On situational analysis and the explanatory power of mechanisms: Analytical sociology and the deductive-nomological model

Abstract

French

According to the dominant view, analytical sociology is largely incompatible with the deductive-nomological model because the latter allows neither accurate and precise explanations, nor explanations that give individuals and their actions a privileged role. This view neglects two relevant facts about the deductive-nomological model as understood by Hempel and Popper and some of their precursors such as J.S. Mill and Weber. The first is the relationship between this model, situational analysis, and the use of probabilistic laws in explanation. The second is that, from the standpoint of the deductive-nomological theory, it is possible to make sense of social mechanisms in terms of Weber’s ideal–typical models. Like these models, mechanisms are functional for the development of concrete empirical sociological hypotheses that, without covering generalizations, lack explanatory power.

Keywords

analytical sociology deductive-nomological model mechanisms methodological individualism situational analysis

Introduction

Analytical sociology aims at explaining social facts on the basis of a methodological strategy that opposes sociocultural determinism and, more generally, any kind of approach that does not take into account the way macro-phenomena are generated by individual motivations, actions, and interactions. As emphasized by Hedström and Bearman (2011: 3–4), analytical sociology explains social facts ‘not merely by relating them to other social facts [. . .] but by detailing in clear and precise ways the mechanisms through which the social facts under consideration are brought about.’ According to analytical sociology, ‘these mechanisms invariably refer to individuals’ actions and the relations that link actors to one another’ (Hedström and Bearman, 2011: 4).

Analytical sociology is based on a variant of methodological individualism (MI) that is nonreductionist and can be called, following Udehn (2001) and Wippler (1978), ‘structural individualism,’ as opposed to the atomistic variant of MI that is used especially in economics (see Demeulenaere, 2011b; Manzo, 2007). As pointed out by Demeulenaere (2011b: 11), this nonatomistic variant of MI must not be regarded as a recent invention, but is rooted in the tradition of interpretative sociology ‘from the very beginning’ (Demeulenaere, 2011b: 11; see also Bulle, 2018; Bulle and Phan, 2017; Di Iorio, 2015). The most original aspect of analytical sociology is that, unlike other agent-centered approaches, it promotes the analysis of micro–macro causal mechanisms and interactions that produce social phenomena through computational modeling in terms of agent-based simulation (ABS; see Manzo, 2010, 2014). Analytical sociologists praise this kind of computational modeling because it allows for rigorous and precise analyses of complex systems.

Following Elster (1983, 1989), analytical sociologists conceive social explanations as mechanism-based (Hedström & Sweldberg, 1998). Most assume that explanations in terms of mechanisms are opposed to the deductive-nomological (D-N) model (Barbera, 2004). The dominant standpoint in analytical sociology can be summarized as follows: (1) the explanations in terms of mechanisms are not necessarily based on covering laws and (2) the D-N approach allows for shallow explanations and does not give action and intentional explanations, in terms of structural individualism, the privileged roles they should have.

In this article, in agreement with Opp (2013a, 2013b), we criticize this standpoint and maintain that it is possible to make sense of mechanisms in terms of the D-N model. To clarify our view, we focus on two points that have been missing in debates on analytical sociology. The first is the role of Popper’s situational analysis in D-N explanations.¹ We shall argue that, because of the strict relationship between the D-N model and situational analysis, the former allows for sophisticated and detailed explanations that give human action and intentionality central roles. The second is the analogy between social mechanisms and Weber’s ideal–typical models of causal explanation. Building on Weber’s methodological writings, the article maintains that social mechanisms can be meaningfully interpreted as non-empirical sociological models that help sociologists to develop D-N empirical explanations.

This article is based on a historical comparative approach. Methodological debates in analytical sociology have been influenced by contemporary analytic philosophy of the social sciences (see Little, 2021), which is partly characterized by a certain abstractness and lack of historical perspective. As a consequence, sometimes a detailed reference to the methodological work of classical authors is missing in these debates. In our opinion, the relationship between the D-N model and analytical sociology must be analyzed while paying more attention to what important precursors of this kind of sociology like Weber and Popper had to say on the nature of nomological explanation and its compatibility with MI. This article is an attempt to correct a partial lack of historical perspective with respect to the definition of the methodological and explanatory presuppositions of analytical sociology.

In tying explanations in terms of mechanisms to the D-N model we have two motivations. The first is that we wish to correct a widespread misunderstanding about the latter and reject the view that the D-N model is inappropriate and unhelpful in the social or historical sciences. The second is our desire to emphasize that, without elucidating the implicit nomological nature of the mechanism-based approach, it is impossible to correctly appreciate in which sense analytical sociology is scientific and objective. Popper (2001) famously argued that understanding the nature of science means understanding that the logic of explanation and causal imputation is nomological in every research field. As it should be clear at this point, our goal is not to provide a radical criticism of mechanism-based explanations. It is rather to clarify that mechanisms are models that are useful because they are functional for the development of concrete empirical sociological hypotheses that, without covering generalizations, lack explanatory power.

D-N model and indeterminism: Some preliminary remarks

In our view, analytical sociologists who argue against the D-N model have a misplaced, narrow understanding of it. By the term D-N explanations they usually mean deterministic explanations that are at odds with the interpretative approach of MI and do not give individuals and their actions a privileged role. We consider this view to be incorrect because it is in conflict with the way the D-N model is conceived by its most important theorists such as Hempel and Popper. If correctly understood, this model can account for the explanatory logic of nondeterministic social phenomena.

