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Counterfactuals and cotenability Gleb, Gary Timothy 1977

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COUNTERFACTUALS AND COTENABILITY by GARY TIMOTHY GLEB B.A., University of Bri t i s h Columbia, 1975 A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF ARTS in THE FACULTY OF GRADUATE STUDIES The Department of Philosophy We accept this thesis as conforming to the required standard THE UNIVERSITY OF BRITISH COLUMBIA August 1977 Gary Timothy Gleb, 1977 In presenting th i s thes is in p a r t i a l fu l f i lment of the requirements for an advanced degree at the Univers i ty of B r i t i s h Columbia, I agree that the L ibrary shal l make it f ree l y ava i lab le for reference and study. I fur ther agree that permission for extensive copying of th is thes is for scho lar l y purposes may be granted by the Head of my Department or by his representat ives . It is understood that copying or publication of th is thes is for f inanc ia l gain sha l l not be allowed without my wri t ten permission. Department of Philosophy The Univers i ty of B r i t i s h Columbia 2075 Wesbrook Place Vancouver, Canada V6T 1W5 August 29 r 1977 i i Abstract If philosophers had an acceptable theory of counterfactuals, counterfactuals would be an extremely useful philosophical tool. Unfortunately, analysis of the truth-conditions of counterfactuals has proved to be a d i f f i c u l t task. I examine Nelson'Goodman's attempt in Fact, Fiction, and Forecast to develop a criterion of truth for counterfactuals, an attempt which ended with the discovery of a notorious problem, that of cotenability. This problem arises directly out of Goodman's inclusion of what is known as the "cotenability condition" within his tentative criterion. I explore in some detail the evidence that Goodman adduces in favour of this coniiit i o a condition, and in doing so, argue that the cotenability condition as i t stands is viciously circular. However, I also argue that this evidence is best seen as giving rise to two distinct problems, of which the solution to neither requires use of the cotenability condition. Resolution of the f i r s t , I claim, ultimately depends on the notion of explanation. With respect to the second, on the other hand, I contend that i f the approach I suggest is borne out, then no modification of Gbddman's criterion is necessary, other than that required to resolve the f i r s t problem. I l l Table of Contents 1. Introduction 1 2. Counterfactuals and Conditionals 2 3. Goodman and the Problem of Counterfactuals 5 4. On the Road to the Ideal S 9 5. Cotenability 12 6. The Problem of the S-related Counterfactuals 15 7. The Problem of the Undercutting Phenomenon 22 8. The Missing Link (1) 26 9. The Missing Link (2) 34 10. An Approach to the Undercutting Phenomenon Problem 43 Bibliography 51 iv Acknowledgements I would like to thank my supervisor, Michael Beebe, and Steve Savitt for their comments on preliminary drafts of this thesis, as well my wife, Rosslyn, for her care and patience throughout i t s creation. 1 1. Introduction If philosophers had an acceptable theory of counterfactuals, ' counterfactuals would be an extremely useful philosophical tool. Unfortunately, the above i s both true and counterfactual. Says Nelson Goodman: a solution to the problem of counterfactuals would give us the answer to c r i t i c a l questions about law, confirmation, and the meaning of potentiality. ([10], p.3) However, the three decades since his own attempt, which ended in despair, have not produced a generally acceptable theory of counterfactuals. Goodman's ground-breaking attempt to discern their truth-conditions ended with the discovery of an exceedingly d i f f i c u l t problem, that of cotenability ([10], esp. pp.13-16). Philosophers have disagreed over the nature of this problem, and have advocated different solutions, none of which, I believe, are successfu>il(cf. e.g. Rescher [18]; Sellars [19]). Recently, others have abandoned Goodman's general approach for an analysis couched in terms of possible worlds and a notion of comparative similarity (Lewis[14]; Stalnaker[20]). However, this analysis appears afflicted with grave, even f a t a l problems arising out of the requisite notion of similarity (Bennett[3]). In light of the d i f f i c u l t i e s facing this newer view, I suggest a reappraisal of the Goodman approach. Unlike Goodman, however, I have a more sanguine view of this matter: the cotenability problem, 2 I believe, can be solved. The key to this problem, I shall contend, is that i t is the confused and misshapen product of lumping together two distinct problems, each of which, though formidable in i t s own right, appears soluble. A real advance, I argue, could be made i f the two were pryed apart, thus exposing their distinct natures and preventing the matters raised by each from obscuring those of the other. Indeed, the core of my argument is directed towards this separation. However, in addition,,I shall discuss what appear to me to be the most promising routes towards resolving each problem, although I do not claim, in either case, to have a f u l l solution. 2. Counterfactuals and Conditionals What are counterfactuals ? They are conditionals of some sort, but what sort There is no simple answer to this question. It has long been recognized that many so-called " counterfactuals" do not l i t e r a l l y deal in "counterfacts", that i s , have false antecedents or consequents*(Chisholm[4], p.236). They do, however, carry some presupposition of belief by the utterer that at least the antecedent is false. My discussion here follows that of Lewis ([14], pp.3-4) closely. 3 Says Lewis: Counterfactuals with true antecedents — counterfactuals that are not counterfactual — are not automatically false, nor do they lack truth-value ... Granted, the counterfactual constructions of English do carry some presupposition the antecedent is false. It is some sort of mistake to use them unless the speaker does take the antecedent to be false, and some sort of mishap to use them when the speaker wrongly takes the antecedent to be false. But there is no reason to suppose that every sort of presupposition failure must produce automatic f a l s i t y or a truth-value gap. ([14], p.3) Another eommbnrfeature i s that counterfactuals are often stated in the subjunctive. However, while this mode of construction may be a sufficient feature of counterfactuals, that i t is not necessary is illustrated by Lewis' non-subjunctive, "No Hitler, no A-bomb" ([14], p.4). Complicating this issue is M.R. Ayers' contention that no philosophical interest resides in distinguishing counterfactuals from other conditionals. He argues that: philosophers who are now s t i l l attempting to solve the so-called problem of counterfactuals or subjunctive conditionals by finding a special analysis for one or the other of these classes of statement, or by giving a special account of their significance or verification, would do better to widen the scope of their inquiry, and try instead to provide us with a philosophical description, which, i f i t applies to an empirical conditional, does so regardless of whether the condition i s f u l f i l l e d or unfilled, and of whether the statement i s expressed in the subjunctive or in the indicative mood. ([2], p.264) 4 Hence, i f Ayers i s correct, our discussion of cotenability should include some consideration of i t s relation not just to counterfactuals, but to conditionals in general. The only way to refute such a claim — that i s , that there are no interesting differences between counterfactuals and, say, indicative conditionals — i s to find interesting differences. As Lewis notes, an example i s supplied by' Ernest Adams, who contends that of the following conditionals, the f i r s t , an indicative conditional, i s likely true, and the second, a counterfactual, i s li k e l y false: 1. If Oswald did not k i l l Kennedy, then someone else did. 2. If Oswald had not k i l l e d Kennedy, then someone else would have. ([1], P. 90) With Lewis, therefore, I conclude that: there are really two different sorts of conditional; not a single conditional that can appear as indicative or as counterfactual depending on the speaker's opinion about the truth of the antecedent. ([14], p.3) The task which remains — spelling out a sound set of distinguishing marks for counterfactuals — is not one I shall undertake. On the assumption that we have a solid grasp of counterfactuals, and that this intuition is philosophically justi f i a b l e , I shall proceed with a discussion of cotenability. Our i n i t i a l set of characteristics — that counterfactuals carry some presupposition of the antecedent's falsehood, and are usually expressed in the subjunctive — though rough-and-ready, w i l l have to serve as f i r s t approximation. Following Lewis I shall use V L J t / ' to represent the counter-factual connective and purely grammatical transforms thereof. It is read as "If i t were the case that . .. ., then i t would be the case that I shall introduce other symbols and technical apparatus when necessary. 3. Goodman and the Problem Of Counterfactuals What is the problem of counterfactuals ? Material conditionals are true i f their antecedents are false; however, we often deny counterfactuals even though their antecedents are false, or are believed to be false. For example, we assert: 3. There i s no moon there are no solar eclipses, and reject: 4. There i s no moon { there are solar eclipses. despite the fact that we know that "There i s no moon" i s false. Counter-factuals, therefore, are not truth-functional. What is the nature of 2 their truth-conditions ? Goodman's guiding intuition i s that "a counterfactual i s true i f a certain connection obtains between the antecedent and consequent" ([10], pp.7-8). This connection, as he sees i t , can be analysed in inferential terms. That i s , he believes i t to be expressible in a truth-criterion of the following form: 2 This, of course, i s not the only problem peculiar to counterfactuals. However, with Goodman, I shall ignore those special d i f f i c u l t i e s assoc-iated with counterfactuals with problematic antecedents, such as counter-identicals and countercomparatives (cf.[10], pp.5-6), and w i l l stick to counterfactuals of a straightforward sort, e.g. (3) and (4). 