Counterfactuals and Possible Worlds

Canadian Journal of Philosophy

Counterfactuals and Possible WorldsAuthor(s): Jonathan BennettSource: Canadian Journal of Philosophy, Vol. 4, No. 2 (Dec., 1974), pp. 381-402Published by: Canadian Journal of PhilosophyStable URL: http://www.jstor.org/stable/40230514 .

Accessed: 17/06/2014 17:35

Your use of the JSTOR archive indicates your acceptance of the Terms & Conditions of Use, available at .http://www.jstor.org/page/info/about/policies/terms.jsp

.JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range ofcontent in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new formsof scholarship. For more information about JSTOR, please contact [email protected].

.

Canadian Journal of Philosophy is collaborating with JSTOR to digitize, preserve and extend access toCanadian Journal of Philosophy.

http://www.jstor.org

This content downloaded from 195.34.79.158 on Tue, 17 Jun 2014 17:35:27 PMAll use subject to JSTOR Terms and Conditions

http://www.jstor.org/action/showPublisher?publisherCode=cjp

http://www.jstor.org/stable/40230514?origin=JSTOR-pdf

http://www.jstor.org/page/info/about/policies/terms.jsp


CANADIAN JOURNAL OF PHILOSOPHY Volume IV, Number 2} December 1974

Counterfactuals and Possible Worlds

JONATHAN BENNETT, University of British Columbia

1. Introduction

This article is a selective review of David Lewis's Counterfactuals (Cambridge, Mass., 1973), a challenging, provocative, absorbingly interesting attempt to analyze statements of the form "If it were the case that P, then it would be the case that Q."1 I shall follow Lewis in calling these "counterfactuals," and shall nearly follow him in abbreviating them to the form P-+Q.

Chapter 1, which is nearly a third of the whole, gives the analysis and proves that it endows counterfactuals with some properties which they evidently do have. Chapter 2 presents some "alternative formulations" of the analysis-a logical jeu d'esprit which I shall not discuss except for the section (§ 2.6) about "cotenability." In Chapter 3, Lewis compares his analysis with "the metalinguistic theory"- a phrase which he uses to cover the theories of Chisholm, Goodman and Mackie- and also with a theory of Stalnaker's which is a sibling rival of Lewis's (I would have said a parent of it, but Stalnaker informs me that the two theories were developed independently of one another). Chapter 4 discusses two load-bearing concepts in Lewis's analysis-poss/6/e world and similarity.

In Chapter 5, Lewis relates his theory of counterfactuals to certain matters in deontic and temporal logic and in the logic of definite descriptions. I think I have understood this chapter, though only with difficulty; but, packed as it is with solid content, it does not bear on the central question: has Lewis given a tenable analysis of counterfactuals? Chapter 6, in which Lewis regiments his

1 Robert Stalnaker commented patiently on an earlier version of this paper. His

generous help saved me from one gross blunder, as well as showing me many places where the argument was weak or unclear or unfair. I am deeply indebted to him.

381



Jonathan Bennett

materials into systems for which he proves metatheorems, is beyond my competence. I shall not discuss these two chapters.

After three sections in which I sketch Lewis's analysis and display some of its merits, my discussion will be mostly negative. I am abashed about this, for I admire the capable and imaginative way in which Lewis has gone about his task, and am reluctant to attack the results. But I believe that the task was a mistaken one, that Lewis's fundamental concepts are wrong for the job and that a good understanding of counterfactuals requires us to leave this kind of theory and return to where Goodman left off twenty years ago.

2. Lewis's Analysis

The bare bones of Lewis's theory are displayed in his opening sentences:

"If kangaroos had no tails, they would topple over" seems to me to mean something like this: in any possible state of affairs in which kangaroos have no tails, and which resembles our actual state of affairs as much as kangaroos having no tails permits it

to, the kangaroos topple over. (p. 1 )

In Lewis's firming-up of this, "possible state of affairs" gives place to "possible world," and counterfactuals of the form P->Q are equated with statements to the effect that PDQ holds true in every member of a certain class of possible worlds. What class is it? The quoted passage gives the answer, but we shall be helped by a mild dose of Lewis's technical apparatus.

We are to think of a set of possible worlds as constituting a kind of filled sphere, with the actual world in the centre and other worlds so arranged that the nearness of world x to the centre depends upon how similar x is to the actual world. Lewis does not propose a metric for similarity, and in § 2.4 he argues against trying to develop one. All he needs are comparisons: x is more like the actual world thany is, and so it is closer to the centre thany is.

The sphere is made up of a nested sequence of sub-spheres-"nested" in that of any two sub-spheres one wholly contains the other. So if a possible world belongs to sub-sphere S, then it belongs to every sub-sphere in the sequence which is larger than S. Accordingly, if x is nearer to the centre thany is, then at least one sub-sphere contains x but noty, and none containsy but not x. In all of this, nothing is implied about whether two possible worlds can be equally similar to the actual world: a "shell" of worlds which are equidistant from the centre might have any number of members.

The sphere need not include every possible world: we might omit some worlds which were too unlike the actual world to be worth considering. Also, we could construct a sphere whose centre was some non-actual world, e.g. for purposes of analyzing "If Grant had been drunk at Appomattox, then it would have been the case that if the Federal cavalry had been kept in reserve Lee would have won the battle"; but I shall ignore all such spheres.

382




I shall use "P-world" ("Q-world" etc.) to mean "possible world in which P (Q etc.) is true"; and I shall call a sub-sphere "P-permitting" if it contains at least one P-world.

The truth-conditions which Lewis gives for counterfactuals are best split into two. Firstly, P-*Q is vacuously true if there are no P-worlds anywhere in our sphere, i.e. if P is impossible or somehow unentertainable by us. Secondly, and more interestingly, P -> Q is true if there is a sub-sphere throughout which P D Q is non-vacuously true, that is, a P-permitting sub-sphere in which every P-world is a Q-world (see p. 16). By this account, P-»Q can survive there being any number of (P <& ~Q)-worlds, just so long as each of them is further from the centre-Z.e. is less like the actual world- than is some (P & Q)-world.

Lewis notes that for a given P there may be no smallest P-permitting sub-sphere (see his § 1.4); for it could be the case that, given any P-world j other than the actual world, there is some other P-world which is closer to the centre than / is. If he could always avail himself of smallest sub-spheres of the relevant

kinds, Lewis says, he could "make the truth conditions for counterfactuals simpler" in the non-vacuous case, by saying that P -* Q is true if P D Q is true in the smallest P-permitting sub-sphere (p. 20). But that is no "simpler" than what Lewis has already offered, namely that P->Q is true if P D Q is true in some

P-permitting sub-sphere.

