16The MMTS Analysis of Causation

HORACIO SPECTOR*

I. IntroductIon

Causation in moral and legal contexts is generally analysed through two different accounts. One is the conditio sine qua non or ‘but for’ account. This account is usually formulated in terms of counterfactual dependence.1 Thus formulated, it holds that a cause c of an out-come e is an event c such that, had c not occurred, e would not have obtained. Suppose a physician moved by pious motives turns off the life-sustaining equipment of a terminally ill patient. If he had not turned off the equipment, the patient would not have died. The physician’s act is a ‘but for cause’ of the patient’s death.

The other account is variously called the nomonological, regularity, or ‘covering law’ theory of causation. Basically, it holds that a cause c of an outcome e is a relevant part of a complex condition that is sufficient, according to a law of nature, for the occurrence of e. The best known version of this account among legal theorists is the so-called INUS/NESS account, originating from Hart and Honoré in their seminal Causation in the Law and developed by John Mackie (INUS).2 Mackie analysed a cause of e as an individual exempli-fication of what he called an ‘INUS’ condition, that is, an insufficient but non-redundant part of an un-necessary but sufficient condition of e. Richard Wright popularised this analysis in legal circles under the label ‘NESS’.3 According to Wright, a particular condition c was a cause of e if and only if c was a necessary element of a set of antecedent actual conditions that was sufficient for the occurrence of e. A part of a sufficient condition is redundant if without that part this condition is equally sufficient. The antecedent condi-tions must be restricted to those that are ‘weakly’ necessary for the sufficiency of the set;

* Earlier versions of this paper were presented at Universidad Torcuato Di Tella, the University of Aberdeen, Southwestern Law School in Los Angeles and the ‘Ethics Colloquium’ of the Humboldt University in Berlin. I am indebted to my audiences on those occasions for excellent questions and points. I am also grateful to Richard Wright for enriching conversations during the early drafting of the paper, as well as to Eric Blumenson, Eleonora Cresto and Carolina Sartorio for helpful comments.

1 Counterfactual dependence is understood in terms of subjunctive conditionals and ‘possible worlds’ seman-tics; see: D Lewis, ‘Causation’ and ‘Postscripts to “Causation” ’, in D Lewis (ed), Philosophical Papers Vol II (New York, Oxford University Press, 1986).

2 JL Mackie, The Cement of the Universe: A Study of Causation (Oxford, Clarendon Press, 1980) 60–6; HLA Hart and T Honoré, Causation in the Law, 2nd edn (Oxford, Oxford University Press, 1985) 13–22.

3 RW Wright, ‘Causation in Tort Law’ (1985) 73 California Law Review 1735, 1788–91; RW Wright, ‘Causation, Responsibility, Risk, Probability, Naked Statistics, and Proof: Pruning the Bramble Bush by Clarifying the Concepts’ (1988) 73 Iowa Law Review 1001, 1018–34; RW Wright, ‘Once More Into the Bramble Bush: Duty, Causal Contribution, and the Extent of Legal Responsibility’ (2001) 54 Vanderbilt Law Review 1071, 1101–08.

340 Horacio Spector

this kind of necessity is called ‘weak’ because it is relative to the sufficiency of the set of antecedent conditions.4

The main advantage of the INUS/NESS account over counterfactual dependence theor-ies is that it can better explain cases of overdetermination. Two kinds of overdetermination are here relevant. First, unlike counterfactual dependence, the INUS/NESS account is capa-ble of handling cases of ‘concurrent causation’. A condition was an INUS/NESS cause if it was necessary in the circumstances for the sufficiency of an actually sufficient set, even if it was not ‘strongly’ necessary because there were other sufficient sets. The common example is: two careless hunters shoot a person dead simultaneously.5 While each of the shots is not a causal condition of the death in the ‘but for’ sense, both are INUS/NESS causal conditions because each of them is part of a complete instantiation of the antecedent of a causal law that links shooting to dying.

Second, the INUS/NESS theory can handle cases of ‘ex ante’ pre-emption, that is, cases in which the conditions corresponding to a certain cause c

2 (the ‘backup cause’) will not

instantiate until a temporally prior cause c1 failed to bring about the effect. Strevens pro-

poses a clear example: ‘Smith and Jones commit a crime, but if they had not done so the head of the criminal organisation would have sent other members to perform it in their stead, and so it would have been committed anyway’.6 Strevens claims that in this case the requirements of the INUS/NESS test are satisfied with respect to Smith and Jones’s action (ie, cause c

1) and that it is irrelevant to apply the test to the backup plan (ie, pre-empted

cause c2). In contrast, Smith and Jones’s action is not a ‘but for’ causal condition because, in

the closest possible world in which this action is not performed, the crime is still commit-ted, perhaps at the same time and in exactly the same manner.

Those advantages notwithstanding, the INUS/NESS account has been criticised on the grounds that it cannot exclude spurious conditions as causes and that it cannot properly resolve cases of pre-emption (‘early’ and ‘late’), as well as cases of ‘alternative causation’, omission and double pre-emption. Wright has tried to respond criticisms by shifting from ‘lawful sufficiency’ to ‘causal sufficiency’, that is, sufficiency grounded on a ‘causal law’.7 He says: ‘a condition was a cause of some consequence if and only if it was part of the complete instantiation of the antecedent of a causal law that links the antecedent and the consequent’.8 The concept of ‘causal law’ is the cornerstone of this new analysis, but critics have retorted that it is precisely this change that renders the account viciously circular.9 Jane Stapleton says that the account can nonetheless be maintained as a helpful algorithm to identify various forms of agent involvement in the law.10

4 T Honoré, ‘Necessary and Sufficient Conditions in Tort Law’, in D Owen (ed), Philosophical Foundations of Tort Law (Oxford, Oxford University Press, 1990) 364.

5 J Stapleton, ‘Choosing What We Mean by “Causation” in the Law’ (2008) 73 Missouri Law Review 438.6 M Strevens, ‘Mackie Remixed’ in J Keim, M O’Rourke and D Shier (eds), Causation and Explanation

(Cambridge, MIT Press, 2007) 44.7 For the distinction between ‘lawful sufficiency’ and ‘causal sufficiency’, see: R Fumerton and K Kress,

‘Causation and the Law: Preemption, Lawful Sufficiency, and Causal Sufficiency’ (2001) 64:4 Law and Contemporary Problems 83. This distinction is not clear to me.

8 RW Wright, ‘Acts and Omissions as Positive and Negative Causes’ in JW Neyers et al (eds), Emerging Issues in Tort Law (Oxford, Hart Publishing, 2007) 297.

9 Fumerton and Kress, ‘Causation and the Law’ (n 7) 102–05; JJ Thomson, ‘Some reflections on Hart and Honoré, Causation in the Law’, in MH Kramer et al (eds), The Legacy of H.L.A. Hart: Legal, Political, and Moral Philosophy (Oxford, Oxford University Press, 2008), 152–53; MS Moore, Causation and Responsibility: An Essay in Law, Morals, and Metaphysics (Oxford, Oxford University Press, 2009) 495.

10 Stapleton, ‘Choosing What We Mean’ (n 5) 444.

The MMTS Analysis of Causation 341

My purpose in this chapter is not to participate in these disputes. Rather my project is to present a new theory of causation that I call the minimal–maximal three-set (MMTS) analysis. I claim that this analysis is especially apt to clarify issues of causation within moral and legal contexts, and I try to show how this analysis supersedes alternative accounts. Causation is still an important notion in those contexts, mainly when the question is whether we should hold someone responsible for an event, either legally or morally. Causal responsibility of some kind seems to be a necessary condition of both moral and legal responsibility. Other contexts may be dissimilar. For instance, Bertrand Russell maintained almost one hundred years ago that the notion of cause is ‘a relic of a bygone age’ in the sci-entific language.11 But philosophers of science and scientists alike have continued to use this notion.12 I remain agnostic about whether the language of science needs the concept of cause, but I do think that, if science uses the concept of cause, either in a necessary or optional manner, the MMTS analysis deserves consideration as a hypothesis for scientific contexts too. It is, of course, controversial whether one single notion of cause is used across various scientific contexts and, in any case, I do not make any attempt to explore this issue in this essay.

