On my causal powers account of modality, p is possible provided that either p is true, or something has an nth order power to make p true for some n. Here, a first order power to make p true is just a power to make p true. A second order power to make p true is a power to make there be a first order power to make p true. A third order power to make p true is a power to make there be a second order power to make p true. And so on.
Here's a serious problem. It seems quite possible that there is a sequence of false propositions p1,p2,p3,... with the following properties:
- It is possible that all the propositions are true.
- For each n, something has an nth order power to make pn true, but nothing has a lower order power to do so.
For concreteness, we might suppose that there are infinitely many planets, and on the nth planet there is a fertile asexually reproducing person xn who has no children. Let pn be the proposition that xn has nth level descendants (where first level descendants are children, second level descendants are grandchildren, and so on).
What should I do? I can think of one option I don't like and two I can live with.
The option I don't like is to adopt strong assumptions about the nature of time that rule out the above story, such as an open future view plus discreteness assumptions.
The two I can live with both involve my scrapping the nth order power stuff. The first option is to make my thesis more modest: causal powers are the ground of metaphysical possibility, but I eschew giving an account of metaphysical modality in terms of causal powers. Then I can say that the possibility of P is grounded in powers, without giving a specific account. This is unattractive because it's unambitious.
The second option I can live with is to say that a thing can have a causal power to produce an effect even when it cannot directly produce the effect. Thus, I not only have a causal power to have children, but a causal power to have grandchildren. Then in the infinitely many planets scenario, the childless people jointly have a power to make P true. This seems to be the best option, but I really liked the iterated account.