20.08.03 · philosophy / phil-of-science

Causation and explanation: counterfactual analysis, mechanistic explanation, causal inference

stub3 tiersLean: nonepending prereqs

Anchor (Master): Lewis, D. — Causation (1973)

Intuition Beginner

What makes one event cause another? David Hume (1748) argued that we never observe causation itself — only one event following another, repeatedly. We infer a causal link from constant conjunction. The cue ball strikes the eight-ball; the eight-ball rolls away. We say the first impact caused the motion. Yet all we witness is succession — a sequence — never a necessary tie binding the two.

David Lewis (1973) reshaped the question with a counterfactual test. To say C caused E is to say that had C not occurred, E would not have occurred either. Had the patient never smoked, she would not have developed lung cancer — so the smoking caused the cancer. The test shifts causation from what we see (regular succession) to what would have happened in the nearest world where the cause is absent.

Jim Woodward's interventionist account recasts causation in terms of manipulation. C causes E when a suitable intervention — an outside manipulation of C, leaving other factors fixed — would change E. Judea Pearl gave this idea formal teeth: his do-calculus distinguishes seeing that C happened from doing C, and lets us compute causal effects from data, separating genuine causes from mere correlations.

Scientific explanation travels with causation. To explain an event is to lay out what brought it about. Wesley Salmon's mechanistic account adds a further demand: a real explanation describes the mechanism — the chain of parts and activities, the gears and levers — that actually produces the phenomenon. Causes without the underlying machinery are, on this view, incomplete.

Visual Beginner

Figure: A four-quadrant map of how philosophers analyse "C causes E". Top-left, Humean regularity: two events linked by repeated succession and a question mark over the "necessary connection". Top-right, Lewis counterfactual: an arrow from the actual world to the nearest world where C is absent and E is gone. Bottom-left, Woodward-Pearl interventionism: a hand intervening on C and watching E change, contrasted with passive observation. Bottom-right, Salmon mechanism: a box of interlocking gears labelled entities and activities producing the output. Dashed arrows between quadrants mark where each account borrows from and corrects the others.

The quadrants disagree on what kind of dependence makes a cause. Every later section refines this map: the Intermediate tier formalises each analysis, and the Master tier traces where they survive and where they break.

Worked example Beginner

Suzy and Billy each throw a rock at a glass bottle. Both throws are accurate. Suzy's rock arrives a split second earlier and shatters the glass. Billy's rock flies through the empty space a moment later. The bottle is broken; the question is what caused the breaking.

Apply Lewis's counterfactual test to Suzy's throw. Had Suzy not thrown her rock, what would have happened? Billy's rock, already in flight and on target, would have shattered the bottle anyway. So in the closest world where Suzy does not throw, the bottle still breaks. The simple counterfactual test therefore says Suzy's throw did not cause the shattering.

This is the problem of late preemption. A backup cause (Billy) stood ready to do the very work Suzy actually did. Lewis's counterfactual analysis, in its simplest form, cannot distinguish Suzy's genuine hit from Billy's idle backup. The smoking-and-cancer case has no such backup, so the test works there; the rock case exposes its edge.

The lessons generalise. Whenever two causes compete, the loser's counterfactual looks just like the winner's, because the winner's absence would have let the loser take over. Later refinements — fine-grained events, structural-equation models, the interventionist test — all aim to repair exactly this gap. Each agrees Suzy caused the break; each disagrees about why.

Check your understanding Beginner

Formal definition Intermediate+

Definition (Humean regularity; Mackie's INUS conditions). On the regularity analysis, C is a cause of E when events of type C are constantly conjoined with events of type E, with C temporally prior to E and spatiotemporally contiguous with it. Mackie refined this into INUS conditions: C is an Insufficient but Non-redundant part of a condition that is itself Unnecessary but Sufficient for E. A struck match is insufficient alone (oxygen and dryness are needed), non-redundant (remove the strike and no flame), part of a complex sufficient for fire, yet unnecessary (a lighter would do).

