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Philosophy of Science 101: Causation


The Philosophy of Science series explores both general questions about the nature of science and specific foundational issues related to the individual sciences. When applied to such subject areas, philosophy is particularly good at illuminating our general understanding of the sciences. This 101 series will investigate what kinds of serious—often unanswered—questions a philosophical approach to science exposes through its heuristic lens. This series, more specifically, will look at the ‘Scientific Realism’ debate throughout, which questions the very content of our best scientific theories and models.

Philosophy of Science 101 will be divided into the following chapters of content:

5. Philosophy of Science 101: Causation

6. Philosophy of Science 101: Scientific Models

7. Philosophy of Science 101: Models of Explanation

8. Philosophy of Science 101: Laws of Nature

9. Philosophy of Science 101: Science and Social Context

Philosophy of Science 101: Causation

Causation, broadly speaking, explores the relation between a cause, c, and an effect, e. The metaphysics of causation is a major and central area of study within the philosophy of science, investigating specifically the relation that holds between two temporally simultaneous or successive events when c brings about e. Compare two sequences of events, for example:

1. Simon flicks the switch, and the bathroom light turns on.

2. Simon flicks the switch, and his cat walks into the bathroom.

What is the difference between (1) and (2)? Clearly, in (1), the flick of the switch is the cause of the bathroom light turning on; whereas, in (2), it is a mere coincidence that Simon’s cat walks into the bathroom the moment the light is switched on. The problem, known as "Hume’s problem" since modern philosophical study of causation starts with David Hume (Baumgartner, 2008), is that it is very hard to explain further what makes (1) and (2) different. Differentiating between a causal sequence and a mere coincidence informatively and truthfully proves particularly difficult, as this next article in the Philosophy of Science 101 series will discuss.

Having explored the scientific realism debate previously, the series now turns to the fruitful research topics in and around causation in the philosophy of science, namely regularity theories of causation, and non-reductive manipulability accounts of causation.

Figure 1: Pendulum graphic: laws of succession give rise to causal explanations, but laws of coexistence cannot. A case in point is the law that connects the length of a pendulum with its period (John Z., 2005).

Nature of the Analysis: Conditions of Adequacy

One must start with causation terminology, the conditions of adequacy to sufficiently account for causation, and the very nature of the analysis. First, consider a few more claims about causation:

a) The emergence of political opposition caused the Civil War.

b) Driving under the influence causes car crashes.

c) How much iron one consumes influences their bodily growth and development.

d) How much nitrous oxide a woman receives in labour affects how much pain she feels during giving birth.

As Dmitri Gallow (2022) describes, the metaphysics of causation is concerned with what it makes for claims—like above—to be true. Study in causation explores what kind of relation the claims are about, and in virtue of what these relations obtain. According to some, such as Gallow (2022), both (a) and (b) are broadly causal claims but they are not about the same kind of causal relation. This is to say that their relata are different: these causal relations are differentiated by their relata since claim (a) relates tokens whereas claim (b) relates types. Claim (a), that the emergence of political opposition caused the Civil War, talks about a particular emergence of political opposition and civil warnot political opposition and civil war in general (Gallow, 2022). On the contrary, claim (b) is not talking about any particular instance of driving under the influence, but rather driving under the influence in general. Perhaps there are different kinds of causal relation corresponding to these different kinds of relata, as many hold (Sober, 1985; Eells 1991, for example).

Now compare (a) and (b) with claims like (c) and (d). Like Gallow (2022) explains, the causal verb “influences” is not flanked by token happenings, nor types of happenings. Instead, it is flanked by variable expressions since—in claim (c)—one’s bodily growth and development depends on how much iron one consumes. Prima facie, (c) is not a claim about any particular variable because it is talking about how iron consumption affects bodily growth and development in general. Likewise, claim (d) is not a claim about the relationship between any particular individual’s nitrous oxide intake and pain sensation. Claim (d) is a claim about how nitrous oxide affects sensation in general.

Figure 2: Norton’s (2008) Dome is a fascinating counterexample in classical mechanics since the failure of CM to dictate a well-defined result can be seen as a failure of causal determinism.

Notably, there is little agreement about what actually differentiates these four different kinds of claims, nor is there any standard terminology to mark the distinction between causal claims like (a) and (b) and causal claims like (c) and (d). Disagreement is often concerning whether relations are reducible, and if so, what they can be reduced topossibilities, regularities, counterfactuals, mechanisms, agency, dispositions, processes, or counterfactuals (to name but a few). Before going any further and surveying the various types of analyses and accounts of causation, however, it is important to first consider the conditions of adequacy to establish what makes any account sufficient in the first place. The adequacy conditions are as follows, and will be considered throughout this article in relation to the theories discussed thereafter:

  1. An account of causation must rule out accidental relations (i.e., it must distinguish between "real" causal relations and accidental relations).

