Lewis's Account of Fundamentality — Epoche B2
Distinctness Does the Work: The Counterfactual Test Is Grounding Theory's Problem The complaint to be examined A familiar complaint about David Lewis's counterfactual analysis of causation runs like this [1] . Counterfactual dependence is everywhere, including where nothing is caused. If the particles had not been arranged in that way, the table would not have existed; if the member had not existed, its singleton set would not have existed. Since the arrangement does not cause the table and the member does not cause the singleton, counterfactual dependence cannot be what causation is [2] , and a theory built on it will run causation together with the non-causal dependence that metaphysicians now call grounding. This essay argues that the complaint is aimed at the wrong party. Lewis has a device for excluding these cases, it is stated in the 1973 paper itself and elaborated afterwards, and it does the job by a criterion that has nothing to do with counterfactuals: the requirement that cause and effect be distinct . The grounding theorist has no comparable device, because the relata of grounding are standardly not distinct in Lewis's sense — that is what makes them grounding relata. So the burden of saying which dependences are causal and which are grounding falls on the party that introduced the distinction. The claim would be false if a criterion for grounding were available that does not rest on the 'in virtue of' idiom or on prior classification of the case. Lewis's analysis, and the condition that is usually dropped Lewis's 1973 paper analyses causation in two steps. The first defines causal dependence between events. Where c and e are distinct possible particular events, e depends causally on c when two counterfactuals hold together: had c occurred, e would have occurred, and had c not occurred, e would not have occurred. Both are needed; summaries that keep only the second lose half the analysis. The second step defines causation itself as the ancestral of causal dependence: c causes e when there is a chain of causally dependent events running from one to the other. This is what handles the match, the flame and the fire, and it is also Lewis's response to early counter-examples of pre-emption, where a back-up cause stands ready. The counterfactuals are evaluated over possible worlds ordered by comparative similarity to the actual world. To assess 'if c had not occurred', one looks to the closest worlds in which c does not occur and asks what holds there. Now the condition that matters here. Lewis requires c and e to be distinct events, and in his later work on events he says what distinctness excludes: c and e may not be identical, neither may be a part of the other, and they may not overlap by sharing a part. Nor may they be related as an event and one of its implications. The requirement is prior to the counterfactual test and independent of it. What the requirement rules out Apply it to the cases the complaint offers. The table and the particles arranged tablewise are not distinct: whatever else one says about their relation, the table is not a wholly separate item located elsewhere, and the arrangement's occurrence is not the occurrence of some further event alongside it. The singleton and its member are not distinct either; the member is not a part of the set in the mereological sense, but the two are logically related in exactly the way Lewis's condition excludes, since the existence of the one entails the existence of the other. So Lewis's theory does not say that the particles cause the table. It says the question does not arise, because the analysis has no application to a pair that is not distinct. This is not a repair added later to meet the grounding literature; it is in the original definition, and it is there because Lewis needed it for cases that had nothing to do with grounding — I do not cause my own writing of this sentence by writing its first half, and my saying 'hello loudly' does not cause my saying 'hello'. The complaint therefore misidentifies its target. Counterfactual dependence does indeed hold in constitution cases; what does not hold is Lewis's analysans, which is a conjunction of the counterfactual condition and the distinctness condition. The problem transferred The interesting question is what the grounding theorist can say in the same place, and here the asymmetry appears. Grounding is characterised as non-causal explanatory determination: one fact obtains in virtue of another, the ground metaphysically explains the grounded, the grounded is nothing over and above the ground. Kit Fine treats it as an operator rather than a relation and distinguishes metaphysical [3] , natural and normative varieties; Jonathan Schaffer treats it as a primitive structuring relation which orders the world into the fundamental and the derivative [4] . Neither offers a test that operates on a candidate pair and returns a verdict without a prior view of the case. Nor could the counterfactual supply one, and this is the point the original complaint had upside down. Take a case where a moral fact is said to be grounded in a natural one: killing is wrong because it causes suffering. It is true that if killing did not cause suffering it would not be wrong. It is equally true that if the striking had not occurred the match would not have lit. The two counterfactuals have the same form and the same truth-value, and nothing about the counterfactual distinguishes them. On the causal side Lewis can appeal to distinctness. On the grounding side that appeal is unavailable, since ground and grounded characteristically overlap, entail one another in one direction, or stand as whole to part — the very relations distinctness forbids. Notice that a further property usually attributed to grounding is disputed on grounding's own side. Schaffer has argued that transitivity fails for grounding [5] , with counter-examples of the same shape as the well-known counter-examples to the transitivity