The Problem of Infinite Regress: A Stopping Rules Approach

The proximate cause stopping rule

The first stopping rule for infinite regress is to avoid weighing causes at all and focus instead on proximate causes. For example, in A System of Logic, Mill (1882:404) argued that a cause of an outcome should be separated from the “conditions” apparent before the outcome. He ultimately advised focusing on proximate causes: “the one condition which came last into existence.” Rigby (1995:227) argued that the most a historian could hope to accomplish when it comes to ranking causes is to state that “a number of factors must be taken into account.” He focused on proximate causes while discounting an endless trove of background conditions, quoting Mill that these conditions can be “understood without being expressed” (p. 236). This rule can be expressed as follows:

As an example, consider research on the origins of European democracy. Moore’s (1966) Social Origins of Dictatorship and Democracy: Lord and Peasant in the Making of the Modern World offers a complex historical argument (focusing largely on the commercialization of agriculture), but he summarizes a key component of his theory with the pithy line: “No bourgeois, no democracy” (p. 418). This is the proximate cause in his work, and it is clear that Moore is documenting a necessary cause of democracy: without the bourgeoisie, democracy could not emerge. Therefore, we can model this argument as follows: X₁ (emergence of the bourgeoisie) – n → Y₁ (early European democracy). According to the proximate cause stopping rule, there is no reason to go back further in the analysis.

The upside of this approach is its simplicity: scholars need only look for the proximate cause and focus their energies on explicating it. All antecedent causes are merely background conditions. Unfortunately, the downsides to this stopping rule are numerous. First, it is unclear how this is even a solution to infinite regress because it does not engage at all with causes of causes but rather sidesteps the issue entirely. Second, the proximate cause is often unclear because scholars may disagree about the cause “which came last into existence.” But the biggest problem with the proximate cause approach is that antecedent causes could be more important than proximate ones.

Using sequence elaboration as a basic test of this rule and going one step back in the causal chain of Moore’s book highlights this problem. If Moore focuses on the emergence of the bourgeoisie, then it is only natural to ask: what caused their rise in the first place? Downing’s (1992) The Military Revolution and Political Change: Origins of Democracy and Autocracy in Early Modern Europe provides a rival historical explanation but one that is useful here because it was written partly in response to disagreements with Moore’s thesis. Downing argues that medieval constitutionalism is a cause of early European democracy that “has been largely ignored by almost all modern social scientists” (p. 5).

Downing (1992:10) defines medieval constitutional government as “a system of decentralized government” that included “parliaments controlling taxation and matters of war and peace; local centers of power limiting the strength of the crown . . . independent judiciaries and the rule of law; and certain basic freedoms and rights enjoyed by large numbers of the population.” Downing then summarizes his main argument: “Medieval constitutionalism, where it survived, laid the foundations for liberal democracy in the eighteenth and nineteenth centuries” (p. 10).

Logically speaking, Downing’s argument is that medieval constitutionalism is a necessary cause of early European democracy. In fact, he states this directly: “medieval constitutionalism was not democracy, nor was it sufficient cause of it” (p. 54). We can model this argument as follows: X₁ (medieval constitutionalism) – n → Y₁ (early European democracy). But what is the relationship between medieval constitutionalism and the emergence of the bourgeoisie that is the cornerstone of Moore’s thesis? Following Mahoney et al. (2009), if it is a necessary cause of bourgeoisie emergence (and the final outcome of interest), then it would be the less important cause.

However, Downing shows that medieval constitutionalism is sufficient for the development of the bourgeoisie: the middle classes emerged due to parliaments, independent judiciaries, the rule of law, and so on. Yet the case of Sweden shows that medieval constitutionalism is not necessary for the development of the bourgeoisie: Sweden had constitutionalism but “no bourgeois, yet democracy” (p. 245). In this case, the bourgeoisie did not emerge after medieval constitutionalism, showing that the latter is therefore only a sufficient but not necessary cause. ⁸ In this causal chain, the proximate cause is not the most important cause: Downing’s antecedent cause is more important, or to use Mahoney et al.’s (2009) terminology, it is a diminishing cause. Moore’s endorsement of Downing’s work implicitly noted this: “This book takes a big step beyond my Social Origins of Dictatorship and Democracy.”

