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Australian Journal of Philosophy Vol. 70, No. 2; June 1992 EVENTS, COUNTERFACTUALS, AND SPEED Lawrence Brian Lombard I. Introduction Recently, Jonathan Bennett has stressed the idea that counterfactual claims about events bear important relations to claims concerning the properties that events have essentially. 1 This idea is surely correct. If, had a certain condition, C, not been met, an event, e, would have occurred anyway, then it is not essential to e that C be met. And if e has a property, F, essentially, then if e had lacked F, it would not have occurred. To illustrate this idea, Bennett presents an argument which, if sound, would show that an event could have occurred more quickly than it in fact did. Actually, there are at least two senses in which it might be said that an event could have occurred more quickly than it actually did. In one sense, to say that an event could have occurred more quickly than it in fact did is to say that it could have been the case that, though the event began to occur at the very same time at which it in fact began to occur, it ended at a time earlier than it in fact did. In this sense, an event that could have occurred more quickly than it in fact did is an event that could have occurred over a shorter period of time than it actually did. A second sense in which it might be said that an event could have occurred more quickly than it in fact did is one in which it is possible that, though an event occurs over the same stretch of time at which it in fact occurred, it occurs more frenetically. Suppose, for example, that Bennett waved his hand for a period of ten seconds, his wave being composed of several sub-waves. If that very wave of his hand could have been composed of more and, perhaps, different sub-waves, then instead of the wave's being composed of, say, three left-to-right motions and two right-to-left motions it might have been composed of six left-to-right motions and five right-to-left motions. In such a case, while Bennett's wave still took ten seconds to complete, there is a clear sense in which Bennett waved more quickly than he actually did. In his argument for the claim that an event could have occurred more quickly than it in fact did, Bennett does not distinguish between these two senses of 'more quickly'. But I think that it does not matter. Nothing in Bennett's argument for that claim hangs on the distinction. If his argument established that an event J. Bennett, 'Event Causation: The Counterfactual Analysis', J. E. Tomberlin (ed.), Philosophical Perspectives, I: Metaphysics, 1987 (Atascadero~ CA: Ridgeview Publishing Company, 1987), pp. 367-386 (hereafter referred to as ~Event Causation'). See also Bennetfs book, Events and Their Names (Indianapolis: Hackett, 1988), p. 55. 187
Lawrence Brian Lombard 188 could have occurred more quickly than it in fact did in the first of the two senses l distinguished, it would also establish that an.event could have occurred more quickly than it in fact did in the second. And my comments on Bennett's argument will apply, I believe, regardless of which sense of 'more quickly' was intended. Therefore, I shall, in what follows, be indifferent to the distinction. I shall refer indifferently to the two inessentialist theses that an event could have occurred more quickly than it in fact did as 'Quicker' and indifferently to the essentialist theses that an event could not have occurred more quickly than it in fact did as 'No-Quicker'. In this paper, I argue that Bennett's argument, as initially formulated, is invalid, and that it thus fails to be an illustration of the connection between certain counterfactuals and certain essentialist claims about events. I also show that, when siapplemented in a way that makes it valid, Bennett's argument cannot be sound, and hence, that it fails to be a demonstration of the view that an event can occur more quickly (in either sense) than it in fact does. 2 II. Bennett's Argument a Bennett's argument, Argument (Q), for Quicker occurs in the following passage: Suppose that at noon precisely I wave my fight hand, and someone makes the statement S: If that hand wave had not occurred, the auctioneer wouldn't have thought you were bidding. Now, if I had waved my right hand a fraction faster than I actually did... the auctioneer would still have thought I was bidding; so if S is to come out true, those possible waves must count as the wave I actually did. That implies that my actual wave could have been a bit faster... than it was...4 This argument for Quicker seems to have the following two premises: (1) if the hand wave that Bennett actually produced hadn't occurred, the auctioneer would not have thought that Bennett was bidding, and 2 Both versions of Quicker are largely independent of the inessentialist view that an event could have occurred earlier than it in fact did (in the sense of both beginning and ending before it in fact began). There is also, I think, a sense of 'Bennett's hand wave could have occurred more quickly than it actually did' which is inconsistent with the thesis of the essentiality of 'wholly earlier', a thesis for which I argued in my Events: A Metaphysical Study (London: Routledge, 1985), pp. 206-216. And I defend my view against the view of David Lewis's that it is inconsistent with the counterfactual analysis of event causation in 'Causes, Enablers, and the Counterfactual Analysis', Philosophical Studies, 59 (1990) pp.195-211. If it is this latter inessentialist view that Bennett's argument (Q) is directed at, then this paper is also a defence of the essentiality of 'Not Wholly Earlier'. 3 Since the argument to be discussed seems to be intended by Bennett only as an illustration of the connection between certain counterfactuals and essentialist claims about events, it is not clear whether Bennett actually endorses its anti-essentialist conclusion. Bennett, of course, must think the argument valid; otherwise he could not think it to be an illustration of what he takes it to be an illustration of. In light of this latter point, I shall refer to the argument as Bennett's. What is perhaps unclear is whether or not Bennett endorses the argument's premises. 4 'Event Causation', p. 369; the argument is repeated in Events and Their Names, p. 55.
