on the supposed temporal asymmetry of counterfactual dependence; or: it wouldn’t have taken a...

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Vol. 60, N° 4 (2006), pp. 461–473

© 2006 The Author. Journal compilation © 2006 Editorial Board of

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Published by Blackwell Publishing Ltd., 9600 Garsington Road, Oxford, OX4 2DQ, UK and 350Main Street, Malden, MA 02148, USA

posed Temporal Asymmetry of Counterfactual DependenceGabriele Contessa

On the Supposed Temporal Asymmetry of Counterfactual Dependence; or: It Wouldn’t Have Taken a Miracle!

Gabriele C

ontessa

†

A

BSTRACT

The thesis that a temporal asymmetry of counterfactual dependence characterizes our worldplays a central role in Lewis’s philosophy, as, among other things, it underpins one of Lewismost renowned theses – that causation can be analyzed in terms of counterfactual dependence.To maintain that a temporal asymmetry of counterfactual dependence characterizes our world,Lewis committed himself to two other theses. The first is that the closest possible worlds atwhich the antecedent of a counterfactual conditional is true is one in which a small miracleoccurs – i.e. one whose laws differ from the actual laws in a small spatiotemporal region. Thesecond is that our world is characterized by a temporal asymmetry of miracles. In this paper, Iwill argue, first, that the latter thesis is either false or incompatible with the picture of therelations among temporal asymmetries endorsed by Lewis and, second, that former thesisconflicts with some of the intuitions which seem to guide us when engaging in counterfactualreasoning. If there is any fact of the matter as to which possible worlds in which the antecedentof a counterfactual conditional is true are closest to the actual world, these are not worlds atwhich a small miracle occurs.

1. What is the temporal asymmetry of counterfactual dependence?

In our world, there are apparently many asymmetries in time. For example, effectsseem never to precede their causes; lower entropy states (almost?) never followhigher entropy states; human beings have memories of their past but not of theirfuture. Some philosophers claim that some of these asymmetries can be explainedin terms of other, more fundamental asymmetries. One of these philosophers wasDavid Lewis.

According to Lewis, ‘[. . .] the asymmetry of counterfactual dependence servesto explain [. . .] more familiar asymmetries’ (Lewis 1979, 459), including the

temporal asymmetry of causation

– the fact that causes always precede theireffects – and what Lewis called the

asymmetry of openness

, ‘[. . .] the obscurecontrast we draw between the “open future” and the “fixed past” [. . .]’ (Lewis1979, 459).

At the beginning of his paper ‘Counterfactual Dependence and Time’s Arrow’,Lewis characterised the

asymmetry of counterfactual dependence

as follows:

†

Department of Philosophy, University of Rochester, Box 270078, Rochester, NY14627-0078, USA; Email: [email protected]

462 Gabriele Contessa


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The way the future is depends counterfactually on the way the present is. If thepresent were different, the future would be different; and there are counterfactualconditionals, many of them as unquestionably true as counterfactuals ever get, thattell us a good deal about how the future would be different if the present weredifferent in various ways. [I]n general the way things are later depends on the waythings were earlier. Not so in reverse. Seldom, if ever, we can find a clearly truecounterfactual about how the past would be different if the present were different.Such a counterfactual, unless clearly false, normally is not clear one way or theother. It is at best doubtful [. . .] whether the way things are earlier depends on theway things will be later (Lewis 1979, 455).

A few pages later, Lewis provided a more precise description of the asymmetryof counterfactual dependence:

Consider those counterfactuals ‘if it were that

A

it would be that

C

’ in which thesupposition

A

is indeed false, and in which

A

and

C

are entirely about states of affairsat two times

t

A

and

t

C

respectively. Many such counterfactual are true in which

C

isalso false and in which

t

C

is later than

t

A

. These are counterfactuals that say how theway things are later depends on the way things were earlier. But if

t

C

is earlier than

t

A

, then such counterfactuals are true if and only if C is true. These are the counter-factuals that tell us how the way things are earlier does not depend on the way thingswill be later. (Lewis 1979, 458)