  2. An account of causation must rule out common causes: it may be that two events are perfectly correlated but not because c causes e, rather because they are concomitant effects of a common cause "a" (see figure 3).

  3. An account of causation must maintain and explain causal asymmetry: if c causes e, then e does not also cause c.

  4. An account of causation must deal with pre-emption (i.e., it must distinguish between "real" and pre-empted causes).

On condition (1), mere coincidences mistaken as causal relations are addressed. Much like the "Simon-and-his-cat" example given earlier, an effective account of causation must not allow for such cases to qualify as causation for obvious reasons. As for condition (2), take a simple example. Lung cancer is known to commonly result from years of smoking. In everyday language, one might even assert that "smoking causes lung cancer". Smoking also, however, often results in stained teeth. The common cause "a" has concomitant effects here, and as condition (2) describes, it may well be the case that two events are perfectly correlated. Crucially, however, this is not because c causes e. It is because of a common cause a (as illustrated in figure 3). Condition (3) is then that an effective account of causation must maintain causal asymmetry. Indeed, a general metaphysical question about cause and effect is what kind of entity can be a cause, and what kind of entity can be an effect (Whitehead, 1929). One of the important tasks of a theory of causation is thus to explain the difference between causes and effects, to reveal the true point of the "arrow" of causation (c e). Another is to explain why the arrow of causation is so well aligned with the arrow of time. The latter task of course presupposes the former: if the causal relation were symmetric, it could have no preferred temporal orientation (Price, 1992). Finally, condition (4) holds that an account of causation must deal with pre-emption. Though the exact meaning of "pre-emption" is elusive, a possible cause can generally be regarded as having been preempted if there is independent evidence to support such an inference (Dyrkolbotn, 2017). There is indeed a problem if there are several candidates that compete for the title of "the cause" of a given effect and one—or an account—must decide which is the "real" cause. Hence an account of causation should distinguish between real and pre-empted causes (pre-emption can further be divided into "early" and "late" pre-emption, see Menzies & Beebee (2001) for more on this).

Figure 3: Common causes diagram: C and E are concomitant effects of a common cause A (Gallow, 2022).

Types of Analyses

As mentioned, the conditions of adequacy are of utmost importance for any account of causation to be sufficient. The type of analysis is therefore important to consider as well, since this determines the aim of the account of causation. The various types of analyses can be divided into two camps and reflect Hume’s influence on this field of study (Coventry, 2006). The two types of analyses are (a) reductive and (b) non-reductive accounts of causation. Type (a) provide truth conditions for causal claims in non-causal terms (Gijsbers, 2021). Famously, type (a) includes regularity theories of causation (Coventry, 2006). The motivation is notably epistemic since causality cannot be observed directly (Wilson, 2018). It is also metaphysical because ontological parsimony urges one to keep the number of basic constituents of the world small. Type (b) analyses, on the other hand, hold causality as basiccausal claims can therefore not be rephrased in non-causal terms (Baumgartner, 2009). Manipulability accounts of causation fall under type (b) since they resist the motivation for reductive accounts. First, they (manipulability accounts) resist the epistemic motivation and either deny that one cannot observe causality directly or they understand causal claims as being on par with claims about theoretical entities. Second, they resist the metaphysical motivation by holding that causal relations are indispensable. The overarching aim of type (b) analyses is to understand the relation between causality on top of other concepts of interest such as the laws of nature or intervention (as becomes apparent in James Woodward’s (2015) account discussed later). For now, this article starts by outlining type (a) analyses and their deficiencies, in particular various regularity theories of causation given by David Hume, John Stuart Mill (1862), and John Mackie (1980).

Regularity Theories: Hume’s Account

Though regularity theories of causation are not currently popular (Psillos, 2011), Hume’s "original" regularity theory famously set this very study in motion. Roughly speaking, 20th century efforts to analyse causation up until the 1970s were mostly regularity theories. They took their cue from Hume and sought to analyse causation in terms of patterns among actual events. Hume’s account, in fairly simple terms, is as follows (Andreas & Guenther, 2021):

C causes E if and only if (iff):

(a) C is (spatiotemporally) contiguous to E

(b) C occurs before E

(c) All C’s are invariably followed by E’s (constant contingent)

The simplest regularity analyses, like Hume’s, suffer from obvious defects (Broadbent, 2007). First, there is the problem of non-sufficiency. This is to say that relations can be non-causal and yet satisfy Hume’s conditions, such as accidental causes and concomitant effects. Concomitant effects which have a common cause satisfy (a)-(c), but they are still not real causes. Problems with pre-emption also arise here too, for the conditions above do not help one distinguish which cause is real if there are multiple candidates.

Figure 4: For Hume, one imagines causality since one experiences contiguity between certain events. Hence the white and red balls appear contiguous in space and are never in another order (Giles, 2021).