189 Events. Counterfactuals. and Speed (2) if Bennett had (just once) waved his right hand a bit faster than he actually did, the auctioneer would still have thought that he was bidding. And the reasoning that is supposed to lead from (1) and (2) to the intended conclusion is this. (2) says that, had there occurred some right hand wave or other by Bennett that was slightly faster than his actual hand wave, the auctioneer would still have thought that Bennett was bidding. But if (2) is true, and an event cannot occur even a bit more quickly than it does, then (1) could not be true, for the occurrence of one of those possible waves would have made the auctioneer think that Bennett was bidding. So, (1) and (2) can both be true only if one or other of those possible hand waves - the ones such that, had one of them occurred it would have been slightly faster than Bennett's actual hand wave and would have made the auctioneer think that Bennett was bidding - would have been Bennett's actual hand wave. Therefore, since Bennett's actual hand wave could have been one of those faster waves, it could have occurred more quickly than it actually did. III. (Q) Needs Another Premise (Q) is invalid, for the truth of(l) and (2) is compatible with No-Quicker, the claim that an event cannot occur more quickly than it actually does. If an argument from (1) and (2) to Quicker is to be valid, another premise must be added. Here is the reason for this. A counterfactual of the form, 'If it were the case that p, then it would be the case that r', is true at, say, the actual world if and only if the closest to the actual world of all the possible worlds in which it is the case that p are also worlds in which it is the case that r. That is, all the closest p-worlds are r-worlds. ~ The possible worlds relevant to the evaluation of a counterfactual of that form are not given in advance; they are determined by its antecedent. Once the worlds in which its antecedent is true are determined (the p-worlds), one then determines, in part on the basis of some standards of world-closeness, and in part on the basis of the facts about the actual world, which of those p-worlds are 'closest' to the actual world. Let 'P' be the claim that Bennett's actual hand wave does not occur, and 'Q' the claim that Bennett (just once) waves his right hand a bit more quickly than he actually does. The worlds relevant to the evaluation of (1), then, are the P-worlds, the 'no actual hand wave' worlds, while the worlds relevant to the evaluation of (2) are the Q-worlds, the 'faster hand wave' worlds. It is obvious that there are possible worlds that are both P-worlds and Q- worlds, possible worlds in which Bennett's actual hand wave does not occur and in which Bennett (just once) waves his right hand a bit faster than he actually does. But that fact is not sufficient to generate a contradiction from (1), (2), and In Stalnaker's counterfactual logic, there is only one closest p-world; in David Lewis's, there may be more than one. In this paper, I will be assuming that something like the account of counterfactuals offered by either Lewis or Robert Stalnaker is true. Bennett appears to assume so as well; see Events and Their Names, pp. 54f.
