Maybe we can think of the verificationist as posing a certain challenge:
Whenever we are in doubt whether a sentence S or expression e is cognitively meaningful, we know that S, and any atomic sentence in which e occurs (transparently), is not observational. Non-observational sentences are cognitively meaningful in a language or theory only if they bear in certain relations to other sentences in the language or the theory. (Just as words become meaningful in virtue of occurring in certain sentential contexts, non-observational sentences become meaningful in virtue of occurring in certain theoretical or linguistic contexts.) The relation of interest is probably something like probabilistic non-independence, although it might turn out to be something slightly different. But it is clear that non-observational sentences do not qualify as cognitively meaningful if they bear in that relation to just any other sentences in just any language or theory. For instance, we might posit a theory, or a language, in which there is a class of observational sentences, and a disjoint class of non-observational sentences. Suppose that the theory or language specifies the probabilistic relationships between each member of the latter class, and that every sentence of the latter class is probabilistically independent of every sentence of the first class. If this our strongest theory containing the sentences of the latter class, or if there are no other facts about the truth- or assertibility-conditions of these sentences in the language, then it is clear that the sentences do not qualify as cognitively meaningful if they bear in the probabilistic relations that they do. But then what sort of sentences does a sentence need to be probabilistically non-independent of, in a theory or language, in order to be cognitively meaningful in that theory or language?
The verificationist answer: the observation sentences. The verificationist challenge: what else could it be?