Another problem resulting from Hume’s regularity theory is concerned with non-necessity: relations that are causal but do not satisfy Hume’s conditions (Gallow, 2022). Imperfect regularities are an example, whereby C can cause E but not all occurrences of a C are followed by an E. Consider the smoking example again: not every smoker gets lung cancer, for instance. Non-temporally ordered causes prove to be yet another issue here since not all causes are prior to their effects like condition (c) suggests. Functional relations, for example: if an individual is turning an amplifier loudness button, the music gradually gets louder at the same time. Hence the requirement of succession is not satisfied, nor is causal asymmetry. The obvious defects of a simple regularity account like Hume’s mean that such analyses become increasingly complex for little—obvious—gain in explanatory power. To deal with various problems, regularity analyses become more developed post-Hume.

Regularity Theories: Mill and Mackie

Mill’s (1862) account, though a regularity view of causation, is slightly different to that of Hume’s. According to Mill’s theory, there is never a single circumstance responsible for an effect, but a set of conditions. Regularities are thus not in the fabric of the universe but are mere regular occurrences. Hence, a total cause is a set of conditions which is invariably followed by its effect according to Mill (1862) here:


(ABC being A & B & C)

This article will not evaluate Mill’s account in any real detail, but it is worth noting that his regularity theory somewhat improves on problems of imperfect regularities. It does not, however, thoroughly solve the other—and serious—problems that regularity theories encounter. This is where Mackie (1980) comes into the picture, for Mackie added to Mill’s account that there can be several sets of conditions leading to E. Mackie’s (1980) important addition to this kind of regularity view is his plurality principle:

ABC or A’B’C’ or… or… E

Importantly, a cause is a factor in one of the disjuncts in the above such that:

(i) If the entire disjunct occurs, E follows

(ii) If the disjunct minus the factor occurs, E does not follow

(iii) If the factor occurs in isolation, E does not follow

A cause (as above) is therefore known as an "INUS" condition: an insufficient but non-redundant part of an unnecessary but sufficient condition (Kim, 1971). More specifically, as with the factor "B" in the disjunct "ABC" leading to E (see above), B is a cause iff the following hold:

(i) If ABC occurs, E follows

(ii) If AC occurs, E does not follow

(iii) If B occurs in isolation, E does not follow

Hence "INUS" (Kim, 1971).

Figure 5: Illustration of INUS conditions: Wickham-Crowley's work on guerilla movements (Sweet, 2014).

Mackie’s regularity theory develops Mill’s account and has clear advantages (Strevens, 2007). For example, it can deal with complex situations and does justice of a plurality of causes. What’s more, temporal succession is no requirement so non-temporal causes are allowed. Mackie’s account indeed proves rather different to Hume’s regularity theory, even if both accounts are reductive analyses of causation.

Manipulability Accounts of Causation: Woodward

As mentioned, there are also non-reductive analyses of causation. Manipulability accounts of causation are an example of this type of analysis. This article shall now consider philosopher of science James Woodward’s (2015) particular manipulability account. Indeed, causes are a means to produce an effect on Woodward’s account. What is especially different is that agents can use causes to manipulate and control effects: an agent thus intervenes on c to bring about e. Hence, c causes e iff someone manipulates c and thereby brings about e. An immediate objection is of course that causality can be effective in things that are in the past, are far away, or are too large to manipulate, yet Woodward’s (2015) account elaborates on this. Consider an example to illustrate what causation consists of according to Woodward’s (2005) account:

Let x and y be variables, where x is the position of an oven dial and y is the temperature of the oven.

Causation: x causes y iff the value of y would change if an agent were to intervene on the value of x.

Notably, an intervention need not be feasible. All that is needed is counterfactual dependence, which allows one to account for causal relations in things that de facto cannot be manipulated since one event e counterfactually depends on another event c just in case if c had not occurred then e would not have occurred (Vihvelin, 1995). The counterfactual therefore state "dependences" of whether, when and how one event occurs on whether, when, and how another event occurs. The key idea in the formulation of these counterfactuals is that of an alteration of an event (Menzies & Beebee, 2001). Of course, this is not to say that every counterfactual dependence is indicative of causality: two counterfactuals might well be true, for example, but only the former causal. Woodward (2015) cleverly introduces a solution to distinguish the two cases, however, known as invariance. The dividing criterion—between causal and non-causal counterfactuals—is therefore invariance, whereby a functional relationship is considered "invariant" under an intervention if it continues to hold under the intervention. That is, the relation correctly describes how the value of the dependent variable would change under an intervention. Counterfactual dependences therefore must be invariant for the relation to be causal. In sum, c causes e if intervening on c can bring about e and if the relation between c and e is invariant under the intervention. It is intervention and invariance that indeed identify causal relations, where the intervention is formulated counterfactually to account for cases where humans de facto cannot intervene. Woodward’s manipulability account is thus a non-reductive analysis of causation since intervention is itself a causal concept. As Woodward (2005) puts it, causal explanations “furnish information that is potentially relevant to manipulation and control” (p. 6).

