Reconsidering Lewis on Causal Asymmetry in Grounding — Epoche B2
Where Grounding's Asymmetry Comes From: Lewis, Fine and the Cost of an Axiom Metaphysicians say that facts about a table hold in virtue of facts about the particles arranged tablewise, that a set exists in virtue of its members, that an action is wrong in virtue of the suffering it causes. The relation invoked is grounding, and it is standardly held to be asymmetric: if A grounds B, then B does not ground A. This essay asks a single question [1] . Where does that asymmetry come from? One natural answer looks to David Lewis [2] , who gave the best-known explanation of why a dependence relation has a direction. I argue that the Lewisian route cannot be taken, that the usual reason given for this is the wrong reason, and that once the right reason is seen, the asymmetry of grounding turns out to be an axiom rather than a finding — a substantive commitment that identifiable philosophers, in two quite separate traditions, reject. What is being claimed for grounding Kit Fine reintroduced ground into analytic metaphysics as a primitive notion of non-causal explanation in 'The Question of Realism' (2001 [3] ), and set out its structure in 'Guide to Ground' (2012). The distinction that matters here is between strict and weak ground. Weak ground allows a fact to ground itself; strict ground does not. Strict ground is the notion doing the work in claims about fundamentality, and Fine gives it three structural conditions: it is irreflexive, asymmetric and transitive. Together these make the grounding relation a strict partial order, which is exactly what is needed if reality is to have levels, with the fundamental at the bottom. Two features of this presentation should be noticed. First, the conditions are imposed rather than derived. They belong to the logic Fine constructs; nothing in the notion of explaining-in-virtue-of forces them. Second, they are meant to hold necessarily. Nobody thinks that grounding runs one way in our world and might have run the other way in a world with different physics. If asymmetry were contingent in that sense, the hierarchy of fundamentality would be a local accident. Lewis on the direction of dependence Causation raised a structurally similar problem, and Lewis's answer is the model an account of grounding might hope to copy [4] . In 'Causation' (1973) he analysed causation in terms of counterfactual dependence between distinct events: e depends on c when, had c not occurred, e would not have occurred. Causation is then the ancestral of that relation — a chain of dependences — a refinement Lewis made in order to handle cases where a backup cause is standing by. The analysis by itself gives no direction. So in 'Counterfactual Dependence and Time's Arrow' (1979) Lewis explains the direction by appeal to what he calls the asymmetry of overdetermination. A determinant of an event is a minimal set of conditions jointly sufficient, given the laws, for that event to occur. Lewis's claim is about how determinants are distributed in time. An event typically has very many determinants after it and few or none before it. The struck match leaves smoke, ash, a scorch mark, a smell and a witness's memory, and any one of these, with the laws, suffices for the striking. Before it, there was no comparable redundancy. It is worth being exact, because the point is easy to state backwards. Lewis's thesis is that the past is overdetermined by the future, not the other way round. That is why a counterfactual supposition about the past would require a large and messy violation of law — every one of those traces would have to be undone — while a supposition about the future needs only a small local one. The pattern of counterfactual dependence therefore runs forward, and causation goes with it. Why the transfer fails, and why not for the usual reason The usual objection to importing Lewis into the theory of ground is that grounding is atemporal and non-causal, whereas Lewis's machinery is about times and events. This objection is weaker than it looks. Lewis's explanation has two parts, and only one of them is about time. The general strategy — locate a de facto imbalance in the world and let the direction of dependence fall out of it — is not tied to temporal order. One could look for an analogous imbalance among facts at a time. The decisive difficulty is elsewhere, and Lewis states it himself. He is careful that the asymmetry of overdetermination is contingent. It is a feature of how things happen to be arranged in our world, it may fail in some regions, and there are possible worlds in which it does not hold at all. Where it fails, on his account, counterfactual dependence has no preponderant direction, and causal direction is correspondingly indeterminate. Lewis accepts this. It is a virtue of his account that it does not smuggle in a necessity nobody has independent reason to believe. That is precisely what makes the strategy unusable for ground. Import it, and grounding's asymmetry becomes contingent too: a fact about the arrangement of our world rather than a structural truth about dependence. Levels of reality could then be a local phenomenon, and there could be regions where nothing is more fundamental than anything else. That result is not available to anyone who wants ground to underwrite fundamentality in the way Fine's structural conditions do. The Lewisian route is closed not because grounding is atemporal, but because Lewis's kind of explanation delivers the wrong modal status. An axiom, then The consequence is that the asymmetry of ground is stipulated. It is written into the logic at the start, and the argument usually offered in its support is short: grounding is explanation, explanation cannot be circular, so grounding cannot be circular. Stipulations can be perfectly reasonable. But they are commitments, and a commitment can be denied. It has been denied. Carrie Jenkins asked directly [5] , in 'Is Metaphysical Dependence Irreflexive?' (2011), whether the structural con