The MMTS analysis is a mixed theory of causation. On the one hand, it is a regularity conception based on causal generalisations. Antecedent conditions in causal generalisa-tions, both positive and negative, are called MMTS conditions. They are causal factors in a generic sense. Yet I take causal relata stricto sensu to be events, that is, discrete, particular changes. Causes are events that instantiate some positive MMTS conditions according to a rule of correspondence that I will introduce below. All concrete causes correspond to abstract causal factors in the generic sense, but the converse does not hold: some causal factors do not correspond to causes in the strict sense; for instance, states of affairs and negative conditions are not causes even if they can be MMTS conditions, that is, causal factors in the generic sense.

On the other hand, the intervention of human behaviour in causal processes is explained by a supplementary counterfactual dependence account. On this account, forms of behav-iour are not often causes sensu stricto or even causal factors in the generic sense. This is the case with omissions: propositions denoting omissions are generally not MMTS conditions. In brief, agents can condition changes in the world in different ways. I will use the label agent-conditioning to dub all those ways. I believe that agent-conditioning is a Janus-faced phenomenon that must be accounted for by resorting to both regularity and counterfactual dependence views. Agents either make things happen or let things happen. These two behaviours are typically different. Whereas making things is typically a form of causation by events, letting things happen is typically a form of counterfactual determination.

My plan is as follows. In the next section, I set out the MMTS analysis. In the following sections (III, IV and V) I will show how the MMTS analysis can respond to the objections raised against the INUS/NESS analysis. In the last section (VI) I will also delineate a coun-terfactual dependence theory that explains how agents can relate to MMTS conditions in both MMTS and non-MMTS forms. Causal claims in moral and legal contexts are system-atically ambiguous. I will disentangle their different senses and define them as precisely as possible.

11 B Russell, ‘On the Notion of Cause’ Proceedings of the Aristotelian Society (1913) 13, 1–26.12 See eg, M Bunge, Causalidad, el principio de causalidad en la ciencia moderna (Buenos Aires, Eudeba, 1961).

342 Horacio Spector

II. the MInIMal–MaxIMal three-Set analySIS

The minimal–maximal three-set (MMTS) analysis can be considered a variety of the regu-larity or ‘covering law’ theories that tries to solve the problems assailing the INUS/NESS formulation. The most important difference with the INUS/NESS formulation is that the MMTS account adds two sets of propositions: a second set of causal generalisations and a third set of empirical consequences following from the set of antecedent conditions and the set of causal generalisations but not from each of these sets on its own. Thus the MMTS account is formulated in terms of three sets of statements. The first set includes statements that instantiate antecedent conditions in causal generalisations (‘the MMTS conditions’); the second encompasses relevant causal generalisations, and the third set contains empiri-cal statements that follow from the first set with the aid of the second, but not from the first or the second set alone. The introduction of the third set seeks to resolve controversial cases of pre-emption (especially ‘late’), where it might be alleged that the set of initial conditions of the relevant causal generalisation was fully instantiated so that a pre-empted cause was an actual cause (see section IV below).

Unlike standard formulations of the INUS/NESS account13, the MMTS analysis avoids the expressions ‘law of nature’ and ‘causal law’ and opts for ‘causal generalisation’. There are two main reasons for this choice. On the one hand, many physical laws are ‘association laws’ that ‘tell how often two qualities or quantities are co-associated’, but cannot be conceived as stating causal relationships.14 It is only causal general propositions that can be appealed to to analyse causation; association laws establish constant universal regularities but not causal relations or causal processes. On the other hand, many cases of causation in the law do not depend on ‘universal laws’ that are true in ‘every physically possible world’ or even in every spaciotemporal configuration of our physical universe. This is the case with respect to social generalisations that only hold within certain historical periods. I agree with Ernest Nagel when he says that ‘the “historically conditioned” character of social phenomena is no inherent obstacle to the formulation of comprehensive transcultural laws’.15 However, as Nagel himself concedes, generalisations stated to explain social phenomena often use vague concepts taken from social practice, and ‘it is difficult to eliminate from them essential ref-erence to matters specific to some particular society (or particular social tradition)’.16

Causal generalisations are essential for the MMTS analysis. The MMTS analysisans is not circular precisely because it uses ‘causal generalisation’ as a meta-linguistic term. That is, whereas the analysandum (‘cause’) denotes a non-linguistic relationship, the analysans refers to a logical relation among sets of propositions. Circularities do not hold across dif-ferent language orders. In order to set out the MMTS analysis I need to supply a basic con-ceptual apparatus that includes four concepts: ‘causal generalisation’, ‘satisfaction of a causal generalisation’, ‘proper logical parthood’ and ‘maximal satisfaction of a set of causal generalisations’. The definitions of these concepts are as follows:

13 See eg Thompson, ‘Some reflections on Hart and Honoré, Causation in the Law’ (n 9) 148.14 N Cartwright, How the Laws of Physics Lie (Oxford, Oxford University Press, 1983) 21.15 E Nagel, The Structure of Science: Problems in the Logic of Scientific Explanation (New York, Harcourt, Brace &

World, 1961) 464.16 Nagel (n 15) 464. Bunge also says that many sociohistorical laws are general rather than universal; see: Bunge

(n 12) 283.

The MMTS Analysis of Causation 343

1. Causal generalisation. A causal generalisation g is a true universal conditional statement that (a) asserts that there is an invariant or robust sequential correlation between em-pirical facts within a certain domain, and (b) sustains or warrants a technical rule R or entails a causal generalisation g’ that sustains or warrants a technical rule R. Condition (a) requires that a causal generalisation must establish an invariable or robust tempo-rally patterned sequence of facts. By ‘robust’ I mean a sequence of facts that holds with a degree of regularity sufficiently high for the generalisation to be capable of satisfying condition (b). This means that there is a pragmatic encroachment on the definition of condition (a). In turn, condition (b) specifies that a causal generalisation must have actual or potential technical application or entail a causal generalisation that has actual or potential technical application. Though causal generalisations are not technical rules, there is a logical connection between them: for any causal generalisation g there is a technical rule R that is grounded on g or on a causal generalisation g’ that derives from g. Technical rules respond to the general form ‘You can bring about (avoid) y by making x to be the case (not to be the case)’.17 Therefore, technical rules are not hypothetical im-peratives or normative requirements but rather technical guides. Here are two examples. Consider the causal generalisation ‘If a substantial dose of arsenic is applied to a human being, then she will die’. For instance, this generalisation sustains the technical rule ‘You can kill a human being by making him ingest a substantial dose of arsenic’. In other cases causal generalisations sustain technical rules that indicate how certain outcomes can be avoided. For instance, the generalisation ‘If an earthquake that measures 5.0 or more on the Richter scale hits a populated area, then a number of people will die’ sustains the technical rule ‘You can diminish or avoid human losses by evacuating a populated area to be hit by an earthquake of the mentioned magnitude’.

2. Satisfaction of a causal generalisation. Let C be a non-empty set of singular empirical propositions true in spatiotemporal region R. C satisfies a causal generalisation g in R iff g together with C entails a non-empty set E of empirical propositions (none of which is entailed by either g or C alone).

3. Proper logical parthood. Logical parthood is a relation defined for propositional sets. Let S

1 and S

2 be two sets of propositions: S

2 is a logical part of S

1 iff S

1 entails S

2. For example,

if S1 is a singleton set including the proposition ‘Caesar died at time t’, and S

2 is a single-

ton including the proposition ‘Caesar died’, S2 is a logical part of S

1 because the former

proposition entails the latter. Any subset of a propositional set S is a logical part of S, but the converse is not true: a logical part of S need not be a subset of S. (However, a logical part of S is necessarily a subset of the set of logical consequences of S.) Proper logical parthood is then defined in the standard way: S

2 is a proper logical part of S

1 iff S

1 entails

S2 but S

2 does not entail S

1.

17 Condition (b) has affinity with the interventionist conception of causation. This conception was defended by RG Collingwood, An Essay on Metaphysics, revised edn (Oxford, Clarendon Press, 1998) 296–97, as well as by Douglas Gasking, ‘Causation and Recipes’ (1955) 64 Mind 479–87, and GH von Wright, Explanation and Understanding (Ithaca, Cornell University Press, 2004) (first published in 1971). Von Wright quotes Thomas Reid as the classic originator of the view. In recent times other authors have endorsed ‘experimentalist’ or ‘manipula-tionist’ views of causation. See eg, Cartwright, How the Laws of Physics Lie 36–38; E Flichman, ‘Causación y antro-pomorfismo’ (1985) 5(2) Análisis Filosófico 37–56; J Pearl, Causality (Cambridge, Cambridge University Press, 2000); H Price, ‘Agency and Probabilistic Causality’ (1991) 42 British Journal for the Philosophy of Science; D Hausman, Causal Asymmetries (Cambridge, Cambridge University Press, 1998); J Woodward, Making Things Happen: A Theory of Causal Explanation (Oxford, Oxford University Press, 2003).