6 a counterfactual is true i f and only i f i t s antecedent, some laws, logical or empirical, and a description of relevant conditions, permitethe derivation of the consequent. Goodman uses 'A' for the antecedent, 'C' for the consequent, and 'S' "for the set of statements of the relevant conditions or,. indifferently, for the conjunction of these statements" ([10], p.9). With minor modifications, I shall follow these conventions. In addition let me introduce, as an expository device, the notion of the set of relevant conditions or situation — c a l l i t 'K' — in which the truth-value of a given counterfactual is to be assessed. Goodman's criterion, so rephrased, looks like this: a counterfactual i s true i f and only i f A, some laws, and some K-describing S, entail C. Beside the conventions mentioned above, I shall follow these: (i) 'S1' w i l l be used to represent e x p l i c i t l y individual members or, as the context demands, conjunctions of members of S; and (i i ) f K j ' w i l l be used to represent distinct situations. As we shall see, not every K-description w i l l be satisfactory, hence the criterion must be made complex. Various conditions w i l l be added which must be met by any such description before i t is accepted as counterfactual-supporting. For the moment, however, let us dub any acceptable K-description for a given counterfactual :an 'S-ideal set', or an 'ideal S', to distinguish i t from the imposters we shall be considering. Three points to note. F i r s t , one should not assume the necessity of a non-empty S-ideal set for every true counterfactual: some may be true, as Goodman observes, because A and some laws alone entail C 7 ([10], p.17). Call these 1S-independent' counterfactuals. Second, one should not assume that a counterfactual, i f true, i s always supported by the same ideal S, that i s , that i t can be true in situations f i t t i n g only one description. It is apparent that counter-factuals may be true for different reasons in different situations. For example, 5. I throw this switch { ^ the light turns on may be true in one situation because the light switch i s properly connected; and in another, because snapping the switch, though ineffective in i t s e l f , w i l l cause, by pre-arranged signal, an accomplice in the darkness to make the real connection. Finally, one should not believe that a true counterfactual is always supported by a unique S in any K. It seems likely that many non-equivalent S-ideal sets can be found in K i f a counterfactual i s true, i f only because statements of irrelevant fact may be included in an ideal S. However, in the cases to be considered, the following w i l l be assumed: i f a counterfactual is true in situation K. because of the J existence of an associated non-empty S-ideal set, then i t w i l l be supposed that there i s only one such set — c a l l i t 'ideal S_.'. There is no reason to believe that this i s always true, as I have suggested, but in assuming this I gain simplicity of exposition without, I believe, sacrificing certainty of result in the cases to be considered. 8 Besides employing a description of K, the A-C connection has another significant feature: i e is law-dependent. From Goodman's discussion i t i s clear that he lumps under the category of laws both logical laws, or rules of inference, and natural, physical, or causal laws (henceforth disjunctively referred to as empirical laws). This is implied by his warning that in the usual case the A-C connection i s not purely logical because some of the laws employed in the inference from A to C w i l l be empirical in nature ([10], pp.8-9). A peculiarity demanding explanation is that Goodman apparently countenances the use of empirical laws as rules of derivation. With regard to 6. Match m is scratchedQ^m lights he remarks that: The principle which permits inference of That match lights from That match i s scratched. That match i s dry enough. Enough oxygen i s present. Etc is not a law of logic but what we c a l l a natural or physical or causal law. ([10], pp.8-9) The role attributed to the empirical law here is ambiguous: i t could be either that of premise or of inference-rule. However, later on Goodman argues that: 9 the distinction between [the] connecting principles and the relevant conditions is imprecise and arbitrary; the 'connecting principles' might be conjoined to the condition-statements and the relation of the antecedent-conjunction (A'S) to the consequent thus made a matter of logic. ([10], p.17) implying that the role i n i t i a l l y attributed to the empirical law was that of inference-rule, not premise. This idea, that of treating empirical laws as inference principles, has been advanced in various forms by Schlick, Ryle, Dray, and Toulmin, according to Hempel ([11], pp.354-356). I shall duplicate Goodman's tolerance of this view, although in general I shall treat empirical laws as statements. 4. On the Road to the Ideal S The completion of Goodman's analysis saddles him with two tasks: (i) discovering the conditions on an ideal S; and ( i i ) defining empirical laws ([10], pp.8-9). From our previous discussion (Section 3) i t should come as no surprise that Goodman argues, as a preliminary step towards ( i ) , that an ideal S contains only true members: We do not assert that [a] counterfactual i s true i f the circumstances obtain; rather, in asserting the counterfactual we commit ourselves to the actual truth of statements describing the requisite relevant conditions. ([10], p.8) On the other hand, an ideal S cannot always contain every statement true of K, since in cases where A is false "among the true sentences i s the negate of the antecedent, so that from the antecedent and a l l true sentences everything follows" ([10], p.9). Indeed, as 10 i t turns out, (i) is more complex a task than i t f i r s t appears, for cases arise in which certain tentative K-descriptions (a) t r i v i a l l y permit the derivation of C or (b) support false counterfactuals. The second task, one I shall not undertake, consists of discovering those characteristics which separate empirical laws, as well as a wider class of law-like generalizations, from non-law-like generalizations (cf. [10], pp. 17,-27; Chisholm [5]). Instead, I shall take the concepts of empirical law and law-like generalization as undefined (although not undefinable). After a terse but lucid survey of cases of kinds (a) and (b) Goodman advances the following criterion: a counterfactual is true i f and only i f there i s some set S of true sentences such fehat S is compatible with C and -C, and such that A'S i s self-compatible and leads by law to C; while there i s no set S* compatible with C and -C, and such that A'S* is self-compatible and leads by law to -C. ([10], p.13) together with the proviso that: neither S nor S* follows by law from -A ([10], p.13) added in response to a counterexample raised by Parry in [17]. One w i l l notice that Goodman's original intuition has become more elaborate, partially because of a logical feature of counterfactuals and partially because of problem cases f a l l i n g under (a) and (b). Fir s t of a l l , not only must there be an inference-route from A through some K-describing S to C ( c a l l this the criterion's positive condition), 11 but no such route from A to -C ( c a l l this the negative condition). Why this addition ? As Goodman notes, counterfactuals of the form <j> \ tjf and ^ [ J - ^ a r e contraries: only one can be true in a given K, although both can be false. Hence we must take care that "our criterion not only admits the true counterfactual we are concerned with but also excludes the opposing conditional" ([10], pp. 12-13) . Secondly, the criterion employs the notion of compatibility, which requires explication; As mentioned, Goodman wishes to exclude any K-description which permits t r i v i a l derivation of C. One sort of t r i v i a l derivation, already described, i s that which results when A'S entails P"-P. Another sort, the result of employing an S which entails violation of an empirical law — c a l l i t 'L' — occurs when A'S entails -L, or equivalently, when A-S-L entails P'-P ([10], pp.10-11). Hence, given Goodman's remarks, we can define the following:. (i) (fils logically incompatible with S, and is logically non-self-compatible i f and only i f j6"S entails P'-P; (i i ) <P±s physically incompatible with S, and etc. i f and only i f ^'S'L — but not ^ -S alone — entails P'-P; and ( i l l ) $ is compatible with S, and ^ 'S i s self-compatible i f and only i f ^ is neither logically nor physically incompatible with S. Having discussed the rationale for the amendments to the criterion, especially the conditions on S, I shall presuppose their application but avoid their mention in what follows. 12 5. C o t e n a b i l i t y These m o d i f i c a t i o n s a s i d e , the c r i t e r i o n . i s s t i l l d e f e c t i v e . I t s f a i l u r e to r e j e c t c e r t a i n K - d e s c r i p t i o n s which support f a l s e c o u n t e r f a c t u a l s i s both s p e c t a c u l a r and n o t o r i o u s . The rock upon which the c r i t e r i o n founders i s the rock of c o t e n a b i l i t y , and a durable rock i t has proved to be ; What i s the problem of c o t e n a b i l i t y ? Goodman's p r e s e n t a t i o n of i t i s b r i s k and l a c o n i c . I t w i l l p r o f i t us to see the problem as Goodman describes i t , then to explore p a r t s of that d e s c r i p t i o n i n d e t a i l . Says Goodman: ..i . many statements that we would regard as d e f i n i t e l y f a l s e would be true according to the s t a t e d c r i t e r i o n . As an example, consider the f a m i l i a r case where f o r a given match m, we would a f f i r m [ 6 . Match m i s scratchedQf^m l i g h t s ] but deny [ 7 . Match m i s scratchedj3^m i s not dry] According to our t e n t a t i v e c r i t e r i o n , statement [7 ] would be q u i t e as true as statement [ 6 ] . For i n the case of [7 ] we may take as an element i n our S the true sentence Match m d i d not l i g h t which i s presumably compatible w i t h A (otherwise nothing would be r e q u i r e d along w i t h A to reach the opposite as consequent of the true c o u n t e r f a c t u a l statement [ 6 ] . As our t o t a l A'S we may have Match m i s scratched. I t does not l i g h t . I t i s w e l l -made. Oxygen enough i s present ... e t c . and from t h i s , by means of a l e g i t i m a t e general law, we can i n f e r I t was not dry. 13 And there would seem to be no suitable set of sentences S* such that A'S* leads