If we reject propositional monism, then given that propositions alone can be true – and, hence, propositions alone can be known – we must assert there are unknowables. Does this not seem paradoxical, perhaps contradictory? How can we know [of] something that is not knowable?
Ironically, even on the assumption of propositional monism there would be unknowables: “One cannot know what is false” (Gordon Clark, Clark and His Critics, pg. 399). Sure, we can say something about false propositions – we can say “x is false” where x means “A is not A” – but x itself is not knowable. The same principle applies to meaningless statements.
One may object that this is not a relevant counter-example because falsities and meaningless statements can still function as subjects of true propositions. Maybe the objection has a point. Maybe not. The objector will have to specify why it is relevant that “their” unknowables can function as subjects.
But either way, that propositional monism is false is demonstrated – or, at least, is purported to be demonstrated (link, cf. here) – by elenctic or reductio ad absurdum argumentation. In such cases we assume a position for the sake of argument in order to show why it can’t be true – it’s self-defeating. The method is not to begin with the contradictory of propositional monism. As such, we don’t have to act as if we can really communicate or refer to the unknowable [non-propositions] qua the unknowable [non-propositions]. And surely along these lines the correspondence theory of truth is worth some attention (though not to the exclusion of, say, the coherence theory of truth).