In metaphysics these days, nearly everyone accepts that there really are these things: possibilities. Nobody is quite sure what a possibility is. But possibilities appear to be absolutely indispensable to philosophical theorizing. Thus, almost all of us accept that there are possibilities.
There is an interesting disagreement, though, among those who think that there are possibilities. The disagreement is this: are possibilities representations or are possibilities the things represented by representations?
For instance, many of my friends think that possibilities are something like sets of sentences, perhaps in some idealized language. This would be a view on which possibilities are representations. That set of sentences represents a way the world could be down to the finest detail.
Lewis thought that possibilities were cosmos-like. For Lewis, possibilities were no more representational than stars or stones are representational. Lewis' view falls in the second category, where possibilities are the things that are represented.
I think the majority of people who believe that possibilities exist think that possibilities are representational somehow. I know that I used to think that possibilities are representational, in part because I was timid about positing strange things like non-representational possibilities. But now, I can't make sense of the idea that possibilities are representions. Here are my thoughts.
Start from the view that possibilities are representations. You can think of possibilities as long conjunction of sentences, or sets of sentences, or some such. Now consider the following questions: what do possibilities represent? It would seem that the representation relation is existence entailing. That is, if X represents Y, then X and Y must both exist. Moreover, if possibilities are representational, then they must represent something. What could it be? What could possibilities represent? Honestly, I don't know. I don't think there are any good answers to this question. Here are bad answers.
1. "Possibilities represent ways the world could be." But, then, what are possibilities? I thought possibilities were ways the world could be. More exigently, what are ways the world could be? Surely they aren't representational also. For what could they be representing? If possibilities represent non-representational ways the world could be, we might as well jettison possibilities for the non-representational ways the world could be that they represent.
2. "Possibilities represent possibilities." Think about how strange this is. We have sets of sentences that represent other sets of sentences, where those other sets of sentences represent still further sets of sentences. That would be totally weird. Worse, it would have catastrophic consequences. It would be a resultant mystery why we care about possibilities, or why they're useful in other philosophical definitions.
3. "Possibilities represent themselves." This is totally strange too. Think of other representations. Think of an arrow on a map, and imagine someone telling you that the arrow on the map represents that very arrow on that very map. My reaction would be: what do you mean, you've confused me. And, again, on this view, it is a mystery why we would care about things are possible.
3. "Nothing. Representational possibilities don't in fact represent anything." This is also really weird. First, it makes us wonder whether the possibilities are really representational. It might seem that in such a case possibilities are failed attempts to represent. But worse, why admit that there are possibilities, if later you are going to retreat to the view that possibilities are representational and then later retreat to the view that possibilities don't represent anything. What theoretically virtuous role could possibilities play if possibilities are representations of nothing? Also, if possibilities are representational, but don't represent anything, what makes them different possibilities? Do the possibilities have different representational properties? It would seem that they don't, since none of the possibilities represent anything.
I think that possibilities must be the things represented by other things. Possibilities can't be representational devices.