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Oh, you// anything that rhymes is not true.

If this statement is true, then it is false.

First, although it seems very logic to me, is this reasoning correct? If so, how do you call this kind of "situation" in logic? Could we say that it is a paradox in the strict definition of the word? Do you have other interesting examples?

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  • Let that sentence be called S. Then S is either True of False. If S is true, then it is false. So, contradiction! So S is false and nothing happen.
    – Darae-Uri
    Commented Nov 23, 2015 at 10:46
  • If you want to construct an interesting example, google "Liar paradox"
    – Darae-Uri
    Commented Nov 23, 2015 at 10:48

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Your sentence implies its own falsity, therefore it is false. However, its being false does not imply that it is true. As such, it might be said to be half of the liar paradox. In a liar paradox ("this sentence is not true") the truth of the sentence implies its falsity, while its falsity implies its truth. There is a huge amount of literature trying to explain the liar paradox.

I wouldn't say your example is genuinely paradoxical, it is merely strange to say something that implies its own falsehood. Another example would be "all generalisations have exceptions". This is clearly itself a generalisation, so if it is true, it has an exception, which implies that it is false. But it being false does not imply that it is true, so it is simply false.

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