Context



Chapter 14: Causes, Contrasts, and the Nontransitivity of Causation1

Cei Maslen

1. Introduction

Whether one event causes another depends on the contrast situation with which the alleged cause is compared. Occasionally this is made explicit. For example, a toothpaste company claims that regular brushing with their product will cause teeth to become up to two shades whiter than with “another leading brand”. Here, the comparison not only helps to specify a range of shades of white, but also to specify a contrast situation. Regular brushing with their product is not compared to, say, irregular brushing with their product or not brushing at all, but to regular brushing with another leading brand.

More often the contrast situation is not made explicit, but is clear from the context. Hence, in general, the truth and meaning of causal statements depend on the context in which they occur. In section 2, I give a more complete formulation of this claim, illustrate it with an example and compare it to similar and superficially similar views. The theory is incomplete without a description of how contrast events are fixed by the context, which I supply in section 3. In section 4, I discuss the context dependence of counterfactuals. Of course, a major motivation for the theory is the extent to which it can avoid obstacles that have defeated other theories of causation, problems such as the nontransitivity of causation, preemption, causation by absences, and causation under indeterminism. In section 5, I explain how a contrastive counterfactual account solves the first of these problems: analyzing the nontransitivity of causation.2

2. A Contrastive Counterfactual Account

Causal statements are systematically dependent on context.3 The meaning and truth-conditions of causal statements are dependent on contrast events that are seldom explicitly stated, but are fixed by conversational context and charity of interpretation. Occasionally confusion about contrast events leads to misunderstandings and indeterminacy of meaning and truth-value. This may be expected when causal statements are taken out of context, for example, in some philosophical discussions.

This isn’t to make causation a subjective matter. The causal structure of the world is an objective, mind-independent three-place relation in the world between causes, contrasts, and effects. (Compare this to discovering that motion is relative to frame of reference. This is not to discover that motion a subjective matter.)

It would perhaps be ideal to study the properties of causal statements (e.g. nontransitivity and context dependence) without appealing to a specific formal analysis of our concept of causation. All formal analyses of causation are controversial, and complicated. The claims that causation is context-dependent, and that causation is non-transitive are partly independent of any specific analysis. However, in practice it is impossible to have detailed discussions of these aspects without settling on one analysis. The few philosophers who discuss the context dependence view can be classified into all the major schools of thought on causation. Hitchcock4 incorporates it into a probability-raising account. Field5 discusses probabilistic and non-probabilistic versions of a regularity or law-based view. Holland6 presents a counterfactual account. I support a counterfactual account also, and concentrate on singular causal claims.

2.1 Account1

For distinct events c, c* and e, c is a cause of e relative to contrast event c* iff c and e actually happened and if c had not happened, but contrast event c* had happened instead, then e would not have happened.

This account takes events as the fundamental causal relata. Either Kim’s or Lewis’s definitions of events would serve this purpose.7 My hope is that causal sentences with other kinds of relata (physical objects, processes, facts, properties, or event aspects) can be reexpressed in terms of event causation, but I will not argue for this claim here.8 I discuss counterfactuals briefly in section 4 below. I think that our intuitive understanding of this grammatical form is strong, so I do not commit myself to an analysis here.9

The only restrictions I place on the contrast event is that it be compossible with the absence of the cause and distinct from the absence of the cause.10 I also require that the cause, effect and contrast event be distinct events.11 This may seem hopelessly liberal. What is to stop someone from claiming that brushing my teeth this morning, in contrast to being hit by a meteorite, was a cause of my good humor, or that the price of eggs being low, in contrast to the open fire having a safety guard, was a cause of the child’s burn? The inanity of these examples arises from inappropriate contrast events. Describing appropriateness of contrast is a difficult task, and I have little more to say about it at this stage than that events are usually contrasted with events that occur at a similar time, and that might have replaced them.12

Let’s assume that any complex of events (the event which occurs just in case the constituent events occur) is itself an event. It will be useful to define a contrast situation as the complex of a contrast event and the event in which the absence of the cause consisted.13 With this terminology, account1 is:

Event c is a cause of event e relative to a contrast situation iff had the contrast situation happened, then e would not have happened.

