Classifying Conditionals: The Traditional Way is Right Jonathan Bennett Mind, New Series, Vol. 104, No. 414. (Apr., 1995), pp. 331-354. Stable URL: http://links.jstor.org/sici?sici=0026-4423%28199504%292%3A104%3A414%3C331%3ACCTTWI%3E2.0.CO%3B2-%23 Mind is currently published by Oxford University Press.
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Classifying Conditionals:
The Traditional Way is Right
JONATHAN BENNETT
1. Introduction Despite much dispute about how conditionals of different sorts should be analysed, few have denied that there are two basic sorts, and for years we agreed about where the line falls between them. Over the past fifteen years or so, however, the traditional placing of the line has come under challenge. Consider these three: Didn't-did: If Booth didn't kill Lincoln, then someone else did, considered as said by us because we think that someone killed Lincoln; Doesn't-will: If Booth doesn't kill Lincoln, then someone else will, as said before the assassination by someone who thinks that reliable arrangements have been made for a stand-by killer; Hadn't-would: If Booth hadn't killed Lincoln, someone else would have, as said now by someone who thinks that such arrangements had been made. Parties to the dispute about classification have agreed that Didn'tdid is of a different basic type from Hadn't-would. I shall say that Didn'tdid is a "straight" conditional and Hadn't-would a "corner" one. The former are often expressed with a straight arrow (A + C), and the latter with a corner symbol (A > C). Occasionally using those devices, I shall reserve the neutral form Con(A, C) to stand for conditionals that do not uncontroversially belong to either type. The dispute concerned Doesn't-will. It does not have a "were" or a "would"; nobody wants to call it "subjunctive" or "counterfactual"; and for many years it rested comfortably in the straight category. There were flickers of trouble with that classification in remarks by Timothy Smiley, Brian Ellis and Allan Gibbard, suggesting that perhaps Doesn't-will belongs in the corner category; the flickers became outright flames when V. H. Dudman (198 1, 1983, 1984) argued hard for that relocation of Doesn't-will; and a paper of mine-insolently titled "Farewell to the Mind, Vol. 104.414. April 1995
0Oxford University Press 1995
332 Jonathan Bennett
Phlogiston Theory of Conditionals" (1988)-poured gasoline onto the fire.' I defended something like Dudman's relocation of the line between the two types of conditional without invoking his particular views about how each type should be analysed-views which are not widely shared. In my case for Dudman's conclusion I relied on the majority view that straight conditionals are a matter of subjective conditional probabilities, and corner ones a matter of relations between sets of possible worlds or states of affairs. If you see the two types in that way, I argued, you should classify conditionals not in the traditional way but in Dudman's; or in something close to it: I dissented from his precise placing of the line, but that was minor in comparison with our agreement that Doesn't-will is corner rather than straight. That view seems now to be gaining acceptance. In this paper I shall try to stop the fire from spreading. The reasons I gave for re-classifying Doesn't-will do not work, I shall show; and when we properly understand their failure we shall see that Doesn't-will should be left where it was, which means that the old placing of the line through conditionals was right all along. I say nothing about Dudman's reasons for relocating the line: they are tied to his views about the analysis of the two types, and may be untouched by the arguments that have moved me first one way and then the other. Although the pristine classification of conditionals was correct, it has been worthwhile to explore the case against it. As I hope this paper will show, things can be learned from observantly treading this circular path. First, a word about my chosen examples. Like some others I shall mention, they have two accidental features which must not be thought of as essential. (a) They all have the form PersonISomeone-else, so Didn't-did could be based purely on the belief that someone killed Lincoln. There is no need for this, however. I developed my latest results through examples about the dousing of a camp fire, with "Andrew didn't" in the antecedent and "Charles did" in the consequent. None of these could have been based on the mere premise that someone doused the fire. (b) The examples all concern the behaviour of people. Although people are more fun to conditionalize about than most other things, nothing in what follows will depend on that. Here is a trio that would serve all my purposes and that have neither of those features. (i) We observe an acre of flattened trees that have been dead for about twenty years. The present state of the trees convinces us that this was the scene of a blow-down, failing which an avalanche; so we agree that "If wind didn't flatten these trees, snow did". (ii) Twenty years ago someone was in the presence of those trees, still standing; he knew I
Dudman (1989) responded.
Classifying Conditionals: The Traditional Way is Right 333
that they were threatened by wind, and was pretty sure that there was an avalanche coming which would flatten the trees if they were still standing when it arrived. He said: "If wind doesn't flatten these trees, snow will". (iii) At the present time someone surveys the trees while knowing what the person in scenario (ii) knew, and knowing also that the wind got there first. This person can say "If the wind hadn't flattened these trees, snow would have". All the issues to be discussed here could be handled through that trio instead of the BoothiLincoln one.
2. The objectivity point Of all the reasons that led some of us to classify Doesn't-will with Hadn't-would as a corner conditional rather than with Didn't-Did as a straight one, the most powerful cluster are really aspects of something unitary which I call the objectivity point. (a) Plenty of clear-headed people accept Didn't-did and reject Hadn'twould. (With other examples the difference would be even more apparent. Those of us who are confident that Shakespeare wrote "Hamlet" are even more sure that if he didn't then someone else did; but we would have to be crazy to accept that if he hadn't then someone else would have.) On the other hand, Doesn't-will stands or falls with Hadn'twould. The only thing that can make it true now that if Booth hadn't someone else would have is the existence back then of certain reliable causal structures; but the existence of those would have made it true to say, back then, "If Booth doesn't kill Lincoln someone else will". The converse also clearly holds: If Doesn't-will was true back then, Hadn'twould is true now. Thus, when we classify conditionals on the basis of whether they could differ in truth value or acceptability, Didn't-did seems to belong in one class while Doesn't-will and Hadn't-would belong together in the other. (b) Someone who asserts Didn't-did is guided by a connection in his belief system between "Booth didn't" and "Someone else did". The various bits of evidence that he has are connected up in such a way that he is disposed, on coming to believe that Booth didn't, to believe that someone else did; his frame of mind does not include anything about an objective connection between states of affairs (possible worlds), such that Booth's not killing Lincoln would lead to someone else's doing the job. The evidence that he goes by is objective enough, but the only connection that he has to deal with is the one between a couple of potential beliefs. In con-
334 Jonathan Bennett
trast with that, the asserter of either Doesn't-will or Hadn't-would believes in an objective connection between states of affairs. (c) These days philosophers agree that we should understand straight conditionals such as Didn't-did in terms of conditional subjective probabilities, and comer ones such as Hadn't-would in terms of something like the possible-worlds semantics of Stalnaker and Lewis. It now seems clear that the possible-worlds approach fits Doesn't-will: at the closest worlds at which Booth doesn't kill Lincoln, someone else does. That fits Hadn'twould also, and it is plainly wrong for Didn't-did. Those three arguments add up to the objectivity point about our three initial conditionals-namely, the point that Doesn't-will and Hadn'twould are objectively connecting in a certain way in which Didn't-did is not. It is the heart of the case for relocating Doesn't-will; there is more, but I want to discuss this thoroughly before dealing with the remainder in 557-9 and 11.
