Abstract: The standard account of counterfactuals that most philosophers endorse—Lewis's 'Analysis 1' — is wrong. The correct theory is one invented by Jonathan Bennett in 1984 which he called 'The Simple Theory'. Bennett later argued himself out of that theory and went on to champion the standard account. But those arguments fail. The Simple Theory has been right all along.
Let us, following Lewis, help ourselves to the idea that some possible worlds more or less overlap other worlds in matters of particular fact and say that the extent to which this is true measures how much one world "resembles" another. We'll also help ourselves to the idea that two worlds might resemble each other at one time but not others.
Let us, following Bennett, call worlds with exactly the same natural laws as our world "legal" worlds. Call our world, "a". For the sake of simplicity we will assume, in this post, that the laws of a are deterministic.
Laws of nature are unrestrictedly universal so that if any world has a's laws at any time it has them at every time. And yet there is a way in which a possible world can at least appear to only partially overlap ours with respect to laws: it seems logically possible that a world might, for some period of time, behave as if it obeyed exactly the same laws as our world but then suddenly, at time T, begin behaving in ways that were inconsistent with our laws. In such a case let us say that this world "behaves legally until time T". Likewise we can imagine a world which, up until a time T, behaved in ways inconsistent with the laws of a but, after T, suddenly began behaving as if it were a legal world. Let us say, of such a world that it "behaves legally after time T".
Finally let us help ourselves to the idea that some statements are about some times and not others. So we will say
Obama became president.
is about something that happened in 2008 and
Obama was reelected.
is about something that happened in 2012. We'll write 'TP' to indicate time the proposition p is about.
Our topic is counterfactual statements of the form:
If ANTECEDENT had been the case then CONSEQUENT would have been the case.
which we'll write:
To keep things simple, we will only deal with cases where A is false at a but nomologically possible: that is, where A it is true in at least one legal world. We'll call worlds where A is true 'A-worlds'.
In these terms we can frame five different analyses of counterfactuals:
THE FIXED LAWS THEORY
A > C iff C is true at the legal A-worlds which most resemble a.
THE FIXED PAST THEORY
A > C iff C is true at A-worlds exactly like a prior to TA and which behave legally after TA.
THE SMALL MIRACLES THEORY
A > C iff C is true at the A-worlds which exactly resemble a until some time TM prior to TA; behave legally after TM; and resemble a as much as possible at TM.
THE LEGALIZED MIRACLES THEORY
A > C iff C is true at the legal A-worlds which exactly resemble the closest SMALL MIRACLES worlds at TM.
THE SIMPLE THEORY
A > C iff C is true at the legal A-worlds that most resemble a at TA.
Hooray for Small Miracles!
Everyone agrees that the FIXED LAWS theory is wrong. To see why, take a mundane counterfactual:
(1) If the match had been struck it would have lit.
said on an occasion when the match was not struck. According to FIXED LAWS, to decide if this is true we would have to consider (entirely) legal worlds in which the match was struck; ask which of them most resembles the actual world and then determine if the match lights in those worlds.
Now we can be confident that there are some legal worlds where the match is stuck insofar as we are confident that it is physically possible for the match to be struck; to say that it is "physically possible" just is to assert that it happens at some legal world. But to be confident on this score is not the same thing as being confident about what such a world might be like. If the laws of a are deterministic then a world in which the match is struck will have to have had a different past from a's, different for all eternity at every moment. Those differences will in turn will make for other differences— in some worlds small differences, in some worlds large; differences that will extend far beyond the lighting or not lighting of the match. None of us can be sure what even one such world be like, let alone compare alternatives for overall — that is over all time and space — resemblance to a.
The problem with FIXED LAWS, then, is it would make it impossible for us to determine if any counterfactuals were true or false.
Contemplating the unknowable eternal pasts of the closest FIXED LAW worlds, we might well think we should stick with the past we know (or, if we don't know, we can at least point at). So what if we forget about preserving the laws and focus on preserving the actual past? Thus, the Cf. Frank Jackson, 'A Causal Theory of Convertfactuals'. Australasian Journal of Philosophy, 55:3-21" FIXED PAST theory.
On the FIXED PAST account we treat the closest worlds as ones which have exactly the same past as a right up to the time of A. This will make the truth of A a miracle according to a's laws, but we will require that these worlds behave legally after TA.
The merit of FIXED PAST as compared to FIXED LAWS is that does give us a viable way of determining if counterfactuals are true or false. Unfortunately it gives us the wrong answers. Consider this Inspired by Goggans' "Do the Closest Counterfactual Worlds Contain Miracles"Pacific Philosophical Quarterly 73 (2):137 - 149 (1992)example.
(2) If President Obama were in North Korea right now he would have no secret service protection.
This is risibly false, said at any time in the Obama presidency, but it comes out true on the FIXED PAST account. Even if Obama and his retinue are now safely ensconced in the White House, the closest worlds where the antecedent is true but which have exactly our actual past are worlds in which Obama is instantaneously transported to North Korea. And (2) will be true according to those worlds since worlds at which Obama is teleported alone and his retinue remains in Washington will more resemble the actual world than ones in which they are teleported with him. Counterexamples like this to FIXED PAST can be multiplied indefinitely.
What is most obviously wrong with a world like this—the reason we don't count it as relevantly close to ours— is the sudden jump that takes Obama instantly from the USA to the DPRK. The problem we, may think, is not just that the jump would be a miracle— we have already seen problems that can arise from trying to avoid miracles— but that it seems altogether too big and sudden a miracle.
We think (2) is false because we know that the president never goes anywhere without secret service protection and would not make a state visit like this without many months of prior planning leading to a long flight on Air Force One. A world where that happens would have to have a different past than ours — at least over the last several months— and if it would have taken miracle to set this alternate course of events in motion it could at least have been a small miracle—say a change of someone's mind some months ago— rather than the big discontinuity required if we kept the past entirely fixed.
Thus: the SMALL MIRACLES theory.
In this setting SMALL MIRACLES appears as a kind of compromise between FIXING the past and FIXING the laws. SMALL MIRACLES, like FIXED LAWS, requires that A come about legally and, like FIXED PAST, it prizes similarity in matters of past particular fact. But SMALL MIRACLES allows for miracles and past differences prior to TA provided they are small miraculous divergences just big enough so that A comes about lawfully.
Here is Lewis's canonical formulation of SMALL MIRACLES in Reprinted in Philosophical Papers II "Counterfactual Dependence and Times Arrow" (CD&TA):
"Analysis 1. Consider a counterfactual "If it were that A, then it would be that C" where A is entirely about affairs in a stretch of time TA. 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 TA; (3) w conforms to the actual laws of nature at all times after TA; and (4) during TA and the preceding transition period, w differs no more from our actual world than it must to permit A to hold. The counterfactual is true if and only if C holds at every such world w." Philosophical Papers II,p. 39•
Which he elsewhere glosses in CD&TA as:
"Roughly, a counterfactual is true if every world that makes the antecedent true without a gratuitous departure from actuality is a world that also makes the consequent true. "Philosophical Papers II,p.41 •
And here is Jonathan Bennett's version in "Still the best introduction to this topic.A Philosophical Guide to Conditionals":
"... the closest A-worlds exactly resemble a until shortly before TA, diverge from a in an inconspicuous manner that may be a small miracle, and conform strictly to causal laws of a thereafter." Philosophical Guide p. 291 •
Lewis is properly credited with inventing SMALL MIRACLES but it was never quite his official position. He certainly thought that SMALL MIRACLES gave mostly the right answers about which counterfactuals were true or false but he thought he could get those same results with a different account: the one he gives in CD&TA. The merit of the CD&TA account was supposed to be that it doesn't assume — as the SMALL MIRACLES model does— that past resemblance is more important than future resemblance. Lewis wanted such a time-neutral account for all sorts of interesting See belowreasons but, alas, there are good Reviewed in my last post.reasons to think the CD&TA account doesn't work: there are counter-examples; they are moreover counterexamples where the CD&TA account gets things wrong and where the SMALL MIRACLES gets them right.
So SMALL MIRACLES became and remains the standard theory. "Standard" both in the sense that it is the model most philosophers assume when they want to put the logic of counterfactuals to work on topics like causation, the laws of nature or free will and also in the sense that it is generally accepted by philosophers that it accurately describes how non-philosophers ("folks", as the professionals call them) go about deciding which counterfactuals are true.
Troubles with Small Miracles
But if SMALL MIRACLES is a compromise between FIXED PAST and FIXED LAWS it is, I think, an uneasy compromise. It seems to get the right results, but why and how it does so is not so clear.