There may also be explicit and implicit alternatives to the effect. For example, a friend’s opinions were a cause of my renting the video “Annie Hall” rather than the video “Mighty Aphrodite”. Account1 can be generalized in the following way to allow for contrasts to the effect and for a range of implicit contrasts. (However, I will mostly continue to work with the simpler account1).

2.2 Account2

Event c, relative to contrast situations {c*}, is a cause of event e, relative to contrast situations {e*}, iff had any events from {c*} occurred, then an event from {e*} would have occurred.14

2.3 Illustrations

Here are two examples to illustrate the context dependence of causation. First, suppose I have three cookie recipes: hazelnut cookies, walnut cookies and pecan cookies. I decide to make hazelnut cookies, then offer one to Stuart. Unfortunately Stuart has a nut allergy; he is allergic to all nuts. He eats the cookie and becomes ill. Was making the hazelnut cookies one of the causes of his illness?

Well, if I hadn’t made the hazelnut cookies I would have made the pecan cookies, because I have only three cookie recipes and I have no walnuts in the house. So in one sense, making the hazelnut cookies was not a cause of his illness. Relative to making pecan cookies, making hazelnut cookies was not a cause of his illness. However, relative to the alternative of making no cookies at all, making the hazelnut cookies was a cause of his illness. Taken out of context, there is no correct answer to the question whether making hazelnut cookies was a cause of Stuart’s illness. Out of context, the only valid claims we can make are relative claims. However, the conversational context and unspoken assumptions can make some alternatives more salient than others. Our awareness that I only have nut cookie recipes made the alternatives of baking pecan cookies and walnut cookies salient alternatives for us, and in the context of this paper the causal claim “making hazelnut cookies was a cause of his illness” is naturally interpreted as meaning “making hazelnut cookies, relative to making pecan cookies or walnut cookies, was a cause of his illness.”

The second example, of an electric circuit, comes from Daniel Hausman, though he uses it for a different purpose. “The ‘weak circuit’ and the ‘strong circuit’ power a solenoid switch, which closes the ‘bulb circuit’. If only the weak circuit is closed, the current through the solenoid is 4 amperes. If only the strong circuit is closed, the current through the solenoid is 12 amperes. If both are closed, about 16 amperes flow through the solenoid. It takes 6 amperes to activate the solenoid switch, close the bulb circuit, and turn on the light bulb. Whether the weak circuit is closed or not affects how much current is flowing through the solenoid, but it has no influence on whether the light goes on.”15

[Figure 1]

Suppose that on this occasion, I close both the strong and the weak circuit, a current of 16 amperes flows through the coil, the solenoid switch closes, and the bulb lights. Was the presence of a current of 16 amperes through the coil a cause of the bulb lighting? The answer to this question is relative to the contrast event.

16 amperes flowing through the coil, rather than 12 amperes flowing through the coil, was not a cause of the bulb’s lighting.

16 amperes flowing through the coil, rather than 4 amperes flowing through the coil, was a cause of the bulb’s lighting.

16 amperes flowing through the coil, rather than 0 amperes flowing through the coil, was a cause of the bulb’s lighting.

The fact that there are cases like these where the context dependence is clear, gives excellent support to the context dependence view.

2.4 Other views

At this point, it will be helpful to compare account2 to similar and superficially similar views.

I am not proposing a revisionary account of causation. The realization that causation is context-dependent and that this can lead to misunderstandings might prompt us to propose a revisionary account of causation. We could suggest that in the future, in order to avoid misunderstandings in precise or important uses of causal claims, we should always state alternative events together with our causal claims. We could even follow Bertrand Russell in suggesting that we abandon the concept of causation altogether.16 Instead we would only use precise counterfactuals with our assumptions spelt out. But the state of our causal concept does not warrant such an extreme reaction.

