There is more than one way to understand Russell’s famous logical puzzle about the present king of France, and moreover it’s one of those puzzles that is used to show more than one thing (even things that Russell never intended), but suppose you understand the puzzle like this:
“The present king of France is bald” must be either true or false. But it is not true, for there is no PKoF. But it is not false either, for then the contradictory statement would be true: “The PKoF is not bald”, which is not the case, since he doesn’t exist. In other words, both sides of the contradiction are false for the same reason: there is no King of France. Both sides of a contradiction are false! The principle of contradiction has no value!
The simpler response is that the affirmation “…is bald” is false, and the contradictory is true, precisely as it contradicts. It is true to say that the PKoF is “not bald” where “not bald” is taken as indeterminate to whether the PKoF exists or not. The PKoF is not bald because he is not anything at all. Our current president is not bald, but neither is last Tuesday or happiness, though for different reasons: the first because he has hair, the second because they are not the sort of things that can be bald or not. When we say “not bald”, both must be taken as possibilities, and the second possibility verifies the truth of the statement “the PKoF is not bald”.
This is generally true of truths that are generated out of the principle of contradiction. The falsity of the affirmation guarantees the truth of the denial only so far as the denial prescinds from whether something exists or not. To say “either p or not p” is deceptive, since “not p” must be taken as open to the existence or non-existence of the subject.