2.0122 The thing is independent in so far as it can occur in all possible states of things, but this form of independence is a form of connection with the state of affairs, a form of dependence. (It is impossible for words to appear in two different ways: alone and in propositions.)

On objects being independent, see Russell’s Logical Atomism: “Particulars have this peculiarity, among the sort of objects that you have to take account of in an inventory of the world, that each of them stands entirely alone and is completely self-subsistent. It has that sort of self-subsistence that used to belong to substance, except that it usually only persists through a very short time, so far as our experience goes. That is to say, each particular that there is in the world does not in any way logically depend upon any other particular.” (p. 179)

Stokhof (pp. 46-47) notes that the reference to dependence here “strongly suggests that [objects] cannot be conceived of as material atoms (elementary particles, or wave packets, or whatever), since for such objects the very possibility of an independent existence, however short-lived this may be, cannot be ruled out a priori.” Much the same goes for sense data: “For such objects, too, it holds that no logical property prevents their independent occurrence, even if other properties would.” (p. 47)

My original reaction: "Propositions" following Frege's use of Satz. A word has meaning potentially, we might say, on its own. But then so does everything. They actually mean only in a proposition or sentence. And proposition can be understood to mean thought, so you can't have half a one as you can half a sentence. Parsing or analyzing a thought is somewhat arbitrary, being relative to a given purpose. Really the thought is a whole. And states of affairs are the same, so things seems to have a somewhat arbitrary status.