In paradoxes such as the Epimenides 'liar' example, is it not sufficient to say that all such sentences are inherently contradictory and therefore without meaning? Like Chomsky's 'the green river sleeps furiously', it's a sentence, to be sure, but that's all it is. Thanks in advance :)
Chomsky's sentence was actually: "Colorless green ideas sleep furiously". Several people have argued that, embedded in the right kind of context, it can be taken as meaningful. For some examples, see a handout from one of my courses here.