3. Some Upshots of the Analysis

On Lewis's analysis, counterfactuals are vague. But then so they manifestly are, and Lewis can plead that his analysis does its duty by pinpointing the source of the vagueness-specifically in the concept of comparative similarity. "I seek to rest an unfixed distinction upon a swaying foundation," Lewis says, "claiming that the two sway together rather than independently" (p. 92). As regards the notion of similarity, Lewis says that "Not anything goes," because:

There is a rough consensus about the importances of respects of comparison, and hence about comparative similarity. Our standards of importance and similarity do

vary; but mostly within a certain range, narrow by comparison with the range of variation permitted by the formal constraints in my definition of a system of

spheres. ... It is natural that we should have vocabulary conventionally reserved for

use within that . . . range. If special interests or eccentricity lead us outside the

mutually expected range of variation, we have no right to take our conventionally reserved vocabulary with us. (pp. 93-94)

So, although the notion of comparative similarity of worlds is a "swaying" one, there are standards which partially govern its employment, and what we say in the language of counterfactuals is answerable to them.

My later criticisms of Lewis's theory will not turn on the vagueness of

"comparative similarity"; quite the contrary.

*****

383



Jonathan Bennett

There are several formal properties which the relation -> arguably has, and which are conferred upon it by Lewis's analysis. He discusses these in § § 1 .2-3,

§ 1.8 and § 3.4. Counterfactuals would not be conditionals at all unless they obeyed

modus ponens and modus tollens] that is, unless Q followed from P -> Q and P

together, and ~P from P -> Q and ~Q together. It is easy to see that on Lewis's account -> honours both those inference-patterns.

More interestingly, there are three inference-patterns which - does not

honour, although they are valid both for the weaker material implication and for the stronger logical entailment. Lewis shows that each of these

inference-patterns fails, and why, on his account of -.

(/) From P -> Q, it does not follow that (P & R) -+Q. Indeed, there is no

incompatibility between the non-vacuous truth of P-*Q and the non-vacuous truth of (P & R) -»~Q. For example, it could be true both that

(a) If I walked on the ice, it would remain firm, and also that

(b) If I walked on the ice and you walked on the ice, it would not remain firm.

One might try to argue that if (b) is true, then (a) as it stands is not true, and that we accept it only because we construe it as an ellipsis for "If I alone walked on the ice, . . ." etc. But we have to cope with the truth not just of (b) but also of

(c) If I walked on the ice and I wore 60 Ib. boots, it would not remain firm.

Must we then say that (a) is really an ellipsis for "If I alone walked on the ice

wearing normal footwear, . . ." etc.? But there are plenty more where (b) and (c) came from, each requiring a further expansion of (a). Clearly, we shall get nowhere by trying to reconcile (a) with (b), etc. through the plea that (a) is an

ellipsis. Lewis's analysis handles this matter nicely. It says that if (a) is

non-vacuously true, that is because there is a sub-sphere S such that: S contains at least one world in which I walk on the ice, and the material conditional "I walk on the ice D The ice remains firm" holds true throughout S. What is

required for the non-vacuous truth of (b) is that there is a sub-sphere S* such that: S* contains a world in which you and I walk on the ice, and the material conditional "You and I walk on the ice D The ice does not remain firm" holds true throughout S*. For (a) and (b) both to be satisfied, S* must be larger than S; for S* has to contain worlds where you and I tread the ice and crack it, whereas S cannot contain any worlds where I tread the ice (however garbed or accompanied, etc.) and crack it. But that is what one would expect: worlds where you and I tread the ice are less like the actual world than are worlds where

384




I alone tread the ice. (That presupposes that in the actual world you kept off the ice. But if you didn't, then (a) would not be clearly true and the example would collapse.)

(2) It follows that - cannot be transitive, but Lewis examines non-transitivity separately (pp. 32-35). If there were snow on the valley-floor, I would be skiing along it; and if there were an avalanche just here, there would be snow on the valley-floor; but it is false that if there were an avalanche I would be skiing on the valley-floor (because I would be either dead or digging out victims). One might argue that the first premise is true only if expanded into "If there were snow on the valley-floor and there had not been an avalanche, . . ." etc.; but that expansionist approach will come to grief here, as it did before. We have to accept that -> is not transitive.

This is another fact which is elegantly handled by Lewis's analysis. The case I have just described can obtain, by the analysis, if there are worlds in which snow falls gently onto the valley-floor (and I then ski on it) which are more like the actual world than any world in which snow is deposited on the valley-floor by an avalanche. If the valley in question is of such a kind as to make this false, then the example collapses and Lewis's analysis is under no obligation to support it.

(3) Lewis shows that contraposition fails for -*, and he explains this in terms of his analysis. The details can perhaps be worked out on the basis of the

foregoing treatment of premise-strengthening and transitivity. In working them

out, bear in mind that one can best discuss the relationship between P->Qand ~ Q-»~P by taking a pair of what Goodman calls "semi-factuals," i.e. conditionals with a false antecedent and a true consequent, which could be

expressed in the form "[Even] if it were the case that . . . , it would still be the case that . . . ."

Having written uninhibitedly about worlds which contain you, and me, and a certain valley, I hasten to add that Lewis holds that no individual thing

belongs to more than one possible world (§ 1.9). According to that view, there

is no world where Lewis does not write on counterfactuals; but there are, Lewis

would allow, worlds where counterfactuals are ignored by people who are

sufficiently like Lewis to qualify as his "counterparts" in those worlds. This is a

large topic which I cannot explore here. I shall just write as though there were

no difficulty about inter-world identities, and as though Lewis agreed: it is a

routine matter to re-write everything with identities replaced by sufficient

similarities. I shall also ignore another controversial aspect of Lewis's thought,

namely his realism about possible worlds.

385



Jonathan Bennett

4. Lewis and Stalnaker

Lewis gives the label "Conditional Excluded Middle" to the principle that [(P-*Q) v (P-»~Q)] for all values of P and Q that are not entirely excluded from our sphere (pp. 79-80). This principle fails, on Lewis's analysis, if (P & Q)-worlds and (P & ~Q)-worlds tie for similarity to the actual world. Lewis convincingly defends this, though he allows that one is inclined to accept "offhand" the "opinion" that the principle is true. I am not sure that one is; but some comments of Stalnaker's on this point have convinced me that this is a complex matter, and I shan't go into it here.