344 Horacio Spector

4. Maximal satisfaction of a set of causal generalisations. Let G be a set of causal generalisa-tions. G can be as large as the causal inquiry demands, depending on the practical con-text. For instance, in a given case investigators or expert witnesses can take G to be the set of causal generalisations related to ballistics and the action of bullets and projectiles in the human body. Now any set C of true singular empirical propositions maximally satis-fies G in spatiotemporal region R iff the set E of empirical propositions that are entailed by G together with C (none of which is entailed by either G or C alone) is not a proper logical part of any set E* of empirical propositions that are entailed by G together with any other set C* of true singular propositions that also satisfy G in R (but are not entailed by either G or C* alone).

As I have anticipated, I follow the mainstream philosophical literature on causation holding that in a strict sense causal relata are events, that is, discrete, spatiotemporally located changes.18 Facts and states of affairs are too abstract or too inactive to be the refer-ents of singular terms occurring in causal statements. Thus, it is not the fact that Brutus stabbed Caesar, but rather Brutus’s stabbing Caesar, the cause of Caesar’s death. Whereas descriptions of events designate discrete entities, spatiotemporally located and possessing all their concrete richness and complexity, propositions denote abstract entities whose con-tours are demarcated by the relevant abstract terms. Therefore, Brutus’s stabbing Caesar is the same event as Brutus’s stabbing Caesar on 15 March 44 BC, but the fact that Brutus stabbed Caesar is not the same fact as the fact that Brutus stabbed Caesar on 15 March 44 BC. And while Brutus’s stabbing Caesar is the same event as Brutus’s stabbing Caesar with a dagger, the fact that Brutus stabbed Caesar is not the same fact as the fact that Brutus stabbed Caesar with a dagger.

At the same time, singular causal statements are causal in virtue of their relation to causal laws/generalisations that are canonically formulated in terms of propositions picking out relevant properties of the events causally related. But how do event-descriptions instantiate the abstract, propositional antecedents in causal generalisations? This is a complex ques-tion. Donald Davidson’s well-known proposal involves a very cumbersome rendering of causal laws/generalisations in terms of statements universally quantified over events.19 I want to maintain the standard, simple schema of causal laws/generalisations as universal conditional statements: [(x) (Fx ⊃ Gx)]. When the generalisation encompasses relations rather than properties, the standard schema becomes: [(x) (F (x,y) ⊃ G (x,y))]. Therefore, I need a rule of correspondence linking event-descriptions to propositions that allows mak-ing singular causal statements instantiate the abstract antecedents of causal generalisations. For this specific purpose I propose a rule of correspondence that may be called Denominalisation. This rules works as follows. I will say that for any event e described by a participial expression, there is a true denominalising proposition p

e, that is, a true pro-

position that denominalises the participial description of e into the indicative mood of the corresponding verb. For instance, if the participial description were Brutus’s stabbing Caesar, p

e would be Brutus stabbed Caesar. Formally, for any event e described by a parti-

cipial expression of the form x’s F-ing y, in which ‘x’ and ‘y’ are names, and ‘F’ is a dyadic predicate, there is a true denominalising proposition [F (x, y)]. I will assume that events are truth-makers and propositions are truth-bearers. Accordingly, I will take it that the event e

18 The locus classicus is: D Davidson, Essays on Actions and Events, ‘Essay 7’ (‘Causal Relations’) (New York, Oxford University Press, 1980).

19 ibid, 158.

The MMTS Analysis of Causation 345

described by an event-description of the form x’s F-ing y is the truth-maker of the proposi-tion [F (x, y)]. Simply put, the event e is the truth-maker of the denominalising proposition p

e.With the above conceptual apparatus in place, we can say that an event e caused an event

e’ iff the following conditions are met for the denominalising proposition pe and the

denominalising proposition pe’:

(i) there is a set C of true singular empirical propositions that maximally satisfies G in spatiotemporal region R and p

e is a member of C;

(ii) there is a set E of true singular empirical propositions that includes all the empirical propositions that are entailed by G together with C (none of which is entailed by either G or C alone) and p

e’ is a member of E; and

(iii) No proper logical part of C together with G entails E.

Let me explain the MMTS conditions in order. Condition (i) I call the maximality condi-tion. It requires the maximality of E, and, indirectly, of C. C must maximally satisfy G in spatiotemporal region R so that E possesses the maximal empirical content that can be deduced from G and C. Unlike the INUS/NESS test, which only appeals to the notion of a minimal sufficient condition, the MMTS analysis introduces the idea of maximality.

I call condition (ii) the web condition. It secures that effect e’ is placed within the whole of empirical consequences relative to sets C, G, and E. As we will see, the web condition is critical for allowing MMTS to place e and e’ in the actual causal process, rather than in any pre-empted causal process. The MMTS analysis only picks out actual causes because they alone are correlated with a multitude of empirical consequences that are denoted by E. A pre-empted causal process may match p

e, but will generally fail to match other empirical

propositions that must also be included in E.Condition (iii) lays down the condition of minimality for C.20 This condition is needed to

exclude both redundant and spurious conditions to be causes according to the MMTS analysis. In excluding redundant conditions, it plays a role similar to that played by the ‘internal necessity’ element in the INUS/NESS account. However, as I will show in the next section, my minimality condition is also capable of ruling out spurious conditions.

We can put together the three conditions in the following formula:

An event e caused an event e’ iff pe is a member of a minimal set C of true singular empirical

propositions that maximally satisfies set G in spatiotemporal region R, and pe’ is a member of a set

E of true singular propositions that includes all the empirical propositions that are entailed by G together with C (none of which is entailed by either G or C alone).

There might seem that there is a contradiction between the ideas of maximality in (i) and minimality in (iii). This is not so. C must be ‘minimally maximal’, so to speak: it must maximally satisfy set G in spatiotemporal region R but must do so minimally, that is, excluding all redundant and spurious conditions. The basic idea of the MMTS analysis is to pick out the minimal set C of true singular empirical propositions that maximally satisfy G in spatiotemporal region R. If C meets that condition, it entails together with G the

20 For alternative definitions of minimality, see M McDermott, ‘Redundant Causation’ (1995) 46(4) British Journal for the Philosophy of Science, 535; N Hall, ‘Two Concepts of Causation’ in J Collins, N Hall, and LA Paul (eds), Causation and Counterfactuals (Cambridge, MIT Press, 2004) 260; M Ramachandran, ‘A Counterfactual Analysis of Causation’ (1997) 106 Mind 270. Unlike the set-theoretical notions used by these authors, the ‘mereo-logical’ concept introduced in the text also excludes spurious conditions from set C.

346 Horacio Spector

maximal set of empirical propositions E. A kind of efficiency animates my account: output maximisation and input minimisation.

In simple cases, the MMTS analysis yields the same results as the INUS/NESS account. Consider this case:

Lethal remedy. Alfred and Evelyn put bromide, a precipitating agent, into Emily’s regular medicine. The generally innocuous strychnine constituents of the medicine accumulated at the bottom of the bottle forming a lethal concentrate. Emily eventually consumed the fatal dose of strychnine and died from asphyxiation.21

Alfred and Evelyn’s putting bromide into Emily’s medicine caused Emily’s death accord-ing to the MMTS account insofar as the denominalising proposition ‘Alfred and Evelyn put bromide into Emily’s medicine’ is a member of a minimal set C of true empirical proposi-tions that maximally satisfy a set of causal generalisations centrally including those con-cerning the chemistry of precipitation by bromides and the chemistry of strychnine poisoning. In addition, the denominalising proposition ‘Emily died’ is a member of the set of all the empirical propositions that are entailed by C and the mentioned set of chemical generalisations. The INUS/NESS account seems to concord since we can accept that the couple’s action is a non-redundant part of the ‘complete instantiation’ of the antecedent of a causal law (in fact there are more than one) and that Emily’s death is an instantiation of the consequent of that causal law.