Definition (counterfactual analysis, Lewis 1973). Event C causes event E iff, in the closest possible world to actuality in which C does not occur, E does not occur either. Closeness is governed by weighted similarity of facts, with heavy weight on avoiding large, widespread departures from actual law and fact. The analysis delivers an asymmetry and temporal direction that bare regularity cannot, but struggles where backup causes stand ready to take over.

Definition (probabilistic causation, Suppes; Cartwright). C causes E iff C raises the probability of E: $P (E ∣ C) > P (E)$ . Cartwright's contextual refinement requires the inequality to hold within every sufficiently specified background context $K$ : $P (E ∣ C, K) > P (E ∣ \neg C, K)$ . Reichenbach's principle of common cause says that when two events are correlated, neither causing the other, they share a common cause that screens off the correlation (conditioning on it removes the dependence).

Definition (interventionism, Woodward 2003). Variable X is a cause of variable Y iff there exists a possible intervention $I$ on X — an exogenous manipulation that sets X to some value while holding fixed all other causes of Y except those downstream of X — such that varying X under $I$ changes the value or the probability distribution of Y. Causation is analysed through what an idealised manipulator could achieve.

Definition (do-calculus, Pearl). In a structural causal model whose assumptions are encoded as a directed acyclic graph (DAG), the operator $do (X = x)$ represents an intervention that sets X to $x$ and deletes every arrow into X. This separates seeing from doing: observing $P (Y ∣ X = x)$ passively conditions on X, while $P (Y ∣ do (X = x))$ computes the distribution of Y under an active manipulation. The three rules of do-calculus are complete for identifying interventional quantities from a DAG plus observational data.

Definition (mechanistic explanation, Salmon; Machamer-Darden-Craver). A mechanism for a phenomenon is a set of entities and activities organised such that they produce the phenomenon. To explain is to exhibit this organisation — the parts, their activities, and their spatial-temporal arrangement. Salmon's earlier causal-mechanical model required causal processes that transmit marks; the Salmon-Dowe refinement identifies causal processes with the transmission of conserved quantities (energy, momentum, charge).

Distinguishing the four analyses Intermediate+

Regularity vs counterfactual. Regularity reads causation off from actual patterns of succession; the counterfactual analysis reads it off from what would happen in nearby non-actual worlds. Regularity cannot handle spurious correlations (barometer and storm); the counterfactual analysis can, but pays in modal metaphysics.
Probabilistic vs deterministic. Probabilistic theories handle causes that raise risk without guaranteeing the effect (smoking and cancer); deterministic accounts fit well in physics but strain in the life and social sciences.
Interventionism vs mechanism. Interventionism gives a test (would manipulating X change Y?); mechanistic explanation gives an ontology (which parts and activities produce the phenomenon). They are often complementary, sometimes rivals.
Seeing vs doing. Pearl's distinction between conditioning and intervening is the formal heart of causal inference: many correlations vanish or invert once we intervene rather than observe.

Key argument — counterfactual analysis, preemption, and the interventionist repair Intermediate+

The case for the counterfactual analysis rests on a reconstruction of what causation could be, given Hume's challenge.

Premise L1. Causation is not given in observation (Hume's point); it must be analysed in terms of something else — regularity, probability, counterfactual dependence, or mechanism.

Premise L2. The dependence of the effect on the cause is best captured counterfactually: had the cause not occurred, the effect would not have occurred.

Premise L3. Counterfactuals are made true by facts about the closest possible worlds — those most similar to actuality in which the antecedent holds.

Conclusion L. C causes E iff, in the closest C-absent world, E is absent too.

The analysis handles ordinary cases — the smoker, the struck match — elegantly. But it falters where a backup cause stands ready.

The preemption objection.

Premise P1. In cases of late preemption (Suzy and Billy, both rocks on target), the closest world in which the actual cause (Suzy's throw) is absent is one in which the backup (Billy's throw) still shatters the bottle.

Premise P2. So in the closest Suzy-absent world, the bottle still breaks.

Conclusion P. By Lewis's biconditional, Suzy's throw did not cause the break — contradicting the plain fact that her rock struck first.

