Why is there anything weird about the sentence 'This very sentence is false'? If

Why is there anything weird about the sentence 'This very sentence is false'? If

Why is there anything weird about the sentence 'This very sentence is false'? If it is that the sentence seems to be true AND false, what makes it so different from certain ambiguous sentences which are true and false as well? If it is that the sentence seems to be neither true NOR false, what makes it so different from imperatives and questions which are neither true nor false as well? (The reformulation 'The proposition expressed by this very sentence is false' does not help, it seems, because it fails to express a proposition at all.)

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