Yet the MMTS analysis does not necessarily agree with the INUS/NESS account. Consider this case:

Deadly wife. In Nazi Germany a woman denounces her liberal husband to the Gestapo as ‘enemy’ of the Third Reich. The husband is condemned to death and executed a few days after.22

There is an indubitable causal relationship between the wife’s denunciation and the hus-band’s death, but this relationship cannot be understood in terms of a ‘law of nature’ or a ‘causal law’ and, therefore, cannot be captured by the INUS/NESS account, which essen-tially appeals to those notions. In contrast, the causal connection in this case can easily be captured by the MMTS analysis. In fact, both Lethal remedy and Deadly wife involve causal generalisations in the sense previously defined. No appeal to ‘laws of nature’ or ‘causal laws’ is needed.

Deadly wife is a hard case for the INUS/NESS account because there does not seem to be a universal law, either ‘natural’ or ‘causal’, that could establish a universal invariable connec-tion between the wife’s action and the husband’s death. In a different social situation a denunciation of someone as enemy of the government would cause laughter. There is nonetheless a true causal generalisation that links the denunciation with the death of the denunciated person under the special circumstances of Nazi Germany. True, one might try to see this generalisation as a statement derived from a universal law. In order to get that universal law we might try to substitute ‘purely qualitative predicates’ for the predicates ‘Nazi Germany’, ‘Gestapo’ and ‘Third Reich’, which make reference to a particular historical situation. Yet I believe that universal statements resulting from our attempts would be sub-jected to several exceptions and, therefore, could not really count as universal laws. Eventually we would probably be led to a universal statement formulated in terms of a

21 This case is taken from Agatha Christie’s famous first novel The Mysterious Affair at Styles.22 This hypothetical is adapted from a real post-war German case. See: G Radbruch, ‘Gesetzliches Unrecht und

übergesetzliches Recht’ (1946) 1 Süddeutsche Juristenzeitung 105–08.

The MMTS Analysis of Causation 347

concept like ‘police state’, which could rule out all ‘exceptions’ as falling beyond its range of application. At that point, however, our ‘universal statement’ would really establish a logical or conceptual relationship, rather than a causal, contingent one. Police states are by defini-tion states that kill people under certain conditions.

In the following three sections we shall see that the analysis defended in this essay can clearly deal with all the difficult problems presented in the literature, that is, spurious con-ditions, causal pre-emption, alternative causation, ‘causation’ by omissions, and ‘causation’ by double preventions. These problems can only be treated by the INUS/NESS account, if at all, in ad hoc ways, and I believe that parsimony is an important virtue of philosophical theories.

III. SpurIouS condItIonS

A serious problem for the INUS/NESS variety of the regularity account is that any condi-tion can figure in an INUS/NESS set S if S also includes a ‘backing’ disjunctive condition that contains a proposition negating that that condition holds and a proposition affirming that an actual causal condition obtains.23 In this way spurious conditions might become causal conditions. Thomson gives the following example.24 Suppose David shoots Charles in the head. Suppose also that David’s shooting was a necessary condition for the set of conditions to be sufficient, in conjunction with the relevant causal generalisations, for Charles’s death. Now David’s shooting Charles is also denoted by the following conditions:

(1) Caesar crossed the Rubicon.(2) Either Caesar didn’t cross the Rubicon or David shot Charles.

If the fact that David shot Charles is a necessary member in a set of conditions that is sufficient for Charles’s death, the conjunction of the facts denoted by propositions (1) and (2) is also a necessary member in a set of conditions that is sufficient for Charles’s death. In fact, given the disjunction in proposition (2), the set cannot be sufficient for Charles’s death (according to the relevant causal generalisation) unless we also include condition (1), so it seems that Caesar’s crossing the Rubicon was a causal condition of Charles’s death under the INUS/NESS account. Strevens holds that, in order to avoid this problem, ‘causal suffi-ciency ought to be defined, then, so that a set of conditions is causally sufficient for an event e only if the conditions represent a causal process that produces e’. He adds: ‘A set of condi-tions entailing e represents a causal process producing e, I propose, just in case each step in the entailment corresponds to a strand in the relevant causal web’.25 The problem with this account is that it must give up its goal to provide a non-circular analysis of causation. In fact, this solution is circular as an account of causation in that it employs the expression ‘relevant causal web’.

The MMTS analysis supplies a straightforward solution to the problem of spurious con-ditions. Let’s assume that the proposition ‘David shot Charles’ (p

e) is a member of a single-

ton set C of true propositions that maximally satisfy G in a certain spatiotemporal region.

23 Strevens, ‘Mackie Remixed’ (n 6) 26; Thomson, ‘Some reflections on Hart and Honoré, Causation in the Law’ (n 9) 151–53; Fumerton and Kress, ‘Causation and the Law’ (n 7) 95.

24 Thomson (n 9) 151.25 Strevens, ‘Mackie Remixed’ (n 6) 28.

348 Horacio Spector

The proposition ‘Charles died’ (pe’) is a member of E. Because C together with G entails E,

David’s shooting caused Charles’s death. Let C* be a set that contains proposition pe1

‘Caesar crossed the Rubicon’ and proposition p

e2 ‘Either Caesar didn’t cross the Rubicon or David

shot Charles’. Because C* together with G also entails E, it might seem that Caesar’s crossing the Rubicon is also a cause of Charles’ death. In fact, if we remove p

e1 from C*, C* no longer

entails E, so pe1

is necessary for the sufficiency of C*. However, MMTS does not allow Caesar’s crossing the Rubicon to be a cause, which is what we want. Let’s see why. C is a proper logical part of C*, because C* entails C but C does not entail C*. In fact, C does not entail C* because C* also contains the proposition ‘Caesar crossed the Rubicon’. Therefore, there is a set of propositions C, such that (i) C is a proper logical part of C* and (ii) C together with G entails E. (I assume that Caesar’s crossing the Rubicon is empirically irrel-evant in relation to G and E.) This shows that C* does not meet the minimality condition. Basically, sufficient sets that contain spurious non-redundant conditions as well as those that contain redundant conditions do not meet the minimality condition. MMTS puts both spurious and redundant conditions on a par.

IV. pre-eMptIon

We have already said that the INUS/NESS account is able to resolve properly cases of ‘ex ante’ pre-emption in which a ‘backup’ causal process would have been initiated if and only if the actual causal process had not been initiated or successfully completed. However, the INUS/NESS account has a harder time to resolve ‘early’ and ‘late’ pre-emption cases. In ‘early’ pre-emption, both the conditions corresponding to causes C

1 and C

2 (where C

1 is

temporally prior to C2) are instantiated, but cause C

2 pre-empts cause C

1 by cutting off or

negating one of the conditions corresponding to cause C1. The problem is that in ‘early’

pre-emption the sufficient set of pre-empted cause C1 is instantiated at a moment prior to

the moment in which the effect occurs. In ‘late’ pre-emption cases the pre-empted causal process had not only actually initiated but all its relevant conditions had also been fully instantiated so as to guarantee the occurrence of the effect if not for the intervention of the pre-empting causal process. That is, ‘late’ pre-emption cases are those in which the pre-empted causal process has been completed except for its effect.26 In these cases the INUS/NESS theorist seems committed to accepting that the conditions that are necessary in the sufficient set of the pre-empted causal process are INUS/NESS causes, an obviously counterintuitive conclusion. One way out of this conclusion would be for the INUS/NESS theorist to appeal to some notion of physical contiguity between the sufficient set (or some of its members) and the effect. This move would exclude negative conditions as possible causes, a result that some INUS/NESS theorists might not be prepared to accept.

Is the MMTS analysis affected by pre-emption? To see how it works in practice, consider some common examples:

Final destination 1. A traveller enters a desert with a water keg. An enemy secretly puts a fatal dose of poison in the water. Before the traveler drinks the water, another person steals the keg thinking it contains pure water. The traveller dies of thirst.27

26 Moore, Causation and Responsibility: An Essay in Law, Morals, and Metaphysics (n 9) 493.27 Hart and Honoré, Causation in the Law (n 2) 239.

The MMTS Analysis of Causation 349

Final destination 2. A man, Charles, drinks a fatal dose of poison at a certain time. The poison would normally take 15 minutes to produce Charles’s death. An enemy shoots him dead shortly after. Charles’s death occurs one minute later.28

Final destination 3. A barge carrying supplies to the port is delayed by a collapsed bridge A that obstructs the waterway. If the barge had not been delayed by bridge A, it would have been delayed anyway by a second collapsed bridge B that also obstructs the waterway.29

Because the MMTS analysis includes the web condition, the effect must always be encompassed in a set of empirical consequences E. I claim that this feature of the MMTS analysis makes its applications fit with our common intuition that pre-empted causes are not actual causes. In Final destination 1 (‘early’ pre-emption), for the poisoning of the water supply to be the cause of the traveller’s death, there must be a set E that maximally includes all the empirical consequences in accordance with the relevant set of causal generalisations concerning the action of poisons in the human body. Therefore, E must include proposi-tions stating the time, the manner and other relevant traits of the traveller’s death. One member of E must say, for instance, that the traveler’s corpse contained residues of poison. For inferring this proposition from C and the relevant set of causal generalisations, C must include the proposition that the traveller drank the poison and this proposition must be true according to the maximality condition. However, this proposition cannot be true, and, therefore, it cannot be a member of C because the keg was emptied before the traveller could drink the water.

