Can sentences refer to themselves? Take the "Liar" paradox: (1) This sentence is false. Does "This" really refer to the sentence I've labeled as (1)? Can sentences predicate properties to themselves in this way?

Your sentence (1) is often given as an example of a paradoxical sentence. The paradox arises from interpreting the phrase "this sentence" as referring to sentence (1) itself. If the sentence is true, then what it says is incorrect, so it is false. But if it is false, then what it says is correct, so it is true. It is tempting to think that the problem is caused by the interpretation of the phrase "this sentence". I suspect that this is the motivation for your question. Can we avoid the problem by saying that the phrase "this sentence" can't be interpreted in this way? The answer is no: the paradox can be created without using this phrase. To see how to do it, first note that it is possible for a sentence to talk about a linguistic expression. The usual way to accomplish this is to use quotation marks. For example, here is a sentence that talks about sentence (1): (2) "This sentence is false" is a paradoxical sentence. Of course, there's nothing paradoxical about sentence (2). ...