3. A discovery The treatment of the objectivity point in my "Phlogiston" paper was gravely defective. A pair of obvious but neglected facts brings it down in ruins. (i) First, the objectivity point fails for some occurrences of Doesn'twill, such as the following. An eavesdropper on the fringes of the conspiracy hears someone being ordered to kill Lincoln; he thinks it was Booth, but he isn't sure; he is sure that whoever gets the order will carry it out. He then accepts Doesn't-will: "If Booth doesn't kill Lincoln, someone else will", and his basis for this gives him only a subjective and not an objective connection between antecedent and consequent. His epistemic state disposes him, upon coming to think that Booth does not kill Lincoln, to think that someone else does. Those two propositions happen to be linked thus in his belief system; he is not guided by any thought of an objective link between Booth's not killing Lincoln and someone else's killing him. So this instance of Doesn't-will fits my account of straight conditionals. Jackson (1990, p. 145f) has called attention to such cases, but it seems that nobody has attended to them p r ~ p e r l y . ~ (ii) Second, the objectivity point applies to some cases of Didn't-did, such as the following. Arrangements were made for someone else to kill Jackson speaks of the subjectively based acceptance of Doesn't-will as an "exception" to a "norm"; if my arguments in this paper are right, that concedes too much to his opponents.
Classifying Conditionals: The Traditional Way is Right 335
Lincoln in the event of Booth's failing. These arrangements are known to-and trusted by-one of the conspirators. An hour after the time fixed for the assassination, he has heard no word of the outcome, but he is confident of something he can naturally express in the words of Didn't-did: "If Booth didn't kill Lincoln, then someone else did". He bases this on his belief in an objective connection between states of affairs; it is indeed just the belief that lies behind Hadn't-would, and also behind Doesn'twill in its objectively connecting version. So this instance of Didn't-did fits my account of corner conditionals. I stumbled on this fact about Didn't-did only recently. It now seems obvious, but apparently we all missed it down the years. It is the most important thing I have to offer in this paper. It means that my main reason in the "Phlogiston" paper for regarding Doesn't-will as a corner conditional applies equally to Didn't-did! If it was a good enough case for reclassifying the one, it was good enough for the other; but if Didn't-Did is a corner conditional then we no longer have two types of conditional. Anyway, it obviously would be wrong to plunge on in that fashion, when clearly the whole line of argument was cankered. The illusion that Doesn't-will is a corner conditional while Didn't-did is straight was produced purely by thinking of one kind of basis for one and a different kind for the other, when actually each can have either kind of basis. My case for reclassification has collapsed. (I don't know about Dudman's.)
4. The ambiguity thesis So far as I can see, only two conclusions are possible. One is that the objectivity point distinguishes between two kinds of proposition, not two kinds of sentence, and some sentences can be of either kind. (I am using "proposition" to mean, roughly, "item that can be meant by a sentence", allowing that there may be propositions that do not have truth values.) More exactly: any sentence that can express a straight conditional could instead express a corner one; but the converse does not hold, because Hadn't-would and its like can express only corner conditionals. That implies that I was wrong to argue with Dudman about what the verbal markers are of the line through conditionals. According to the ambiguity thesis there can be no such markers, because some sentences can express conditionals of either of the two main types. Dorothy Edgington has convinced me that the ambiguity thesis is wrong. (Everything in the rest of this section is essentially hers.) Accord-
336 Jonathan Bennett
ing to the thesis, the sentences Didn't-did and Doesn't-will mean one thing (express a comer conditional) when the speaker goes by a belief in an objective connection between states of affairs and they mean a different thing (express a straight conditional) when he goes merely by a connection within his own belief system. I have been unable to find good evidence for that. On the other hand, there is strong intuitive evidence against it. Suppose that a bit before the fatal time, one conspirator is sure that plans are in place for Booth to make the attempt and for someone else to take over in the event that he fails. This conspirator, Oscar, has objectively connecting grounds for accepting something which he expresses in the words Doesn't-will: If Booth doesn't kill Lincoln, then someone else will. Another conspirator, Sam, has subjectively connecting grounds for accepting something that he expresses in the very same sentence. Edgington issues this challenge: why not say simply that Doesn't-will expresses a single proposition-or means just one thing-which Oscar and Sam accept for different reasons? Suppose that Sam assertively utters the sentence for his subjectively connecting reasons, and Oscar hears him, knowing what his grounds are. What is wrong with Oscar's agreeing with Sam, and saying "You are right-if Booth doesn't, someone else will-and I have better reasons than you for thinking so"? Or suppose that Oscar has his objectively connecting reason and doesn't know Sam's reason. Sam says "I think that if Booth doesn't kill Lincoln, someone else will-don't you agree?" It would be excessively odd for Oscar to say "It depends on what you mean". All of this can be replayed with Didn't-did. Consider the case of Olive, who accepts Didn't-did: If Booth didn't kill Lincoln, someone else did on the objectively connecting ground that she thinks stand-by arrangements were made etc., and Samantha, who accepts that very same sentence on the subjectively connecting ground that she has seen Lincoln with a bullet in his heart. (What is subjective is not of course the man with a bullet in his heart, but rather the way in which this connects antecedent with consequent.) Now compare those two with Owen and Steve who agree that Lincoln has been killed. Owen accepts this because he believes that people planned to kill Lincoln, and trusts them to have succeeded; Steve accepts it because he has seen the body. The difference between these closely resembles that between Olive and Samantha, but nobody will say that Owen means one thing by "Lincoln has been killed" while Steve means
Classifying Conditionals: The Traditional Way is Right 337
another. They simply have different reasons for the same c o n c l ~ s i o nIn .~ addition to these powerful lines of thought, Dorothy Edgington has also adduced a theoretical argument which I shall present in $6, after an introduction which some readers may need.
