Lewis, D. ‘Counterfactual Dependence and Time’s Arrow’.
https://drive.google.com/file/d/1dOCO0md9b0ht9E-Eee8djwHK9Q11jBYi/view?usp=sharing
Kment, B. ‘Counterfactuals and Explanation’.
https://drive.google.com/file/d/12P7sN718p0yMFgyX48P3ArxzSnT8H3Ay/view?usp=sharing
Counterfactual conditionals are the propositions expressed by sentences like the following:
(1) If I did not get a computer today to watch my favourite show, Martin Luther King would have gotten it and watched it for me(to tell me all about it later)
It is tricky to say exactly which grammatical features of counterfactuals distinguish them from other conditional constructions, but perhaps the most prominent identifying feature is the presence of ‘would’ in the consequent. (Very roughly, the antecedent of a conditional is the proposition expressed by the sentence that comes after the ‘if’, and the consequent is the proposition expressed by the other sentence, so that in ‘if A, (then) C’ and ‘C if A’, A is the antecedent and C is the consequent. Counterfactual conditionals are to be distinguished from indicative conditionals, as illustrated by the following famous pair:
(2) If Oswald didn’t shoot Kennedy then someone else did.
(3) If Oswald hadn’t shot Kennedy then someone else would have.
There is also a difference in how we judge indicatives and counterfactuals when the same person who is entertaining the conditional judges its antecedent to be false:
(4) If I am not watching my favourite show, Martin Luther King will do it for me.
(5) If I were not watching my favourite show, Martin Luther King would be doing it for me instead.
This difference is perhaps even more pronounced when comparing counterfactuals to material conditionals, as material conditionals are automatically true when their antecedents are false, whereas the truth value of the antecedent of a counterfactual seems to have no bearing whatsoever on its truth. At first glance, this might sound odd: aren’t the antecedents of counterfactuals at least presumed to be counter to fact and hence false? Typically, but not always:
(6) If he had measles he would be exhibiting precisely these symptoms. Therefore he has measles.
This argument instantiates the form of inference to the best explanation, which often involves (to a reasonable approximation) inferring the truth of the antecedent of a counterfactual from the truth of its consequent. And since we are often predisposed to reason in this way with counterfactuals whose consequents are true, we are often comfortable with counterfactuals with true antecedents.
Lewis
In broad strokes, Lewis (1979) says that a counterfactual A > C is true just in case either there are no possible worlds at which A is true, or there is a world at which both A and C are true that is ‘closer’ to the actual world than any world at which A is true and C is false.
Why not just says that A > C is true just in case C is true at all the ‘closest’ A-worlds? Because Lewis wants to allow that there might be a never-ending series of A-worlds such that each A-world in the series is closer to the actual world than the last, in which case there are no closest A-worlds. But since it will be easier to talk as though there are always some closest A-worlds, let’s just do that. (A couple of other important features of Lewis’ semantics for counterfactuals are that if A is true at the actual world then the actual world is the lone closest A-world to itself, and that even if there are some closest A-worlds to a given world w, there can be more than one such closest A-world.)
A pressing question is just what closeness to a world consists in. Lewis’ answer is that one world is close to another to the extent that it is similar to that world. Thus Lewis is thinking: A > C is true just in case C is true in all the A-worlds that exhibit the most overall similarity to the actual world. But, as Fine (1975) pointed out, this idea seems to assign the wrong truth values to certain counterfactuals:
(7) If Nixon had pressed the button, there would have been a nuclear holocaust.
This counterfactual strikes us as true. Yet, intuitively, worlds in which a nuclear holocaust took place are very dissimilar from our own, in which no such event occurred. This suggests in turn that the most similar worlds to our own in which Nixon presses button are worlds in which, for one reason or another, a nuclear holocaust nonetheless fails to eventuate. Lewis’ truth conditions for counterfactuals thus threaten to render (7) false, as at least some of the most similar button-pressing-worlds seem to be worlds in which there is not nuclear holocaust.
Counterfactual Dependence and Time’s Arrow is in large part a response to Fine’s challenge. Lewis responds by insisting that the standards of similarity relevant to counterfactuals are not those that guide our offhand explicit judgements of overall world similarity. He gives a really clever little argument for this:
‘Sometimes a pair of counterfactuals of the following form seem true: “If A, the world would be very different; but if A and B, the world would not be very different.” Only if the similarity relation governing counterfactuals disagrees with that governing explicit judgments of what is “very different” can such a pair be true [given the idea that A > C is true iff C is true in all the A-worlds most similar to the actual world].’ p. 466
So if the similarity relation governing counterfactuals isn’t the intuitive one, which one is it? One proposal Lewis considers and rejects is ‘Analysis 1’:
(Analysis 1) Consider a counterfactual A > C where A is entirely about affairs in a stretch of time T. Consider all those possible worlds w such that: (1) A is true at w; (2) w is exactly like our actual world at all times before a transition period beginning shortly before T; (3) w conforms to the actual laws of nature at all times after T; and (4) during T and the preceding transition period, w differs no more from our actual world than it must to permit A to hold. Such worlds w are the most similar possible A-worlds, and A > C is true iff C holds at all such worlds. Analysis 1 largely guarantees the asymmetry of counterfactual dependence in a way that excludes a backtracking interpretation of the counterfactual. The following counterfactual, for instance, will come out false on Analysis 1:
(8) If I had jumped from the Empire State Building then (there would have to have been a net there, are I am not suicidal, and hence) I would not have died.