Lewis and later writers offered repairs: fine-grained events (Suzy's actual shattering differs from Billy's would-be shattering), structural-equation models that trace the actual causal route, and temporal-precedence requirements. Each repair handles some preemption cases but yields odd verdicts elsewhere — overdetermination (two lethal doses simultaneously), trumping (a senior officer's order preempts a junior's identical order), and early preemption (the backup never fires its decisive shot). Hall and Paul survey the ongoing instability in "Causation: A User's Guide" ^{[Hall Paul 2013]}.

The interventionist alternative (Woodward, Pearl).

The interventionist reframes the test. C causes E if an intervention on C would change E. In the Suzy case, an intervention that deflects only Suzy's rock (holding Billy's fixed) changes whether and how the bottle breaks; the dependence is intact even with a backup present. Interventionism sidesteps the closest-world metaphysics and replaces it with a manipulation test, at the cost of idealising "intervention" in ways critics find quietly circular: to specify an intervention on C one already needs a causal model.

The probabilistic theories face an analogous objection: raising probability is not sufficient for causation (a barometer's reading raises the probability of a storm without causing it), and Cartwright's contextual fix needs a prior partition of background conditions, which is itself a partly causal matter.

Bridge. This reconstruction builds toward the mechanistic and Bayesian-network material below, and outward to 20.08.02 pending (realism about unobservable mechanisms), [26.] (statistical causal inference), and [37.] (the probabilistic foundations of do-calculus). The foundational reason the causation debate resists closure is that every analysis — regularity, counterfactual, probabilistic, interventional, mechanistic — reconstructs the same causal judgements from a different dependence relation, and each dependence relation breaks on some class of cases the others handle. The pattern generalises from 20.05.03 pending (selection of vs selection for) to [29.01.] (singular vs general causation in clinical judgement) and [35.02.] (Bradford Hill criteria in epidemiology).

Exercises Intermediate+

Exercise 2 (easy, multiple choice).

The barometer falls and a storm arrives shortly after. The barometer reading raises the probability of the storm. Why does this not make the barometer a cause of the storm?

A. Because the barometer reading is not temporally prior to the storm. B. Because the falling barometer and the storm share a common cause (falling atmospheric pressure) that screens off the correlation. C. Because probability-raising is never a sufficient condition for causation. D. Because the barometer is an unobservable entity.

Answer

Option B. Falling atmospheric pressure causes both the barometer's drop and the storm; conditioning on pressure removes the correlation (Reichenbach's screening off). A is false (the barometer does fall first); C overstates the failure of probabilistic theories; D is irrelevant.

Exercise 3 (medium, argument reconstruction).

Two assassins, A and B, each fire a fatal shot at the victim at the same instant; either shot alone would have killed him. The victim dies of two simultaneous wounds. Reconstruct the counterfactual analysis's verdict (did A cause the death?) and explain why this overdetermination case is a problem for Lewis.

Hint

Ask: in the closest world where A did not fire, is the victim still dead? What does the biconditional then conclude about A's shot?

Answer

In the closest world where A did not fire, B's shot still kills the victim, so the victim is still dead. By the simple counterfactual biconditional, A's shot did not cause the death — and by symmetry neither did B's. Yet the victim is dead of two bullet wounds, and intuition says each shot was a cause. Overdetermination thus breaks the biconditional in the direction opposite to preemption: in preemption the analysis denies a real cause, in overdetermination it denies both real causes. Lewis's refinements (fine-grained events, the "quasi-dependence" of the death on each shot) aim to repair exactly this.

Exercise 4 (medium, symbolic).

Consider a DAG with three variables: $X \to Y \leftarrow Z$ , where X and Z are independent causes of Y. Write the difference between $P (Y ∣ X = x)$ (observing X) and $P (Y ∣ do (X = x))$ (intervening on X). Explain why the two can differ even in this simple graph, and state what the do-operator removes.

Hint

Conditioning on Y opens a path between X and Z (collider conditioning). What does doing X do to the incoming arrows?

