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The Paradox of Epimenides rests on an inconsistent statement
ARISTODEMOS -- Αριστόδημος -- Luigi Tellini --
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I think everybody must be interested in paradoxes: life is not only a tautology but also a mysterious paradox. So I created this site to share opinions about a much more simple problem, the
Epimenides Paradox
In our opinion the statement of the cretan Epimenides ( "All Cretans are liars" = I am a liar ) is logically impossible if it is believed that a Liar is always obliged to declare false sentences.
In this case nobody who pretends to be logical, can say " I am a liar ". We must be made aware of a well camouflaged trick: the sentence is inconsistent. But there's more.
The statement "I am a Liar" should not come to be classified as true or false. In a logical world of Liars who must always tell lies, the statement is objectively inexpressible.
The statement is "ineffable". The adjective "ineffable" does not define a truth value (True/False) but it does define an existence value (Real/Imaginary).
Raymond Smullyan had imagined an island inhabited only by Knights who always told the truth and Knaves who always told lies and, in this context, he enjoyed creating paradoxical situations.
Today, or in the near future, it would be possible to create two evolved Robots capable of fluent, human-like conversation. One Robot is programmed to make only true statements and the other to make only false statements. The robots are locked in a room and their conversation is continuously recorded. In this situation, even if we recorded their conversation for ten years, we could never record a statement of "status" such as "I am a liar". For the logic with which they have been programmed, this declaration is "ineffable" for them.
If we think that a Liar is allowed to say even true sentences then you can jump directly to the solution set out in the section "Three Kinds of Liars".
If you are also interested in the other form of paradox expressed as "This sentence is false", then you can skip directly to the subsection "Some Variants of the Paradox".
Please, read more.
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To share opinions you can contact me at this email address: l.tellini77@gmail.com
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