Lawrence Brian Lombard 190 the claim that Bennett's actual hand wave could not have been a faster hand wave. (Q)'s validity requires that there be a possible world that is both a closest P-world and a closest Q-world. To see this, suppose that, contrary to (Q)'s conclusion, an event cannot occur more quickly than it actually does. And let us suppose that (1) and (2) are true. Let us also make the further supposition embodying the additional assumption just mentioned: (3) there is a possible world that is both a closest P-world and a closest Q- world. The claim that no event can occur more quickly that it in fact does, No- Quicker, implies that every closest world in which (2)'s antecedent, Q, is true is a world in which (1)'s antecedent, P, is true. And that, together with (3) (and the claim that there is at least one closest Q-world), implies that there is a world, w, that is not only a closest Q-world but is also a closest P-world. But now we have a world, w, that is a world closest to the actual world in which the antecedents of(l) and (2) are jointly true. Given the truth of(l) and (2), such a world is one in which the consequents of both (1) and (2) are also true. But that is impossible, since (1)'s consequent, in saying that the auctioneer does not think that Bennett made a bid, and (2)'s consequent, in saying that the auctioneer does think that Bennett made a bid, contradict each other. So if (1), (2), (3), and No-Quicker were true, a contradiction would be true. And (Q), supplemented by (3), concludes that it is the essentialist thesis No-Quicker that should be given up to restore consistency. (3), or something very much like it, must be assumed, 6 for (1) and (2) do not by themselves entail (Q)'s anti-essentialist conclusion. For if (3) is not true, we could have a possible world that is (i) a world closest to the actual world in which Bennett (just once) waves his right hand a bit faster than he actually does, (ii) a world in which Bennett's actual hand wave does not occur, but (iii) not a world closest to the actual world in which Bennett's actual hand wave does not occur. But, even if all that were so, we would still have no reason think that there is a world which is both a closest P-world and a closest Q-world. And if we have no reason to think that, then we have no reason to think that any of the worlds No-Quicker says there are -- worlds that are closest to the actual world in which Bennett's actual hand wave does not occur and are such that in them Bennett (just once) waves his hand more quickly than he actually does -- are worlds in which a contradiction is true. IV. Can the Premises All be True? The argument from (1), (2), and (3) to the claim that an event can occur more quickly than it does -- Argument (Q+) -- is indeed valid. And (Q+) would establish its anti-essentialist conclusion, if its premises could all be true. But it can be shown that the premises cannot all be true. 8 In 'Event Causation', p. 378, Bennett seems explicitly to assume something like (3) in order to deduce another contradiction.
191 Events, CounterfactuMs, and Speed Since (Q+) is valid, (1), (2), and (3) cannot be held consistently with No- Quicker. This, of course, is obvious. But, the defender of Quicker can take no comfort in this, tor it can also be shown that (1), (2), and (3) are not consistent with (Q+)'s anti-essentialist conclusion either! (2) says that if some hand wave or other of Bennett's had occurred and been a slightly laster hand wave than his actual hand wave, the auctioneer would still have thought that Bennett was bidding. So understood, (2) is eminently plausible. There are many actions that Bennett could have performed -- waved his left hand, pulled on his ear, nodded --all of which are standardly taken by auctioneers to express a wish to bid, and are such that had Bennett performed any of them, the auctioneer would have taken him to have made a bid. (2) is more than reasonable, and I shall hereafter regard it as true. Suppose that it is true that some closest P-world, w, is also a closest Q-world. In w, Bennett's actual hand wave does not occur. Since w is also a closest Q- world, w is a closest world in which Bennett waves his hand a bit more quickly than he actually does. But then how is one who believes that Bennett's hand wave could have been a slightly faster hand wave to justify belief in (1)? The only reason one could have for thinking that, in a closest P-world, the auctioneer does not think that Bennett made a bid is that in such a world Bennett does nothing at all to indicate a bid; in particular, he keeps his hand in his lap. If Bennett's actual hand wave could have been a slightly faster wave, then in those worlds in which the actual hand wave does not occur, none of those faster ones, with which the actual one could have been identical, occurs either. But how can that be, if there is a closest world in which he waves his hand a bit faster than he actually does that is also a closest world in which Bennett's actual hand wave does not occur? If (2) is true, then no one who accepts Quicker can accept both (1) and (3). Putting this result together with that of the previous section, it can be seen that, given the truth of (2), from (1) and (3) one can deduce not only the falsity of No- Quicker, but also the falsity of Quicker. So, if one accepts (2), which seems perfectly reasonable, one cannot accept both (1) and (3). Thus, the problem cannot be