In his SEP entry on propositions, Matthew McGrath presents what he calls the 'Metaphysics 101' argument for propositions. Rather than quote him, I will put the argument in my own more detailed way.
1. With respect to any occurrent (as opposed to dispositional) belief, there is a distinction between the mental act of believing and the content believed. Since believing is 'intentional' as philosophers use this term, i.e., necessarily object-directed, there cannot be an act of believing that is not directed upon some object or content. To believe is to believe something, that the door has been left ajar, for example. Nevertheless, the believing and the believed are distinct.
3. There are occurrent beliefs.
Therefore
4. There are propositions.
To understand this argument, one must understand that no particular theory of propositions is being argued for. (It even allows for such wacky theories of propositions as that propositions are sets of possible worlds. That penetrating minds have championed such theories shows that such minds can descend into wackiness under various materialist and extensionalist pressures.) The argument is to the conclusion that something or other must play the roles of truth-bearer, object of such attitudes as knowing and believing, and ground of the possibility of two or more minds' coming to believe or know the same thing. It is an argument for the existence of propositions that leaves open their exact nature. (Analogy to be explored: in the way Aquinas' God-arguments leave open the exact , and indeed largely unknowable, nature of God.)
Perhaps the argument could be strengthened by restricting it to de dicto as opposed to de re beliefs. Compare 'S believes of some black that he is articulate' with 'S believes that some black is articulate.' The first is de re, the second de dicto. The first does not entail the second. Suppose S is a redneck who believes that no black is articulate. He hears a man on the radio speaking in an articulate manner, a man who, unbeknownst to S is black. It follows that S believes of some black man that he is articulate without believing that some black man is articulate.
Be this as it may. Like any argument, the Metaphysics 101 argument for propositions can be countered in several ways. Alan Rhoda discusses one way in his post, Propositions and Make-Believe. My own view is that the argument is more credible than any of its attempted counterings. More later.