Suppose we think of a variety of a natural language--say, African-American Vernacular English (AAVE)--as an object language, in the Tarskian sense. The metalanguage we use to state Tarskian truth schemas (following convention T) would presumably be AAVE plus whatever logic we need for those schemas. So far, pretty routine.
But what if we stretch out the time dimension really far? Suppose we allow for time enough to get syntactic change to occur in AAVE? If AAVE as object language has syntactic feature f, while AAVE as metalanguage is alike in every respect except for its logical "richness" and feature f, then the semantic openness Tarski insists is needed to avoid liar paradoxes would be monkey-wrenched, no?
In fact, if syntactic change stood between any object language and its metalanguage, wouldn't those two languages stand with respect to each other just as any two (distinct) languages stood with respect to each other? Suppose, for instance, that AAVE is the object language and standard English is the metalanguage, differing in the syntactic features associated with negation. AAVE possesses such features as are required to license negative concord phenomena, while standard English lacks them. Wouldn't liar antinomies be unresolvable in such a situation?
To withstand this, we need to distinguish logical richness from logical difference in the metalanguage (presumably in the proof theory and model theory of such language).
I realize this is dense. I'll try to unpack it later.