A first step to answering those questions would be to get clear about what in principle is wrong with the abrupt changes we got from FIXED PAST? In CDTA Lewis tells us that FIXED PAST fails because it:
" ... makes for abrupt discontinuities. Right up to T, the match was stationary and a foot away from the striking surface. If it had been struck at T would it have travelled a foot in no time at all? No; we should sacrifice the independence of the immediate past to provide an orderly transition from actual past to counterfactual present and future. That is not to say, however, that the immediate past depends on the present in any very definite way. There may be a variety of ways the transition might go, hence there may be no true counterfactuals that say in any detail how the immediate past would be if the present were different." Philosophical Papers II p.39-40•
As we saw, FIXED PAST does indeed give us worlds with abrupt discontinuities in the position of matches and presidents. But why are spatio-temporal discontinuities in the positions of things a bad thing? Remember that that Lewis cannot be complaining here that the jumps would be miraculous. On the SMALL MIRACLES, and on Lewis's final CD&TA account, the closest world will Again,assuming determinism.always contain a miracle.
The merit of the slow transition Lewis says is that it is more "orderly" than the instantaneous one. But that doesn't seem right. First the match is here and then, suddenly, it's there: that is an order. True, it is a quick order, but if sheer slowness makes for orderliness in the relevant sense we would have to suppose that worlds are closer as the match moves ever more slowly. In which case must we not wonder if it really would have lit if its striking were so asymptotically slow?
Is it that the abrupt transitions introduce "gratuitous" differences with the actual world? That would depend, of course, on what 'gratituous' means here. Remember, not every difference from a other than A can be counted as gratuitous. The FIXED PAST worlds include worlds as similar to a at TA as it is nomologically possible for A-Worlds to be. But those are not the worlds we want. So if the world after the sudden jump looks odd it is not just because it differs from the actual world in more matters of particular fact at TA than the ones SMALL MIRACLES selects.
Is the problem that the FIXED PAST world violates clause (4) of Analysis 1? That is: is it that case that during TA and the preceding transition period the jump world differs "more from our actual world than it must to permit A to hold?" No. In fact, quite the opposite: suppose at a the match is not struck at TA. Here is a world Wjump with the jump and here is Wsmooth with the smooth transition to the match's striking. Wsmooth overlaps a in matters of particular fact but only up to the time of the beginning of the smooth transition. Wjump exactly overlaps both worlds up to that time and keeps on exactly matching a for however long the transition takes right up to the time of the TA. True Wjump contains a miracle but so does Wsmooth and Wjump's last minute miracle "permits" Wjump to resemble our actual world more and over a longer period of time than the miracle at Wsmooth. Again, If a is deterministic it is always going to take a miracle to "permit" A to hold, so why not the resemblance maximizing miracle of Wjump?
Having failed at this point to explain why we need an extended transition we should also be puzzled about what determines how long the transitions have to be. The worlds relevant to evaluating (2) are surely ones which began to diverge from a at least a few weeks ago. But the worlds where the match was struck may have diverged only a moment ago. Why the difference? In Analysis 1, Lewis requires
"...during TA and the preceding transition period, w differs no more from our actual world than it must to permit A to hold."
But if the actual world is deterministic (as we and Lewis are assuming here) it is always going to take a miracle to "permit" A to hold; otherwise the transition period will comprise the whole history of the universe. So, again, if we are going to have a miracle at the closest worlds anyway, why not a big, instantaneous jump at the last moment?
Perhaps we can get some clarity from Bennett's version. Bennett said that the closest worlds should "…exactly resemble a until shortly before TA" and then "diverge from a in an inconspicuous manner that may be a small miracle". If that is right, then maybe the problem with the big jumps is that they are too conspicuous. When we think of Obama suddenly snatched from the oval office to find himself startled and alone in Kim Il Sung Square, we see what Bennett is getting at. That would be a conspicuous change. People would be bound to notice.
The small miracles SMALL MIRACLES requires will indeed be inconspicuous. They are after all supposed to be small. But this doesn't tell us why small miracles are best unless we take their inconspicuousness to be their defining characteristic and we cannot. To see why, notice first that, while Bennett takes his version of SMALL MIRACLES to be consonant with Lewis's, taken literally, it is anything but. A goings on is conspicuous in the dictionary sense, to the extent that it is hard to overlook. But there is nothing in Lewis's account of miracle size that entails that big miracles be easy to spot or small ones hard to see. Indeed it is not hard to construct counterexamples in which we make a divergence from a less conspicuous by adding more miraculous differences to distract attention (Look, a squirrel!)
And if we can't read Bennett's formulation as a gloss on Lewis's, it cannot stand on its own. Not just because it is vague. Nor even because it makes closeness, hence the truth conditions of counterfactuals, a subjective matter. But for the more conclusive reason that the conspicuousness of any goings on is a dispositional property. To make sense of it we have to cash it out in counterfactual terms: a goings on is conspicuous iff it would command the attention of someone who.... . Which means conspicuity can be included in our analysis of counterfactuals only on pain of circularity.
It might be offered in Lewis and Bennett's defense that real rigor cannot be expected here since what they are attempting to capture is the rationale behind a folk practice: the plain man's methods of evaluating counterfactuals.
But that would be unfair to folks.
The plain man can tell you precisely what he thinks wrong with jumps. What's wrong, he will tell you, is that it would take a miracle for the match or a president or anything else to move instantaneously from one spot to the other. And he will likely tell you that (2) is false because it would take a miracle to get Obama to North Korea without his secret service. And he will say this meaning to convey that requiring a miracle is a bad thing: that is he will take the fact that a scenario involves a violation of natural law as showing it is irrelevant to answering serious questions about "what would happen if".
Folk policy, if we take them at their word, seems to be no miracles, big or small.
The philosopher who adheres to SMALL MIRACLES cannot speak with the plain man here because the worlds he counts as closest always contain a miracle. Granted, they are supposed to be miracles so "small" and "inconspicuous" that the plain man wouldn't notice them. And the standard view has it that so many different small miracles might do the job that the philosopher can't be expected to say what particular miracle might be relevant. All of which makes the tension with the folk less—- well—conspicuous. But the tension is there nevertheless: folks invariably take arguments to the effect that it would take a miracle to make both A and C true, as arguments that C would be false if A; that is, as arguments that A > C is false. But folks don't think all counterfactuals are false.
Folks talk as if the closest worlds should be legal. But that is not to say that folks adhere to the FIXED LAWS theory. FIXED LAWS said that the closest worlds are the legal ones that most resemble a. The problem was that any legal world different from a must have been different from a for all eternity and who knows what differences those might have been or what other differences those differences might entrain throughout the eons? Certainly not folks.
But why should folks care about resemblance in the distant past?
When folks consider a counterfactual like (1) they want to know what happens at a world that is as much like a as possible—that is as is nomologically possible —when the match is stuck: that is, a world which is much like a at time TA. Of course it is true that any legal world that differs from a at TA must have a different history than a. But folks don't need to know any details of those histories provided they know that those different pasts wouldn't make for relevant differences at TA.
But can folks know that? Do they — that is, do we— have any way knowing how A-worlds resembling a at TA could legally come about?
According to the SMALL MIRACLES theory we must.
To see this: take the A-worlds that SMALL MIRACLES says are closest. Each of these worlds exactly resembles a up until some time prior to TA at which point a small divergence miracle occurs that results in A. Call an arbitrary one of such worlds 'WM''and call the time just after its divergence miracle occurs, 'The closest worlds may have their miracles at different times so TM may vary.TM'. According to SMALL MIRACLES, after TM everything that happens in WM will obey the laws of nature. That means that the total state of WM at TM is nomologically possible (according to the laws of a). That in turn means that there is at least one legal world, WL, in which this state comes about legally. Call WL a "legal counterpart" of WM. Call this way of finding a legal WL by first imagining a miraculous WM, "legalizing" a miracle.
This legal world, WL will not resemble a or WM before TM and WL will never exactly resemble a. But because they exactly overlap at TM and obey thereafter the same laws, WL and WM will resemble each other forevermore. In particular WL will resemble a in exactly the ways WM does at TA and the theory we are considering now is that is resemblance at TA that matters. If that is so it doesn't matter how WL got to be the way it was prior to TM. A fortiori, we can be as confident that there is a WL, as described, as we are confident that there is a WM.
If we count as the closest worlds – not the miraculous ones like WM – but instead their legal counterparts like WL, we are going to get the same results as SMALL MIRACLES with no miracles. The only attraction of SMALL MIRACLES in the first place was that it seemed to get the right results – that is the ones folks get. This way of doing things gives us those results while respecting the folk disdain for the miraculous.
Thus the theory I've labeled the "Legalized Miracles" theory. It is the invention of Phillip Goggans in a "Do the Closest Counterfactual Worlds Contain Miracles" Pacific Philosophical Quarterly 73 (2):137 - 149 (1992)paper in 1992 and from now on I'm just going to call it 'Goggans' Theory'.
Thinking of Miracles
If Goggans' theory did not garner many supporters it was probably because it seemed conceptually parasitic on the SMALL MIRACLES theory: If it is legal worlds that are relevant to counterfactuals, why should we bother first thinking of a miraculous world to legalize?