Final destination 2 (‘late’ pre-emption) is different because the proposition that Charles drank the poison at a certain time was true and, consequently, it can be included within set C. The issue is whether Charles’s drinking of the poison was the cause of his death in accordance with MMTS. Now C together with the relevant set of causal generalisations entails a set E of empirical consequences. Recall that the web condition requires that the proposition ‘Charles died’ be included within set E, and that the definition of maximal sat-isfaction of G requires as well that E be maximal. For the set E containing the proposition ‘Charles died’ to be maximal, it must also contain propositions that specify the manner and time of Charles’s death. For instance, E must contain the proposition ‘Charles died 15 min-utes after drinking the poison’. Now the proposition ‘Charles died 15 minutes after drinking the poison’ cannot be a member of E because it is not true. Nor are true other propositions that presumably are members of E and that refer to occurrences that take place after Charles’s death. For instance, E may include a proposition to the effect that Charles goes into convulsions 10 minutes after the drinking. This proposition is obviously false because Charles is dead by that time.

Final destination 3 (‘late’ pre-emption) is controversial for the INUS/NESS account because, depending on how the relevant causal generalisation is framed, it might be thought that the whole gamut of initial conditions of the set C has been fully instantiated as regards both bridge A and bridge B. Of course, this is not the case if the set C is temporally stretched as to capture the physical contact of the ship with the bridge. This contact presumably occurred with respect to bridge A but not with respect to bridge B. Yet if the relevant causal generalisation is framed in such a way that it covers conditions such as the characteristics of the ship, its position, speed and direction, the currents of the river, the collapse of the bridge

28 Wright, ‘Causation in Tort Law’ (n 3) 1773, 1781, 1795; Thomson, ‘Some reflections on Hart and Honoré, Causation in the Law’ (n 9) 151.

29 Hart and Honoré, Causation in the Law (n 2) 250.

350 Horacio Spector

and so on, short of any condition that logically entails the physical contact of the ship with the bridge, then it might be alleged that both the collapsed bridge A and the collapsed bridge B are causes of the ship not reaching port on time. Indeed, under this ‘time-bounded’ framing of the causal generalisation, its set C of initial conditions has been fully instanti-ated even with respect to bridge B. The point is that the success of the INUS/NESS account to discard bridge B as a putative cause relies on how we frame the relevant set of causal generalisations. Needless to say, framing of generalisations is a controversial matter.

According to MMTS, the case of the two bridges has a clear resolution. As applied to bridge B, E includes not only the proposition that the ship did not reach port on time but also propositions denoting other facts associated with the ship colliding with bridge B, or being stopped by bridge B, such as the presence of the ship in the nearby of bridge B, or traces of the paint of bridge B on the hull of the ship. Because these other facts denoted by the propositions included in E did not occur, E cannot be true and, therefore, the causal claim with respect to bridge B is false, whereas the causal claim with respect to bridge A is true because both C and E are true relative to bridge A.

I have argued so far that, if c1 is the actual cause, as opposed to c

2, the relevant set E of

empirical consequences will generally be different from the set that we would have if c2 were

the actual cause. This claim might be challenged. For example, it might be suggested that a ‘lately’ pre-empted causal process is conceivable that is empirically indistinguishable from the actual process. I cannot imagine an interesting case like this in a moral or legal context, and so I leave its construction to my imaginary challenger. My sense is that, if the actual causal process and the supposedly ‘lately’ pre-empted causal process are empirically equiv-alent, there is no basis to assert that one causal process has been pre-empted by the other. That is, if two causal processes ran to their respective completions without differentiating themselves at all in empirical terms, I would be inclined to regard them as cases of concur-rent causation rather than as cases of pre-emption. In my analysis causal pre-emption is also an empirical notion.

V. alternatIVe cauSatIon

Cases of alternative causation present problems of set selection for the INUS/NESS account.30 Consider the following cases:

Bachelor party. Dandy’s 10 friends are crazy about his bride, Mary. In the bachelor party each of them puts one drop of poison in Dandy’s wine. Each friend acted on his own (with no previous agreement). Six drops of poison were sufficient to kill Dandy. Dandy drinks the wine and dies.

Collegiate decision. The 10 members of a club’s board expel one member from the club by unani-mous vote. Each voter acted on his own (with no previous agreement). A majority of only six votes was necessary according to the club’s rules.31

30 ibid 235–53.31 Stapleton, ‘Choosing What We Mean’ (n 5) 443; Stapleton’s board has nine members. The case is a version of

the so-called ‘leather spray case’, in which the German Federal Supreme Court convicted a company’s board mem-bers for intentional bodily harm: 37 BGHSt 106 (1990). The board had failed to recall the dangerous spray from the marketplace. I am indebted to Marcelo Sancinetti for quotation of this case.

The MMTS Analysis of Causation 351

According to the INUS/NESS account each drop is a cause of Dandy’s death because it is a member of a (possible) six-drop set that is sufficient for Dandy’s death, being each drop necessary for the sufficiency of that set. The same applies to the board’s decision. Each member’s vote is a ‘weakly’ necessary member of a (possible) six-vote set that is sufficient to expel the member. I do not take exception to this conclusion. I agree that each drop and each vote is a causal condition. My problem is with the explanation. It yields two counter-intuitive results. First, there are 210 possible six-member sets that are INUS/NESS sets in regard to the relevant outcome (ie, death, expulsion).32 It seems arbitrary to pick out any of those sets to hold one drop/vote to be a causal condition. Second, suppose we pick out set S that contains drops/votes A, B, C, D, E and F. Then each drop/vote is an INUS/NESS causal condition of the outcome. But with respect to S drop/vote H, for instance, is not an INUS/NESS causal condition. Notice that the INUS/NESS account is formulated in terms of the connective ‘if and only if ’. Therefore, we must turn to a different set S’ that contains H (there are many possible combinations). Now H is not a causal condition with reference to set S and is a causal condition with reference to set S’. This is not a contradiction, but dis-plays a sort of relativity in our causal claims. It seems ad hoc to choose the reference set of initial conditions so that each drop/vote becomes a causal condition. Naturally, an arbitrary choice of the reference set runs afoul of the presumed objectivity of causal claims.

According to the MMTS analysis, the set selection problem is avoided because there is one single reference set of initial conditions. The relevant set C of true singular propositions must include the propositions denoting the 10 drops/votes, because the relevant set of causal gen-eralisations, G, must be maximally satisfied. That is, each of the 10 drops/votes is an MMTS causal condition because the corresponding proposition is a member of the minimal set C that is required to generate the maximal set E of empirical consequences. In fact, C maximally satisfies the relevant generalisation when the set E of empirical consequences that are entailed by that generalisation together with C is not a proper logical part of any set E* of empirical consequences that are entailed by that generalisation together with any other set C*. The maximality condition ensures, with respect to Bachelor party, that the time of the death, its manner and other empirical features are included in E. Once maximality is met, we obtain the minimalist antecedent set by excluding all spurious and redundant conditions. Now the sup-posedly ‘more than needed’ drops/votes must be included in C because some empirical con-sequences would otherwise be absent from E, in which case G would not be maximally satisfied. This means that the ‘more than needed’ drops/votes are MMTS causal conditions as well. For instance, the additional drops might have speeded up death thus altering time, or they might have modified the quantity or quality of residual substances in the victim’s blood, and so on. So we don’t need the additional drops for ‘sufficing’ death, but we certainly need them to ‘suffice’ other consequences that must be included in the maximal set E. Collegiate decision is more difficult, because the fact that a vote is unanimous as opposed to merely majoritarian does not normally make great empirical differences, but even in this case una-nimity must be included in C for some empirical consequences to be present in E. Some of those empirical consequences are, for instance, the emotional reactions on the part of the expelled member and other people in the club, differences in the board proceedings, differ-ences in potential legal actions, and so on. The gist of the web condition is to see every effect as part of a set of empirical consequences, rather than as a free-standing event.

