A Summary of the "Tractatus Logico-Philosophicus" Post 13
According to K.T. Fann Wittgenstein is trying to answer two questions “How are propositions related to the world?” and “How are propositions related to one another (Wittgenstein’s Conception of Philosophy, p. 8)?” These questions are related to Wittgenstein’s goal, viz., “My whole task consists in explaining the nature of the proposition (Nb. p. 39).”
It's already been stated in earlier posts that Wittgenstein assumes a priori that if we can talk about the world, then some propositions must be connected with the world. These propositions are called elementary propositions, and what determines their truth or falsity is the world, not other propositions. Complex propositions, made up of elementary propositions, are truth-functions of elementary propositions (e.g., T. 5). Elementary propositions are combined using truth-functional connectives such as disjunction, conjunction, negation, and implication (T. 5.101).
We know that elementary propositions consist of names in immediate combination (T. 4.221). “It is a nexus, a concatenation, of names (T. 4.22)” We also know that Wittgensteinian names are not the kind of names we’re used to, viz., dog, cat, Plato, pencil, etc. Names are simples that cannot be dissected “…by means of a definition: it is a primitive sign (T. 3.26).” “Names are simple symbols: I [Wittgenstein] indicate them by single letters (‘x’, ‘y’, ‘z’) (T. 4.24).”
Wittgenstein was a traditionalist in his early philosophy because his view was that the meaning of a name was the object it denotes. “A name means an object. The object is its meaning (T. 3.203).” So, elementary propositions, composed of names, if true, are arranged in a way that pictures or mirrors the objects in the corresponding atomic facts, which make up states of affairs. Objects are important in that they provide meaningful referents for our language. Objects are the building blocks of states of affairs, and thus the world (reality). Objects also play an important role in showing the limits of language and what can be meaningfully said. There is nothing for names in elementary propositions to latch onto besides objects in atomic facts, which make up the substance of the world (T. 2.021). In other words, you can't go beyond the substance of the world using language. The mystical, for Wittgenstein, which does go beyond the world, can only be shown not said.
Some of this has already been said, but hopefully wording it a bit differently will help to clarify misunderstandings.