Since the most common interpretation of the D-N model is quite different from the one underpinning our analysis, to avoid any misunderstanding about our view that the D-N model and analytic sociology are compatible, in this section we are going to provide a preliminary schematic account of this model; as we understand it, that can help the reader to follow our line of reasoning in the subsequent sections. According to what we consider as a charitable interpretation of the D-N model, explaining a phenomenon means deducing its description, that is, its explanandum, from an explanans that includes one or more either deterministic or probabilistic laws and a description of the particular circumstances or initial conditions in which the phenomenon in question occurs (see Di Iorio, 2015: 149 ff.; Di Nuoscio, 2018: 27–78; Little, 1991). The D-N model assumes that the use of covering laws in explanation is logically necessary because, without these laws, it is logically impossible to select, among the infinite facts of the world, the fact/facts that is/are causally relevant from the standpoint of the explanation (Ayer, 1936). This does not mean that the laws are always mentioned in the explanation. Very often they are implicit. In such cases the explanation can be called, following Hempel (1959), an ‘explanation sketch.’

Since the D-N model is compatible with the use of probabilistic covering laws, it can account for nondeterministic social phenomena. The following pages are devoted to the clarification of this point, which seems to be often neglected in the literature. To explain this topic, we are going to refer not only to Hempel’s writings, but also to those by Popper and Weber. As pointed out by Hempel (1965) and Popper (1957, 1966), the use of probabilistic laws, which is quite common in the social sciences (but also present in the natural ones), entails that the same explanandum is compatible with different explanans. As a consequence, Popper (1957) contends that the situational analysis, which is a basic assumption of MI, is fundamental to developing sound nomological explanations in this field. We are going to analyze this point in detail in the section ‘The role of situational analysis in D-N explanations.’ While Popper is, along with Hempel, the most important theorist of the D-N model, and analyzed the relationship between this model and MI, his contribution to the debate on the D-N model has been widely neglected by analytical sociologists. Similarly, Weber’s contribution to this debate has not been considered in a proper way because he is often erroneously regarded as a critic of the D-N model, while in fact he is a forerunner of Hempel and Popper. It is true that Weber did not defend the nomological nature of explanation in all his works, but in Roscher and Knies: The Logical Problems of Historical Economics, his standpoint clearly matches the logical structure of the explanation as understood by Hempel (see Weber, 2012). In the subsequent sections we shall often refer to this book.

Mechanism-based explanations versus D-N explanations

Following Elster (1983, 1989), the great majority of analytical sociologists argue that the human sciences must be based on explanations in terms of mechanisms rather than on D-N explanations (see Little, 2009). In their opinion, this kind of explanation is necessary to account for social phenomena in terms of objectively valid scientific knowledge. As clarified by Elster (1998), the D-N model is to be rejected because it is committed to determinism. The problem, as he contends, is that, since there is no room for determinism in the social sciences, only mechanism-based explanations avoid falling back on narrativism or other anti-scientific positions.

Regarding social phenomena, the same cause is compatible with different effects, and the same effect with different causes. As a consequence, it is impossible to use laws like ‘If A, then always B’, while it is necessary to refer to mechanisms such as ‘If A, then sometimes B’ or ‘If A, then sometimes C, D, and B’ (Elster, 1998: 49). To use Hedström’s words, ‘the deductive-nomological model is not applicable because the deterministic social laws that it presupposes do not exist’ (Hedström, 2005: 22). The core idea behind the mechanistic approach is that ‘we explain not by evoking universal laws, or by identifying statistically relevant factors, but by specifying mechanisms that show how phenomena are brought about’ (Hedström, 2005: 22).

On this reading, the D-N model is useless in the social sciences because ‘the laws of covering-law explanations are typically seen as perfectly general and without exceptions while the mechanisms of mechanism-based explanations are not’ (Hedström, 2005: 15). In other words, as highlighted by Mayntz (2004), laws cannot be used to explain social phenomena because laws refer to ‘causal factors’ (which produce deterministic effects), while social phenomena are (nondeterministic) ‘causal processes.’ According to Hedström and Ylikoski (2010), the problem is that in fields ‘like psychology and social sciences there is an embarrassing scarcity of covering laws’ and ‘there are very few observable empirical regularities that could be considered explanatory’ (p. 12).

In Hedström’s opinion, not only the D-N model, but also ‘the inductive-probabilistic model’, is not useful as an explanatory tool. In his view, both these models (1) allow for and thereby legitimize ‘superficial theories and explanations,’ and (2) do not give action and intentional explanations ‘the privileged role they should have’ (Hedström, 2005: 22). As a consequence, Hedström maintains that social scientists have no other option than using the explanatory approach in terms of mechanisms.

Hedström and Ylikoski argue that the criticism leveled at the D-N model by analytical sociologists is reinforced by various arguments developed against this model by the general philosophy of science during the past decades. We shall consider these arguments, which are not strictly related to the problem of explanation in the social sciences, but concern the logical structure of the D-N model from a more general standpoint, in the section ‘Further remarks on the D-N model and its applicability.’ We shall first show why we believe that the D-N approach is compatible with the explanation in terms of mechanisms.

D-N explanations and common-sense laws

According to the majority of analytical sociologists, although explanations in terms of mechanisms are based on the causality principle, they are, because of their indeterminism, incompatible with the D-N model. However, as pointed out above, the D-N model and its concept of causality are compatible with and functional for the explanation of nondeterministic social phenomena.

The D-N model assumes that both in the natural and social sciences, explanations do not necessarily require deterministic laws (see Di Iorio, 2015: 149 ff.). The defense of nomological explanations in the social sciences is rooted in an old tradition that includes, among others, famous methodological individualists such as J.S. Mill, Weber, and Popper, all of whom strongly criticized both sociocultural and historical determinism (see Di Nuoscio and Di Iorio, 2019). According to Weber (1997: 113 ff.), in social sciences causal relationships are established on the basis of ‘rules of experience,’ which are only probabilistic and have been acquired through the trial-and-error learning process that has produced our common sense (see Demeulenaere, 2011a). They are common-sense maxims about everyday life that are not universal because they are often, but not always, valid. In his opinion, these ‘rules of experience’ reflect the typical ways in which individuals tend to react to typical situations. They refer to a ‘nomological knowledge’ about ‘concrete causal’ connections between typical actions and typical situations (Weber, 2012: 73–83). Hempel (1965: 153) calls these common-sense rules ‘law-like sentences’ (see also Little, 1991; Scriven, 1959: 464 ff.).²

As clarified by Popper (1957: 97 ff.), Weber’s nondeterministic ‘rules of experience’ can be regarded as nomological knowledge because they have nothing to do with existential statements. In other words, these common-sense rules are neither accidental generalizations (such as ‘all members of Louis XVI’s court were corrupted’) which, unlike laws, refer to a finite number of singular facts about a specific historical period, nor trends (such as ‘with Industrial Revolution the number of proletarians tends to increase’), which are equally not laws, but a finite sequence of causally related events that can only be explained through laws. Since these common-sense rules do not refer to a limited number of cases, they can be used to develop counterfactual hypotheses and thus explanations in terms of the D-N model.

