P and ~P = F, and truth value can be assigned to the statement, hence, it is not a logical paradox. This is sentential logic, which can be sound and complete, that means there cannot be any paradox in sentential logic. Paradox exists because of incompleteness, that means, it has to be at least first order logic, where self-referencing/recursive definition is possible, like liar paradox, "this statement is false," there cannot be any meaning truth assignment to the sentence without contradicting itself.