Figure 4 displays the full logical relationship discussed here using sequence elaboration. One unique aspect of Downing’s analysis is that although he focuses on medieval constitutionalism, an intervening variable (that occurs temporally after the medieval period) plays a prominent role in the causal chain and must be accounted for: the “Military Revolution,” or “the shift from small, decentralized knight service to large standing armies” (p. xi). I call the Military Revolution an intervening variable because it was not caused by medieval constitutionalism. It was caused by other factors—territorial expansion, agrarian transformations—and is mainly important in Downing’s analysis for the effect it had on the legacy of medieval constitutionalism (p. 65). Ultimately, in the example of Moore and Downing, the proximate cause stopping rule fails to locate the deepest cause in the sequence.

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Figure 4.

The proximate cause stopping rule.

The critical antecedent stopping rule

Slater and Simmons (2010) offer a second stopping rule for infinite regress, built on discovering what they call critical antecedents. They break up antecedent conditions into four types: descriptive context, background similarities, critical antecedents, and alternative explanations. They emphasize critical antecedents, or “factors or conditions preceding a critical juncture that combine with causal forces during a critical juncture to produce long-term divergence in outcomes” (p. 889). For example, in Political Process and the Development of Black Insurgency, 1930–1970, McAdam (1982:40–48) notes three causes that are individually necessary and jointly sufficient to produce Black insurgency: the political opportunity structure, indigenous organizational strength, and cognitive liberation. Slater and Simmons (2010:893) argue that a critical antecedent of McAdam’s work is the decline of the cotton economy.

The critical antecedent stopping rule can be understood as an extension of the proximate cause stopping rule: here we are looking for the cause of the proximate cause. This rule can be expressed as follows:

The advantage of this approach is that it does engage with the infinite regress problem—it is not enough to find proximate causes because the causes of causes must also be explored. But the critical antecedent approach has two main downsides. First, as Slater and Simmons (2010:912) write, “we submit that attempting to apportion the precise, partial causal weight of critical junctures and critical antecedents is not necessarily a productive approach.” In order words, there is no attempt to weigh causes. As noted in the previous section, dealing with the infinite regress problem necessitates weighing causes. This is the only means by which we can know if an antecedent cause is more important than a proximate one.

The second problem with this stopping rule is that, like the proximate cause stopping rule, there are clear examples where the critical antecedent approach does not locate the deepest cause. To return to McAdam’s (1982) work on Black insurgency, Slater and Simmons (2010:893) focus on the decline of the cotton economy (a “successive” antecedent cause). Because Slater and Simmons are not weighing causes, they do not label this as either a necessary or sufficient cause. In McAdam (1982:73), however, the decline of the cotton economy appears to be a necessary cause of Black insurgency

If one had to identify the factor most responsible for undermining the political conditions that, at the turn of the century, had relegated blacks to a position of political impotence, it would have to be the gradual collapse of cotton as the backbone of the southern economy.

If cotton had not declined, then African Americans would have remained in a powerless political position—this seems to be a necessary cause. If this reading is correct, and following Mahoney et al. (2009:135), the sufficient cause is more important in the chain. Therefore, in this case, the critical antecedent approach is actually uncovering a less important cause. Figure 5 diagrams the full relationship.

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Figure 5.

The critical antecedent stopping rule.

Relatedly, if we want to go back one level beyond Slater and Simmons’s stopping rule, we run into the problem of whether critical antecedents can have critical antecedents. Is there a critical antecedent of the decline of cotton? McAdam (1982:66), for example, discusses the important effects of the controversial 1876 election. Slater and Simmons (2010:890–91) recognize this possibility and the danger of infinite regress it entails but simply state that scholars should focus on nontrivial causes. But how this advice works in practice is not obvious because the 1876 election is certainly not a trivial cause, and therefore the causal chain regresses indefinitely.

The insufficient data stopping rule

A third potential solution to dealing with infinite regress is to use the insufficient data stopping rule, which can be expressed as follows:

An example of this rule in action comes from Putnam’s (1993) Making Democracy Work: Civic Traditions in Modern Italy. Putnam’s goal was to explain the striking divergence of governance across, broadly speaking, north and south Italy. Using 12 indicators of government performance from the 1970s and 1980s, he finds that “the northern regional governments as a group have been more successful than their southern counterparts. . . . In the words of a thousand travelogues, ‘the South is different’” (p. 83).

