R I C H A R D C R E A T H

C O U N T E R F A C T U A L S F O R F R E E *

(Received 25 June, 1988)

Quine does not like counterfactuals. ~ He thinks them unclear, and so he eschews them. It is enough, he thinks, for science to say of what it is that it is and that it is all that is. There is no need to say of what is not that it is not, or even worse, to say of what is not what it would be if things were other than they are. Quine is, of course prepared to use counterfactuals in the short run, but ultimately they must be abandoned altogether.

Other philosophers, including some of Quine's friends, urge that counterfactuals are so useful, both in science and in everyday life, that Quine should relax his strict standards and embrace whatever unclarity may result. Though friendly to at least some counterfactuals, I shall not go so far. I shall urge instead that a plausible account of counterfactuals can be given using only resources already available within Quine's philosophy. This would mean that without relaxing his standards Quine can have counterfactuals for free.

In order to argue that this is so, we shall need to see first what counterfactuals are and why they are problematic. Second, we shall examine a widely accepted analysis of counterfactuals. Quine rejects this analysis, but seeing how it works and why Quine rejects it will be a useful preliminary step in providing a new account more satisfactory to Quine. The final portion of this paper will sketch and develop that new account of counterfactuals.

As a first approximation we might say that a counterfactual is any sentence which says what would happen under specified conditions, even though those conditions do not in fact obtain. We might regiment such sentences into this form: rIf it were the case that 4, then it would be the case that ~0 ~ or in Lewis's symbolism: re D-, ~p'. For con- venience, call ~ the antecedent and ~0 the consequent. A typical, if somewhat shopworn, example of a counteffactual is: 'ff I had struck that

Philosophical Studies 57: 95-- ! 01, 1989. �9 1989 KluwerAcademic Publishers. Printed in the Netherlands.

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match, it would have lit'. In ordinary life we readily use such claims, especially in evaluating alternative courses of action, and often we unproblematically recognize such sentences as true or false. While counterfactuals are conditional in form, the truth of the whole depends on more than just the truth values of the parts. In the match example at hand, we would want to know whether the match was wet, whether there was sufficient oxygen in the ambient air, and so on. It might be thought that the described auxiliary information is either easily specified or unnecessary. Decades of fruitless philosophic discussion suggests that it is neither. Thus, the first great problem posed by counterfactuals is that of indicating the information required for evaluating them beyond what is contained in the counterfactual itself and the truth values thereof. We may call this the problem of auxiliary information.

Unfortunately, this is not the only problem besetting the counter- factuals. Sometimes we can replace the antecedent of a counterfactual with something logically equivalent in such a way that our ordinary judgements about the truth of the whole are entirely changed. Consider some examples made infamous by Quine. 2

If Bizet had been a compatriot of Verdi, Bizet would have been Italian. If Verdi had been a compatriot of Bizet, Bizet would have been Italian. If Bizet and Verdi had been compatriots, Bizet would have been Italian.

Ordinarily the first would be counted true, the second false, and the third would provoke 'Not necessarily', which presumably counts it as false. Yet the three antecedents seem logically equivalent, and the general expectation is that replacing a component with something logically equivalent should leave the truth of the whole unaffected. That truth is not preserved in counterfactuals when parts thereof are replaced with apparently logically equivalent alternatives we may call the non-equivalence problem. Ultimately, it may require us to revise the way some counterfactuals are regimented. (Provisionally, they were schematized re [3--, ~0Z)

The approach to counterfactuals that is currently most widely

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accepted began in 1970 with Robert Stalnaker's claim 3 that sentences of the form rqi I--l~ ~p~ are true iff in the closest possible world in which r is true, ~p is also true. This assumes (the limit assumption) that there is a r world (i.e., world in which r is true) such that there is no closer r world, instead of an unending series of ever closer qi worlds. Even if there is such a limit it is also assumed (the uniqueness assumption) that there is only one ~b world this close to the actual world. David Lewis detected both assumptions and provided the technical means to circumvent them. 4 The required complications need not detain us yet. It is fairly widely believed that these devices avoid the problem of auxiliary information and that thus, the Stalnaker-Lewis approach legitimates a large and useful body of counterfactuals, namely those that do not involve the problem of non-equivalence.

In any case the Stalnaker-Lewis analysis employs two central notions. The first of these is that of possible worlds, which Quine rejects totally. The other notion is that of closeness or similarity of worlds. The similarity relation involved is in fact a three place relation because we need to be able to say at least that our world is closer to a second world than our world is to a third. Quine does allow for a similarity relation, of sorts, but not one that even could hold between possible worlds. As a consequence, Quine rejects the whole Stalnaker- Lewis approach to counterfactuals.

