12 - Armstrong on combinatorial possibility

Summary

D. M. Armstrong, A Combinatorial Theory of Possibility, Cambridge University Press, 1989.

TWO UNFAMILIAR QUESTIONS, JOINTLY ANSWERED

Later we shall see how Armstrong answers some familiar questions about the metaphysics of modality. But the core of his theory lies elsewhere. He raises two unfamiliar questions, and answers them jointly as follows.

1. What is the range of different possibilities? – The range of all re-combinations of actually instantiated universals.

2. What does it take to make a possibility statement true? – The universals thus recombined.

ARMSTRONG'S COMBINATORIALISM: THE POSITIVE SIDE

The range-of-possibilities question is everyone's question. It can be framed in different ways to suit different views about the nature of possibilities; and no matter how we frame it, we can, if we like, borrow Armstrong's answer. We can say that for any way of recombining all or some of the universals that are found within our actual world, there is another ‘concrete’ world wherein these constituents are thus recombined; or there is an ‘abstract’ ersatz world that represents these universals as being thus recombined; or it is primitively possible, without benefit of any entities to play the role of possible worlds, that they might have been thus recombined.

If we like, we can say positively, as Armstrong (almost) does, that no recombination is excluded: there are no exclusions or necessary connections between genuine, distinct universals. Roughly, anything can coexist with anything, and anything can fail to coexist with anything.