The way I’ve always understood propositions is the way in which the philosopher Quine argued was a problematic presumption. However, it’s a pretty sticky presumption, and useful despite its problems, so I’ve stuck with it!
So there are often multiple different ways to say the same thing when you use sentences to talk about the world. For example, we use the word “bachelor” to talk about men who aren’t married, so the sentences “Jim is a bachelor” and “Jim is an unmarried man” are said to mean the same thing.
A proposition might be understood as the “meaning” that all the sentences trying to say the same thing as each other are aiming at. Both “Jim is an unmarried man” and “Jim is a bachelor” express the same proposition. Similarly, sentences in other languages that are translations of those sentences are expressions of that proposition in other languages.
According to some influential philosophy of language positions, propositional content can also feature in non-linguistic contexts, like thoughts, representational depictions and metaphysical systems - what matters essentially is that all of these things are in some sense “about” the propositions they are expresssing.
So what kinds of things are propositions? Well, one view is that they are abstract objects like mathematical sets - all of the things that express the same proposition just form a set, and there might be no deeper sense of what this means than just that they are all the same. If you’re building an AI model of language use, something like this is probably at work.
Another view is that this sameness ties to one’s underlying metaphysics of the world - that what matters is that the sentences correspond to Reality in some key way. This is often why Truth-functional equivalence enters the picture, because the intention is that an underlying semantics determines whether two sentences mean the same thing - they are true in exactly the same situations as each other.
But importantly, one’s underlying theory of meaning doesn’t necessarily tie in with the practical question of learning to interpret what other people are trying to say, and this is why a lot of theorising about propositional content doesn’t always progress.
The practice of understanding whether two things mean the same is a constantly shifting sand, but getting by in a social world often means recognising a plurality of fictions about it across different contexts. Find a tool that works for you and see where it gets you, and you might find others useful at different stages of life!