with the thesis that an event cannot occur more quickly than it in fact does. The problem~ given (2), must be with (1) and (3); they cannot both be true. And here's why. According to (3), there is a world closest to the actual world in which Bennett (just once) waves his hand a bit faster than he actually does, that is also a world closest to the actual world in which his actual hand wave does not occur. But according to (2), the closest 'faster hand wave' worlds are worlds in which the auctioneer believes that Bennett made a bid. But then no such world can be a world closest to the actual world in which Bennett's actual hand wave does not occur; for, if (1) is true, in such worlds the auctioneer does not believe that Bennett made a bid. So, anyone who accepts (2) must reject either (1) or (3). The problem with (1) and (3), given (2), is that, while (3) pulls together the closest worlds in which Bennett's actual hand wave does not occur and the closest worlds in which Bennett waves his hand a bit faster than he actually does,
Lawrence Brian Lombard 192 (1) pushes such worlds apart. Given the truth of (2), (1) and (3) cannot both be believed to be true by anybody. So, why is it thought that (Q+) is a problem for the No-Quicker? V. (Q) as an ad hominem Perhaps those who deny No-Quicker believe that (Q+) constitutes an ad hominem against that essentialist view. Perhaps they have something like the following in mind: We are prepared to agree that (1), (2), and (3) cannot be held consistently. But we Quickerites are not required by our view to accept (3), while you No- Quickerites are. Thus, you are required to accept all the propositions which together entail the falsity of your view, while we are not required to accept the propositions that entail the falsity of ours. It seems obvious that the believer in Quicker is free to reject (3). There is nothing in the view that an event can occur more quickly than it in fact does that requires the acceptance of the claim that some closest P-world is a closest Q-world. Indeed, it may be that the believer in Quicker must reject (3). Can one believe that Bennett's actual hand wave could have occurred more quickly and also believe that a world closest to the actual world in which Bennett waves his hand a bit more quickly than he actually does is a world in which his actual hand wave does not occur? Perhaps inessentialists must think that closest Q-worlds are not P- worlds at all, let alone closest P-worlds. But is one who accepts No-Quicker required to accept (3)? If so, then, given that those who deny that essentialist view are not, it would be clear that (Q+) would constitute a successful attack on that essentialist view. But, that essentialist thesis does not require the acceptance of (3). Perhaps some or all of the closest worlds in which Bennett's actual hand wave does not occur are ones in which Bennett keeps his hand in his lap; perhaps some or all such worlds are ones in which he waves a bit faster; perhaps some or all such worlds are ones in which he nods his head. None of these alternatives is entailed by the view that Bennett's actual hand wave could not have been a faster hand wave. What a world closest to the actual world in which a certain counterfactual condition is met is like is determined by the facts about the actual world and by the standards of world closeness. The essentialist thesis No-QuiCker, by itself, simply has no implications Concerning what would have to happen in a world closest to the actual world in which Bennett's actual hand wave does not occur; for it says nothing about what the actual world is like or about what the standards of world closeness are. That essentialist thesis does not entail that there is a possible world that is not only a closest P-world but also a closest Q- world. Of course, it might be suggested, on grounds independent of No-Quicker, that if Bennett's actual hand wave had not occurred, he would have waved his hand a bit faster than he actually did. Indeed, Bennett, at least in one place, indicates
193 Events, Counterfactuals. and Speed that he believes this; in Events and Their Names, he says that (Q) establishes its conclusion unless one supposes that at the closest world where I don't make that hand wave I don't wave my hand at all, whereas worlds where I wave it a little faster.., than I actually did are more remote. But no tenable standards of world closeness would let one suppose thaty So, here at least, Bennett seems to think it quite reasonable to believe (indeed, quite unreasonable not to believe) that, in worlds closest to the actual world in which his actual hand wave does not occur, he waves his hand a bit faster than he actually does. Two things should be noticed about this suggestion concerning the closeness of worlds. First, even if correct, all it amounts to is the insistence that a closest P- world is a Q-world. And that is not enough to justify (3), which says that some closest P-world is a closest Q-world. Secondly, Bennett's suggestion cannot be accepted by anyone who accepts Quicker. Any world in which Bennett's actual hand wave does not occur is a world in which nothing with which his actual hand wave could have been identical occurs. If Bennett's actual hand wave could have been a slightly quicker hand wave, then in worlds in which the actual hand wave does not occur no slightly quicker hand wave occurs; for those quicker hand waves would have been, according