Indicative and Subjunctive Conditionals

Indicative and Subjunctive Conditionals Wayne A. Davis The Philosophical Review, Vol. 88, No. 4. (Oct., 1979), pp. 544-564. Stable URL: http://links.jstor.org/sici?sici=0031-8108%28197910%2988%3A4%3C544%3AIASC%3E2.0.CO%3B2-H The Philosophical Review is currently published by Cornell University.

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The Philosophical Review, LXXXVIII, No. 4 (October 1979)

INDICATIVE AND SUBJUNCTIVE CONDITIONALS

Wayne A. Davis

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ndicative and subjunctive conditionals have different truth conditions. I seek to account for this difference within the general possible-worlds framework developed by Stalnaker and Lewis. I argue that their truth conditions hold for indicative conditionals, and that similar but different conditions hold for subjunctive conditionals. An indicative conditional is true only if its consequent is true in the antecedent-world that is most similar to the actual world overall. A subjunctive conditional is true only if its consequent is true in the antecedent-world that is most similar to the actual world before the antecedent event. A whole set of extant counterexamples to the Stalnaker-Lewis account of subjunctives confirms it for indicatives. This simple development renders similarity theory both more general and more accurate. I also point out that a subjunctive conditional is incorrect in some way if its consequent refers to a n earlier time than its antecedent. Indicative and subjunctive independence will be briefly defined and distinguished.'

In "A Theory of Conditionals," Robert Stalnaker proposed that a natural language conditional is true iff its consequent is true in the closest possible world in which its antecedent is true. I refer to this principle, which gives truth conditions for conditionals in terms of the truth values of their components in certain possible worlds, as The Stalnaker Principle. I have in my hand a very expensive and fragile crystal wine glass. Now suppose I release the glass five feet above a concrete floor. What will happen? By the Stalnaker Principle, this question can be reformulated in terms of possible worlds as follows. Consider all the I' This is the first of a series of three papers on conditionals. In the second I distinguish what I call weak and strong indicative conditionals, and in the third weak and strong subjunctive conditionals. Strong conditionals, which contain then, have stronger truth conditions, and consequently a different logic. In the present paper, I confine my attention to weak conditionals.

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worlds in which I release the glass; what happens in the world that is most similar to the actual world (in the actual world I do not release it)? For one thing, the glass will fall to the ground accelerating ever so slightly on the way. This is so even though in the actual world the glass does not fall at all. For any world in which gravity operates will be more similar to the actual world than a world in which gravity does not operate. The glass will also disturb the air molecules as it falls; any world in which it did not would be very different from the actual world, more different certainly than one in which it did. The glass will shatter when it hits the ground. Since the glass is very fragile in the actual world, and in the actual world fragile crystal glasses shatter when dropped on concrete floors, any world in which the glass does not shatter will be more dissimilar to the actual world than one in which it does. And so on. In the closest world in which the glass is released, then, the glass falls to the ground, accelerating slightly on the way, disturbing the air in the process, and shattering upon impact. Then by the Stalnaker Principle, all this will happen zfas we supposed I release the glass. In general, if the antecedent A of a conditional is true, then the closest world in which the antecedent is true (the closest "Aworld") is the actual world, since no world is more similar to the actual world than itself. But if A is false, the closest A-world cannot be the actual world. The fact that A is true in the closest A-world but not in the actual world will imply innumerable further differences between them. The closest A-world is to be that world in which the differences are fewest and least important. In Counterfactuals, David Lewis develops a more elaborate version of the Stalnaker Principle that accommodates cases in which there is no unique closest A-world: a conditional is true iff some world in which its antecedent A and consequent C are true is closer than any world in which A is true and C is false. For my purposes, the simpler Stalnaker Principle is adequate. Conditionals appear in either the indicative or the subjunctive mood. "If I release the glass, it will fall" is an indicative conditional, for its consequent is in the indicative mood. "If I released the glass, it would fall" is a subjunctive conditional, its consequent being in the subjunctive. There are furthermore two types of subjunctive conditional: open, which typically contain

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"should" in the antecedent (for example, if the light switch should be flipped, the light would come on; if the switch should have been flipped, it would have come on);' and counterfactual, which contain "were" or "had" in the antecedent (for instance, if the light switch were flipped, the light would come on; if the switch had been flipped, the light would have come on). Counterfactual subjunctive conditionals are usually called simply counterfactuals, and open subjunctive conditionals are usually called simply subjunctive conditionals. Counterfactual conditionals differ from open conditionals in their implication or presupposition that the antecedent is in fact false. Thus "If the switch were flipped, . . ." implies that the switch will not be flipped, whereas "If the switch should be flipped, . . ." does not. I believe that this implication is not a truth implication, but merely an utterance implication. "If the switch were flipped, the light would come on" is not necessarily false if the switch will be flipped, though it is inappropriate and misleading if the speaker believes that the switch will be flipped.' Nor do I believe that the failure of this presupposition leads to a truth value gap. That is, I do not believe that "if the switch were flipped, the light would come on" is neither true nor false if the switch is in fact flipped. Consequently, the difference between open and counterfactual subjunctive conditionals on my view is not a matter of logic or truth conditions, and will therefore be ignored. If the reader thinks otherwise, he should treat what I say as only applying to open subjunctive conditionals.