The following example, taken from Benedetto Croce’s A History of Italy, helps us to understand the role of common-sense maxims in explanation. Croce explains here why many Italian voters did not renew their electoral support for the Italian Republican Party in the 1880s:

Republicans included in their election manifestos – see, for instance, their 1882 manifesto – universal suffrage, an all-volunteer army, the abolition of the Law of Papal Guarantees, confiscation of ecclesiastical property, regional autonomies, convocation of the Constitutional Assembly and other things that they should have known – and surely many of them knew – were impossible. As a consequence, the Republican Party became increasingly small. (Croce, 1966 [1927], translated by the authors: 70)

Considering the electoral behavior of Italian voters (which is, in this case, the explanandum), Croce provides a causal explanation for the party’s lack of support by listing a collection of initial conditions –that is, causes – on the basis of a simple common-sense rule which is implicit in his analysis: ‘voters tend not to support political parties that have an election manifesto which looks completely unworkable.’³ As pointed out by Hempel (1965), because of their trivial nature, probabilistic common-sense laws about typical human behaviors are almost always used in an implicit manner.

Following the analysis developed by Weber (2012: 103 and ff.) in Roscher and Knies: The Logical Problems of Historical Economics – a work in which he clearly supported the unity of method and the nomological approach, and also the similar line of reasoning taken later by Popper and Hempel – it is possible to say that, according to the D-N model, the only difference between explanations in the natural and social sciences is that the latter tends to use nondeterministic ‘empirical generalizations’ more often than the former. However, the logical structure of explanation is identical (see also Menger, 1985). As shown, for example, by quantum mechanics, medical biology, and meteorology, the natural sciences use probabilistic laws and cannot always develop deterministic predictions. A similar viewpoint is shared also by J.S. Mill (2009 [1843]), who argued that it is only in the simplest branches of the natural sciences ‘that empirical laws are ever exactly true; and not always in those’ (pp. 1046–1047).

From the standpoint of the D-N model, without covering generalizations causal mechanisms lack explanatory power (see Bouvier, 2008). According to this model, arguing, as Elster (1998) did, that social mechanisms are useful to explain relations such as ‘If A, then sometimes B’ or ‘If A, then sometimes C, D, and B’, means arguing that social mechanisms refer to causal relationships, which necessarily involve probabilistic laws (p. 49). The D-N model does not rule out the possibility of nondeterministic accounts of social phenomena. It only assumes that probabilistic explanations and predictions without probabilistic laws are impossible. Given the above, it is unclear why many analytical sociologists consider the D-N model to be incompatible with the antideterminism of the individualist approach.

The role of situational analysis in D-N explanations

Among those analytical sociologists who criticize the D-N model some, like Hedström (2005: 22), recognize that it is compatible with the use of probabilistic laws. However, they argue that any account of social phenomena in terms of covering laws, no matter whether these laws are deterministic or probabilistic, allows for and thereby legitimizes ‘superficial [. . .] explanations’ and does not give action and intentional explanations ‘the privileged role they should have’ (Hedström, 2005: 22; see also Goldthorpe, 2001; Manzo, 2014). In their opinion, mechanism-based explanations are radically incompatible with any kind of nomological explanation. In this section, we will challenge this view and explain why the D-N model allows for accurate explanations that give action a privileged role.

To understand this point, it is necessary to focus on the role of what Popper (1957, 1963; Jarvie, 1972) calls ‘situational analysis’ in D-N explanations (see also Di Nuoscio and Di Iorio, 2019). The analysis of this role is missing in the literature on the relationship between social mechanisms and analytical sociology. It is necessary to fill this gap because situational analysis is fundamental both to understanding in which sense MI is compatible with nomological explanations and why the D-N model allows for the accurate empirical study of human action and social phenomena. Popper (1982) conceives nomological explanation and situational analysis as intimately connected in the social sciences.

According to the D-N model, the laws used in the social sciences are logically necessary for explanation because they allow us to establish causal relationships which we would not be able to establish without these laws. However, since they are less-than-universal, they can generate only incomplete explanations in the sense that they do not allow us to deduce for sure the explanans from the explanandum. As pointed out by Hempel (1965), this means that it is possible to have explanatory overdetermination; that is, it is possible to have either different explananda that are compatible with the same initial conditions or different explanations that are compatible with the same explanandum.

