I think you're misreading it . . .
Okay, that's a good point. Let's take for example the statement
"One plus one is two."That's a given mathematical statement. But according to Davies, if I say,
"Class, that statement must either be true or false,"then I am mistaken because, according to him, you can't make that claim about ANY given mathematical statement, including one so trivial as this. At least that's how I read it, and I think that's how a lot of people will read it.
Do you think I'm making a mountain out of a molehill? Maybe so. It just struck me as sooooo wrong and misleading. Is Davies a Brit? Gotta make exceptions for those guys, lol.
I read it differently. Davies has gainsaid the proposition that any given mathematical statement MUST necessarily be true or false. He presumably accepts that any given statement MAY be true or false. As it turns out, most mathematical statements are in fact either true or false. Davies is simply pointing out that there are exceptions.
Davies is using sloppy language, though. Gödel's theorem doesn't say that some mathematical statements are neither true nor false. What it says is that, in some formal systems, there exist some statements whose truth or falsity cannot be proven, one way or the other, within the system itself. But even these statements may themselves actually be true or false. In Davies's defense, however, I'll say that this distinction is lost on most people.