In chapter five, Putnam (1993:121) delves deeply into Italy’s history to explain the “roots” of this divergence. This exploration locates civic culture as the main cause of Italian governance. According to Putnam, the civic culture of north Italy is based on horizontal relationships, robust associational life, and care for the common good. By contrast, the civic culture in the south is based on hierarchy and “private greed” (p. 115), what Banfield (1958) called “amoral familism.” Although Putnam (1993:90) never makes clear what kind of cause civic culture is, in an earlier part of the book, he reviews literature showing that “associationism is a necessary precondition for effective self-government,” and presumably this applies to the Italian case as well. Therefore, the initial relationship here is: civic culture (X₁) – n → Italian governance (Y₁). Following Mahoney et al. (2009), an antecedent factor will diminish this relationship if it is sufficient for the independent variable and necessary for the dependent variable (Z₁ – s → X₁; Z₁ – n → Y₁).

The importance of civic culture naturally prompts the “cause of a cause” question: what accounts for the differences in civic culture across Italy? Going to the second level of analysis, Putnam suddenly jumps to a distal cause: the formation of new political regimes that occurred in the eleventh century, almost a millennium prior. Critically, these political regimes were very different. In the north, a unique form of “communal republicanism” (Putnam 1993:130) was created, which included the growth of communes that extended beyond the traditional ruling classes. By contrast, the autocratic regimes of the south were created by Norman mercenaries (p. 122). Although administratively and economically advanced, they created a “steep social hierarchy [that] came to be ever more dominated by a landed aristocracy” (p. 124).

Logically speaking, the formation of new political regimes would be a more important cause of Italian governance than civic culture if it were sufficient for civic culture and necessary for Italian governance. However, the creation of new political regimes in the medieval period is necessary for both downstream causes: for example, without the creation of communal republicanism in the north, then the “correct” type of civic culture could not have been created. Likewise, without communal republicanism, government performance in the north could not have been high. Thus far, civic culture remains the most important cause in Putnam’s work.

Putnam stops his analysis here. But if the eleventh century is so important, then why not the tenth or ninth centuries? In a footnote, Putnam (1993:228, note 1) explains his decision

Our story begins in the eleventh century primarily because the character of social and political life in the Dark Ages between the fall of Rome and 1000 remains in many respects obscure. Most unfortunate from the point of view of the theoretical argument we pursue here, the origins and prehistory of the northern communes are still shrouded in mist.

How does this stopping rule fare if we go one step back in his analysis? That necessitates asking why different political regimes were created in eleventh-century Italy. Putnam (1993:121) does not explore the question in depth but hints at a deeper cause while quoting historian J. K. Hyde

Throughout the peninsula during the eleventh century, the time-honoured imperial system of government—Byzantine in the south, German in the north—passed through a time of strain and weakness, ending in virtual collapse, which handed the initiative to local forces.

Therefore, the third-level cause is the collapse of imperial (Byzantine and German) government. Again, this seems to be a necessary cause: without the collapse of imperial government, the initiative for local forces to create new political regimes could not have occurred. Similarly, the collapse of imperial government only seems necessary for governance.

Figure 6 diagrams the full causal chain of the book. Because it is a chain of necessary conditions, the most proximate cause (civic culture) is the most important cause (Mahoney and Vanderpoel 2015:82). As in Downing’s work, intervening variables occur between the formation of political regimes (c. eleventh century) and the creation of civic culture: the Black Death and the Hundred Years War in the fourteenth century and European wars that often featured Italy as a key battleground in the fifteenth and sixteenth centuries (Putnam 1993:131, 133–34). These intervening variables are external factors that had an effect on the causal chain. Putnam (1993:135) argues that even through this pestilence and war, although the communal republicanism of the north was weakened, the divergence across north and south Italy remained: “Despite the social and economic gloom provoked by several centuries of foreign depredation, pestilence, and domestic strife, the ideal of the vita civile persisted in the regions of communal republican traditions.”

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Figure 6.

The insufficient data stopping rule.