' Future tense antecedents of open subjunctive conditionals may not contain "should." Instead, the main verb may appear in the past tense, or the "should" may simply be deleted. Thus, "If John should flip the switch, he would turn on the light" may be transformed into "If John flipped the switch he would turn on the light," and "If the switch should be flipped, the light would come on" may be transformed into "If the switch be flipped, the light would come on" (though this is a bit archaic). This has been held by Downing (1958-9. p. 127ff; 1975, p. 88ff), Ayers (1965), Harrison (1968, p. 373ff), Stalnaker (1968, p. 99, fn 3), Young (1972, p. 61ff), Lewis (1973, pp. 3,27), Mackie (1973, pp. 65, 71), and Edwards (1974, p. 90). See especially Ayers. Contrast Von Wright (1957, p. 162). " If the difference between open and counterfactual conditionals is a matter of truth conditions, then we could simply define an additional connective: A > C =df -A & A > C. Another alternative would be to say that A > C h<s no truth value if A is true, the same truth value as A >C otherwise.

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Stalnaker believed that subjunctive and indicative conditionals have the same truth condition^.^ This Equivalence Thesis is attractive for several reasons. First, its obvious economy. Second, the a priori implausibility that such a grammatical difference should mark a semantic distinction of any importance. And third, the apparent equivalence of many corresponding indicative and subjunctive conditionals. For example, "If the light switch should be flipped, the light would come on" seems to have the same truth value as "If the light switch is flipped, the light will come on." The equivalence of corresponding subjunctive and indicative conditionals with some or even a wide range of antecedents and consequents does not of course prove that they are equivalent for all antecedents and consequents. Are there any instances that disconfirm the equivalence thesis? J. L. Mackie has argued5 that accidental generalizations provide such cases. As it happens, ( I ) Everything in my pocket is silver, since I have two old mercury dimes in my pocket and nothing else. Now compare the following open sentences. (2) x is in my pocket 3 x is silver. (3) If x is in my pocket, x is silver. (4) If x were in my pocket, x would be silver. (4) is definitely not true for all x . It is not true, for example of any penny, of my coffee cup, or of Yankee Stadium. (2) is definitely true for all x . Now Mackie believes (1) entails that (3) is true of all x , which would mean that indicative and subjunctive conditionals are not e q ~ i v a l e n tBut . ~ (3) is false for pennies and other nonsilver things just as (4) is. It is certainly not true that if a

T h i s has been held by Mayo (1957, pp. 292ff), Stalnaker (1968, p. 99, fn3), Edwards (1974, p. go), and Downing (1975, p. 88ff). See also Barker (1975, section 4). ' 1973, pp. 115ff. See also Walters (1967, p. 215), Von Wright (1957, p. 147), Chisholm (1949, p. 492ff), and Clark (1974, p. 78). V h i s h o l m , in his classic study "The Contrary-to-Fact Conditional" seems to equate "indicative conditional" with "material conditional." See especially pp. 486-7. Thus he says "Our problem is to render a subjunctive conditional . . . into a n indicative statement which will say the same thing" (p. 486). "Consider this example: If the vase were dropped, it would break. Is a n adequate translation ~ i e l d e dby replacing the 'were' and 'would' by 'is' and 'will' and interpreting the statement as a truth functional material conditional?" (p. 486). H e

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penny is in my pocket, it is silver. O n the contrary, if a penny is in my pocket, then not everything in my pocket is silver. ' 3 Note that according to the Stalnaker Principle, (3) and (4) are false for pennies. The nearest world in which a penny is in my pocket is not a world in which it is silver, but rather a world in which not everything in my pocket is silver. Unlike genuine laws, accidental generalizations often do not hold in neighboring worlds. While accidental generalizations do not provide them, there are many cases in which corresponding indicative and subjunctive conditionals differ in truth value. We begin by examining the examples David Lewis used in Counterfactual following Ernest Adams. Let A+C symbolize indicative conditionals and C subjunctive conditionals. (Since A and C stand for inA dicative sentences, they will have to be transformed into the subjunctive mood in familiar ways if A -- C is to be expressed in ordinary English as a subjunctive conditional.) Consider the following three sentences, and four conditionals formed from them.

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goes on to show that it can not be interpreted as a material conditional, and seems to assume that therefore the indicative translation fails. But as ordinarily used, "If the vase is dropped, it will break" is not a material conditional (see below, pp. 7-8). The problem Chisholm attempted to solve is better formulated as the problem of analyzing nonmaterial conditionals using only the means of "extensional" logic, i.e., truth functional logic plus quantification theory. I would not of course deny that the following conditional is true: if everything in my pocket is silver and this penny is in my pocket, this penny is silver. But then so is: if this penny were in my pocket and everything in my pocket were silver, this penny would be silver. "3) also comes out true if the phrase "If x is in my pocket, . . . " is understood as a universal quantzjer with unrestricted scope, i.e., as meaning "For all x such that x is in my pocket: . . . " or "Let x designate any object in my pocket; then . . . " Note that on this interpretation (3) is a closed sentence. A similar reading is impossible for (4), because it makes no sense to say "For all x such that x were in my pocket." But even if such a reading of (3) is acceptable (it seems to be the proper reading of "if x is any object in my pocket, then x is silver," but not of (3) itself), it is not the one we are interested in. "ee Lewis (1973, p. 3) and Adams (1970, p. 90). Mackie's examples are basically the same (1973, p. 14). Let X' be "Jones took cyanide," Y' be "Cyanide is not a deadly poison," and Z' be "Jones is dead." Mackie imagines that Jones is known to be alive, and consequently known not to have taken cyanide. In Mackie's example, X'+Y' presupposes that Jones is alive and is accordingly Y ' does not presuppose that Jones is alive, and accordingly true, while X' ~7 is false.

