Here is a very common philosophical scenario. I'll present it in terms of a dialog.
A: Possibilities are exhausted by BLAH. (Where BLAH could be the spatiotemporal arrangments of the particles, or the distributions of the qualities, or the distributions of the qualities plus the modal properties, or whatever.) Thus, if possibility X and possibility Y do not differ in terms of BLAH, then possibility X and possibility Y are one and the same possibility.
B: Ah, but consider these two possibilities. [Fill in the blank with the two descriptions for the possibilities]. Intuitively, these are two different ways the world could be.
A: Yes. It does seem that way. But what you have shown is that there are at least two ways of describing the same possibility. The difference that we feel in your two descriptions is a linguistic difference, not a metaphysical or modal difference.
B: But it seems to be a real difference. People might care about the difference. [Fill in other enjoining complaints].
A: Well, you agree that the two descriptions pick out possibilities that do not differ in terms of BLAH. In what might the difference consist? Could you design a test to determine whether you were in of the worlds and not the other?
B: No, I couldn't design such a test. And I already told you what the difference of the two possibilities consists in. They are the same in terms of BLAH, but differ in other terms. What more do you want from me,
A: I see only one possiblity and two ways of describing it.
Back to the main thread. I wish we had some rules for when A's move and when B's move are legitimate. Being in B's shoes more often than not, it seems to me that A could forever cling to her view that the difference I am positing is merely a linguistic difference. I can't think of any decisive way of putting the point that would rationally compel her to acknowledge what plainly seems to me two possibilities.
But now I think I might be able to turn that into an argument. Maybe A's position is unstable. Consider the person who think that possibilities are exhausted by the distribution of the qualities. And then consider a more conservative person who thinks that possibilities are exhausted by the spatiotemporal relations among the fundamental particles. The person who thinks that possibilities are exhausted by the distribution of qualities posits more possibilities than the person who thinks that possibilities are exhausted by the spatiotemporal relations among the fundamental particles.
But now we can put the person who thinks that possibilities are exhausted by the distribution of qualities in a tricky situation. Point out to this person that the person who thinks possibilities are exhausted by spatiotemporal relations could make the same moves that she is making right now trying to defend the view that possibilities are exhausted by the distribution of the qualities. Then ask her why the other person is mistaken in making that move. If she can't come up with something--as I think she can't--then either she has to grant you that there are distinct possibilities alike in terms of qualities or move to the more conservative position.
I will try to give an example of exactly this line of argument in a later post.