Goggans' answer was psychological. On his account, to find the legal worlds relevant to 'A>C' we must engage in counterfactual backtracking. That is, we must ask ourselves what earlier differences in the world prior to TA would have legally resulted in A. But, he said, this kind of temporally reversed counterfactual reasoning is difficult:
"Why is it more difficult to evaluate backward counterfactuals than forward counterfactuals? I suggest two reasons. First, we always experience time running forward, never backward. Since we lack empirical models of time running backward, it is difficult to picture this in our minds. Second, we have more practice in forward inference." "Do the Closest Counterfactual Worlds Contain Miracles" Pacific Philosophical Quarterly p.145•
Given we are so bad at reasoning in temporal reverse, what are we to do? How do we find a prior, nomologically possible, state of the world that we can be confident would have legally resulted in an A-world? Goggans says:
"Clearly, we need to use past history in selecting the proper TA time slice. We must start at some time in the actual past and imagine how things would have gone in order to result in [Obama's being in Korea]. Only then can we evaluate ['if Obama were in Korea'] counterfactuals. … The appropriate TA time slice will be one which, like all the rest, occurs in accordance with the laws of the actual world. But for the purposes of selecting it, we way may think of it as if it were a divergence from a history identical with that of the actual world. In this way, miracle imagery plays an important role in evaluating counterfactuals. This does not require that the antecedent world contain any violation, however small, of the laws of ." "Do the Closest Counterfactual Worlds Contain Miracles" Pacific Philosophical Quarterly p.146•
So the idea is that we use the SMALL MIRACLES procedure to visualize a world with a miracle sufficient to get A to come about and then we infer that world's legal counterpart to use for the purposes of counterfactual reasoning.
This does not begin to work even on its own terms. To see this, try the experiment: first envisage a nearby WM that would get Obama to Korea right now. If it helps, tell yourself that contains a miracle; "a divergence from a history identical with that of the actual world". Get a picture of that that world at the time TM, just after the miracle. Now get a second image of a world that looks exactly like that world at TM except that it comes about from a different history "without any violation, however small, of the laws of ". Does getting the first image help you get to the second image? No. Because at time TM they are the same image! Goggan's Theory requires that WM and WL be exactly alike at TM, so getting an "image" of one is not going to help you "visualize" the other at that time. And note too that there is no "miracle" imagery in these snapshots. The state of WM and WL at TM and after are supposed to be identical and nomologically possible—that is to say, miracle free. To "visualize" the legal world's history prior to TM you would have to be able to backtrack: to see how things would have to have been to bring it about that they were as they were at TM without the miracle. But, the whole point of the exercise was to somehow avoid doing that because we find legal backtracking so difficult.
The problem that Goggans thinks he has to solve is to explain how we come to think of a world that looks like WM and WL do at TM. He thinks that allowing miracles helps. But the SMALL MIRACLE theory doesn't give us any procedure for imagining the appropriate miracles, only the instruction to prefer "small", "inconspicuous" ones. We cannot compare worlds for the size of the miracles required to bring them about unless we have already thought of what worlds we want to compare and no SMALL MIRACLES theorists—certainly not Lewis or Bennett— tells us how to do that. If there is a psychological problem about how we imaginatively "run the clock backwards" in A-worlds from TA to TM, it is as much a problem for Lewis or Bennett as it is for the man on the street.
In any case, what is philosophically relevant here is not how we come to think of these past states of the world but what distinguishes them from other states that might be imagined. We—that is Lewis, Bennett, Goggans and the rest of us folks— all agree that if you want to evaluate A > C, you will think of a nomologically possible state of the world at some earlier time; a state of the world from which it will legally come about that A and determine if C would also (legally) come about there. What the legalizing move shows us is that whether we imagine that state as coming about miraculously or lawfully from the history of the world to which it belongs will make no difference to how we evaluate the truth of counterfactuals like (1) and (2).
What matters—what we need a theory of counterfactuals to explain— is why we pick the states that we do from the infinity of others that would also legally result in A to decide what would happen if A. The SMALL MIRACLES answer is that these states embody the smallest divergences from the actual past that we can imagine that would bring it legally about that A.
But there is another answer on offer that is consistent with everything we have seen thus far. It is that we are not as bad at turning the clock backward as Goggans thinks and in fact that is what folks are doing when they reason counterfactually: they are identifying states of the world that would legally produce A-worlds that diverge as little as possible from the actual world at TA.
This is the SIMPLE THEORY.
THE SIMPLE THEORY
The Simple Theory was invented by Jonathan Bennett in Philosophical Review 1984,93:57-91"Counterfactuals and Temporal Direction" (Bennett '84). I wish I could call it "Bennett's theory", but I am estopped from doing so because Bennett In his Philosophical Guide to Conditionals, 2003later renounced it in favor of SMALL MIRACLES. "SIMPLE" is the name Bennett gave the theory after he abandoned it so I will stick to that.
In Bennett '84, he introduces and argues for SIMPLE as an alternative to the Lewis's CD&TA theory. I discussed the CD&TA theory and its problems in my last Computational Metaphysicspost and I will not recapitulate all that now. In any case, my arguments there only supported Bennett's criticisms which, in my view, are decisive. Anyone curious about the CD&TA theory and how it goes wrong should read Bennett '84. I will talk more about CD&TA later, but it better suits my purposes here to show how most of Bennett 84's objections to the CD&TA theory can also be brought against SMALL MIRACLES and in support of SIMPLE.
The first point has to do with SIMPLE's ability to explain Folk practice. We have agreed that when folks evaluate counterfactuals they think of prior states of the world which are similar to a recent prior state of the actual world. Normally, it seems, the more similar and more recent, the closer the alternative states are taken to be. SMALL MIRACLES explains this as the upshot of Folks desire for states that can be located in worlds whose histories overlap that of a as much as possible for as long as possible. But there is another explanation.
It is a logical truth that any two worlds governed by the same deterministic laws that are different at any time must be different at every prior time. But it also seems a, contingent but remarkably general, fact about our world that small differences at any time tend to make for bigger differences latter on; indeed, bigger and bigger as time goes on. Small goings on have consequences; they leave traces and those traces in turn have consequences that multiply over time and spread out in space. We can cast the point as a subjunctive generalization.
At a, any small difference would always result in larger differences as time went on.
Why this is true is an interesting question, but one that need not distract us just now. It is enough that we agree that AMPLIFY captures a gross contingent truth about the actual world. Certainly Lewis would agree; as we shall see, in CD&TA Lewis stakes the whole of his argument on AMPLIFY.
Given AMPLIFY, if you want to find a prior state of the world which leads to an A-world as much like a at TA as possible, you should look for states that resemble prior states of a as much as possible, as recently as possible, prior to TA. And that is so whatever history those states are imagined to have. If what matters is deriving an A-world which resembles a at TA as much as possible consistent with a's laws then more recent states are more likely to serve. Less recent states will be more likely to produce gratuitous differences from a— that is, irrelevant differences in addition to A—at TA than the later ones
In this way SIMPLE can account for our bias towards small changes in the recent past as readily as SMALL MIRACLES. And, unlike SMALL MIRACLES, SIMPLE can also explain why we need periods of transition prior to TA: the past must be different if A is to come about lawfully, as it must, according to SIMPLE, at all the closest worlds.
The SIMPLE theorist can also agree with Lewis that we want A-words with "smooth" and "orderly" transitions from the past but, unlike Lewis, can say why. Remember that Lewis said that the problem with the jumps that FIXED PAST gives us is that they involved objects abruptly jumping around. Bennett didn't like the fact that such jumps were "conspicuous". But while it is true, as a matter of fact, the laws of our world require macro-physical objects to move "smoothly"— that is with no conspicuous, spatiotemporal gaps— that fact should not be built into our analysis of counterfactuals. The macro-physical laws of a world very much like ours could allow for spatiotemporal discontinuities. Imagine a world where matches and everything else always moved discontinuously: a deterministic world with perfectly Newtonian laws but granular time. It would look like a coarse stop motion film of our world. At such a world, it would surely be true to say that that if the match had been struck it would have traveled from a foot away in an instant; that is what the laws of that world would require. And that would be so even if we tinkered with the laws so as to make those jumps noticeable – and hence not inconspicuous—to the inhabitants of that world. At the world we inhabit we think closest worlds should incorporate smooth and inconspicuous transitions because those happen to be the kind of transitions that are legal given the laws of a.
Of course, according to SIMPLE, the closest A-worlds will not come about after a miraculous "transition" from a past exactly like a's. If a is deterministic then the closest legal worlds must always have differed from a. But those differences in the distant past are irrelevant to the SIMPLE analysis unless they make for a difference at TA and, given a's laws, they can make a difference at TA only if they also make very for recent differences. AMPLIFY tells us that the smaller and more recent those differences are, the fewer differences there are likely to be at TA.