5. Lewis's theorem I shall say that a conditional Con(A,C) has "the Confidence Property" just in case a person's confidence in it is proportional to the probability that she accords to C on the supposition of A. Some say that a conditional that has the Confidence Property "passes the Ramsey test". That is in honor of the author of this famous footnote: If two people are arguing "If A will C?'and are both in doubt as to A, they are adding A hypothetically to their stock of knowledge and arguing on that basis about C.. . . We can say they are fixing their degrees of belief in C given A. (Ramsey 1929, p. 143) I prefer to use a name which can remind us of what the property is. Didn't-did has the Confidence Property: someone who accepts it must, ceteris paribus, be disposed, upon becoming satisfied that Booth didn't, to believe that someone else did; and it seems clear that this is a proportional matter, meaning that if she is extremely (very, fairly, slightly) confident of Didn't-did, she should be disposed to be extremely (very, fairly, slightly) sure that someone else did upon becoming convinced that Booth didn't. Nobody, I think, denies that all straight conditionals have the Confidence Property. David Lewis (1976) has proved that the Confidence Property cannot be possessed by any conditional that meets certain fairly modest constraints. According to Lewis's theorem, -
-
It cannot be that the probability of a conditional is always equal to the conditional probability of the consequent given the antecedent (Lewis 1976, p. 84), unless there are conditionals which do not satisfy the constraints that are required by Lewis's proof. Given the powerful intuitive evidence that all straight conditionals do satisfy that equality, i.e. do have the Confidence Property, we need some way of showing that they do not satisfy the constraints that would put them within the scope of Lewis's theorem. There
' The difference between Owen and Steve does not involve objectivelsubjective. That distinction enters our story only in saying how the antecedent of a conditional is linked with its consequent; and Owen and Steve are not asserting any conditional.
338 Jonathan Bennett
are two viable theories about the nature and meaning of straight conditionals, and each has a way of keeping Lewis at arm's length. The two theories are more alike that they seem on the surface, and their ways of evading Lewis's theorem are similar. Still, I shall present them separately. (a) According to Ernest Adams (1975), straight conditionals do not have truth values. They are devices for letting people know facts about one's conditional probabilities, which are one's dispositions to acquire certain beliefs under certain circumstances, but they are not assertions about those probabilities. This theory does allow for a straight conditional to be accepted with more or less strength of conviction, and such degrees of conviction might as well be called subjective probabilities. For Adams, then, the probability of a conditional for a given person is that person's conditional probability for the consequent given the antecedent. Rather than saying that the two are equivalent, Adams says that "they" are one: the only account he has of confidence in (A + C) is that it is confidence in C given A. That makes the Confidence Property essential to straight conditionals, which looks like a head-on collision with Lewis's theorem. It cannot be avoided simply by saying that straight conditionals lack truth values: the thesis that they do have truth values plays no part in Lewis's proof (1991, pp. 84f). However, the proof does assume that the conditionals of which it treats can be freely nested in larger propositional compounds; this would be safe if they were truth-valued propositions, but otherwise it is questionable. In particular, Lewis's proof involves assigning a probability to the conjunction (Con(A, C) & P) where P is some truth-valued proposition. If Con(A, C) itself has a truth-value, we can routinely build it into conjunctions, and calculate the probability of the conjunction from the probabilities of its conjuncts plus some other data. But if Adams is right about (A -+ C), then we are not handed the conjunction ( ( A+ C) & P) on a plate. We have to work for it, constructing a sense for it. Adams does that, as also for some other compounds containing straight conditionals; but his way of doing this does not provide a sense for Prob((A + C) & P). In the context of Adams's theory, the probability of (A + C) is one kind of thing, the probability of P is another, and no algorithm could unite them into a probability for the conjunction. So the class of conditionals for which Lewis's theorem holds excludes straight conditionals, if Adams is right about the latter. (b) According to Frank Jackson (1987, pp. 17-42), the truth conditions of (A + C) are those of the material conditional (A 2 C). The truth that Booth killed Lincoln therefore suffices to make it true that if Booth didn't kill Lincoln then the South won the civil war, and that if Grant was a heavy drinker then Booth killed Lincoln. Straight conditionals differ from material ones in having a strenuous "assertibility" condition which the lat-
Classifying Conditionals: The Traditional Way is Right 339
ter lack. Although it is true that if Booth didn't kill Lincoln then the South won the war, it is improper to say this unless one is disposed upon coming to believe that Booth didn't kill Lincoln to infer that the south won the war. So one ought not to assert (A --+ C) purely on the grounds that one disbelieves A or purely on the grounds that one believes C. That might seem to provide a defence against Lewis's theorem. The probability of truth of (A + C), on Jackson's account of the latter, is the probability of (A 2 C); and that is nothing remotely like the probability of C given A. For you and me "There will be no sunlight on earth tomorrow 3 Human life will go on as usual tomorrow" has a probability of nearly 1 because of our confidence that the antecedent is false; but our conditional probability for the consequent given the antecedent is tiny. However, Jackson's view that the assertibility for me of (A + C) is proportional to my probability for C given A does endow straight conditionals with a kind of Confidence Property. It concerns assertibility rather than probability, but that may not be enough to keep Lewis's theorem at bay. Lewis's proof depends not on the use of the word "probability" but on the formal properties that it takes probability to have. If Jacksonian assertibility also has them, Jackson's theory of straight conditionals is in trouble. However, a formal point about assertibility rescues it: Jackson contends, for good reasons, that his theory about what makes a straight conditional assertible applies to such conditionals only when they are not embedded in larger compounds. Because they have truth values, they can occur in any larger compound; but they do not cany (their version of) the Confidence Property into those occurrences, so Lewis's proof does not go through for them.
6. Troublefrom Lewis Lewis's theorem, then, does not threaten either Adams or Jackson, but it condemns outright the ambiguity thesis of 54 above. The claim was that Doesn't-will has two readings, one as a straight and the other as a corner conditional; and it cannot be denied that it has the Confidence Property on each reading. The person who accepts "If Booth doesn't, someone else will" because of his trust in certain causal structures is still committed to inferring that someone else will upon coming to believe that Booth won't; and this seems clearly to be a proportional matter: the greater the confidence in the conditional, the greater the conditional confidence. But if what this person accepts is a corner conditional, and thus a fully-fledged truth-valued proposition, it must be freely embeddable in larger structures
340 Jonathan Bennett
(which blocks Adams's escape), and it should carry the Confidence Property with it into those structures (which blocks Jackson's). It cannot be kept out of the scope of Lewis's theorem. So we should conclude that the probability of this conditional cannot be proportional to the probability of the consequent given the antecedent. That means that this conditional does not have the Confidence Property. But it plainly does have it! Something has to give; and the only candidate is the thesis that Doesn't-will can express a corner conditional. This is further evidence that Didn't-did and Doesn't-will are not ambiguous. The case against the ambiguity thesis is overwhelming. Each of those conditionals, we should contend, is unambiguously a straight conditional which someone might accept for reasons which would also support a corner conditional. Then we can tell either Adams's or Jackson's story about how they should be analysed, and either way they will lie outside the scope of Lewis's theorem. In saying that each of those conditionals is straight, I espouse the traditional classification which I dismissed as "the phlogiston theory of conditionals". I apologize for that phrase; when being as rude as that, one should at least be right. Straight conditionals differ from corner ones in ways that I have not yet mentioned. In the remainder of this paper I shall discuss them, explaining how they bear on the case for reclassifying Doesn't-will and the failure of that case.
