Difference-Making without Making a Difference∗ Sander Beckers
arXiv:2606.24832v1 [cs.AI] 23 Jun 2026
University College London [email protected]
Abstract Over a series of seven papers, Andreas & Günther have introduced seven definitions of actual causation and have classified them as belonging to three different, competing, types of accounts: factual difference-making, counterfactual difference-making, and regularity-based. I show that their most recent – factual difference-making – definition instantiates all three types, thereby proving that these are distinctions without a difference. I further compare their novel account to the other six accounts on several crucial examples, revealing that this undermines all seven of their accounts.
1
Introduction
Andreas and Günther (2025) have recently proposed an account of actual causation, aka token causation, and compare it favorably to the accounts of several other authors by making two claims: first, it offers better verdicts on examples, and second, it replaces a muddled appeal to counterfactual difference-making with a consistent and simple appeal to factual difference-making. Yet Andreas & Günther’s (AG from now on) comparison to the literature contains an important oversight: AG fail to compare their novel account to the other six accounts of causation that they have themselves previously proposed (AG1-7 from now on, where AG7 is the current account). I show that comparing the current account to these earlier accounts results in falsifying both of AG’s claims, and that it undermines all seven of their accounts. Their six earlier accounts engage with a similar set of examples as the current one, and several of them are likewise motivated explicitly by invoking an appeal to some form of difference-making. So the question presents itself: does this novel difference-making account make a difference in comparison ∗ Preprint
1
to their existing accounts? I answer this in the negative by proving that the current account (AG7) is equivalent to one of their most recent accounts (AG5) (which they acknowledge is itself almost identical to another recent account of theirs (AG6)). Furthermore, I prove that there exists an equivalent formulation of their account as a counterfactual difference-making account, thereby revealing the distinction between factual and counterfactual difference-making to be one without a difference. AG present AG5 and AG6 as regularity-based accounts, which they claim also stand in contrast to counterfactual difference-making accounts. As a consequence of the above equivalence, the distinction between regularity and counterfactual differencemaking accounts is likewise revealed as one without a difference. I then compare the verdicts on examples given by their current account to the verdicts on these and similar examples that they have defended throughout their other six accounts, and show that they are faced with an unappealing dilemma: either they stick with their earlier view (AG1, AG2, AG4) that the examples Simple Switch and Early Preemption are to be distinguished solely on the basis of their structural properties, in which case all of their later accounts offer the wrong verdict – by AG’s own light – on several variants of the switch example that they discuss, or they stick with their more recent view (AG5, AG6, AG7) that the distinction between these examples is due to the (non-structural) deviancy condition, in which case all of their accounts offer the wrong verdict on cases of Early Preemption for which the backup-process is not deviant. Additionally, choosing the second horn undermines one of the most frequent and important criticisms that AG offer of other accounts, namely that those accounts fail to structurally distinguish between Simple Switch and Early Preemption. Concretely, I will use the following labels to refer to the seven definitions of actual causation proposed so far by AG: • AG1: Andreas and Günther (2020) • AG2: Andreas and Günther (2021a) • AG3: Andreas and Günther (2021b) • AG4: Andreas and Günther (2022) • AG5: Andreas and Günther (2024b) • AG6: Andreas and Günther (2024a)
2
• AG7: Andreas and Günther (2025)
2
Equivalence of AG7 and AG5