Answer

Observationally, $P (Y ∣ X = x)$ reflects the generative distribution in which X and Z are independent and both feed Y. The intervention $P (Y ∣ do (X = x))$ deletes every arrow into X (here X has no parents, so in this specific graph the two coincide numerically for the marginal of Y). They come apart as soon as X has a parent W: then conditioning on X tells us about W (and hence about W's other effects), whereas $do (X = x)$ cuts that link. The do-operator thus converts a passive observation into an idealised experimental manipulation by severing X from its natural causes.

Exercise 5 (hard, case analysis).

A new drug is associated with better survival, but sicker patients are less likely to be prescribed it. Without randomisation, the raw comparison of takers vs non-takers is biased. Explain, in terms of the do-operator and DAGs, why naive conditioning $P (survival ∣ drug)$ misestimates the causal effect, and how randomisation repairs the problem.

Hint

Severity is a confounder: it causes both prescription and survival. What does randomisation do to the arrow severity $\to$ prescription?

Summary

Severity is a common cause of prescription and survival, so the DAG is severity $\to$ prescription $\to$ survival with severity $\to$ survival. Conditioning on prescription without conditioning on severity leaves the back-door path open, so $P (survival ∣ drug)$ mixes the drug's effect with the severity effect. Randomisation replaces the natural prescription mechanism with a coin flip, severing severity $\to$ prescription; equivalently it makes prescription independent of severity, so the observed association now equals $P (survival ∣ do (drug))$ . This is the formal content of the claim that randomised controlled trials identify average causal effects.

Exercise 6 (hard, critique).

The interventionist defines a cause via what an intervention would do, and defines an intervention as a manipulation that sets the cause without affecting other causes of the effect. Critics call this circular. Assess the objection: does interventionism presuppose causation in its own analysans, and if so, is the circularity vicious?

Hint

Distinguish definitional circularity from a regressive analysis. Does the account need a prior causal fact to count as an analysis, or only to apply the test?

Answer

There is a genuine circularity: an intervention must be exogenous to the cause-effect pair and must not influence the effect through side channels, and "exogenous" and "side channel" are themselves causal notions. Woodward replies that the account need not reanalyse causation from scratch; it situates a particular causal claim within a larger causal model whose other causal relations are taken as background. The circularity is thereby made non-vicious at the cost of holism — interventionism analyses a cause only relative to a model, never in isolation. Whether this is a feature (causation is constitutively model-relative) or a bug (the analysis never bottoms out) remains the live point between Woodward and his critics.

Mechanisms, causal models, and the architecture of explanation Master

Mechanistic explanation: Salmon and the MDC framework Master

Salmon's causal-mechanical model, consolidated in "Four Decades of Scientific Explanation" (2006) ^{[Salmon 2006]}, shifted explanation away from Hempel's deductive-nomological subsumption and toward the tracing of causal processes. A causal process is one that transmits a mark — a local change persisting without further intervention; causal interactions occur when processes intersect and exchange marks. The Salmon-Dowe conserved-quantity theory sharpens this: a process is causal iff it transmits a conserved quantity such as energy, momentum, or charge.

Machamer, Darden, and Craver ("Thinking about Mechanisms", 2000) ^{[MDC 2000]} reframe mechanisms as entities and activities organised to produce a phenomenon. Craver's "Explaining the Brain" (2007) ^{[Craver 2007]} adds multilevel structure: a mechanism is explained by its components and in turn embeds in higher-level mechanisms, yielding a constitutive explanation that is simultaneously temporal and spatial. This framework travels well: molecular biology (see 20.05.04 pending, [17.]), neuroscience (see [29.02.]), cognitive and developmental psychology (see [29.06.]), and clinical medicine (see [35.]) all describe their explananda as mechanisms. It reaches further into the philosophy of mind, where IIT and global workspace theory are evaluated partly as mechanistic proposals (see 20.06.03 pending).

The live dispute is whether mechanism and interventionism compete or complement. Woodward's invariance-under-intervention supplies a criterion for which relationships are explanatorily relevant; MDC supplies the parts-and-activities ontology. Craver and Woodward each read the other as a special case. The unresolved question is whether a purely interventionist account can capture constitutive (part-whole) explanation without smuggling in mechanism — that is, whether "an intervention on the whole changes the part" is intelligible without an independent mechanistic premise.