The thesis that an asymmetry of counterfactual dependence characterises ourworld plays a crucial role in Lewis’s philosophy. First, this thesis underpins oneof Lewis’s most renowned theses – that causation can be analysed in terms ofcounterfactual dependence (Lewis 1973a). If counterfactual dependence weretemporally symmetric in our world, then, an advocate of a Lewisian account ofcausation would have a hard time trying to explain why ‘backward’ counterfactualdependence does not open the door to backward causation. Second, the thesis thatan asymmetry of counterfactual dependence characterises our world is in turnunderpinned by other theses that commit the advocate of the Lewisian account tovery specific views about, among other things, counterfactual reasoning and thecloseness of possible worlds.

In this paper, I am more concerned with this second cluster of theses. First,I argue that Lewis’s own strategy, which grounds the asymmetry of counterfactualdependence in an asymmetry of miracles, is either ineffective or incompatible withthe picture of the relations among temporal asymmetries endorsed by Lewis.Second, I argue that the principle proposed by Lewis to order possible worldswith respect to their closeness to the actual world conflicts with some of theintuitions which seem to guide us when engaging in counterfactual reasoning.

2. Counterfactuals, determinism, and the nomocentric principle

According to Lewis’s analysis of counterfactual conditionals, the propositionschema ‘If it were that

A

, then it would be that

C

’ is (non-vacuously) true if and

On the Supposed Temporal Asymmetry of Counterfactual Dependence 463


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only if some possible world in which both

A

and

C

are true is closer to the actualworld than any possible world in which

A

is true and

C

is false, or, more concisely,if and only if the closest

A

-world (i.e. the closest possible world in which

A

istrue) is a

C

-world (i.e. possible world in which

C

is true) (see, for example, Lewis1973).

So, for example, the counterfactual conditional ‘If the pilot of Enola Gaydecided not to press the button, the atomic bomb would not have been droppedon Hiroshima at 8:15 a.m. on August 6, 1945’ is true if in the closest possibleworld in which (a counterpart of) the pilot of Enola Gay decided not to press thebutton no atomic bomb was dropped on Hiroshima at 8:15 a.m. on August 6, 1945.The problem now is that of determining which of the possible worlds in whichthe pilot decided not to press the button is the closest to the actual world.

For the sake of simplicity, Lewis assumed that the actual laws of nature (i.e.the ones which are true of the actual world) are (bi-directionally) deterministic.Lewis claimed that ‘[. . .] indeterminism is neither necessary nor sufficient for theasymmetries [he is] discussing’ (Lewis 1979, 460). Moreover, as Lewis pointedout, the success of quantum mechanics, which is our best reason to believe inindeterminism, ‘[. . .] is reason to believe that the world is indeterministic in bothdirections, so that the actual future and present are nomically compossible withvarious alternative pasts’ (Lewis 1979, 460).

Following Montague, Lewis defined a deterministic system of laws as follows:

A

deterministic

system of laws is one such that, whenever two possible worlds bothobey the laws perfectly, then they are exactly alike throughout all time, or else theyare not exactly alike through any stretch of time. They are always alike or never.They do not diverge, matching perfectly in their initial segments but not thereafter;neither do they converge (Lewis 1979, 460–461).

Now, the problem is that, if the actual laws are deterministic and the closestpossible world in which the pilot decides not to press the button is a nomicallypossible world (i.e. a world whose laws are the same as those of the actual world),then we would have to conclude that counterfactual dependence in our world issymmetric in time. If we represented the history of the actual world as a trajectoryin a sufficiently large state-space, the trajectories of all nomically possible worldswould be parallel to it. So, the world at which the pilot decides not to press thebutton is a world whose entire history differs (to some degree) from the historyof the actual world.

I will call the

nomocentric principle

the principle according to which somenomically possible

A

-world are always closer to the actual world than any other

A

-worlds. If the nomocentric principle is correct, then there are as many truebackward counterfactual conditionals as there are forward counterfactual condi-tionals and, therefore, the thesis that an asymmetry of counterfactual dependencecharacterises our world would turn out to be false. One could pursue a number of



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strategies to avoid this conclusion. In this paper, I will focus on the strategy Lewishimself actually pursued.