In (Andreas and Günther, 2025) AG define a causal model < M, V > as consisting of a set M of structural equations of the form X = φ for some binary variable X and propositional formula φ, and a consistent set of literals V . (A literal is either a variable (X) – representing truth – or the negation of a variable (¬X) – representing falsehood.) They also implicitly assume there to be a fixed set of variables P out of which the literals in V and the formulas φ can be constructed. If V does not contain a literal involving X, then X is said to be unsettled. For each variable in P there is at most one equation in M . We say that X is a child of C if C occurs in the equation for X. The descendant relation is the transitive closure of the child relation, and the ancestor relation is the reversal of the descendant relation. The semantics of a causal model are given by combining M with V in the following manner. V ⊧ (X = φ) iff X ∈ V and V classically implies φ or ¬X ∈ V and V classically implies ¬φ. V ⊧ M iff V satisfies each equation in M . < M, V >⊧ φ for some formula φ iff φ is classically implied by V and M . < M, V > is unsettled about a formula φ iff < M, V > satisfies none of φ and ¬φ.1 An intervention I is a consistent set of literals that functions as an operator on causal models, turning < M, V > into < M, V > [I] ∶=< MI , V ∪ I >. Here MI is defined as MI ∶= {(X = φ) ∈ M ∣X ∈/ I and ¬X ∈/ I}. Lastly, for each X ∈ P we assume that either X or ¬X is labelled as the default value, so that the opposite value can be labelled as deviant. (For now we set aside what determines this labelling.) With these elements in place, we can present AG7. Definition 2.1: [Actual Causation (AG7)] Let < M, V > be a causal model such that V ⊧ M and < M, V >⊧ C ∧ E. Then C is a cause of E relative to < M, V > iff there is V ′ ⊆ V and M ′ ⊆ M such that • (C1) < M ′ , V ′ > is unsettled on C and E, • (C2) there is no V ′′ ⊆ V such that V ′ ⊂ V ′′ and < M ′ , V ′′ > is unsettled on C and E, and • (C3) < M ′ , ∅ > [V ′ ][C] ⊧ E. 1 In (Andreas and Günther, 2021a) and (Andreas and Günther, 2022) they offer the same definitions but using the terminology of uninformativeness instead of unsettled.
3
• (C4) the structural equation of each descendant of C is in M ′ .2 • (C5) for any literal C ′ ∈ V ∖ V ′ whose variable is neither a descendant nor an ancestor of C, C ′ is more deviant than ¬C ′ . Let us walk through a simple example to illustrate AG7. In cases of symmetric overdetermination, two independent events are both directly sufficient for producing an outcome. (Think of two soldiers shooting a victim at the same time, or less morbid, two children throwing rocks at a bottle that shatter it at the same moment.) This can be captured by the single equation causal model E = C ∨ D, and set of literals V = {C, D, E}. The intuitive verdict here is that each of the two overdetermining events by itself is a cause of the outcome. AG7 delivers this verdict for C as follows. Take V ′ = ∅ and M ′ = M . Since M combined with V ′ leaves open the truth value of both C and E, it satisfies (C1). Furthermore, all of the sets qualifying for (C2) either contain C or E and are thus settled on at least one of them, or they contain D, which combined with M settles E. Also, C combined with M implies E, and thus (C3) is satisfied. (C4) is trivially satisfied by taking M ′ = M . (C5) is satisfied because as a general rule, AG take truth – which usually represents an event – to be more deviant than falsehood – which usually represents an omission – in the absence of any overriding information. Aside from using different notation and terminology, AG define causal models and their semantics identically in (Andreas and Günther, 2024b) as they do in (Andreas and Günther, 2025). The subsequent definition of actual causation, AG5, differs from the current proposal only in that conditions (C1) and (C2) are replaced with the following conditions: • (D1) < M ′ , V ′ >/ ⊧E • (D2) there is no V ′′ ⊆ V such that V ′ ⊂ V ′′ and < M ′ , V ′′ >/ ⊧ E. Yet despite this close resemblance, AG do not specify the precise relation between their novel proposal and their previous one, other than mentioning in a footnote that some of the conditions in AG7 are “similar” to those in AG5 (Andreas and Günther, 2025, fn. 14). As the following result shows, that is quite the understatement, for the two definitions are equivalent. (Weslake (2025) also remarks that both definitions consist of the “identical formal theory”, but without offering proof.) 2 Note that AG have appealed to a syntactic criterion for determining the graph structure. As a result, adding the semantically vacuous subformula Y ∨ ¬Y to the equation of C allows one to make any variable a descendant of C. This counterintuitive behavior can be avoided by using Halpern’s standard semantical criterion for the child-parent relation (Halpern, 2016).