The advantage of the insufficient data stopping rule is that, like the previous rule, it is fairly cut and dry: scholars can stop when they do not have historical evidence regarding antecedent causes. The downside of the insufficient data stopping rule, however, is determining whether the scholar is correct in claiming there are insufficient data for analyzing antecedent causes. This is a highly subjective claim. And in the Putnam example, the evidence is contradictory. In the very next footnote after the aforementioned one, Putnam (1993:228) notes that the medieval north-south dichotomy seems to mirror the Roman-Byzantine boundaries of Italy from “the preceding epoch,” arguing that this similarity is “an important question for future research.” But there is already significant historical research on Roman and Byzantine Italy, even on civic culture (see e.g., Haldon 1990; Nicol 1988). And reconstructing the past based on limited data is exactly what historically-oriented social scientists are trained to do. Therefore, the causal chain in Putnam’s work could continue even further still.

The critical juncture stopping rule

A first solution to infinite regress is to use the critical juncture stopping rule. As a cognate term, this could also be called a “theory-driven stopping rule” because in practice, a critical juncture always involves a scholar making a theoretical claim about why the analysis stopped at a particular point. The critical juncture framework was popularized by Collier and Collier (1991) in their study of Latin American politics. A critical juncture is a historical moment in which changing an institutional path is possible. This juncture consists of permissive conditions that loosen constraints on human agency and productive conditions that produce divergence in outcomes (Soifer 2012). As Mahoney (2000:527) notes, critical junctures can be beneficial for wrangling with infinite regress: “By focusing on such breakpoints, analysts of reactive sequences offer one possible solution to the problem of infinite historical regress” (see also Pierson 2004:89). The implication here is that scholars should truncate their historical analysis at a critical juncture and then explain precisely why this particular breakpoint was chosen. This rule can be expressed as follows:

An example of using the critical juncture stopping rule comes from Morgan’s Working Mothers and the Welfare State: Religion and the Politics of Work-Family Policies in Western Europe and the United States. Morgan’s work is a regional case study, examining outcomes in four states: France, Sweden, the Netherlands, and the United States. Her dependent variable is work-family policies such as “child care policy but also . . . parental leave and flexible work-time arrangements” (p. 2). Morgan is trying to explain the variation between France and Sweden, which have more generous policies for mothers, and the Netherlands and the United States, which offer less generous policies.

From the beginning, Morgan points out the historical nature of her analysis. She argues that most prior work focused on the expansion of the welfare state during the “golden age” of 1945 to 1975 while paying less attention to deeper causes from the nineteenth century. But Morgan (2006:2–3) explains: “These golden-age policies also did not emerge sui generis but were influenced by the political and policy legacies of an earlier period.”

In this case, Morgan points to the deeper cause of secularization, specifically the secularization of religious authorities involved in public education. As Morgan (2006:3) notes, in France and Sweden, “religious authorities were subordinated to secular state ones, facilitating an active state role in family policy and furthering the secularization of politics and social life,” whereas in the Netherlands and the United States, “social conservatives gained more influence over politics than in France and Sweden—although by different means—and tried to shield the family from state influence while also espousing traditional gender roles.” Therefore, secularization appears to be a necessary cause of mothers’ employment; its absence in the Netherlands and the United States led to less generous policies for mothers.

Morgan (2006:35) argues that the nineteenth century represents a critical juncture, and she offers clear theoretical reasons in explaining why

Why must we go back to the late nineteenth and early twentieth centuries to make sense of the contemporary politics of child care and policies on mothers’ employment? For one thing, the roots of modern political parties and ideologies lie in this period. As Seymour Martin Lipset and Stein Rokkan show in their seminal work on political development, nineteenth-century cleavages and conflicts in Western Europe formed the basis of political parties and systems that were in place by the 1920s.

At this point, it might be worth asking why one would not use the critical antecedent approach and look beyond the critical juncture. Yet Morgan (2006:36) effectively explains why earlier time periods are important but the key causes occurred in the nineteenth century

Although many countries experienced a gradual secularization of political authority beginning in the Renaissance, the century following the French Revolution brought direct, sharp challenges to the power and influence of organized religion in many countries.

Moreover, we can ask: does the critical juncture stopping rule prevent at least one deeper antecedent cause that is more important? Given that Morgan’s (2006) main cause is a necessary one, an antecedent factor will diminish this relationship if it is sufficient for the independent variable and necessary for the dependent variable (Z₁ – s → X₁; Z₁ – n → Y₁). Morgan does not ignore this causes of causes question. The immediate question is: why did public authorities become secularized in France and Sweden but not in the Netherlands and the United States?