According to Popper (1957: 149, 1966: 205), to deal with the problem of the existence of several explanations that are consistent with the phenomenon under investigation, social sciences and especially history, need to use situational analysis, that is, make reference to an in-depth historical reconstruction of the unique combination of typical conditions that generated the explanandum (see also Di Nuoscio, 2018: 35 ff.). The situational analysis is an interpretive strategy used to empirically understand the individual’s choice and its (intended and unintended) consequences through detailed reconstruction of the problem situation confronting the individual. In other words, this interpretative strategy, which is based on the assumption that the individual is subjectively rational, aims at empirically ascertaining the initial conditions that underlie the agent’s choice (Popper, 1966: 205). The more careful the situational analysis, the more it is possible to reduce the number of possible explanations that are consistent with the explanandum (see Di Nuoscio, 2018: 35 ff.).⁴

In The History of the Peloponnesian War, Thucydides (1972) explains why Pericles was elected again even though Athens had been invaded by the Lacedaemonians and Athenians ‘began to find fault with Pericles, as the author of the war and the cause of all their misfortunes’ (p. 335):

[T]hey again elected him general and committed all their affairs to his hands, having now become less sensitive to their private and domestic afflictions, and understanding that he was the best man of all for the public necessities. For as long as he was at the head of the state during the peace, he pursued a moderate and conservative policy; and in his time its greatness was at its height. When the war broke out, here also he seems to have rightly gauged the power of his country. He outlived its commencement two years and six months, and the correctness of his previsions respecting it became better known by his death. (Thucydides, 1972: 336–337)

In this passage, as well as in the succeeding pages of The History of the Peloponnesian War, Thucydides developed a detailed reconstruction of the causes of Pericles’ re-election. The explanandum (Pericles’ re-election) is hypothetically compatible with different causes. For example, the Athenians could have been obliged to re-elect him by the use of force, or they could have been deceived about the war situation. Thucydides ruled out both these hypotheses by carefully ascertaining the empirical truth about the initial conditions. The explanandum is linked to the initial conditions (or causes) via the following implicit law: ‘if citizens get convinced about the value of a governor and the goodness of her policies, they are ready to change their mind about her and provide her electoral support.’ Obviously, this trivial covering law is, though logically necessary, not the most important aspect of this explanation. The probabilistic validity of this law is common-sense evidence that does not need to be tested because it presupposes a long learning process by trial and error that allows us to regard it as trivially correct. Popper (1957, 1982) argues that, from the standpoint of the D-N model, given the mundane and non-problematic nature of the common-sense laws used by the social sciences, usually the problem of explanation in these sciences lies not in the testing of laws, but in the empirical study of the initial conditions through the situational analysis (see also Di Nuoscio, 2018: 35 ff.). The more detailed the situational analysis, the more complete and convincing the explanation. Checking the initial conditions allows the social scientist to select the appropriate probabilistic law for the explanation among different potentially appropriate probabilistic laws whose empirical validity is unquestioned because they are all common-sense true (Di Iorio, 2015: 149 ff.; Di Nuoscio, 2018: 59 ff.). From the standpoint of Popper’s nomological individualist approach, despite the trivial and probabilistic nature of the common-sense laws required in social explanations, these explanations are not ‘superficial’ (Hedström, 2005: 22) because situational analysis allows the social scientist to make them well-founded. Situational analysis shows how the causal relationship of the explanation comes about (Di Nuoscio, 2014). Moreover, according to Popper’s nomological individualist approach, given that the D-N model is strictly linked to both the situational analysis and the concept of nondeterministic explanation, and since situational analysis is centered on the empirical study of the individual’s motivations for acting, the D-N model allows the social scientist to give action and intentional explanations a privileged role (Popper, 1957, 1982).

Mechanisms as models

In the previous sections we focused on some misunderstandings linked to the applicability of the covering law approach to the individualist analysis of social phenomena. It is time now to analyze what social mechanisms exactly are from the standpoint of the D-N model. We do not see any reason to regard them as heuristic tools that are antithetical to, or incompatible with the nomological approach. In contrast with what has been argued by many analytical sociologists, it seems to us that social mechanisms should be described in Weberian terms as non-empirical abstract ideal–typical models that are useful for developing concrete empirical explanatory hypotheses in the sense of the D-N model (see Di Nuoscio, 2018).

The conceptual analogy between mechanisms and Weber’s ideal-types of social interaction is explicitly acknowledged by Hedström (2007: 73–76) who, however, does not endorse Weber’s view that models are compatible with the nomological approach.⁵ As pointed out by Elster (1998), ‘mechanisms are frequently occurring and easily recognizable causal patterns that are triggered under generally unknown conditions’ (p. 45). They ‘provide a continuous and contiguous chain of causal or intentional links between the explanans and the explanandum’ (Elster, 1983: 24). In other words, mechanisms are (1) ‘templates, schemes or recipes for the search of causes. The knowledge about a possible mechanism tells the researcher what to look for and where’ (Ylikoski, 2011: 7–159); (2) conceptual tools that allow us to make ‘causal claims [. . .] more secure’ (Ylikoski, 2011); and (3) ‘the locus of generality (and explanatory power) in social scientific knowledge’ because ‘the social sciences do not have many valid empirical generalizations and those that they have are not very explanatory.’⁶

In agreement with this view, Weber (1997: 90) regards ideal-types as useful precisely because of the lack of deterministic and universal causal relationships in the social sciences. Given this lack of empirical universal laws, ideal-types are, in his opinion, pure and abstract ‘analytical’ constructs whose function is to ‘help to develop our skill in imputation in research’ (Weber, 1997). According to Weber (1997: 90), they are not empirical or falsifiable hypotheses, but they do offer ‘guidance to the construction of hypotheses,’ In other words, they are means of developing testable sociological explanations. Establishing typical (and thus broadly nomological) assumptions, ideal–typical models allow social scientists to describe typical trends, dynamics and possible interactions that in the pure and abstract form described by these models cannot be found in any empirical case. As pointed out by Boudon (1986: 222), given the conceptual purity of Weber’s ideal–typical models, it is necessary to avoid the ‘snare of realism’ which consists in considering these abstract models to be exact descriptions of reality.

Like Weber, Popper (1994: 162 ff.) argues that the use of models is complementary to the development of empirical D-N explanations because models help the social scientist to give an order to things and understand how to use the D-N model to provide empirical explanations. Moreover, Popper (1994: 162 ff.) maintains that, because of the nondeterministic nature of the majority of social phenomena, the social sciences use models (i.e. non-empirical tools) more often than do the natural sciences (see also Di Iorio, 2015: 176; Di Nuoscio, 2018: 49–52; Oliverio, 2010).

