1.21 Each can be the case or not be the case and all else stay the same.

This does not say that everything else necessarily will stay the same. One fact's changing might cause others to change, as far as we know so far, but this is not necessary. We don't know much yet, including what these "facts" are.

If we take them to be complex then Wittgenstein is wrong, as Black points out (p. 37). One fact’s being the case (e.g. the cat being on the shelf) would mean that others were affected (e.g. the cat’s being too big to fit on the shelf). Black thinks Wittgenstein means atomic facts here, or else conjunctions of atomic facts. He points out also how awkward it is to refer to a fact’s not being the case.

Cf. 5.135.