Counterfactuals by David Lewis Review - Steven E. Boër and William G. Lycan

7/29/2019 Counterfactuals by David Lewis Review - Steven E. Bor and William G. Lycan

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Counterfactuals by David LewisReview by: Steven E. Bor and William G. LycanFoundations of Language, Vol. 13, No. 1 (May, 1975), pp. 145-151Published by: SpringerStable URL: http://www.jstor.org/stable/25000898 .

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David Lewis, Counterfactuals,Basil Blackwell,Oxford, 1973, 150pp.In thiswork, Lewis formulates and defends a type of 'possibleworlds' semantics for counterfactualconditionals, sentencesof the form 'If itwere thecase that 4, then itwould be the case that0' (symbolized 'D--*1'). Lewis'presentation ispellucid; he explainshis enterpriseand argues forhis positionwith brilliant clarity, and forcefullyanticipatesmany formidableobjections.Consider our standardKripke-style semantics for alethicmodalities: Weare to thinkof an assignment to each possibleworld i of a set of worlds S,,called the sphere of accessibility around i and representing the set of allworlds accessible from iunder thecorrespondingaccessibility relationR ('isaccessible from'). Such an assignment is called an accessibility assignment,and is used to give truth-conditions for standard modal sentences, asfollows:

LJ is true at world i iff 4 is true at each worldj e Si.0 ) is true at world i iff 4 is true at some worldJ e Si.

Various accessibility assignmentswill underlie various sorts of necessity(and possibility), varying in degree of strictness (logical necessity; physicalnecessity; necessity forhuman life;necessity forhuman thinkingtobe as it is;etc.)It is tempting to suggest that a counterfactual is a strictly necessary conditional, which corresponds to a particular accessibility assignment determined by 'overalsimilarity'of worlds, an assignmentwhich assigns, to eachworld i, the set of allworlds similar in at leasta certain (fixed)degree to i.This view isnot implausiblewhen only singlecounterfactualsareconsidered;but, Lewis points out, it is plainly inadequate for sequences of counterfactuals of theform:

(1i-?4) & ()10- 04)(t1 & 02i1-0 4) & -(01 & 02L-0,)(01& 42& 3La-/) & (01& 02 & 43L-0'4).

For it is often the case that what would be true under one set of counterfactual suppositionswould be falseunder a suitablyexpandedsetof counterfactual suppositions; itmay be thatall theconjunctions in an instanceof theforegoing sequenceare true. (E.g., briefly: "IfOtto had come, itwould havebeen a livelyparty; but ifbothOtto andAnna had come, itwould have beena drearyparty; but ifWaldo had come as well, itwould have been lively,1 'It is necessary that i,' symbolized 'ED', and 'It is possible that O', symbolized 'O0'.

Foundations of Language 13 (1975) 145-151. All rights reserved.


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but..." (p. 10; Lewis attributes this revealing sort of case to J. HowardSobel).)But true sentencesof this formare impossibleon the suggested interpretation of counterfactuals, since thefirst conjunctof any stagewould contradict the second conjunctof thenext stage in the sequence.The problem isthat, as we move down the list,we must constantly expand the relevantspheresof accessibility so as to accomodate the truthof succeeding stages.Lewiswrites,... itmay be that for every stage of the sequence, there isa choice of strictness that is rightfor that stage. But as we go down the sequence, we need stricter and stricter conditionals.The choice thatworks at any one stage makes false all the counterfactuals at previousstages, and all the negated opposites at subsequent stages. If counterfactuals are strictconditionals we have no hope of deciding, once and for all, how strict theyare. (p. 12)

The way out, Lewis argues, is to construe a counterfactual,not as anyone (constantly) strictconditional, but as a 'variably trict'conditional.Thesemanticalanalysis of such conditionals is a natural extension of thatgivenabove for constantly strict conditionals. Corresponding to a variably strictconditional we shall have an assignment $ to each world i of a set $i ofspheresof possibleworlds. $ is called a systemof spheres,and themembersof each set$ are called spheresaround i, ifffor eachworld i:

(1) S, T e $i implies (Sc T) v (T S), and(2) pc $i implies U p e $i, and(3) pc$L & p A implies pe $i.