The nature of explanations in terms of mechanisms can be understood, according to Hedström (2007), by considering, for example, the relationship between the Desires, Beliefs, Opportunities theory (DBO theory) and Tocqueville’s analysis of the rapid secularization that took place in France at the end of the 18th century. As pointed out by Hedström (2007), the DBO theory is an abstract scheme that assumes that ‘the desires, beliefs and opportunities of an actor are [. . .] the proximate causes of the actor’s action’ (Hedström, 2007: 76). According to this scheme, ‘a desire is [. . .] a wish or want for something to happen (or not to happen)’; a belief is ‘a proposition about the world held to be true’; and opportunities represent ‘the “menu” of action alternatives available to the actor’. These three factors ‘can be said to cause an action, in the sense of providing reasons for the action’ (Hedström, 2007: 76). Considering the ways in which these three factors can be typically combined in the interaction structures where human action takes place, Hedström distinguishes different typologies of mechanisms (e.g. the dissonance-driven desire formation, the rational-imitation, the vacancy chain, wishful thinking, and the self-fulfilling prophecy). According to Hedström (2007), these typologies are ‘ideal-typical schemes’ which allow us to develop empirical hypotheses and ‘precise and realistic [. . .] explanations’ (pp. 73–76).

Since mechanisms are ideal–typical models, it is possible to argue, following Weber (1997), that mechanisms are, as pointed out above, non-empirical schemes whose function is to help the development of empirically testable explanations in terms of ‘rules of experience’ or – to use more modern language – covering laws (p. 113 ff.). Hedström argues that the following passage from Tocqueville about the rapid secularization that took place in France at the end of the 18th century is a relevant example of empirical explanation guided by the DBO theory:

Those who retained their beliefs in the doctrines of the Church became afraid of being alone in their allegiance and, dreading isolation more than the stigma of heresy, professed to share the sentiment of the majority. So what was in reality the opinion of only a part [though a large one] of the nation came to be regarded as the will of all and for this reason seemed irresistible even to those who had given it this false appearance. (Tocqueville, 2001 [1856]: 49)

In our view, Tocqueville’s analysis is an example of a D-N explanation sketch in Hempel’s sense: the explanandum (why ‘the opinion of only a part of the nation came to be regarded as the will of all’) is traced back to its causes (‘those who retained their beliefs in the doctrines of the Church became afraid of being alone in their allegiance and, dreading isolation more than the stigma of heresy’) on the basis of a covering law which is implicit: ‘if those who are outnumbered consider their situation disadvantageous, they tend to conform to the dominant standpoint.’ Of course, this law is non-universal and counterexamples do exist. However, it is applied by Tocqueville on the basis of a situational analysis in Popper’ sense that he develops in the preceding passages of his book and allows him to regard this covering law as the most appropriate for the explanation. Without this implicit covering generalization, which is not mentioned by Tocqueville because it is commonsensical, the explanation cannot be given because it is logically impossible to link the explanandum to its causes.

MI and nomological explanation

In the preceding pages we have clarified that mechanisms and D-N explanations are not antithetical to one another. We need to focus now on the relationship between D-N explanations and MI or, at least, on its nonatomistic variant endorsed by analytical sociologists.

According to Boudon (1991), one of the originators of analytical sociology, explaining a social phenomenon in terms of MI means answering the following three questions: (1) Who are the individuals whose actions generated the social phenomenon under investigation? (2) Why did these individuals act the way they did? and (3) How did macro-level outcomes result from the micro-level of individual actions? From the standpoint of the D-N model, answering these three questions means considering the causal chain that links individual reasons, actions and macro-outcomes. In other words, it requires: (1) explaining human actions by making clear their causes that are the individuals’ ‘good reasons’ and (2) explaining the macro-outcomes by assuming that their causes are meaningful actions.

As emphasized by Popper (1957), according to MI, every action stems from the need to solve a problem. Its causes are reasons (the agent’s goals, knowledge, resources, values, character, and so on) that can be understood only by understanding the agent’s problem. As already pointed out, Popper (1957) believes that explaining an action through the interpretation of its meaning presupposes the use of situational analysis as an instrument of correct causal ‘imputation’ and also that situational analysis is based on the D-N model.⁷ Moreover, like other methodological individualists, he also maintains that the possibility of explaining an action in terms of reasons requires the unity of thought, that is, the existence of a rationality that is common to all human beings (Popper, 1957).⁸

Let us consider a paradigmatic example of explanation in terms of MI taken from Max Weber’s The Protestant Ethic and the Spirit of Capitalism:

We thus take as our starting-point in the investigation of the relationship between the old Protestant ethic and the spirit of capitalism the works of Calvin, of Calvinism, and the other Puritan sects. But it is not to be understood that we expect to find any of the founders or representatives of these religious movements considering the promotion of what we have called the spirit of capitalism as in any sense the end of his life-work. We cannot well maintain that the pursuit of worldly goods, conceived as an end in itself, was to any of them of positive ethical value [. . .]. The salvation of the soul and that alone was the centre of their life and work. Their ethical ideals and the practical results of their doctrines were all based on that alone, and were the consequences of purely religious motives. We shall thus have to admit that the cultural consequences of the Reformation were to a great extent, perhaps in the particular aspects with which we are dealing predominantly, unforeseen and even unwished-for results of the labours of the reformers. They were often far removed from or even in contradiction to all that they themselves thought to attain. (Weber, 1992 [1905]: 47–48)

In this famous passage, Weber answered Boudon’s above-mentioned three questions. Who caused the phenomenon under investigation? The Calvinist entrepreneurs who did not accumulate profits, but continuously reinvested them. Why did they act this way? Because they shared a religious belief that led them to consider professional success to be a sign of salvation (signum salutis), a proof of belonging to the elected by the Lord (electi): seeing things in that way reduced Calvinist entrepreneurs’ distress about their after-life – a distress related to their belief in predestination. How did the micro-level of individual actions generate the macro-level global outcome? The simple aggregation of a very high number of actions that comply with the typical way of thinking shared by Calvinist entrepreneurs generated ‘the spirit of capitalism’. Weber reenacted Calvinist entrepreneurs’ problematical situation; he explained why they chose to act as they did to cope with this situation (their choice of a means to an end); and, finally, showed that the emergence of capitalism is the unintended result of their actions.