The principle of Conditional Excluded Middle is preserved in a theory of Stalnaker's of which Lewis's is a close relative. Stalnaker says that P - Q is true if Q obtains in the P-world which is most like the actual world. This ignores the possibility that two P-worlds might tie for first place in the similarity-to-the-actual-world stakes (only one of them being a Q-world); and, incidentally, it thereby obliterates Lewis's good distinction between (P-*Q) and "If it were the case that P, it might be the case that Q." Stalnaker's account also rules out the possibility that, given any P-world j, some other P-world is more like the actual world than/ is. In § 3.4 Lewis shows that Stalnaker's theory is equivalent to a special case of Lewis's, namely the case where there are no ties-for-closest and no asymptotic-approaches-to-closest.

5. True Antecedents

The Stalnaker-Lewis kind of theory does not rest the truth of P - Q upon the obtaining of a connection between P and Q. In this respect it is unlike those previous theories which Lewis lumps together as "the metalinguistic theory." That label is supposed to cover the theories of Chisholm, Goodman, and Mackie; but Mackie's theory is not "metalinguistic" at all, and, for a reason which Lewis himself gives (p. 69), the metalinguistic aspect of the approaches of Chisholm and Goodman is not an important feature of them. So that label is better dropped. I shall use the phrase "the consequence theory" to designate Chisholm 's and Goodman's hypothesis that the best way to elucidate counterfactuals is along these lines: P->Q is true if and only if Q is derivable from P together with laws of nature together with true propositions which satisfy certain conditions.

Without minimizing the problems which beset the consequence theory, we should still look critically at what Lewis is led to through eschewing the notion of a connection between antecedent and consequent or of the derivability, subject to certain constraints, of the consequent from the antecedent.

Consider a statement of the form P - Q where P is true. I agree with Lewis that although "If it were the case . . ." and related forms are "customarily

386




reserved for antecedents taken to be false" (p. 28), the falsehood of the antecedent is not entailed by the counterfactual as a whole, and the latter might be true even though its antecedent is true. So far, so good. But in Lewis's theory, if P is true then P->Q comes out as true just so long as Q is also true. This is because, if P and Q are both true, then the sub-sphere whose only member is the actual world is a P-permitting sub-sphere throughout which the material conditional PDQ holds true; and that, by the Stalnaker-Lewis theory, entails P-*Q.

Lewis shows on p. 29 that his account could be freed from this feature if there were several worlds which were as similar to the actual world as the latter is to itself (in the sense of differing from it only in negligible ways). In that case, there would be no such thing as "the sub-sphere whose only member is the actual world," and so the derivation of P -> Q from P, Q would not go through. But that, although it is correct, goes no way towards conciliating those who reject the inference from P, Q to P^-Q because they think that the truth of a counterfactual depends upon the obtaining, between antecedent and consequent, of some connection which does not hold between every pair of truths. Indeed, Lewis's move doesn't achieve much at all, for it blocks the inference from P, Q to P -> Q only for negligible values of Q, that is, values such that two worlds could differ only in negligible respects although Q holds in one of them and not the other.

In defence of the view that P - Q is true if P and Q are both true, Lewis presents a snatch of conversation, in which I say "If Caspar had come, it would have been a good party," and Lewis gives the "perfectly cogent" reply: "That's true; for he did, and it was a good party. You didn't see him because you spent 'the whole time in the kitchen, missing all the fun" (p. 27). Now, Lewis admits that the cogency of this reply doesn't prove his case, because the cogency might depend in part on something which is not explicitly said; but he does not explore this possibility thoroughly enough. He acknowledges that certain counterfactuals which come out as true on his theory would be "odd" ones to assert, rightly says that "oddity is not falsity," and in his chosen kinds of cases seeks to explain the oddity in other ways (p. 28). The explanation succeeds, because the "odd" case he discusses is one where someone says P-*Q, where P and Q are "completely unrelated truths" and the speaker says what he does simply "on the strength of" the truth of P and of Q in the actual world. But in those circumstances it would be "odd" to assert even the indicative conditional of the form "If P is the case, Q is the case," let alone the stronger counterfactual form P->Q. (I follow Lewis, p. 3, in this use of "indicative" and "counterfactual" as antonyms, and in affirming that counterfactuals are stronger than their indicative analogues.) That suggests that the example involves a counterfactual which is, so to speak, too odd for its oddity to be seen clearly: there is an unintended truth in Lewis's remark that "The oddity dazzles us."

Let us test Lewis's view against a case where things go awry in a less extreme way. Suppose that I believe (perhaps on hearsay) that Caspar didn't

387



Jonathan Bennett

come to the party and that the party was a bad one, and I say "If Caspar had come, the party would have been a good one." You hear me say this, and you know that Caspar did attend the party and that it was a good party; but you also know that Caspar ruins most parties he attends, and that he nearly ruined this one. It was a good party despite the fact that Caspar came to it. Everyone on whom I have tried this example insists that the statement "If Caspar had come, the party would have been a good one" is not true] most say that it is false) and none will allow that the statement is true but "odd." It may be replied that this is a theoretical matter on which the responses of intelligent native speakers are not decisive. But still a tenable theory must be capable of explaining such responses, and Lewis's explanation does not suffice, for it is addressed to the too-easy case where I say "If the sky were blue then grass would be green," in which "the oddity dazzles us [and] blinds us to the truth-value of the sentence."

I suggest that in the case I have described, the statement "If Caspar had come, the party would have been a good one" is not true because there is not the requisite kind of connection between "Caspar was at the party" and "The' party was a good one." If I am right about that, then Lewis's theory is wrong.

6. The Consequence Theory

The consequence theory would deal with this case by saying that the truth of the counterfactual depends upon the derivability of "It was a good party" from "Caspar was at the party" together with other truths which satisfy certain constraints. I believe, though I shall not argue the point here, that these constraints could be so fixed as to make the truth of "If Caspar had come it would have been a good party" depend upon how much Caspar contributed to the success of the party. The consequence theory, at any rate, has some chance of getting this matter right, whereas Lewis's theory seems committed to getting it wrong.

Since Chisholm's first paper in which the consequence theory was launched, some theorists have worried about the concept of a law of nature. The theory says that P-*Q is true only if Q is derivable by laws of nature from certain premises, and this requires us to distinguish laws from accidentally true generalizations. If we have to draw the line by saying that only laws of nature support counterfactuals, then the consequence theory turns into a vicious circle. There are other approaches to the problem of explaining what a law of nature is, however, and one of the best I have seen is Lewis's own adaptation of "a theory of lawhood held by F. P. Ramsey in 1928" (pp. 73-74).

