Avoiding gerrymandering

Occasionally a philosopher tries to avoid some gerrymandered counterexamples to a theory by specifying that some sentence s involved in the theory must be atomic. But every sentence is equivalent to an atomic sentence. After all, the sentence s is equivalent to the atomic sentence "s is true". So it's a move we should beware of. I guess we do better if we restrict to first order sentences. But even so, one can always just stipulate a new predicate. Thus, "The sky is blue or snow is white" is equivalent to "CreatedBlueSkyOrWhiteSnow(God)". So not only must one restrict to first order atomic sentences, but probably to first order atomic sentences with perfectly natural terms.