3. Miracle and the strong historiocentric principle

In his article ‘Causation’, Lewis wrote:

The respects of similarity that enter into the overall similarity of worlds are manyand varied. In particular, similarities in matters of fact trade off against similaritiesof law. The prevailing laws of nature are important to the character of a world; sosimilarities of law are weighty. Weighty, but not sacred. We should not take it forgranted that a world that conforms perfectly to our actual laws is

ipso facto

closerto actuality than any world, where those laws are violated in any way at all. Itdepends on the nature and the extent of the violation, on the place of the violatedlaws in the total system of laws of nature, and on the countervailing similarities anddifferences in other respects (Lewis 1973a, 197).

What Lewis seemed to have in mind in this passage is what he calls a

smallmiracle

. According to Lewis, a possible world in which a small miracle occurs isa world in which ‘[t]he deterministic laws of [the actual world] are violated [. . .]in a simple, localized, inconspicuous way’ (Lewis 1979, 468). As a matter offact, however, a possible world in which a small miracle occurs is simply a worldwhose laws differ from the laws of the actual world in a small spatio-temporalregion.

Consider, for example, the nomically impossible world

W*

.

W*

is exactly likethe actual world in every detail until just before

t

A

, which is the time at which thepilot decides to press the button in the actual world. According to the actual laws,that state would lead to the pilot deciding to press the button. In

W*

, however, thelaws in the spatio-temporal region around the aircraft when the pilot takes thedecision are slightly different from those of the actual world. According to the setof laws of

W*

, the very state of the world that in the actual world leads to thepilot deciding to press the button leads to the pilot deciding

not

to press it. Theworld trajectory of the actual world and that of

W*

lie on the same trajectory untiljust before

t

A

but, when the miracle occurs, the point which represents the stateof

W*

‘jumps’ on a parallel trajectory, the trajectory of a world at which the pilothas decided not to press the button.

The question is now whether

W*

is closer to the actual world than anynomically possible world. The answer to this question partly hinges on the criteriaone chooses to adopt to order

A

-worlds with respect to their closeness to the actualworld. If we adopt the nomocentric principle as I have suggested above, then ouranswer must be negative. Since the laws of

W*

differ from the laws of the actualworld,

W*

is a nomically impossible world and, according to the nomocentricprinciple, there is always some nomically possible

A

-world that is closer to theactual world than any nomically impossible one.



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However, according to Lewis, the question should be answered positively. Thisis because Lewis rejected what I have called the nomocentric principle initiallyin favour of what I will call the

strong historiocentric principle

, according towhich some ‘miraculous’

A

-world (i.e. a world at which

A

is true as a result of asmall miracle) is closer to the actual world than any other possible

A

-world.Lewis’s stated motivation for this move is that the histories of miraculous

A

-worlds match the history of the actual world perfectly up to a certain point whilethe history of nomically possible

A

-worlds do not match the history of the actualworld for any extent of time and as Lewis put it, ‘[. . .] a lot of match of particularfact is worth a little miracle’ (Lewis 1979, 469).

4. The weak historiocentric principle and the asymmetry of miracles

As Jonathan Bennett (1974) and Kit Fine (1975) independently pointed out,however, the adoption of the strong historiocentric principle would have disastrousconsequences for Lewis’s theory of counterfactuals. Consider the world

W**

. In

W**

, a small miracle occurs to the effect that the pilot decides not to press thebutton, but, then, another small miracle occurs, the pilot’s thumb contracts, thepilot involuntarily presses the button exactly at the same instant in which hepresses it in the actual world and the atomic bomb is dropped. Except for the shortinterval between the two miracles, the history of

W**

would seem to match thehistory of the actual world perfectly and, according to the strong historiocentricprinciple, this perfect match would seem to be worth two small miracles. If‘doubly miraculous’

A

-worlds such as

W**

actually were the closest

A

-worlds,then most counterfactual conditionals we ordinarily take to be true would be false.