Causal discovery and Bayesian networks Master

Pearl's DAGs and do-calculus supply not only a logic of intervention but a programme for causal discovery — inferring the structure of the graph from data. Spirtes, Glymour, and Scheines ("Causation, Prediction, and Search", 1993/2000) ^{[SGS 2000]} developed the PC and FCI algorithms, which start from correlations and conditional independences and prune the graph of possible causal links. Pearl's "Probabilistic Reasoning in Intelligent Systems" (1988) ^{[Pearl 1988]} grounds Bayesian networks — DAGs annotated with conditional probability distributions — as a representation both for efficient inference and for articulating causal assumptions. (See [37.05.] for Markov chains and [37.] for Bayesian foundations; see [35.07.*] for Bayesian pharmacokinetics.)

The discovery programme is powerful but bounded. It recovers a DAG only up to its Markov equivalence class: two graphs producing the same conditional independences cannot be distinguished from observational data alone. The causal-sufficiency assumption (no hidden common causes) is rarely satisfied in the wild; where confounders lurk, FCI returns a partial ancestral graph rather than a full DAG. This boundary is precisely where do-calculus earns its keep, identifying effects that are estimable despite hidden variables and flagging those that are not.

Causal inference has crossed into statistics and econometrics: the potential-outcomes framework of Neyman and Rubin, the Angrist-Imbens-Rubin analysis of instrumental variables, regression discontinuity, and differences-in-differences (see [26.], [30.01.]). The 2021 Nobel awards to Card, Angrist, and Imbens mark the field's institutional arrival. Bradford Hill's criteria thread the same logic through epidemiology (see [35.02.], [35.06.]), and Pearl's "The Seven Tools of Causal Inference" carries the programme into machine learning (see [50.], [43.], [36.*]).

Explanation beyond causation: unification and the kairetic account Master

Hempel's deductive-nomological (D-N) model ("Aspects of Scientific Explanation", 1965) ^{[Hempel 1965]} held that an event is explained by subsuming it under a law: the explanandum is deduced from a law plus initial conditions. The model's failures — explanatory asymmetries, the irrelevance of true-but-irrelevant laws, the scarcity of genuine laws in much biology — motivated the causal-mechanical turn (see 20.08.01, 20.08.02 pending).

Two non-causal alternatives survive. Kitcher's unificationism ("Explanatory Unification", 1989, with roots in Friedman) ^{[Kitcher 1989]} argues that explanation reduces the number of argument-patterns needed to derive the phenomena: science explains by showing that many facts follow from few premises. Strevens's kairetic account ("Depth", 2008) ^{[Strevens 2008]} refines causal explanation by distinguishing the difference-makers from the rest of the causal chain — only stable, high-level difference-making relations enter the explanation, and the microphysical detail is set aside as explanatorily irrelevant. Woodward's invariance criterion offers a related test: explanatory relations are those that hold across a wide range of interventions.

The unification and kairetic programmes disagree about whether explanation tracks causation at all, but they converge on invariance and stability as the operative virtues. Where they leave the question open is whether a single theory of explanation fits all the sciences — from physics's law-subsumption (see [20.03.]) to biology's mechanism-sketches (see [20.05.], 20.05.04 pending) to the narrative explanations of history and the social sciences (see [30.01.], [31.], [32.*]).

Causal selection and the plurality of causes Master

Hesslow's "Causality and Determinism" raises a puzzle the theories above skirt. In any complete causal history, an indefinite number of factors are jointly necessary for the effect — the match's strike, the oxygen, the dryness, the match's manufacture, the laws of chemistry. All are equally causes in the sense of being on the producing chain. Yet we pick the strike and call it the cause. Why? This is the problem of causal selection.

Woodward answers via variance and invariance: the cause we cite is the factor whose intervention makes the most stable, relevant difference. Strevens's kairetic account offers a parallel selection rule. Hesslow and the older Huxley-Whitehead line worry that selection is pragmatic rather than metaphysical — a fact about us and our interests, not about the causal structure of the world.

