamed Cretan author, Titus 1,12 LUT :

12 One of them, their own prophet, said: The Cretans are always liars, wicked animals and lazy bellies.
12 εἶπέν τις ἐξ αὐτῶν ἴδιος αὐτῶν προφήτης · Κρῆτες ἀεὶ ψεῦσται , κακὰ θηρία, γαστέρες ἀργαί.

The hexameter from a poem that has not survived has been attributed to the Epimenides of Crete (5th, 6th or 7th century BC ) since Clement of Alexandria (150–215 AD ).

The Cretan Paradox was placed first in the series of mathematical-logical paradoxes by Bertrand Russell in 1908 and has been the subject of modern philosophical and mathematical logic ever since. He put it in the popular short form quoted above.

Problems and solutions

The Epimenides saying is not a paradox in the sense of an antinomy , because no logical contradiction can be derived. Rather, there are different consistent solutions, depending on how you specify the term "liar":

  1. Weak reading : a liar is someone who sometimes lies. There is no antinomy here, regardless of whether the statement of Epimenides is true or false. Either the statement of Epimenides is true (according to Paul in Tit 1.13) because all Cretans sometimes lie, including Epimenides, who in this case did not lie, or it is false because there are other Cretans who never lie.
  2. Strong reading according to Russell: Liars never say anything true, they always lie. Here, too, no antinomy can be derived. For assuming that Epimenides' statement is true, it follows that all Cretans always lie, including Epimenides. This contradicts the assumption, which can be considered refuted: So the statement of Epimenides is wrong and there are Cretans who do not always lie. Whether Epimenides is one of these or one of the notorious liars is open. What is certain is that in this case he lied.

However, when tightened by Bertrand Russell to "A man says: I am lying", the Epimenides saying results in the real liar paradox , since the assertion only relates to the current utterance.

variant

In the Old Testament there is a more general form in the book of Psalms 116.11 EU :

"In my dismay, I said: All people are liars!"

Web links

  • Christoph Zimmer: The liar antinomy in Titus 1:12. (PDF; 328 kB) In: Linguistica Biblica 59, 1987, pp. 77-99, 2nd Ed. 2006. 2nd Ed. 2006, accessed January 6, 2013 .

Individual evidence

  1. ↑ a b c d Bertrand Russell: Mathematical logic as based on the theory of types , in: American Journal of Mathematics 30 (1908), page 222.
  2. ↑ It does not come from a quatrain of the poem "Cretica", because this is a modern construction that can be read in: James Rendel Harris : The Cretans always liars , in: The Expositor, Volume II, 1906, pp. 305-317 ( Archive.org ). Harris: A further note on Cretans, in: The Expositor, Volume III 1907, pp. 332-337; there p. 336 ( archive.org ) the constructed quatrain was rated by the author himself as “Perhaps that will do for a first attempt to restore the lost passage of Epimenides”.
  3. ↑ Diels-Kranz : The Fragments of the Pre-Socratics, 2005 edition, I 3B1
  4. ^ Bertrand Russell, Alfred N. Whitehead : Principia Mathematica , Volume I (1910), p. 63.