In order to avoid this disastrous consequence, Lewis (1979) appealed to whathe calls an

asymmetry of miracles

. Lewis argued that ‘divergence’ miracles aresmaller than ‘convergence’ miracles. In other words, whereas it takes

one

miracleto make the history of a possible world diverge from the history of the actualworld, it takes

many

little miracles to bring back the possible world in which onemiracle has occurred to a

perfect

match of fact with the actual world. To supporthis claim, Lewis argued that anything that happens at a certain time leaves amyriad of ‘traces’ in the future. The erasure of

each

of these traces, according toLewis, requires

one

little miracle. So, it takes one little miracle for the pilot toinvoluntarily press the button, another little miracle to replace the memories ofthe pilot, so that he falsely remembers that he has pressed the button, and so onfor each of the traces of the pilot’s decision. In worlds like

W**

, Lewis argued,we either have only

two little

miracles and imperfect match or many little miraclesand perfect match. According to Lewis, imperfect match of fact is not worth alittle miracle. I will call this the weak historiocentric principle. According to it,some singly miraculous A-world (i.e. a world at which one and only one little


© 2006 The Author. Journal compilation © 2006 Editorial Board of dialectica

miracle occurs) is closer to the actual world than any other A-world. In otherwords, according to the weak historiocentric principle a lot of match of fact isworth one little miracle but no more than one.

But are there any reasons to prefer the weak historiocentric principle to thenomocentric principle independently from the fact that the adoption of the weakhistoriocentric principle provides the advocate of the Lewisian analysis with thedesired sort of temporal asymmetry of counterfactual dependence? I will turn tothis crucial question in Section 7 and give it a negative answer. Before that, inSections 5 and 6, I will argue that that the strategy that Lewis followed in orderto maintain that the asymmetry of counterfactual dependence characterizes aworld whose laws are temporally symmetric is either ineffective or incompatiblewith the picture of the relations among temporal asymmetries that Lewissketched.

5. Debunking the asymmetry of overdetermination

According to Lewis, the asymmetry of miracles is not a brute fact about our world.It is a consequence of a deeper temporal asymmetry: the asymmetry of overdeter-mination. Lewis defined the determinant(s) of a fact at a certain time as follows:

Any particular fact about a deterministic world is predetermined throughout the pastand postdetermined throughout the future. At any time, past or future, it has at leastone determinant: a minimal set of conditions jointly sufficient, given the laws ofnature, for the fact in question. Members of such set may be causes of the fact, ortraces of it, or neither). (Lewis 1979, 474)

Lewis then went on to suggest that: ‘[. . .] what makes convergence take so muchmore of a miracle than divergence [. . .] is an asymmetry of overdetermination[. . .]’ (Lewis 1979, 474). In other words, Lewis claimed that at the actual worldand at the closest possible worlds, events, like the pilot’s decision to press thebutton, have more determinants at any time in the future than in the past. Lewissuggested that the asymmetry of overdetermination, which underpins the asym-metry of counterfactual dependence is a de facto asymmetry that contingentlycharacterises our world and the possible worlds closest to it. It cannot be reducedto any other asymmetries that are not de facto themselves. In this and the nextsections, I will challenge this analysis.

Consider again the pilot’s decision to press the button. The pilot’s decisionundeniably had a great number of consequences. Once the pilot decided to pressthe button, the muscles in his thumb contracted, the thumb pressed the button, themechanism released the bomb, and the bomb fell on Hiroshima with the tragicconsequences we all know. Beside these consequences, there were also a numberof less momentous ones, such as the fingerprint of the pilot being impressed onthe button, the pilot’s memory of that moment, and so on.



Lewis seemed to think that each of these consequences of the pilot’s decisionis one of its determinants, but, I will argue, this is not the case. Consider theactual world in which the pilot has decided to press the button thus initiating thechain of events that will culminate in the explosion of the atomic bomb onHiroshima and, in particular, focus on the exact instant at which the bombexploded. Is the explosion of the bomb a determinant of the pilot’s previousdecision at that time?