by law to the negate of this consequent. Hence the unwanted counterfactual is established in accord with our rule. ([10], pp.14-15) He concludes: the trouble is caused by including in our S a true statement which though compatible with A would not be true i f A were. Accordingly, we must exclude such statements from the set of relevant conditions; S, in addition to satisfying the other requirements already la i d down, must be not merely compatible with A but 'jointly tenable' or cotenable with A. A is cotenable with S, and the conjunction A'S is self-cotenable, i f i t is not the case that S would not be true i f A were. ([10], pvl5) But this requirement is disastrous, since i t demands that selecting 3 S (and presumably S* as well) requires determining the truth-values of an indefinite number of counterfactuals, involving us, as Goodman notes, "in an i n f i n i t e regressus or c i r c l e " ([10], p.16). This is the cotenability problem. Is this requirement necessary ? The answer, I believe, is 'No !', but establishing this w i l l require patient effort. For the moment, however, let us briefly consider Goodman's match argument. He notes that in the 'familiar case' we affirm (6) and reject (7). Why ? Let us examine our unwashed intuitions. With regard to (6), we know that in the right circumstances, that i s , when match m is dry, Why ? Just as we do not wish to establish a false counterfactual with a non-cotenable S which allows inference of C, we do not want to reject a true counterfactual on the basis of some non-cotenable S* which permits derivation of -C. 14 oxygenated etc., scratching the match w i l l cause or causally explain the lighting of m. It is upon this fact, which is causal in nature, that we affirm (6). Why then do we reject (7) in the same set of circumstances ? Clearly, that a match i s oxygenated, scratched, and unlit does not cause or causally explain i t s 'non-dryness'. Some sort of causal fact, present for (6), i s absent for (7), given the circumstances as described. This i s not to deny, of course, that there are imaginable situations in which (7) would be true. One could suppose, in addition to the features of the 'familiar case', the presence of a special fire-prevention device, which» upon detecting the noise of a match being scratched, directs a powerful jet of water towards the noise's source. In this situation i t is plausible to affirm (7); but here again we base this judgment on the presence of features by which the match's potential wetness could be caused or causally explained. Therefore, i f these insights are on track, the solution to the di f f i c u l t y raised by Goodman's match argument, for at least some counterfactuals, i s to be found in causation and related areas. Goodman, of course, does not take this route. Rather, he hopes to analyse the A-C connection in an inferential manner, using only notions such as logical and physical compatibility, as well as that of empirical law. However, since Goodman's criterion constitites an analysis of counterfactual connection, and since the criterion establishes both (6) and (7) when i t should only establish the f i r s t , i t follows that the 15 conditions described in the 'analysans' cannot be sufficient for the 'analysandum', though their necessity i s unchallenged. Some feature of the connection, some v i t a l link, escapes the criterion as i t stands. Our intuitions identify i t as causation or some related notion, at least in the 'familiar case'; Goodman, on the other hand, identifies i t as cotenability. In the next two sections, we shall examine precisely . why Goodman is mistaken. 6. The Problem of the S-related Counterfactuals Let us look closely at Goodman's match argument. Let ^  be "Match m is scratched", $ be I'm lights", S 1 be "m is dry", S 2 be 3 "m i s oxygenated", and S be "m is well-made". Moreover, let our general causal law, presumably: L. Scratching dry, oxygenated, well-made matches causes them to light 4 be interpreted as: L'. (x)(Match x is scratched "xis dry " x is oxygenated x i s well-made 3 x lights) Our K, that i s , the 'familiar case', i s such that j> and tji are false 1 2 3 while S , S , and S are true. L' can be regarded either (i) as the logical form of L, or ( i i ) as an entailment of L. The match argument works regardless of which view we adopt. If ( i ) , the argument proceeds as described; i f ( i i ) , since (a) L entails L', and (b) L is one of our true causal principles, we can simply infer L', and the argument proceeds as above. This indicates that the argument i t s e l f , and therefore any solution, does not turn in any obvious way on a particular conception of the logical form of causal laws. ~*L should actually be interpreted as: L". (x) (x is a match " x is scrat-ched * x is dry ' x is oxygenated ' x is well-made 3 x lights). However, I employ L' for simplicity of exposition. 16 a n c e Goodman assumes that: 6. March m i s scratchedQ^m l i g h t s { 1 2 3*L S , S , S J constitutes an i d e a l K-description, and that there i s no S* permitting inference of - ifr . However, as Goodman notes, since -if) i s actually true i n K, <£s 2, S 3, -ffy i s also.acceptable to the c r i t e r i o n as i t stands. Si ( s 2 , S 3, - f j}and 0 , together with L', e n t a i l -S , and there i s no appropriate S*, 7. Match m i s scratchedD^m i s not dry i s established as wel l . Moreover, (7) i s not alone. A number of equally acceptable K-descriptions, each formed through the union of a 1 1^ some subset of { s \ S 2, S"^ } , establish a range of bizarre counterfactuals i n K: e.g. 8. Match m i s scratched m i s not oxygenated 9. Match m i s scratched m i s not well-made (?) and even 10. Match m i s scratched either m i s not dry or m i s not oxygenated or m i s not well-made (??) (takingtyfy alone as the K-description), a l l of which are i n t u i t i v e l y f a l s e . In order to f u l l y convey the implications of this argument, l e t me introduce the notion of an 'S-related' counterfactual. As we have seen, i f a counterf actual ^D ^ 0 is true i n a given K, i t i s usually because some non-empty i d e a l S exists which, together with <j) and some laws, e n t a i l s . Given such an S and oSffo lf>> we can construct an S-related counterfactual by (i ) retaining ^ as 17 antecedent, and ( i i ) employing the negate of some S 1, where S1^. S, as consequent. The general form of an S-related counterfactual of i s : where S 1 is a member, or conjunction of members, of S. For any K_ in which <£>U^ ty is true because of the presence of an ideal S.. , we can construct an S-related 'family' of counterfactuals. Of course, as we noted in Section 3, there may be many distinct situations in which ^ O ^ i s true, hence there w i l l be a distinct K-description S^...Sn for each such K^...K^, provided ^D"^ is true for different reasons in every K... Thus 0 C J " ^ ty m a Y possess many distinct S-related families, each associated with a particular K.. J However, this complication w i l l be ignored in what follows. The defect illustrated by the match argument may now be described as follows: i f (i) <f)\j£} ty is true in K.., ( i i ) <f) D " ^ ty i s n o t S-independent (is supported by some non-empty ideal S^) , and ( i i i ) (fj is false in K.., then there exist criterion-acceptable K-describing sets — formed through the union of {"ty} a n c* s o m e subset of the ideal S. — which support each of the S.-related counterfactuals in K.. J J J Unfortunately, the latter ought to be false, at least in the match example, and — as we shall see — in the general case as well. Let us c a l l this the "S-related counterf actuals'1' problem. What deficiency does this betray in the criterion ? Why does the criterion support the true ty as well as i t s S^-related counter-parts in-Kj. Let us review Goodman's diagnosis. With respect to the 18 unacceptable (7) he says: The trouble is caused by including in our S a true statement [i.e. - (fj ] which though compatible with A would not be true i f A were. ([10], p.15) That i s , - (ff should not be included in any K-description because i t is not cotenable with (j} It must be granted that there is something plausible about Goodman's remedy. Nevertheless, I believe i t is wrong, although demonstrating this w i l l require pulling the roots of this illusory plausibility painstakingly, one-by-one. How well does the cotenability condition fare as a solution to the S-related counterfactuals problem ? As we have already observed, Goodman admits by adding this condition to the criterion i t appears we find ourselves in a regress or circle because "we can never explain a counterfactual except in terms of others" ([10], p.16). However, he doesn't quite close the door on this issue: he considers the possibility that the criterion could be revised: so as to admit f i r s t those that depend on no conditions other than the antecedent, then use these counterfactuals as the c r i t e r i a for the cotenability of relevant conditions with the antecedents of other counterfactuals, and so on. ([10], p.17) The motivation behind this suggestion, however, i s unclear. That i s , Goodman may perceive the problem facing himself in at least two ways, each of which admits a different interpretation of this suggestion, (i) On the one hand, he may not be convinced that, in the f i n a l analysis, 19 the cotenability condition as i t stands produces a vicious cir c l e or an infinite regress, despite appearances to the contrary. That i s , he may believe that given the cotenability condition as i t stands, checking for cotenability involves no ci r c l e , but only an arbitrarily long regress, terminating with S-independent counterfactuals, a fact to be made apparent through an appropriate revision of the criterion, ( i i ) On the other hand, Goodman may be certain that the cotenability condition as i t stands produces vicious circularity or i n f i n i t e regress, hence that any solution to the S-related counterfactuals problem on the basis of cotenability must involve a radical overhauling of the notion of cotenability as well as his treatment of counterfactuals. Is (i) an open alternative ? The answer is "No": i t can be shown that the cotenability condition as i t stands produces vicious circularity. Why ? Let us f i r s t determine what cotenability amounts to. 