32 210 is the binomial coefficient 1 10 2  = 10! = 10•9•8•7 6 (10–6)!6! (4•3•2•1)

352 Horacio Spector

VI. actS, oMISSIonS and double preVentIonS

Consider the following cases:

Bad nurse. A patient has an anaphylactic reaction upon drinking a medication. The nurse fails to give him proper anti-allergic medication, which she could have easily done. The patient dies later on.

Bad captain. A ship captain finds a shipwreck survivor drowning in the sea but fails to throw him a lifebelt, which he could have easily done. The survivor dies later on.

It is clear that the captain and the nurse have both let the survivor and the patient die. Their behaviour is wrongful just as an instance of an omission to aid. But the question now is not whether the behaviour is wrong but whether the nurse and the captain have caused via their omissions the patient’s and the survivor’s deaths. Defenders of the INUS/NESS approach assume that omissions generally are negative causal factors, just as acts are posi-tive causal factors. For instance, Wright associates an omission with the absence of preven-tion.33 Thus, non-treatment and non-floating-device are negative factors that are ‘weakly’ necessary for the set of relevant causal conditions to be sufficient. On this view, the nurse’s failure to give the patient anti-allergic medication and the captain’s failure to throw the lifebelt are instantiations of those negative conditions and, consequently, INUS/NESS causal conditions of the deaths. This is an erroneous view, however. It is true that the set of NESS/INUS conditions of the allergic patient’s death must include the negative condition that he is not given medication, but the nurse’s failure is not a truth-maker of this negative condition, because someone else could have given the patient proper medication. By the same token, it is true that the set of NESS/INUS conditions of the shipwreck survivor’s death must include the negative condition that he does not have a floating device, but the captain’s failure is not a truth-maker of this negative factor. For instance, a member of the crew could have thrown the drowning person a life-belt. Omissions are not truth-makers of negative causal factors. Whether they are causally sufficient conditions of negative causal factors depends on the circumstances and the relevant causal generalisation.

The key to discussing omissions as possible causes is to notice that acts and omissions are forms of behaviour that condition causal processes in different ways. Acts are generally truth-makers or causally sufficient conditions of the positive (or negative) conditions established in the antecedent of a causal generalisation. From the practical viewpoint of the agent, acts function through the application of the technical guides sustained or warranted by causal generalisations. It is only because causal generalisations sustain technical guides that agents can use such generalisations in order to produce outcomes in the world. Technical guides do not exhaust the variety of practical guides that causal generalisations may sustain, but they are essential to understand the connection that there is between causal generalisations and agent-conditioning by acts.

Now, whether an act involves a truth-maker or a causally sufficient condition depends on the type of behaviour. Shooting makes true one of the positive conditions (ie, shooting) established in the antecedent of a causal generalisation that relates shooting and death. Alternatively, triggering the gun is a causally sufficient condition of the instantiation of a

33 Wright, ‘Acts and Omissions’ (n 8) 290–92. Wright says: ‘Omissions generally operate as negative causes of some consequence, by precluding the occurrence of a possible preventing cause’ (291).

The MMTS Analysis of Causation 353

positive condition in the antecedent of the generalisation (ie shooting). In the latter exam-ple, there are two causal processes: in one process the causal relata are the bodily movement (ie, triggering) and the gun shooting; in the other the causal relata are the shooting and the victim’s death. One causal generalisation relates the shooter’s triggering and the gun’s shooting. The other generalisation links the shooting with the victim’s death. While causation is the general term for both concepts, I introduced the label agent-conditioning to designate the various ways in which agents can relate to the world in making things happen or letting things happen.34 In this example agent-conditioning is just a form of MMTS cau-sation in which one of the conditions in the antecedent of the relevant causal generalisation is a bodily movement of the agent. Accordingly, we can roughly say that a property concep-tually required by ‘P does X’ (or ‘P makes X happen’, as something different from ‘P lets X happen’) is that P makes bodily movements that are truth-makers or causally sufficient conditions of the instantiation of a positive condition established in the antecedent of a causal generalisation one consequence of which is X.35

Whereas acts are typically truth-makers or causally sufficient conditions of the instantia-tion of positive conditions established in the antecedent of a causal generalisation, omissions are ‘but for’ conditions of the instantiation of negative conditions established in the antecedent of a causal generalisation. More precisely, I must restrict my claim to non-preventive omissions, that is, failures to prevent. In fact, as I will show later on, other omissions may have a different character.

My chief assertion in this section is that non-preventive omissions are ‘but for’ condi-tions of negative MMTS conditions. This is quite different from saying that omissions are MMTS conditions (or NESS/INUS conditions) of negative MMTS conditions. It is also different from asserting that omissions are MMTS conditions (or NESS/INUS conditions) of the outcome of the causal process. The captain lets the survivor die in the sea by omitting to throw him a lifebelt. The causal generalisation leading to the survivor’s death includes in its antecedent a number of negative conditions: the survivor does not have a lifebelt or any other floating device, no other rescue comes in time, and so on. The captain’s omission is neither a truth-maker nor an MMTS condition (or a INUS/NESS condition) of any of those negative conditions. This means that omissions are not negative antecedent condi-tions in causal generalisations. Omissions are generally forms of behaviour that intervene in the world by allowing certain causal process to run (to completion).

As said before, omissions are not truth-makers of negative conditions (save in rare cir-cumstances). They often are not causally sufficient conditions either. Rather, omissions are typically negative ‘but for’ conditions of negative conditions that figure in the antecedent of a causal generalisation. By incurring an omission an agent typically ‘collaborates’ with a causal process. He does not set up the causal process, nor does he change or redirect it. Non-preventive omissions conceptually presuppose that the agent could have counteracted the relevant causal process by negating one of the negative conditions laid down in the antecedent of the causal generalisation. Indeed, the captain could have made the negative condition ‘non-floating-device’ false by throwing the survivor the lifebelt. The nurse could

34 Agent-conditioning in the sense explained must not be confused with agent causation, which refers to the relation of internal volitions and external outcomes; see eg T O’Connor, ‘Agent Causation’ in T O’Connor (ed), Agents, Causes, and Events: Essays on Indeterminism and Free Will (New York, Oxford University Press, 1995) 173–200; T O’Connor, ‘Why Agent Causation?’ (1996) 24 Philosophical Topics 143–58.

35 This is a variation on a position I defended elsewhere. H Spector, Autonomy and Rights (Oxford, Clarendon Press, 1992) 149.

354 Horacio Spector

have made the negative condition ‘non-treatment’ false by giving the patient proper medi-cation. An omission is not a form of ‘negating’ a condition, positive or negative, in the antecedent of a causal generalisation. Instead, an omission typically is a negative ‘but for’ condition of a negative condition. Omissions are generally ‘but for’ ‘causes’, rather than INUS/NESS or MMTS causal conditions. However, the negative conditions in respect to which omissions are ‘but for’ causes are certainly causal conditions of the relevant outcome. That is, ‘non-floating-device’ and ‘non-treatment’ are MMTS conditions of the survivor’s and patient’s deaths.36

We may conclude that there is generally a causal asymmetry between acts and omissions because acts are typically truth-makers or MMTS causal conditions of MMTS positive con-ditions, that is, of positive conditions in the antecedent of a causal generalisation. (Sometimes, acts are MMTS causal conditions of MMTS negative conditions.) In contrast, omissions are not truth-makers or causally sufficient conditions of negative conditions. Instead, they must typically be analysed under the counterfactual dependence account of causation. Non-preventive omissions are negative ‘but for’ conditions of negative MMTS conditions. One could then expect this account of non-preventive omissions to reproduce a general trait of the counterfactual dependence account, namely, its inability to handle cases of concurrent causation. Indeed, one of the most intricate issues in the literature is how to resolve cases of overdetermination by non-preventive omissions. Consider a well-known case:

Defective non-used brakes. A car renter, Amy, failed to repair defective brakes in a car that he rented to Martin, and Martin failed to use the brakes to avoid running into a pedestrian.37

Unlike other non-preventive omissions, Amy’s and Martin’s omissions are not but- conditions of the outcome (ie, the crashing into the pedestrian). If Amy had repaired the brakes, the crash would have nonetheless occurred (the brakes were not used). If Martin had used the brakes, the crash would have anyway occurred (the brakes were defective). However, it is true that the conjunction of Amy’s repairing the brakes and Martin’s apply-ing them would have negated one negative condition in the relevant MMTS causal gener-alisation (ie, absence of effective braking) and, consequentially, would have prevented the crash. We can state this in this way:

(1) If Amy had repaired the brakes and Martin had applied them, the crash would not have occurred.