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X: Oswald did not kill Kennedy. (I?) Y: Someone else killed Kennedy. (F) Z: Kennedy was not killed. (F) Indicative Subjunctive X+Y (T) X 7 Y (F) X+Z (F) X > Z (T) I assume that in fact Oswald acted alone in killing Kennedy." The truth values of the statements are indicated. For example, X+Y is true: it is true that if Oswald did not kill Kennedy, someone else did; X > Y is false: it is not true that if Oswald had not killed Kennedy, someone else would have. We seek to account for this difference in truth value. Since X+Y and X > Y differ in truth value, the Stalnaker Principle cannot give the truth conditions for both. The following question arises. Does the Stalnaker Principle hold for indicative conditionals or subjunctive? According to Lewis, subjunctives. Let us see. Note first that X+Y seems to presuppose in some sense that Kennedy was killed, while X > Y does not. Now then, we need to examine the closest possible world in which Oswald did not kill Kennedy. It is a world in which Kennedy was not killed, or a world in which someone else killed Kennedy? T h e assassination of Kennedy is obviously one of the most important events of recent American and world history. The fact that Oswald in particular was the assassin, rather than some other very unimportant person, is in contrast of minor significance. Consequently, a world in which someone else killed Kennedy is considerably more similar to the actual world than a world in which Kennedy was not killed." I conclude from this and

lo If this assumption bothers you, change the example to the Lincoln assassination. " Lewis asserts on the contrary that a world with no killing is closer to the actual world than a world with a different killer (1973, p. 71; see also the footnote on p. 72). This seems to me dead wrong. And to others: Fine (1975, p. 452), Creary and Hi11 (1975, p. 343), Slote (1978, p. 23), and especially Bennett (1974, p. 395ff). Fine offered an especially compelling example. "The counterfactual 'If Nixon had pressed the button there would have been a nuclear holocaust' is true or can be imagined to be so. Now suppose that there never will be a nuclear holocaust. Then that counterfactual is, on Lewis's analysis, very likely false. For given any world in which antecedent and consequent are both true it will be easy to imagine a closer world in which the antecedent is

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many other examples that, pace Lewis, the Stalnaker Principle holds for indicative rather than subjunctive conditionals. SP(+) The indicative conditional A+C is true 2ff C is true in i ( A ) , where i ( A ) is the closest possible world in which A is true. I shall hereafter refer to this as The Stalnaker Principle for Indicative Conditionals. The only other account of the indicative conditional I know of identifies it in some way with the material conditional.12 This cannot be done. Material conditionals have different truth conditions from indicative conditionals. A C may be true even though A+C is false. For example, in the next few minutes I will neither flip the living room light switch, nor turn on the radio. It follows that "I will flip the light switch 2 I will turn on the radio" is true. However, "If I flip the light switch, I will turn on the radio" is false. Going back to the Oswald example, X 3 Z is true while X+Z is false. The Stalnaker Principle gives the right truth values in both examples. See also Mackie's example. In general, -A logically implies A 3 C but not A+C (orA%).13 This is the so-called paradox ofmaterial implication. It is a paradox only to those who think material conditionals and natural language conditionals have the same truth conditions. It is irrelevent

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true and the consequent false. For we need only imagine a change that prevents the holocaust but that does not require such a great divergence from-reality" (1975, p. 452). See also Schlossberger (1978, p. 81) and Slote (1978, p. 20). '' See Edwards (1974, p. 87ff); Von Wright (1957, p. 134ff); Mackie (1973, pp. 75-82); Grice, "Logic and Conversation; The William James Lectures given at Harvard University in 1967," discussed in Lewis (1976, pp. 305-308); and Lewis (1973, p. 72, fn*). '" According to Dummett (1958-9, pp. 101-106), Jeffrey (1963), and others, the truth value of an indicative conditional is indeterminate-neither true nor false-if its antecedent is false. Adams holds that "the term 'true' has no clear and ordinary sense as applied to conditionals, particularly to those whose antecedents prove to be false . . . " (1965, p. 169). These views are incorrect. In fact, I will not flip the living room light switch in the next five minutes. Nevertheless it is true that t f I do I will turn on the light and false that if I d o I will turn on the radio. "Someone has green hair if I do" is logically true while "No one has'green hair if I do" is logically false, though my hair is black. Truth and falsity are here used in their ordinary sense, whatever that is. T h e conditionals are true and false, respectively, in the same sense in which, and for the reason that, it is true that the light switch turns on the light and false that the light switch turns on the radio. More generally, the sentence schema S is true Qf'S which is the core of both the redundancy and correspondence theories of truth, applies to indicative conditionals as well as to other declarative statements.