A systemof spheres is said to be centered iff, for each world i, {i} e $i. Intuitively,a centeredsystemof spheres is tobe thoughtof as carryinginformation about comparativeoverall similarity of worlds. A particular spherearound aworld i is just the set of worlds which resemble i to a certain degree.The smaller the sphere, themore similar to i are theworlds in that sphere;for any worlds j and k, if there is a sphere S such that j e S and k S, then jismore similar to our world i than is k. (Of course, no world ismore similarto i than i itself.)Truth-conditions forcounterfactuals(quavariably strictconditionals)maynow be formulatedquite simply:

ID-lI is true at world i (according to a system of spheres $)iffeither(1) no 0-world belongs to any sphereS in$,, or(2) some sphere S in $i does contain at least one +k-world, and =~ /holds at everyworld inS. (p. 16)

This analysis, in termsof centered systemsof spheres, neatly solves Sobel's

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problem concerning the fluctuating sequencesof counterfactuals, since nosingle sphere around i need be chosen as the sphere of accessibilityaround i.So long as thereare only finitelymany spheresaround a world i, thenanynon-empty set of those sphereswill have a smallestmember. But there isnosuchguaranteewhen thereare infinitelymany spheresaround i, sincewe mayfind an infinitelydescending sequenceof smallerand smallersphereswithoutend.Let us calla sphere4-permittingif itcontainsat leastone 4-world, and letus say that ) is entertainableat i if some sphereSe$i is0-permitting. Thenthe assumption that for everyworld i and antecedent ) that is entertainable at i there is a smallest 4-permitting sphere (= theLimit Assumption)cannot be accepted. Counterfactual suppositions regarding continuouslyvariablemagnitudes (such as the supposition that this page ismore thantwelve incheswide) will give rise to an infinitely descending sequence ofspheres.There isno smallestwidth exceeding twelve inches;henceno 'closest'world to ours amongworlds with pagesmore than twelve incheswide; henceno smallest spherepermitting thesupposition inquestion.Lewis notes and defends various consequences of his analysis - e.g., thatcounterfactualshaving impossible antecedents are vacuously true, and thatcounterfactualshaving trueantecedents2collapse intomaterial conditionals.He concludes his first chapter by using the analysis to account for severalcounterfactual fallacies (e.g., taking 'Lj--' to be transitive),and to explain(via his well-known theoryof 'counterparts')thenotion of a 'potentiality',or counterfactualpropertyof an individual.InChapter 2 Lewis provides eight different reformulationsof his spheresystemmodel, somepreciselyequivalent to it,others equivalentjust to specialcases. One of these reformulations isparticularly importantas regardscom

parisons between Lewis' theory and previous accounts of counterfactualsin the literature. Let us call a premiss X cotenable with )at a world i (relativeto a sphere-system$) iff either (1) x holds throughoutU $i, or (2) Xholdsthroughout some 4-permitting sphere in $,. Then it is easily proved thatOL---*f is true at world i (relative to $) iff there is some premiss X, contenable

with 0 at i (relative to $), such that 0 & X logically implies 4.Lewis applies this theorem in Chapter 3, to solve the problem whichhas plagued the 'metalinguistic'theoryof counterfactualssuggestedbyChisholm, Goodman, and others. According to the metalinguistic theory,2 Some linguistswill complain that awell-formed counterfactual presupposes the falsity ofitsantecedent. On one popular account of 'presupposition' (due to Strawson), presupposition failure results in truth-valuelessness. If this is right, then itwould seem to be impossiblefor the counterfactual to have a true antecedent and come out true (or false). Lewis convincingly forestalls thisobjection on pp. 3, 26-31.



