Here’s a thought: suppose somebody wants to argue that meaning is not public property, but in fact meaning is irreducibly subjective and arbitrated, such that the natural conclusion will be that meanings recognized by different persons are incommensurable. Such an argument leads to the conclusion that ideas are incommunicable; they aren’t the kinds of things we can share with one another. This provides, I think, an in-built defeater for such arguments. The argument’s conclusion, if correct, entails that the argument itself is incommunicable, and so to publish the argument in any medium is presumably to presume, at least, that it’s meaning is not incommensurable. This is a presuppositional argument against any argument whose conclusion is that meanings are not public property or truly communicable.
I also think, though I won’t write out the argument here, that the problem of meaning incommensurability can be solved on non-presuppositional grounds, the considerations of which may lead to the formulation of an argument for the existence of God.