Why? Because in fact there is no net that would catch me if I jumped from the building, and a world that differs no more from our own than is necessary to make it true that I jump will contain no net, as a net would be a gratuitous addition.
That said, Analysis 1 does not completely guarantee the asymmetry of counterfactual dependence: it makes an exception for the immediate past. Why the exception? Because we don’t want it to come out true that, e.g., if Obama had visited North Korea he would have travelled thousands of miles instantaneously. Despite its successes, Lewis does not like Analysis 1 for two reasons: it is insufficiently general (what about e.g. counterfactuals with antecedents like ‘if kangaroos had no tails…’ that aren’t about a specific time?), and it rules out a priori cases of time travel and backward causation. Instead, Lewis opts for the following account of the similarity relation governing counterfactuals.
(a) It is of the first importance to avoid big, widespread, diverse violations of law.
(b) It is of the second importance to maximize the spatiotemporal region throughout
which perfect match of particular fact prevails.
(c) It is of the third importance to avoid even small, localized, simple violations of law.
(d) It is of little or no importance to secure approximate similarity of particular fact, even in matters that concern us greatly.
Couple with an account of similarity based on (a)-(d), Lewis’ theory seems like it will assign the right truth values to all the counterfactuals we have looked at so far, and will do so in a way that generalizes to kangaroo counterfactuals and which refrains from imposing asymmetry by fiat. Rather, Lewis gets asymmetry from an alleged de facto feature of our world: for any given event, few events in its past lawfully suffice for it to occur, but many events in its future lawfully suffice for it to occur. More generally, this promises to secure the general lack of counterfactual dependence of past on future.
The closest worlds in which I didn’t watch my favourite show are the worlds I still got my computer, as they are worlds in which a small miracle results in my not watching my favourite show, and no small miracle will be enough to rid the world of all the other traces of me watching my show that lawfully suffice for me to have watched it—at least not while maximizing perfect match of particular fact. But this same tactic of Lewis’ seems liable to backfire. What of the following
counterfactual?
(9) If all future traces of me watching my favourite show had not been present, I would not have watched it.
On the intended interpretation, (9) seems false. But notice that the easiest way to get rid of all these traces of me getting watching my favourite show is, by the standards enshrined in (a)-(d), to have a small miracle prevent me from watching it shortly before I watched it. Otherwise we’d either need the entire past to be different, or we’d need a big miracle to eliminate all these diverse traces after I watched it. So the closest worlds in which these traces are absent are worlds in which I do not watch, and hence (9) comes out true on Lewis’ theory.
(Along similar lines, you might worry that we should allow for there to be events that are overdetermined by past events moreso than by future events without having been caused by future events. But if counterfactual dependence suffices for causation, Lewis cannot accomodate this. Another problem along vaguely similar lines: what if no small miracle can make the antecedent of a counterfactual true? (E.g. ‘had a motley assortment of stars spread out randomly across space exploded simultaneously…’) Is the past then allowed to be arbitrarily different in order to make antecedent true since approximate match doesn’t count for much if anything? This seems wrong. Surely the past would have been only as different as was required. But Lewis can’t seem to secure this result.
A closely related problem is this: suppose that after a nuclear holocaust we say that if as many people were alive today as were alive in the year 2000, most of them would be living short and miserable lives. This seems plausible, but it is also plausible that the best way to make the antecedent true consistent with (a)-(d) is with a small miracle that prevents the holocaust from ever taking place, in which case the consequent will be false, and the counterfactual along with it!)
Here’s another problem faced by Lewis’ theory. Consider:
(10) If Usain Bolt had broken is leg the day of the 100m sprint final, he would still have won.
At the very least, this counterfactual is dubious. But on Lewis’ theory, (10) would appear to be clearly true. This is because the closest world in which Bolt breaks his leg on the day of the final is one that maximizes match of particular fact, and this requires that Bolt break his leg as late in the day as possible, and hence that he break his leg after he’s already won the race.
It also seems like despite what Lewis says, his view seems to commit him to an awful lot of counterfactual dependence of past on future in ordinary situations. This is because of the ‘ramp period’ he allows between the miracle and the antecedent event in order that we won’t have to say that, e.g., if Obama had visited North Korea he would have travelled there instantaneously from the US. Lewis hopes that the closest possible antecedent worlds will include an assortment of different ramps so that nothing definite in the past can be said to depend on the antecedent event. But I don’t see how this is supposed to work. Lewis is committed to saying that if Obama had visited North Korea at time t then he would not have been in the US at time t−1 second. And these events are no less definite than the sorts of events that typically feature in causal relationships. But if counterfactual dependences like these are tied to causation, Lewis commits us to a ton of implausible backward causation on the cheap.