And the SIMPLE theorist can agree with Lewis that when we evaluate A>C we look for A-worlds without gratuitous differences from a. But he can go one better and say exactly what makes a difference gratuitous: a gratuitous difference is a TA fact which would not have been required by the laws of a to make A true in a world like a at TA.
Indeed SIMPLE gives us a kind of procedure for deciding if any A>C is true. First think of the prior states of the world that include all those facts that would have to have been the case if A were true given the laws of a; then select from among these the ones most like a at TA.
This is the kind of counterfactual backtracking that Goggans complained was too hard for us. I've already suggested that folks find it easier than he thought, though to make philosophical sense of it we are going to need an account which explains the truth conditions of this kind of backwards counterfactual.
As Bennett argues in Bennett '84, one of the great merits of the SIMPLE theory over SMALL MIRACLES is that it does give us just such an account.
Backtrackers are counterfactuals in which the time of the consequent is earlier than the time of the antecedent. Some backtrackers seem true. Thus, assuming determinism, it looks like it should be true of any un-struck match that.
(3) If that match had been struck the entire history of the universe would have (I discuss the "have/have to have" distinction below.to have) been at least slightly different.
After all, determinism entails that it is logically impossible for that match to be struck given the history and laws of a. But, (3) doesn't come out true under SMALL MIRACLES since, on that account, in the closet worlds where the match is struck, the history of the universe is exactly like ours right up till some recent TM. So even if SMALL MIRACLES is right for forward trackers like (1) we are going to need a different theory— at least a different similarity metric— to make back-trackers like (3) come out true
This was fine by Lewis. Lewis didn't like backtrackers much. He wanted to define causation in terms of counterfactual dependence. But in our world causation goes forward and so it had better be that counterfactual dependence goes forward too. There especially ought not to be true any backtracking event counterfactuals of the form:
If event e1 hadn't occurred at TLATER then event e2 wouldn't have occurred at TEARLIER.
Or, if there were any plausible examples of this sort, then it had better be that they were true in a different way— or on different grounds— than the forward-tracking ones.
And for a period it seemed that there were good reasons for expecting backtrackers and forward trackers to have different logics. In his 1974 J.F.Bennett, (1974). "Counterfactuals and Possible Worlds", Canadian Journal of Philosophy 4:381-402review of Lewis's Counterfactuals, Bennett— following P.B.Downing, (1959) 'Subjunctive Conditonals, Time Order, and Causation'. Proceedings of the Aristotelaian Society 59: 125-40. P. B. Downing— had found an argument that seemed to show that any account that evaluated backward and forward counterfactuals in the same way— that is any theory that treated the same worlds as closest for purposes of evaluating forward and backtracking counterfactuals— would give contradictory results.
The argument went like this: Suppose we ask ourselves what would happen if Obama were in North Korea right now? Well, given that the USA and the DPRK are technically at war and given the North Korean regime's notorious brutality and contempt for international law, we might conclude:
(4) If Obama were in North Korea right now, he would be in great danger.
On the other hand, if we allow ourselves to backtrack, we will reflect that for Obama to make this trip there would have to have been some sort of prior diplomatic breakthrough in the relations between the two countries and extensive arrangements would have been made to make him safe and welcome on arrival. So:
(4') If Obama were in North Korea right now, he would not be in great danger.
(4) and (4') should count as inconsistent on anybody's account of counterfactuals and in Bennett '74, he offered cases like this as demonstrating the perils of treating forward and backtracking counterfactuals as if they were made true by the same worlds. Backtrackers would need a separate theory. This was welcome news to Lewis who was happy to push backtrackers offstage.
But by Bennett '84, Bennett had decided that the Downing style stories didn't work. They derived a contradiction all right but only by exploiting vagaries that had nothing to do with temporal direction.
Our commonsense standards treat some counterfactuals as clearly true or false but others are toss ups that can be decided either way. The phenomenon was famously memorialized by Quine with the examples:
(5) If Caeser had been in command in the Korean War, he would have used the atom bomb.
(5') If Caeser had been in command in the Korean War, he would have used catapults.
Both of which can heard as true or false. It is one of the merits of the Lewis-Stalnaker semantics for counterfactuals that it can explain what is going on in terms of the vagueness of the similarity relation. Worlds greatly similar in some respects may greatly differ in others. Which respects we take as relevant may vary as our interests vary from context to context. As Lewis says:
"…we call on context… to resolve part of the vagueness of comparative similarity in a way favorable to the truth of one counterfactual or the other. In one context, we may attach great importance to similarities and differences in respect of Caesar's character and in respect of regularities concerning the knowledge of weapons common to commanders in Korea. In another context we may attach less importance to these similarities and differences in respect of Caesar's own knowledge of weapons. The first context resolves the vagueness of comparative similarity in such a way that some worlds with a modernized Caeser in command come out closer to our world than any unmodernized Caesar. It thereby makes  true. The second context resolves the vagueness in the opposite direction, making [5'] true."Counterfactuals 1973, Cambridge,Mass.:Harvard University Press.•
The phenomenon doesn't require that we give (5) and (5') different analysis only that, in the context of any particular argument we should keep in mind which resolution of the vagueness is at work or run risk of contradicting ourselves.
Both (5) and (5') are forward counterfactuals, but the same vagueness can invade backtracking arguments and that seems precisely what is going on in cases like (4) and (4'). Worlds with Obama in Korea now are different from a in varying respects. Some of these worlds are very much like a now with respect to the diplomatic hostility between the USA and DKRP but so unlike a in respect to their standards of presidential security that Obama finds himself alone behind enemy lines. Other worlds guard the president's safety just as much as we do in a but have different and more amicable diplomatic histories. There is no right answer to the question "which worlds are closer to a"? And we may answer either way depending on what kinds of similarity are relevant to our dominate concerns. The apparent contradiction here arises from switching standards mid- stream. It may be a fallacy easier to commit when one is mixing forward and backwards counterfactuals but the reasons it is a fallacy have nothing to do with temporal direction.
With the Downing style arguments out of the way, nothing prevents us from demanding a unified analysis of forward and backward counterfactuals. But this is not a demand that the SMALL MIRACLES theory can meet Though for an (uneasy) attempt to do so look at Bennett's Philosophical Guide pp.276-277. Note, this doesn't succeed in making (3) come out true. easily. At legal, deterministic worlds, we can, in principle, predict the future given all the present facts and, from those same facts, retrodict every possible legal past. But SMALL MIRACLES worlds are legal only from TM forward. The laws will tell us how things would have been different after— and back to— TM, but not earlier. Indeed Small Miracles seems to require us to say that, even in deterministic worlds, for any A at any TA there must be some prior time TM such that nothing prior to TM would have been different if A had been true; so on a strict SMALL MIRACLES analysis, (3) comes out as analytically false.
In contrast, the closest SIMPLE worlds are legal always. Once contextual vagaries are factored out, the same ordering of worlds is relevant to forward and backward counterfactuals. SIMPLE tells us A > C iff C is true at the legal A-worlds most similar to a at TA. And it does not matter if TC is before or after TA or how much before or after.
This unified treatment of the truth conditions of forward and backwards counterfactuals in turn gives a unified logic for arguments that mix the two. Allowing us to explain when and why one may validly infer, say,
(6) If the match had lit the entire history of the universe would have been different.
From (3) and:
(7) If the match had lit it would have been struck.
Moreover we can, drawing on materials already at hand, explain the distinction—often at work in the preceding paragraphs—between the ways things would have been different and the way they would have to have been.
Would Have to Have Been
We sometimes want to express our counterfactual opinions not just in terms of what "would have been the case if…" but in terms of what "would have to have been…". The contrast shows up with forward counterfactuals as well: we sometimes want to say not just "in that case things would be thus and so" but, more strongly "in that case things would have to be thus and so." What difference are we getting at?
Let us symbolize this "have to" connection as:
A >> C
Obviously, A>>C entails A>C but not vice versa. When is A >> C true? The first part of the answer is clear enough:
A >> C if C is true in every legal-A world.
In other words, A>>C if C is nomologically necessary or nomologically necessary given A. Thus:
If Obama traveled to North Korea he would have to travel (have travelled) at less than the speed of light.
If Obama travelled to North Korea he would have to (have) expend(ed) some energy.
But while this is sufficient, for A >> C, it isn't always necessary. I noted early on that the man on the street would likely insist:
(6) If Obama were in North Korea the secret service would have to have gone with him.
But clearly no law of nature requires that that man be accompanied by those people. Indeed, while it seems true that:
(7) If Obama were in North Korea now he would have to have travelled there at less than light speed.
We cannot explain why this is so simply by appealing to nomological necessity alone. After all, there is a legal world in which Obama is in North Korea without travelling there at all: a world where his parents made different decisions so that Obama was born in Pyongyang, not Hawaii. Of course, a world like that is vastly unlike a now and has been increasingly so for many decades. So different that it is a non-starter the competition for closest-world. Yes, we can contemplate counterfactuals that begin "If Obama had been born in North Korea then…" but the worlds relevant to this antecedent are very different from those relevant to (6).
