Here are some somewhat disjointed musings. There are at least two kinds of ways of grounding modality:
- Necessitarian Theories: First necessities are grounded in certain "restrictive" realities, and then we say that p is possible provided that not-p is not necessary.
- Possibilitarian Theories: First possibilities are grounded in certain "possibilitating" realities, and then we say that p is necessary provided that not-p is not possible.
On necessitarian theories, were there (per impossibile) nothing, then everything would be possible, since there would be nothing to restrict possibilities. On possibilitarian theories, were there (per impossibile) nothing, then nothing would be possible, except perhaps the empty possibility of nothing existing.
Lewis's extreme modal realism is a possibilitarian theory. Leibniz, too, was a possibilitarian, with the grounding of possibility being in God: "if God didn't exist nothing would be possible" ("Making the Case for God" [PDF]). The common maxim that something is logically possible unless its negation is impossible is closer to a necessitarian theory grounding modality in the rules of logic.
There are two kinds of Aristotelian groundings for modality. One kind, defended by Timothy O'Connor in his latest book grounds modality in the essences of things which restrict the options for things, and hence seems to be necessitarian—were there no essences, there would be no restrictions. The other kind, defended by myself, grounds mere possibility in the powers of things which make various events possible, and defines possibility as the disjunction of mere possibility and actuality, and hence is possibilitarian.
Platonic theories on which the abstract properties of possibility, necessity and impossibility are had by Platonic entities such as propositions may be necessitarian, possibilitarian or neither, depending on whether they take necessity, possibility or neither as primitive.
Those who offer us a theory of modality owe us a story about why the actual is possible. On my own possibilitarian theory this is easy, because actual things are automatically deemed possible. Necessitarians who believe in restrictive rules or essences need to give a story as to why it never happens that a restrictive rule or essence never ends up prohibiting something actual. This can be a surprisingly difficult task. For instance, on Platonic theories it is surprisingly difficult to say why it is that we never find a false proposition that happens to have the property of necessity.