Kment
Kment is primarily concerned to resolve two problems with Lewis’ theory: some differences in matters of particular fact detract from closeness, while others do not, and some violations of law detract from closeness, while others do not.
‘In a certain world w, Bugsy has two indeterministic and fair coin-tossing devices, A and B. Each device, once activated, automatically tosses a coin after five minutes. Immediately before each toss, a random process is initiated inside the device and the outcome of this random process determines the outcome of the coin toss. Bugsy activates device A. Five minutes later, the coin is tossed and lands heads. Consider,
(11) If Bugsy had used device B, the coin would still have landed heads.
I think, as do most people I have asked, that this counterfactual is not true. If device B had been used, the coin might have landed heads, or it might have landed tails.’ p. 272
Here, whether or not antecedent worlds match the actual world in respect of how the coin lands seems not to matter to their closeness. By contrast:
‘A little later in the history of the same world w, Bugsy again activates one of the coin-tossing devices and then offers you a bet on heads on the toss, but you decline it. Five minutes later, the coin is tossed and lands heads. Assume that your decision whether to accept the bet causally affects some of the goings-on inside the coin-tossing device: your decision causes a certain utterance of yours, and the sound waves of this utterance penetrate the walls of the device and slightly change the distribution and motion of the air molecules inside it. However, the processes inside the device that are influenced by your decision do not in turn causally affect the outcome of the random process in any way. (This might not be compatible with the laws of the actual world, but it does not seem to be metaphysically impossible. I stipulate that it is compatible with the laws of the world w in which the coin toss takes place.) There is thus no causal connection whatsoever between your decision whether or not to accept the bet and the outcome of the coin toss. Now suppose that Bugsy says:
(12) If you had accepted the bet, you would have won.
Most people I asked believe that Bugsy is right. I, too, feel inclined to agree with him. But if Bugsy is right, then it must be true that the coin would still have landed heads if you had accepted the bet. ’
Here, whether or not the antecedent worlds match the actual world in respect of how the coin lands does seem to matter to their closeness. In the case of laws it seems obvious that sometimes whether or not actual laws are violated in a possible world contributes to its closeness, and at any rate this is suggested by the way match of particular fact sometimes contributes to closeness, as violations of law are also mismatches in particular fact if the actual laws are never violated in the actual world (contra Kment). But consider:
(13) If the Law of Gravitation had not been a law, then events would still have at least approximately conformed to it.
This seems false, despite the consequent being true in those worlds where the LOG is not a law that minimise violations of the actual laws. Kment explains these data with his principle (C).
(C) If some fact f obtains in both of two worlds, then this similarity contributes
to the closeness between the two worlds if and only if f has the same explanation in the two worlds. (In the special case in which f has no explanation in either world, this condition counts as vacuously satisfied.) But is (C) true? Kment canvasses some worries.
‘Suppose that we are watching an indeterministic lottery draw. The lottery was instituted ten years ago. As part of this process, one of the people in charge, call her ‘Susie’, made an important phone call. Susie has two qualitatively identical cell phones in her office, A and B. Every morning her secretary randomly chooses one of them and puts it on Susie’s desk, and this cell phone will be used for all phone calls during that day. As it happens, on the day of the aforementioned phone call ten years ago, the secretary chose A, and this phone was used for the phone call. Consider:
(14) If Susie had used B rather than A for the aforementioned phone call ten years ago, the outcome of the lottery draw would have been just the same.
If the antecedent had been true, then the causal history of the lottery draw would have been different. Among the factors that figure in its actual causal history are certain processes inside A. By contrast, in the antecedent-world these processes are replaced by ones featuring the parts of B.’ pp. 297-98
Yet, (14) seems true. Think about it this way: ‘Suppose that Nixon’s missile system is indeterministic. When the button is pushed, there is some chance of a nuclear explosion and some chance that the signal will fizzle out. In this case, we want to say that there might have been a nuclear explosion or the signal might have fizzled out if Nixon had pressed the button. Explosion-worlds and fizzling- worlds are equally close. But note that there are countless matters of particular post- antecedent fact that obtain both in the chancy- fizzling world and in our world, but not in the nuclear-explosion world (e.g. all the business as usual in Moscow, London or L.A.). Moreover, it would seem that these matters of fact are produced by the same factors in the chancy-fizzling world and in our world. And yet, since the world with chancy fizzling is no closer than the world with nuclear war, the extra post-antecedent similarities in the chancy-fizzling world must be irrelevant to closeness.’ p. 299
Another way to think about the issue: ‘Suppose that the king tosses a fair coin and it comes up heads. On the eve of the coin toss, a would-be assassin who is about to plant a bomb at the royal palace is poisoned by his enemy x. x’s action is an element of the complete explanatory history of the king’s coin toss, since it prevented the assassin from killing the king and thereby interfering with the causal process that led up to the coin toss. Hence, in a world in which a different person, y, poisons the assassin, the complete explanatory history of the coin toss is different. And yet we want to say that the coin toss would have yielded the same outcome if the assassin had been poisoned by y rather than by x.’ p. 300