7. The Opt-out Property If Con(A, C) has the Confidence Property, then someone who is sure of Con(A, C) and becomes sure of A ought, ceteris paribus, to infer C. That is clearly right for straight conditionals, but dramatically wrong for conditionals of the "had-would" hnd. To see this, take one whose antecedent you know for sure to be false. Here is one of mine. In 1970 I went to the University of British Columbia, where I worked for nine years; I am sure that if I had not gone to UBC I would have left Canada. However, I am not even slightly disposed to infer, upon learning that I did not go to UBC, that I left Canada. On the contrary, if "I did not go to UBC" is added to my belief system with its multitude of seeming memories of life there, the resulting system implies that I have gone mad and cannot tell what I did in 1970. Try it out with a comparable example of your own. Or think of Hadn't-would as accepted by someone who saw Booth kill Lincoln.
Classifying Conditionals: The Traditional Way is Right 341
I shall express this by saying that Hadn't-would has "the Opt-out Property". It can properly be accepted by someone who would, if he became sure of its antecedent's truth, simply drop it, opt out, say that his conditional had presupposed something false and was therefore inoperative. It is as though his conditional had meant "The non-actual world which is the closest A-world is a C-world" on a Strawsonian rather than a Russellian understanding of "the non-actual world which is the closest A-world". Compare "The present king of France is wise" as said at a time when France has no king. I say that it is as though that's what his conditional had meant, not that the conditional actually has that meaning. On the contrary, as has often been pointed out, conditionals like Hadn't-would are sometimes asserted by a speaker whose point is to establish the truth of the antecedent. "Why do you think he is hostile to you?" "Well, you'll agree that if he had been hostile to me, he would have behaved towards me with conspicuously formal courtesy. Right? Well, that's just how he did behave; and that's my evidence for his hostility." So someone who accepts a conditional having the Opt-out Property may well believe its antecedent; I am not denying that. I say merely that a conditional which has the Property can be comfortably accepted by someone who is entirely confident that the antecedent is false; that is an aspect of the meaning of such a conditional. No conditional can have both the Confidence Property and the Opt-out Property. If Con(A,C) has the Confidence Property, it commits its supporter, in the event that he becomes sure of A's truth, to being as sure of C as he is of the whole conditional. The Opt-out Property blocks that very committal. It is easy to see that a conditional might have neither property: the two are contraries, not contradictories. This contrast between Didn't-did and Hadn't-would favours the traditional way of classifying conditionals, because clearly Doesn't-will is like Didn't-did in having the Confidence Property and lacking the Optout Property. This is too obvious to need arguing. Frank Jackson alerted me to this contrast by observing that although someone who accepts Hadn't-would can sensibly say "If Booth hadn't killed Lincoln things would have worked out differently from how they actually did", it would always be absurd to say "If Booth doesn't kill Lincoln, things will work out differently from how they actually will" or "If Booth didn't kill Lincoln, then things worked out differently from how they actually did". This difference between what some of us have thought to be two corner conditionals can be presented like this. Interpreted as a corner conditional (and skipping the future tense), Doesn't-will means:
342 Jonathan Bennett
At the closest world where Booth does not kill Lincoln, someone else kills him. Doesn't-will (construed as a corner conditional) asserts this just as it stands, implying that it holds even if the closest Booth-kills-Lincoln world is the actual world. That is entailed by the fact that this conditional has the Confidence Property. On the other hand, Hadn't-would (skipping the past tense) means something like this: At the closest non-actual world where Booth does not kill Lincoln, someone else kills him, with a presupposition that at the actual world Booth kills Lincoln. Hadn't-would does not say that Booth actually kills Lincoln; indeed it does not address the possibility that Booth does so; and a fortiori it says nothing about who if anyone actually kills Lincoln if Booth does not. It leaves the door open for its supporter to drop out if he learns that in fact Booth does not kill Lincoln. That way of putting the matter shows how the term "counterfactual" might come into play here. Hadn't-would addresses a range of possibilities at each of which the antecedent is false. Hadn't-would does not assert the falsity or counterfactual status of the antecedent, but presupposes it; the antecedent's falsity frames the picture which Hadn't-would sets before us. Neither Didn't-did nor Doesn't-will is "counterfactual" in that sense. The mere label does not matter much, but the crack in the rock which gives it a finger-hold matters greatly. We have here a solid similarity between Didn't-did and Doesn't-will as against Hadn't-would; which is a further point in favour of the traditional placing of the line through conditional^.^ Back when I was entertaining the idea that Didn't-did and Doesn'twill are ambiguous, I concluded that corner conditionals divide into two groups, those that have the Opt-out Property and those that lack it; and that this division appears on the verbal surface, so that it corresponds to a line between two sorts of sentence. That amounted to throwing a bone to the traditional classification of conditionals: "You are right that a significant line separates Hadn't-would from the other two, namely the line between conditionals which do and ones which don't have the Opt-out I cannot rescue the other traditional label, namely "subjunctive". No grammatical source that I can find supports the claim that the verbs in Hadn't-would are in the subjunctive mood. I conjecture that they are not, and in particular that this use of "would" is related somehow to the use of the word to refer to past futures. (Compare the French conditional tense, in which "would have" is handled by "aurait"-a past ending on a future root.) All that matters, anyway, is whether "subjunctive" can be defended in a way that illuminates the syntax or the semantics of the conditionals in question; and nobody has even tried to get such light from that source.
Classifying Conditionals: The Traditional Way is Right 343
Property". But it was a small bone, I thought, because that line seemed minor compared with the one between two sorts of conditional proposition: straight conditionals and corner ones. That was all wrong, I now see: all corner conditionals have the Opt-out Property. That fact, however, implies something which my discussion has veiled. Let us strip it bare.