And that, I submit, is precisely what we are insisting on when we speak of what would "have to have been" the case. What we are doing, when we escalate from 'A>C' to 'A>>C' is signaling that we regard the consequent as nomologically guaranteed by the conjunction of A with other truths that we assume to hold at all closest A-worlds.
The point here compliments our observation about the vagueness of the similarity relation. Worlds may be similar in some respects but different in others and which differences count as relevant may vary with context. But these are tradeoffs at the margins. Not every fact about the a can be traded away. It is not true that:
(8) If Caesar had fought in the Korea War he would have to have known about the atom bomb.
Because the Korean War might have been fought millennia earlier and worlds like that are more similar to the actual world in some respects than ones in which Caesar was born millennia later. On the other hand, it is not only true that:
(9) If Obama were in Korea now he would have travelled there.
It is also true that:
(9') If Obama were in North Korea now he would have to have travelled there somehow.
because while it is nomologically possible that Obama be a lifelong resident of North Korea there are no worlds like that are that are compossible with the facts about Obama that everyone would hold constant in evaluating (9).
Of course, in saying this I am making some assumptions not just about what makes for similarity among worlds in general but about the actual facts about a to which similarity binds. In this way arguments about "what would have to have been the case" are another way of arguing about facts about a. Two people might agree about all the facts but disagree about (8) because they are differently construing the context. But the man who asserts:
(10) If Romney had defeated Obama it would have to have been the upshot of voter fraud.
and the man who says:
(10') If Romney had defeated Obama there would have to have been no voter fraud.
Unequivocally have a disagreement about the actual political facts.
I think it is true that:
(11) If Obama were in Korea right now he would have to have flown there.
Yes, there are nomologically possible worlds where he takes The Slow Boat or dog sleds across the Pole but these options are impossible given the obvious realities of presidential life and travel.
On the other had while I think that it is true that:
(12) If Obama were in Korea right now, he would have flown there on Air Force One
I wouldn't say:
(12') If Obama were in Korea right now, he would have to have flown on Air Force One.
Because I think a world where, say, he takes Air Force Two because of some mechanical malfunction, is not beyond the realm of, as we say, "real world" possibility.
This way of making sense of "would have been" and "would have to have been" is available to the SMALL MIRACLES theorist but only over limited intervals. He may allow himself to say how things would have to have been different after TM, but not before. He could say "If the match were lit it would have to have been struck" since the striking presumably occurs after the miracle that leads to the lighting but, as we noticed above SMALL MIRACLES, applied to backtrackers, denies that anything would have been or would have to have been different in the distant past to bring about the lighting even in a deterministic a.
SIMPLE's unified treatment of back and forward trackers is the upshot of its temporal neutrality. Unlike SMALL MIRACLES it does not explicitly require the closest worlds resemble a before or after TA. And this, Bennett noted, should all by itself be counted as a merit of SIMPLE. Certainly it should have been counted as such by Lewis. Recall that Lewis himself tabled SMALL MIRACLES precisely because of its built in appeal to the difference between past and future. The whole point of the very un-simple CD&TA account of counterfactuals was to give an account that gives the same results as SMALL MIRACLES without the explicit requirement that past, but only past, similarities be preserved. SIMPLE has that temporal symmetry built in: resemblance to a prior to TA is as irrelevant to closeness as resemblance after. As Bennett says.
If [TA] is the present, then we must put away our history books and crystal balls, using only our eyes and our capacity for causal inference in both temporal directions. Philosophical Review 1984,p.841•
Bennett Abandons Simplicity
So why did Bennett give up on the SIMPLE theory?
Bennett proposed SIMPLE in 1984. By 1992—the date of Goggans' article—he had rejected it, as Goggans, a Bennett student, there reports. In Bennett's 1996 , Philosophical Guide to Conditionals, he explains why. His arguments there turn on few examples—to my mind, ill-chosen examples— which we'll have to look at very closely.
The first is:
If the German army had reached Moscow in August 1941, it would have captured the city.
AUGUST > CAPTURE
Bennett, I think, believes this is true, though not obviously so. I think so too and will so assume in what follows.
The problem with SIMPLE, Bennett says, is not that it counts AUGUST > CAPTURE as false, but that it makes it come out true for the wrong reasons. That is, it picks out the wrong worlds as closest.
"The closest A-worlds, according to the Simple Theory, are to be identified initially by their similarity to a in August 1941 except for the difference that at them the German troops are reaching Moscow (the time of the antecedent need not be a duration-less instant; it can be more or less long, depending on what the antecedent is.) In August 1941 at those worlds, then, matters stand thus: the German troops reach Moscow, and otherwise things in Russia are pretty much as they were then at a – the layout of the Moscow streets, the weather, the durable aspects of the German and Russian national characters, the small number of Soviet troops (most of them fresh and inexperienced) in the immediate vicinity of Moscow.
Stop! Something has gone wrong here. Most of the listed similarities are all right, but not the last one. At a in August 1941 Moscow did indeed contain few defenders (I am supposing), but we will not let that fact affect how we evaluate August>Capture. Most of us will not, anyway. After putting unloaded questions about this to thoughtful informants, I concluded that when evaluating August >Capture most people will assume that if Hitler's troops had assaulted Moscow in August 1941 there would have been more Soviet troops in the vicinity, and most would have been battle weary. The Soviet armies did in fact spend the summer and autumn of 1941 falling back before the advancing Germans. If the Germans had reached Moscow by August, the retreating Soviet troops would have been crowded back into its vicinity also."Philosophical Guide pp.211-212•
Bennett's thought here is that that even if AUGUST > CAPTURE is true it isn't true because the battle for Moscow would have been a walkover. This thought is more complicated than it needs to be. The simpler point is this: Bennett thinks that the SIMPLE THEORY makes it come out true that:
If the German army had reached Moscow in August 1941, they would have found the city virtually undefended.
If so, that certainly would count against SIMPLE since AUGUST > UNDEFENDED is obviously false (thus, one would have thought, making it a better counter-example than AUGUST >CAPTURE).
So why does Bennett think the SIMPLE THEORY gives us AUGUST > UNDEFENDED? His reasoning seems to be as follows: since UNDEFENDED is true at a, any legal world at which UNDEFENDED is true is closer to a than a world at which it is not, other things being equal. The conjunction AUGUST & UNDEFENDED is not inconsistent with any laws of nature, so there are legal worlds where AUGUST and UNDEFENDED are both true and, other things being equal, they are a fortiori closer to a than worlds at which AUGUST & DEFENDED.
The problem with this line of reasoning lies in that "other things being equal" clause. Every legal world at which the German army reaches Moscow in 1941 is a world at which that army traveled there. The travel of that huge and heavily mechanized force would have—would have to have— left causal traces that endured up till 1941 and beyond. Those traces will mark differences between each such world and a in 1941 and while not all of these differences will be nomologically required for AUGUST, neither will they be, at any world, gratuitous differences.
It follows that the SIMPLE theorist cannot be required to say that
Indeed generalizing the inference apparently at work here:
C & Possibly (A & C)
∴ A > C
would make every A > C true provided C was true and compossible with A. In which case A > C would always be true if C, unless A >> not-C. just because:
UNDEFENDED & Nomologically Possible (AUGUST & UNDEFENDED)
it must be that:
AUGUST > UNDEFENDED
Because each world at which AUGUST & UNDEFENDED is true might differ— indeed, might have to differ— from a in ways that make it less like a than worlds where AUGUST & DEFENDED.
To see what difference this makes let us return to the front with Bennett.
At some legal worlds the German troops attack Moscow in August 1941, opposed only by the few reserve divisions that were actually there then. Many logically possible histories yield that result: invent one to suit your fancy. But when we talk soberly, carefully, about 'what would have happened if they had reached Moscow in August', most of us think not of any of those worlds but rather of ones at which some time before August 1941 things are nearly or completely as they were at a, and then move off the track of the actual world through some shift: the Germans start earlier or fight harder or have better weather or leadership than at a, so that their eastward drive reaches Moscow sooner, against defenders who are increasing concentrated into the area around the city. In the Simple Theory, too, there is a history for the obtaining of the antecedent; but that theory gets the history wrong because it is not constructed so as to start from a state of affairs exactly like a's.Philosophical Guide p.212•
Bennett is confused here. It is not up to the defender of the SIMPLE THEORY to tell a fanciful story that gets the Germans to an undefended Moscow; it is up to Bennett. That is: if Bennett wants to give us a counter-example to the SIMPLE THEORY he must describe a world in which AUGUST & UNDEFENDED and which is more like a in 1941 than any world in which AUGUST & DEFENDED. And note that not just any fanciful, "logically possible history" will do. SIMPLE requires that he tell us a nomologically possible story; a story about a legal world. This is going to be hard to do.