A determinant of an event was defined by Lewis as a minimal set of conditionsjointly sufficient, given the laws of nature, for the event in question to occur. Butthe explosion of the bomb, in and of itself, is not sufficient to (post)determine thepilot’s decision to press the button to drop the bomb. There are many ways inwhich the bomb could have exploded exactly as it did without the pilot havingdecided to press the button. The explosion of the bomb is, thus, compatible withalternative past histories in which the pilot decides not to drop the bomb, includingthe one in which the pilot decides not to press the button but there is a fault inthe electric circuit of the plane and the bomb is released at exactly the same instantin which it was released in the actual world. In other words, the explosion of thebomb alone is not a determinant of the pilot’s previous decision.

The determinant of the pilot’s decision at the moment at which the bombexplodes, thus, must contain more than just the explosion of the bomb if it is to(post)determine the pilot’s previous decision. For example, it must contain thepilot’s fingerprint on the button. But the set formed by the explosion of the bomband the pilot’s fingerprint on the button is not a determinant of the pilot’s previousdecision either. There are worlds in which the bomb exploded and in which thereis a thumbprint on the button exactly like in the actual world, but the pilot has notdecided to drop the bomb. One of them is the world in which the pilot decidesnot to press the button, but his thumb involuntarily contracts and presses thebutton.

The determinant of the pilot’s decision at the moment in which the bombexplodes, thus, must contain more than just the explosion of the bomb and thepilot’s fingerprint on the button. For example, it has to include the pilot’s mem-ory of his decision to press the button. This might still not be sufficient how-ever. It is likely that there are worlds at which the bomb explodes, thethumbprint is on the button and the pilot remembers to have decided to pressthe button without him actually having decided to do so. For example, worlds atwhich the pilot falsely remembers to have decided to press the button even if hehas decided not to.

These alternative scenarios may well be implausible but they show that it takesa very large set of consequences of the pilot’s decision to press the button to havea determinant of that decision in the future and, once we have one such set ofconsequences, it seems extremely unlikely that we will be able to find other



determinants of the pilot’s decision that do not include any of the consequencesthat are already members of that first determinant.1

At close scrutiny, Lewis’s assumption that each of the consequences of anevent (post)determines the event thus appears to be false. In our example, the onlydeterminant of the pilot’s decision at each time in the future is likely to be eitherthe whole set of consequences of the decision at that time or a very large subsetof them. Therefore, there seems thus to be no reason to believe that eventsordinarily have more determinants in their future than in their past.

6. Two asymmetries of causation

Even if the asymmetry of overdetermination is not a genuine asymmetry, however,Lewis seemed to be onto a genuine asymmetry when talking about the asymmetryof ‘traces’. The problem, I suspect, is that Lewis misrepresented the nature of thatasymmetry.

It seems hardly deniable that everything that happens in our world has a greatnumber of consequences, or, to put it in Lewis’s terms, every event leaves anumber of ‘traces’ in the future. If the notion of ‘trace’ is properly construed,Lewis might have even been right in claiming that there are more ‘traces’ of theoccurrence of an event in the future than in the past. What Lewis disregarded,however, is that, if there is such an asymmetry, this is a consequence of a temporalasymmetry of causation.

In discussing the asymmetry of overdetermination, Lewis talked of deter-minants and ‘traces’ but could not completely avoid causal language. It is not achance that, as an example of how rare overdetermination of the present from thepast is in our world, Lewis employed a standard example of causal overdeter-mination – the case of the victim whose heart is contemporarily pierced by twobullets shot by two independent shooters.

As Lewis noted (while at pains to avoid causal language), cases of (causal)overdetermination are relatively rare in our world. Most events have no more thanone cause. On the other hand, events seem often to have many effects. Causalforks are all but rare in our world. The pilot’s decision to press the button, for

1 Adam Elga has argued that ‘[. . .] the existence of apparent traces of an event (togetherwith the laws, and together with the absence of evidence that those traces have been faked) fallsfar short of entailing that the event occurred” (Elga 2001, S324). His argument differs frommine, among other things, in that mine does not make any (explicit) assumptions about thenature of the actual laws and the sensitivity of thermodynamically irreversible processes tochanges. More importantly Elga’s conclusion is stronger than the one I wish to draw, as myargument does not preclude that a wide enough set of traces of an event may be a determinantof it in the actual world. What my argument shows is rather that, if determinants are properlyunderstood, it is implausible to assume that an event has more determinants in the future thanin the past.