'If Goodman actually adheres to ( i ) , then he is convinced that judging the truth-value of a counterfactual depends, in part, upon determining that a l l the S 1 i n S are cotenable with A: that i s , that for a l l S 1 in S, i t is not the case that S 1 would not be true (or the case) i f A were true (or the case). Now, ignoring for the moment "It is not the case that", "If A were the case, then S 1 would not be the case", is logically equivalent to, 20 i 6 "If A were the case, then -S would be the case". Hence the cotenability requirement is equivalent to: for a l l S 1 in S, i t is not the case that -S 1 would be the case i f A were the case or, employing the ' 1 }^ 1 symbol: for a l l S 1 in S, i t is not the case that A f"T^-SX. The requirement, in other words, amounts to demanding that the S-related counterf actuals of <j> CJ^^be rejected as false bef orem^ ft is accepted as true. "If there is any doubt about this, consider the following. When discussing the law of excluded middle, that i s , Either S or not-S for, say, "Jack f e l l " , Either Jack f e l l or Jack did not f a l l , we assert: (i ) I f i t were not the case that Jack f e l l , then i t would be the case that Jack did not f a l l and ( i i ) I f i t were the case that Jack did not f a l l , then i t would not be the case that Jack f e l l . But (i) and ( i i ) entail: ( i i i ) I t would not be the case that Jack f e l l i f and only i f * i t would be the case that Jack did not f a l l provided nothing lurks in the innocuous-looking grammatical moves from "were" to "would" and vice-versa. This suggests that (iv)It would not be the case that S i f and only i f i t would be the case that not-S is analytic. 21 Cotenability's vicious circularity can now be demonstrated. Remember that in the match example stands for "Match m is scratched", • 1 2 (1) for "m lights", S for "m is dry", S for "m is oxygenated", and S for "m is well-made". (i) In determining the truth-value of in the 'familiar case', given the criterion as .i t now stands, we must establish that, besides meeting other requirements, a l l the members of are cotenable with , before we can accept this K-description as S-ideal. ( i i ) However, establishing cotenability is equivalent to rejecting as false those S-related counterfactuals constructed fromjs 1, S 2, S 3^ , that i s (7), (8), (9), (10) etc. (Cf. pp. 15-16) ( i i i ) In turn, rejecting those counterfactuals in the 'famili'ar case' means demonstrating that certain K-descriptions which support them are illegitimate because, as Goodman observes, they include a certain truth, that i s , -ijj , among their members which is non-cotenable with . (iv) However, since demonstrating that - ft is cotenable with (^f would mean showing that i t is not the case that <^Q^-(- ^ ) , demonstrating that - (j/ is not cotenable with ^> means showing that i t i s not the case that ( i t i s not the case that <j)t& -(- (fj ))» or equivalently, that ^CT"^0« ' We have come f u l l c i r c l e , and the circle is vicious: i t cannot be broken by any S-independent counterfactual. What about alternative ( i i ) ? Although I admit that the argument offered above does not rule out, in any straightforward way, this interpretation of Goodman's suggestion, that i s , the possibility of radically overhauling the cotenability condition and Goodman's treatment 22 of counterfactuals in terms of some step-by-step procedure based on S-independent counterfactuals,^ I am afraid that I must agree with Goodman when he says that "this idea seems i n i t i a l l y rather unpromising in view of the formidable d i f f i c u l t i e s of accounting by such a step-by-step method for even so simple a counterfactual as If the match had been scratched, i t would have lighted" (]10], p.-17). 7. The Problem of the Undercutting Phenomenon We have seen that the cotenability condition as i t stands places hopeless demands on the criterion. As a solution to the S-related counterfactual problem, therefore, i t s employment seems akin to using an H-bomb to capture a rabbit: just as the H-bomb would destroy the rabbit, the original cotenability condition destroys the possibility of determining the truth-value of a given counterfactual. However, as we saw earlier, our intuitions t e l l us that in the match example, the S-related counterfactual (7) is false while (6) i s true because the former lacks in f u l l the underlying A-C connection possessed by the latter. Indeed, in many cases this appears to beea feature of the S-related counterf actuals of a given ^Q^^when ^ C r ^ ^ i s true. For example, suppose that Martin, a frierid, leaves the key in the ignition of his Alfa Romeo. Provided that the Alfa i s in working order, i t is 1^ thank Steve Savitt for pointing this out to me. 23 true that: 11. The key is turned [ \^ Martin's Alfa starts and false that: 12. The key is turned \ the Alfa's starter malfunctions since turning the key, in this situation, would start the car but not bring about a starter malfunction. On the other hand,.if our intuitive judgments about (6) and (7), or ^11) and (12), were based on the original cotenability condition i t is impossible that they could be made at a l l . In view of the formidable d i f f i c u l t i e s facing the cotenability approach, therefore, l e t us set i t aside, and turn instead to a search for the causal feature possessed by (6) and (11) but lacked by (7) and (12). For convenience, let us dub this feature of the A-C connection underlying (6) and (11) the "missing link". That there is something plausible about Goodman's introduction of the cotenability condition was noted earlier (Section 6). However, given the relatively straightforward observations made about the causal nature of the missing link in Section 5, this residual pl a u s i b i l i t y remains somewhat mysterious. The source of this plausibility,. I believe s is a feature of the S-related counterfactuals I have hitherto avoided discussing, a feature that Goodman may have observed, but failed to identify clearly. Indeed, this feature is such that i t appears to force use of the cotenability condition independently of any consideration of the S-related counter-factuals problem or of the missing link. What is i t ? 24 We noted that in the familiar case (7) and the rest_of ..the S-related counterfactuals are false, while (6) is true. Indeed, isolating the basis for this fact and modifying the criterion accordingly is the gist of the S-related counterfactuals problem. However, we have also observed that in other, less familiar situations, at least some of the S-related counterfactuals would be true. An example of this was our fire-prevention device case: in that situation (7) was true. But notice this as well: in the same situation i t appears correct to assert that (6) in this situation can be explained this way: "Since the fire-prevention device is present, i f the match were struck, i t would be wet. But wet matches normally can't light, even i f they are scratched. Hence, i t is not the case that i f the match were scratched, i t would light". The upshot of this i s that in certain situations >K the truth of (7) "undercuts" the truth of (6). Does this "undercutting" phenomenon hold for other counterfactuals as well ? Remember the situation discussed earlier in which we decided (11) is true and (12) is false. Imagine that this situation i s now altered in the following way: suppose that an envious acquaintance places a small bomb on the Alfa's starter, wired to the ignition switch. In this new situation we would assert (12) and deny (11), reasoning thus: "Since the bomb w i l l go off when the key is turned, destroying the starter, i f the key were turned, the Alfa's starter would malfunction. But cars without starters cannot turn over. Hence, i t i s not the case that i f the key were turned, the Alfa would start". Consideration of this and other cases, I believe, w i l l bear out 25 the following contention: in many situations K, i f an S-related counterf actual of ^D^^ I s true, then i t s truth undercuts the truth of (f>^\^ lp. In Section 10 I shall attempt to provide an analysis of this phenomenon, in the course of which I shall try to isolate some of the features of the situations in which i t can occur. Our original problem, as demonstrated by the match argument, was that the criterion -automatically establishes e.g. (7) when i t establishes the true (6), a problem we hope to solve not with cotenab-i l i t y , but by finding the missing link. However, we have discovered a feature of S-related counterfactuals which, independent of our f i r s t problem, threafens reinstatement of the cotenability condition: the undercutting phenomenon. Why ? The undercutting phenomenon entails that in many situations K, i f an S-related counterf actual of | fjj is true, its truth undercuts the truth of <f) I (jf. Hence, when determining the truth-value of ^ Q^^in any such K, we must ensure that i t s S-related counterfactuals are false. One method of ensuring this is Goodman's: that i s , the cotenability condition, at least in i t s original form. We have in this, I believe, an explanation of the original cotenability condition's intuitive plausibility, despite i t s absurdity as a solution to the specific d i f f i c u l t y raised by the match argument. Let us c a l l our new d i f f i c u l t y the problem of the "undercutting phenomenon". Are we therefore stuck with cotenability ? Is there no way of determining that S-related counterfactuals are false without stooping to "explain a counterfactual ... in terms of others". The answer to both 26 these questions, I believe, is "No": the approach to take with this new problem is quite simple, and the greater portion of i t is easily solved; but more about this later. We shall return to this problem in Section 10, after devoting two sections to a discussion of the S-related counterfactuals problem. 8. The Missing Link (1) Goodman's leading insight about counterfactuals i s that they are supported by an antecedent-consequent (A-C) connection. v As we have seen, this connection cannot f u l l y be analysed by the stock of notions Goodman wishes to employ: some important feature, rooted in causation, escapes the criterion. This we dubbed the 'missing link'. I shall contend that this link amounts to a residual form of A-C connection which the Goodman criterion, given i t s limited set of concepts, cannot capture. Nevertheless, I think i t can be explained in terms of inference-routes from A to C.