I think I have found the basis for a solution to the Liar Paradox that stands as an alternative to Tarski's truth-hierarchy, and which allows self-reference. It rests upon a disambiguation of certain terms in mathematical logic.
First, I distinguish a *concrete* statement, which is a particular instance of a statement such as an individual utterance, from an *abstract* statement, which is the very idea of the statement apart from any of its instantiations in writings or utterance. An example of a concrete statement is a statement as it appears on a particular sheet of paper in someone's particular handwriting, or perhaps in a particular coding system (e.g., Goedel-numbering), as distinguished from its abstract referent in what we might call "statement space."
This disambiguation immediately results in another ambiguity -- namely, what "this statement" refers to in the sentence, "This statement is not true" (S). Does it refer to the *concrete* instance of that statement, or to the abstract statement (whatever it may be)?
Let us take the most obvious example and consider "this statement" to refer to the concrete statement, i.e., the statement as it appears on paper as an instance of a statement. We must then modify our conception of truth to apply to such statements. The usual paradox is that if that statement is true, then it must be not true, and if it is not true, then it must be true. But it cannot take on two values at once!
To solve this, I propose that we simpy make an exception in our concept of truth for the Liar statement, and call the statement "not true." We then deny to the concept of truth the ability to infer the truth of the Liar statement from its grammatical syntax. So if someone offers the usual objection, "That's just what S is *saying*!" we respond that even though the intensional subject of "this statement" satisfies the intensional predicate "is not true," we cannot define it to have more than one truth value. Again, all we need do is make an exception in our notion of truth for the Liar statement. Additionally, we may clarify our response by adding that "what S is saying" remains ambiguous until we specify whether S refers to a concrete statement or an abstract statement.
We may then proceed to write concrete sentence T, "Statement S is not true." In this way we evade self-reference in T and make a true statement about S. Now, statement S is still not true, but since T is, concretely speaking, a different statement, it is allowed to be true about S.
What do you think of this solution? Can you think of any "revenge" paradoxes that would leave my solution in jeopardy? Has anything like this solution been attempted before? If so, are there any good references? I'm looking particularly for a discussion of concrete and abstract statements, however they are so called.
I also accept better suggestions on what to name these concepts.