4
Theorem 2.2: AG7 iff AG5 Proof: Given the above, it suffices to prove that in the presence of the other conditions, (C1) and (C2) are equivalent to (D1) and (D2). We refer to the preamble of the definition as (C0). First, note that by the monotonicity of classical entailment, for any V ′′ ⊆ V and M ′ ⊆ M , V ⊧ M together with either < M ′ , V ′′ >⊧ ¬E or < M ′ , V ′′ >⊧ ¬C implies that < M, V >/ ⊧ C ∧ E. (To be clear, this inference does require the innocuous assumption that V and M are jointly consistent.) Therefore (C0) implies that < M ′ , V ′′ >/ ⊧ ¬E and < M ′ , V ′′ >/ ⊧ ¬C for any V ′′ ⊆ V and M ′ ⊆ M . Second, note that for (C3) we have: ′ ′ < M ′ , ∅ > [V ′ ][C] ⊧ E iff < M{V ′ ,C} , {V , C} >⊧ E. Invoking again the monotonicity of classical
entailment, the latter implies that < M ′ , {V ′ , C} >⊧ E. We now prove the equivalence of (D1) and (C1), where the implication from right to left follows per definition. Assume (D1). Combined with < M ′ , {V ′ , C} >⊧ E, we get that < M ′ , V ′ >/ ⊧ C. Combined with our first observations, it follows that < M ′ , V ′ > is unsettled on C and E. (Take note that one consequence of this, is that without loss of generality, V ′ may be assumed not to contain C, for otherwise obviously V ′ is settled on C.) Remains to prove the equivalence of (D2) and (C2). Note that by the first observation, (C2) iff there is no V ′′ ⊆ V such that V ′ ⊂ V ′′ and < M ′ , V ′′ >/ ⊧ C ∨ E. In turn, this is equivalent to: for all V ′′ ⊆ V such that V ′ ⊂ V ′′ , it holds that < M ′ , V ′′ >⊧ C ∨ E. Similarly, we have: (D2) iff for all V ′′ ⊆ V such that V ′ ⊂ V ′′ , it holds that < M ′ , V ′′ >⊧ E. As a result, the implication from left to right is trivial, and thus we proceed with proving the implication from right to left. Assume (C2). Consider some V ′′ ⊆ V such that V ′ ⊂ V ′′ . We need to show that < M ′ , V ′′ >⊧ E. First consider the case where < M ′ , V ′′ >⊧ C.
By our second observation, we know that <
M ′ , {V ′ , C} >⊧ E, which implies – again by monotonicity – that < M ′ , {V ′′ , C} >⊧ E. Combining these two, we get that < M ′ , V ′′ >⊧ E, as required. Second consider the case where < M ′ , V ′′ >/ ⊧ C. By (C2), we know that < M ′ , V ′′ >⊧ C ∨ E. Therefore it must be that < M ′ , V ′′ >⊧ E, as required. Furthermore, definition AG5 is itself almost equivalent to AG6: as Andreas and Günther (2024b) point out, the two definitions differ only regarding the precise formulation of the deviancy condition (C5). AG present (C5) as an improvement that is able to handle some counterexamples to their previous formulation, so that AG5 is strictly to be preferred over AG6. As a result, we have that three of AG’s seven definitions are essentially reduced to one. 5
3
Differences in Difference-Making
AG present AG7 as a factual difference-making account of causation, whereas they present AG5 and AG6 as regularity-based accounts of causation. They remain silent on the relation between both types of accounts. As we have just shown the equivalence of AG7 and AG5, it follows that there is in fact no difference between them. AG contrast both types of account with the more well-known counterfactual difference-making accounts of causation. In fact, this contrast forms a large part of AG’s motivation for their novel accounts. Counterfactual difference-making accounts have taken over as the most popular approach to analysing causation over the past decades, to the detriment of regularity-based accounts. Well-known examples of the latter are those of Mackie (1974) and Wright (1988, 2011), whereas wellknown examples of the former are (Lewis, 1973; Halpern and Pearl, 2005; Weslake, 2015; Halpern, 2016; Beckers and Vennekens, 2018; Beckers, 2021a) and many more. AG argue that the superiority of their two regularity-based accounts should make us reconsider this evolution. I now show that the distinction between these two kinds of accounts is also one without a difference, and thus the supposed rivalry between the two classes of approaches as they are characterized by AG is a chimera. (Beckers (2021b) makes a similar point by showing how Wright’s NESS account of causation also includes a counterfactual difference-making condition. In fact, it is easy to show that AG7 satisfies an additional counterfactual condition to the NESS definition – called Counterfactual in (Beckers, 2021b)) – placing it at a similar location on the spectrum between regularity accounts and counterfactual accounts as my Counterfactual NESS account.) Consider the following variation on AG5 (and thus on AG7), that replaces (D1) and (D2) (resp. (C1) and (C2)) with counterfactual variants. Definition 3.1: [(AG7*)] Let < M, V > be a causal model such that V ⊧ M and < M, V >⊧ C ∧ E. Then C is a cause of E relative to < M, V > iff there is V ′ ⊆ V and M ′ ⊆ M such that • (E1) < M ′ , V ′ > [¬C] ⊧ /E • (E2) there is no V ′′ ⊆ V such that V ′ ⊂ V ′′ and < M ′ , V ′′ > [¬C] ⊧ / E, and • (C3) < M ′ , ∅ > [V ′ ][C] ⊧ E. • (C4) the structural equation of each descendant of C is in M ′ . • (C5) for any literal C ′ ∈ V ∖ V ′ whose variable is neither a descendant nor an ancestor of C, C ′ is more deviant than ¬C ′ . 6