„ For now, however, I shall refer to i t as the causally-grounded, or 'causal' A-C link. Presumably, the causal aspect of this connection has something to do with the use of causal laws in the inference-route from antecedent to consequent. Let us define as 'causal counterfactuals' those which, when true, are supported by inference-routes employing only (i) logical and ( i i ) causal laws (as opposed to other kinds of empirical laws and law-like generalizations). Therefore, i t i s for causal counterfactuals that the causal link is yet unanalysed. Not a l l counterfactuals are causal, however. Does the S-related counterfactuals problem a f f l i c t them as well ? Let us explore an example. Suppose that an application form provides two blanks, the f i r s t for one's Christian name, and the second for one's surname. I have written "John" in the f i r s t blank, but nothing in the second. Therefore, i t is true that: The relationship between antecedent and consequent here i s not causal: writing "Black" does not cause, or causally explain, the writing of "John Black". However, by admitting a certain truth — that I have not written "John Black" — into a criterion-acceptable situation-description, as in the match case, i t is apparent that the false: can be established as well. As we have seen, characterizing the missing link w i l l resolve our problem for causal counterfactuals alone. Once this task is complete, therefore, we must consider the prospects for a general solution. How are we to understand the nature of the missing causal link ? The word "cause" often means the production of one event by another. Can the link underlying e.g. (6) but not (7) in the 'familiar case' be explained in terms of this sense of "cause" ? It w i l l be remembered that, i n our discussion of Goodman's match argument (Section 6) we saw that both: 13. I write "Black"in the second blank I have written "John Black". 14. I write "Black" i n the second blank I T ^ I have not written "John" in the f i r s t blank 28 6. Match m is scratched j \^ m lights and 7. Match m is scratched( f*^  m is not dry are supported by sets of K-describing sentences —- c a l l them 'S*' and 1 S'lT , respectively — each of which i s equally acceptable to the criterion as i t stands. S*is <^"m is dry", "m i s oxygenated", "m is well-made"} , and S*'is "^m is oxygenated", "m is well-made", "m does not light" } . The suggestion under consideration amounts to this. Given the causal laws of our world, we know that, with respect to (6), (i) any possible event described by A'S*— thatj,is, "Match m i s scratched • m is dry " m i s oxygenated " m is well-made" — c a u s a l l y produces the lighting of m. On the other hand, we know that, with respect to (7), ( i i ) any possible event described by A'S* — that i s , "Match m is scratched " m is unlit • m is oxygenated * m is well-made" — cannot by i t s e l f causally produce m's wetness. How can this insight be adapted to the inferential nature of the criterion ? Let us divide the classs of a l l causal statements into two kinds:. causal reports, and causal laws. Causal reports, which I shall c a l l simple causal statements, are appropriate for the description of instances of causal relations. Examples of these are': 15. The scratching of match m caused i t to light and 16. The fact that match m was scratched caused i t to be the case that m lights 29 (Note: we shall see later that (15) and (16) have distinct, non-equivalent, logical forms). Causal laws, on the other hand, are general assertions of kinds of causal relations, for example, L. Scratching dry, oxygenated, well-made matches causes them to light. One expects the following logical relationship to hold between these kinds of statement: that from causal laws and sets of descriptive sentences — sentences describing particular circumstances — one g can infer simple causal statements. Our original insight can now be cast in inferential terms. Given L, i t seems plausible that from a description of an event of type ( i ) , that i s , A'S*, we can infer not only "m lights", but also the simple causal statement, "The fact that match m is scratched * m is dry ' m is q oxygenated * m is well-made causes (ed) i t to be the case that m lights". However, while we can infer "m i s not dry" from L and a description of an event of type ( i i ) , that i s , A"SM, we cannot infer, "The fact that m is scratched " m is unlit " etc. caused i t to be the case that m i s not dry". "Davidson discusses this matter to some extent in \[8], pp.90-92 . g The tense of the verb "to cause" here i s the simple present, whereas in the causal law L the verb is untensed. To prevent confusion, I shall use "caused", which is the verb's simple past, in simple causal statements, retaining the untensed form in causal laws. 30 This reasoning suggests a condition which, though restricted to causal conditionals, appears to resolve the S-related counterfactuals problem: that i s , A-S, besides meeting the criterion's other conditions, must permit not only the derivation of C, but also the simple causal statement, "The fact that A'S caused i t to be the case that C". (Presumably, an appropriate condition must be added to the negative side of the criterion as well.) Moreover, the nature of the causal link thus formulated is purely inferential, based ont'the assumed derivability of simple causal statements from general causal laws and descriptive statements. However, one large problem remains: f i l l i n g in the details of this kind of inference. Davidson has argued that causal relations occur between events, which he contends are unrepeatable individuals of some sort ([7], p.25). This conclusion is based on a general feature of the language with which we describe the properties and relations of events: that is li n g u i s t i c a l l y speaking, events correspond to singular terms, not sentences ([7], p.25). On this view, the role of the expression "caused" in a singular causal statement such as 15. The scratching of match m caused i t to light i s seen, not as a non-truth functional sentential connective, as in 16. The fact that match m was scratched caused i t to be the case that m lights but as a two-place predicate, linking two singular terms or definite descriptions, as in 17. ( Jx) (Is scratched(m,x)) caused ( Jy)(Lights(m,y)) 31 which may be read, somewhat sloppily, as "The x which is a scratching of m caused the y which is a lighting of m" ([6], p.87). However, i f this view-is correct, how can we infer a causal statement of the form, "the fact that ^ caused i t to be the case that ty ", where ty and ty are sentences, from any group of causal laws and descriptive statements, when simple causal statements such as (15) do not express connections between facts — which correspond to sentences —: but between events which correspond to singular terms ? Nevertheless, we can find a place for statements of the form, "The fact that ty caused i t to be the case that ty ". An interesting feature of (17) is that, in order to construct definite descriptions for events, i t was necessary to construe " i s scratched" and "lights" as two-, not one-place predicates. Someplace must be found for a variable ranging over events'? Indeed, Davidson has defended the view that certain predicates, usually associated with action or change, are best regarded as having an additional place for events ([8], p.93). He regards: 18. Caesar died for example, as an existential statement constructed from a two-place predicate, "died", and a singular term, "Caesar", that i s , 19. (3X) (Died(Caesar,x)) or,.loosely put, "There exists an event x such that Caesar died i t " ([9], p.83). This view — that some verbs contain "one more place than we generally think, a place for events" ([9], p.83) -- allows Davidson to explain a number oft.the logical features of the language of action, 32 change, and causation (cf.[6]; [7]; [8]). Let us c a l l such verbs 'event-predicates' . An upshot of this i s that we can find an interpretation of some causal statements of the form, "The fact that £ caused i t to be the case that ". This i s accomplished by interpreting "Match m is scratched" as 20. ' (jf x) (Is scratched(m,x)) ; "m lights" as 21. (.3y) (Lights(m,y)); and (16) as the complex existential statement 22. (3x)(3y)[(Is scratched (m,x)) • (Lights (m,y)) • (Caused(x,y))] that i s , as "There exist events x and y such that x is a scratching of m, y i s a lighting of m, and x caused y" (cf.[6], pp.86-87). Here, of course, "caused" retains i t s construal as a two-place predicate. Therefore, this interpretation of statements of the form, "The fact that <f) caused i t to be the case that^", i s restricted to those statements <fa and (j) which contain, in an appropriate fashion, an event-predicate such as " i s scratched" or "lights". However, (22) betrays a feature which raises a d i f f i c u l t problem for our present approach: i t entails the existence of both a 'cause-event' and an 'effects-event', In general, treatment of "caused" as a two-place event-predicate restricts our interpretation of "The fact that <^  caused i t to be the case thatj^ " to ^ s and (j) s which assert the existence of events. But what about those counter-factuals whose antecedent ^ and consequent are causally linked, 33 in some fashion, yet whose causal link seems to depend on the possibility of the absence of an event being responsible or accounting for the absence of another ? For example, there are imaginable situations in which i t would be true that: 23. Match m is not scratched \ m does not light. Clearly there i s some positive sense i n which not scratching m could be potentially responsible for m's non-lighting. Yet the causal link underlying (23), unlike that underlying (6), seems dependent on the absence of events, not their presence. Our precise d i f f i c u l t y i s this. According to the suggested condition, i f (23) i s true, then we ought to be able to infer from "Match m i s not scratched", some S, and some causal laws the statement "The fact that match m.iis not scratched 'S caused i t to be the case that m did not light". However, i f the latter adequately expresses the causal link underlying (23), then i t ought not to entail either the existence of a cause-event (unless S does) or an effect-event, although i t should express a positive causal connection of some kind. Therefore, i t i s d i f f i c u l t to interpret along the lines of (22) , whose assertion of causal connection is intimately tied to the existence of two events: a cause and an effect. Hence our problem, in short, is this: to assert causation, i n this sense of "cause", one needs events. Perhaps the absences of events can be treated as events in themselves ? This seems unnatural: "Match m is not scratched" seems best expressed by: 34 24. - ( J x )(Is scratched(m,x)) that i s , "No scratching exists", rather than by: 25. (]Jx)(Is not-scratching(m,x)) that i s , "Some non-scratching exists". Indeed, ,(24) appears to express a kind of state or condition. Nevertheless, Davidson hints at this approach to absences, and Mackie, in a slightly different context, attempts i t . ( [ 6 ] , p.93; [15]). However, this idea raises a host of serious ontological problems (cf. Kim [13], pp.51-54). Therefore, I shall pursue a more promising notion: that we have been investigating the wrong sort of causal connection. 