Menzies on causation: difference-making and its flaws by Hayden Wilkinson

Early counterfactual theories of causation such as that of Lewis (1973) tend to be beset by various counterintuitive consequences such as the proliferation of profligate causes, and an insensitivity to context[1]. As I describe in this paper, Menzies (2004) builds on Lewis’ account and formulates a novel interpretation of causation as difference-making; that is, what is meant by claiming that some event or factor makes a difference to another. Menzies’ approach attempts to limit profligate causes and allow for context-sensitivity. However, as I will argue, he is not entirely successful as his theory still faces problems of profligacy of causes specifically in absence causation. Moreover, its context dependency has anti-realist implications and provides an untoward interpretation of cases of so-called ‘redundant causation’.

I will begin by introducing Menzies approach. He specifies the relata of his causal relation as factors rather than just events, in order to include the many causes and effects that are recognised by our common sense view, including “…events, states of affairs, absences, omissions, and other nonoccurrences.” (Menzies, 2004, p151) Notably, this leaves open the possibility that some person’s failure to act, or some absence of an object or property, may indeed count as a cause for some effect.

Menzies then claims that such a factor C is a cause of another factor E only if C makes a difference to E. Temporarily leaving aside his definition of difference-making, it is important to note that this is not Menzies’ only requirement for causation. He states in his introduction that difference-making is a necessary condition for C to cause E, but it is not sufficient. A sufficient condition would be both difference-making and some “…concept of a process linking cause with effect…” (ibid., p140) though he does not expand on this in his (2004) paper, titled and restricted to the subject of Difference-making in context. Whilst those factors C which satisfy the aforementioned condition are, according to Menzies, a subset of the set (S) of causes of E, he does not specify, in the (2004) paper at least, all of the conditions for membership in (S).

Menzies’ exact definition of a difference-maker is (D):

(D): “Where C and E are distinct factors, C makes a difference to E if and only if every most similar C-world is an E-world and every most similar ~C-world is a ~E-world.” (ibid., p153)

Here, Menzies has in mind a very precise interpretation of the world-similarity metric; what constitutes being a most similar world, how similarity is measured and thus what type of worlds are to be considered in the accessibility relation.

Instead of the maximally consistent worlds which are normally invoked in modal and counterfactual reasoning and which span all of spacetime, Menzies ‘worlds’ are “miniworlds”; that is, small-scale systems consisting of the alternative courses of development of the system in question. More specifically, they are trajectories in an n-dimensional space corresponding to the state variables {S1, . . . ,Sn} which describe the system. (ibid., p153)

The most similar worlds, so defined, are those situated within the sphere of normal worlds; where the sphere is specified by the modelM=<K,L>. K here is the kind of system i.e. a set of systems sharing the same intrinsic properties and state variables as the system under consideration (within the ‘world’ specified to be actual), and L is the set of laws governing that system (in that same specified world).

The model stipulates that the sphere contains all and only those worlds w which satisfy the following conditions:

“(i) w contains a counterpart to the actual system and this counterpart has exactly the same K-determining intrinsic properties and relations as the actual system at time t0;[2]

(ii) w does not contain any interfering factors[3] (with respect to the kind K and laws L) during the interval (t0tn);

(iii) w evolves in accordance with the laws L during the interval (t0tn).” (ibid., p160)

Notably, the actual world may not be in the sphere of normal worlds. This is because it may contain interfering factors3, depending on the scale of the system under consideration and the model which is chosen. This is in stark contrast with the strong centring assumed in Lewis’ theory.

Finally, Menzies weights the similarity of his worlds according to the Weightings of similarity principle:

“In determining the respects of similarity to the normal worlds generated by a model M, it is of first importance to preserve the initial conditions and the laws of the relevant kind of system; and it is of second importance to preserve the absence of interfering factors.” (ibid., p165)

This is similar, but not identical, to Lewis’ ranking of similar worlds. For instance, Menzies stipulates that small miracles, as Lewis defines them, are interfering factors whenever they originate outside the system[4].

Thus, according to Menzies, whether some world is, or is not, one of the most similar will be relative to the model M (and indeed the exact system specified). Hence C makes a difference to E in some actual scenario if and only if C counterfactually entails E and ~Ccounterfactually entails ~E, both relative to M. This is where context dependence is incorporated into Menzies concept of causation, as what constitutes the relevant model will depend on the context in which it is considered.

