Joseph S. Fulda
A plausible theory of counterfactuals should distinguish between the following four propositions:
(1) If I am rich, then I shall tour the world.
(2) If I were to marry Lorena Bobbitt, I'd have a perfect life.
(3) If I were to marry Lorena Bobbitt, I might not have a perfect life.
(4) If I saw a ghost, I'd be afraid.
(1) and (4) are vacuously true, (2) is false, and (3) is non-vacuously true. Yet the standard semantics used for counterfactuals developed by Lewis and elaborated on by both him and Stalnaker, the possible-worlds account, does not distinguish between (3) and (4). As Joseph Melia has argued,<49>Foot note 3_1 the ontology necessary for Lewis' theory is qualitatively unparsimonious: It «is committed to the unicorns, to the gods, to the ghosts and to the qualia which occur in other possible worlds.» That is to say, it is committed to that which in the actual world would be regarded as impossible. The complexity of Lewis' theory, requiring multiple quantification and spheres of possible worlds from which close possible worlds are to be picked out via the existential quantifier -- a Skolem function, in effect -- or via a selection function à la Stalnaker, is a direct result of the plurality of possible worlds and its qualitatively unparsimonious ontology.
In this paper, we present an alternative truth-functional semantics for counterfactuals which is (a) qualitatively parsimonious in its ontology, (b) requires neither multiple quantification nor a selection function, and (c) gets the truth values of (1)-(4) right. This semantics does not provide an adequate grounding for modal logic, where concerns of necessity and possibility are concerns of logical necessity and possibility, but it serves very neatly for the explication of counterfactuals and, more particularly, subjunctive conditionals.
First, let us classify counterfactuals into three groups: indicative counterfactuals such as (1), subjunctive conditionals such as (2) and (3), and what we shall call -- extending a term from metaphysics -- counteressentials, such as (4). We and others have already defended the case of indicative counterfactuals as a simple and defensible instance of material implication with a false antecedent.<50>Foot note 3_2 A counteressential, as here intended, is any state of affairs that could not have arisen from the actual world by natural laws. Thus our ontology allows blue swans, for mutation and natural selection could have produced such, but does not allow ghosts, for there is no way for them to have arisen from the actual.
Perhaps this explication is more nearly a «possible world,» meaning one that could have arisen rather than one that can be imagined, but to distinguish our conception from Lewis' we will refer to it as a timeline. The key distinction between a timeline and a possible world à la Lewis is that a timeline is rooted in the actual world at some time in the past after which a change consistent with natural laws occurs and the result, projected into the future indefinitely, is a new timeline. It is clear that there is no timeline that could satisfy the antecedent of (4),<51>Foot note 3_3 and equally clear that there are many timelines that could satisfy the antecedent of (2) and (3). (One can, for example, imagine going back and making a significant intervention during Lorena Bobbitt's childhood, among many other possibilities.) Hence, if we accept indicative counterfactuals as defensible instances of vacuous truth represented by the material conditional, we can do so with equal assurance for counteressentials. The real task we face, of course, is explicating the middle case -- subjunctive conditionals such as (2) and (3) which have non-vacuous truth values -- and to this the remainder of this paper is devoted.
We treat subjunctive conditionals as universally general propositions<52>Foot note 3_4 quantified over timelines. Thus (2) is represented ([[forall]]x)(Mx->Px), where x ranges over timelines. We then treat the universal quantifier as an (implicit) conjunction of indicative conditionals (each in its timeline) and it becomes quite clear why (2) is false: At least one of its conjuncts -- the indicative conditional using that substitution instance of x which represents the timeline in which we actually live -- is false, making the conjunction and hence the universal generalization -- i.e., the subjunctive conditional -- false. It is also now clear why (3), represented as ~([[forall]]x)(Mx->Px), is non-vacuously true: It is simply the negation of a proposition that is false, with «might not» clueing us in to its proper representation.
It remains only to show that this explication of subjunctive conditionals prevents Lewis' «counterfactual fallacies.»<53>Foot note 3_5 We will not consider strengthening the antecedent here, since, as Lewis notes, it is subsumed by the transitivity fallacy, which follows:
(5) If Ronald Reagan had been born a Russian, he would have been a Communist.
(6) If he had been a Communist, he would have been a traitor.
(7) If Ronald Reagan had been born a Russian, he would have been a traitor.
If (5) and (6) are taken as material conditionals, we would have a sound argument with a false conclusion, a straightforward instance of the failure of transitivity. But taken as universally general propositions, we do not have a sound argument, since (6) is false, for only in some timelines in which Reagan had been a Communist would he have been a traitor.
The third and final fallacy that Lewis points out is the failure of contraposition. Consider:
(8) If John had gone to the party, Jane would still have gone.
(9) If Jane had not gone, John would still not have gone.
In the presence of (10)-(12) below, the apparently valid argument fails, since (10) & (11) makes (8) true and (11) & (12) makes (9) false.
(10) Jane likes John.
(11) John wants to go to the party.
(12) John avoids Jane.
Yet, if (8) and (9) are taken as material conditionals, the validity of the argument turns on no contingent propositions such as (10)-(12). Taken, however, as universally general propositions, we again do not have a sound argument, since there are timelines in which the instantiation of (8) is false (~(10) is a good start), making (8) itself false.
The central idea is simple enough: Instead of an existential quantifier or an explicit function, we allow natural laws to act as an implicit selection function, with the result being a mathematically cleaner, ontologically leaner, and logically keener theory of counterfactuals.<54>Foot note 3_6
Joseph S Fulda
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