Informally the difference between both definitions can be put as follows: instead of merely considering a minimal submodel in which the truth of C and E is unsettled, (E1) and (E2) require that we consider a minimal submodel in which the counterfactual supposition ¬C does not make E true. That this is indeed a counterfactual difference-making account by AG’s own lights can be seen in two ways. One characterization AG offer to classify a definition of causation as a counterfactual differencemaking account is that it asks a counterfactual question regarding what would have happened, had the putative cause not obtained, which is precisely what occurs in (E1). Concretely, AG express the contrast as follows (Andreas and Günther, 2024a, p. 2169): Our regularity theory does not rely on any condition of counterfactual dependence. It does not ask what would have happened, had the putative cause not obtained. Thereby our theory does not rely on counterfactual dependence ... . Our regularity theory is not counterfactual. AG also offer a second characterization, namely that counterfactual dependence is a sufficient condition for causation. Counterfactual dependence, for a model such that V ⊧ M , holds when both < M, V >⊧ C ∧ E and < M, V ∖ {C} > [¬C] ⊧ ¬E. If we ignore (C5), then it is trivial to see that AG7* also satisfies this characterization: simply take M ′ = M and V ′ = V ∖ {C}. Adding (C5) on the other hand prevents the sufficiency of counterfactual dependence. But the presence of a deviancy condition cannot be what separates counterfactual difference-making accounts from other types of accounts, for the most infuential counterfactual account – that of Halpern (2016) – also comes with a deviancy condition that would preclude it from satisfying this characterization (as do many other such accounts (Hall, 2007; Hitchcock, 2007; Gallow, 2021)). The only conclusion to draw is that the presence or absence of a deviancy condition stands orthogonal to the distinction between counterfactual, factual, and regularity accounts, and AG7* is thus squarely a counterfactual difference-making account. Yet as the following result shows, AG7* and AG7 are equivalent. Therefore AG’s factual differencemaking account is revealed to be itself an instance of a counterfactual difference-making, as opposed to an alternative. Theorem 3.2: AG7* iff AG7 Proof: Assume (C0), (C3), (C4), and (C5). As proven by Ackermans (2025), we can assume without loss of generality that M ′ does not contain an equation for C. We prove that AG7* iff AG5, from which the result follows by Theorem 2.2. This means we need to show that for all V ′′ ⊆ V such that 7
V ′ ⊆ V ′′ : < M ′ , V ′′ > [¬C] ⊧ / E iff < M ′ , V ′′ >/ ⊧ E. Equivalently, for all V ′′ ⊆ V such that V ′ ⊆ V ′′ : < M ′ , V ′′ > [¬C] ⊧ E iff < M ′ , V ′′ >⊧ E. We start with the implication from right to left. Assume that < M ′ , V ′′ >⊧ E. Given that M ′ does not contain an equation for the variable in C, the result is immediate by the monotonicity of classical entailment. Now the implication from left to right. Assume < M ′ , V ′′ > [¬C] ⊧ E. By (C3), we have that < M ′ , ∅ > [V ′ ][C] ⊧ E. By monotonicity, it follows that also < M ′ , V ′′ > [C] ⊧ E. Combined with < M ′ , V ′′ > [¬C] ⊧ E, it follows that < M ′ , V ′′ >⊧ E. Ackermans (2025) similarly proves the equivalence of AG7 to an alternative definition that has counterfactual elements. I prefer AG7* to his variant because it is easier to interpret and compare with AG7. I disagree with Ackermans, however, that AG7 sets itself apart from counterfactual accounts by invoking the idea of variables whose values are unspecified, for the same idea is presented in (Beckers, 2021a) under the label of strong sufficiency, and it appeared already in (Weslake, 2015). (Concretely, letting N ⊆ P denote the variables whose equation is in M ′ , (C3) expresses that {V ′ ∪ C} is strongly sufficient for E along the network N .) In sum, AG’s attempt to distinguish between regularity-based accounts, factual difference-making accounts, and counterfactual difference-making accounts, has failed.