example, is the initial link of a number of causal chains that propagate in thefuture, but it is likely to be the link of a single causal chain from the past. If atrace of an event is defined as one of the links of the causal chain of which theevent itself is a link, then Lewis may well be right in claiming that a vast majorityof the events in our world leave more traces in their future than in their past. Hemight be also right in claiming that it takes one miracle to break each causal chainto and form the event in question. However, in a world in which events are likelyto have as many causes as effects, there would be no asymmetry of miracles.

The problem for Lewis was that he could not appeal to an asymmetry of causalforks to underpin the asymmetry of miracles without thereby undermining theoverall project of explaining the temporal asymmetry of causation in terms of thetemporal asymmetry of counterfactual dependence. The asymmetry of causalforks, in and of itself, is not a temporal asymmetry. It only tells us that eventsusually have more effects than causes. If the asymmetry of causal forks is tounderpin a temporal asymmetry of miracles, however, we also have to assumethat a temporal asymmetry of causation characterises the actual world, to the effectthat effects never precede their causes. If backward causation was as likely asforward causation, there would be as many traces of the present in the past asthere are in the future. In which case there would be no reason to believe that ittakes more miracles for reconvergence than for divergence.

If either the asymmetry of causal forks or the temporal asymmetry of causationfailed to obtain in our world, miracles and counterfactual dependence would betemporally symmetric, with all of the disastrous consequences this would havefor Lewis’s views on counterfactuals and causation. However, if in the actualworld the asymmetry of miracles obtains as a consequence of the asymmetry ofcausal forks and temporal asymmetry of causation, then the relations among thevarious asymmetries in time are different from what Lewis envisaged. It wouldbe the temporal asymmetry of causation that explains the temporal asymmetry ofcounterfactual dependence, not the reverse. So, even if in the actual world coun-terfactual dependence is time asymmetric, this cannot explain why causation istime asymmetric, which undermines what seems to be Lewis’s fundamental moti-vation for claiming that counterfactual dependence is asymmetric in time.

7. Would it really have taken a miracle?

So far, I have argued that the strategy that Lewis followed in order to maintainthat the asymmetry of counterfactual dependence can characterise a world whoselaws are temporally symmetric is either ineffective or incompatible with thepicture of the relations among temporal asymmetries that Lewis sketched. Thetrouble with Lewis’s account of the temporal asymmetry of counterfactual depen-dence, however, runs even deeper.



Whether or not our world is characterised by a temporal asymmetry of coun-terfactual dependence depends to a great extent on which A-worlds are closest tothe actual world. Therefore, if the temporal asymmetry of counterfactual depen-dence is to be a genuine asymmetry of our world on par with the other morefamiliar asymmetries in time, there must be a fact of the matter as to whichA-worlds are closest to the actual world. So, since the nomocentric principle andthe weak historiocentric principle disagree about which A-worlds are closer to theactual world, they cannot be both correct. In the remainder of this section, I willargue that, if there is a fact of the matter as to which A-worlds are closer to theactual world (and I take this to be a ‘big if’), then the nomocentric principle ismore likely to be correct than the weak historiocentric principle. To do so, I willfirst argue that Lewis’ reasons for preferring the weak historiocentric principleover the nomocentric one are unconvincing and, then, I will argue that there arepositive reasons to favour the nomocentric principle over the weak historiocentricone.

Lewis’s stated reason for preferring the weak historiocentric principle over thenomocentric one was that, according to the weak historiocentric principle, largeportions of the history of the closest miraculous A-world match large portions ofthe history of the actual world in every detail, while no portion of the history ofthe closest nomologically possible A-worlds matches perfectly the history of theactual world. As Lewis suggested, a lot of match of particular fact may well beweightier than a small discrepancy in the laws, however, the relation betweenmatch of history and match of laws is not necessarily a trade off, as Lewis seemedto suggest. If we abandon the assumption that the actual world is deterministic(which is at least dubious anyway), partial match of histories is compatible withperfect match of laws. If the actual world is to some extent indeterministic, as,according to Lewis himself, our best theories seem to suggest then there arenomically possible A-worlds portions of whose history matches perfectly withportions of the history of the actual world.

