Sean at common sense philosophy discusses the sentence: "Caesar is a prime number."
Apparently some people (including Carnap) think this claim is not false. They don't think it's true either, of course, but rather meaningless -- just like "Caeser is and." Though I agree about the latter, I think the former sentence is simply false. This is because, as Sean points out, there is a set of all prime numbers, and Caesar is not among its members. This undeniable fact immediately entails that Caesar is not a prime number, and hence "Caesar is a prime number" is false. I wonder if some might be tempted to deny it meaning simply because it is so very false, necessarily and obviously so, that no-one would ever even dream of seriously entertaining the thought that it might be true. Then, rather like how something might be so cold that it "burns", so some sentences might be so false that they no longer seem it. Very odd.
Despite the failure of this particular example, there are some sentences that seem genuinely meaningless despite syntactic conformity, such as Chomsky's famous example: "Colourless green ideas sleep furiously." Though I'm actually tempted to just call that one false too. It is not the case that colourless green ideas sleep furiously. Ideas don't sleep -- furiously or not, and whatever shade of colourlessness they might come in!
What do people usually make of claims about non-existent subjects, e.g. "The present king of France is bald." False or meaningless? Is there any sort of consensus on this issue?
What is it about a sentence that makes it meaningful (or not)? Consider the condition that a sentence either violates syntactical requirements or else contains nouns that fail to refer. Is that condition necessary for meaninglessness? Is it sufficient? Are there any better criteria you can offer?