8. Sam and Pure-Oscar We must return briefly to the case of Sam, who has subjectively connecting grounds for accepting: Doesn't-will: If Booth doesn't kill Lincoln, then someone else will. Oscar accepts it for objectively connecting reasons, but the difference in grounds does not infect the singleness of meaning of the sentence. However, because the two men's grounds for accepting Doesn't-will are different, their frames of mind are different. Can we make this difference apparent by getting them to assert different conditionals? There is no conditional Sam can assert that Oscar would reject; but Oscar accepts one that Sam would reject. One or perhaps two: Weren't-would: If Booth were not to kill Lincoln, someone else
would do so.
Hadn't-would (future): If it hadn't been the case that Booth will
kill Lincoln, it would have been the case that someone else will.
The status of the former of these is perhaps shaky. The different things it could mean are clear enough, as are their semantic and logical properties; but it would be rash to be confident about how the natives will actually hear that sentence. I take it as equivalent to Hadn't-would (future), which I understand as a future-tense version of our original Hadn't-would. (Don't confuse Hadn't-would (future) with something meaning "If it had not been the case that Booth is now on a path to kill Lincoln, it would have been the case that someone else is now on a path to kill him". Keeping these apart is an aspect of the general problem of distinguishing "P will obtain" from "The world is now in a state which will lead to P's obtaining".) Now let us pair Sam with Pure-Oscar. Pure-Oscar accepts Hadn'twould (future) and Weren't-would on my understanding of it; but his confidence that Booth will kill Lincoln goes so deep and so permeates his belief system that he has no idea of what he should conclude if he turned out to be wrong about that. His attitude is: "If I am wrong about Booth's
344 Jonathan Bennett
actually killing Lincoln, what I have just said is undercut; it is neither true nor false; and I don't know what to say instead of it." His acceptance of Weren't-would and its mate is a belief about what happens at the closest worlds where Booth does not kill Lincoln, framed by the assumption that the actual world is not among them. Pure-Oscar can take this attitude because the conditional that he accepts, namely Hadn't-would (future), has the Opt-out Property. His accepting a conditional with that property does not oblige him to take the attitude I have described, but it permits him to. He differs from Oscar only in availing himself of this permission or freedom, whereas Oscar declines it and instead accepts Doesn't-will. (If you find something strained about the idea that Pure-Oscar's confidence that Booth will kill Lincoln is so strong and pervasive as to motivate the Opt-out move, that is an accident of the example. Beliefs about the future tend to be like that, especially ones about human conduct: the dominance in my present scheme of things of "I have lived in Canada" could not be matched by "I shall again live in Canada", even though I am sure that I shall. That is a mere distraction, however, and we can filter it out by taking strong, pervasive predictions, for example from the secure parts of physics. As I write this, the comet Shoemaker-Levy 9 is close to Jupiter and on a collision course with it. There are now plenty of true corner conditionals of the form (i) "If Shoemaker-Levy 9 were not to hit Jupiter in the next week, Jupiter's surface would be F two weeks from now", but competent astronomers would not accept (ii) "If Shoemaker-Levy 9 doesn't hit Jupiter in the next week, Jupiter's surface will be F two weeks from now". If they were alert, they would now say "If that comet doesn't hit that planet in the next week, something must be so wrong in my understanding of the situation that I don't know what to think".) Now we have a fresh, clean contrast: Sam accepts Doesn't-will but not Weren't-would; Pure-Oscar accepts Weren't-would but not Doesn'twill. What blocks Pure-Oscar from accepting Doesn't-will is not his acceptance of Weren't-would; those two are compatible, and Oscar indeed accepts both. But Pure-Oscar's overall epistemic state, which leads him to accept Weren't-would, also blocks him from accepting Doesn't-will. Now we can see something which I think has not been previously noticed. Early in $2 above, arguing for a corner conditional status for Doesn't-will, I followed others in writing: Doesn't-will stands or falls with Hadn't-would. (a) The only thing that can make it true now that if Booth hadn't someone else would have is the existence back then of certain reliable causal structures; but the existence of those would have made it true to say, back then, "If Booth doesn't kill Lincoln someone else will".
Classifying Conditionals: The Traditional Way is Right 345
(b) The converse also clearly holds: If Doesn't-will was true back then, Hadn't-would is true now. Thus, when we classify conditionals on the basis of whether they could differ in truth value or acceptability, Didn't-did seems to belong in one class while Doesn't-will and Hadn't-would belong together in the other. This has become a virtual commonplace, but both halves of it are false. (a) The truth now of Hadn't-would does require that there were certain reliable structures back then, but neither the existence of those structures nor knowledge of them would automatically make it true (or acceptable, or all right) to assert Doesn't-will. Nobody should assert the latter unless she is disposed, upon coming to believe that Booth won't, to believe that someone else will. No level of knowledge of the relevant structures can guarantee that disposition, because such knowledge might be accompanied by evidence that Booth will kill Lincoln, the evidence being deep and pervasive enough to generate the Opt-out attitude to the discovery that Booth does not kill Lincoln. (b) Obviously, Doesn't-will could have been true or acceptable back then-as it was to Sam-without any thought of causal structures and thus without anything that could support Hadn'twould after the event. So far as I can discover, there is no one conditional through which Oscar can show his whole hand-that is, show that he accepts both Weren't-would or Hadn't-would (future) and Doesn't-will. If he wants to make fully clear his acceptance of both, he probably has to assert both, or to assert one and add a rider letting in the other. He could amplify Doesn'twill like this: If Booth doesn't kill Lincoln, someone else will (because arrangements are in place for a stand-by assassin). Or he could amplify Weren't-would like this: If Booth weren't to kill Lincoln (and for all I know he won't), then someone else would do it. Why cannot Oscar express his position more economically? A perfectly intelligible job waits to be performed by some conditional, but we have in English no conditional that does it. It is the job of saying that G At all the closest A-worlds, C is the case, with this so understood as to stand its ground even if the closest A-world is the actual world. That is, it is a causally based conditional which lacks the Opt-out Property: asserting it commits one, upon discovering that A obtains at the actual world, to concluding that G obtains there too. G is pretty much what we have been given to saying that any counterfactual conditional means, but we have erred: no counterfactual has that meaning. They all leave room for the opt-out manoeuvre: that is part of their meaning, although theorists often ignore it.