9. The Missing Link (2) At the end of [6], Davidson makes a pregnant observation about the use of the word "cause". After outlining his view that in many contexts "cause" should be treated as a two-place event-predicate, he says: This i s not to say there are no causal idioms that directly raise the issue of apparently non-truth-functional connectives. On the contrary, a host of statement forms, many of them strikingly similar .... challenge the account [previously presented]. Here are samples: 'The failure of the sprinkling system caused the f i r e ' , 'The slowness with which controls were.applied caused the rapidity with which the inflation developed', 'The collapse was caused, not by the fact that the bolt gave way, but by the fact that i t gave way so suddenly and unexpectedly', 'The fact that the dam did not hold caused the flood'. Some of these sentences may yield to the methods I have prescribed .... but others remain recalcitrant. What we must say in such cases is that in addition to, or in place of, giving what M i l l calls the 'producing cause', such sentences t e l l , or suggest, a causal story. They are, in other words, rudimentary causal explanations. Explanations typically relate statements, 35 not events. I suggest therefore that the 'caused' of the sample sentences in this paragraph i s not the'caused' of straightforward singular causal statements, but is best expressed by the words 'causally explains'. ([6], p.93) This suggestion — that the word 'cause', when i t means 'causally explains', serves as a sentential connective — has been explored by others,, in particular, Mackie ([16], Chap. 10). Can i t help us ? Two d i f f i c u l t i e s previously encountered disappear immediately. Fi r s t of a l l , explanations connect statements. Hence we no longer face the logical problem of moving between sentences and singular terms, or the ontological problem of moving between states or facts, and events. Secondly, while on our.earlier view i t was problematic to assert that the non-existence of one event caused the absence of another, there i s nothing d i f f i c u l t about asserting that the absence of the f i r s t causally explains the absence of the second. A l l that i s required i s an account of how the absence of the f i r s t , that i s , the fact that m was hot scratched, resulted in the absence of the second, that i s , the fact that m did not light, given the web of causal relations in nature. Can this idea assist us with our central concern — the S-related counterfactuals problem — as well ? Explanations, says Hempel, are responses toe.the question, "Why i s i t the case that p ?" ([Il], p.334). However, they are not the only form of response to a why-question; why-questions which ask, "Why is i t believed that p ?", which Hempel terms "reason-seeking or epistemic", demand not explanations but "evidence or grounds or reasons in support of the given assertion" ([11], pp.333-335). 36 Let us imagine, for the moment, a situation much like the 'familiar case', differing only in that match m has been scratched and is l i t . Were we to ask, "Why is i t the case that m lights ?", we could reply: "m lights because i t is a dry, oxygenated, well-made match, and such matches light when, scratched". This account, though brief, i s entirely adequate a response. On the other hand, let us imagine a slightly different situation: our oxygenated and well-made match is scratched but does not light, because i t is wet.- Were we now to ask, "Why i s i t the case that m is not dry ?", our reply, i f adequate, must indicate circumstances in m's past which rendered i t damp. It is not sufficient to merely point out that m is oxygenated, well=made, scratched, and unlit: these facts do not explain why m is not dry. At best, they could be adduced in favour of one's belief that m is not dry, i f that belief were the subject of a reason-seeking why-question. One could reply: "Well, m must be so, since i t didn't light when scratched, and since m is oxygenated etc". Why do these two sets of facts differ in explanatory power ? A hint was given in our second case: what we look for in the causal explanation of a fact F, besides causal laws, are facts which are causally prior to F and responsible for i t . The facts adduced in the f i r s t case are such; those i n the second are not. Hempel concurs with this observation..' He says: in the context of explanation, a 'cause' must he allowed to be a more or.. less . complex set of circumstances and events, which might be described by a set of statements C 1, C 0, . C,^ . 37 And, as i s suggested by the principle "Same cause, same effect", the assertion that those circumstances jointly caused a given event implies that whenever and wherever circumstances of the kind i n question.occur, an event of the kind to be explained takes place. Thus causal explanation implicitly claims that there are general laws — let us say L^, I^, .... L r — in virtue of which the occurrence or the causal antecedents mentioned in C,, C^, .... is a sufficient p'condition for the occurrence of the phenomenon to be explained. ([11], pp.4348-349) However, Hempel appears to take too narrow a view of the kind of state which can explain, or be explained, in a causal explanation. As we saw earlier, the absence of an event — which is presumably a stater}, not an event — can also explain, or be explained. Therefore, we must widen our notion of explanatory causal antecedents to cover not only the occurrence of events, but the absence of events as well. Clearly, these insights have implications for the S-related counterfactuals problem. In our discussion of the familiar situation K involving match m, we saw that this problem arose because the criterion allows selection of a set of K-describing sentences — c a l l i t ' s ' 1 — which supports 6. Match m is scratched m lights and also another — c a l l i t 's"j — which supports the false 7. Match m is scratched C3"^ m ^ s n o t dry. Now we see that by imagining two situations, one described by "Match m is scratched" (A), S 1, and "m lights" (C), the other by A, Stf, and "m is not dry", we discovered that A'S* possesses a feature lacked by A'S": in the f i r s t situation, A'S', together with our causal law (L), explains the 38 fact that C, while in the second, A'S" and L do not explain the fact that m is not dry. But how can we adapt this insight to speak directly to our problem ? After a l l , the situation in which the truth-values of (6) and (7) are to be assessed, that i s , K, is unlike either imaginary situation in that A is false in K. Crudely put, an explanation of empirical fact i s constructed in some fashion from a set of descriptive sentences and empirical laws. Hempel distinguishes two types of explanation: 'true' and 'potential'. In the former, a l l the members of the set of descriptive sentences and laws must be true; in the latter, although other requirements must be met, they need not be so ([12], pp.247-249). When p describes an actual state or event, therefore, one expects a true explanation in response to "Why is i t the case that p ?"; however, when p describes a possible state or event the best one can expect is a potential  explanation based on a description of a possible set of antecedents. Adopting this terminology allows us to describe the causal link underlying (6) but not (7) as follows: in A, S', and L we have the materials with which to construct a potential causal explanation for the lighting of m, while in A, S", and L, we do not for m's wetness. It appears, therefore, that resolution of the S-related counter-factuals problem, at least for causal counterfactuals, requires (i) an adequate analysis of causal explanation, including ( i i ) a description of those characteristics which make a set of circumstances explanatory causal antecedents. Lacking both (i) and ( i i ) , however, we can but note that.some A-C inference-routes presently accepted by the criterion 39 employ materials (A,S, and causal laws) which are potentially explanatory of the fact asserted by C; that others do not; and that f i n a l amend-ation of the criterion depends on a f u l l analysis of the difference. In lieu of this, let us c a l l paths of the f i r s t type 'explanatory' inference-routes. It is worthwhile, but not necessary to hitch these observations to the Deductive-Nomological "(D-N) model of s c i e n t i f i c explanation. As Hempel observes, explanation, as normally understood, is a pragmatic concept: Very broadly speaking, to explain something to a person is to make i t plain and i n t e l l i g i b l e to him, to make him understand i t . Thus construed, the word 'explanation' and its cognates are pragmatic-terms: their use requires reference to the persons involved in the process of explaining. In a pragmatic context we might say, for example, that a given account A explains fact X to person P^. We w i l l then have to bear in mind that the same account may well not constitute an explanation of X for another person P^, who might not even regard X as requiring an explanation, , or who might find the account A unintelligible or unilluminating, or irrelevant to what puzzles him about X. Explanation in this pragmatic sense is thus a relative notion: something can be significantly said to constitute an explanation in this sense only for this or that individual. ([11], pp.425-426) However, Hempel contends that the fact that a notion X is context-relative does not entail that a related, context-free notion X' cannoto.be abstracted: proof i s one such notion ([11], p.426. The D-N model is Hempel's attempt to repeat this feat for s c i e n t i f i c explanation. What is the D-N model of explanation ? A D-N explanation, as conceived by Hempel, has an "explanans" \('which