Does the world have objective structure? As Jack defines it: "That is, for any two simples x and y, there is a fact of the matter about whether their fusion, x&y exists."
This strikes me as a fascinating question, because it's so difficult to understand what such facts would consist in. (Thus my skepticism about whether there is any such thing.) I have no objection to the analytic project of systematizing our intuitions, or finding the most coherent and sensible way to project structure onto the world. That -- like its ethical analogue -- makes perfect sense. But why go the extra step of thinking that the answer is really "out there", built into the world, an additional fundamental fact about the universe?
Perhaps there could be "objective structure" in a derivative sense, say if the structural facts supervened on (or reduced to) the distribution of physical qualities, or some such. That would seem less objectionable. But let's put that aside for now and consider the hard-core realist view of objective structure as primitive, and wholly independent of other facts.
Doesn't that mean there could be a world with two physically identical "chairs" (speaking loosely), only one of which actually counted as an object in its own right? That is, it's a primitive fact that the first bunch of simples-arranged-chairwise comprise a chair, whereas the qualitatively identical second bunch - for no particular reason - do not. That seems weird.
Maybe this is just my deflationary intuitions repeating themselves, but it just doesn't seem like there should be any further (i.e. unsettled) question about whether the simples compose a fusion. Fix the base facts about the qualitative nature of the world, and all else follows. That makes most sense to me. What need do we have to posit further fundamental facts about "objective structure"? (That's a genuine question -- I haven't read enough to know how proponents of objective structure motivate their position, but would be curious to learn...)