to this inessentialist position, Bennett's actual hand wave. The antiessentialist view and the passage from Bennett just quoted are incompatible. The anti-essentialist must maintain that the closest P-worlds are not Q-worlds at all (let alone closest Q-worlds). Regardless of the effect on the anti-essentialist's view of the idea that the closest P-worlds are Q-worlds, that idea may, after all, be correct. Still, that idea is simply not entailed by No-Quicker. Moreover, if it is a plausible suggestion, and if it leads to (3), s it is not a special problem for the essentialist's view. No one can accept (3) along with (1) and (2). The acceptance of (3), as I argued earlier, in conjunction with (2), leads, on anyone's view, directly to the rejection of (1). In any case, if encouraged to accept (3), one can give up (1). The view that an event cannot occur more quickly than it does bears no special relationship to (1). And to the extent ttiat there are reasons for accepting (3), those reasons would, together with (2), undercut whatever reason we might have for believing (1). If a world closest to the actual world in which Bennett's actual hand wave does not occur is a world closest to the actual world in which Bennett waves his hand a bit faster than he actually does, then in such a world, given (2), the auctioneer does think that Bennett made a bid. So, whatever might make (3) plausible makes (1) implausible. 9 But again, there is no reason to be found in the essentialist position No- Quicker for thinking that it is committed to (3). Events and Their Names, p. 55, fn. 7 (my emphasis). 8 Whether it does is not clear, for closest P-worlds may well be Q-worlds without being closest Q-worlds. 9 Whether (1) is so plausible that essentialists and well as inessentialists must accept it is an issue I shall be taking up in section VII.
Lawrence Brian Lombard 194 It is clear that No-Quicker entails that any possible world in which Bennett waves his hand (just once) a bit faster than he.actually does is a world in which Bennett's actual hand wave does not occur. The Q-worlds are P-worlds; and so the closest Q-worlds are P-worlds. However, (3) says more than that; it says that some closest Q-world is a closest P-world. But surely it is compatible with No- Quicker that in the closest P-worlds, Bennett keeps his hand in his lap. It is surely possible, for example, that the actual world is such that, for physiological reasons, Bennett simply could not have waved his hand any faster than he did. But if that were so, then the closest Q-worlds would not be closest P-worlds. That this is possible can hardly be thought to be inconsistent with the view that an event could not have occurred faster than it actually did. If this is right, then No- Quicker does not entail (3), Again, perhaps (3) might be made plausible on grounds independent of the essentialist's view. But even if so, one will no more be forced to give up No- Quicker than will the anti-essentialist be forced to give up Quicker. All can give up (1) instead. Unless, of course, (1) is, somehow', irresistible to right reason. VI. What's So Wonderful About (1)? Neither the defender nor the opponent of No-Quicker holds a position that entails that (1) is true. And (1) and (3) are not contradictories, but only contraries; so, even if there were good reasons for rejecting (3), that wouldn't count as a reason for thinking (1) true; (1) and (3) might both be false. And (1) surely does not have the intuitive plausibility that (2) has. Yet anyone who believes that either (Q) or (Q+) refutes No-Quicker must think either that that essentialist view is committed to (1), which it plainly is not, or that (1) can, on independent grounds, be shown to be true. 1 For if neither alternative is satisfied, then the anti-essentialist has an argument against the essentialist's view one of whose premises is one which neither disputant need accept! So, what reason might there be for thinking that (1) is true? 11 10 11 In either case, the anti-essentialist would have to saddle the essentialist with (3) as well, which, I argued earlier, can't be done. It might appear that (1) could get some support from the counterfactual analysis of event causation. If we thought that the hand wave that Bennett actually produced caused the auctioneer to come to believe that Bennett had made a bid, then, barring overdetermination, if Bennett's actual hand wave had not occurred, then its effect, the auctioneer's coming to think that Bennett had made a bid, would not have occurred. However, the counterfactual analysis does not require that if an event, c, causes an event, e, then ifc had not occurred than e would not have occurred, unless c is an immediate cause of e. The reason for this is that, whereas the causal relation is transitive (so that the immediate causes of e. the causes of those causes, and so on are all causes of e), the counterfactual conditional is not transitive. From the fact that ifc hadn't occurred then d wouldn't have occurred and the fact that if d hadn't occurred then e wouldn't have occurred, it does not follow that, if c hadn't occurred, e wouldn't have occurred. Therefore, on the plausible assumption that Bennett's actual hand wave was a remote cause of the auctioneer's coming to believe that Bennett had made a bid (after all, the auctioneer must see the hand wave), the truth of (I) does not follow from the counterfactual analysis of event causation.