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to remark that it is pointless or misleading to assert A > C on the grounds of -A. Even if this were so, it would not change the fact that A+C is sometimes false when A 2 C is true. Furthermore, it is positively fallacious to assert A+C on the grounds of -A. Finally, while the material conditional is truth functional (its truth value is completely determined by the truth value of its antecedent and consequent), the indicative conditional is not. For example, a n indicative conditional with false antecedent and consequent, such as "If I flip the switch, I will turn on the light," may be either true or false depending on other facts, such as whether or not the switch works. Since they have different truth conditions, the indicative conditional and material conditional have quite different logics. T o name a few differences (which can all be derived from the Stalnaker Principle): the argument form -A, therefore A+C is invalid; A+C and A+-C are incompatible ("If I flip the switch, I will turn on the light" and "If I flip the switch, I will not turn on the light" cannot both be true even if I will not flip the switch); (AB)+C is not equivalent to A+(B+C) ("If I eat this apple and I know it is poisoned, I will eat it" is true; "If I eat this apple, I will eat it if I know it is poisoned" is false); A+C does not entail AB+C (it is true that this glass will break if I drop it, but false that it will break if I drop it and it does not break); finally, A+C is not transitive ("If I drop this glass and it does not break, I will drop the glass" and "If I drop the glass, it will break" are true, but "If I drop the glass and it does not break, it will break" is false). In short, the indicative conditional differs as much from the material conditional as the subjunctive conditional does. What can be said about the truth conditions for subjunctive conditionals? I believe we can maintain the basic structure of the Stalnaker Principle, namely: A > C is true zffC is true in s(A), where s(A) is a certain world in which A is true. O u r problem, then, is to characterize definitely and explicitly this world s(A). We know one thing it is not, namely, the A-world that is most similar to the actual world. For if it were, A > C would be equivalent to A+C. Let us return to our examples, where A is X. We know in particular that s(X) is not the X-world that is most similar to the actual world, since X+Y and X Y are not equivalent. We can learn more about s(X) from the fact that X > Z is true,

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that is, that if Oswald had not killed Kennedy, Kennedy would not have been killed. Z must therefore be true in s(X). Since Z is true in s(X), Y must be false in s(X). We have therefore accounted for the falsity of X 7 Y, since X 7 Y is to be true iff Y is true in s(X). We saw that the truth of X+Y follows from the assumption that Z is false in i(X); now we see that the falsity of X 7 Y follows from the assumption that Z is true in s(X). We still need a characterizaton of s(A), however, that will make this latter assumption plausible. My suggestion is that s(X) is that world in which Oswald did not kill Kennedy that is most similar to the actual world before the time at which Oswald killed Kennedy (in the actual world). T o evaluate indicative conditionals, we must compare worlds in the entirety of their temporal extension; i(A) is that A-world most similar to the actual world, considered as a whole. I call this the condition of total similarity. T o evaluate subjunctive conditionals, I am suggesting, we compare worlds only over part of their temporal extension, completely disregarding the rest. s(A) is that A-world most similar to the actual world, considered in part. I call this the condition of partial similarity.14 It might be the case that world K is more similar to N than M is, when considering only times before a given time t , while M is more similar to N than K is when considering all times. Lewis likens similarity among worlds to similarity among cities. Comparing worlds in order to evaluate indicative conditionals is like comparing New York and Boston over the entirety of their history. Comparing worlds ' T h i s suggestion was anticipated by Jonathan Bennett (1974, pp. 397ff), who went on to develop a modification of Lewis's theory incredibly like my modification of Stalnaker's. Cf. Downing's statement that "the past, unlike the future, can be taken as 'given' for the purpose of certain speculations" (1958-9, p. 136). Whereas the past but not the future may be taken as given with respect to the evaluation of subjunctive conditionals, the future as well as the past may be taken as given with respect to the evaluation of indicative conditionals. Compare also Slote's statement that "the base times of past-tense counterfactuals will clearly be past. . . . I think a careful investigation of cases will tend to show, for example, that if the antecedent and consequent of a past tense counterfactual have the same single reference time, then the base time of the counterfactual is identical with that time" (1978, p. 10). By "base time," Slote means the time at which the "cotenable conditions are thought of as existing." Csing the partial similarity condition, the possible worlds framework can handle the problems raised by Slote (1978, pp. 20ff).

to evaluate subjunctive conditionals is like comparing New York to Boston only as they existed before 1800, say, ignoring the way they are after 1800. It might very well be that New York is more similar to Boston than Chicago considering only times before 1800, but more similar to Chicago than Boston considering the entire history of the cities. I think it is plausible to assume that Kennedy was not killed (that is, that Z is true) in the nearest world in which Oswald did not kill Kennedy, considering only times before that at which Oswald actually did kill Kennedy. This assumption is plausible because in the actual world, Oswald acted alone in killing Kennedy. So a world just like the actual world before the assassination, except for, say, the fact that Oswald did not aim properly (or for the fact that Oswald changed his mind at the last minute, or that Oswald was arrested by the secret service as he entered the Book building, and so on) is more like the actual world than one in which, say, there were other assassins besides Oswald (or in which there was a back-up team in case Oswald failed, and so on). Furthermore, if the actual world were such that Kennedy was killed in the nearest world in which Oswald did not kill Kennedy, considering only times before the actual assassination, then I think X > Y would be true, that is, it would be true that if Oswald had not killed Kennedy, someone else would have. In my opinion, then, the nearest X-world, considered as a whole, is a world in which Kennedy was killed, while the nearest X-world, considered in part, is one in which Kennedy was not killed. As this example illustrates, indicative conditionals in a certain sense stick closer to the actual world than subjunctives. Assuming that the nearness of worlds depends on total similarity, i(A) can be no further from the actual world than s(A) is, but is generally closer. If we say that A+C and A > C are "about" i(A) and s(A), respectively, then indicative conditionals are generally "about" closer worlds than subjunctives. If you will, subjunctive conditionals are more "hypothetical" than indicative conditionals. There are more facts about the actual world that are relevant to determining the truth of a n indicative conditional than there are to determining the truth of a subjunctive. T h e suggestion of the previous paragraphs leads us to fill in the specification of s(A) as follows: s ( A ) is the A-world that is most