The plurality bites hardest in medicine and social science, where risk factors multiply (see [35.03.], [35.06.], [30.06.]). Smoking causes cancer, but so do radon, asbestos, genetics, and air pollution; identifying the operative cause in a given patient is a clinical and statistical act, not a metaphysical one. The same plurality structures psychiatric diagnosis (see [29.09.]) and the classification of chronic disease (see [35.03.], [31.04.]).

Counterfactuals, possible worlds, and causal decision theory Master

Lewis grounded his counterfactuals in modal realism ("On the Plurality of Worlds", 1986) ^{[Lewis 1986]}: all possible worlds are real, and the closest C-absent world is the one most similar to ours. Stalnaker's "Theory of Conditionals" (1968) ^{[Stalnaker 1968]} offers a lighter-weight selection-function semantics, and Williamson's "Modal Logic as Metaphysics" (2013) ^{[Williamson 2013]} defends the necessity of the counterfactual connective itself. Modal realism connects outward to the multiverse and many-worlds readings of quantum mechanics (see 20.03.02 pending, 20.03.03 pending) and to the conceivability-possibility arguments about consciousness (see [20.06.*]).

Eells's type/token distinction ("Probabilistic Causality", 1991) ^{[Eells 1991]} and Sober's selection-of versus selection-for distinction ("The Nature of Selection", 1984) ^{[Sober 1984]} separate general (population-level) from singular (token) causation — the difference between "smoking causes cancer" and "this person's smoking caused her cancer" (see [20.05.], 20.05.03 pending, [29.01.]).

Causal decision theory (Lewis 1981; Joyce, "The Foundations of Causal Decision Theory", 1999) ^{[Joyce 1999]} uses counterfactual dependence rather than evidential correlation to evaluate acts: choose the action whose causal consequences are best, even when the act correlates with bad news. This separates the smoker who enjoys smoking (evidentially bad news about character, causally fine to indulge) from the medical advice that should govern the choice (see [29.05.], 20.02.07 pending, [37.]).

Laws, necessity, and natural kinds Master

Two further questions frame the whole debate. Armstrong's "What is a Law of Nature?" (1983) ^{[Armstrong 1983]} treats laws as necessitation relations among universals; Cartwright's "How the Laws of Physics Lie" (1983) ^{[Cartwright 1983]} counters that the fundamental laws are idealised and frequently false of real systems. Whether laws govern or merely describe bears directly on whether D-N explanation can work at all (see [20.03.], 20.08.02 pending, [28.04.]). The status of laws in cosmology (FLRW, LCDM — see [28.04.]), stellar structure (see [28.02.]), and population genetics (Hardy-Weinberg, Wright-Fisher — see [19.02.], [19.04.]) are live instances of this abstract dispute.

Ellis's "Scientific Essentialism" (2001) ^{[Ellis 2001]} and Bird's "Nature's Metaphysics" (2007) ^{[Bird 2007]} defend essentialism about natural kinds: the real kinds are picked out by their essences and dispositions, not by our classificatory conventions. This bears on the species problem in biology (see [20.05.]), on the classification of mental disorders (see [29.09.]), on cancer taxonomy (see [35.03.]), and on the contested biology of race (see [31.04.], 31.04.03 pending). Where kinds are essenced, causal-explanatory claims inherit modal force; where kinds are conventional, causation is a more local, model-relative affair.

Synthesis. The unifying thread across these accounts is that causation is analysed through dependence — counterfactual, probabilistic, interventional, or mechanistic — and that each notion of dependence yields a corresponding notion of explanation. The choice between them is not idle: it determines which inferences from data to cause are licensed, which explanations count as complete, and which interventions will work. This is why the same formal machinery — DAGs, do-calculus, mechanisms — recurs from physics and biology to clinical medicine and machine learning, and why the bridge runs through [26.] statistics, [37.] probability, and the special-science units [20.05.], [29.], [30.], [35.].