4
To Flip, Or Not To Flip?
Throughout all of their work AG evaluate definitions of causation by comparing their verdicts on a small set of paradigmatic examples, under the assumption that there is a unique, correct, and intuitive, verdict for each example. So failure to offer the right verdict on at least one of these examples is taken as a sufficient criterion for disqualifying a definition. This methodology is highly questionable, both because there is in fact no consensus on the verdicts for many of these examples (as AG admit in their more recent work), and more fundamentally, because one might prefer a more systematic foundation for causation than mere intuitions (Glymour et al., 2010; Beckers, 2021a, 2025). I here offer a much more basic problem for AG’s method: the judgments and arguments used for some of the examples in defending their later definitions directly conflict with those of their earlier definitions. As a consequence, we cannot simply interpret AG’s various definitions as a sequence of modifications that steadily improve upon each other. Rather, the fact that AG changed their minds on what the
8
D
C
A
D
E
C
B
E
B
(a) Early Preemption
(b) Simple Switch
correct analysis is for these paradigmatic examples, undermines the very idea that definitions ought to be evaluated on the basis of what are supposed to be intuitive and universal verdicts about them. There are two examples of causal models in particular that AG make heavy use of: Early Preemption and Simple Switch. Here Early Preemption and Simple Switch are nothing but the labels that AG – following Hall (2007) – give to the causal structures depicted in Figures 1a and 1b, respectively. In most of their papers – (Andreas and Günther, 2020, 2021a, 2022, 2024b,a) – they point out that other definitions fail to distinguish between them, whereas the allegedly correct verdicts on these examples are different, and they use this as an important argument in favor of their definitions. Concretely, the idea is that C is a cause of E in Early Preemption but not in Simple Switch. The only definition of theirs that does not distinguish between them and calls C a cause in both, is AG3 (an observation that to my knowledge has gone unnoticed so far). The graphs in Figures 1a and 1b are examples of so-called “neuron diagrams”, which are often used in the literature on causation to visually represent causal models. The nodes represent binary variables, and a node is gray iff the variable is set to true. The edges represent causal influence in the following manner: the receiving node is true whenever any of the edges with an arrowhead comes from a true node and there is no edge with a circlehead coming from a true node. For Early Preemption this means that the values of the variables are determined by the following equations: C = 1, A = 1, D = C, B = ¬C ∧ A, and lastly, E = D ∨ B. For Simple Switch the equations are: C = 1, D = C, B = ¬C, and E = D ∨ B. Here is a classic scenario by (Hitchcock, 2001, p.276) that often accompanies Early Preemption: “Backup”: an assassin-in-training is on his first mission. Trainee is an excellent shot: if he shoots his gun, the bullet will fell Victim. Supervisor is also present, in case Trainee has a last minute loss of nerve (a common affliction among student assassins) and fails to pull the trigger. If Trainee does not shoot, Supervisor will shoot Victim herself. In fact,
9
Trainee performs admirably, firing his gun and killing Victim. The idea is that Trainee’s shot (C = 1) causes Victim’s death (E = 1), despite the existence of a backup process that would have resulted in the same result in case assassin had not shot. The backup process consists of Supervisor’s intention (A = 1) to shoot Victim (B) in case Trainee does not. AG7 arrives at this conclusion by taking V ′ = {¬B}. Note that A is the only variable that we have removed from V which falls under the scope of (C5). In other examples of this sort, AG state that a literal is more deviant than its negation if it violates a moral norm, which is clearly the case here. So far so good. The standard scenario used by AG – and many others – to illustrate Simple Switch is due to (Hall, 2000, p. 205): “The Engineer”: an engineer is standing by a switch in the railroad tracks. A train approaches in the distance. She flips the switch (C), so that the train travels down the right-hand track (D), instead of the left (¬B). Since the tracks reconverge up ahead, the train arrives at its destination all the same (E); let us further suppose that the time and manner of its arrival are exactly as they would have been, had she not flipped the switch (¬C). The majority view is that switches are not causes. That AG7 is able to respect