Goodman uncovered a new problem for the consequence theory, stemming from his claim that the truth of P - Q requires the derivability by law of Q from a conjunction of premises which include P and other propositions which are cotenable with P. "R is cotenable with P" means, according to Goodman, that it is not the case that if P had been the case R would not have

388




been the case (Fact, Fiction and Forecast, p. 15 and n.). This raises a problem, because if the truth-conditions for P->Q include something of the form ~ (P->~ R) our endeavour to eliminate the -> seems to run into an infinite regress.

I think I can solve the cotenability problem, but this is not the place to do it. I mention cotenability only because it is the crux of Lewis's attempt to use his theory as a basis from which to derive the consequence theory as a special case, this being part of his endeavour to "show that to the considerable extent that other theories succeed, my new theory has enough in common with them to share in their success and to explain it" (p. 65). This derivation goes through on either of two definitions which Lewis offers for cotenability. He is prepared to

equate "R is cotenable with P" with either

(1 ) R holds throughout some P-permitting sub-sphere (p. 57) or as

(2) R is true and P->R (p. 70).

(1) says that R is true in every world we meet as we move out from the actual world at least until after we have encountered our first P-world, whereas (2) says only that R is true in the actual world and in the P-worlds which are closest to it. Lewis says that (1) "captures the intentions of [consequence] theorists" better than (2), because according to (1) "a cotenable premise is not only true, but also necessary to some extent."

This preference for (1) is puzzling: I can find no basis for it in the writings of any consequence theorists, and it seems to be much too strong for the

requirements of an analysis of counterfactuals. Suppose someone claimed that "If Chilliwack were flooded, Smith would use his radio transmitter to relay

requests for help," and tried to defend this by deriving "Smith uses his radio" etc. from premises which included "Smith's auxiliary power supply is in working order," this being true in the actual world. Now, it might be the case that in

mildly damp weather Smith's auxiliary power supply stops being in working order, though whenever there is the slightest chance of a flood he takes special

steps which ensure the functioning of the auxiliary supply. If that were the case, it would surely be all right-so far as cotenability was concerned- to avail oneself

of "Smith's auxiliary power supply is in working order" in defending that

counterfactual; and yet it would not be cotenable with "Chilliwack is flooded"

according to Lewis's definition (1), for between the actual world and the nearest

in which Chilliwack is flooded there are many worlds where Chilliwack is only mildly damp and Smith's auxiliary power supply doesn't work.

Admittedly, I have implicitly separated off the laws of nature, and taken

cotenability to relate P to premises about particular matters of fact, whereas

Lewis takes it to relate P to everything else which is used in the derivation of Q, laws and all. But that does not justify his preference for definition (1); for one

does not render a conjunction "necessary to some extent" simply by including necessary conjuncts in it.

*****

389



Jonathan Bennett

So definition (2) is better, because desirably weaker, than (1). Now consider a still weaker definition of "R is cotenable with P," namely:

(3) Ristrueand~(P-»~R). On that definition, the floodedness of Chilliwack needn't guarantee the

workability of Smith's auxiliary power-supply: cotenability is secured just so

long as the auxiliary supply is in working order and its being so would not be ruled out by Chilliwack's being flooded. If the principle of Conditional Excluded Middle were true, (2) would not differ from (3); but Lewis and I reject that principle, and so for us (2) is stronger than (3), and the question arises as to which of them better captures the notion of cotenability which is employed in the consequence theory.

I answer that (3) is decisively preferable, historically and philosophically. Historically, just because "cotenable" was first introduced into the literature of counterfactuals by Goodman, and he clearly uses definition (3). But also philosophically, because if a consequence theorist used the concept of cotenability in Goodman's kind of way, while defining it by (2) rather than (3), his theory would collapse under the extra weight. I now proceed to show this.

The consequence theory goes something like this: P -> Q is true if and only if Q is law-derivable from P together with true premises which are jointly cotenable with P. On definition (3), the defender of P->Q can try to derive Q from a rich body of premise-material- think of it as compressed into a single conjunction R- many items in which are not secured by P but are not ruled out by it either. But if R must be cotenable with P according to definition (2), then R itself must be law-derivable from P. (Attempts to avoid this conclusion merely postpone the evil day. We can say that R is law-derivable from P and truths which are law-derivable from P; but that boils down to R's being law-derivable from P simpliciter. Similarly for all longer versions, in which R is law-derivable from P together with truths which are law-derivable from P together with . . . together with truths which are law-derivable from P.) But to require that Q be law-derivable from P together with truths which are law-derivable from P is just to require that Q be law-derivable from P. In short, if one adopts the consequence theory while defining cotenability by means of (2), the only counterfactuals one can allow as true are ones which don't depend on any particular matter of fact but only on the law-connection of the antecedent with the consequent. That conflicts violently with the spirit of the consequence theory; and so Lewis's definition (2), although better than (1), is still quite inadequate to its announced purpose.

This is important, because of what it implies for Lewis's purported derivation of a version of the consequence theory within his own theory. This derivation, which at first looks like a rather dashing capture of enemy territory, is really no such thing. It goes through on definitions (1 ) and (2) of cotenability, but it fails for definition (3); and so it fails absolutely.

390




7. Back-tracking

So far, I have argued two points against Lewis: that his handling of counterfactuals with true antecedent and consequent is defective, and cannot be

otherwise; and that his attempt to capture and "explain [the] success" of the

consequence theory needs a wrong account of cotenability. I now approach some more serious difficulties in Lewis's position.

I have to start with something on which Lewis is right and rather

original- a point he makes which seems to have occurred only once before in the

literature (P. B. Downing, "Subjunctive Conditionals, Time Order, and

Causation/' Proceedings of the Aristotelian Society, N.S. Vol. LIX [1958-59],

pp. 125-140). Stated in my terms, it is the point that in evaluating a

counterf actual one need not envisage a history for the antecedent-situation.

Suppose we are trying to establish a counterfactual P -* Q, where P mentions no

time earlier than t. We have to show that Q is law-derivable from (P & R) where

R is a conjunction of truths which is cotenable with P. The thesis that we

needn't envisage a history for the antecedent-situation (P) is the thesis that the

cotenability of R with P does not have to survive back-tracking claims, i.e. ones

about what would have to have been the case before t for P to have been the

case at t. Usually we will count R as cotenable with P just so long as there is no

suitable route from P to ~R which does not involve tfack-tracking, i.e. which

does not involve going by law from P to something earlier than t and from that

forward again to R. In some individual cases back-tracking may be allowed as

relevant, either explicitly or as implied by the context, but unless there is special indication that (limited) back-tracking is allowed or required, back-tracking is

irrelevant to the evaluation of counterfactuals. I assert this on three grounds.

