What is the the truth value, if they have one, of propositions whose subject do not exist? "The current king of France is bald" is the famous example. Is that true or false, or neither? I have a hard time understanding how the current king of France can be neither bald nor not bald, even though I have no trouble understanding that there is no current king of France.
Philosophers have given various answers to questions like yours. See, for example, this SEP entry . Here's one approach: "The current king of France is bald" is false because it implies the existence of a current king of France when in fact there isn't one. "The current king of France is not bald" is likewise false if it's construed as implying the existence of a current king of France (and asserting of him that he's not bald). On a possible but perhaps less likely interpretation, the second quoted sentence is simply the wide-scope negation of the first quoted sentence: i.e., "It's false that the current king of France is bald." On that interpretation, the second quoted sentence comes out true since it simply asserts that the first quoted sentence is false. On neither interpretation is anyone neither bald nor not bald, so that particular claim of classical logic -- everything is either bald or not bald -- is preserved.