Law of Excluded Middle

Hmm, so we're doing proofs now. I sort of liked logic more, but maybe we'll start doing logic proofs. So far the proofs are pretty easy, so I'll have to see. I sort of find the indenting and commenting and necessity of introducing very obvious statements somewhat tedious. In Calculus, the proofs are less formal without all that indenting and I don't have to explain so many steps.

I was recently getting distracted by Wikipedia and read the article on the law of excluded middle: either P or not P. Basically, a statement is either true or false, and obviously can't be both. This reminded me of an essay I read about Bertrand Russell. The essay started with the statement: "The king of France is bald." Clearly, this statement is not true, which according to the law of excluded middle, means that the opposite must be true: "The king of France is not bald." However, this does not seem to be any more true, since France does not have a king. Yet, we can't just discard these statements and call them meaningless. They do have a clear logical form. Logic seems so much more clear when you are only using symbols. When applied to natural language, logic seems to screw up a lot of times. In any case, Russell's solution to treat sentences of the form "The F is a G" as three separate claims: "There is an F", "no more than one thing is the F", "and if anything is an F, then it is G." Basically, he tries to treat it as universally quantified. In the case of the king of France, this resolves the problem, because there is no king of France. But, what if I made the statement: "Santa Claus is jolly." Once again, there is no Santa Claus, but intuitively, even though there is no Santa Claus, this seems to be a true statement to me, especially in contrast to its negation. In any case, Russell's solution appears in an essay On Denoting, which I have never read. Maybe he addresses the issue of fictional characters. I would have to read his essay to find out.

Another thing that is also bugging me is this pair of sentences: "The next sentence is false. The previous sentence is true." If every statement is either true or false, then which one of these statements is true and which one is false? Or, is it meaningless to assign truth and false values to these statements; that these statements are neither true nor false? Even if it is meaningless to do assign truth and false values, I don't think these statements themselves are meaningless.