Connections Master

Demarcation, falsification, and paradigms 20.08.01. The predecessor frames the methodology within which causal claims are tested. The Duhem-Quine thesis and Kuhn's paradigms supply the background against which any single causal inference must be evaluated: a failed prediction can always be blamed on an auxiliary assumption rather than the causal hypothesis.
Scientific realism 20.08.02 pending. Realism about unobservable mechanisms is the metaphysical underpinning of mechanistic explanation. To accept Salmon's causal processes or MDC's hidden activities is already to take a realist stance toward the unobservables that carry the explanation.
Epistemology and inference to the best explanation 20.01.01. The counterfactual and interventionist analyses are themselves defended by inference to the best explanation; the no-miracles argument of 20.08.02 pending is the paradigmatic case of IBE doing this work.
Quantum mechanics 20.03.02 pending and spacetime 20.03.03 pending. Bell's theorem trades realism against locality in a way that bears directly on what causal processes can be; the many-worlds interpretation supplies a literal reading of Lewis's modal realism.
Biology 20.05.04 pending, neuroscience [29.02.], and medicine [35.]. These are the special sciences in which mechanistic explanation dominates, and where the type/token and selection-of/selection-for distinctions do their heaviest work.
Statistics [26.], probability [37.], and causal inference. The formal home of do-calculus, potential outcomes, and the identification problems that make causal inference a discipline rather than a slogan.
Ethics 20.02.07 pending and decision theory [29.05.*]. Causal decision theory evaluates acts by their causal consequences, separating the causal from the evidential reading of expected utility.

Historical and philosophical context Master

The modern problem of causation is Hume's. In the "Treatise" (1739) and the "Enquiry Concerning Human Understanding" (1748) ^{[Hume 1748]}, Hume argued that the idea of necessary connection is not copied from any impression: we observe only that one kind of event is constantly followed by another, and the mind, carried by custom, projects a tie. The regularity analysis — constant conjunction, temporal priority, contiguity — dominated the next two centuries, and its inadequacies (spurious regularities, the asymmetry of causation, its intrinsic direction) set the agenda for everything after.

The counterfactual turn is mid-twentieth-century. The strict conditional analysis ("C causes E iff $\neg C \supset \neg E$ ") failed, because material conditionals are too weak and track actual rather than counterfactual dependence. Stampe and then Lewis, in "Causation" (1973) ^{[Lewis 1973]}, rebuilt the analysis around possible-worlds semantics for counterfactuals. Lewis's "On the Plurality of Worlds" (1986) ^{[Lewis 1986]} supplied the heavy metaphysical machinery — modal realism — that made the closest-world relation respectable. The 1970s and 1980s then produced the counterexamples — preemption, overdetermination, trumping — that have driven the literature since (Hall, Paul, Schaffer).

The probabilistic tradition runs parallel. Reichenbach's "The Direction of Time" (1956) introduced the principle of common cause and screening off; Suppes's "A Probabilistic Theory of Causality" (1970) formalised probability-raising; Cartwright's "Causal Laws and Effective Strategies" (1979) added the contextual refinement. These theories found their natural home in the sciences of risk — epidemiology, medicine, the social sciences.

The mechanistic and interventionist turns belong to the late twentieth century. Salmon's "Scientific Explanation and the Causal Structure of the World" (1984) launched the causal-mechanical model; Machamer, Darden, and Craver (2000) refashioned it as the entities-and-activities framework that now dominates the philosophy of the life sciences. Woodward's "Making Things Happen" (2003) ^{[Woodward 2003]} crystallised interventionism. Pearl's "Causality" (2000) ^{[Pearl 2000]} and "The Book of Why" (2018, with Mackenzie) ^{[Pearl Mackenzie 2018]} supplied the formal apparatus — DAGs, do-calculus, structural causal models — that unified the interventionist intuition with a workable methodology, crossing from philosophy into statistics, computer science, and econometrics.

The causal-inference revolution in the social sciences (Angrist, Imbens, Rubin; recognised by the 2021 Nobel Prize) and the rise of causal machine learning are the contemporary frontier, carrying the philosophical analyses of Hume, Lewis, and Woodward into the empirical practice that tests them.

Bibliography Master

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