2.03 In a state of affairs, the objects hang one in another like the links in a chain.

A chain seems a bit too flexible for what Wittgenstein surely means here. After all, objects are fixed, whereas the links of a chain can move around. His point is presumably that in a state of affairs, a configuration of objects, the objects are interconnected or linked together, this degree of hardness with that color and so on.

Mounce says (p. 19): “A state of affairs, like a chain, is not just a collection, but a collection that holds together in a determinate way. But what holds together the links of a chain? Nothing, except their fitting into one another. Their fitting into one another is how they hold together. The same point applies to the combination of objects in a state of affairs. That they hold together in a determinate way shows something about their logical form. But logical form is not a further fact about them, that which holds them together.”

Anscombe (p. 37) argues that “in the elementary proposition there must be nothing corresponding to bracketing.” That is, the meaning of the proposition must be such that it needs no ‘collecting’ or ‘punctuating’ of terms in the way done by brackets. See 5.461-5.4611.

Black (p. 66), like Mounce, says the point is that there is nothing else in a fact (a ‘bond,’ say) that holds its components together.