this judgment is due to the absence of A, for this prevents the possibility of keeping {¬B} ∈ V ′ and yet not settling C. Although there is more or less consensus on the causal judgments for these informal scenarios, views diverge widely over whether or not the causal models in Figures 1a and 1b offer appropriate representations of them. At present the goal is not to take sides on this issue. What matters is that there exist two other causal models that have been proposed as alternative representations of the scenario that is captured by Simple Switch, and as a result AG extend their analysis to show that their definitions offer the same verdicts on these representations as well. The first of these models, labelled Extended Switch by AG (Andreas and Günther, 2022), was presented by Hitchcock (2009) to challenge the alleged difference between Early Preemption and Simple Switch. The second of these models – that I label Halpern Switch – was presented by Halpern (2016) in order to show that his definition is capable of offering the right verdict on switch examples after all. Furthermore, Halpern (2016) argues that his definition also offers the right verdict on Simple Switch once one invokes a normality condition, which is similar in spirit to the deviancy condition (C5).
10
AG discuss all three representations in their work, but in very different manners. Initially AG focus solely on the contrast between Early Preemption and Simple Switch, and do so relying solely on the structural features of these models (Andreas and Günther, 2020, 2021a). Andreas and Günther (2022) then adds a discussion of the other variants as well. There they criticize Halpern’s appeal to normality considerations for handling Simple Switch, and show that their definition (AG4) arrives at the same verdict on all three switch representations by relying only on structural features of the models. This approach is abandoned in (Andreas and Günther, 2024b,a). Instead, there they show that AG5 and AG6 require invoking their non-structural deviancy condition in order for the verdicts on the two alternative switches to agree with Simple Switch. On this latter view, therefore, cases of Early Preemption and cases of switches cannot be distinguished purely on structural grounds. As a result, AG’s defense of their recent accounts directly conflicts with the alleged clear-cut stuctural distinction between Early Preemption and Simple Switch that played such an important role in their earlier accounts. We can make this more concrete by considering a variation of Early Preemption in which the deviancy conditions differ. Imagine our Backup story continues as follows. “Backup 2”: We spoke too soon: Victim did not die, but their life is hanging by a thread. A doctor-in-training is on her first residency as our gunshot Victim enters the ER. Trainee is an excellent surgeon: if she operates, the bullet will be successfully removed and Victim survives. Supervisor is also present, in case Trainee has a last minute loss of nerve (a common affliction among student doctors) and fails to operate. If Trainee does not operate, Supervisor will operate Victim himself. In fact, Trainee performs admirably, removing the bullet and saving Victim’s life. Both backup scenarios are structurally identical. Plausibly, so are the most intuitive verdicts for both of them: trainee causes the outcome (death or survival) in both. Yet in the latter scenario, supervisor’s intention is in accordance with a moral norm, and their failure to supervise the operation would be in violation of one. Therefore AG5, AG6, and AG7, force us to conclude that trainee’s action did not cause the outcome in Backup 2. Regardless of what one makes of these opposing verdicts in isolation, the general point is that AG’s flip-flopping makes it very hard to identify a persuasive motivation for any one of their seven accounts.
11
5
Conclusion
Over a series of seven papers, Andreas & Günther have introduced seven definitions of actual causation using several variations of definitions of causal models and the tools that we equip them with. Throughout their work they present their definitions as belonging to competing types of accounts of causation, culminating in the contrast between (counter)factual difference-making and regularity-based accounts. I have shown that their most recent addition (AG7) does not in fact make a difference (as it is equivalent to an earlier definition (AG5)), that the distinction between these three types of accounts also does not in fact make a difference (as AG7 can be interpreted as an instance of all three of them), and that the change in their analysis of two key examples undermines the coherence of their work as a whole.