195 Events. Counterfactuals, and Speed (1) is the claim that, had Bennett's actual hand wave not occurred, the auctioneer would not have thought that Bennett was bidding. What is the intuition that could ground one's confidence in this claim? I suggest that it is quite plausible -- it is at least as plausible as (2) is -- to believe that, unless the auctioneer's thought that Bennett was bidding was overdetermined (say, by Bennett's nodding his head while waving his hand), if Bennett does not wave his hand at all, then he does nothing at all that would have made the auctioneer believe that Bennett was bidding. It is quite reasonable, then, to suppose that the following expresses a truth that all parties to the dispute can accept: (4) in the possible worlds closest to the actual world in which there does not occur an event that is Bennett's hand wave, the auctioneer does not think that Bennett was bidding. (4) is, on the assumption that the auctioneer's thought is not overdetermined, quite plausible, for in understanding it, we need not suppose the referent of 'Bennett's hand wave' to be the hand wave that Bennett actually produced; any unique hand wave produced by him will do. So, had there been no such wave, and nothing else to indicate a bid, the auctioneer would not have thought that Bennett was bidding. (4), however, is not a claim that is strong enough (even in conjunction with (2) and (3)) to support (Q)'s (or (Q+)'s) conclusion, for it says nothing about Bennett's actual hand wave or about what would have happened had it not occurred. What is needed is a large scope version of (4): (4L) Bennett's hand wave (the one he actually produced) is such that, in the possible worlds closest to the actual world in which it does not occur, the auctioneer does not think that Bennett was bidding. According to (4L), worlds closest to the actual world in which Bennett's actual hand wave does not occur are worlds in which the auctioneer does not think that Bennett has made a bid. (4L), of course, is just (1). In any case, even~if the truth of (1) is simply granted, the option of rejecting (3) is still available to one who accepts No-Quicker. And such an option would be well-motivated, since whatever the considerations are that suggest that (1) is true undermine (3). 12 But, one simply need not grant (1). The thought that it is obvious (or, at any rate, that it is as obvious as (2) is), can stem, I think, only from the obviousness of (4) and the fact that (4L), that is, (1), can be inferred from it by means of a scope fallacy. It simply does not have the intuitive plausibility that would recommend it to everyone. In sum, then, (1), (2), and (3) are incompatible with both views concerning whether an event can occur faster than it in fact does. (2) is independently quite plausible. So, neither position can accept both (1) and (3). The defender of No- Quicker is free from any commitment to (3). But if forced to accept (3) on independent grounds, so is everyone; and everyone can then reject (1). And if forced to accept (1), all can reject (3). 12 Of course, this option is open as well to, and must be taken by, those who assert Quicker.