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similar to the actual world before a certain time t.15 Now we must face the problem of characterizing this certain time t. It is, I believe, the time referred to in the antecedent A. I am unable to give a precise account of this notion of time-reference. In some cases, it is obvious what time is referred to. For example, in "If Jack had called at 1:00 a.m., he would have awakened me," the time referred to explicitly in the antecedent is 1:00. In "If Oswald had not killed Kennedy, Kennedy would not have been killed," the time referred to implicitly in the antecedent is the time, whenever it was, at which Oswald killed Kennedy in the actual world. In some cases, however, it is not clear what time is referred to. Consider, for example, "If Jack had called at 1:00 a.m. and (or) at 2:00 a.m., he would have awakened me." Lewis has pointed out that, since counterfactuals are notoriously vague, our analysis of them should somehow locate the vagueness. One source of vagueness, if the Stalnaker Principle is basically correct, is the notion of similarity. Another source, perhaps, is this notion of time reference. We now have a gratifyingly definite Stalnaker Principle for Subjunctive Conditionals. SP( > ) The subjunctive conditional A > C is true l f f C is true in s(A), where s ( A ) is the A-world that is most similar to the actual world before t(A), the time reference of A. Note that according to SP( > ), subjunctive conditionals are neither stronger nor weaker than indicative conditionals; they are simply different. This is required by our examples, for X+Y is true while X > Y is false (so indicatives are not stronger), but also X > Z is true while X+Z is false (so subjunctives are not stronger). One complication should be noted. In "If you ever took cyanide, you would die," the time reference of the antecedent may be represented by a variable bound by a universal quantifier on the whole conditional: given any (future) time t, if you should take cyanide at t, you would die immediately after t. Sentences like these are best handled by using the Stalnaker Principle to

'' Cf. a related idea of Lewis's. "Corresponding to a kind of time dependent al lime 1, a n d its strict conditional, we assign necessity we may call inevitabili~~~ to each world i as its sphere of accessibility the set of all worlds that are exactly like i a t all times u p to time t , so (@ 3 4)is true a t i if a n d only if 4is true a t all +-worlds that are exactly like i u p to t" (1973, p. 7 ) .

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give truth conditions for the open sentence obtained by removing the quantifier, and then applying the usual truth conditions for the quantifier. Another complication requires modification of SP( 7 ). Some antecedents do not refer to any time. I will say that they are timeless. For example, in "If 1877 were divisible by 3, it would not be prime" and "If kangaroos had no tails, they would topple over," the antecedents are timeless. When the antecedent is timeless, the partial similarity condition obviously cannot be applied. I believe that in such cases, the total similarity condition should be applied. s(A) should therefore be specified as follows: z f A is not timeless, s(A j is the A-world that is most similar to the actual world before t(A j; while zfA is timeless, s ( A j is the A-world that is most similar to the actual world overall. This makes subjunctive conditionals with timeless antecedents equivalent to the corresponding indicative conditionals, which seems to be the case. l6 After using the Oswald example to show that counterfactuals are not in general equivalent to their corresponding indicative conditionals, Lewis pointed out that subjunctive conditionals pertaining to the future, like "If you should flip the switch five minutes from now, you would turn on the light," do seem equivalent to their corresponding indicatives. A conditional "pertaining to the future" is one whose antecedent refers to some time in the future. Now the Stalnaker Principles entail that subjunctive conditionals pertaining to the future are not in reality equivalent to their corresponding indicatives. But the Stalnaker Principles nevertheless enable us to see why they should appear equivalent. For it is a truism that our knowledge of the future is based inductively on our knowledge of the past. Consequently, if A refers to a present or future time, we will not at present be able to distinguish the A-world that is most similar to the actual world be-

"' f. the opening paragraph of Lewis's Countefactuals: " 'IJ'kangaroos had no lads, thty would topple over' seems to me to mean something like this: in any possible state of affairs in which kangaroos have no tails, a n d which resembles our actual state of affairs as much as kangaroos having no tails permits it to, the kangaroos topple over." Whereas Lewis believes that a similar analysis holds for conterfactuals in general, which he uses the Oswald example to distinguish from indicative conditionals, I believe that such a n analysis holds for indicative conditionals in general, a n d only for those counterfactuals like Lewis's kangaroo example which have timeless antecedents.

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fore t(A) from the A-world that is most similar to the actual world overall. Indeed, the A-world we judge most similar overall, or before any time in the future, will be the very A-world we judge most similar up to the present. SP( > ) also eliminates Lewis's roulette wheel problem. Lewis is discussing laws of nature and the special status accorded them by metalinguistic theories of counterfactuals like those of Goodman and Chisholm. He sketches a n account of laws that nicely explains why laws are so important to us. So he is able to concede to the metalinguistic theorist that It makes a big difference to the character of a world which generalizations eniov ., , the status of lawhood there. Therefore similaritv and difference of worlds in respect of their laws is an important respect of similarity and difference, contributing weightily to overall similarity and difference. [1973, p. 751

But he is also able to add, plausibly I think, that Though similarities or differences in laws have some tendency to outweigh differences or similarities in particular facts, I do not think they invariably do so. Suppose that the laws prevailing a t a world i are deterministic . . . Suppose a certain roulette wheel in this deterministic world i stops on black a t time t, and consider the counterfactual antecedent that it stops on red. What sort of antecedent-worlds are closest to it? O n the one hand, we have antecedentworlds where the deterministic laws of i hold without exception, but where the wheel is determined to stop on red by particular facts different from those of i. Since the laws are deterministic, the particular facts must be different a t all times before t, no matter how far back. . . . O n the other hand we have antecedent-worlds that are exactly like i until t or shortly before; where the laws of i hold almost without exception; but where a small, localized, inconspicuous miracle at t or just before permits the wheel to stop on red in violation of the laws. Laws are very important, but great masses of particular fact count for something too; and a localized violation is not the most serious sort of difference of law. The violated deterministic law has presumably not been replaced by a contrary law. Indeed, a version of the violated law, complicated and weakened by a clause to permit the one exception, may still be simple and strong enough to survive as a law. Therefore, some of the antecedent worlds where the law is violated may be closer to 1 than any of the ones where the particular facts are different a t all times before t. At least, this seems plausible enough to deter me from decreeing the opposite. [1973, p. 751

