Unravelling Time's Arrow in Causation — Epoche B2
Traces, Miracles and the Arrow of Causation Strike a match, and the world afterwards is full of the striking. There is smoke, a scorch mark, a smell, a spent match, a memory in whoever watched. Before the striking there was nothing comparable: no set of prior conditions that recorded, several times over, that this match was about to be struck. The same holds of a footprint in wet sand and of a photograph. Events leave many traces behind them and few ahead. This note asks whether that imbalance is what makes causation point forwards [1] , which is what David Lewis's best-known argument claims [2] . The conclusion here is that the imbalance does the work only if a particular physical claim is true, that the claim is disputed on good grounds, and that if it fails, the arrow in Lewis's system is being supplied by the machinery he uses to evaluate counterfactuals rather than found in the world. Why the direction has to come from somewhere else In 'Causation' (1973) Lewis analysed causation in terms of counterfactual dependence. An event e depends on a distinct event c when, had c not occurred, e would not have occurred; causation is a chain of such dependences. The analysis is meant to be reductive: causal facts are to fall out of non-causal ones, namely facts about which counterfactuals are true. Nothing in that analysis says which way causation runs. Dependence is defined by a conditional, and a conditional has no built-in temporal direction. Lewis could have added a clause requiring causes to precede effects, but he did not want to, partly because he wanted backward causation to remain a coherent possibility rather than being ruled out by definition. So the direction has to be earned, and 'Counterfactual Dependence and Time's Arrow' (1979 [3] ) is where he tries to earn it. Overdetermination, stated in the right direction Lewis calls a minimal set of conditions jointly sufficient, given the laws, for an event a determinant of that event. His claim is about how determinants are distributed: an event has very many determinants after it and few or none before it. The traces of the match-striking are determinants of it. Any one of them, together with the laws, is enough to fix that the striking occurred. This is the point at which expositions most often go wrong, so it is worth saying flatly: on Lewis's view the past is overdetermined by the future, not the future by the past. The redundancy lies in the record, not in the preparation. The argument then proceeds through what Lewis calls miracles — small local violations of the actual laws, used to make a counterfactual supposition true. Suppose the match had not been struck. To arrange that, one need only tamper slightly with the moments just before: a hand that stays still, a nerve impulse that does not fire. That is a small miracle, and after it the world simply unrolls differently. Now suppose instead that we hold the future fixed and ask what the past would have been. To get a different past that still produces this exact present, every one of the traces would have to be accounted for, and no small local tampering will do it. It would take a widespread, messy violation of law. Since Lewis ranks worlds for similarity by, above all, avoiding large widespread violations of law, worlds with a different past and the same future come out very dissimilar, while worlds with the same past and a different future come out close. Counterfactual dependence therefore runs forward. Causation, being a chain of counterfactual dependence, runs forward with it. What Lewis does not claim Lewis is explicit that the asymmetry of overdetermination is a contingent, de facto feature of the world. It is not a law, it may fail locally, and there are possible worlds where it does not hold. Where it fails, counterfactual dependence has no preponderant direction, and there is then no fact about which way causation runs. Readers sometimes take this to be a concession extracted from Lewis. It is not; it is the point. An account that made the arrow necessary would have to explain why, and no one has an explanation. Anyone who objects to Lewis merely on the ground that the asymmetry is contingent has not touched him. A tradition that made antecedence definitional The Nyāya school of Indian philosophy took the other option, and the contrast shows what the option costs. The standard Nyāya definition of a cause, given in Annaṃbhaṭṭa's Tarkasaṃgraha and inherited from a long line of earlier work [4] , is that a cause is a niyata-pūrvavṛtti — an invariable antecedent — with the further condition that it be ananyathāsiddha , not otherwise accounted for. Temporal priority is written into the definition, and immediacy is required too, so that remote antecedents do not qualify. The interesting part is the second condition, and why it was needed. Invariable antecedence by itself catches far too much. The Naiyāyikas collected the counterexamples: the donkey that carried the potter's clay is an invariable antecedent of the pot, and so is the colour of the potter's stick, and so is the potter's father. None is a cause. So the school built up a list of ways in which an antecedent can be superfluous — being present only through something else that is doing the real work, being a mere accompaniment of a genuine cause — and the definition holds only once these are excluded. The refinements continued for centuries; Gaṅgeśa and the later Navya-Nyāya logicians spent considerable effort on them. The lesson transfers directly. Adding a temporal clause does not solve the problem of causal direction; it leaves the whole problem of separating genuine dependence from mere constant accompaniment, and that problem has to be solved by something else. Nyāya solved it with a doctrine of superfluous antecedents. Lewis solves it with counterfactuals, and then owes an account of direction that Nyāya got free. Each pays somewhere. The strongest objection to the present thesis A Lewisian will say the complain