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1[---* is true just in case it is somehow 'backed' by a deductively validargument

01 Xi* ..>Xn

in which Xi,..., Xn are 'suitably chosen' further premises. The problem, ofcourse, is to explainwhat 'suitablychosen' comes to. Lewis' answer is thatXi, *., Xn are premises suitable for use in 'backing' 4[-1-- (at a given worldi) just in case X,&... & X, is cotenablewith 4 at i. In lightof the foregoingtheorem, therefore, themetalinguistic theory can be identifiedwith Lewis'account.3

Lewis concludes his third chapter by comparing his theory to thewellknown analysis of counterfactualsproposed by Robert Stalnaker. Briefly,Stalnaker's account is shown to rest upon an assumption which is evenstronger than the dubious Limit Assumption: that for everyworld i andantecedent ) (in our language) that is entertainable at i, there is a spherearound i containing exactly one +-world. Lewis demonstrates that the resultof adding this assumption to his own apparatus yields a theorypreciselyequivalent toStalnaker's.Further,Lewis points out thatStalnaker'sanalysisimplausiblyvalidates ( -L1--+v (D-l->- 0). This defect could be repairedif we were to abandon 'Stalnaker's Assumption' in favor of the weaker Limit

Assumption; but Lewis regardsacceptanceof the latteras too high a priceto pay.Lewis isby nomeans insensitive to the controversies shaking the foundations of his enterprise.He devotes Chapter 4 to a spirited defense of hisappeal to 'possibleworlds' and of his crucial use of the tenuous notion of'similarity'.He isan unabashed realistabout possibleworlds. He argues thatwe sometimesaccept such sentencesas "There aremany ways thingscould have beenbesides theway they actually are" (p. 84). This sentence has the superficialform of an existential quantification committing us to objects called "waysthingscould have been",which objectsLewis identifieswith possibleworlds.He proposes to take this apparent quantification "at its face value" unlesshe is shown some strong logical reasonnot to do so (and, he says,no suchreason is forthcoming).He concludes,

Our actual world is only one world among others. We call it alone actual not because itdiffers in kind from all the rest but because it is theworld we inhabit. The inhabitants ofother worlds may truly call theirown worlds actual, if theymean by 'actual'what we do;for themeaning we give to 'actual' is such that it refersat any world i to thatworld i itself.'Actual' is indexical, like'I' or 'here',or 'now'.... (pp. 85-86)3 Lewis neatly explains why lawsof nature are so frequently invoked as background premisses inargumentswhich back counterfactuals (seepp. 72-77).



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Thus, for Lewis, all possibleworlds (including ours) exist, and are equal inontological status, just as all times(or places or persons)are.For an individual tobe 'actual'isjust for it to existhere, 'at'ourworld.4The denizens of ourworld, Lewis says, are confined to it (p. 87) - theydonot spanmore than one world. Lewis therefore facesno problem of providing criteria of trans-world identity. Rather, he says, each of us closelyresemblesother (numericallydistinct) individuals in otherworlds whom we

may call our 'counterparts' in those worlds.5 For Boris to be such that hemight have been killed in an accident is for there to be, in some non-actualpossibleworld, a counterpartof Boris who is in factkilled ina counterpartof theaccident.Formally, thisparaphrasereceivescleanand elegant semantictreatment.But we question the adequacy of the paraphrase to beginwith:Itwould scareBoris considerably to realize that hemight have been killedin the accident; itwould troublehim not at all that some distinct individual(howevermuch he resemblesBoris) dies in some unrelated (though similar)accident.6

