Monday, August 26, 2024

Rooted and unrooted branching actualism

Branching actualist theories of modality say that metaphysical possibility is grounded in the powers of actual substances to bring about different states of affairs. There are two kinds of branching actualist theories: rooted and unrooted. On rooted theories, there are some necessarily existing items (e.g., God) whose causal powers “root” all the possibilities. On unrooted theories, we have an ungrounded infinite regress of earlier and earlier substances. In my dissertation, I defended a theistic rooted theory, but in the conclusion mentioned a weaker version on which there is no commitment to a root. At the time, I thought that not many would be attracted to an unrooted version, but when I gave talks on the material at various department, I was surprised that some atheists found the unrooted theory attractive. And such theories have indeed been more recently defended by Oppy and Malpass.

I still think a rooted version is better. I’ve been thinking about this today, and found an interesting advantage: rooted theories can allow for a tighter connection between ideal conceivability and metaphysical possibility (or, equivalently, a prioricity and metaphysical necessity). Specifically, consider the following appealing pair of connection theses:

  1. If a proposition is metaphysically possible (i.e., true in a metaphysically possible world), then it is ideally conceivable.

  2. If a proposition is ideally conceivable, it is true in a world structurally isomorphic to a metaphysically possible one.

The first thesis is one that, I think, fits with both the rooted and unrooted theories of metaphysical possibility. I will focus on the second thesis. This is really a family of theses, depending on what we mean by “structurally isomorphic”. I am not quite sure what I mean by it—that’s a matter for further research. But let me sketch how I’m thinking about this. A world where dogs are reptiles is ideally conceivable—it is only a posteriori that we can know that dogs are mammals; it is not something that armchair biology can reveal. A world where dogs are reptiles is metaphysically impossible. But take a conceivable but impossible world w1 where “dogs are reptiles”—maybe it’s a world where the hair of the dogs is actually scales, and contrary to immediate appearances the dogs are cold-blooded, and so on. Now imagine a world w2 that’s structurally isomorphic to this impossible world—for instance, all the particles are in the same place, corresponding causal relations hold, etc.—and yet where the dogs of w1 aren’t really dogs, but a dog-like species of reptile. Properly spelled out, such a world will be possible, and denizens of that world would say “dogs are reptiles”.

Or for another example, a world w3 where Napoleon is my child is conceivable (it’s only a posteriori that we know this world not to be actual) but impossible. But it is possible to have a world w4 where I have a Napoleon-like child whom I name “Napoleon”. That world can be set up to be structurally isomorphic to w3.

Roughly, the idea is this. If something is conceivable but impossible, it will become possible if we change out the identities of individuals and natural kinds, while keeping all the “structure”. I don’t know what “structure” is exactly, but I think I won’t need more than an intuitive idea for my argument. Structure doesn’t care about the identities of kinds and individuals.

Now suppose that unrooted branching actualism is true. On such a theory, there is a backwards-infinite sequence of contingent events. Let D be a complete structural description of that sequence. Let pD be the proposition saying that some infinite initial segment of the world fits with D. According to unrooted branching actualism, pD is actually a necessary truth. But pD is clearly a posteriori, and hence its denial is ideally conceivable. Let w5 be an impossible world where pD is false. If (2) is true, then there will be a possible world w6 which is a structural isomorph of w5. But because pD is a structural description, if pD is false in a world, it is false in any structural isomorph of that world. Thus, pD has to be false in w6, which contradicts the assumption that pD is a necessary truth.

The rooted branching actualist doesn’t get (2) for free. I think the only way the rooted branching actualist can accept (2) is if they think that the existence and structure of the root entities is a priori. A theist can say that: God’s existence could be a priori (as Richard Gale once suggested, maybe there is an ontological argument for the existence of God, but we’re just not smart enough to see it).

3 comments:

  1. As someone who subscribes to a for of rooted branching actualism I am fully in agreement with your overarching point but it seems to me that (2) is wrong. As surely if you were to adopt a naturalistic version of rooted actualsim God would be metaphysically impossible on such a view but would still be ideally conceivable despite the fact that the two worlds are not isomorphic.

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  2. There is precedent for what I am saying: Chalmers thinks that God is metaphysically impossible iff God is ideally inconceivable (and he thinks that both sides of the biconditional are true).

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  3. To me it seems (2) ties your metaphysical belief (if you accept RBA) to your belief about conceivability when it comes to Naturalism, as if they were to differ they would no longer produce isomorphic worlds( in most cases). This is a obstical I would struggle to overcome as I believe God is ideally conceivable but as a naturalist, who believes in RBA, on my view there would be no possible world containing God as the necessary item ( as my rooting necessary item would be natural )which to me would disqualify it from being isomorphic.

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