Tractarian Ontology: Mereology or Set Theory?

I analyze the relations of constituency or “being in” that connect different ontological items in Wittgenstein's Tractatus Logico-Philosophicus. A state of affairs is constituted by atoms, atoms are in a state of affairs. Atoms are also in an atomic fact. Moreover, the world is the totality of facts, thus it is in some sense made of facts. Many other kinds of Tractarian notions—such as molecular facts, logical space, reality—seem to be involved in constituency relations. How should these relations be conceived? And how is it possible to formalize them in a convincing way? I draw a comparison between two ways of conceiving and formalizing these relations: through sets and through mereological sums. The comparison shows that the conceptual machinery of set theory is apter to conceive and formalize Tractarian constituency notions than the mereological one.