The context dependence that I have described in the concept of “a cause” is additional to the generally accepted context dependence of “the cause” or “the decisive cause”. I am only concerned here with what it takes to be “a cause” or “one of the causes” of a given effect. The context dependence of the concept of “the cause” is more obvious. It might be suspected that there is only one source of context dependence here and that is from the concept of “the cause”. It could be argued that we confuse “a cause” for “the cause” when we read the examples, and this is why we find them convincing. However, this simply isn’t borne out by our intuitions. We do have an additional contextual element here.

The context dependence of causation is distinct from the widely accepted view that explanation is context-dependent. Van Fraassen is the major defender of the latter view: “If, as I’m inclined to agree, counterfactual language is proper to explanation, we should conclude that explanation harbors a significant degree of context-dependence.”17 He argues that the context dependence of explanation takes the form of determining both the salience of explanatory factors and also the contrast class. However, those who claim that explanation is dependent on context assume that causation is independent of context. For example, it seems to be implied by van Fraassen’s claims that the propositions of the causal net are scientific propositions, and “scientific propositions are not context-dependent in any essential way”18 that causal statements are (essentially) independent of context. I disagree; both explanation and causation are context-dependent.

Account2 is similar in many ways to Lewis’s recent “Causation as influence” view and to event-feature views of causation, for example, Paul’s “Aspect Causation” view. I do not have space to discuss all the similarities and differences here. However, note that all three views imply that causal statements are strongly context dependent. Lewis talks of “a substantial range of not-too-distant alterations” of the cause; what constitutes a substantial range, and what constitute not-too-distant alterations of the cause presumably differs with context. Event-feature views require the context to determine event features from event nominalizations.

3. Contrast Events and Context

The context of a statement is the circumstances in which it occurs. The truth of a statement may depend on features of the context as well as on matters of fact. Dependence on matters of fact is contingency; dependence on features of context is context dependence. Following the two-stage scheme of Stalnaker, an interpreted sentence together with a context determines a proposition, and a proposition together with a possible world determines a truth value.19 Hence, which proposition is expressed by an interpreted sentence may depend on the context in which it occurs. A classic example of a context-dependent sentence is “I went to the store”; its interpretation depends on the identity of the speaker, due to the indexical “I”.20

In general, a large variety of contextual features may be required to interpret a sentence on a particular occasion. For example “the intentions of the speaker, the knowledge, beliefs, expectations, or interests of the speaker and his audience, other speech acts that have been performed in the same context, the time of utterance, the effects of the utterance, the truth-value of the proposition expressed, the semantic relations between the proposition expressed and some others involved in some way”.21 Features of context such as speaker and time of utterance are almost always obvious and readily observable. The set of contrast events is a theoretical feature of context; hence, we owe a description of how contrast events connect with more obvious features of context. Otherwise, when disputes arise it might seem as though the metaphysician is magically summoning the set of contrast events or choosing the set to fit her case.

Suppose that the contrast event is what the speaker has in mind for replacing the cause. That is, it is what the speaker has in mind to be different in an imagined counterfactual situation where the cause is removed. Two objections to this immediately arise. Firstly, unphilosophical speakers may not have anything of the right sort in mind when uttering causal statements. When asked what they had in mind, many speakers may admit that they hadn’t thought about it. However, usually these speakers then have no problem responding with a contrast event when prompted. These responses give the intended interpretation of the original causal statement, in some sense of “intended”. Secondly, as we are not mind readers, if the “have in mind” picture were the whole story then communication would be very haphazard.

The rest of the story is that which contrast set the speaker has in mind, if not communicated directly, may be clear to the audience by the previous course of the conversation, acknowledged assumptions, limitations, plans, and presuppositions. General pragmatic principles play a large part in this. The set of contrast events is what Lewis calls a “component of conversational score”.22 We have a tendency to interpret utterances generously or charitably, as true or probable, relevant, useful and informative. The set of contrast events is fixed and developed through the course of the conversation. Sometimes the set is left unsettled or vague until a dispute arises. In a few cases this vagueness even leads to ambiguity in the causal statement.

Often there are physical limitations on the ways in which the cause could have been omitted. This gives us a “default” set of contrast events. Consider the following example. My opponent and I are both very competitive. We each would have been happy to win, but we are both unhappy when we reach a draw at chess.