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Why do we not in ordinary English have conditionals which do mean what we theorists have been saying that all comer conditionals mean? The only conditionals we have which imply something about causal structures, i.e. whose meanings demand that they have an objectively connecting basis, also have the Opt-out Property. A straight conditional blocks the opting-out move, but at the price of silence about causal structures. Why does no conditional, unaided, do both jobs? One which did both jobs would lack both the Opt-out Property and the Confidence Property-the former because the job description says so, the latter because a comer conditional lies within the scope of Lewis's theorem. But that does not answer my question. As I remarked earlier, although nothing could have both properties something might have neither. I do not know why there are no conditionals of the kind in question.
9. The Zero Property I shall say that Con(A,C) has the Zero Property if it is a conditional for which nobody could have any serious use while giving A a probability of 0. Most of us agree that straight conditionals have this. There is a technical reason for this, which relies on the idea that Prob(A -+ C) is measured by Prob(C, given A), which is understood to be equivalent to For someone for whom Prob(A) = 0, this division sum has no answer, which means that the notion of Prob(A -+ C) has no meaning for such a person. (All of this holds also for Jackson's theory of straight conditionals, with "probability" replaced by "assertibility" throughout.) That argument succeeds within its limits, but it could not be our whole reason for crediting straight conditionals with having the Zero Property. If this were not independently plausible, we should do well to undercut the technical argument by dropping that account of conditional probability. However, there are good independent reasons to accept the conclusion of the technical argument. One is general: straight conditionals are devices for intellectually managing states of partial information, and for preparing oneself for the advent of beliefs which one does not at present have. There is no reason for it to be fitted to cope with the acquiring of a belief which one thinks one has no chance of acquiring. That would be like having a corkscrew that could burrow down to the end of a foot-long cork.
Classifying Conditionals: The Traditional Way is Right 347
Our intuitive sense of specific examples bears this out. Two scholars have a difference of opinion about a certain text: one holds that if Eusebius didn't write it, it is a medieval forgery; the other thinks that if Eusebius didn't write it, Lactantius did. Something like this might be a perfectly sober topic of contention; but if proof positive turns up that Eusebius did write the text, the question dies; nothing remains to be discussed; nobody has any use for either conditional. Of course the disputants could still disagree about which of their attitudes to the conditional had been the more reasonable (e.g. is the text more like a medieval forgery than like Lactantius' work?), but for them the conditional itself has died. Corner conditionals do not have the Zero Property. No conditional that has the Opt-out Property could also have the Zero Property: the former implies that the conditional can-to put it mildly-flourish in the presence of utter disbelief in its antecedent, which is the exact opposite of the Zero Property. Still, corner conditionals do have something that might remind one of the Zero Property. Just as (A + C) is useless to someone who knows that A is false, so (A > C) is useless if A is causally impossible, that is, false at all the relevant worlds. Let us call this the Superzero Property of corner conditionals. The two properties differ as falsehood does from impossibility, and as knowledge does from fact; one concerns what someone knows about the actual world, the other what is the case at all the worlds. They differ also in a deeper way. If someone gives his attention to (A > C) only to learn that A is causally impossible, he thereby discovers that he has been wasting his time, that his conditional was based on a mistake. We believe and hope that most of our dealings with corner conditionals are not like this; if God silently preserved us from ever taking seriously a corner conditional with an impossible antecedent, our linguistic and intellectual life would not run very differently from how it actually does-or so we hope. In contrast with that, a great deal of the daily life of straight conditionals involves ones whose antecedents are false. The Zero Property kicks in when the person discovers for sure that the antecedent is false; the conditional is then no longer any use to him; but before he knew of its falsity he was not living in a fool's paradise, thinking he had something serious to deal with when really it was all shadow play. When I say that if A is impossible then (A > C) is useless, I am talking about how corner conditionals figure in our lives. One might for theoretical convenience classify all such conditionals as vacuously true, or instead as necessarily false; and this might matter for logical or other theoretical reasons. That choice, however, cannot affect the reality that the
348 Jonathan Bennett
purposes for which we have comer conditionals are not met by any conditional whose antecedent is causally imp~ssible.~ I have seen a challenge to the thesis that all straight conditionals have the Zero Property on the grounds that I may believe and care about "If I touch that stove, I will be horribly burned" at a time when I am utterly confident that I shall not touch that stove (Blackburn 1986,p. 222). In my Phlogiston paper I offered this as further evidence that this conditional-like Doesn't-will and all of its kind-is really a corner rather than a straight conditional. For someone already convinced that the line between conditionals should be shifted, this little argument confirms the result in a way that is so neat and convenient as to be almost irresistible. It should be resisted, however. I contend now that the straight conditional about the stove does have the Zero Property, though the corresponding corner conditional-"If I were to touch that stove, I would be horribly burned"-does not. The Zero Property also bears on something else which I mis-handled in my Phlogiston paper. I reported there on Jackson's good criticisms of Grice's theory about the meanings of straight conditionals. Most of them accuse Grice's theory of constraining such conditionals too weakly, failing to condemn some which are clearly unacceptable. One criticism, however, goes the other way, contending that Grice's constraints are also too strong, because they condemn some conditionals which are perfectly all right, for example: "If the sun goes out of existence in ten minutes' time, the earth will be plunged into darkness in about eighteen minutes time". If that conditional is all right, then Grice's analysis is in trouble-no doubt about that-but so also is the thesis that all straight conditionals have the Zero Property. In presenting this point, Jackson did not comment on that aspect of it, or on the striking contrast between this and his other charges against Grice's analysis. In my Phlogiston paper, of course, I took this as further evidence that the conditional about the sun is of the corner and not the straight type. I now believe that the "sun" conditional is not acceptable for anyone who knows for sure that the sun won't go out of existence in ten minutes' time, and that it seems so only because people mix it up with the corner conditional "If the sun were to go out of existence in ten minutes' time, the earth would be plunged into darkness in about eighteen minutes time". Apparent counterexamplesto this are discussed in Bennett (1984, pp. 57-91).