To answer these three questions, Weber, who defended both MI and the covering-law model (he endorsed the latter in Roscher and Knies: the logical problems of historical economics), provided a double nomological explanation. First, to argue that Calvinist entrepreneurs reinvested their profits because they believed that professional success was a sign of salvation, he assumed the existence of a causal relationship between their actions and the reasons that produced these actions on the basis of the following implicit and trivial covering law: ‘those who want to grow their business tend to reinvest their profits.’ Second, to explain the relationship between the Calvinist entrepreneurs’ actions and the development of the ‘spirit of capitalism,’ he used another implicit covering law that may be stated as follows: ‘large-scale deployment of the tendency to grow the business generates the system of economic relationships called capitalism’ (see also Di Nuoscio and Di Iorio, 2019).

As already pointed out, if correctly understood, the D-N model is perfectly compatible with MI (see Bouvier, 2008). The view that ‘mechanism-based explanations are action-based while covering-law explanations typically are not’ (Hedström, 2005: 24) seems mistaken to us.

Agent-based simulation

A number of analytical sociologists use Agent-Based Simulation (ABS), that is, the ‘computational study’ of social processes ‘as open-ended dynamic systems of interacting agents’ (Tesfatsion, 2017: 384). ABS can be regarded as an implementation of MI (see Di Iorio and Chen, 2019; Kollár, 2021; Manzo, 2020).

From the standpoint of ABS, a good explanation is a ‘generative’ explanation, that is, a demonstration via computer simulation of how it is that a group of actors bring about an empirically observable complex macro social outcome (see Epstein, 2006). A generative explanation postulates a set of decision rules that are used by the actors. These rules are defined by considering micro-level mechanisms that can trigger the macro-outcome (Manzo, 2007: 5–6). As clarified by J.M. Epstein (2006: 9), the same macro-outcome can be compatible with different micro-level mechanisms. According to ABS methodology, empirical analysis of the micro-level allows the researcher to select the relevant micro-level mechanisms for the explanation of the macro-phenomenon under analysis (Epstein, 2006: 9). The generative explanation via computer simulation provides an experimental analysis of the transition between the micro- and macro-levels.

From the standpoint of the D-N model, generative explanations refer to cause-and-effect relationships that are nomological. The causal relationship between the micro-level dynamics and the agents’ behavior is accountable in terms of common-sense laws about human action that are (implicitly) used to define the agents’ decision rules. The causal relationship between micro-level dynamics and the unintentional macro-outcome is accountable in terms of laws about aggregation effects. According to the D-N model, the same macro-outcome can be compatible with different micro-level mechanisms because the laws about social phenomena are mainly probabilistic. Like Popper, J.M. Epstein (2006: 9) suggests dealing with this problem via situational analysis, that is, the careful empirical study of the initial conditions of the explanation.

Let us consider an example of generative explanation. In their article ‘The emperor’s dilemma: a computational model of self enforcing norms,’ Centola et al. (2005) focus on a fascinating phenomenon, that is, the ‘compliance with, and enforcement of, privately unpopular norms’ (p. 1012). This can happen, for example, because of ‘the exposure of the ‘politically incorrect’ by the righteously indignant who thereby affirm their own moral integrity’ (Centola et al., 2005: 1012). To explain why agents may comply with and enforce norms that they secretly dislike Centola, Willer and Macy use either explicitly or implicitly common-sense probabilistic laws. Laws such as, for example, the following ones: (1) in a context in which those who do not comply with a certain norm are accused being retrograde and reactionary, people tend to think that ‘the safest course is to go along with the charade’ (Centola et al., 2005: 1013); (2) ‘people rarely turn the tables on their inquisitors’ (Centola et al., 2005: 1013); and (3) ‘those who enforce conformity appear to be the genuine article’ and are not accused of falsity (Centola et al., 2005: 1013).⁹ An interesting point emphasized by Centola et al. (2005) is that it is possible to show via computer simulation that a very small number of true believers ‘can spark a cascade of compliance’ only if they are ‘clustered’ (p. 1025). Otherwise, in each neighbor ‘their numbers are too small to compel even the most spineless disbelievers to join their crusade’ (Centola et al., 2005: 1024). When agents are clustered ‘rather than randomly distributed, a skeptic exposed to a true believer can now expect to have other true believers in his/her neighborhood’ (Centola et al., 2005: 1024). As a consequence, the skeptic has good reasons to behave as a believer. This leads to a generalized enforcement of the norm in this neighborhood. When this happens, since the inhabitants of the bordering neighborhoods incur a higher risk of meeting people who enforce the norm, they also develop good reasons to behave as believers. Their apparent conversion affects in turn others neighborhoods. Little by little, cascades of compliance invest the entire society and false believers spread everywhere (Centola et al., 2005: 1028). Here a set of causal relationships that presuppose implicit and trivial covering laws is considered by Centola, Willer, and Macy, for example, (1) the ones mentioned above that explain the behavior of false believers and their situated rationality; (2) every time a risk is perceived as very low, people do not care about it; and (3) if individuals have good reasons to enforce a norm, the observable result is a generalized enforcement of this norm.

Further remarks on the D-N model and its applicability

In this concluding section we will consider some further logical and epistemological presuppositions of the aversion often shown by analytical sociologists to the D-N model. We have placed these further remarks on the applicability of this model at the end of our article, because they have more to do with the general philosophy of science than analytic sociology and can be thus analyzed in a separate way from the rest of the topics we have taken into account in the previous pages. Following various epistemologists who during the past decades have criticized the D-N model (e.g. Salmon, 1989; Woodward, 2003), Hedström and Ylikoski (2010) have argued that it must be rejected not only because of the reasons analyzed in the section ‘Mechanism-based explanations versus D-N explanations,’ but also because of the following three sets of reasons.