“Reaching a draw at chess was a cause of us both being unhappy.”

Presuming that we finish the chess game, there are only two ways in which the event of reaching a draw could have been omitted: by my winning the game, or by my opponent winning the game. Hence, there are two natural interpretations of the causal statement:

“Reaching a draw at chess, in contrast to my winning the game, was a cause of us both being unhappy”;

“Reaching a draw at chess, in contrast to your winning the game, was a cause of us both being unhappy.”

Either of these alternative outcomes would have left one of us happy. Hence reaching a draw can truly be called a cause of us both being unhappy. The natural set of contrasts here are the events which the absence of the cause would have consisted in. Given our assumption that we did actually finish the chess game, the absence could only have consisted in my winning the game, or my opponent winning the game.

In some cases, there is only one probable way in which the cause would have been omitted and this is the natural or default contrast. Suppose that my opponent is a much better chess player than I. If we hadn’t reached a draw, he would almost certainly have won. Given our assumptions, the contrast situation here is naturally limited to one alternative. The following causal claim is probably true in that context.

“Reaching a draw on the chess game was a cause of my opponent being unhappy.”

The default contrast is always overruled by what the speaker has in mind or intends as the contrast. For instance, suppose I mistakenly believe that I am the better player. I could have in mind a contrast with the case in which I had won the game and deny the above causal claim. (If my opponent does not realize I have this mistaken belief, then this will probably lead to misunderstanding). Even if I recognize that my opponent would have won the game if we hadn’t drawn, I could make it clear that I’m contrasting with a wider set, and then deny the causal statement above. I could contrast with the set {playing the chess game and my winning, playing the chess game and his winning, not playing the chess game at all}.23

4. The Context Dependence of Counterfactuals

The counterfactual analysis of causation is one of the most popular approaches to analyzing causation. Hence, it is strange that counterfactuals are widely acknowledged to be context-dependent, while causation is not widely acknowledged to be so.

The context dependence of counterfactuals has been observed and discussed in most major works on counterfactuals.24 Here are some classic examples exhibiting context dependence.

If Caesar had been in command in Korea he would have used the atom bomb.

If Caesar had been in command in Korea he would have used catapults. [Example due to Quine]

If this were gold it would be malleable.

If this were gold then some gold things would not be malleable. [Example due to Chisholm]

If New York City were in Georgia then New York City would be in the South.

If New York City were in Georgia then Georgia would not be entirely in the South. [Example due to Goodman]

All of these counterfactuals are context-dependent. Consider just the first pair. Each statement can be reasonably asserted in the same situation. (We presuppose that Caesar was ruthless, ambitious and indifferent to higher authority.) Yet the first statement implies that the second statement is false. (We presuppose that it is possible that Caesar was in command in Korea and it is not possible that he uses both catapults and atom bombs.) The second statement cannot be both true and false, so it must express at least two different propositions depending on factors other than the background facts. It is context-dependent.

Acknowledging the context dependence of counterfactuals can help us to understand the context dependence of causation. I do not wish to commit myself to one analysis of counterfactuals here. However, let me mention how two successful and sophisticated analyses of counterfactuals account for their context dependence. One formulation of Lewis’s analysis of counterfactuals is as follows:

“A counterfactual ‘If it were that A, then it would be that C’ is (non-vacuously) true if and only if some (accessible) world where both A and C are true is more similar to our actual world, overall, than is any world where A is true but C is false”25

On his account, the context dependence of counterfactuals arises because our judgments of overall similarity of possible worlds depend on context. “The delineating parameter for the vagueness of counterfactuals is the comparative similarity relation itself: the system of spheres, comparative similarity system, selection function, or whatever other entity we use to carry information about the comparative similarity of worlds”.26

The tacit premise view of counterfactuals is presented by Chisholm and by Tichy.27 On this view, a counterfactual is true iff its antecedent together with its tacit premises logically entail its consequent, and the tacit premises are true. The tacit premises are simply those assumptions which have been presupposed in the conversation or which the speaker has in mind on the occasion of utterance. The context dependence is obvious on this view.