If the actual world is indeterministic, it is plausible to assume that the clos-est A-world is a world that is governed by the same indeterministic laws thatgovern the actual world and whose history matches perfectly the history of theactual world until a certain time tD < tA as close as possible to tA and whosehistory diverges from the history of the actual world thereafter due to the inde-terministic character of the laws. The later tD is the less a small miracle seemsworth the surplus match of fact between tD and tA which would be available inthe closest miraculous A-world. So, if we abandon the dubious assumption thatthe actual world is deterministic, it doesn’t necessarily take a ‘miracle’ to havea lot of match of particular fact. Indeterministic nomologically possible A-worlds have the best of both worlds: perfect match of law and perfect match ofhistory up to tD.



If the reasons for favouring the weak historiocentric principle over thenomocentric principle are unconvincing, are there any positive reasons for prefer-ring the latter to the former? I think there are. First of all, in many cases, whenconsidering counterfactual conditionals we are not only interested in what wouldhappen if the antecedent was true, but also what would have had to happen inorder for the antecedent to be true. In other words, we are not always interestedin ‘forward’ counterfactual reasoning. Sometimes we are also interested in‘backward’ counterfactual reasoning. ‘What would have happened if the pilot haddecided not to press the button?’, a historian might ask. However, a psychologistmight ask: ‘What would have had to happen for the pilot to decide not to pressthe button?’. The acceptance of the weak historiocentric principle would seem tomake all backward counterfactual reasoning hopelessly sterile. If Lewis’s weakhistoriocentric principle is the one that orders possible worlds correctly withrespect to their closeness to the actual world, then, as strange as it may seem, thecorrect answer to the psychologist’s question would be: ‘The laws of nature in asmall spatio-temporal region around the aircraft would have had to differ fromwhat they actually were’. Our intuitions though seem to tell us that a less out-landish difference would have been sufficient to make the antecedent of thecounterfactual true. We seem to believe that there are alternative histories that areperfectly compatible with the laws of the actual world and would lead to the pilot’sdecision not to press the button. When the psychologist engages in backwardcounterfactual reasoning, she seems to be interested in the most plausible of thosestories, not in ones that involve Lewisian miracles.2

The weak historiocentric principle however seems to be no less at odds withour intuitions in those cases in which we engage in forward counterfactual rea-soning. Whereas in some cases it may be irrelevant how in the closest A-worldthe truth of A comes about, there are cases in which the causal chain that leadsto the occurrence of the event described in the antecedent has an influence onwhether the event described in the consequent occurs. A safety inspector whofinds out that a sprinkler is not working, for example, is likely to conclude that if

2 Note that I do not thereby mean to deny that we usually find it harder to engage inbackward counterfactual reasoning than in its forward counterpart. There seem to be many waysin which the pilot could have reached the decision not to press the button and, in many cases,it does not seem possible to give a unique answer to questions such as ‘What would have hadto happen for the pilot to decide not to press the button?’. But, first, the situation here is notentirely different from the one involving forward counterfactual reasoning. One might argue thatthere are many answers also to the question ‘What would have happened if the pilot decidednot to press the button?’. Would some other member of the crew have pressed the button? Orwould no bomb have been dropped on Hiroshima? Second, the fact that it is more it more difficultfor us to find true of backward counterfactual conditionals than it is to find true forward onesdoes not imply that there are more true forward counterfactual conditionals than backward ones.The difference between forward and backward counterfactual dependence may well be epistemicrather than ontic.



