The statement “This statement is false.” is as arbitrary as the statement “Invisible pink elephants are very smart.”. Hence they are neither true nor false. Only statements that about something that exists can be true or false. A proposition cannot be both true and false at the same time, because a contradiction cannot exist. But, as above example demonstrates, there’s such a thing as a bad proposition. The proposition in question is invalid because it is detatched from reality. To what does “this statement” refer to?