It is interesting that Lewis observes in his original paper on causation “The vagueness of similarity does infect causation, and no correct analysis can deny it”.28 His original theory already accounts for some context dependence, admittedly in a subtle way.

5. The Nontransitivity of Causation

Is causation transitive? That is, is it true for all events a, b and c that if a is a cause of b and b is a cause of c then a is a cause of c? Some causal chains are clearly transitive. Suppose that the lightning is a cause of the burning of the house, and the burning of the house is a cause of the roasting of the pig. (Suppose that the pig was trapped in the house). Then surely the lightning is also a cause of the roasting of the pig. But is this true for all events a, b, and c?

In the past, the transitivity of causation was commonly assumed in the literature without argument.29 But more recently a host of ingenious examples have been presented as counterexamples to the transitivity of causation.30 Before discussing these examples, let’s briefly consider one argument for the transitivity of causation.

The only argument that I have found in the literature for the claim that causation is transitive comes from Hall. Hall argues “rejecting transitivity seems intuitively wrong: it certainly goes against one of the ways in which we commonly justify causal claims. That is, we often claim that one event is a cause of another precisely because it causes an intermediate, which then causes another intermediate, ... which then causes the effect in question. Are we to believe that any such justification is fundamentally misguided?”31

This is an important consideration. I agree with Hall that it is common practice to refer to intermediates in a causal chain in justifying causal claims. This seems to apply across many different fields of application of the singular causal concept: history, science, law, and ethics. I don’t think that this practice is fundamentally misguided, but it may be a rule of thumb, which should be supplemented with restrictive guidelines. If we are to reject transitivity, we have a pressing need for a general rule for distinguishing the cases in which transitivity holds from the cases in which it fails, and an explanation of why transitivity sometimes fails. Hall agrees with me here. He issues a challenge: “Causation not transitive? Then explain under what circumstances we are right to follow our common practice of justifying the claim that c causes e by pointing to causal intermediates.”32 I take up this challenge in the next section after presenting the counterexamples.

The alleged counterexamples to transitivity are diverse; I will describe three difficult and representative cases - ‘bomb’, ‘birthday’, and ‘purple fire’. The first comes from Field.33 Suppose that I place a bomb outside your door and light the fuse. Fortunately your friend finds it and defuses it before it explodes. The following three statements seem to be true, thus showing that causation is nontransitive.

(1a) My placing the bomb outside the door is a cause of your friend’s finding it.

(1b) Your friend’s finding the bomb is a cause of your survival.

(1c) My placing the bomb outside the door is not a cause of your survival.

On a more cheerful note, suppose that I intend to buy you a birthday present, but when the time comes I forget. Fortunately, you remind me and I buy you a birthday present after all. The following three statements seem to be true, thus showing that causation is nontransitive.

(2a) My forgetting your birthday is a cause of your reminding me.

(2b) Your reminding me is a cause of my buying you a birthday present.

(2c) My forgetting your birthday is not a cause of my buying you a birthday present.

Finally, consider Ehring’s purple fire example.34 I elaborate. Davidson puts some potassium salts into a hot fire. The flame changes to a purple color but otherwise stays the same, because potassium compounds give a purple flame when heated. Next, the heat of the fire causes some flammable material to ignite. Very soon the whole place is ablaze, and Elvis sleeping upstairs, dies of smoke inhalation. The following three statements seem to be true and again show that causation is nontransitive.

(3a) Davidson’s putting potassium salts in the fireplace is a cause of the purple fire.

(3b) The purple fire is a cause of Elvis’ death.

(3c) Davidson’s putting potassium salts in the fireplace is not a cause of Elvis’ death.

6. A Contrast Analysis of the Counterexamples

Transitivity is only defined for binary relations, but, on the context dependence view, causation is not a binary relation. (It is either a three place relation between a cause, a context, and an effect, or a four-place relation between a cause, two sets of contrast events, and an effect, depending on how you count it.) We will discuss a related property, the “variable-context transitivity” of the three-place causal relation. The three-place causal relation has “variable-context transitivity” just in case for all events e1, e2, e3, and for all contexts c1, c2, c3, if e1 causes e2 in context c1, and e2 causes e3 in context c2, then e1 causes e3 in context c3. That is, the causal relation has variable-context transitivity just in case it appears transitive no matter how you change the context.