References Lennart B. Ackermans. 2025. Factual Difference-Making is Equivalent to a Counterfactual Theory. Australasian Philosophical Review 9, 2 (2025), 205–212. Holger Andreas and Mario Günther. 2020. Causation in Terms of Production. Philosophical Studies 177, 1565-1591 (2020). Holger Andreas and Mario Günther. 2021a. Difference-Making Causation. Journal of Philosophy 118, 12 (2021), 680–701. Holger Andreas and Mario Günther. 2021b. A Ramsey Test Analysis of Causation for Causal Models. British journal for the philosophy of science 72, 2 (2021). Holger Andreas and Mario Günther. 2022. Actual Causation. Dialectica 76 (2022). Holger Andreas and Mario Günther. 2024a. A Lewisian Regularity Theory. Philosophical Studies 181, 2145-2176 (2024). Holger Andreas and Mario Günther. 2024b. A Regularity Theory of Causation. Pacific Philosophical Quarterly 105 (2024), 2–32. Holger Andreas and Mario Günther. 2025. Factual Difference-Making. Australasian Philosophical Review (2025).
12
Sander Beckers. 2021a. Causal Sufficiency and Actual Causation. Journal of Philosophical Logic 50 (2021), 1341–1374. Sander Beckers. 2021b. The Counterfactual NESS Definition of Causation. In Proceedings of The Thirty-Fifth AAAI Conference on Artificial Intelligence. 6210–6217. Sander Beckers. 2025. Actual Causation using Nondeterministic Causal Models. In Proceedings of the 4th Conference on Causal Learning and Reasoning (CLeaR 2025). PMLR. Sander Beckers and Joost Vennekens. 2018. A Principled Approach to Defining Actual Causation. Synthese 195, 2 (2018), 835–862. J. Dmitri Gallow. 2021. A Model-Invariant Theory of Causation. Philosophical Review 130, 1 (2021), 45–96. Clark Glymour, David Danks, Bruce Glymour, Frederick Eberhardt, Joseph Ramsey, Richard Scheines, Peter Spirtes, Choh Man Teng, and Jiji Zhang. 2010. Actual causation: a stone soup essay. Synthese 2 (2010), 169–192. Issue 175. N. Hall. 2000. Causation and the price of transitivity. Journal of Philosophy 97, 4 (2000), 198–222. N. Hall. 2007. Structural equations and causation. Philosophical Studies 132, 1 (2007), 109–136. J. Halpern and J. Pearl. 2005. Causes and Explanations: A Structural-Model Approach. Part I: Causes. The British Journal for the Philosophy of Science 56, 4 (2005), 843–87. Joseph Y. Halpern. 2016. Actual Causality. MIT Press. C. Hitchcock. 2001. The intransitivity of causation revealed in equations and graphs. Journal of Philosophy 98 (2001), 273–299. C. Hitchcock. 2007. Prevention, Preemption, and the principle of Sufficient Reason. The Philosophical review 116, 4 (2007), 495–532. C. Hitchcock. 2009. Structural equations and causation: six counterexamples. Philosophical Studies 144 (2009), 391–401. Issue 3. David Lewis. 1973. Causation. Journal of Philosophy 70 (1973), 113–126. John Mackie. 1974. The Cement of the Universe. Oxford University Press. 13
Brad Weslake. 2015. A Partial Theory of Actual Causation. The British Journal for the Philosophy of Science forthcoming (2015). Brad Weslake. 2025. Commentary on Factual Difference-Making. Australasian Philosophical Review 9, 2 (2025), 167–176. Richard W. Wright. 1988. Causation, Responsibility, Risk, Probability, Naked Statistics, and Proof: Pruning the Bramble Bush by Clarifying the Concepts. Iowa Law Review 73 (1988), 1001–1077. Richard W. Wright. 2011. The NESS Account of Natural Causation: A Response to Criticisms. In Perspectives on Causation, Richard Goldberg (Ed.). Hart Publishing.
14