(1) It squares with my own intuitions about counterfactuals. (2) It is supported

by the answers I get when I put counterfactual questions to literate

non-philosophers. (3) We must excuse ourselves from unlimited back-tracking if

we are to have good grounds for believing any counterfactuals. Point (3) holds if

our v/orld is governed by fairly deterministic laws, for then almost any antecedent will imply an earlier difference which will imply a still earlier one

which . . . and so on back for a million years, say, and then forward along other

branches of the downward-spreading causal tree. Of course we cannot do this, but that is my point: because we cannot do it, we adopt standards which don't

require us to do it.

Lewis, in the terms of his own theory, makes something like this point about back-tracking. He considers a counterfactual of the form "If that

roulette-wheel had stopped on red at t, . . ." where in fact the wheel stopped on

black at t. For purposes of this example, assume that the actual world is

completely governed by deterministic laws. Now, we must choose between

(a) associating this coumerfactual with wheel-on-red worlds which are just like

ours in the laws governing them and in being totally obedient to those laws, so

that those worlds differ a little from the actual world in their states at t-d, and

391



Jonathan Bennett

thus at t-2d, and thus at t-3d, and so on backwards forever, and (b) associating it with worlds which are just like ours up to t-d, and which are wheel-on-red worlds

by virtue of a "small, localized, inconspicuous miracle" between t-d and t

(Lewis, p. 75). Lewis opts for (b) as being closer to the actual world than (a). (He carefully makes this all relative to the pretence that determinism is true; but I suggest that so far as most of our counterfactuals are concerned determinism

might as well be true.)* I agree that the latter kind of world is more like the actual world than is

the former, and so Lewis's theory seems to explain why in evaluating counterfactuals we don't need to back-track. But the explanation collapses under pressure.

Its defects can be exhibited through a question which Lewis candidly raises:

If I have decided that a small miracle before t makes less of a difference from [the actual world] than a big difference of particular fact at all times before t, then why do I not also think that a small miracle after t makes less of a difference from [the actual world] than a big difference of particular fact at all times after ti That is not what I do think, (p. 76)

But why not? Somewhat hesitantly, Lewis suggests two possible answers.

(1) "It seems to take less of a miracle" to produce a wheel-on-red world which is just like ours before t than it does to produce a wheel-on-red world which is just like ours after t:

For the first, all we need is one little miraculous shove, applied to the wheel at the right moment. For the second, we need much more. All kinds of traces of the wheel's having stopped on red must be falsified. The rest position of the wheel; the distribution of light, heat, and sound in the vicinity; the memories of the spectators-all must be changed to bring about a reconvergence of particular fact between [the wheel-on-red world and the actual world] .

Lewis is clearly suggesting that this difference in miracle-size may be present in most cases, and he says that it may have "something to do with the de facto or

nomological asymmetries of time that prevail" in the actual world. In fact, though, the difference in miracle-size depends on special features of Lewis's

example. Suppose that in the actual world the given roulette wheel was B* at

t-2d} which led by law to its being B at t-d and then to its stopping on the black at t. (Think of B* and B as successive states of the wheel during the single black-ending spin of it which we are considering-each consisting in the wheel's

position, mass, frictional properties, orientation with relation to gravity, velocity, rate of deceleration and so on at a given moment.) Now, Lewis allows that the world j might count as very similar to ours up to time t if j was

indistinguishable from ours up to t-d and then a small miracle intervened so that in j the wheel stopped on the red and not on the black. What he won't allow as consistent with a high degree of similarity between worlds is a further

392




gap-healing miracle so that/ continues as though in it the wheel had stopped on the black. But now suppose that we take a world k which is indistinguishable from ours up to f-2d, then by the intervention of a small miracle in k the wheel

goes from being B* at t-2d to being R instead of B at t-d; this should lead by the

prevailing laws to its stopping on the red at tt but a further small miracle occurs in k so that the wheel in k stops on the black just as it does in the actual world. The difference between k and the actual world consists only in a momentary state of a moving roulette wheel, and an accompanying pair of tiny and

extremely inconspicuous miracles. There is just no foundation for the idea that whereas divergence-creating miracles can be small, divergence-preventing ones must be, or even tend to be, large.

The consequence theory is in no difficulty here. It says that a counterfactual asserts the obtaining of a certain kind of law-abiding connection between antecedent and consequent: that is not an impressive remark about

counterfactuals, but it does head in the right direction. As regards my present point, it lets us explain why in evaluating a counterfactual (a) we can usually neglect to envisage a history for the antecedent situation although (b) we can never make room for the idea of the intervention of a miracle- a breach of a law of nature- between the antecedent and the consequent. Lewis is forced to get both of these wrong by his adherence to the concept of comparative similarity of worlds. He handles (a) in terms of the notion of a small miracle; but in fact

(a) holds true even if the antecedent-situation would have required a very large miracle. At any rate, I think so, for the reasons I have given; but the point may be controversial. On the other hand, I can see nothing controversial about the claim that (b), which Lewis handles in terms of large miracles, holds good even if the required miracle would be very small. Take the case I described, where the actual wheel was B at t-d and this led by law to its stopping on the black at t; and consider the statement that if the wheel had been R at t-d it would have

stopped on the red at t. This counterfactual would be accepted by anyone who

agreed that the relevant sort of lawful link obtained between antecedent and

consequent; no one would be deterred by the thought that there is a possible world in which the wheel is R at t-d and then by the intervention of a really tiny miracle it stops on the black at t. Lewis's similarity-of-worlds approach won't let him account for this.

(2) Lewis's other suggested explanation is that there is no explanation: "Perhaps it is just brute fact that we put more weight on earlier similarities of

particular fact than on later ones." If this meant only that it is a "brute fact" that in evaluating counterfactuals we ordinarily ignore the causal ancestors, but not the causal progeny, of the antecedent-situation, then my only complaint would be that Lewis treats as a brute fact something which the consequence theory can explain.

393



Jonathan Bennett

8. The Fatal Defect

Really, though, Lewis is saying something quite different from that, something about how we handle the notion of comparative similarity of worlds', and that world-similarity is involved is not a casual circumstance, but rather a deep requirement of Lewis's theory. But when the "fact" which is in question is seen in that light- never mind whether it is claimed to be "brute"- it emerges as simply not a fact at all. Since Lewis is firmly committed to claiming that it is one, his whole approach must be wrong.