Menzies holds that this integrated context dependence puts his theory at an advantage over rival theories, such as that of Lewis (L):

(L):“Where c and e are distinct actual events, e causally depends on c if and only if e counterfactually depends on c: That is, (i) if cwere to occur, e would occur; and (ii) if c were not to occur, e would not occur.” (ibid., p141)

To illustrate the differences between Lewis’ theory and that of Menzies, consider the scenario of a gardener failing to water a plant (which they otherwise regularly water). For Lewis, the failure of the gardener (~GW), or of any given person (~SW), to water the plant would qualify as a cause of the plant’s death (PD) because, if any such person did water it then it would survive and if all failed then it would die. The gardener’s failure is counterfactually no different to, say, Queen Elizabeth’s failure – both entail PD if all other watering-failures are held fixed, and the negation of either would entail ~PD, so both are causes of PD.

Menzies, however, adopts a model restricted to the system of plant and gardener. The gardener’s tendency to water it is included in the initial conditions and the plant’s tendency to survive once watered, without external interference, is maintained by the laws. Thus, the sphere of normal worlds consists entirely of worlds in which the gardener waters the plant (GW) and in which the plant survives (PS), as depicted in the below diagram[5] taken from (ibid., p174).

Hayden Wilkinson - Menzies

A minor interfering factor[6] which prevents GW‘s occurrence, such as the factor of the gardener becoming sick on that particular day, puts us in at least the second sphere of similarity, according to the chosen model and Menzies’ weighting of similarity. Worlds of greater interference[7] – of bringing an entirely separate person into the scenario to rescue the plant, or of simultaneously having the gardener fall sick and the plant overcoming its need for water – would place us further out in at least the third sphere. Hence, the most similar GW-worlds are all PS-worlds (i.e. PS and GW both hold in the sphere of normal worlds) and the most similar ~GW worlds are all ~PS-worlds (i.e. the ~GW-worlds in the second sphere don’t intersect with PS). Thus, GW makes a difference to PS and conversely, for the actual case, ~GW makes a difference to ~PS. However, the most similar ~SW-worlds are PS worlds so ~SW is not a difference-maker here.

Thus, while Lewis’ 1973 theory allows profligate causes in this case (of each of the seven billion other humans failing to water that same plant)[8], Menzies’ appears to restrict difference-makers (and hence potential causes) to a more intuitively acceptable domain. It distinguishes the context of a gardener failing to water his/her own plant from the significantly different context of considering Queen Elizabeth’s failure to travel to the particular garden and, against all likelihood, water the particular plant, as the latter is a far greater departure from normality[9]. This is a definite advantage of the theory, and results from the context dependency implicit in his method of model selection.

However, the context dependence in Menzies’ theory does not quite remove all unwanted profligate causes. For instance, there are normal occurrences (W), such as a person writing a paper (P) or an alarm clock ringing (R) at a particular time, for which there exist many possible factors (NG) which might interfere with or prevent them – the presence of nerve gas would prevent P, and a meteor colliding with the building would prevent both P and R as, perhaps, would a large earthquake. If the model is restricted to the writer and the surrounding room, or the alarm clock and the immediate surroundings, then the sudden appearance of nerve gas, the impact of a meteor, and the sudden earthquake would each count as an interfering factor – each relegated to the far outer spheres by the model[10], as in the diagram below, from (ibid., p175).

Hayden Wilkinson - Menzies 2

The most similar ~NG-worlds are W-worlds and the most similar NG-worlds are ~W-worlds. According to Menzies’ theory as outlined above, ~NG is then a difference-maker for W. i.e. the absences of nerve gas, meteors and earthquakes are all difference-makers for the writing of a paper. Primarily, this results from Menzies emphasis that the relata of his difference-making, factors, may include absences and omissions. Menzies hence seems to retain some of the profligate difference-makers produced by basic counterfactual theories[11].