Let us assume now that De Morgan’s laws can treat omissions as negations, since this is intuitively plausible in this context.38 By De Morgan’s laws, (1) is equivalent to:

36 While it is common to regard a failure to prevent as a ‘but for’ condition of the relevant effect, or even as a ‘but for’ condition of the causal relation, I was unable to find an account of failures to prevent as ‘but for’ conditions of negative conditions. See, for instance: Stapleton, ‘Choosing What We Mean’ (n 5) 433, 436–37 (she discusses a hypothetical where a gardener fails to provide water to a plant that consequentially dies); Moore, Causation and Responsibility: An Essay in Law, Morals, and Metaphysics (n 9) 351–54, 399–400, 451–52, 478–79 (Moore holds that counterfactual dependence is essential for omission liability, but he denies that ‘but for’ condi-tions are causes). For an analysis of omissions in terms of counterfactual claims about ‘genuine’ causal processes, see: P Dowe, Physical Causation (Cambridge, Cambridge University Press, 2000) 136–40.

37 Wright, ‘Causation in Tort Law’ (n 3) 1801.38 De Morgan’s laws say that ‘not-(A and B)’ is equivalent to ‘not-A or not-B’, and that ‘not-(A or B)’ is equiva-

lent to ‘not-A and not-B’. Of course, we can substitute ‘not-A’ for ‘A’, and ‘not-B’ for ‘B’, in which case we obtain, by double negation, the following equivalences: ‘not-(not-A and not-B) iff A or B’, and ‘not-(not-A or not-B) iff A and B’. The latter equivalence can be reversed: ‘A and B iff not-(not-A or not-B)’. This law was used in the text to equate (1) and (2).

The MMTS Analysis of Causation 355

(2) If the disjunction of Amy’s and Martin’s omissions had not occurred, the crash would not have occurred.

This means that the absence of effective braking and, consequentially, the crash counter-factually depends on the disjunction of Amy’s and Martin’s omissions. Therefore, concurring non-preventive omissions are disjunctive ‘but for’ conditions of MMTS negative conditions (and of the relevant outcomes as well). Because both Amy’s and Martin’s omissions are on a par in regard to their non-preventive relation to the absence of effective braking and crash, there are no reasons to differentiate between both omissions, nor to regard one as pre-emptor of the other.

In his monumental Causation and Responsibility,39 Michael Moore holds that a disjunction of omissions cannot be a ‘but for’ condition of an outcome because an outcome cannot coun-terfactually depend on a disjunction without at the same time depending on each of the dis-juncts.40 Moore invokes De Morgan’s laws for this conclusion, but his application of these laws is different from the one made above. If this argument were sound, then it would also apply to the disjunction of omissions as a counterfactual determiner of negative MMTS conditions. The argument is not well-articulated, so I will interpret it in the only way in which it seems intelligible to me. Moore says: ‘If one makes sense of negative and disjoining events, then from not (fire

1) and not (fire

2), one should be able to infer not (fire

1 or fire

2), and vice versa’.41

Though Moore formulates the original version of his argument as regards disjunction of events (eg fires), he extends it to omissions in discussing an argument from Phil Dowe.42 The core of his argument seems to be on page 355. There he says:

If the negation of this larger event [~(F1 v F

2)] is equivalent to the conjunction of the negations of

each smaller event [(~F1 . ~F

2)], one might well conclude that whatever is not true of each fire

considered separately is not true of the larger event that is the disjunction of these fires.

Therefore, for Moore it violates De Morgan’s laws to say ‘that the larger event caused e while neither of the disjuncts making up the larger event caused e’. However, I contend that this is a misapplication of De Morgan’s laws. Indeed, it is possible for a disjunctive event to be a cause of an outcome e even if it is false of each disjunct that it caused e. Let’s assume that it is false of each fire that it caused e. By De Morgan’s laws this entails that it is false that fire

1

caused e or that fire2 caused e. But this is not to say that it is not true that fire

1 or fire

2 caused

e. This is so because causal predicates do not distribute over disjunction according to the counterfactual dependence account. That is,

(3) (A or B) caused e

is not equivalent to:

(4) (A caused e) or (B caused e)

In fact, drawing (4) from (3) is fallacious. We can illustrate this fallacy with a simple exam-ple. Let’s accept that Leibniz and Newton independently invented infinitesimal calculus and that no one else was actually working on calculus in the seventeenth century.43

39 See, generally, Moore, Causation and Responsibility: An Essay in Law, Morals, and Metaphysics (n 9).40 Moore (n 9) 355 and 450.41 Moore (n 9) 355. One additional problem is that there is a misprint on this page. Moore adds: ‘This means

(F1 . ~F

2) ≡ ~(F

1 v F

2)’. This formal representation is mistaken. It should instead say: ‘This means (~F

1 . ~F

2) ≡

~(F1 v F

2)’. Since this is a misprint, I will take the correct formulation.

42 Moore, (n 9) 450.43 GG Leibniz and I Newton, El cálculo infinitesimal (Buenos Aires, EUDEBA, 1977).

356 Horacio Spector

Accordingly, we can take the following counterfactual as true:

(5) (Newton’s invention or Leibniz’s invention) caused calculus to be known in the seventeenth century.

If causal predicates in the counterfactual dependence account distributed over disjunc-tion, (5) would be equivalent to:

(6) (Newton’s invention caused calculus to be known in the seventeenth century) or (Leibniz’s invention caused calculus to be known in the seventeenth century.)

But (6) is false because each of its disjuncts is false. In effect, in the closest possible world in which Newton did not invent calculus, calculus is still known (in the seventeenth cen-tury) through Leibniz’s discovery, and in the closest possible world in which Leibniz did not invent calculus, calculus is still known through Newton’s discovery. Yet (5) is true under our historical assumption because in the closest possible world in which neither Newton nor Leibniz invented calculus, calculus is unknown (in the seventeenth century). Therefore, we must reject the distributiveness of causal predicates (in the counterfactual dependence sense) over disjunction. As long as causal predicates are non-distributive over disjunction, (3) may be true even if (4) is false.

Moore’s argument is unsound because he conjoins De Morgan’s laws with an implicit ‘law of distribution of causal predicates over disjunction’ that is not valid. In terms of our prior example, this means that the disjunction of Amy’s and Martin’s omissions can be a ‘but for’ condition whereas each omission on its own is not a ‘but for’ condition. De Morgan’s laws only say that, given that each disjunct is not a ‘but for’ condition, it cannot be true that Amy’s omission is a ‘but for’ condition or Martin’s omission is a ‘but for’ condi-tion. This is compatible with asserting that Amy’s omission or Martin’s omission is a ‘but for’ condition of the non-operation of the brakes.

Yet our intuitions tend to blame Martin’s failure more than Amy’s. I speculate that our intuitions are affected by a confusion of normative and empirical claims. The failure to apply the brakes in the face of a pedestrian may be more blameworthy than the failure to repair the brakes (though the latter is also a grave misdeed).44 Empirically, however, con-curring non-preventive omissions symmetrically constitute a disjunctive ‘but for’ condi-tion of an MMTS negative condition. This means that the relevant MMTS negative condition (ie, absence of effective braking) counterfactually depends on Amy and Martin’s disjunctive failure. As is obvious, this is totally different from saying that Amy and Martin’s joint failure was a ‘but for’ condition of the relevant negative condition and of the outcome.

In other cases, a non-preventive omission can pre-empt a later non-preventive omission. Consider the following example, proposed by Judith Jarvis Thomson:

Bad guards. Two guards must take care of a prisoner in a cell. Sally must give him water; Bert must supply bread. Neither fulfilled, but the prisoner dies from dehydration rather than starvation.45

Unlike Defective non-used brakes, this example involves pre-emption rather than concur-rent causation. Indeed, in terms of the relevant G whereas Sally’s omission is a ‘but for’

44 Wright says that Martin’s failure preempts Amy’s: ‘Causation in Tort Law’ (n 3) 1801; Wright ‘Acts and Omissions’ (n 8) 304. From an empirical, non-normative viewpoint, I see no ground to differentiate both failures, which seem symmetrical to me. David Fischer holds the same view; see DA Fischer, ‘Causation in Fact in Omission Cases’ (1992) Utah Law Review 1335, 1349. The fact that both failures occurred at different stages in the sequence makes no difference in terms of the counterfactual dependence account.