does the explaining) 40 consisting of fact-stating sentences, C^...,C^, and empirical laws, L1...,L, , as well as an "explanandum", E (which expresses the phenomenon to be explained). To qualify as an explanation of E, the explanans must meet at least the f i r s t three of the following adequacy-conditions (briefly sketched): the explanans must (i) entail E; (i i ) employ empirical itaws in the derivation of E; ( i i i ) have empirical content; and (iv) consist of true sentences ([12], pp.247-249). As mentioned earlier, an explanation meeting (i) through (iv) is a true explanation; and that meeting only (i) through ( i i i ) , a potential explanation. The D-N model, therefore, constructs explanations from materials abundantly supplied by the Goodman criterion. The truth of a causal counterfactual, on Goodman's view, depends on the derivability of C from A (which presumably describes some expirically possible fact, i f the counterfactual i s causal in nature), S, and some causal laws. Indeed, i f one regards A, S, and the causal laws as a tentative explanans, and C as explanandum, the features of the Goodman criterion satisfy adequacy-conditions (i) through ( i i i ) . Thus, i t i s appealing to view the criterion, from the point of view of the D-N model, as attempting to determine, at least for causal counterfactuals, the features of counter-factualg'Supporting potential explanations; and, specifically, to regard the criterion as demanding no more than that a causal counterfactual be judged true i f and only i f A, S, and some causal laws appropriately 41 explain C; and no such explanation exists for -C. On this view, given our earlier discussion, the defect i n the criterion betrayed by the S-related counterfactuals problem stands out starkly: i t does not adequately characterize the explanans of a counterfactual-supporting explanation because,/as we saw in the match example, i t does not invariably pick out sets of causally explanatory antecedents for the phenomenon described by C. What features characterize these sets ? I do not know, although I do Know that the answer must l i e with analysis of the notion of cause and causal explanation. Hitherto I have focussed discussion on causal counterfactuals. Can our results be extended to other kinds as well ? It w i l l be remembered, in the application-form case (Section 8), that: 13. I write "Black" in the second blank j_J7 I have written "John Black" is true. K was such that "I have written 'John' in the f i r s t blank" (S) is true, while "I write 'Black' etc." (A) and "I have written 'John Black" 1 (C) are false. If I ask of K, "Why would i t be the case that I have written 'John Black' i f I were to write 'Black'. ?", I direct my listener, in effect, to imagine a possible situation described by A, S, and C, and request him to account for the happenings therein. The reply here is straightforward: "Well, i f both 'John' and 'Black' are Inscribed in the appropriate blanks, 14. I write "Black" in the second blank [ T7 I have not written "John" in the f i r s t blank was illegitimately established in a situation K in which: 42 the result i s 'John Black" 1. This reply, based on A and S, is a potential explanation of C: thus, A and S explain C. On the other hand,.asking "Why would i t be the case that I have not written 'John' i f I were to write 'Black' ?", directs the listener to a situation described by A, -S, and -C. Here the reply is not simple: i t i s inadequate to point out that despite the fact that "Black" has been inscribed, "John Black" is not, hence "John" has not been written. These facts, that i s , A and -C, do not explain why "John" was not written in the possible situation,.though they may support our belief that this must be so. These btfief observations, which parallel those made earlier about (6) and (7), suggest a surprising conclusion. Our original intuition about the S-related counterfactuals problem was that i t s solution for causal counterfactuals such as (6) and (7) lay with the notion of causation. Further examination, however, indicated that the key idea was causal explanation. Now our evidence suggests that the general solution to the S-related counterfactuals problem lies with explanation alone; the notion of causation drops out of the picture, except for causal counterfactuals. Thus, i f this i s true, two related questions remain: (i) can a general notion of counterfactual-supporting explanation be made out in a form amenable to a Goodman-style criterion ?; and ( i i ) i f so, what general characteristics do the sets of descriptive conditions adduced in explanations of this sort share with causal antecedents ? 43 10. An Approach to the Undercutting Phenomenon Problem We noted, in a situation described in Section 7, that both: 11. The key is turned { t""^  Martin's Alfa starts and 12. The key i s turned | .H^ the Alfa's starter malfunctions are not true. Specifically, thanks to the antics of a bomb-happy friend, we observed what was called the "undercutting phenomenon": that i s , (11) i s false because (12), an S-related counterfactual, is true. This phenomenon threatened reinstatement of the original cotenability condition, a d i f f i c u l t y we dubbed the "undercutting phenomenon" problem. ' How are we 'to deal with this issue without inviting vicious circularity, the Horseman of Cotenability ? The only way, I believe, is to take the undercutting phenomenon seriously, and turn i t to our advantage. Let us begin by noting that the undercutting phenomenon appears to occur only in situations K in which the S 1 in the true S-related (fa \ -S*" i s a member of the particular S^  with which we wish to establish, (js \ fp. Suppose, for example, that in addition to the car's starter Martin's Alfa has a special mechanism - c a l l i t "X" - that w i l l also turn over and start the car when the key is turned. Imagine, furthermore, that K i s such that the key i s not turned, and that both the car's starter and X are in working order. In this K we would affirm (11) and deny (12). Of course, in any situation in which the key i s actually turned there may be some dispute about which mechanism was causally responsible for the starting of the car. Depending on which mechanism is so regarded, however, i t is obvious that (11) may be 44 supported by e i t h e r of two d i s t i n c t S - i d e a l sets i n K. Now l e t us modify K. Suppose that Martin's colleague places a bomb on the s t a r t e r , but, because he i s ignorant of the car's s p e c i a l f e a t u r e , does nothing which i n t e r f e r e s w i t h X. That i s , l e t us assume that the bomb i s very s m a l l , and incapable of damaging anything other than the s t a r t e r . In t h i s s i t u a t i o n we would now affirm:. ( 1 1 ) even though we a l s o a f f i r m ( 1 2 ) . Why? Roughly put, because there i s an inf e r e n c e route, independent of the existence of the s t a r t e r , but dependent upon that of X, which i s capable of supporting ( 1 1 ) . That i s , i t appears that ( 1 2 ) does not u n d e r c u t t ( 1 1 ) i n K, even though the S-related ( 1 2 ) i s t r u e , because the consequent of ( 1 2 ) i s not the d e n i a l of any sentence i n the p a r t i c u l a r i d e a l S w i t h which we support ( 1 1 ) . Thus, i n our d e s c r i p t i o n of the undercutting phenomenon as the f a c t t h a t , i n many K, c o u n t e r f a c t u a l " r e f e r s only to those constructed from the p a r t i c u l a r K-des-Given t h i s p r o v i s o , l e t us look c l o s e l y at ( 1 1 ) and ( 1 2 ) . The t r u t h of e i t h e r , i n any s i t u a t i o n , i s p a r t i a l l y a f u n c t i o n of c e r t a i n causal laws governing the motion of e l e c t r i c i t y , the combustion of hydrocarbons, et c . — i n s h o r t , both are causal c o u n t e r f a c t u a l s . Moreover, these c a u s a l laws d i c t a t e a number of causal r e l a t i o n s h i p s between v a r i o u s s t a t e s - o f -a f f a i r s . Imagine, f o r a moment, that X does not e x i s t and that Martin's f r i e n d has indeed placed a bomb on the car's s t a r t e r . The key i s turned i f an then i t s t r u t h undercuts must be understood that the expression " S - r e l a t e d c r i b i n g S w i t h which 45 and boom!. the starter disintegrates. The turning of the key, along with some facts and causal laws, explains this result. But there i s another result as well, one which i s partially explained by the starter's destruction: because this v i t a l component no longer works, and no other means of starting the car by turning the key exists, the car does not start. What i s the moral of this story ? We noted earlier that whenever a causal counterfactual such as (12) is true, there is ah explanatory  inference-part from "The key is turned" (A) to "The Alfa's starter malfunctions". What our story suggests is that when (12) is true in a situation K there may also be an explanatory inference-route from A to "Martin's Alfa does hot start" (-C). Given Goodman's criterion (with the modifications suggested in Section 9), i f this i s so, then (11) cannot be true in K when (12) i s , since (11) can be true, only i f (i) there i s an appropriate route from A to "Martin's Alfa starts" (C), and ( i i ) no such route from A to the negate of this sentence. Therefore, this idea — that when the S-related (12) is true there is an appropriate path from A to the denial of (11)'s consequent— i f true, would explain the undercutting phenomenon in K. Can we demonstrate this to be the case ? Yes, but the demonstration w i l l require some ground-work. Fir s t of a l l , demonstrating the existence of an explanatory inferential path from A to -C in K when (12) is true involves two distinct considerations: showing that (a) there is an inferential path simpliciter from A to -C; and that (b) this path is explanatory. For the moment we shall set aside (b)> and'discuss (a), in 46 the course of which we shall establish a set of conditions on the K in which (a) holds. Our f i r s t condition w i l l be put forward in the following fashion and then modified progressively. Let us pretend, for the moment, that (i) a state described by "The key is turned • the starter i s in working order" (A'S) constitutes the only set of possible causal antecedents for the fact that the Alfa starts, ignoring momentarily both the complexities^offautomobiles, and the possibility of starting the automobile in other ways. By condition (i) I mean the following: we are to suppose that, given the causal laws of the world, there i s only one possible state — described by A'S — that can causally account for the fact described by C; or, in other words, that the causal make-up of the world i s such that the truth of A'S is a necessary, as well as sufficient condition for the truth of C."