Curiously, there are within Quine's own epistemology analogs of the notions of possible world and similarity, and these can be used to construct an alternative account of counterfactuals. This means that there is no additional intellectual cost to Quine in sanctioning their use. The proposal will give conditions of truth relative to a theory (and, derivatively assertability conditions) rather than truth conditions sim- pliciter.

The Quinean analog of a possible world is that of a theory. The most natural analog to the actual world in the Stalnaker-Lewis approach would be that theory which comprises exactly the complete body of beliefs that a given person actually holds. Not all theories are this broad. Since we will be relativizing the truth of counterfactuals to a theory, however, a better analog of the actual world would be the theory to which the counterfactual is relativized. Corresponding to the alternative possible worlds are the alternative theories available for

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consideration. There are of course, important differences between theories and possible worlds: theories are less complete. But remember that what is being sought are conditions of truth relative to a theory rather than truth conditions, and for the former the incompleteness of theories is no impediment. The three-place similarity relation has as its analog a notion which is one of the pillars or Quine's epistemology. Science proceeds, we are told, by the experience-prompted modifica- tion of pre-existing belief in conformity with two principles: simplicity and conservatism. According to the latter we are to change our current belief as little as possible; we are to choose the most conservative modification of current theory that we can, other things being equal. Recalcitrant experience and the principle of simplicity, of course, often pull us in the opposite direction, but if the principle of conservatism means anything at all there has to be some sense to the claim that one set of alternative beliefs (theory) is a more conservative modification than is a second such set, at least in comparison to our current theory. This is so close to the similarity relation of Stalnaker-Lewis that a corresponding account of counterfactuals is not difficult to devise: A sentence fl is true relative to a theory T i f f either fl is of the form re VI-* ~0 7 and ~0 is true relative to the most conservative modification of T such ~ is true relative to that modification or fl is a logical conse- quence of T. A sentence fl is assertable iff fl is true relative to a theory which is assertable. When, as is customary, we omit a specification of the theory, T, to which a counterfactual is relativized we may assume that it is to be relativized to that theory which compromises our actual beliefs. While as it stands this account makes the uniqueness and limit assumptions, these can be avoided by devices completely analogous to Lewis's. Lewis, however, must deal separately with a case in which there is no possible world in which the antecedent of the counterfactual is true. We need no analog of this. This is because Quine holds that any sentence can be held true come what may, and afortiori that every sentence is true relative to some potentially assertable theory.

Just to make the proposal a bit clearer, consider a very simple case. Let T be the theory we currently (and reasonably) hold. Assume if you like that T is wholly in the indicative mood. Consider a counterfactual of the form r~ VI~ ~0 7. If Quine's epistemology is workable then we are able to determine which alternative theories involve the least change

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from T. Perhaps each of these are in the indicative mood as well. Of these alternatives take those of whom ~ is a consequence, and of these choose that theory (Call it T') which is the most conservative modifica- tion from T. Is ~p a consequence of T'? If so, then r~ I-]~ ~0 7 is true relative to T, and rO 12~ ~0 7 is assertable as well.

Though the cases are more complicated, the proposed account deals with nested counteffactuals, e.g., rr U]~ (~p U]~ @)7 and r(~b ~ ~p) [3--" 0 7, in a straightforward way. More theories have to be investigated, but that would be expected. Note, however, that not all nested conditionals need be nested counterfactuals. They might for example have the form ~O V]~ (~p D 0 ) 7. This allows us to treat cases discussed by van Fraassen. 5

Relative to a theory, the proposed account does as well as the Stalnaker-Lewis version at resolving the problem of auxiliary informa- tion. It does so, moreover, with far greater ontological economy. In addition, insofar as Quine's epistemology is sound, the proposed account of counterfactuals seems far more helpful than others in discovering which counterfactuals to accept and which to reject.

Just as there are those who complain that the similarity relation is hopelessly vague, there will be those who will worry that the notion of conservativeness is seriously uninformative. Presumably, Quine will not be among the worriers here. He can hardly complain that what is constructed in accordance with the uniform building code upon what is most basic in his own work is in danger of falling from an infirm foundation. I must confess that I am myself somewhat uneasy about conservatism and will be a lot more comfortable when it is satisfactorily clarified. In the meantime, I suppose, both Quine and I shall have to be satisfied if whatever unclarity may remain in standard counterfactuals is attributed to the notion of conservativeness.

