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That is the liar's paradox.


There are many solutions. The most practical being the limitations of language in assigning truth values.


Another solution is that one merely assumes the principle of bivalence to the statement -- the excluded middle. The more popular alternative to binary logic is involves three possible truth values -- true, false and unknown. there are also finite-valued and infinite-valued logical systems.


This is essentially what godel proved in his incompleteness theorem.


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