Digging into Morgan’s work reveals that a precondition of secularization is the preexisting fusion of church and state. For example, Catholicism had been the official state religion in France (except for a brief period during the Revolution), and Sweden experienced a “church-state fusion” (Morgan 2006:26). In the Netherlands, on the other hand, the Dutch Reformed Church lost its status as the official church in 1796 (Blei 2006:50). And in the case of the United States, a separation of church and state was established in the Constitution. Church-state fusion appears to be a necessary cause of secularization; without it, secular forces could not have had a centralized force to oppose. This antecedent factor is not sufficient but only necessary for X₁ (secularization) and appears necessary to generate the outcome of mothers’ employment (Y₁); therefore, it is not the more important cause in the chain. As Figure 7 shows, we have another chain of necessary causes, and so the most proximate one is most important.

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Figure 7.

The critical juncture stopping rule.

An ancillary example of this rule comes from Daniel Ziblatt’s (2006) book Structuring the State: The Formation of Italy and Germany and the Puzzle of Federalism. The book compares two influential European cases, in which Italy created a federal system and Germany did not. Yet in the mid-nineteenth century, Prussia under Bismarck and Piedmont under Cavour both began the project of national unification with similar goals. The two paths diverged in important ways over the next several decades. Despite its political power, Prussia used a process of “negotiated unification” that created a federal state. Piedmont, in contrast and despite its weaker position relative to Prussia, pursued a policy of “unification by conquest” (Ziblatt 2006:7).

Ziblatt argues that the key factor explaining this outcome is infrastructural capacity. Germany had a strong system of subnational units, which constrained leaders’ abilities to build a unitary state. Italy, by contrast, did not have similar levels of subnational infrastructural capacity, which allowed Italian politicians to impose a unitary system of government. Ziblatt’s (2006:13) central thesis seems to be an argument about a necessary cause: he calls infrastructural capacity a “precondition”; it was necessary for federalism. Because it did not exist in Italy, Italy could not create a federal state. Therefore, we can model this argument as follows: X₁ – n → Y₁. Given this, an antecedent factor will diminish this relationship if it is sufficient for the independent variable and necessary for the dependent variable (Z₁ – s → X₁; Z₁ – n → Y₁).

Why is the early nineteenth century the critical juncture? In chapter six, Ziblatt, like Morgan, takes up the issue and argues that the period after 1815 was important because the German states experienced a wave of constitution writing: “In contrast to the constitutionally arid landscape of post-1815 Italy, there was a flowering of constitutions after 1815 guaranteeing parliaments to the individual German states” (p. 116). That is, German states began the process of building infrastructural capacity: they wrote constitutions, which led to the creation of new parliaments and administrative reforms, such as expanding civil services. Ziblatt’s narrative explains how pre-1815, these kinds of reforms were nonexistent.

The advantage of the critical juncture stopping rule is that all scholars have some theoretical commitments when conducting research, and this stopping rule simply lays them bare. Moreover, from a practical standpoint, social scientists are rarely experts on multiple historical eras. However, this stopping rule also has drawbacks. First, critical junctures rely on a theory, and it is not obvious what exactly scholars mean when using this term. As Abend (2008:174) makes clear, this is not just a philosophical problem but also a practical one. Using Abend’s (2008:177) terminology, Morgan’s theoretical interests fall into the classification of “theory₁”: “it is a general proposition . . . which establishes a relationship between two or more variables,” but other studies on mothers’ employment may approach theory using a different classification. In fact, Ziblatt’s theoretical interests seem to fall into the classification of “theory₂” because he focuses on a specific phenomenon, time, and place (i.e., the emergence of European federalism). The other issue is that using the critical juncture stopping rule may help with infinite regress but exacerbate the rival historical explanations problem: that is, which critical juncture is the most critical of all?