Now for the problem. My example of the deterministic roulette wheel raises a problem for me: what about differences of particular fact a t times after t? . . . if I have decided that a small miracle before t makes less of a difference from i than a big difference of particular fact at all times before t, then why d o I not also think that a small miracle after t makes less of a difference from 2 than a big difference of particular fact a t all times after t? T h a t is not what I do think: the worlds with no second

CONDITIONALS miracle a n d divergence must be regarded as closer, since I certainly think it true (at 1 ) that if the wheel had stopped on red a t t, all sorts of particular facts afterward would have been otherwise than they are at 2 . T h e stopping on red would have plenty of traces and consequences from that time on. [1973, p. 761

The reason why Lewis must believe that worlds without a miracle after t are closer to i than worlds without a second violation of law is, not only his belief that a certain counterfactual is true, but also his belief that the total similarity condition applies to counterfactuals. But if, as SP( > ) says, only the partial similarity condition applies, then we can hold both that that counterfactual is true and that the world with two law violations will be more similar to i overall than the world with only the earlier law violation. For the truth of the counterfactual, according to SP( > ), would require only that the world with one violation be more similar to i before t than the world with two violations. After sketching out the above theory in a remarkably similar fashion, Jonathan Bennett raised the following objection. If a given sphere expresses worlds' similarity to the actual world in respect of their states u p to time t, what basis have we for saying what they are like after t? If no information on that score has been fed into the sphere, none can be extracted from it. Yet we need such information: we need to sort out Cworlds from -C-worlds, a n d C may mention times later than t. T h e only solution I can find is to restrict our spheres to worlds which obey the laws of nature of the actual world. [1974, p. 398ff; I changed Q t o C ]

What we must do, however, is use the laws o f s ( A ) , not of the actual world. The laws of s(A) are to be as similar to the laws of the actual world as possible, but need not be the same. Another problem immediately arises. if two worlds differ in the laws of nature which obtain in them, this will tend to be a big overall dissimilarity between them; but now we are comparing worlds only in respect of their similarity u p to time t, a n d that range of comparisons is utterly untouched by any differences regarding miracles or lawchanges after t. If Lewis is to link pre-t comparisons with post-t ones, he must require lawlikeness in the worlds in his spheres-presumably by requiring that they all obey the laws of the world a t the centre of the sphere. [1974, p. 3991

We can begin to solve this problem by distinguishing dated from undated features of a world. In the actual world, the stock market crashed on October 29, 1929; the stock market crashed on some date; the speed of light is c at all times and places; and 2 2 = 4. The first is a dated feature of the actual world, the rest undated. Now, when we are comparing two worlds before a time t, we

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clearly must consider only those dated features that are dated before t. But what about undated features? There is no clear answer to our question. The injunction to compare worlds before a certain time is inherently vague on this point. I suggest the following resolution, which seems as reasonable as any other, and makes the Stalnaker Principle work. First distinguish existentially undated features (such as, the market crashed at some time), from universally undated features (such as, the speed of light is c at all times). Count timeless statements (2 2 = 4) as universally undated. My suggestion is that when comparing worlds before a certain time, universally undated features must be considered, but not existentially undated features. Since general laws of nature, mathematics, and logic are universally undated, they must be considered in any comparison. Since the fact that Oswald killed Kennedy at some time is existentially undated, it should be ignored. We may think of it as dated at the time of the assassination. Note that I have not stipulated any special status for laws as opposed to accidental generalizations. The latter are universally undated too, and so must be considered; but they do not count for much. Suppose that in another world w , the speed of light is c before t and 2c after t. Bennett would say that a law "changed" in w at t. Nevertheless, this feature is universally undated, so it must be counted as an important respect of dissimilarity even if we are just comparing worlds before t. It may appear dated until you consider what the law says in full: A t all times before t the speed of light is c and at all times after t the speed of light is 2c. It is admittedly tempting to say that w is "just like" the actual world before t. But this is clearly true with respect to dated features only. We must similarly not think of laws with exceptions as dated. "At all times except t the speed of light is constant" would still describe a universally undated feature. The above resolution enables us to meet a n objection raised by Eugene Schlossberger (1978, p. 81). I adapt his argument to the Oswald example. Let us suppose that those worlds most similar to the actual world in which Oswald did not kill Kennedy, considering only times before the actual assassination, are worlds in which Oswald did not aim properly. Let us allow for the moment that there may be more than one most similar world, so that Lewis's principle must be applied rather than Stalnaker's. I must

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maintain that there are no most similar worlds in which Kennedy was killed. Let J be one most similar in which Kennedy was not killed. Schlossberger's objection is that there is another world H exactly like J before the time t of the actual assassination, but in which shortly after t a flash flood occurs in which Kennedy is drowned. (As Bennett would put the objection, how do we know what happened in J after t?) My reply is that any world at all like the actual world before t in which a flash flood occurred after t would have to differ from the actual world before t in many respects either of law or of particular fact in which respects J need not differ from the actual world. For in a world whose laws are similar to ours, flash floods do not come from nowhere. Having accounted for the truth-value differences between corresponding indicative and subjunctive conditionals in the Kennedy assassination examples, have we accounted for all such differences? Unfortunately not. The following corresponding conditionals are both true.