Let us return to the roulette-wheel example, in Lewis's version where the divergence-healing miracle would have to be'complex and conspicuous. There are two possible worlds to be considered:

/, which is indistinguishable from the actual world until t-d; then a small miracle intervenes so that the roulette wheel stops on red at t; then one thing leads to another, and; diverges progressively from the actual world throughout the rest of time;

and /?, which is just like; up to t (including the small miracle at t-d); then in

the relevant casino at t+d a rather large and complex miracle occurs which wipes out the traces of the wheel's having stopped on the red at t, leaving only states which would have occurred unmiraculously if the wheel had stopped on black; and from there on k is indistinguishable from the actual world.

Lewis is deeply committed to saying that; is more like the actual world than/? is. Forget about the cases where a tiny miracle would heal the divergence, and about the problem of relating this matter properly to the facts about back-tracking. With all of that set aside in Lewis's favour, the fact remains that he must declare/ to be more like the actual world than k is. I have carefully tried this out on many people, philosophers and others, putting the question as fairly as I could; and everyone insisted that by his standards of similarity k is much more like the actual world than j is. Lewis points out that similarity is a vague, shifting and somewhat subjective notion, and that fact aggravates his difficulty: accommodating as the concept of similarity is, Lewis's theory entails something about it which nearly everybody rejects as false.

*****

Other examples of this same general difficulty are easy to find. I shall offer just one, taken from Lewis's own pages.

Lewis is inclined to think that Lee Harvey Oswald killed John Fitzgerald Kennedy without help and with no second killer waiting. Let that Warrenite proposition be an hypothesis of the present section, just so that the example will work in agreed ways. Now, consider these:

394




(1) If Oswald had not killed Kennedy, someone else would have, and

(2) If Oswald had not killed him, Kennedy would not have been killed. We Warrenites are inclined to deny (1) and to affirm (2), and so is Lewis. This commits him to something which is obviously false; he notes the commitment

himself, but does not hint that it might be found dubious. The truth of (2), by Lewis's theory, requires that some worlds in which no one kills Kennedy are

more like the actual world than is any world in which Kennedy is killed by someone other than Oswald. Without budging from my pretended Warrenism, I

claim that this is incredible. Any possible world where Kennedy is not killed

must differ enormously from the actual world, because the political and other

consequences of that killing were so large and ramifying. On the other hand, there is a possible world in which Kennedy is killed not by Oswald but by some

other disaffected Dallas resident: that world differs from ours in certain events

before the assassination, and in some of the legal and journalistic upshots; but

those differences will be tiny when compared, by any reasonable standard, with

the differences involved in Kennedy's not being killed at all (and serving out his

first term, being succeeded by himself or by someone other than Johnson, and

so on). This seems to me obvious, and yet Lewis denies it: 'The worlds where

Oswald did kill Kennedy, working alone, with no other killer waiting ... are

worlds to which worlds with no killing are closer than worlds with a different

killer" (p. 71). That quotation is lifted from a more complex statement, but in

the latter Lewis clearly commits himself to the position expressed in the above

sentence. The reader may suspect that Lewis is thinking only of the similarity of

worlds up to the time of the assassination. Perhaps he is; but his theory does not

permit that restriction to pre-assassination similarities, as I shall show. First,

though, let us see if he has any other way out of the difficulty I have presented. It is presumably clear that the concept of miracle-size, even if it had served

Lewis's turn in handling the previous example, would not help him with this

one. For here we can balance off one tiny miracle, namely a slip of Oswald's

finger, against another tiny miracle, namely some brain-changes in another Dallas

resident which lead to his conceiving and executing a plan to kill Kennedy five

minutes before the time at which in fact Oswald killed him.

Nor can Lewis get any help here from the supposed fact-which he says

may be a "brute fact"-that in comparing worlds "we put more weight on earlier

similarities of fact than on later ones." It is not very clear what this "fact"

comes to, but however generously we construe it, and however freely we allow

that it is a fact, it does not salvage the Oswald-Kennedy difficulty. One might think otherwise if one contrasts a world / in which at T minus

one second Oswald's finger slips, with a world j in which at T minus one month

John Doe starts planning to kill Kennedy and executes his plan at T minus five

minutes (I here use "T" to name the time when the assassination in fact

395



Jonathan Bennett

occurred). Of those two worlds, / parts company from the actual world nearly a month earlier than /does; and so if one accepted Lewis's "brute fact" one might say that; is overall less similar to the actual world than / is. This would involve

giving infinitely more weight to earlier than to later (dis)similarities of fact, for it is being claimed that / is more like the actual world than; is, however great the

post-T differences are between / and the actual world. I have remarked that that is false if our ordinary notion of similarity is involved, but that is not my present point. For purposes of argument, I shall take it that everything Lewis claims about how similarity relates to time has been secured- not as argued for, nor as brute fact, but rather by stipulation. Specifically, I shall pretend that Lewis's entire theory employs a special concept of overall similarity, such that:

For any worlds / and/, and for any time t, if / is exactly like the actual world in respect of its states up to t, and j is unlike the actual world in

respect of some state earlier than t, then / is more overall similar to the actual world than/ is.

The special concept of overall similarity which is partly defined by that condition still does not handle the Oswald-Kennedy problem. There are two fatal difficulties which it fails to cure.

Firstly, in the second of time between Oswald's finger-slip and T some Dallas policeman might have whipped out his gun and shot Kennedy. A world where that happened would not part company from the actual world earlier than the one where Oswald's finger slips and Kennedy survives; and so the "special concept" of overall similarity is irrelevant. We are therefore free to say that the world of the cop-turned-killer is more like our world than is the one where

Kennedy survives; and so, by Lewis's theory, it is false that if Oswald had not killed him Kennedy would have survived his visit to Dallas. Lewis is thus

deprived of his Warrenite counterfactual, not by new evidence out of Dallas but

by the exigencies of his own theory. Secondly, consider the counterfactual "If Oswald had been run over by a

bus at T minus one month, Kennedy would have survived his visit to Dallas." There seems to be no cogent reason why a Warrenite should reject this; and yet it comes out false on Lewis's theory, even when the theory is permitted to insist that any (dis)similarity of particular fact has infinitely more weight, when

comparing worlds, than any later (dis)similarity of particular fact. For now we have a world k in which at T minus one month Oswald dies in an accident, Kennedy is not killed, and the world carries on from there; and a world / in which at T minus three weeks John Doe conceives a plan to kill Kennedy and executes it at about T minus five minutes. The special concept of similarity now favours / rather than k because /'s departure from the course of the actual world occurred later than /?'s; and in addition to that there are all the post-T facts which also make / more like the actual world than k is. So, even with the help of the "special concept," Lewis's theory will not let him say that if Oswald had been killed at T minus one month Kennedy would have survived his trip to Dallas.

