2.0233 Two objects of the same logical form are -- apart from their external properties -- differentiated from one another only by the fact that they are different.
And what kind of fact is that? This seems to be irony. Two objects of the same logical form are identical, apart from their external properties. But if objects are mere possibilities, or possibility place-holders, what external properties could they have? And what are external properties, after all? Perhaps they are signs for objects, or something of that sort. External properties must be inessential, and objects seem to be all about essence, so it is hard to conceive of their having anything that might be called external properties. But since Wittgenstein does not say that they do have such properties, and besides has not told us what he means by "external properties," we need not worry about this yet. On the other hand, perhaps there is no irony here. Perhaps simply being different is a relation or property that two objects could have. I think we need to read on before we make up our minds.
Anscombe (p. 111): “The only ‘external properties’ his [i.e. Wittgenstein’s] simple objects can have, of course, are those of actually occurring in certain facts.” See 5.5302, where, Anscombe says, “he is explicit that it makes sense to say that two objects have all their properties in common.”
See 4.123 for more on external properties.