The necessary and sufficient cause stopping rule

A second way to end the cycle of infinite regress is to utilize the necessary and sufficient cause stopping rule, which is the simplest stopping rule discussed here. This rule can be expressed as follows:

For example, consider Daniel Goldhagen’s (1996) book Hitler’s Willing Executioners: Ordinary Germans and the Holocaust. Goldhagen offers the controversial thesis that “eliminationist antisemitism” is a necessary and sufficient cause for why Germans killed Jews during the Holocaust—that is, how they became “willing executioners” for Hitler. Goldhagen (1996:417–18) writes

The claim here is that this virulent brand of German racial antisemitism was in this historical instance causally sufficient to provide not only the Nazi leadership its decision making but also the perpetrators with the requisite motivation to participate willingly in the extermination of the Jews. . . . Not only was German antisemitism in this historical instance a sufficient cause, it was also a necessary cause for such broad German participation in the persecution and mass slaughter of Jews.

The advantage of the necessary and sufficient cause stopping rule is that necessary and sufficient causes are considered the “gold standard” (Mahoney et al. 2009:124) in explaining historical outcomes. And there is new research on how to logically determine when we see a necessary and sufficient cause (García-Montoya and Mahoney 2020). Therefore, the necessary and sufficient cause stopping rule is the easiest rule to implement of those discussed in this article: simply put, there is no cause that could be more important.

To see this, consider going one step back in Goldhagen’s causal chain. Given his provocative thesis, it is incumbent on Goldhagen to explain the source of eliminationist antisemitism. In chapter two of his book, Goldhagen argues that antisemitism is “a corollary of Christianity” (p. 49). As he notes, Christianity from its earliest days held discriminatory views on Jews. As one example, Goldhagen mentions the teachings of John Chrysostom (c. mid-fourth century), whose influential views were widely disseminated; therefore, “Christian anti-Jewish teachings” is an antecedent cause of eliminationist antisemitism (p. 50). But when weighing this (or any) antecedent cause, it will not be more important than a necessary and sufficient one, as Figure 8 shows. The cause of eliminationist antisemitism (X₁) already perfectly overlaps with the final outcome of the German willingness to kill Jews during the Holocaust (Y₁).

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Figure 8.

The necessary and sufficient cause stopping rule.

An ancillary example of a necessary and sufficient cause argument can be found in Schweller (1992). Schweller (1992:248) argues that “[a] power transition involving a declining democratic leader is both a necessary and sufficient condition for the absence of preventive war.” This argument is interesting because the final outcome is the absence of preventive war, or ~Y₁. Again, there is no cause that could logically be more important than the necessary and sufficient cause of a declining democratic leader in this example—there will already be perfect overlap between cause and effect in Schweller’s argument.

While the upside of a necessary and sufficient cause is its logical power, the downside is that these causes are “rare or nonexistent” in the social sciences (Mahoney et al. 2009:123–24), so they are an unlikely stopping point for many causal chains. To that point, Goldhagen’s work has come under significant criticism, including for the logic of its necessary and sufficient cause of eliminationist antisemitism (Mahoney and Ellsberg 1999).

The mechanism stopping rule

A third and final solution to infinite regress lies in the now ubiquitous study of mechanisms. It may be surprising for mechanisms to be considered a solution to infinite regress, given that the mechanismic framework has been criticized for being particularly vulnerable to infinite regress. For example, King and colleagues (1994:86) write

If we posit that an explanatory variable causes a dependent variable, a “causal mechanisms” approach would require us to identify a list of causal links between the two variables. This definition would also require us to identify a series of causal linkages, to define causality for each pair of consecutive variables in the sequence, and to identify the linkages between any two of these variables and the connections between each pair of variables. This approach quickly leads to infinite regress.

However, this objection wrongly equates mechanisms with intervening variables. ⁹ To the extent that we use Gerring’s (2007b:178) rather different definition—a mechanism as “the pathway or process by which an effect is produced or a purpose is accomplished”—then mechanisms could be useful in resolving infinite regress. Mahoney (2016:495) argues, for example: “Mechanisms can also be understood as general processes and properties that generate associations, and this use of mechanisms provides a stopping rule and a solution to the problem of infinite regress” (see also Kitschelt 1999). In other words, if mechanisms are not present connecting an antecedent cause and an outcome, then there is no causal connection to be made, and researchers can stop their analysis. Concurrently, causal mechanisms should be more important the further back in time you go. Gerring (2010:1506) writes: “Our principal concern, therefore, must be with structural (distal) causes, where X is situated a long way from Y (with multiple intervening factors lying in between). Here, the need for empirical testing of causal mechanisms is readily apparent.” This rule can be expressed as follows:

Note that the mechanism stopping rule reaffirms the value of Mahoney et al.’s (2009) sequence elaboration method. Sequence elaboration explicates the relationship between antecedent causes and both proximate causes and the final outcome of interest—there must be mechanisms connecting all causes together. As George and Bennett (2005:147) note: “Theories or models of causal mechanisms must undergird each step of a hypothesized causal process for that process to constitute a historical explanation of the case.” In some cases, however, mechanisms only connect the antecedent cause and the proximate cause, and in these cases, the mechanism stopping rule can be very useful.