Again, it is not enough to simply say that AUGUST and UNDEFENDED are nomologically compossible and assume that there must therefore be a nearby world where both are true. Think of all the other things that are true in a in August 1941: Neither the Axis or Allied leaders believe that the German Army has reached Moscow. All those pins on all the maps in Moscow and Berlin show the German army far to the west. In a the Germans are facing thousands and thousands of Russian troops, tanks and artillery pieces hundreds of miles from Moscow all of which are defending westward. Hitler is exasperated with Guderian. Stalin is refusing to evacuate. Churchill is praising the Russian defence. All around the world newspapers are reporting the stalled German advance… and so on. Now try to tell a story which preserves all of those facts but still makes AUGUST true.
It cannot be done. In any legal story you can tell the Germans will have to have travelled to the outskirts of Moscow somehow. The German and Russian leaders would have to have noticed and taken steps. And the Russian army of 1941 simply could not be West of the German army facing the wrong direction oblivious to the fact that the entire German army had somehow (miraculously!) slipped by them. Something has to give. Some actual facts will have to be different at any AUGUST world. And, prima facie, the changes required by any story that keeps Moscow UNDEFENDED (Stalin Dies? Surrenders? The entire Russian Command gets drunk for the whole month of July? The Germans get the atom bomb in 1940?) will make for a far different 1941 than one in which retreating Russian troops fall back to defend the city.
Later in A Philosophical Guide Bennett uses this same style of argument again.
"If we apply the [SIMPLE THEORY] to a counterfactual of the form 'If dinosaurs had been roaming the world in 2001…' it requires us to consider worlds that are as like a as possible in 2001,consistently with dinosaurs roaming through them. Those worlds contain not only dinosaurs but also mammals, indeed humans, nay skyscrapers and the Internet! This is absurd: we would never look at such a conditional in this fashion." Philosophical Guide p.279•
Here, as before, Bennett is asserting there is a counter-example without bothering to tell us what it is. Take the "absurd" counterfactual
If dinosaurs roamed the earth in 2001 then the Internet would still exist.
If DINOSOAURS >INTERNET is to serve as a counter-example to the SIMPLE THEORY , it is Bennett who must tell us a story about a legal world at which it is true that DINOSAURS & INTERNET and which is more similar to the actual world at 2001 than any world with DINOSAURS and NO-INTERNET. That would be quite a story. Michael Crichton tried to tell just such a tale and came close. Alas, the science Crichton relied on was fictional. It is now generally agreed that that the world of Jurassic Park is not nomologically possible (the half-life of DNA is too short). Perhaps Bennett can tell a better, legal story (if so, I recommend he keep the movie rights!) but he doesn't tell it here and until he does he has not given a counter-example.
All the factors that make the prospect of DINOSAURS & INTERNET world absurd—- how could human beings have evolved with all those giant predators around?— are arguments that there is no legal world remotely like ours—hence no closest SIMPLE world—with DINOSAURS and INTERNET. And if Bennett could tell a story in which DINOSOURS and INTERNET legally come about in a world very much like ours the story would necessarily make DINOSAURS > INTERNET seem less absurd. Indeed if Bennett weren't careful, he might convince us—SIMPLE minded folk that we are— that the counterfactual is true!
Bennett's argument against the SIMPLE THEORY of backward counterfactuals takes us back to the Russian front.
"In actuality, in July 1941 there were few Soviet soldiers in Moscow or in the area stretched for several hundred miles west of it; most were further west still, battling the Germans. Now consider a backward counterfactual 'If the German army had reached Moscow early in August 1941…' What worlds must we consider in evaluating this? According to the proposed theory, we should look to worlds at which the Germans stroll towards Moscow through countryside devoid of opposing armies. Here, as in the dinosaur case, the insistence on likeness to a at TA leads to a handling of counterfactuals that does not accord with any of our interests, and it infects backwards as well as forwards conditionals."Philosophical Guide p.279•
Once again, Bennett takes it as obvious that there was a nomologically possible world where the Germans get to stroll unopposed toward Moscow leaving all those Russians behind them (One wonders, in this world, are the Russians still facing west? Where do they think the Germans are? Does anyone tell Stalin or Hitler?) but which is otherwise more like the actual world in 1941 than ones in which the "the Germans start earlier or fight harder or have better weather or leadership" and the "Soviet armies spend the summer and autumn of 1941 falling back." Once again, we wish Bennett had explained how the Germans could have pulled this off (and are thankful Guderian didn't know the trick). Absent such an explanation it is hard to believe that there is any nomologically possible world anything like ours in which the entire German army manages to waltz through the Russian lines unnoticed and unopposed.
So how would the SIMPLE theorist find the closest AUGUST worlds? It is true, as Bennett says, that SIMPLE does not require us to start with a world which is exactly like a's at any time in the past, but it does require that we come up with a history that ends up with a world as much like a in 1941 as legally possible without violating any laws along the way. Given AMPLIFY, that is, given that at our world, small differences at any time tend to amplify over time, the SIMPLE theorist would try to think of worlds very much like a at some point in the recent past of 1941 (again as recently as the laws allow). He would try to ("carefully" and "soberly") think of legal worlds that are, at some time before 1941, nearly as they were at a then but are just different enough that staying on a legal "track" will result in AUGUST.
That, I submit, is exactly what Bennett's "thoughtful informants" and rest of us folks actually do.
BACK TO THE FUTURE
Bennett gives one other reason for abandoning his SIMPLE THEORY.
"Anyway, an even sterner difficulty beset the Simple Theory— an old, familiar point which I negligently overlooked. Consider someone who in 2003 says: 'If that hill outside Syracuse had not been leveled last year, it would have been a superb site for a memorial to the Athenian soldiers who starved to death in the marble quarries there 2416 years ago.' This cannot be true unless at the closest A-world Athenian soldiers did die a Syracuse in 413 BCE; but the Simple Theory refuses to let us assume that. We cannot know how different things might be 413 BCE at the closest legal world at which the bulldozers spare that Sryacusan hill in 2003 CE. No thoughtful person would have the faintest sense of this speakers running any such risk; and that is because we would all hear him as speaking about a world that exactly resembles a shortly before the landscaping plan was launched in 1999. Similar cases abound. We often characterize a state of affairs in a way that logically reaches back to earlier times; and when this happens in the consequent of a subjunctive conditional, we need the closest worlds to relate suitably to a at the earlier time, even if it precedes TA, the time of the antecedent." Philosophical Guide p.214•
This does indeed sound familiar. It sounds like the kind of epistemological objection we (and Bennett) made to FIXED LAWS. Take Bennett's (woefully cumbersome) example:
(13) If that hill outside Syracuse had not been leveled last year, it would have been a superb site for a memorial to the Athenian soldiers who starved to death in the marble quarries there in 413 BCE.
If he is true to his standards, the FIXED LAW theorist who endorses (13) would be claiming, among other things, that he had surveyed the various ways that the entire history of the universe might have unfolded so as to bring it about that the Hill was not leveled and concluded that among these worlds the ones which most resemble a are all ones in which the Athenians do indeed starve in 413 BCE. The claim would be absurd. No one could know how different things would have to have been 2415 years ago to change a contemporary landscaping decision and no ordinary person who heard someone assert (13) would understand the speaker to be committed to such an absurdly grandiose epistemic claim.
So much the worse for FIXED LAWS. What would the SIMPLE theorist who asserted (13) be claiming?
According to SIMPLE, past differences are irrelevant to closeness unless they make for a difference at TA. Yet if he asserts (13) the SIMPLE theorist is committed to saying that the legal worlds closest to a where the hill still stands in 2003 are worlds where it would serve as a memorial site for long dead Athenians. That entails, in turn, that in all these worlds the Athenians did die way back when. In that case, Bennett protests, the SIMPLE theorists takes (13) to be asserting some connection between those ancient deaths and that recent landscaping decision and how could anyone claim to know that?
To see the answer we need to get clearer about what exactly SIMPLE construes (13) to entail. Remember that SIMPLE is temporally symmetric; the same worlds that are closest for forward are also closest for backwards counterfactuals. So the simple theorist will take (13) to entail.
(14) The hill is not leveled in 2012 A.D. > The Athenians die in 413 B.C.E.
Which it seems most natural to express as
The Athenians would still have died even if that hill had not been leveled.
Now (14) does indeed assert a kind of connection between the distant past and recent events, but given that its consequent is already true it amounts to claiming the counterfactual independence of this fact about the past from this fact about the present. And that is not a risky claim. Given that the Athenians actually died, any world at which they die is more similar to a than one at which they don't, other things being equal. To cast doubt on (14) you would have to provide an argument that other things were not equal: Some argument which showed that the Athenians would have to have lived in order for the hill to be spared.
There can be that sort of backwards running counterfactual dependence. Bennett Philosophical Guide p.212 himself gives us an example:
If Adlai Stephenson had been the undisputed President of the USA in February 1953 he would (have to) have been elected in November 1952.