The first concerns ‘explanatory relevance’ (Hedström and Ylikoski, 2010: 11), that is, the idea that the D-N model does not provide sufficient conditions for successful scientific explanation. Regarding this point, there are two main problems that need to be considered. The first is ‘irrelevant information’ (Hedström and Ylikoski, 2010: 12; Ylikoski, 2013: 384). Explanations can be constructed that fulfill all the requirements of the D-N model, ‘but which do not seem to be explanatory’ (Ylikoski, 2013: 384). For example, ‘the fact that a man eats contraceptive pills is not what explains why he does not get pregnant’ (Hedström and Ylikoski, 2010: 12). However, this would be a valid explanation according to the D-N model given that the law no-one who takes birth control pills becomes pregnant is true and also that the explanandum and the initial conditions are true (see Opp, 2013a: 334). However, the explanation cannot be accepted. As highlighted by Ylikoski (2013), counterexamples like this signify something being wrong with this model: they show that it fails ‘to identify the features of explanations that make them explanatory’ (p. 384).

In our view, this criticism of the D-N model must be rejected because, according to this model, one of the requirements to deduce the explanandum from the explanans is, as correctly argued by Hedström and Ylikoski, that the assertions that describe the initial conditions are true (see Hempel and Oppenheim, 1948). From the standpoint of the D-N model, to explain that the cause of why a woman does not get pregnant is that she takes contraceptive pills, we also need to check empirically other initial conditions such as if she is fertile, healthy, and so on. Obviously, the initial condition ‘being fertile’ cannot be true for a man. In other words, the problem with this criticism of the D-N models is that it fails to consider that every explanation in terms of this model is always ceteris paribus (see Demeulenaere, 2011a: 191–192).

The second problem highlighted by Hedström and Ylikoski (and linked to the first set of reasons) is that the D-N model is ‘unable to make sense of the asymmetry of explanatory relations’. As argued by Aristoteles, effects ‘do not explain their causes.’ However, ‘nothing in the covering-law account rules this out’ (Hedström and Ylikoski, 2010: 11; see also Bromberger, 1962; Psillos, 2003; Salmon, 1989). According to the D-N model, given the height of a flagpole, the angle θ it makes with the sun plus the laws describing the rectilinear propagation of light, the length of a flagpole explains the length of its shadow. The problem is that, according to the covering-laws model, the deduction is perfectly legitimate, via the same laws and the same observation on the angle θ, the other way around. However, arguing that the length of the shadow can explain the length of the flagpole makes no sense because the length of the shadow cannot cause the length of the flagpole. Explanations ‘are asymmetric: they explain effects in terms of causes and not conversely’ (Psillos, 2007: 59). As emphasized by Ylikoski (2013), the covering-law model must be rejected because it ‘does not seem to get the direction of explanation right’ (p. 384). The example of the flagpole and its shadow shows that a derivation can satisfy the D-N model ‘criteria and yet fail to identify the causes of an explanandum’ (sometimes the derivation is not explanatory) (Ylikoski, 2013: 384).

Hedström and Ylikoski’s view that nothing in the covering law account rules out the possibility of incorrectly identifying the direction of the explanation, which is rooted in Bromberger’s (1962) work, seems to us mistaken because, according to the D-N model, a fact can be sensibly regarded as the cause or one of the causes of an explanandum only if it is empirically correct to do so. In other words, causal imputation is legitimate only if there is an empirical law that allows us to consider it as such. In the case of the flagpole example, we regard the idea that the length of the shadow is the cause of the length of the flagpole as absurd because no empirical generalization allows us to make sense of this idea. We lack testable evidence. While it is regarded as empirically true that a flagpole generates a shadow that is proportionate to its length, the contrary is not. The empirical nature of the causal imputation is the reason why, from the standpoint of the history and practice of science, correctly determining the direction of the explanation has never been a real concern for scientists, including interpretative sociologists.

According to Hedström and Ylikoski (2010: 10), another set of reasons why the D-N model can be criticized is related to the fact that, as argued by Woodward (2003, 2017) and other scholars (e.g. Holland, 1986), while this model requires that all explanations are based on laws, explanations in the social sciences are based on invariant relations that are not laws. This is because they are not exceptionless and can be understood only in terms of a counterfactual account of causation that is alternative to the D-N model. According to this account, to find a cause–effect relationship, causes should be experimentally manipulable and manipulated to see which effects they produce under different experimental conditions. As pointed out by Goldthorpe (2001),

understood in this way, causality is always relative. It is, in principle, determined by comparing what would have happened to a ‘unit’ in regard to Y if this unit had been exposed to X [treatment] with what would have happened if it had not been exposed to X [control] (p. 5).

In agreement with Psillos (2003: 184–187), we believe that this counterfactual account of causation fails to provide a valid alternative to the covering law model because of two reasons. The first is that, since it is a counterfactual theory, to establish the existence of what it calls invariant relations, it implicitly presupposes the logical scheme of the D-N model: experimental manipulation means, from the standpoint of this model, changing the initial conditions of the explanans and, as a consequence, the covering laws needed to causally link these initial conditions to the explanandum. The second reason is that it does not provide a clear distinction between laws and invariant generalizations that are explanatorily useful but nonlaws. For more details about the weakness of this objection to the D-N model, we refer the reader to Opp (2013a: 404; 2013b: 337–338). As we have argued in previous pages, according to the individualist interpretation of the D-N model, since the regularities that characterize social phenomena are often trivial and not general, and since situational analysis is central to social research, causes cannot be mechanically determined via the use of laws (although the use of laws is necessary). What is most important is the careful empirical analysis of the initial conditions. Understood as situational analysis, the D-N model can make sense of the fact that causality is relative and intimately connected to the ‘manipulation’ of these conditions. Situational analysis allows us to know which nondeterministic generalizations must be used to find empirically valid causal relationships.