An example of this rule comes from Paul Brass’s (2003) book The Production of Hindu-Muslim Violence in Contemporary India. Brass (2003:6) aims to understand the causes of contemporary Hindu-Muslim riots in India and summarizes his argument as follows

[I]t is the principal argument of this book that the whole political order in post-Independence north India and many, if not most of its leading as well as local actors—more markedly so since the death of Nehru—have become implicated in the persistence of Hindu-Muslim riots. ¹⁰

Brass focuses on Hindu nationalist organizations as the key player in the “political order” in post-independence north India. Reading this quote, it is clear that the existence of these Hindu nationalist organizations is—unlike most of the other proximate causes discussed in this article—a sufficient cause of Hindu-Muslim riots. Brass recognizes that riots can occur through other causal pathways—for example, communal riots also occurred during the rule of the (non-Hindu nationalist) Indian National Congress (p. 374)—but the existence of Hindu nationalist organizations is a sufficient cause of riots. Thus, the initial causal relationship in this instance can be denoted as follows: (X₁) Hindu nationalist groups – s → (Y₁) Hindu-Muslim riots. Given this, an antecedent factor will diminish this relationship if it is necessary for the independent variable and sufficient for the dependent variable (Z₁ – n → X₁; Z₁ – s → Y₁).

Brass acknowledges that deeper historical factors are at play in causing modern communal riots. Most important, what caused the emergence of Hindu nationalism? In the pre-independence period, British colonial policies inflamed tensions between Hindus and Muslims and is therefore an antecedent factor to be considered (pp. 25–26). For example, Brass points to the effects of census enumeration (beginning in 1871), which hardened previously fluid religious communities. As for mechanisms connecting colonial policies and the final outcome of interest, modern Hindu-Muslim riots, Brass points to the British policy of “divide and rule.”

Brass’s analysis suggests that colonial policies are a necessary cause of the existence of Hindu nationalist organizations. As he notes, “The consolidation of the heterogeneous Hindu and Muslim groupings on the subcontinent and the politicization of the differences between them are overwhelmingly a modern phenomenon deeply connected with the striving for control over the modern state apparatus,” which seems to indicate that in the absence of colonial policies, Hindu nationalists could not have existed in their modern form (Brass 2003:25). Thus, the antecedent factor here is a necessary cause of X₁ (Hindu nationalists). However, what is the relationship between colonial policies and Y₁ (modern riots)? If colonial policies are a necessary cause of Hindu nationalism and a sufficient cause of riots, then colonial policies are a diminishing cause. Brass’s argument, however, is about necessity: without colonial policies, modern-day riots could not occur. Colonial policies are important in Brass’s account primarily for their effect in generating Hindu nationalism, but these policies alone were insufficient to produce contemporary riots. Following Mahoney et al. (2009), colonial policies must be considered a contextualizing cause. ¹¹ As it stands, Hindu nationalists remain causally more important in Brass’s book.

Brass stops his historical analysis at this point. What if we explored the third-level cause? Going to this level of analysis necessitates asking what caused these particular British colonial policies. This is not an idle question. European colonial powers varied in the strategies they adopted for ruling native populations (Gerring et al. 2011); therefore, it was not predetermined that the British should specifically institute policies that classified and organized Indians. Because most of the colonial policies described by Brass occurred in the late-nineteenth and early-twentieth centuries, investigating the cause of this cause necessitates going back to the preceding historical era. I argue that the cause in this instance is a major event that occurred during the nineteenth-century in India: the 1857 Rebellion.