Classibing Conditionals: The Traditional Way is Right 349
10. Speaker's meaning and sentence meaning If that alleged mix-up is fairly widespread, that looks like evidence that it is not a mix-up after all. People are generally prone to find the straight "sun" conditional acceptable; and my views force me to suppose that what they are accepting, really, is not that conditional but its corner cousin. How can I justify this? By what right do I assert that the many people who would be willing to say "Yes, I agree: if the sun goes out of existence in ten minutes' time, the earth will be plunged into darkness in about eighteen minutes time" would be doing so on the basis of a mistake about the meaning of what they were saying? This challenge applies also to my discussion of the conditional about the stove. Indeed it goes to the heart of my main thesis in this paper. Return for a moment to Oscar, who thinks arrangements have been made for a standby assassin, and therefore accepts Doesn't-will: "If Booth doesn't kill Lincoln, someone else will". I have been saying that this is a straight conditional which may indeed be acceptable to Oscar but which does not express any facts about his grounds for asserting it-that is, it does not imply anything about causal structures linking Booth's not killing Lincoln with someone else's killing him. For Oscar to imply anything of that kind, I have contended, he must either amplify his straight conditional or else shift from it to the corner conditional that I call Weren't-would. Yet Oscar himself might well think he had said all he needed to, and that his conditional-meant as he meant it-did imply something that I say is implied only by Weren't-would. That was my own frame of mind when I concluded that Doesn't-will and Didn't-did are ambiguous. I backed down from that in face of Dorothy Edgington's attack, but the time is now ripe for reconsidering that retreat. Was it too hasty? Does it involve too many accusations that people are wrong about the meanings of things they say? No, it does not. To show this, I need to go slowly. First, we can easily distinguish (a) what sentence S conventionally means from (b) what a given person means by S on a particular occasion. These can easily come apart, because (b) might be idiosyncratic-the upshot of error, ignorance, a momentary lapse or a personal quirk. The challenge I am now facing, however, is to justify distinguishing (a) from (c) what very many people would mean by S in certain circumstances.
350 Jonathan Bennett
The challenge might be either shallow or deep. Shallow: it is highly unlikely that very many people should mean by S something other than what it conventionally means; so a divorce of (a) from (c) is improbable. Deep: what a part of language means is determined by what people mean by it; the meaning of an expression is a logical construct out of what people mean by uttering it; so a divorce of (a) from (c) is impossible. I shall address the deep point, but my remarks will implicitly deal with the shallow one as well. It has to be agreed that what expressions mean comesfiom what people mean by them, but that does not entail that what any expression means is what people mean by it. There are routes from speakers' meanings to conventional meanings that do not yield that result. For example, there is an inner core of very basic and simple sentences which determine the conventional meanings of the words they contain, and which also settle the semantic significance of various facts about word order. Those two jointly establish conventional meanings for countless other sentences, which for ease of discussion I shall call "outer" sentences. (The line between inner and outer is not sharp.) Most outer sentences do not get their meanings from facts about what people mean by them, because they are never uttered. Even if we arbitrarily set an upper limit of 100 words on meaningful English sentences, I would guess that not one such sentence in ten million is ever uttered. The meanings of outer sentences come from the meanings of the words they contain together with the semantic significance of the way those words are put together; and each of those kinds of semantic input is determined by facts about what people mean by what they say. It can happen that a sentence-or form of sentence-is quite often uttered and given a meaning which is different from the one conferred on it by its constituent words and its syntactic form. For example, many people are prone to say "I could care less" as a way of expressing lack of interest in something. This has come, through careless listening and sloppy thought, from "I couldn't care less", meaning "I couldn't care less than I do", which expresses an attitude of indifference. The use of "I could care less" to express indifference is thought by many to be a mistake, and I agree with this. When a speaker makes that sentence carry that meaning, he is in conflict with other aspects of his own system of meanings. This could be shown by asking him, for instance, "What would it be like if you did care less?" to which his answer would probably be "Oh, but I couldn't-I've just told you so". Another example: trainee nurses in the town where I grew up used to be told "No head injury is too trivial to ignore". This was meant as a warning against the mistake of thinking that some head injury is so trivial that
Classifying Conditionals: The Traditional Way is Right 351
it can safely be left untreated. But what the sentence itself means-given the core meanings of its words and the significance of its grammatical structure-is a warning against a mistake that nobody in her right mind would ever make. "No head injury is too trivial to ignore" warns us against ever thinking "This head injury is too trivial to ignore.. .", which naturally goes with this: "...If it were less trivial-i.e. more serious-we might safely leave it untreated; but given how trivial it is we should attend to it." This balderdash would never be accepted by anyone, so we need not be warned against it; yet that is what the head injury slogan does when taken in its conventional meaning. Here again, as with the "could care less" example, someone who at first thinks that the sentence is all right can be led to see that it is not, bringing to bear nothing but that person's own semantic standards. Those two examples illustrate how the properly assigned conventional meaning of a sentence can differ from the meaning that many speakers attach to it; and there is no reason in principle why a sentence's meaning should not differ from what all speakers mean by it in everyday use. Now let us return to Oscar, who asserts Doesn't-will and means it to imply that the antecedent is objectively connected with the consequentthat is, he means by it something that might later support Hadn't-would. For purposes of argument, I'll grant that virtually all competent English speakers in Oscar's position would also be inclined to assert Doesn't-will, intending it to convey that the antecedent is objectively linked with the consequent; but that does not entail that Doesn't-will actually has such a meaning. Once that is clear, the way is open to reasons for saying that that sentence does not have that meaning-the reasons being the ones that Dorothy Edgington gave. I conclude that although Oscar gives the sentence this meaning, and although many others would cheerfully do the same, it is not a meaning that the sentence actually has. That many people think otherwise is natural and understandable, but they are wrong. If this is more than you can swallow, here is an alternative conclusion. Because the tendency to use Doesn't-will in that manner is so prevalent, we should grant that this is a meaning which that sentence form has; but it has that meaning only as an idiom, and not as an upshot of meanings of its constituent terms and the syntactic structure formed out of them. As with the "could care less" example, it does not matter which of these we select.