(5) If John died in his sleep last night, he did not awaken this morning. (6) If John died in his sleep last night, he would not have awakened this morning. But consider their respective contrapositives.

(7) If John awakened this morning, he did not die in his sleep last night. (8) If John awakened this morning, he would not have died in his sleep last night.

(7) is obviously true. We may infer from the fact that a man woke up, that he did not die in his sleep. If it is a possibility for someone to wake up in the morning after having died in his sleep, it is a far-fetched one. (8) on the other hand, is not obviously true, though it is not obviously false, either. It is definitely incorrect in some way. "Could" or "must" would be correct, but not "would." According to the Stalnaker Principle, however, (8) is perfectly true. For whether we consider all times or only times before this morning, the nearest world in which John woke up this morning will surely be a world in which he did not die in his sleep. Peter Downing, in "Subjunctive Conditionals, Time Order,

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and Causation," pinpointed one problem with sentences like (8): they are "temporally backward looking." That is, the time referred to by their consequent is before the time referred to by their antecedents. In general, subjunctive conditionals are true only if they are not backward looking. I call this the antecedence condition. As ( 7 ) illustrates, the antecedence condition does not apply to indicative conditionals. Let us say that A is antecedent to C iff the time reference of A is not after that of C.17There are two ways to impose the antecedence condition: as a truth condition or a presupposition. That is, the modified Stalnaker Principle might be formulated: A > C is true 2 f f A is antecedent to C and C is true in s ( A ); in this case, A > C would be false if A is not antecedent to C. O r the Principle might read: A > C is true 2ffC is true in s ( A ) , provided A is antecedent to C; done this way, A > C would be without truth conditions, and so presumably neither true nor false, if A is not antecedent to C. I do not know which formulation is preferable. Note that as I have defined the antecedence condition, A and C may refer to the same time. This allows counterfactuals like "If the length of this pendulum were L, the period would be T," "If this were a cat, it would be a n animal," and "If John were to stick his arm out the window in a certain way, he would signal for a turn," to be true. While the antecedence and partial similarity condition are independent, they do seem to complement each other nicely. Some true subjunctives appear to be backward looking, but really are not. Suppose a certain flight inevitably takes one hour. ' I The vagueness of "the time reference of A" will of course infect the antecedence condition and make its application unclear in some cases. Consider, e.g., a case discussed by Kim in another connection.

There are however, deductive explanations in which some of the initial conditions occur later than the explanandum. . . . Such a n explanation can result when a law of "variational" form, such as Fermat's principle that the path of a light ray between two points is such as to minimize or maximize the time required in its passage, is used in the explanans. As a n explanation of why a light ray passed through a point P, we may say that the light ray originated a t point P I a t t l , and was observed a t P, a t t,, and that its passage through P a t t, where t , > t > t,, was required by Fermat's formula" (1967, p. 159). Assuming that what Kim says about Fermat's law is correct, I believe the subjunctive conditional "If the light ray passed through P I a t t , and P, a t t,, it would have passed through P a t t" is true. But it is not clear whether this antecedent is indeed antecedent to the consequent.

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Now consider (9) If the plane had arrived at 2:00, it would have to have departed at 1:00. Without the have to, (9) would be in the same limbo as (8). But with it, (9) is perfectly correct. The consequent of (9) appears to refer to an earlier time than the antecedent. I submit, though, that the consequent actually reJkrs to the time when the statement is made, which, if the "had" is appropriate, is after 2:OO. For the consequent of (9) is "The plane has to have departed at 1:00," whose main verb is in the present tense. From the truth of (9) and the Stalnaker Principle, it follows that the nearest world in which the plane arrived at 2:00 is a world in which the plane has to have departed at 1:OO. The consequent of (9) is some sort of tensed modal statement. It entails that the plane could have departed at 1:00, and furthermore that it actually did. Finally, note that the indicative conditional corresponding to (9) is also true, namely, "If the plane arrived at 2:00, then it has to have departed at 1:OO." Some subjunctive conditionals are mixed. While their consequents are subjunctive, their antecedents have a n indicative conjunct and a subjunctive conjunct. For example, consider the false statement

(10) If everything in my pocket is silver, and a penny were in my pocket, it would be silver. This cannot be treated as a pure indicative conditional, nor as a pure subjunctive conditional, for the following statements are true (and the Stalnaker Principles rule that they are true). (11)If everything in my pocket is silver and a penny is in my pocket, it is silver. (12) If everything in my pocket were silver and a penny were in my pocket, it would be silver. I suggest that we treat mixed subjunctives by exporting the indicative conjunct of the antecedent. This gives us a statement of the form A+(B 7 C). We then apply the Stalnaker Principles in succession. A+(B > C) is true iff B > C is true in i(A); B 7 C is true in i(A) iff C is true in s,(B), where s,(B) is the nearest B-world to i(A) considering only times before the time reference