Prior to their experience in India, the British had brought most of their colonies fully under direct rule (Lange 2009:31). The British would likely have conquered the entire subcontinent if not for the 1857 Rebellion, a native uprising led by several small independent kingdoms known as princely states. This conflict began when sepoys—native Indian soldiers serving in the East India Company army—refused to use new rifle cartridges allegedly coated with either beef or pork fat (offensive to both Hindus and Muslims on religious grounds). Several insubordinate sepoys were imprisoned, which resulted in an army mutiny throughout the whole of north India. The uprising took a year for the British to suppress. Afterward, the British recognized that their knowledge of India was severely lacking, and they undertook massive data-gathering projects to learn more about those they ruled (Cohn 1996).

If this historical argument is correct, then the 1857 Rebellion seems to be a necessary cause of colonial policies. All the quintessential colonial policies that Brass discusses, such as the census, were instituted after 1857, and it seems likely they could not have been introduced in the absence of this rebellion (after all, the British came to India in the early seventeenth century and never introduced a national-level census before the uprising). The 1857 Rebellion also seems necessary for everything downstream—for Hindu nationalist groups and modern Hindu-Muslim riots—but not sufficient for either outcome. Figure 9 shows the full relationship.

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Figure 9.

The mechanism stopping rule.

Although Brass does not discuss it explicitly, one key problem in producing a narrative that goes back to earlier periods of colonial rule is the lack of mechanisms that connect causes situated then and other antecedent causes as well the final outcome of modern Hindu-Muslim riots. This connection is especially difficult to see as the 1857 Rebellion featured many Hindus and Muslims uniting against colonialism, so linking this event and modern communal violence (Y₁) seems unlikely. Table 2 lists all the mechanisms connecting different levels of causation in Brass’s narrative, but note that once we reach the third level, there are no longer mechanisms connecting the antecedent cause to anything downstream.

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Table 2.

Mechanisms in Brass (2003).

Relationship between:	Mechanisms
Hindu nationalist groups → Hindu-Muslim riots (X1 → Y1)	Institutionalized riot systems, elections
Colonial policies → Hindu nationalist groups (Z1 → X1)	Census enumeration, separate electorates
Colonial policies → Hindu-Muslim riots (Z1 → Y1)	Divide-and-rule policy
1857 Rebellion → Colonial policies (A1 → Z1)	Crown rule
1857 Rebellion → Hindu nationalist groups (A1 → X1)	N/A
1857 Rebellion → Hindu-Muslim riots (A1 → Y1)	N/A

An ancillary example of the mechanism stopping rule is Charles Tilly’s (1990) Coercion, Capital, and European States, AD 990–1990. Tilly’s book is a compendium of his work over several decades on European state formation. The main question he seeks to answer is why Europe eventually settled on (different types of) nation-states. Like Moore’s work discussed earlier, Tilly’s (1990:58) argument is too complex to detail succinctly, but his general thesis is that war-making led to an increasingly centralized state, and these states, in turn, “set the terms for war, and their form of state became the predominant one in Europe. Eventually European states converged on this form: the national state.”

Tilly’s argument covers roughly 1,000 years, and his full causal chain connects a distal cause (war-making beginning on a small scale in the Middle Ages) to the modern nation-state form in the twentieth century. In evaluating this argument, the mechanism stopping rule would require us to ask whether plausible pathways connect causes from the Middle Ages to effects 1,000 years later. If not, then where does the causal chain actually begin?

The main advantage of using the mechanism stopping rule is that it is easily compatible with process tracing, one of the most popular modes of historical explanation in the social sciences (Collier 2011). A more explicit focus on mechanisms can aid in not only avoiding the peril of infinite regress but also providing clearer focus on how different causes are connected to each other at different levels of analysis.

Naturally, a mechanism stopping rule has its disadvantages. Some issues relate to debates about mechanisms in general; for example, whether they are observable or not, whether they are contextually bounded or not, and whether they are universal or not (see Gerring 2007b). Another complication is that although scholars often focus on a single mechanism, it is possible to generate highly complex causal pathways. Gerring (2007a:181–82), for example, notes that Fogel’s (1992) argument about political realignment in mid-nineteenth-century America involves more than 50 steps, and Skocpol’s (1979) argument about social revolutions involves 37 steps. Therefore, it may be possible to construct a mechanismic explanation connecting, however implausibly, Cleopatra and World War I’s cult of the offensive.