Here the argument for why the past depends on the future is clear enough. Being President requires having been elected. No such argument is on offer to show that the survival of the hill requires the survival of the Athenians. Absent such an argument (13) is the rational default. It is the null hypothesis and in asserting it the SIMPLE theorist is not taking any epistemic "risk".
Or so says the SIMPLE theorist. But does this really reflect the way folks understand counterfactuals. Does a "thoughtful person" who hears someone assert (13) really "hear" the speaker as committed to (14) and thus as "running the risk" that (14) is false. I think so though will I concede that it is hard to hear the commitment to (14) in the assertion of (13) just because the risk that (14) is false is so remote. That, however, is just an artifact of this example.
Take a different case. Suppose that, after the bulldozing of a certain hill in Belgium, Jones says,
(15) If that hill near Quatre-Bras hadn't been leveled in 2013 it would have been a splendid place for a memorial to Napoleon's victory at Waterloo.
Surely Jones must be heard as committed to:
(16) Hill is not leveled in 2013 > Napoleon wins at Waterloo
Now Jones might say (15) because he is confused about history: He thinks Napoleon actually won and he thinks would have done so even if the hill hadn't been bulldozed. But if we know Jones is not confused about the actual facts then it seems we must hear him as claiming:
(17) If that Hill had not been leveled, Napoleon would have (to have) won at Waterloo.
And thus committed to a very "risky"– indeed, absurdly unlikely— hypothesis about the connections between recent landscaping and events long ago.
All of which is exactly what the SIMPLE THEORY predicts.
How could Bennett have gone so wrong? Well, it may be relevant to note that while the Syracuse Hill example fails as an example to SIMPLE or FIXED PAST it is a perfectly good counter example to FIXED LAWS. And while the Russian Front example doesn't work against SIMPLE or FIXED LAWS it would serve as clear counter example to FIXED PAST (compare the German's miraculous appearance near Moscow to Obama's sudden transport to PyongYang). Perhaps the SIMPLE theory emerges unscathed because it got lost in the shuffle?
Or perhaps Bennett took his own instruction that we SIMPLE theorists should "put away our history books and crystal balls" a little too much to heart. The point of that remark was that for SIMPLE only similarity at TA is relevant. That is so. But it doesn't follow that the history can be ignored, because, at our world—the world where we actually evaluate counterfactuals -- present similarity is nomologically tied to past similarity. In the AUGUST > CAPTURE case the SIMPLE theorist doesn't have to cleave to actual history but he would be ill-advised to put his history books away. To evaluate the counterfactual he needs to get the Germans legally to Moscow somehow and he wants to get them there in a way which makes as little difference as nomologically possible to the way things actually were in 1941. Given AMPLIFY, his best strategy will be to open his history books to '1941 and then thumb backwards until he finds a point where a change in the story would have led to AUGUST. In principle, SIMPLE says nothing about how big or small those past changes may be. But again, given the way the actual world works, in telling his alternate history the SIMPLE theorist will be well advised to make his edits as small and recent as he can to avoid the (nomological) need for massive rewrites in the chapters about 1941.
Then again, maybe Bennett was influenced by an argument of Lewis's in a 1986 Postscript to CD&TA…
The device of "legalizing" miracles to find a legal counterpart to a SMALL MIRACLES world did not originate with Goggans '92. It too was invented by Bennett in Bennet'84. However, Bennett, quite correctly, didn't see any need to build the device into the SIMPLE theory he was advocating there. Instead he offered it as a separate argument against some claims Lewis had made in CD&TA.
In his '86 postscript, Lewis defends himself against Bennett '84 by trying argue that the worlds the legalizing device gives you—Lewis called them 'Bennett Worlds'-- are "deceptive". What Lewis meant by that and why he thought it was important is something I am about to explain, but I want to stress before we begin that whatever we make of Lewis argument here it isn't an argument against SIMPLE nor, indeed, was it likely intended to be.
Let us remind ourselves of what the argument was and where it lies in Lewis '86. In CD&TA Lewis had set himself the task of explaining the fact that time has a direction; a fact that he took to be centrally comprised by the temporal asymmetry of causal dependence.
The Temporal Asymmetry of Causal Dependence
At our world, what will happen causally depends upon what has happened but not vice versa.
The qualification, "at our world" is required because Lewis thought that time travel—that is reverse causation—was logically possible so that the asymmetry of causation was only a contingent fact about a.
Now Lewis had elsewhere for argued for a counterfactual account of event causation and if that account were correct it seemed that he could explain the asymmetry of causal dependence in terms of the temporal asymmetry of counterfactual dependence.
The Temporal Asymmetry of Counterfactual Dependence
At our world, what will happen counterfactually depends upon what has happened but not vice versa.
Which Lewis thought was another global truth about the actual world (provided at least that one restricts it to event-counterfactuals under the standard resolution). On a possible worlds rendering, this unequal treatment of past and future will show up in the closest worlds. The pasts of closest A-worlds will more resemble a than do their futures. Call this claim:
The Temporal Asymmetry of Closest Worlds
At any time TA the A-worlds closest to a always resemble a prior to TA more than they resemble it after TA.
So understood the Asymmetry of Counterfactual Dependence is guaranteed by SMALL MIRACLES since that theory stipulates that the history of the closest worlds will exactly match a at least up until TM and TM is supposed to be as close as can be to TA.
But in that guarantee lies the rub. Because SMALL MIRACLES builds in the requirement of prior closeness the asymmetry of counterfactual dependence will hold at every world and that in turn would make the asymmetry of causal dependence a necessary truth.
What Lewis needed was an account of closeness that worked as well as SMALL MIRACLES in getting the right counterfactuals to be true but which didn't build in the requirement of past similarity.
Lewis's solution was, in effect, to drop the explicit requirement that the closest worlds be compared only for past similarity.
THE CD&TA THEORY
A > C is true iff C is true at the A-worlds that most resemble a overall (counting past and future resemblances equally) provided they differ from a by the occurrence of the smallest miracles required for A.
This will give us the same results as SMALL MIRACLES and all the counterfactual asymmetries we want provided that we agree that:
The Asymmetry of Miracles
Small differences at any time between worlds like ours always lead to bigger differences later on. At worlds like a, only big differences now can lead to convergence later.
Which is the "possible worlds" way of expressing of the principle we have called AMPLIFY which can recast as:
At worlds like a, any small divergence would always result in a larger divergence as time goes on.
Any small difference from the way things are will leave traces that spread out and multiply over time leading to greater divergence later on. This doesn't logically preclude later convergence, but to erase those traces—to end up exactly the way things would otherwise have been-- will require more miracles to cancel them out and all these will add up to a bigger miracle.
We've already agreed that AMPLIFY seems true at a though -- like Lewis-- we have not tried to explain why. It clearly has something to do with the facts on the ground and the structure of our actual laws, but it is not analytically guaranteed by the meaning of 'law' or the assumption of determinism. Determinism rules out divergent futures given a common past but it does not rule out the convergence of world histories from different pasts. Yet such convergence seems hard to imagine at worlds like ours. As Lewis puts it, as a matter of contingent fact:
"Divergence from such a world as [a] is easier than perfect convergence to it. Either takes a miracle… but convergence takes a very much more of a miracle."Philosophical Papers II p.49•
And, of course, the contingency of the asymmetry of miracles is precisely the point since now, given the CD&TA analysis, the asymmetry of counterfactual dependence, and thence causal dependence, come out as contingent truths about "worlds like ours".
At this point enter Bennet 84' and his device of finding a legal WL – a 'Bennett World' – corresponding to every WM. The problem this gives Lewis is not that it threatens the CD&TA theory of counterfactuals but rather that it threatens to show that the Asymmetry of Miracles thesis is false.
To see this, take any A > C and think of the closest A-worlds as having histories as much like a's as you like. At any one of those worlds, WM, there will be a prior time TM at which the history of WM and a begin to diverge. Now think of the legal counterpart WL which is exactly like WM at TM but at which its TM state of affairs has come about legally. Now forget about a and look at WM and WL. Of necessity they are going to have very different pasts. WL got to its present state legally, WM by a miracle. Yet at TM and forever after WM and WL are indistinguishable. WM and WL have converged and have done so in virtue of that small miracle at TM in WM. And surely WL is "a world like ours". It has the same laws!
Here is Lewis explaining the problem:
"Begin with our base world [a], the deterministic world something like our own. Proceed to [WM] the world which starts out just like [a] , diverges from it by a small miracle, and thereafter evolved in accordance with the laws of [a]. Now extrapolate the later part of [WM ] backward in accordance with the laws of [a] to obtain what I shall call a Bennett world. This Bennett world is free of miracles, relative to [a]. That is, it conforms perfectly to the laws of [a] ; and it seems safe to suppose that these are the laws of the Bennett world also. From a certain time onward, the Bennett world and [WM] match perfectly, which is to say that [WM] converges to the Bennett world. Further, this convergence is accomplished by a small miracle: namely, the very same small miracle whereby [WM] diverges from [a]. For we had already settled that this small divergence miracle was the only violation by [WM] of the laws of [a] , and those are same as the laws of the Bennett world. Thus the Bennett world is a world to which convergence is easy, since [WM] converges to it by only a small miracle.