396




The Oswald-Kennedy case is not uniquely troublesome for Lewis. The same basic problems are raised for his analysis by any counterf actual in which (a) there is a gap between the time of the antecedent and the time of the consequent, and (b) the truth of the consequent would lead to very large qualitative differences from the actual world.

9. Reconstructing Lewis's Theory

Why should Lewis say anything so implausible as that some worlds where

Kennedy is not killed are more like our world than are any in which someone other than Oswald kills him? Faced with this puzzle, I can only guess that he is really ignoring any differences of particular fact that concern times later than that of the assassination. So when he says that in comparing worlds "we put more weight on earlier similarities of particular fact than on later ones," perhaps he really means: "When we are comparing worlds for purposes of evaluating a

given counterfactual, we consider their similarity to the actual world only in

respect of their states up to the time mentioned in the antecedent of that counterfactual."

That Lewis needs to say something like that is strongly suggested by his treatment of miracles. I have criticized his attempt to secure his position by distinguishing (1) small miracles from (2) large ones; but he might succeed if he relied on the distinction between (1) miracles affecting what leads up to the antecedent-situation in some possible world and (2) miracles affecting what results from that antecedent-situation. Rather than a single line through miracles, that draws a different line for each different counterfactual-antecedent.

If Lewis took this way out, he could no longer offer an all-purpose sphere as representing all relevant similarity-relations amongst worlds. He does have

spheres with other worlds than ours at the centre; but I am contending that even if we consider only what counterfactuals are true in our world, and thus try to construct only a sphere centering on our world, it still cannot be done so as to

provide a basis for a theory of counterfactuals. What we need is, for each time tt a sphere such that the relative distance of a pair of worlds from the centre of the

sphere is a measure of their relative similarity to the actual world in respect of their states up to time t.

If Lewis adopted that position outright, it would solve his

Oswald-Kennedy difficulty and millions like it. For then he could say that some worlds where Kennedy is not killed at all are more like the actual world in

respect of their states before T than is any world where Kennedy is killed by someone other than Oswald. That, on the Warrenite hypothesis, is simply true. Some worlds where Kennedy is not killed differ from ours before T only by a

slip of Oswald's finger, whereas any world where Kennedy is killed by someone other than Oswald must also differ from ours by a good deal of behaviour on the

397



Jonathan Bennett

part of the other killer. Lewis's position is so clearly all right when construed in this way, and so clearly wrong when taken at face-value, that one is forced to

conjecture that he really wants to compare worlds only in respect of their states

up to just before the time referred to in the antecedent of the counterfactual. Let us see what the result would be if Lewis accepted this and modified his

theory accordingly, having a different sphere for each time t. He does mention this as a possible procedure: he remarks that different sorts of necessity correspond to different sub-sets of possible worlds- logical necessity to the set of all possible worlds, physical necessity to those in which the actual laws of nature

prevail, and "worlds that are exactly like [the actual world] at all times up to time t" to "inevitability at time t" (p. 7). This yields an odd notion of

inevitability; but that doesn't matter, because the remark is offered only as decorative and peripheral. The question now is: what becomes of Lewis's theory of counterfactuals if this time-relativizing of his sphere is made structural and central?

(Incidentally, the very fact that Lewis does allude in that marginal way to the notion of worlds which resemble the actual one up to a given time shows that he does not intend to make that notion structural in his own theory. I mention this lest readers should think that my proposal to relativize the sphere must be what Lewis himself intended all along. As further evidence, consider his

wrestlings with earlier/later and with large/small miracles, which would all be otiose if the sphere were time-relative; and also the fact that he does not say that he is relativizing his sphere.)

If we amend Lewis's theory in the manner I have suggested, it gives the

following truth-conditions for counterfactuals:- If t is the latest time mentioned in P, then P -> Q is true if and only if there are (P & Q)-worlds which are more like the actual world in respect of their states up to t than is any (P & ~Q)-world. Or, to put it slightly differently:- Take the sphere of possible worlds which has the actual world at its centre, and in which relative distance from the centre is a measure of comparative dissimilarity to the actual world in

respect of states up to time t; then P-*Q is true if and only if this sphere contains a P-permitting sub-sphere which contains no (P & ~Q)-world.

If Lewis adopted this approach, he would have a problem about what to

say about counterfactuals such as the "kangaroos" one, whose antecedents don't mention times. Also, something would have to happen to his arguments, e.g. for the non-transitivity of -+, which assume that the truth conditions for any two counterfactuals can be expressed in terms of a single sphere. Perhaps these

arguments could be saved by some further theory interrelating the different spheres- this is not a matter I am equipped to discuss. In any case, the suggested relativizing of the sphere has more damaging consequences than that.

If a given sphere expresses worlds' similarity to the actual world in respect of their states up to time t, what basis have we for saying what they are like after tl If no information on that score has been fed into the sphere, none can be

398




extracted from it. Yet we need such information: we need to sort out Q-worlds from ~Q-worlds, and Q may mention times later than t. The only solution I can find is to restrict our spheres to worlds which obey the laws of nature of the actual world.

Lewis would probably resist this. He remarks that he could build into his

system the claim that any world which violates an actual law of nature is further from the centre than any world which conforms to all actual laws of nature, and

says:

I have not chosen to impose any such constraint. I doubt that laws of nature have as much of a special status as has been thought. Such special status as they do have, they need not have by fiat. I think I can explain, within the theory already given, why laws tend to be cotenable, unless inconsistent, with counterfactual suppositions, (p. 73)

Let us set "cotenable" aside, since Lewis's use of it is deviant. What remains is the more general claim that it can be shown- not by stipulation but through proper attention to the notion of a law of nature- that "similarity and difference of worlds in respect of their laws is an important respect of similarity and

difference, contributing weightily to overall similarity and difference" (p. 75). It is indeed good to dispense with stipulations as far as possible, but Lewis's

"explanation" has no force at all once we have relativized our spheres. What he

purports to show is that if two worlds differ in the laws of nature which obtain in them, this will tend to be a big overall dissimilarity between them; but now we are comparing worlds only in respect of their similarity up to time t, and that

range of comparisons is utterly untouched by any differences regarding miracles or law-changes after t. If Lewis is to link pre-t comparisons with postpones, he must require lawlikeness in the worlds in his spheres-presumably by requiring that they all obey the laws of the world at the centre of the sphere.

Apart from wanting to prove rather than stipulate it, Lewis wants the content of his position about laws to be less constraining than the one he thinks is typical of the consequence theory. How much less constraining, he does not

say: his only example is his tolerance of a small antecedent-producing miracle in a world whose only laws are those of the world at the centre of the sphere. Because that approximates to something correct, namely to the insight that one

ordinarily does not need to envisage a history for the antecedent-situation, room should be made for it in the relativized-sphere theory.