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of B. sA(B)need not be the same world as either i(AB) or s(AB). In example (lo), A, namely, "everything in my pocket is silver," is false in sA(B),but true in i(AB) and s(AB). For if we start from the nearest world in which everything in my pocket is silver (that will be a world in which pennies are copper), and move to the nearest world from that one in which a penny is in my pocket, we will be in a world in which not everything in my pocket is silver. But if we start from the actual world, and move to the nearest world in which it is jointly true that everything in my pocket is silver and a penny is in my pocket, we will be in a world in which everything in my pocket is silver (that will be a world in which one penny at least is silver). Indicative independence is expressed by indicative sentences like the following: The picnic will be cancelled whether or not it rains; I will play tennis independent of whether I have a white shirt to wear; it is sunny here regardless of whether it is raining in Siam. Indicative independence may be defined in terms of a conjunction of indicative conditionals A-C €3' -A+C. The picnic will be cancelled whether or not it rains iff (a) it will be cancelled if it does rain, and (6) it will be cancelled if it does not rain. In terms of the Stalnaker Principle, it is true that the picnic will be cancelled whether or not it rains iff it will be cancelled in the most similar world overall in which it does rain and it will also be cancelled in the most similar world in which it does not rain. Either i(A) or i(-A) is the actual world, so if C is true in both, then C is true. Consequently, if the picnic will be cancelled whether or not it rains, then the picnic will be cancelled. Subjunctive Independence is expressed by sentences in the subjunctive mood like: Germany would have lost the war whether or not it had conquered Switzerland; I would have won the game independent of whether you had worn your rabbit's foot; the patient would have died regardless of whether or not they had operated. Subjunctive independence may be defined as a conjunction of subjunctive conditionals: A > C €3' -A > C. It is true that Germany would have lost the war whether or not it had conquered Switzerland, for (i) Germany would have lost the war if it should have conquered Switzerland, and (ii) Germany would have lost the war if it should not have conquered Switzerland. In terms of the Stalnaker Principle, (i) in the most similar possible

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world prior to the envisaged time of conquest in which Germany took Switzerland, Germany lost the war, and (ii) in the most similar world in which Germany did not take Switzerland, namely the actual world, Germany also lost the war. Subjunctive independence is not in general equivalent to indicative independence. Consider the Oswald case again. It is not true that Kennedy would have been killed whether or not he had been killed by Oswald. But it is true that Kennedy was killed whether or not he was killed by Oswald. The difference between indicative and subjunctive independence in this case is explained by the different similarity conditions on indicative and subjunctive conditionals. Also consider backward looking cases. Kennedy was killed in 1963 whether or not the wheat harvest was good in 1964. But "Kennedy would have been killed in 1963 whether or not the wheat harvest had been good in 1964" is incorrect, violating the antecedence condition. Georgetown University REFERENCES Adams, E., "The Logic of Conditionals," Inq., 8, 1965, 166-197. "Subjunctive and Indicative Conditionals," Foundatzons of Language, 6, 1970, pp. 89-94. Ayers, M. R., "Counterfactual and Subjunctive Conditionals," Mznd, 74, 1965, 347-64. Barker, J. A,, "Relevance Logic, Classical Logic, and Disjunctive Syllogism," Phzl. Stud., 27, 361-76, 1975. Bennett, J., "Counterfactuals and Possible Worlds," Can. J.Phil., 4, 381-402, 1974. Chisholm, R. M., "The Contrary-to-Fact Conditional," Mind, 55, 1946, 289-307; amended in H. Feigl and W. Sellars, eds., Readzngs in Phzlosophzcal Analysis, N.Y., 1949, 482-97. Clark, M., "Ifs and Hooks: a Rejoinder," Analysis, 34, 1974, 77-83.

Creary, L., & Hill, C., "Review of Countefactuals," Phzl. ofScz., 1975, 341-44.

Downing, P., "Subjunctive Conditionals, Time Order, and Causation,"

PAS, 1958-9, 59, 125-140. , "Are Causal Laws Purely General?" PASS, 44, 1970, 37-49. Dummett, M., "Truth," PAS, 1958-9, 59; reprinted in G. Pitcher, ed., Truth, Prentice-Hall, 1964, 93-1 11. Edwards, J . S., "A Confusion about 2f-then7Analysis, 34.3, 1974, 84-90. Fine, K., "Critical Notice of Countefactuals," Mznd, 84, 1975, 451-458. Harrison, J.,"Unfulfilled Conditionals, and the Truth of Their Constituents," Mind, 1968. Jeffrey, R. C., "On Indeterminate Conditionals," Phil. Stud., 14, 1963, 37-43.

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W A YiVE A. DA VIS Kim, J., "Explanation in Science," in P. Edwards, ed., Encyclopedza ofphilosophy, 1967, V.111, 159-163. Lewis, D., Counterfactuals, Harvard, 1973. Lewis, D., "Probabilities of Conditionals and Conditional Probabilities," Phil. Rev., 85, 1976, 297-315. Mackie, J. L., "Conditionals," in Truth, Probability, and Paradox, Oxford, 1973, 64-1 19. Mayo, B., "Conditional Statements," Phil. Reo., 1957, 291-303. Pollock, J. L., "Four Kinds of Conditionals," APQ, 12, 1975, pp. 51-59. Schlossberger, k., "Similarity and Counterfactuals," Analysis, 38, 1978, 80-2. Slote, M. A,, "Time in Counterfactuals," Phil. Reo., 87, 1978, 3-27. Stalnaker, R., "A Theory of Conditionals," in Rescher, ed., Studies in Logical Theory, 1968, 98-1 12 (APQ Monographs, 2). Walters, R. S., "Contrary-to-Fact Conditional," In P. Edwards, ed., Encyc. Phil., 1967. Wright, G. H. von, Logical Studies, London, 1957, 127-165. Young, J . J., "Ifs and Hooks: a Defense of the Orthodox View," Analysis, 33, 1972, 56-63.

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