On the topicof similarity:Lewis freelyadmits thatjudgmentsof similarityare vague and highly dependent on the speaker's interestsand purposes.Lewis submits that this is what we should expect, if systematicallyvaguelocutions such as counterfactualsare to be explicated in termsof similarity:I... seek to rest an unfixed distinction upon a swaying foundation, claiming that the twosway together rather than independently. The truth conditions for counterfactuals arefixed only within rough limits; like the relative importances of respects of comparison thatunderlie the comparative similarity of worlds, they are a highly volatile matter, varyingwith every shift of context and interest. (p. 92)IfLewis' analysishas been successful,we are "leftwith onemystery inplace oftwo".Counterfactuals and similarityare "vague ina coordinatedway: firmlyconnected to each other, if to nothing else"; "... the limited vagueness ofsimilarityaccountsnicely for the limitedvaguenessof counterfactuals"(p.94).4 For further discussion of this novel view, see Lewis ' 'Anselm and Actuality', Nous IV(1970), Sec. 9.We wonder about the principle thatmotivates Lewis' taking apparent existential quantifications at their face value unless doing so leads to logical trouble. The principle seemsdirectly to conflict with a plausible principle of parsimony to the effect thatwe ought totreatas much of a surface structure as possible as fused or syncategorematic (non-referential), unless deeper syntactic or semantic considerations positively force us to do otherwiseWhat would Lewis say of such sentences as, 'Thereare two reasonswhy your proof fails','There is tension between two of my desires', 'There is a problem about possible worlds','There are two conditions youmust meet inorder to be admitted', 'There isa high probability thathe will tripover his own feet', etc.?5 For an earlier development of this view, seeLewis' 'Counterpart Theory and QuantifiedModal Logic', Journalof Philosophy LXV (1968).6 Further serious difficulties for the theory of counterparts are formulated by Fred Feldman in 'Counterparts', JournalofPhilosophy LXVII (1971).



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This isplausible.But it suggestsa view of counterfactualsthat is somewhatsurprising:Two individuals,or twoworlds,may be very similarto each otherrelative to one setof interests,and not at all similar to each other relative toa different set of interests. Lewis' truth conditions for counterfactuals,accordingly,are relativizedto the systemsof spheresthat"carry informationabout" similarityof worlds. But it seems to follow that (onLewis' account)a counterfactual is true only relative to a set of interests - a given counterfactualmight be both true and false, depending on the substituendof thehidden parameter.Lewis, however, seems to have inmind an intuitiveconstrainton the eccentricityof interestsandpurposes; at least, inbizarrecases,eccentricpurposesmust be explicitlymentioned if a speaker'sutteredcounterfactual isnot to 'deceive'his audience (pp.93-94).InChapter 5, Lewis illustrates the extraordinaryusefulness of his spheremodel ingiving semanticsfor locutionsof severalkinds thatare related in noobviousway to counterfactuals.To begin, ifwe give up theCentering assumption we can form spheres of similarity around the best possible worlds,yielding an account of conditionalobligation. (Lewisneatly solves the deonticanalogue of Sobel's problem on pp. 102-103.) Then he gives his spheresystems a temporal interpretation,explicating operators such as 'before','whennext', 'when last', 'until',and 'since'.Finally, in a tourde force, hegives an account of the "contextually definite description" (a definite descriptionwhose putative uniqueness implication is purely relative to localcontext and interest, e.g., "the book on the table"). In this account thesphere-systemsare taken to carry information about comparative salienceof objects in the utterance situation. An analogue of Sobel's problem isfound here aswell, and disposed of in a parallel fashion (pp. 114-115).Acontextually definite description is ultimately taken to refer to whateverpossible referentismost salient for the speaker (and hopefully his audience)at the timeof utterance.InLewis' final chapter,which ispurelyof technical interest,he offers completenessanddecidabilityproofs formodal systemsof his sort,and concludeswith a short section on alethic modal logics which can be derived fromthem.

It is not clear just how much relevance Lewis' work has for the syntax ofcounterfactuals. There are no standard syntactic transformationswhichdelete referencesto systemsof spheresof possibleworlds and then introducemodal auxiliaries. Nor, so far as we know, are there surface syntactic phenomena concerning counterfactuals that point towards Lewis' analysis.Therefore, anyonewho holds roughly that syntactic transformationsoperatedirectly on semanticrepresentationsmay findLewis' account implausibleorby theway. On the other hand, the impactof intensional logic on linguistic



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REVIEWS 151semantics,due largelyto thework ofMontague, may well come to provide anaturalway of foldingLewis' results into linguistictheory.7TheOhio State University,Dept. of Philosophy,Columbus,Ohio

STEVEN E. BOERWILLIAM G. LYCAN

7 In this connection, see Lewis' 'General Semantics', inD. Davidson and G. Harman(eds.), Sematics ofNatural Language (D.Reidel: Synthese Library, 1972).

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Counterfactuals by David Lewis Review - Steven E. Boër and William G. Lycan

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