Lawrence Brian Lombard 196 So, while Bennett's basic point, that the truth of at least some counterfactuals about events has implications concerning the properties that events have essentially, is surely correct, (Q), since it is invalid, fails to be an illustration of that point. And (Q+), though valid, is unsound; so it fails to establish that an event can occur more quickly than it in fact does. VII. Arguments Analogous to (Q) Virtually anything that Bennett could have done to attract the auctioneer's attention would have made it the case that Bennett made a bid. Thus, it is plausible to suppose that (5) if Bennett had nodded his head, instead of waving his hand, the auctioneer would still have thought he was bidding is true and just as reasonable to believe as (2) is. If (Q) were valid, then, from (1) and (5), we could conclude that Bennett's hand wave could have been a nod of his head. 13 But I cannot bring myself to believe this conclusion; nor, in light of my criticism of (Q), need I. So far as I can see, the most that (5) shows is that, in conjunction with the truth of (1), different events (head noddings and hand wavings) can have the same outcome. Of course, to validly infer that Bennett's hand wave could have been a nod of his head, from (1) and (5), we would have to add a premise analogous to (3), something like this: there is a world closest to the actual world in which Bennett's actual hand wave does not occur that is also a world closest to the actual world in which Bennett nods his head. But this additional premise is not particularly plausible; and it, in conjunction with (1) and (5), form an inconsistent triad, in just the way that (1), (2), and (3) do. If (Q) were valid, its power to show what Bennett's hand wave could have been like would extend even beyond things Bennett could have done. Consider this argument: Suppose that at noon Bennett waves his fight hand, and his companion later says S': If that hand wave had not occurred, the auctioneer wouldn't have thought you were bidding. Now if Bennett's identical twin, who was sitting next to him, had waved his right hand instead, the auctioneer would still have thought that Bennett was bidding (because he could not see that the waved hand was the twin's or because he mistook Bennett's twin for Bennett); so if S" is to come out true that possible wave (the one the twin produced) must count as the wave Bennett actually produced. Thus, the wave of Bennett's hand could have been a wave of his twin's hand, which means that it is not of the essence of Bennett's hand wave that it be a wave of Bennett's hand. This argument is, of course, invalid for the same reason that (Q) is. To make it valid, it would have to be supplemented by a suitable replacement for (3). The required replacement for (3) here would be something like this: there is a world is See Events and Their Names, pp. 55f.
197 Events, Counterfactuals, and Speed closest to the actual world in which Bennett's actual hand wave does not occur that is also a world closest to the actual world in which Bennett's twin waves his hand! This is hardly a proposition that immediately recommends itself; nor is it something that one who believes that Bennett's actual hand wave could not have been a wave of his twin's hand is required to believe. And the argument from this premise, (1), and the claim that if Bennett's twin (and not Bennett) had waved his hand the auctioneer would still have thought that Bennett was bidding, to the conclusion that an event's subject is inessential to it is, of course, unsound for the same reasons that (Q+) is. 14 If (Q+) were to establish that an event can occur more quickly than it does, then the following argument, suitably supplemented, is would establish that an event can occur more slowly (in senses that correspond to the various senses of 'more quickly') than it does: Suppose that at noon precisely I wave my right hand, and someone makes the statement S" : If that hand wave had not occurred, the auctioneer wouldn't have thought you were bidding. Now, if I had waved my right hand a fraction more slowly than I actually did, the auctioneer would still have thought I was bidding; so if S" is to come out true, those possible waves must count as the wave I actually did. That implies that my actual wave could have been a bit slower than it was. (Q+) and the argument just displayed, suitably supplemented, are formally analogous; so they stand or fall together. If sound, they would establish the full inessentiality thesis, that an event can occur both more quickly and more slowly than it actually does. If unsound, they touch neither half of that essentialist thesis. And they are both unsound. TM Wayne State University Received March 1991 15 16 For an argument in favour of the essentiality of events' subjects, see my Events: A Metaphysical Study, pp. 197-206. It would be supplemented by 3" -- there is a closest P-world that is also a closest Q'-world - - where Q" is the proposition that Bennett waves his hand a bit more slowly than he actually does. I am grateful to Michael McKinsey for his helpful reading of an earlier draft of this paper, for his long and fruitful discussions with me, and for his insightful and penetrating suggestions. I wish also to thank Bruce Russell and Larry Powers for their helpful discussions with me concerning this paper, and for forcing me to be much clearer than I otherwise would have been, I would also like to thank the referees of the Australasian Journal of Philosophy for their very helpful and insightful comments on what was not supposed to be merely the penultimate draft of this paper.