What then becomes of my asymmetry of miracles?"Philosophical Papers II p.56•
Lewis then proceeds-- in an argument as opaque as any he ever allowed himself to put to paper-- to defend the Asymmetry of Miracles by trying to show that Bennett worlds are not worlds like ours. They are fishy. They are "deceptive".
"A Bennett world [WL] is deceptive. After the time of its convergence with [WM], it contains exactly the same apparent traces of its past that [WM] does; and the traces to be found in [WM] are such as to record a past exactly like that of the base world [a]. So the Bennett world is full of traces that seem to record a past like that of [a]. But the past of the Bennett world is not like the past of a." Philosophical Papers II p.57•
In fact, he says, there is no reason to think that the extended history of a Bennett WL will look much like a's at all.
"Further, we cannot suppose that the two pasts are even close. … there is no reason to think that two lawful histories can, before diverging, remain very close throughout a long initial segment of time. To constrain a history to be lawful in its own right, and to constrain it also to stay very close to a given lawful history for a long time and then swerve off, is to impose two very strong constraints. There is not the slightest reason to think the two constraints are compatible."Philosophical Papers II p.56•
The argument here goes like this:
Suppose that Jones is thinking of smoking a cigarette. He draws a match from its box, readies to strike it but then then thinks twice about it. He puts the match back in the box. We all agree that:
(1) If that match had been struck it would have lit.
Lewis says we think this is true because we imagine a world, WM, exactly like ours up until a moment ago when a small miracle— say the miraculous firing of a single synapse in Jones' brain—gets him to strike the match and we see that, in that world, the match lights. There will be other differences from a in that world too, a little more heat, one less match in the box… but mostly small differences at least just then. The match is lit but the pyramids still stand, Nelson's column dominates Trafalgar square and Obama sits in the white house as president. Now think of the legalized counterpart of this WM: a WL in which that tiny synaptic event comes about as a lawful consequence of what has gone before. The past of that WL is going to have to be different prior to that synapse firing. How different? Well suppose that, in fact, the only legal way to get Jones and that match together at TM and to get that synapse to fire would be for WL to have a history radically different than a's. At this WL, the Egyptians never built the pyramids, Nelson lost at Trafalgar and Obama lost to Romney. A vast difference in the past and yet, ex hypothesi, at the time of lighting WL will look for all the world as if its history was almost exactly like a's. All the present traces of the actual past: the pyramids, the column, the man in the oval office will stand in WL as evidence for events that never happened in WL. Thus WL is "deceptive".
This is an odd argument. We have contrived the story so as to fill WL with misleading evidence about WL's past. Looking at how WL is now we would think it has a past like a's and it doesn't. But isn't that our problem not WL's? After all WL is a legal world and everything that we find in it now-- its pyramids, column and president-- will have come to be in perfect accordance with our laws and WL's history. Indeed, if we only knew all the facts about WL at TA, we could correctly retrodict the true history of WL and explain all the artifacts it presently contains.
Lewis concedes the point but says it isn't good enough:
"To be sure, any complete cross section of the Bennett world, taken in full detail, is a truthful record of its past; because the Bennett world, taken in full detail, is a truthful record of its past; because the Bennett world is lawful, and its laws are ex hypothesi deterministic (in both directions), and any complete cross section of such a world is lawfully sufficient for any other. But in a world like [a], one that manifests the ordinary de facto asymmetries, we also have plenty of very incomplete cross sections that post-determine incomplete cross sections at earlier times. It is these incomplete postdeterminates that are missing from the Bennett world. Not throughout its history; but the post-determination across the time of convergence with [WM] is deficient."Philosophical Papers II p.56-57•
Translation: Sure, if you knew all the facts about this Bennett world now you could deduce its true history. But if you just looked at an "incomplete cross section" of WL, say, just the pyramids , you would think the Egyptians built them and you would be wrong. And you wouldn't be able to figure out, by looking at the evidence we usually think is relevant, what the pyramids' "post-determinates" were; that is, you couldn't tell who really built them in WL.
Let us not dispute Lewis's point—elusive though it is. Let us agree that in this complicated way – viz. having present incomplete cross sections that fail to post-determinate past incomplete cross sections-- this Bennett world is indeed "deceptive". And let us agree that this Bennett world at least, is not a "world like ours" and thus not a counter-example to the Asymmetry of Miracles Thesis. Whatever this might show about Time's Arrow, does it tell us anything that suggests the SIMPLE theory is wrong?
Nothing I have said in defense of SIMPLE commits me to disputing any of the asymmetries Lewis defends. Indeed I have frequently appealed to the AMPLIFY phenomenon in making my case. I have used it to argue that, the A-worlds that will most resemble a at TA will indeed be Bennett worlds—legal worlds very much like a was very recently. That this is so is not entailed by SIMPLE's definition of closeness, but rather it is because a is, as matter of contingent fact, a world in which small past differences make for bigger differences later. At worlds like ours, where AMPLIFY reigns, we need to look to worlds with small recent divergences from a if we are going to comply with SIMPLE's requirement to minimize divergence at TA.
AMPLIFY gives us a good reason to expect that the closest SIMPLE worlds will look very much like a did in the recent past. There is no guarantee that all of these worlds will look like a in the distant past but--unlike SMALL MIRACLES and the CD&TA THEORY-- SIMPLE does not require that kind of past similarity so long as there is convergence at TA.
Is there anything in Lewis's argument that might suggest that the SIMPLE theory will end up endorsing counterfactuals like:
If that match had been struck , Nelson would have lost at Trafalgar?
No. Because remember to get to the Bennett world that made this true we had to assume that the only legal way to get that match struck was by way of pasts in which Nelson loses. We had to assume, in other words, that Nelson would have to have lost at Trafalgar if that match had been struck. That assumption is, of course, absurd. Doubtless there are legal worlds where Nelson loses and his loss then leads eventually to that match getting struck now, but there are surely countless other histories in which Nelson's loss is unnecessary for the striking and we have no reason to think that any of the latter must look less like a does now than any of the former.
The Bennett world I described above is massively deceptive, but the SIMPLE theorist would only count it as close to a if he also believed that momentous goings on in the distant past are counterfactually dependent on minute details in the present: that Nelson's fate way back then hinges on the firing of a single synapse now. But, for all the reasons Lewis recites, none of us believe the actual world is like that.
Still, SIMPLE worlds, at least the deterministic ones, must each have pasts that somehow differ from a's. Doesn't that mean that the closest SIMPLE worlds to a must be a little deceptive in Lewis's sense? Perhaps that was the thought that inspired Bennett to renounce the theory. Bennett seemed to think that SIMPLE tells us that that in some world very like a in 1941, the Germans are closing on Moscow even though the world is full of deceptive evidence to the contrary: all the pins on all the maps in Moscow and Berlin falsely show the army hundreds of miles to the west. Hitler and Stalin are deceived about where their forces are; Moscow is undefended!
But once again, it isn't so. It isn't so because there is no legal way to get the German army to Moscow without also changing the consequences of that movement. Hitler and Stalin would have learned about it. The maps would have been updated as accurately as they ever were. Moscow would have been defended. These different histories would have left their different, undeceptive marks on 1941; they would have to have done so.
I conclude that nothing in Lewis's arguments about the deceptiveness of Bennett worlds counts against the SIMPLE theory. Nor do I think there is any evidence that Lewis thought it did. In his postscript, Lewis is entirely preoccupied with saving his account of temporal asymmetry from the threat of Bennett Worlds.
I think this is a charitable reading of Lewis's motives, but if it is correct it means that nowhere in his writings did Lewis ever engage or argue against the SIMPLE theory properly understood. And this seems very odd. After all isn't the whole point of CD&TA to give a temporally symmetric account of counterfactuals? If so then why did Lewis entirely ignore Bennett '84s SIMPLE way of doing just that when he was writing his postscripts in '86?
I will leave it to Lewis scholars to explain, what seems to me, Lewis's uncharacteristic and willful blindness to Bennett's elegant alternative. Doubtless his adherence to a miracles account was deeply connected in myriad and subtle ways with his larger metaphysical program. Lewis is the great systematic philosopher of our age, but the demands of system betrayed him here.
Whatever the explanation for Lewis's mistake, it was a mistake and a tragic one. Tragic because it was Lewis's great achievement to have taught a generation of philosophers how central subjunctive reasoning is to thinking about laws, causation, knowledge, ontology, free will and much else. After Lewis, no one could claim to have a serious opinion on any of these topics unless they had got the relevant counterfactuals sorted out. But, also because of Lewis, they've looked to SMALL MIRACLES to do that for them. Just how this has led us astray is something I will pursue in future posts. As usual, my thanks to Kadri Vihvelin for her help.•