Menzies only responds briefly to this issue. He suggests that the collective absence of those interfering factors should be considered asustaining cause of W, as it is only against a “…field of normal conditions generated by a causal model…” that difference-making is to be established (ibid., p175-176). This may appear to be rather an incomplete and ad hoc measure suggested specifically to overcome this difficulty, specified only vaguely and resting on the somewhat circular assumption that such absences must be included in the model which is used[12]. It certainly does not follow directly from Menzies’ earlier criterion of difference-making.

I would argue, however, that “sustaining causes” are no great threat to the theory overall. A stronger form of the theory would most likely omit them due to the lack of firm justification or clear definition, but even that would not necessarily admit all absences of interferers as causes. Indeed, Menzies is at great pains to avoid confusing the notions of difference-making and causation. In his introduction he claims that causes are difference-makers but difference-makers need not be causes, difference-making being a necessary but not sufficient condition, at least not without his additional “…concept of a process linking cause with effect…” (ibid., p140). Admitting that such absences are difference-makers then does not admit them as causes, so long as they do not entail the linking process which Menzies mentions but does not elaborate on. The absences which produce profligate causes hence do not completely undermine Menzies’ theory of causation, though it remains for his linking process to successfully exclude them or otherwise, like Lewis, accept that his profligate difference-makers are indeed profligate causes.

Another criticism of Menzies is precisely that his theory is context dependent. Lewis accepted that his early theory produced an enormous web of causal dependence between events, but that the discriminatory approach which selects particular events as more significant than others is an aspect of human practice and human enquiry rather than of any underlying causal structure (Lewis, 1986). Menzies alternative approach certainly helps to explain how that discrimination operates but, in doing so, departs from an objective account of causation independent of human observation.

A great many realists, and others who desire objectivity, would agree that causation must exist (or at least be formulated) independently of human considerations. Lewis’ theory appears to satisfy this condition because it is insensitive to context and also provides for a causal structure free of any inter-subjective disagreement of what constitutes a cause[13]. Menzies’, however, does not as there is not necessarily a uniquely acceptable model. For instance, in the plant-gardener example, various differences in the choice of model give different verdicts on difference-making. If the sick gardener’s virus is included in the world, then ~GW and ~PS both hold in FM, and SW is a difference-maker for PS. So too, if some plant-watering hero, who is determined by initial conditions to pass by the plant and save it, is excluded by the system then their action is excluded as a difference-maker, quite counterintuitively, yet if the hero is included in the system then SW is satisfied for all normal worlds and may again be a difference maker (when also including the gardener’s virus, GW is removed as a difference-maker as well). The situation appears to instantiate both kinds K, both models M, and hence SW both is and is not a difference-maker. Menzies claims that he is not supporting a mind-dependent notion of causation, nor“…a crude relativism to the effect that any causal model of a situation is as good as any other…” (Menzies, 2004, p159) but states that if a model M=<K,L> is instantiated by a situation then a factor is a difference-maker if and only if it is so within that model. Of course, there may be some objective means of selecting models above others or it might so happen that there is never, in fact, more than one kind of system and model instantiated in any situation, but Menzies provides no clear such means, merely suggesting that the model M will be the only model instantiated by a scenario once the ‘correct’ context is given. The correct context is, however, a feature of the observer who is enquiring into the scenario –the gardener’s tendency to become ill can be included or excluded from the model, depending on which model we choose, as can the gardener themself or the plant-watering hero. Simultaneous and conflicting models are hence a genuine possibility, and the selection between such models is an observer-dependent matter.

This potential indeterminacy of model selection is inconsistent with not only causal realism, but also the claims that causes or difference-makers are either observer- and context-independent. To allow for Menzies’ theory, one must therefore either adopt a non-realist view of causation or otherwise restrict the theory to describing human practice rather than the actual metaphysical status of events.

The most significant problem for Menzies’ account, however, is that of pre-emption (though similar counterintuitive results emerge in cases of overdetermination). He holds that difference-making is a necessary condition for causation. Thus, no factor which does not make a difference to the effect can be a cause of that effect. In cases of so-called “redundant causation”, which Menzies is at pains to avoid (ibid., p2), factors which we intuitively consider to be causes but which do not satisfy the definition of a difference-maker are hence excluded as genuine causes.

