Correspondence, truth and class paradoxes - tidying up?

Let's suppose that the set of English assertive sentences of less than n (for n>6) words is finite.  We can then associate a physical token (a sound, a scribble, an object) with each of these sentences.

We will now make two piles of these objects - Pile A and Pile B.  We will put all of the objects associated with true assertions in Pile A and all of the objects associated with false assertions in Pile B.

All statements of the form "Object X is in Pile B" are, of course, associated with an object in one of the piles.

Now let Z = "Object P is in Pile B", and let Object P be the token for Z.

If Object P is in Pile B, then Z is true.  However Pile A contains the tokens for true statements.  However, if Object P is in Pile A, then Z is false, and Pile B contains the tokens for false statements.

So far, this is looks like a re-statement of a traditional paradox.

However, this construction of it is particularly awkward for any kind of correspodence semantics, because the paradox is a direct consequence of the kind of token/fact relationship such a semantics would require.