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are presented in the Appendix. To follow the analysis in this book, however, it is not necessary to read the Appendix. Instead, I explain in Chapter 6 how the computational model developed for this research applies Pearl’s theory to model counterfactuals.

      Other Theories of Counterfactuals

      Pearl’s theory of counterfactuals makes a significant contribution to the existing literature on counterfactuals. As Pearl writes, using external interventions to model counterfactuals has major advantages over other theories of counterfactuals (238–40), first addressed by David Hume and later presented by John Stuart Mill, David Lewis, or Saul Kripke. Specifically, Pearl’s theory differs from the works of these authors by focusing on the processes by which counterfactuals are constructed.

      Figure 13. Modeling counterfactuals. (2 graphs)

      There is a vast body of literature about theories of counterfactuals, particularly in the field of philosophy, and the following paragraphs can by no means give a complete overview or analysis. Rather, my aim is to briefly present some of the main features of this literature and identify some of the major contributions offered by Pearl’s approach. Following Pearl’s own references, this section addresses Lewis’s theory of counterfactuals, to which various works in the study of political science refer (e.g., Fearon 1991; Sylvan and Majeski 1998). In addition, the section addresses Hume, because he was the first researcher to explicitly address counterfactuals, and Kripke, whose theory of counterfactuals draws on the work of Lewis; Kripke’s theory has also been applied to the study of political science (Sylvan and Majeski 1998) and computer science (Peralta, Mukhopadhyay, and Bharadwaj 2011).

      According to David Hume, knowledge about cause and effect is available to humans from their experience (rather than from reasoning by itself), in which they frequently find that certain things are conjoined with each other (regularity account of causation) His definition of causation, which was the first to directly address counterfactuals, is (1772: 90; also quoted in Pearl 2000: 238): “we may define a cause to be an object followed by another, and where all the objects, similar to the first, are followed by objects similar to the second. Or, in other words, where, if the first object had not been, the second never had existed.”

      Following Hume, causality and counterfactuals appear to be connected to the regularity of observations. However, this overlooks that counterfactuals are by nature not observed. As Peter Menzies has written (2014): “It is difficult to understand how Hume could have confused the first, regularity definition with the second, very different counterfactual definition.” Pearl understands this definition to indicate that “Hume must have felt that the counterfactual criterion is less problematic and more illuminating” than the regularity account itself (238), and observes that Hume, who never explored counterfactuals more deeply to present a theory about them, does not acknowledge that counterfactual statements are by nature more complicated than causal statements.

      Perhaps the most famous contribution to the study of counterfactuals was presented by Lewis in 1973. In his theory, counterfactuals are considered possible worlds—a term that immediately indicates that Lewis treats counterfactuals as possible, while Pearl models them as if they were real. Lewis’s possible worlds are different from the real world and can be evaluated to have more or less similarity to the real world. Information about this similarity is measured by the truth condition that compares different possible worlds with the real world.³⁶

      Following this understanding, Lewis treats counterfactuals as entirely separate from the real world, that is, to have an independent existence that may be similar to the real world.³⁷ By contrast, Pearl treats counterfactuals as based on the same mechanisms as the real world. In Pearl’s approach, counterfactuals are never entirely separate from the real world. On the one hand, there could be counterfactuals that are exactly like the real world with the only exception that they include one different “thing” (the variable on which the intervention is performed); on the other hand, it is also possible that there are counterfactuals where every “thing” is different from the real world, but their causal connections are the same as in the real world. Accordingly, Pearl’s counterfactuals include different antecedents but the same consequences that exist in the real world, as well as different antecedents and consequences than the ones that exist in the real world. Like Lewis, however, they do not include the same antecedents and consequences that exist in the real world.

      Lewis, moreover, defines causation based on counterfactuals, not counterfactuals based on causation like Pearl. He does so by defining (1) causal dependency between two different possible events, (2) truth conditions for causal dependence that reflect the real world, and (3) a causal chain that consists of a sequence of events. Lewis’s specific definitions have been discussed in a large body of literature and far exceed what can be offered here. Rather, his procedure by itself indicates that, instead of intuiting directly causal connections in the world like Pearl, Lewis approaches causality by looking at what the world is not. Accordingly, counterfactuals are a way to understand the real world and involve looking backward into the past, based on which one knows that certain things in the real world exist. This proceeds in the following way: (1) real world: consequence → (2) modified real world: counterfactual consequence → (3) search for counterfactual antecedents. Pearl’s approach instead directly looks at the mechanisms that make up the world as it is, so that his modeling of counterfactuals can be expressed as (1) real world → (2) modified real world: counterfactual antecedent → (3) search for consequences of counterfactual antecedents.

      The works of Saul Kripke present another account of counterfactuals, based on the semantic analysis of modal logic (1980, 1963).³⁸ Kripke’s account also considers counterfactuals as possible worlds, but rejects the notion that every possible world is entirely different from the real world.³⁹ In this sense, Kripke’s work is closer to that of Pearl. Specifically, Kripke treats the connections between things (represented by functions) to identify different worlds, and treats different worlds as being connected to each other by certain components (represented by necessary propositions). By contrast, Pearl treats the connections between things in the real world and counterfactuals to be the same (causal mechanisms), and counterfactuals to be identified from the modification of particular things in the real world (external interventions). This difference is indicated by contrasting Kripke’s definition of worlds with Pearl’s definition of counterfactuals and the reality: Kripke draws on binary functions that have the output of truth conditions, whereas Pearl draws on directed functions that identify parents and children. Kripke’s account of counterfactuals therefore allows the exploration of particular propositions that are only true in certain as opposed to all worlds, whereas Pearl’s work allows investigation of the effects that particular propositions that are not true in the real world would have on the reality.

      Conclusion

      This chapter has introduced the cognitive mapping approach, which I apply to study the question why some individuals decide to take up arms while others, who live under the same conditions, engage in nonviolent activism instead. Responding to the abandonment of the cognitive mapping approach in the field of political science, I have presented a formalization that allows researchers to systematically analyze cognitive maps. Specifically, I have formalized cognitive maps into DAGs, which makes it possible to develop computational models that process cognitive maps, and presents new possibilities for the application of cognitive maps in political science.

      My formalization is based on Pearl’s theory of causality. It provides new possibilities not only for application of cognitive mapping but also for the study of counterfactuals. Specifically, it suggests how intervening on the belief systems of political actors allows us to explore their behavior in alternative worlds, or in the reality in which they hold different beliefs about religion, or other factors that are not knowledge. This new approach to the study of counterfactuals intervenes on the actors’ beliefs about the world rather than the world itself.

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