(I could not find a suitable picture of Ludwig Wittgenstein so I got one from my date with Katerina Witt.)
Although we have all grown up idolizing Wittgenstein, his assumption of a world of facts is a metaphysicsal construct that sort of assumes what it was to prove, at least in the dim-light-bulb factory of my head.
Propositional logic applies to propositions. Period. A true proposition corresponds to a Fact in the world, at least we hope so.
However, there are no "true" facts in the world - "true" in the same sense as propositions are true.
Wittgenstein wants a Fact to stand for what-is-the-case, which is the surrogate for "true" in the logic of non-propositional worlds.
OK. But how does one finds these happy, happy facts?
We have religion and politics. Consider them. In politics, in a political party, we may have millions of adherents, each of whose belief system varies from that of their fellows in small degree or in large degree; they may contain contradictions.
Indeed, our own beliefs may contain contradictions, for as Christians we believe in love and peace, but as political Christians , we believe in force and compulsion... and that is the way of all flesh.
How does one describe these belief systems? Obviously if they contain contradictions, they cannot correspond to a Fact of the world in the Wittgenstein sense. Even if they differ in varying degrees, it is difficult how to see they correspond to any Fact.
Any reality may have a logic. Propositions have propositional logic. Then there are facts of the world and Wittgenstein tried to speak of what was almost unspeakable: the underlying Facts of the world. These Facts have their own logic, and their "truth value" is defined as "what-is-the-case"
It really does not work.
I also think Wittgenstein's Logical Atomism is responsible for his ability to envisage a clean and pure Fact - sort of like Descartes' clear and distinct ideas - which stands in Being as a tangible and non-volatile What-Is-The-Case.