A final set of problems highlighted by Hedström and Ylikoski concerns the notion of understanding. According to Hedström and Ylikoski (2010), the D-N model

does not seem able to account for what provides understanding in explanations that do not satisfy its strict requirements. For example, the crucial explanatory work is assumed to be done by the relevant laws, but they are often unknown to people providing the explanation. (p. 12)

This means that the D-N model fails to make sense of our understanding in terms of common sense that is crucial in the social sciences and the study of human action. The ‘covering law account seems to fail to make sense of a very fundamental aspect of explanatory cognition’ (Hedström and Ylikoski, 2010: 13; Woodward, 2003: 159–161). In other words, since many explanations (e.g. explanations in terms of common sense) require neither the explicit knowledge of the relevant laws involved in the explanation nor the explicit reference to a deductive argument, these explanations cannot be regarded as based on the D-N model (see Salmon, 1989: 24; Scriven, 1959; Woodward, 2003: 23–24). Explanations of this kind are what Hempel (1959) called explanation sketches, that is, incomplete explanations (Croce’s analysis about the reasons why the Italian republican party lost electoral support in the 1880s, which we mentioned in section ‘D-N Explanations and common-sense laws.’ is an example of incomplete explanation). Explanation sketches do not constitute a problem for the D-N model because their logical structure can still be accounted for in terms of this model by making explicit what is implicit. The reason why individuals are able to produce explanation sketches without being aware of their D-N nature is that, as largely emphasized by cognitive science, our deductive skills are partly subconscious. This point has been clarified by, among others, eminent methodological individualists. Focusing on the nature of knowledge, Popper argued that our mind tacitly interprets the world in the light of our biological and cultural memory. This memory is pattern knowledge in the sense that understanding what is particular and concrete presupposes the use of general and abstract patterns or regularities (see also Di Iorio, 2015: 149; Hayek, 1952b: 142). As pointed out by Hayek (1952a: 67, 1952b), who developed an epistemological theory similar to Popper’s and strongly insisted on the relevance of the tacit skills in cognition, this tacit categorization process is essentially nomological:

Whenever we attempt to explain or understand a particular phenomenon we can do so only by recognizing it or its parts as members of certain classes of phenomena, and the explanation of the particular phenomenon presupposes the existence of general rules.

From the standpoint of the D-N approach, the only reason why Croce’s explanation of the reasons why the Italian Republican party lost electoral support in the 1880s makes sense to us is that it is based on an implicit process of pattern categorization. The merit of the D-N model is that it allows us to make this process explicit and clarify its logical structure as D-N (see section ‘D-N explanations and common-sense laws’ and section ‘The role of situational analysis in D-N explanations’).

Hedström and Ylikoski emphasize that another problem about understanding is that the D-N model suggests that explanation and prediction are the same thing, while this seems to be untrue. As pointed out by Ylikoski (2013), according to the D-N model, ‘explaining a thing is to make it expected’ (p. 385). However, the ‘symmetry of explanation and prediction does not seem to hold’ (Hedström and Ylikoski, 2010: 12). Psillos (2003: 235–236) clarifies this point as follows:

There can be explanations that do not have predictive force and, conversely, there can be perfectly legitimate predictions that offer no explanation [. . .]. A standard counter-example to the view that all predictions can also be explanations is the following. Well-functioning barometers can be used to predict an upcoming storm. Yet neither barometers on their own, nor the hypothesis that they correlate well with storms, explain why the storm has occurred. It is a drop in the atmospheric pressure that explains the occurrence of the storm. In fact, both the drop of the barometer and the subsequent storm are common effects of the same cause; namely, the fall in the pressure. So there can be predictions without explanation.

A standard type of counterexample that aims to show that there can be explanations without prediction is the following one:

Suppose that we DN-explain a past event [e.g. the position of Mars two months ago] by using Kepler’s first law and the present position of the planet as the initial condition. Although this is an explanation licensed by the DN model, it does not amount to a prediction of Mars’s position, since predictions are forward looking. The relevant DN explanation of Mars’s position two months ago may retrodict this position, but it does not predict it. (Psillos, 2003: 236)

It seems to us that this criticism of the D-N model must be rejected because it stems from a confusion about the way this model conceives of the symmetry between explanation and prediction. According to this model, this symmetry exists only in the sense that the same event can be explained ex post or predicted ex ante ceteris paribus, that is given the same initial conditions. For example, the same information provided by a barometer in two different moments can be used to explain why a storm took place in the past and also to predict that a storm is going to happen in the future. In other words, since a nomological relationship links a cause to an effect, the D-N model can also allow us to predict an event given certain initial conditions (see Di Nuoscio, 2018).

Footnotes

Acknowledgements

The authors thank Francisco J. León-Medina, Gianluca Manzo, and Karl-Dieter Opp for having provided valuable remarks on the topic of this article as well as two anonymous reviewers for their useful comments and suggestions. All errors remain ours.

Funding

The author(s) received no financial support for the research, authorship, and/or publication of this article.

ORCID iD

Francesco Di Iorio

Notes

Author biographies

Francesco Di Iorio is an associate professor of philosophy at Nankai University in Tianjin (China). His publications include Cognitive Autonomy and Methodological Individualism: The Interpretative Foundations of Social Life (Springer) and, coedited with Gérald Bronner, The Mystery of Rationality: Mind, Beliefs and the Social Sciences (Springer). He is currently editing with Nathalie Bulle the Palgrave Handbook of Methodological Individualism (in two volumes).

Enzo Di Nuoscio is professor of epistemology at University of Molise and Luiss University (Italy). His latest published books are The Logic of Explanation in the Social Sciences, Bardwell Press, Oxford, 2018; I geni invisibili della libertà. Perché la democrazia non può fare a meno della cultura umanistica, Mondadori, Milano, 2022.

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