During my winter break I had the same argument twice, about definitions. People said that definitions can be disproved, and I said that that doesn’t make sense, since definitions have no truth value.
What do you call a definition (haha, define “definition”)? To put it simply, it’s giving something a name. The thing is described, and a name is assigned to that description. So a definition has no truth value, it’s just a naming. It can’t be true or false, it can only be different from other definitions (whether of the same term or the same thing is irrelevant).
You can say that a definition is “wrong”, if by that you mean that the meaning of a term as set by said definition is different from the generally accepted meaning. But not even that would make it false.
Then, you could say, why does Hawking say that “black holes should be redefined” (note the “should”)? Doesn’t that mean that the definition is invalid? Uh, no. It’s simply that the description in the current definition doesn’t accurately fit the thing that it was intended to point at. He isn’t saying that black holes must be redefined, because it violates some law of logic or nature – he’s asking the rest of the scientific community to accept a new definition for “black hole”, one that suits the needs of research better.
There’s no true or false in there.