Nothing in the foregoing account should suggest that even with the qualifications expressed so far we have thereby resolved all of the problems with counterfactuals. Neither this nor the Stalnaker-Lewis account as yet resolves the problem of non-equivalence. Perhaps that is acceptable. The problem does not infect all or even most counter- factuals, and those counterfactuals most useful in the consideration of alternative courses of action do seem to be more like the match case cited above than like the Bizet-Verdi cases. Even so, perhaps it would

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not be unreasonable to approach the non-equivalence problem in order to see what progress can be made. If the results are only tentative, that is at least no loss.

In considering the Bizet-Verdi cases, the first thing to notice is that they are not in fact expressed in the form, ~If it were the case that ~b, then it would be the case that ~p', which we have been symbolizing re [3--, ~p2 In regimenting the three sentences as we have, we have obscured the differences between the three antecedents, thereby depriv- ing ourselves of an argument that the antecedents are not logically equivalent. Philosophical practice notwithstanding, my guess is that sturdy non-philosophers would not only be able to distinguish the three antecedents, but also to agree among themselves as to what was intended in each case. To be more specific I suppose that when 'If Bizet had been a compatriot of Verdi, Bizet would have been Italian' is typically uttered, the speaker imagines Bizet changing along with enough of the rest of the world as to accommodate this change most economically. The grammatical predicate of the antecedent, however, does not involve change in quite the same way. Indeed, one might rewrite the sentence as: 'If Bizet had been a citizen of the country of which Verdi is in actuality a citizen, then Bizet would have been Italian.' Presumably, the phrase 'in actuality' is an operator indicating that its scope, 'the country of which Verdi is a citizen', is to be evaluated in the actual world (or in the Quinean version, in the theory to which the counterfactual is relativized, presumably our actual theory). Given that, the antecedent as a whole is to be evaluated like the antecedent of 'If Bizet had been a citizen of Italy, then Bizet would have been Italian.' On this reading, the counterfactual as a whole is true, obviously so. The second counterfactual of this set is also an abbrevia- tion of one which contains an actuality operator. But this time the word order in the original has changed; so has what is within the scope of the actuality operator; and the result is a sentence which case can be treated like 'If Verdi had been a citizen of France, then Bizet would have been Italian', which is of course, false.

The non-equivalence problem consisted in the apparent occurrence of counterfactuals with logically equivalent components but with differ- ing truth values. The problem can be avoided, however, by treating these sentences as abbreviations of others which are plainly not

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logically equivalent. In so saying I do not pretend to have given a fully general theory which allows us to recover the unabbreviated forms of

counterfactuals or the scopes of their actuality operators from the common expressions of those sentences. It is rather difficult to provide such a general theory for any interesting part of a natural language, and counterfactuals are no exception in this regard. But that is precisely the

point; there is nothing special about counterfactuals which should make

us reject them. Moreover, the fragmentary logical theory suggested by these remarks appeals to nothing not already available within Quine's

work: we appeal to our current theory (set of beliefs) to discover the semantical evaluation of the actuality clause and then proceed to evaluate the whole counterfactual as outlined in the preceding pages.

Thus, neither the problem of auxiliary information nor the problem of non-equivalence is fatal. The former can be resolved and the latter can be prevented from arising by mobilizing the notions of theory and of conservatism. These notions are already at the heart of Quine's

epistemology, and thus he can have counterfactuals for free.

NOTES

* I would like to thank D. Follesdal, R. Jeffrey, J. Maienschein, B. van Fraassen, and M. White for comments on earlier versions of this paper and for discussion of the ideas involved. Funds to support research leaves during which this was written came from several sources; the NEH (#FB-24865-87), the NSF (#SES 19308), and Arizona State University. All these are gratefully acknowledged. i W.V.O. Quine, Methods of Logic, Revised (New York: Holt, Reinhart and Winston, 1959) 14--15. 2 Ibid. Only the third of these actually appears there. 3 Robert Stalnaker, 'A Theory of Conditionals', Theoria 36 (1970): 23--42. The formulation attributed here is not exactly Stalnaker's, but it is close enough for present purposes. 4 David Lewis, Counterfactuals,(Cambridge, MA: Harvard University Press, 1973). 5 Bas C. van Fraassen, The Scientific Image, (Oxford: Oxford University Press, 1980), pp. 116--7.

Philosophy Department, Arizona State University, Tempe, A Z 85287, U.S.A.