To achieve this, we must modify our account of how the spheres are built.

A first stab might be this: in the sphere-for-time-f, centred on the actual world,

(ij each world's distance from the centre is a measure of its similarity to the

actual world in respect of its states up to t, and (ii) each world perfectly obeys the laws of the actual world from t onwards. But if we do not require perfect lawlikeness before ty what do we gain by requiring perfect similarity before t?

Nothing at all; and so we might as well relax condition (i) by replacing "up to t"

by "atf."

399



Jonathan Bennett

Then we have the following theory, which I offer as my "residual possible-worlds theory" of counterfactuals and claim to be a maximal salvage from the theory offered by Lewis: -

If t is the time mentioned in P, then P - Q is true if and only if there is a

P-permitting sub-sphere throughout which P ID Q holds true, in a sphere in which (i) each world's distance from the centre is a measure of its similarity to the actual world at t, and (ii) each world perfectly obeys the laws of nature at t and at all times thereafter.

10. Possible Worlds Versus the Consequence Theory

The residual possible-worlds theory is suspiciously like the consequence theory. But the two do still differ, and the difference favours the latter.

As an aid to comparing them, let us consider each theory as a set of instructions for trying to establish that P -* Q is true, where P refers only to time t.

The consequence theory dictates the following procedure. Try to construct a conjunction (P & R) from which Q is law-derivable, subject to the condition that R is true, concerns only time ty and is cotenable with P. (There are other conditions too, but they needn't be discussed here.) The cotenability requirement raises a difficulty, as I remarked earlier, but one need not solve that in order to see what general strategy the consequence theory requires. It involves starting with P and then gradually adding true conjuncts. At any given stage one might repent of some of one's additions, delete those conjuncts, and thus be free to add others (in so doing, one would be wrestling with some particular cotenability difficulty). But the general picture is one of the cautious lengthening of a conjunction, in the hope that without breaking the ground-rules one can make it strong enough to law-imply Q or law-imply ~Q; and if neither of those can be done, then neither P -» Q nor P -> ~ Q is true.

Now, the residual possible-worlds theory also tells us to try to construct a P-containing conjunction, subject to certain constraints, from which Q is law-derivable. So the theories must differ, if at all, in the constraints they place on the premise-conjunction. Each requires that it contain P, and that it be consistent with all actual laws of nature; and the temporal requirements need not differ. If there is an essential difference it arises from the following fact.

In the picture evoked by the residual possible-worlds theory, one does not gradually lengthen a conjunction by adding truths to it, but rather one repeatedly modifies a conjunction by replacing some of the truths in it by untruths. The residual theory tells us to start with a P-containing conjunction which contains as many truths as possible about the actual world at t, and then, in search of a variant on this from which Q is law-derivable, gradually to replace truths with falsehoods-thus moving from P-worlds which are maximally like to

400




ones which are increasingly unlike the actual world at t. The question of which of two worlds more closely resembles the actual world becomes, in this context, the question of which of two sets of conjunct-switches represents a more drastic overall change. So what we have to investigate is whether a conjunction from which Q is law-derivable can be reached by a less drastic change from the original conjunction than is needed to reach any conjunction from which ~Q is derivable. If so, then P -> Q is true. If the reverse is the case, P->~Q is true. If there is a dead heat, neither is true.

In allowing that one might add untruths other than P to the premise-conjunction, the residual possible-worlds theory countenances the idea of law-deriving Q from a set of premises which include not only P but also other untruths which are not forced upon one by P; and nothing like this is permitted by the consequence theory. The latter, of course, does allow that the law-derivation of Q might proceed through certain intermediate untruths, but these, being law-derivable from P and truths, will not appear in the

premise-conjunction itself. That is the rock-bottom difference between the two theories, and it is

wholly an advantage in the consequence theory. Suppose that someone tried to defend a statement of the form P -> Q by showing the law-derivability of Q from a certain conjunction including P and another untruth S. We might challenge this

by asking "What right have you to help yourself to S? It is not actually true, nor is it something that would be true if P were true." The residual possible-worlds theory allows the rejoinder: "I agree that S is false, and that it isn't forced on me

by P; but still I am entitled to include it in my premise-conjunction (if the other conditions are met), because the overall change which yields this conjunction is less drastic than any which would yield a conjunction from which ~Q is law-derivable." A rejoinder along those lines would be rejected by ordinary intelligent listeners as reflecting a serious misunderstanding of the truth-conditions for counterfactuals.

Stalnaker has pointed out to me that it would be outright inconsistent to defend P -* Q with the aid of an S which "isn't forced on me by P" if that means that P -> S is false according to the original Lewis theory. But we are now

considering not that original theory, which I claim to have refuted, but rather a residual theory in which "S isn't forced on me by P" means something about the

impossibility of law-deriving S from P and certain other premises. I cannot see that the rejoinder which I have put in the mouth of the residual possible-worlds theorist, when understood in that way, involves any inconsistency; though it

does, I have argued, show how far the residual theory still is from being an

acceptable account of counterfactuals. Anyway, suppose that our theorist doesn't make that rejoinder. Suppose

that for some reason he denies that the residual possible-worlds theory countenances the unforced replacement of truth by falsehood, claiming that it involves the addition to P of as much truth as possible and then, for each true S

401



Jonathan Bennett

which could not consistently be added, the addition of ~S. He might explain that if his premise-conjunction seems to contain more falsehoods than does the

consequence-theorist's, this is simply because a conjunction which specifies a

possible world at t must contain either S or ~S for every S which concerns t, so that the possible-worlds theorist's conjunction cannot leave questions about t

open in the way the consequence-theorist's can. On that account of it, the residual possible worlds theory is the

consequence theory. For it now says that P -> Q is true if and only if Q is law-derivable from a conjunction of P with such truths as P allows (and the contradictories of such truths as P does not allow). But that parenthetical clause can be dropped without loss of content; for whatever follows from (P & ~S), where S is ruled out by P, follows from P alone. So the theory says that P -> Q if and only if Q is law-derivable from P and such truths as P allows; but "truths which P allows" are just truths which are, in Goodman's sense, cotenable with P. The notion of world-similarity is now idle, and we have ended up with just a cumbersome version of consequence theory.

*****

I have learned a lot about counterfactuals from Lewis's book. Although I think that his theory fails, his vigorous, imaginative, and candid working out of it makes for interesting reading and also serves the progress of philosophy by helping to establish a significant negative result.

May 1974

402



Documents

Counterfactuals and Possible Worlds