a fire had broken out the flames would have propagated quickly without beingcommitted to any particular way in which the fire would have broken out in thecounterfactual scenario. As far as she is concerned, the fire could have broken outas a result of a miracle or as a result of the carelessness of a smoker (at leastinsofar as the way in which the fire starts has no influence on how quickly it wouldpropagate). However, this is not always the case. In many cases, the way the eventdescribed in the antecedent comes about is relevant to the way we evaluate thecounterfactual in question and, in those cases, we do not want A to come aboutas a result of a miracle. A detective who is working on the theft of a diamond, forexample, might reason: ‘If the diamond was stolen by someone with no access tothe keys, there would be signs of forced entry’. In this case, how A comes – howa thief with no access to the keys would have got to steal the diamond – seemsto be crucial to the truth of the counterfactual and, in this case, we do not wantthe truth of the antecedent to come about as a result of a miracle. The mostplausible scenarios in which someone with no access to the keys stole the diamondseem ones that involve the thief picking the door lock or breaking in through oneof the windows, and not the one in which the alternative thief finds herselfmiraculously teleported inside the room and steals the diamond.

In general, the idea the closest possible A-world is one in which A is true asa result of a small miracle may not conflict too strongly with our intuitions whenthe miracle that makes A true is unobservable and inconspicuous. Most of theexamples usually discussed in the literature are examples that require miracles ofthis kind (involving inconspicuous unobservable processes such as the misfiringof a neuron). However, for most counterfactual conditionals, the miracle it wouldtake to make A true seems to be more conspicuous and counterintuitive than that.I take it that most people who have any intuitions at all about these matters wouldtend to think that the closest possible world in which I am wearing a blue sweaternow is the one in which I decided to wear one this morning and not one in whichthe colour of my sweater has miraculously changed from red to blue one milli-second ago and the closest possible world in which you are writing this papernow is one in which you have come to write it and not the one in which you havebecome me one millisecond ago.3

The advocates of the Lewisian analysis may well argue that, if we have anysuch intuitions, it is them, not the weak historiocentric principle, that are mistaken.I do not deny that these intuitions may be mistaken. What I deny is that arguments

3 The advocate of the weak historiocentric principle might want to argue that, in thosecases, A is true in the closest A-world as a result of an earlier small miracle. For example, onein which a neuron has ‘misfired’ in my brain this morning and I have decided to wear my bluesweater rather than the red one. The problem with this line of reasoning is that, if that world isthe closest A-world, then a significant number of backward counterfactual conditionals seem tobe true.



proposed by Lewis in favour of the weak historiocentric principle are strongenough to persuade us that, if our intuitions are at odds with it, it is our intuitionsthat should be abandoned.

The assumption that the actual world is characterised by a temporal asymmetryof counterfactual dependence plays a crucial role in the grand scheme of Lewis’sphilosophy. Lewis famously analysed causation in terms of counterfactual depen-dence and, as I have mentioned, if we accepted Lewis’s analysis of causationwithout accepting that our world is characterised by a temporal asymmetry ofcounterfactual dependence, we would have troubles explaining why there is nobackward causation in our world. However, if we do not accept Lewis’s analysisof causation, we do not need to assume that an asymmetry of counterfactualdependence characterises our world and we do not need to reject our intuitionsabout how things might have gone otherwise without Lewisian miracles.*

References

Bennett, J. 1974, “Counterfactuals and Possible Worlds”, Canadian Journal of Philosophy 4, pp.381–402.

Elga, A. 2001, “Statistical Mechanics and the Asymmetry of Counterfactual Dependence”, Philoso-phy of Science 68, pp. S313–S324.

Fine, Kit 1975, “Review of Counterfactuals”, Mind 84, pp. 451–458.Lewis, D. 1973, Counterfactuals, Blackwell: Oxford.Lewis, D. 1973a, “Causation”, Journal of Philosophy 70, pp. 556–567.Lewis, D. 1979, “Counterfactual Dependence and the Time’s Arrow”, Noûs 13, pp. 455–476.

* I would like to thank Robert C. Bishop, Nancy Cartwright, Michael Martin, JamesStazicker and the anonymous referees for this journal for many useful comments on previousdrafts of this paper.

on the supposed temporal asymmetry of counterfactual dependence; or: it wouldn’t have taken a...

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