Let’s analyze the bomb example. The example can be interpreted in many different ways depending on the contrast events assumed in statements (1a), (1b), and (1c). Two natural contrasts with the cause in (1a) are the contrast with my placing nothing outside the door and the contrast with my carefully concealing the bomb outside the door. My placing the bomb outside the door, in contrast to my placing nothing outside the door, is a cause of your friend’s finding the bomb, because if I had placed nothing outside the door your friend wouldn’t have found the bomb. My placing the bomb outside the door, in contrast to my carefully concealing the bomb outside the door, is a cause of your friend’s finding the bomb, because if I had carefully concealed the bomb outside the door your friend would not have found it (let us say).

Some interpretations of the example do not yield counterexamples to transitivity. Statement (4c) of the following is false: it seems plausible that my placing the bomb outside the door, in contrast to my carefully concealing the bomb outside the door, is a cause of your survival. So the following causal chain is transitive.

(4a) My placing the bomb outside the door (vs. carefully concealing it) is a cause of your friend’s finding it (vs. overlooking it).

(4b) Your friend’s finding the bomb (vs. overlooking it) is a cause of your survival (vs. death).

(4c) My placing the bomb outside the door (vs. carefully concealing it) is not a cause of your survival (vs. death).

However, with other natural contrasts, we do have a nontransitive causal chain. For example, all three of the following statements seem true.

(5a) My placing the bomb outside the door (vs. placing nothing outside the door) is a cause of your friend’s finding the bomb (vs. finding nothing).

(5b) Your friend’s finding the bomb (vs. finding nothing) is a cause of your survival (vs. death).

(5c) My placing the bomb outside the door (vs. placing nothing outside the door) is not a cause of your survival (vs. death).

We can develop a sufficient condition for a causal chain to be transitive from a special case of inference by transitivity of counterfactuals:

(T) φ □→ χ , χ□→φ, φ□→ψ (χ□→ψ35

Consider a general causal chain:

(6a) a, with contrast situation c1 is a cause of b, with contrast situation d1.

(6b) b, with contrast situation c2, is a cause of e, with contrast situation d2.

(6c) a, with contrast situation c3, is a cause of e, with contrast situation d3.

Suppose (C1) c1=c3, d1= c2, d2= d3, (in other words, events a, b, and e have the same contrasts throughout) and (C2) if c2 had occurred then c1 would have to have occurred (a backtracking counterfactual).36 From (T), and account2, these conditions are sufficient for a causal chain to be transitive.

This can help us to understand what is going on in example (5) to yield nontransitivity. Example (5) passes (C1), but fails (C2). It is not true that had your friend found nothing outside the door then I would have to have placed nothing outside the door. Had your friend found nothing outside the door then it might have been because I carefully concealed the bomb outside the door and she overlooked it. There is a sense in which the contrast situations in the example are incompatible with each other, and this incompatibility leads to nontransitivity.

Let’s return briefly to the other counterexamples. Here is one natural interpretation of the birthday example:

(7a) My forgetting your birthday (vs. my remembering your birthday) is a cause of your reminding me (vs. your forgetting to remind me, or our both forgetting your birthday).

(7b) Your reminding me (vs. your forgetting to remind me, or our both forgetting your birthday) is a cause of my buying you a birthday present (vs. buying you nothing).

(7c) My forgetting your birthday (vs. my remembering your birthday) is not a cause of my buying you a birthday present (vs. buying you nothing).

Notice that condition (C2) fails. It is not true that if you had forgotten to remind me about your birthday then I would have to have remembered by myself. If you had forgotten to remind me about your birthday then I might have forgotten too. Also, it is not true that if we had both forgotten your birthday then I would have to have remembered your birthday. On the contrary, if we had both forgotten your birthday then I would not have remembered your birthday.