45 J J Thomson, ‘Causation: Omissions’, Philosophy and Phenomenological Research LXVI (2003) 81.

The MMTS Analysis of Causation 357

condition of the MMTS negative condition ‘no water’, Bert’s omission is not a ‘but for’ condition of that negative condition. Bert’s omission is a ‘but for’ condition of the negative condition ‘no bread’, but this condition is not a MMTS condition according to the relevant G. In fact, if we tried to include generalisations relative to starvation in G we could not generate a maximal set E of true empirical propositions.

We conclude that in most ordinary scenarios, like Bad captain and Bad nurse, omissions are negative ‘but for’ conditions of negative causal conditions. These are the omissions I called ‘non-preventive omissions’. However, there are scenarios in which an omission can be both a negative ‘but for’ condition and a negative MMTS causal condition of a positive causal condition. Consider the following case:

Diabolical treadmill. A war prisoner is cheated into a diabolical ergometric treadmill test. The equipment has been modified in such a way that if he stops running he will turn on an electric chair that will electrocute his mate in the next room. He stops running.

The prisoner’s failing to run on the treadmill is a ‘but for’ condition of the chair turning on because if he had continued running on the treadmill, the electric chair would have remained off. It is also an MMTS causal condition of the electric chair turning on because, relative to the relevant set of causal generalisations, C includes the condition that the pris-oner stops running, and E includes the chair setting on as a consequence. Notice that, by transitivity of the causation relation, the prisoner’s omission is a negative MMTS causal condition of the mate’s death as well, because there is a further causal generalisation that links the chair turning on and the mate’s electrocution. In extraordinary cases like this, omissions resemble acts because they are MMTS conditions of positive MMTS causal factors and also MMTS conditions of the relevant outcomes, just as acts generally are.

There are other scenarios in which omissions are truth-makers of negative MMTS con-ditions of the outcome, because C must essentially include an omission according to the relevant set of causal generalisations. Consider this case:

Impoliteness. Peter made a scornful remark on accent pronunciation in a social meeting in which Bessie was introducing his new boyfriend from abroad. Peter failed to apologise after the meeting. Bessie got resentful.

Suppose this example takes place in a culture where there are social norms that make true a causal generalisation to the effect that if you humiliate someone in a social meeting and then fail to duly apologise, you cause the humiliated person to be resentful. Failure to apologise is not a non-preventive omission in the sense defined above, even though by failing to apologize you fail to prevent the humiliated person’s resentment. Indeed, non-preventive omissions are not MMTS conditions of the outcome, but only ‘but for’ condi-tions of negative conditions, because prevention in cases of non-preventive omissions can generally operate through anyone’s behaviour or through non-behavioural processes. In contrast, in this example the relevant causal generalisation essentially refers to the impolite person’s omission. Someone else’s offering his apology would not have prevented Bessie’s resentment; it would have been inappropriate.

We have argued that whereas acts involve MMTS causation both in its agent- conditioning and ordinary causation varieties, omissions generally are negative ‘but for’ causes of nega-tive MMTS causal factors, except in cases like Diabolical treadmill and Impoliteness, where an omission can be causal in a form similar to acts. Just as omissions can sometimes resem-ble acts, acts can sometimes resemble omissions. Acts resemble omissions when they are

358 Horacio Spector

positive ‘but for’ causes of negative MMTS causal factors. This is true of cases where an agent positively removes an obstacle or impediment (eg, a safety device). These actions are called ‘double preventions’ in the philosophical literature. Double preventions are acts that prevent a preventive causal process thus allowing a certain effect to occur. Consider the following cases:

Suicidal husbands. Three husbands in a gated community decide to commit suicide pretending an accident for their wives to be able to claim their life-insurance policies. They turn off the circuit breaker, get into the pool, and throw into the water an electrically operated audio equipment. They die by electrocution.46

Air bombing. Suzy’s mission is to bomb an enemy target. Billy is her lone escort in the mission. At t Billy prevents an enemy pilot from destroying Suzy’s fighter at t

+1, thus allowing Suzy’s triggering

of the bomb at t+2

and the destruction of the enemy target at t+3

. The bombing and destruction would not have happened had Billy not prevented the enemy’s prevention of Suzy’s mission.47

It might be thought that double-preventions (ie, pre-emptive preventions) are causal conditions along with the positive causal conditions of the non-prevented causal process. Thus it might seem that the husbands’ turning off of the circuit breaker caused their electrocution just as much as the throwing of the audio equipment into the water. By the same token, it might seem that Billy’s destroying the enemy fighter at t caused the bombing just as much as Suzy’s triggering. The throwing of the audio equipment into the water and Suzy’s triggering were certainly MMTS conditions with regard to the relevant causal generalisations. Is the turning off of the circuit breaker another MMTS condition of the husbands’ death? Is Billy’s destroying the enemy fighter another MMTS condition of the destruction of the enemy target? Obviously they are not. In effect, there is no causal gener-alisation that includes in its antecedent the turning off of the circuit breaker and death by electrocution in its consequent, just as there is no causal generalisation that includes Billy’s destroying the enemy fighter in the antecedent, the consequent of which is Suzy’s fighter bombing the enemy target.

On the other hand, under the counterfactual dependence account it is clear that the husbands’ turning off the circuit breaker allowed the water in the pool to conduct the elec-tricity, and that Billy’s act allowed Suzy’s fighter being in operation on the occasion of trig-gering. That is, the husbands’ act (setting off the circuit breaker) and Billy’s act were positive ‘but for’ conditions of negative conditions established in the antecedent of the relevant causal generalisations: ‘non-breaking of the circuit’ and ‘non-destruction prior to bomb-ing’. Had the husbands not turned off the circuit breaker, electricity would not have passed through the water. Had Billy not destroyed the enemy airplane, Suzy’s fighter would have been destroyed. Therefore, the husbands and Billy let the relevant causal processes run (to completion). One process resulted in electrocution, the other in destruction of the enemy target. Yet the husbands’ and Billy’s actions were not MMTS causal conditions of those outcomes.

Both omissions and double preventions are ‘but for’ conditions of negative causal fac-tors. However, double preventing acts are positive ‘but for’ conditions of the instantiation of

46 This case is taken from: C Piñeiro, Thursday Night Widows, trans M France (London, Bitter Lemon Press, 2009). Similar cases can be found in the legal literature; see eg Moore, Causation and Responsibility: An Essay in Law, Morals, and Metaphysics 62–63 (turning off of respirator and tying up of lifeguard); M Ferrante, ‘Causation in Criminal Responsibility’ (2008) 11.3 New Criminal Law Review 481 (disabling of scuba diving equipment).

47 Hall, ‘Two Concepts of Causation’ (n 20) 241.

The MMTS Analysis of Causation 359

a negative MMTS condition established in the antecedent of a causal generalisation. The relevant negative MMTS condition would have been negated if the double preventer had not acted so as to block the prevention of the causal process. Like omissions double preven-tions are ‘but for’ conditions related to MMTS causal conditions. The fundamental differ-ence between omissions and double preventing acts is that the former are negative ‘but for’ conditions, whereas the latter are positive ‘but for’ conditions.48

VII. concluSIon

To understand causal claims in moral and legal contexts we must distinguish between ordin ary causation by events and agent-conditioning. Causes are events that correspond to some positive MMTS conditions according to the relevant set of causal generalisations. Other MMTS conditions are causal factors in a generic sense. Agent-conditioning is a different matter. Acts are generally forms of agent-conditioning that rely on an MMTS rela-tionship between bodily movements and certain MMTS positive conditions. In contrast, non-preventive omissions are generally ‘but for’ conditions of negative conditions. Other forms of agent-conditioning (v.gr., double preventions) can be analysed in terms of various forms of counterfactual dependence related to either positive or negative conditions in MMTS causal relations. Whereas the MMTS account bears on ‘commissive’ agent- conditioning (making things happen), counterfactual dependence is the proper account for ‘omissive’ agent-conditioning (letting things happen).

48 Phil Dowe treats omissions and double preventions (which he calls ‘quasi-causation’) as counterfactual claims about ‘genuine causation’. See P Dowe, ‘A Counterfactual Theory of Prevention and “Causation” by Omission’ (2001) 79 (2) Australasian Journal of Philosophy 217. As said in n 36 above, the view defended in this paper is different from Dowe’s because it analyses omissions and double preventions as ‘but for’ conditions of negative causal conditions rather than as ‘but for’ conditions of causal relations.