352 Jonathan Bennett
11. The Stand-ofS Property Allan Gibbard has convinced many of us that straight conditionals with false antecedents have what I call the Stand-off Property. A type of conditional Con(A, C) has this property if it can happen that one person accepts Con(A, C), another accepts Con(A,X), and neither is wrong. Didn't-did has the Stand-off Property. It could happen that one person accepts Didn't-did while another accepts Didn't-didn't: If Booth didn't kill Lincoln, then no one did. So long as in fact Booth did kill Lincoln, neither of those two conditionals has to be wrong. It need not be the case that as facts about the world pour in they will eventually condemn at least one of the two as improbable or false; though if that does not happen, facts will eventually establish that A is false, which will condemn both conditionals as useless (because of the Zero Property). Their having the Stand-off Property does not, therefore, mean that the two opposing conditionals could stand up against the world indefinitely. It means only that they may relate to the world in a perfectly symmetrical way: as the facts come in, the opposing pair survive equally well or badly until the moment comes when they both collapse into inutility. The thesis that straight conditionals with false antecedents have the Stand-off Property fits nicely with each of the two surviving theories about the meanings of those conditionals. In a world where A is false, evidence supporting your disposition to believe C upon coming to believe A may be perfectly matched in strength with evidence supporting my disposition to believe -4upon coming to believe A. So the Stand-off Property is present here, whether we think of evidential support etc. in terms of acceptability or subjective probability (with Adams) or of assertibility (with Jackson). Obviously, comer conditionals with false antecedents do not have the Stand-off Property. Perhaps we cannot now discover whether Hadn'twould is true or not; and according to some theories it could be that Hadn't-would and its conditional opposite "If Booth hadn't killed Lincoln, nobody would have done so" are both false. That would be because of relevant indeterminacies at the actual world in the spatio-temporal vicinity of the killing. But-returning to the Stand-off Property-there could no question of holding that neither is false. (An analogue of the Stand-off Property is possessed by corner conditionals with causally impossible antecedents. If A is false at all the relevant worlds, then it may be that the evidence for (A > C) is matched by in such a way that as the facts come in they the evidence for (A > 4)
Classifying Conditionals: The Traditional Way is Right 353
do not favour either conditional until they reach the point of showing that A is impossible and thus that both conditionals are pointless. The difference between this and the Stand-off Property mirrors that between the Superzero and Zero Properties. It is enormous, and I mention it only because I think it can lead people astray (See Edgington 1991, pp. 2060. Now, what about Doesn't-will? I believe that it has the Stand-off Property, and this is easy to see as soon as one stops muddling this straight conditional with the corner conditional Weren't-would (or Hadn't-would (future)). As between "If Booth weren't to, someone else would" and "If Booth weren't to, nobody would, the world cannot be such as to condemn neither (given that it is not outright impossible that Booth won't); but it can be such as not to condemn either "If Booth doesn't someone else will" or "If Booth doesn't nobody JONATHAN BENNETT
Department of Philosophy Syracuse University Syracuse, NY 13244 USA
REFERENCES Adams, Ernest W. 1975: The Logic of Conditionals. Dordrecht: Reidel. Bennett, Jonathan 1984: "Counterfactuals and Temporal Direction". Philosophical Review, 93, pp. 57-91. -1988: "Farewell to the Phlogiston Theory of Conditionals". Mind, 97, pp. 509-27. Blackburn, Simon 1986: "How Can We Tell Whether a Commitment Has a Truth Condition?", in Charles Travis (ed.), Meaning and Interpretation. Oxford: Blackwell, pp. 201-232. Dudman, V.H. 1981: Tense and Time in English. Macquarie University. -1983: "Tense and Time in English Verb Clusters of the Primary Pattern". Australian Journal of Linguistics, pp. 2 5 4 4 . -1984: "Parsing 'If'-Sentences". Analysis, 44, pp. 145-53. -1989: "Vive la Rkvolution!". Mind, 98, pp. 591-603. Edgington, Dorothy 1991: "Matter-of-Fact Conditionals". Proceedings of the Aristotelian Society, Supplementary Volume, 65, pp. 185-209. Jackson, Frank 1987: Conditionals. Oxford: Blackwell. -1990: "Classifying Conditionals". Analysis, 50, pp. 134-47. Dorothy Edgington has seen the present version of this paper, near enough, and disagrees with some of it. She doubts the importance-and even the existence-of the Opt-out Property, and rejects my separation of the Zero from the Superzero Property. To my regret, I have been unable to address these matters within the confines of this paper; but my intellectual debt to her is profound.
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Lewis, David 1976: "Probabilities of Conditionals and Conditional Probability". Philosophical Review, 85, pp. 297-315. Reprinted in Frank Jackson (ed.), Conditionals. Oxford: Oxford University Press, 1991, pp. 76-101. Ramsey, F.P. 1929: "Law and Causality". In F.P.Ramsey, Foundations: Essays in Philosophy, Logic, Mathematics and Economics, ed. by D.H. Mellor. London: Routledge and Kegan Paul 1978, pp. 128-15 1.
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Vive la Revolution! V. H. Dudman Mind, New Series, Vol. 98, No. 392. (Oct., 1989), pp. 591-603. Stable URL: http://links.jstor.org/sici?sici=0026-4423%28198910%292%3A98%3A392%3C591%3AVLR%3E2.0.CO%3B2-U 5
Counterfactuals and Temporal Direction Jonathan Bennett The Philosophical Review, Vol. 93, No. 1. (Jan., 1984), pp. 57-91. Stable URL: http://links.jstor.org/sici?sici=0031-8108%28198401%2993%3A1%3C57%3ACATD%3E2.0.CO%3B2-A
References Counterfactuals and Temporal Direction Jonathan Bennett The Philosophical Review, Vol. 93, No. 1. (Jan., 1984), pp. 57-91. Stable URL: http://links.jstor.org/sici?sici=0031-8108%28198401%2993%3A1%3C57%3ACATD%3E2.0.CO%3B2-A
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Farewell to the Phlogiston Theory of Conditionals Jonathan Bennett Mind, New Series, Vol. 97, No. 388. (Oct., 1988), pp. 509-527. Stable URL: http://links.jstor.org/sici?sici=0026-4423%28198810%292%3A97%3A388%3C509%3AFTTPTO%3E2.0.CO%3B2-9
Parsing 'If'-Sentences V. H. Dudman Analysis, Vol. 44, No. 4. (Oct., 1984), pp. 145-153. Stable URL: http://links.jstor.org/sici?sici=0003-2638%28198410%2944%3A4%3C145%3AP%27%3E2.0.CO%3B2-U
Vive la Revolution! V. H. Dudman Mind, New Series, Vol. 98, No. 392. (Oct., 1989), pp. 591-603. Stable URL: http://links.jstor.org/sici?sici=0026-4423%28198910%292%3A98%3A392%3C591%3AVLR%3E2.0.CO%3B2-U
Classifying Conditionals Frank Jackson Analysis, Vol. 50, No. 2. (Mar., 1990), pp. 134-147. Stable URL: http://links.jstor.org/sici?sici=0003-2638%28199003%2950%3A2%3C134%3ACC%3E2.0.CO%3B2-E
Probabilities of Conditionals and Conditional Probabilities David Lewis The Philosophical Review, Vol. 85, No. 3. (Jul., 1976), pp. 297-315. Stable URL: http://links.jstor.org/sici?sici=0031-8108%28197607%2985%3A3%3C297%3APOCACP%3E2.0.CO%3B2-T
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