^ The following material equivalence expresses this fact: F. (A'S) == C. Moreover, demonstrating (a) requires a second important condition on K: that ( i i ) the use of F in constructing a set of inferences from A to -C does not violate any of the criterion's requirements (ignoring the question of explanatory power as well). It should be noted, however, that we shall be modifying condition (i) by stag.es, each of which w i l l I am not trying here to analyse the notion of causation in terms of conditions; nor do I presuppose \such an analysis (cf.Mackie[15]). F is simply intended to express a certain relationship between certain states wrought by the web of causal laws. 47 demand introduction of a distinct F-like truth. Condition ( i i ) is intended to cover these as well. Given that K meets conditions (i) and ( i i ) , ! the demonstration of (a) when (12) i s true is as&follows: I. Assume that (12) is true. Therefore, ex hypothesi, there exists an explanatory inference path from A to "The Alfa's starter malfunctions" (-S). II. By a simple logical law, we can infer (-S v -A), or -(A'S), from -S. I I I . From -(S'A) and F we can infer -C. Q.E.D. How important and credible are conditions (i) and ( i i ) ? Condition ( i i ) i s both crucial and plausible. Without F (and as we shall later see, the F-like truths as well), derivation of -C is impossible. However, derivation of C does not seem to depend on any violation of physical or logical law. On the other hand, condition (i) seems essential, but is not credible. It plays a crucial role in establishing F, yet ignores the complexities of automobile mechanics. In reality, f i r s t of a l l , the set of causal antecedents required to start an Alfa by turning the key is much larger — there must be sufficient gasoline, the fuelipump must run etc.; and secondly, there are distinct alternative methods of starting an Alfa — 'push-starting' and 'hot-wiring' — that do not depend on a key and/or starter — otherwise, car thievery would be in a sorry state. Let us assume.in the f i r s t case, that a l l the other circumstances required to start the Alfa, aside those described by A'S, are expressed by R; and , in the second case, that the alternative ways of starting the car are expressed by sentences X,Y,Z,... which are 48 disjoined to form a single sentence, T. The f i r s t complication, I believe, is not serious. (A'S) may not be sufficient for C, but (A'S'R) i s . If (A'S'R) describes the sole set of;, causal antecedents for the car's operation — ignoring the second complication — we can construct an F-like sentence: F 1 . (A*S'R)S=C and, with only slight modification, perform the inference required by step II. It i s as simple to infer (-S v -t^(A'R)) , or -(A'S'R), from -S, as i t is to infer -(A'S).. Step III is then easily performed, employing -(A'S'R) and F"*". The second complication, however, raises greater d i f f i c u l t i e s . In this case, (A'S'R) is no longer necessary for C; however, the disjunction of (A'S'R) and T, i.e. ((A'S'R) v T), i s . That i s , i t is extremely plausible that i f the car starts, i t i s because the Alfa's key was turned etc. or i t is 'push-started' etc. or i t is 'hot-wired' etc. for an indefinite (albeit not infinite) number of alternatives. Once again we can construct an F-like sentence: F 2 . ((A'S'R) v T ) = c 2 F IJ. however:*?, has different logical features from i t s predecessors. 2 In order to demonstrate (a) employing F , we must rely on a third , condition: that ( i i i ) -T is true in K, and no criterion condition excludes employing -T as a K-describing truth in the inference route from A to.-G. Given this condition, the requisite modification in the inference route from A to -C is made in the following way. Step 1 remains the same. Then, as i n the case of F \ we infer -(A'S'R) from 49 -S. But now comes an important change. Since -T i s true of K, 2 we infer -C from F via -(A'S'R) and -T. On the other hand, without -T we cannot perform this last step. Thus far I have contended that given certain conditions on K there w i l l be an inference route simpliciter from A to -C when (12) is true. But what of (b) ? Is this route causally explanatory ? Here we encounter a serious d i f f i c u l t y : we do not have a working account of causal explanation, hence cannot rigorously distinguish routes which are explanatory from those which are not. Thus our guide in this matter must be intuition. What does intuition say ? In Section 9 we determined explanatory power by considering possible situations described by the sentences involved "in the inference routes. In our present case, the possible situation corresponding to the inference route in question i s that given at the beginning of this section: the tale of the bomb-crazy colleague. It w i l l be remembered that this story suggested that the fact that the Alfa's starter malfunction because the key is .turned, together with the absence of other means of starting the car by turning the key, explains the fact that the car does not start. In summary, therefore, our examination of the implications of that story has proved rewarding, for we have discovered that, given a number of conditions on K, an explanatory inference route from A to -C appears to exist when (12). is true,, hence (11') is false. The conditions discovered are these: f i r s t , that some F-like truth exist; secondly, that use of this truth be criterion-acceptable In the route from A to -C; and thirdly, 50 2 that i f the F-like truth Is F , then -T must be true and criterion-acceptable as well. It should be noted, however, that this l i s t i s tentative. Without extended and arduous discussion, i t is impossible to say with certainty that these conditions are adequate as they stand, or that they are necessary as well as sufficient for the occurrence of the undercutting phenomenon in a given situation K. Nevertheless, there Is reason for optimism here. If further examination bears out the sort of analysis of the undercutting phenom-enon advanced here, an upshot i s that no modification of the criterion, beyond that discussed in Sectionn9, is required to resolve the undercutting phenomenon problem. Why ? If our analysis .is correct, then for any |^ » s _ related counterpart <^  fT"^ ~S> and situation K meeting the conditions listed above, i f <fi f""}~^ -S is true in K, then there exists an explanatory inference route from Hence, given the criterion as i t stands, i f ^ C J^-S is true in K, then ^ Q - ^ must be false. Moreover, the contrapositive of our analysis' result is this: i f there is no such route from <j) to- 1p in K, then^CJ-^-S is not true, that i s , is false. Hence, given the criterion as i t stands, i f ^Q-^jjb i s judged true, then ~S must be false. In neither case, therefore, must the criterion concern i t s e l f directly with the truth-value of when determining the truth-value of in K. Specifically, use of the cotenability condition i s unnecessary. 51 11. Summary I have attempted to demonstrate four theses: f i r s t , that the problem of cotenability i s really two problems, not one; secondly, that the cotenability condition is required as a solution to neither; thirdly, that the f i r s t , the S-related counterfactuals problem, w i l l be resolved, at least for causal counterfactuals, by an adequate account of causal explanation, and that a similar approach may be successful for a l l counterfactuals; and f i n a l l y , that the second, the undercutting  phenomenon problem, may require no further modification of Goodman's criterion. However, work remains on both these problems. 52 Bibliography [1] Adams, Ernest. "Subjunctive and Indicative Conditionals". Foundations of Language, 6(1970), 89-94. [2] Ayers, Michael R. "Counterfactuals and Subjunctive Conditionals". Mind, 74 (1965), 347-364. [3] Bennett, Jonathan. "Counterfactuals and Possible Worlds". Canadian Journal of Philosophy, 4 (1974/5), 381-402. [4] Chisholm, R.M. "The Contrary-to-fact Conditional". Mind, 56 (1947), 236-249. [5] Chisholm, R.M. "Law Statements and Counterfactual Inference". Causation and Conditionals, 147-155. Ed. by E. Sosa. London: Oxford University Press, 1975. [6] Davidson, Donald. "Causal Relations". Causation and Conditionals, 82-94. Ed. by E. Sosa. London: Oxford University Press, 1975. [7] Davidson, Donald. "Events as Particulars". Nous, IV (1970), 25-32. [8] Davidson, Donald. "The Logical Form of Action Sentences". The Logic of Decision and Action, 81-95. Ed. by N. Rescher! Pittsburgh: University of Pittsburgh Press, 1966. [9] Davidson, Donald. "On Events and Event-Descriptions". Fact and Existence, 74-84. Ed. by J. Margolis. Oxford: Basil Blackford, 1969. [10] Goodman, Nelson. Fact, Fiction, and Forecast. 2nd edition. Indianapolis, New York: Bobbs-Merrill Inc., 1965. [11] Hempel, C.G. "Aspects of Scientific Explanation". Aspects of Scientific Explanation and Other Essays in the Philosophy of X Science, 331-489. New York: Free Press, 1965. [12] Hempel, C.G. "Studies in the Logic of Explanation". Aspects of Scientific Explanation, 245-291. New York: Free Press, 1965. [13] Kim, Jaegwon. "Causes and Events: Mackie on Causation". Causation  and Conditionals, 48-62. Ed. by E. Sosa. London: Oxford University Press, 1975. 53 [14] Lewis, David. Counterfactuals. Cambridge: Harvard University Press, 19737 [15] Mackie, J.L. "Causes and Conditions". Causation and Conditionals, 15-38. Ed. by E. Sosa. London: Oxford University Press, 1975. [16] Mackie, J.L. The Cement of the Universe. Oxford: Clarendon Press, 1974. [17] Parry, William T. "Re-examination of the Problem of Counterfactual Conditionals". Journal of Philosophy, 54 (1957), 85-94. [18] Rescher, Nicholas. "Belief-Contravening Suppositions and the Problem of Contrary-to-Fact Conditionals". Causation and  Conditionals, 156-164. Ed. by E. Sosa. London: Oxford University Press, 1975. [19] Sellars, W.S. "Counterfactuals". Causation and Conditionals, 126-146. Ed. by E. Sosa. London: Oxford University Press, 1975. [20] Stalnaker, Robert. "A Theory of Conditionals". Causation and Conditionals, 165-179. London: Oxford University Press, 1975. 

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