Here is the example with some other contrast situations. Statement (8b) is false: if I had remembered your birthday by myself then I would have bought you something (let us say!) So the example exhibits transitivity. Furthermore, conditions (C1) and (C2) are satisfied. The same events always have the same contrasts throughout, and if I had remembered your birthday by myself then I would have remembered your birthday.

(8a) My forgetting your birthday (vs. my remembering your birthday) is a cause of your reminding me (vs. my remembering your birthday by myself).

(8b) Your reminding me (vs. my remembering your birthday by myself) is a cause of my buying you a birthday present (vs. buying nothing).

(8c) My forgetting your birthday (vs. my remembering your birthday) is not a cause of my buying you a birthday present (vs. buying nothing).

Finally, here is the purple fire example with some natural contrasts spelled out:

(9a) Davidson’s putting potassium salts in the fireplace (vs. Davidson’s putting nothing in the fireplace) is a cause of the purple fire (vs. a yellow fire).

(9b) The purple fire (vs. no fire) is a cause of Elvis’s death (vs. Elvis’s survival).

(9c) Davidson’s putting potassium salts in the fireplace (vs. Davidson’s putting nothing in the fireplace) is not a cause of Elvis’s death (vs. Elvis’s survival).

This case is nontransitive because it fails both conditions (C1) and (C2). The event of the purple fire is contrasted with a yellow fire in (9a) but contrasted with no fire in (9b). Furthermore, it is not true that if there had been no fire then Davidson would have to have put nothing in the fireplace. If there had been no fire, he might have decided to put potassium salts in the fireplace anyway.

7. A Fine-grained Event Analysis of the Counterexamples

Hausman describes how allowing for fine-grained events enables us to explain examples of this sort without rejecting the transitivity of causation.37 The example is not of the right form to be a counterexample to transitivity, because of the equivocation in which event is being referred to by the phrase “the purple fire”. In terms of Kimian events, “the purple fire” could either designate the triple [the fire, being purple, time] or the triple [the fire, being a fire, time]. In terms of Lewisian events, the phrase could either designate a strong event “the purple fire” which is essentially purple, or designate a weak event “the fire” which is only accidentally purple. It is the strong event of the purple fire (or the triple [the hot purple fire, being purple, time]) which is caused by Davidson’s action, and it is the weak event of the fire (or the triple [the purple fire, being a fire, time]) which is a cause of Elvis’s death.

The fine-grained event analysis of the purple fire example is similar to the analysis in terms of implicit contrasts that I gave above. While Hausman locates context dependence in the reference of the phrase “the purple fire”, I locate the context dependence in the interpretation of the whole sentence, “Davidson’s putting potassium salts in the fireplace is a cause of the purple fire”. However, if the phrase “the purple fire vs. a yellow fire” designates a strong event of the purple fire and the phrase “the purple fire vs. no fire” designates a weak event of a purple fire, which they plausibly do, then it can be shown that the two analyses of this example are equivalent.

However, I do not see how the fine-grained event analysis can explain the nontransitivity of the bomb example in a similar fashion. Perhaps we can locate an equivocation in the event referred to by the phrase “your friend’s finding the bomb” by looking at the contrast analysis of the example. Suppose that there are two different events referred to by the phrases “your friend’s finding the bomb, in contrast to your friend’s overlooking the bomb” and “your friend’s finding the bomb, in contrast to there being no bomb and your friend finding nothing”, and that the phrase “your friend’s finding the bomb could designate either event. Perhaps we could define event1 as an event that occurs in worlds in which I place a bomb outside the door and your friend finds it, and does not occur in worlds in which I place a bomb outside the door and your friend overlooks it or in worlds in which I do not place a bomb outside the door. And we could define event2 as an event that occurs in worlds in which either I place a bomb outside your door and your friend finds it or I place a bomb outside your door and your friend overlooks it, and does not occur in worlds in which I do not place a bomb outside the door. Then, after some work, we could show that the example involves an equivocation rather than a failure of transitivity.

But how could the phrase “your friend’s finding the bomb” designate event2? (Surely overlooking the bomb is not just another way of finding the bomb!) In order to analyze the example in this way we have built conditions external to the event into the event identity conditions for the event. The contrast analysis of this example is more plausible.

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