Suppose that there are ten shooters in a firing squad all of whom, when given a certain signal, fire at a prisoner. Suppose all are talented sharpshooters and that each shot is accurate and would, alone, be sufficient to kill the prisoner (and that, ideally, all aim at slightly different points on the prisoner’s which would result in the prisoner’s death). If the model of the system is such that it contains all ten shooters and the prisoner, the sphere of normal worlds consists only of worlds in which the shots all hit their target and in which the prisoner dies. So all most similar worlds in which shooter A fires (SA) are worlds in which the prisoner dies (PD). But the most similar ~SAworlds (perhaps their finger is temporarily paralysed) still have the other nine shooters hitting their mark and hence are still PD-worlds, so long as the factor PD is sufficiently coarse-grained that the exact manner of the prisoner’s death is not relevant. This result applies to all ten shooters, so no shooter makes a difference to the death of the prisoner. Thus, without some refinement or clarification of Menzies’ account, no individual shooter can be a difference-maker or cause of PD. The only difference-maker in a model containing all shooters is the collective firing of all ten, which may be somewhat counterintuitive. If the model is, however, restricted to any one shooter and the prisoner, then the other shooters are then interfering factors and the shooter included in the model is indeed a cause. Thus, in such cases of overdetermination, the intuition that individual contributing actions ought to count as causes is contradicted (at least in the more inclusive models) as is, again, the intuition that the causal relation between factors is not dependent on the model that some observer happens to select.

Even more counterintuitively, if shooter A fires first and the others fire a short time later if A fails to fire, then the bullet of shooter A is the one that kills the prisoner, but it is not a difference maker if those other shooters are included in the model[14]. Their tendency to fire after A’s failure results in the most similar ~SAworlds being PD-worlds as their firing still brings about the prisoner’s death (albeit perhaps in a slightly different manner). Thus, according to Menzies, shooter A’s firing does not make a difference to, nor does it cause, the prisoner’s death in this scenario of pre-emption.

Unlike the previously mentioned problem of sustaining causes, this problem cannot be resolved by some appeal to the notion of processes with which Menzies wishes to provide sufficient conditions for causation. Given that he sees difference-making as necessary, it must either be accepted that shooter A has not caused the prisoner’s death, contradicting the common sense view, or that Menzies’ account of causation is seriously flawed[15].

In summation, Menzies’ account of difference-making does make a significant contribution to the literature on causation as he succeeds in establishing a definition which is sensitive to context in much the same way as human inquiry is, and which avoids some of the profligacy of causes of Lewis (1973). Nonetheless, his definition is still problematic. It avoids profligate absences as difference-makers only by introducing an ad hoc provision of “sustaining causes” and rejects, counterintuitively, a number of causes in cases of pre-emption. It also largely fails to provide an objective criterion, independent of observers, for what is and is not a difference-maker or cause, which commits one to a non-realist position. If, however, one is willing to accept sustaining causes, dismiss certain causes in pre-emptive cases, and reject causal realism, Menzies’ view may then, and only then, be tenable.

Hayden Wilkinson completed a dual bachelor of arts and science last year and is now studying honours in philosophy at UQ.

[1]    Profligate causes have notably also been used to justify causal eliminativism, as in (Russell, 1912)

[2]    Where the time interval (t0,tn) is that over which the system is being considered .

[3]    Where an interfering factor I is one which “…instantiates an intrinsic property or relation…” in the system, “…is caused by some factor instantiating a property or relation extrinsic to the system…” and “…the laws governing the causation of I by the extrinsic factor are distinct from the laws L.” (Menzies, 2004, p160) There appears to be an implication of circularity in this definition, as it relies on I being caused by some factor. To establish that such a factor did indeed cause I, one must establish that it is a difference-maker, which it can only be if it satisfies (D) and hence fits a possible-world structure which is dependent on possible interfering factors for the model adopted. To establish causation between the factor and I, there would then need to be a causal link established between each such interfering factor in this further model and the factors bringing them about. This descends into either infinite regress or circularity, and provides an additional objection to Menzies’ theory, though unfortunately not one on which I will dwell in this paper. Given that Menzies has not specified the additional sufficient condition for causehood, that condition may potentially overcome the circularity. As the focus of this paper is (Menzies, 2004), this charge of circularity is not one which is necessarily fatal for Menzies view but it should nevertheless still be noted.

