Can two statements be true?
I said two opposite statements. "Biconditional Statement" isnt about two opposite statements.
A more modern example is “this sentence is false”: if it is true the sentence is false, then it is false that it is true.
That one was solved by logical axiom which says that category cannot contain more than itself. To put it simply, a statement cannot contain more than itself, but the statement above tries to do exactly that.
It is like saying:
P = P is false.
In this logical error, P contains both itself and more than itself, which logically cannot happen.
Per logical axiom,
P = P
Thus, P cannot be more than P.
Thus, P cannot contain "P is false" in any formal logic, as "P is false" contains P and more than P, thus cannot be contained by P.