Figure 6: James F. Woodward (Kelly, 2010).


The search for causes is only natural to the human mind, which believes that nothing happens without reason. As a central part of the philosophy of science, this 101 series has therefore introduced and explored the various reductive and non-reductive analyses of causation which aim to effectively account for causation. As philosopher and metaphysicist Alyssa Ney (2014) puts it, a sufficient account of causation is incredibly important since it could amount to “a complete account of the nature of the universe and what it is like” (p. 220). Hence this article has considered the very theories, starting with Hume’s regularity theory, which intend to do just that. The conditions of adequacy that a theory must uphold have therefore been important to factor in, especially when laying out what a sufficient theory must consist of. Hume’s regularity theory, for instance, proved to have many serious downfalls. Other regularity theories don’t have such obvious defects compared, such as Mackie’s (1980) reductive analysis which seeks to develop Mill’s (1862) account. Non-reductive accounts of causation in contrast prove different again, namely Woodward’s (2005) manipulability account holding that absolutely any explanation that proceeds by showing how an outcome depends on other variables or factors counts as causal.

Theories of causation have been refined time and time again, somewhat unsurprisingly. The idea that a cause is regularly followed by an effect is often at the very core of (reductive) theories of causation with thanks to Hume. Effectively accounting for causation like this, however, proves particularly complicated and many different accounts therefore propose many different mechanisms, analyses and explanations to either uphold (or overcome problems with) the various conditions of adequacy. Manipulability accounts in contrast to regularity theories, for instance, have the force of counterfactual dependence to effectively account for causation. Study in the philosophy of science, amongst the many different types of theories of causation, also explores causal models to this end: conceptual models describing the causal mechanisms of a system. Many scientific models indeed are "representational" models in this sense because they represent a selected part or aspect of the world (i.e., the model's "target system") (Frigg & Hartmann, 2006), as this 101 series will delve into next.

Bibliographical References

Andreas, H., & Guenther, M. (2021). Regularity and inferential theories of causation.

Baumgartner, M. (2008). Regularity theories reassessed. Philosophia, 36, 327-354.

Baumgartner, M. (2009). Interdefining causation and intervention. Dialectica, 63(2), 175-194.

Broadbent, A. (2007). Reversing the counterfactual analysis of causation. International Journal of Philosophical Studies, 15(2), 169-189.

Coventry, A. M. (2006). Hume's theory of causation. A&C Black.

Dyrkolbotn, S. K. (2017). On preemption and overdetermination in formal theories of causality. arXiv preprint arXiv:1710.03390.

Eells, E. (1991). Probabilistic Causality, Cambridge: Cambridge University Press.

Frigg, R., & Hartmann, S. (2006). Models in science.

Gallow, J. D. (2022). The metaphysics of causation.

Gijsbers, V. (2021). How (not) to judge a theory of causation. Synthese, 199(1-2), 3117-3135.

Kim, J. (1971). Causes and events: Mackie on causation. The Journal of Philosophy, 68(14), 426-441.

Mackie, J. L. (1980). The cement of the universe: A study of causation. Clarendon Press.

Menzies, P., & Beebee, H. (2001). Counterfactual theories of causation.

Mill, J. S. (1862). Of the law of universal causation.

Ney, A. (2014). Metaphysics: An Introduction (1st ed.). Routledge.

Price, H. (1992). Agency and Causal Asymmetry. Mind, 101(403), 501–520.

Psillos, S. (2011). Regularities All the Way Down: Thomas Brown's Philosophy of Causation. In Causation and modern philosophy (pp. 220-241). Routledge.

Sober, E. (1985). “Two Concepts of Cause”, in P. Asquith and P. Kitcher (eds.), PSA 1984 (Volume 2), East Lansing: Philosophy of Science Association, pp. 405–24.

Strevens, M. (2007). Mackie remixed. Causation and explanation, 4, 93-118.

Vihvelin, K. (1995). Causes, effects and counterfactual dependence. Australasian Journal of Philosophy, 73(4), 560-573.

Whitehead, A.N. (1929). Process and Reality. An Essay in Cosmology. Gifford Lectures Delivered in the University of Edinburgh During the Session 1927–1928. Cambridge: Cambridge University Press.

Wilson, A. (2018). Metaphysical causation. Noûs, 52(4), 723-751.

Woodward, J. (2005). Making things happen: A theory of causal explanation. Oxford university press.

Woodward, J. (2015). Interventionism and causal exclusion. Philosophy and Phenomenological Research, 91(2), 303-347.

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Rebecca Ivory

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