[4]    Moreover, his similarity metric, unlike its rival in (Lewis, 1973), accords higher priority to the preservation of those laws and initial conditions which are operative within the system itself (as opposed to those outside the system).

[5]    FM indicates the sphere of normal worlds, where the field of conditions is held fixed, and @ the actual world in which the gardener fails to water the plant and it dies.

[6]    See Footnote 3.

[7]    It seems to be partly by assumption that these worlds involve greater interference, as the model is chosen in such a way as to produce this result. The gardener’s falling sick in the actual world, in a deterministic universe at least, would have arisen in accordance with the laws and initial conditions of that world – it is only the exclusion of the virus, or whichever other factors, that places @outside FM. Similarly, if SW occurred in the actual world, it would have occurred in accordance with the laws and initial conditions, and hence would indeed lie in FM if that person who watered the plant were included in the miniworld and its model.

[8]    The more refined theory provided by Lewis (2000) also appears to maintain this result of profligate non-plant-watering causes, though this is a more complicated and controversial matter, as the chain of stepwise influence between the failure of some person to water the plant and the plant’s death is somewhat tenuous (though if the person’s failure were altered to them contributing a single drop of water at some point in time, the time and manner of the plant’s death would still be altered, and so too for any quantity of water between zero and a full watering would do likewise), but that’s beyond the scope of this essay.

[9]    Based on the system’s initial conditions (and the initial conditions of the rest of the world in which Queen Elizabeth has no such tendency to frequent that particular garden nor to water plants) and the laws governing it.

[10] If the model and the world under consideration is extended to include the presence of nearby nerve-gas canisters, or the surrounding space, or the tectonic plates below, then this magnitude of the interference may not be as large or, indeed, if the event actually occurs then it might lie in the sphere of normal worlds.

[11] Using the previously mentioned definition from Lewis, W would occur if ~NG occurred (all other factors fixed) and ~W would occur if NG occurred. W then causally depends on ~NG, according to Lewis, so this is a profligacy shared by both theories – though it is one which might potentially be overcome in (Lewis, 2000).

[12] The establishment of the non-absence of NG is also difficult to establish as an interfering factor and encounters further circularity. (See Footnote 3)

[13] Except due to epistemic limitations by which individuals may disagree over the physical state of things or over the underlying physical laws which might not be fully understood;

[14] This may be averted if the chosen model is restricted to only shooter A and the prisoner, as the interfering factors of the other shooters firing are not present in the most similar worlds, but this choice of model is rather arbitrary and it remains that Menzies’ theory does still fail to account for causation in pre-emptive scenarios under various other models.

[15] The counterfactual theory in (Lewis, 1973) encounters the same difficulties with pre-emption unless an extremely fine grain is applied to the event PD, as the nearest ~SAworlds are still PD-worlds. However, it should be noted that Lewis’ later theory in (Lewis, 2000) has some success in overcoming it, as a cause is defined by its difference to how, when and whether the effect occurs. For instance, if shooter A were to fire a split second earlier, or aim at a different part of the prisoner’s body, then the prisoner’s death would occur a split second earlier or in a slightly different manner. Also, importantly, this same relation fails to hold for the nine backup shooters who did not actually fire and who, intuition suggests, did not cause the prisoner’s death.


Lewis, D 1973, ‘Causation’, Journal of Philosophy, no. 70, pp. 556-567.

Lewis, D 1986, ‘Causal explanation’, in Philosophical Papers: Volume II, Oxford University Press, Oxford.

Lewis, D 2000, ‘Causation as influence’, Journal of Philosophy no. 97, pp. 182-197.

Menzies, P 2001, ‘Counterfactual theories of causation’, The Stanford Encyclopedia of Philosophy (Spring 2014). Available from: <> [11 May 2015].

Menzies, P 2004, ‘Difference-making in context’, in Causation and Counterfactuals, eds. Collins, J, Hall, E & Paul, L, MIT Press, Cambridge.

Russell, B 1912, ‘On the notion of cause’, in Proceedings of the Aristotelian society, Williams and Norgate, pp. 1-26.

Photo by Ales Krivec.

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