Counterfactual Thought Experiments: A Necessary Teaching Tool

COUNTERFACTUALS are routinely used in physical and biological sciences to develop and evaluate sophisticated, non-linear models. They have been used with telling effect in the study of economic history and American politics.[1] For some historians, counterfactual arguments have no scholarly standing. They consider them flights of fancy, fun over a beer or two in the faculty club, but not the stuff of serious research.[2] This dismissive attitude may be encouraged by the emergence and popularity of counterfactual historical works as a fictional genre, and the uncomfortable similarities between some recent works of counterfactual scholarship and such fiction. Nevertheless, counterfactuals are an effective research tool, but comprehending this requires a clear understanding of their nature, the circumstances to which they are best suited, and robust protocols for conducting thought experiments.

With these ends in mind, I begin by exploring the differences between counterfactual and so-called “factual” arguments and offer the proposition that the difference between them is greatly exaggerated; it is one of degree, not of kind. I go on to discuss different uses of counterfactual thought experiments for historians. I distinguish between miracle and plausible world and scholarly and folk counterfactuals, and their respective uses, and I propose several criteria to guide plausible world counterfactuals. I conclude by looking at the special problems of applying counterfactual analysis to a problem as broad as the rise and success of the West.

Counterfactuals Versus Factuals

Counterfactuals are “what if” statements, usually about the past. Counterfactual experiments vary aspects of the past and analyze how these changes might have affected the course of events. In history, such experiments always have uncertain outcomes because we can neither predict the future nor rerun the tape of history to see what might actually happen. The speculative nature of counterfactuals thus makes many scholars wary of them. But counterfactual analysis can often be conducted in an evidence-rich environment. In the aftermath of Aldrich Ames’ arrest as a Soviet spy, the Central Intelligence Agency convened a team of counter-intelligence experts to figure out how he might have been unmasked earlier. The team imagined a series of procedures that might have been in place and asked which, if any of them, might have tripped up Ames. Their knowledge of Ames’ personality, motives, and behavior and of the modus operandi of his Soviet spy masters allowed them to conduct their inquiry with what they believed to be a high degree of precision.[3]

Counterfactuals are the heart of all historical interpretations and their putative lessons. The controversy surrounding the strategy of deterrence is an example. One of the principal policy “lessons” of the 1930s was that appeasement whets the appetites of dictators while military capability and resolve restrains them. The failure of Anglo-French efforts to appease Hitler is well-established, but the putative efficacy of deterrence rests on the counterfactual that Hitler could have been restrained if France and Britain had demonstrated willingness to go to war in defense of the European territorial status quo. German documents make this an eminently researchable question, and historians have used them to try to determine at what point Hitler could no longer be deterred.[4] Their findings have important implications for the historical assessment of French and British policy and for the strategy of deterrence more generally.

Quantitative counterfactual analysis is another possibility. Jay Winter exploits counterfactual projections of mortality rates based on pre-war data from Prudential Life Insurance policies to determine the age structure of British war losses. He combines data from the life tables for 1913 and 1915 in roughly two to one proportions, because the war did not begin until August 1914, to create a counterfactual table for 1914. On the basis of the prior decade, he then calculates what the life tables would have been for the period 1914–18 in the absence of war. By comparing the actual death rates in each age group with the counterfactual estimates, he is able to determine the death rates by five-year cohorts for each year of the war.[5]

Real cases can be framed as counterfactuals, and their evidentiary bases can be exploited to make counterfactual comparisons. Tin-bor Victoria Hui employs this strategy to examine state formation in China and Europe. She identified a series of processes common to both regions and has used China as a “real world counterfactual” to evaluate state formation in Europe, and vice versa.[6] Kenneth Pomeranz uses Europe as a real counterfactual case to explain why China did not have an independent industrial revolution.[7] All these experiments are based on the assumption that similar causal mechanisms can have different consequences when they operate in different contexts. By examining the differential impact of these mechanisms, and the extent to which they were determined by local conditions, we can learn a lot about different trajectories of historical development.[8]

Even when evidence is meager or absent, the difference between counterfactual and “factual” history may still be marginal. Documents are rarely “smoking guns” that allow researchers to establish motives or causes beyond a reasonable doubt. Actors only occasionally leave evidence about their motives, and even when they do historians rarely accept such testimony at face value. More often, historians infer motives from what they know about actors’ personalities and goals, their past behavior, and the constraints under which they operated. Janice Gross Stein and I spent several years researching a book on Cold War crises. We scoured archives in four countries, utilized documents collected or declassified by other researchers, and conducted extensive interviews with former American, Soviet, Israeli, and Egyptian policy makers. We accumulated a mass of relevant information but still had no hard evidence about the motives for some of the key decisions of Kennedy and Khrushchev. We suspect that Khrushchev was never clear in his own mind about the relative importance of the several goals that made a missile deployment in Cuba attractive to him. Given the delicate nature of many crisis decisions, neither leader was willing to share his goals and reasoning with even his most intimate advisors. Khrushchev further complicated the picture by telling various officials what they wanted to hear and thus what he thought most likely to garner their support.[9]

When we move from the level of analysis of individual actors to small groups, elites, societies, states, and regional and international systems, the balance between evidence and inference shifts decisively in the direction of the latter. Structural arguments assume that behavior is a response to the constraints and opportunities generated by a set of domestic or international conditions. Mark Elvin’s elegant study of China starts from the premise that empires expand to the point at which their technological superiority over their neighbors is approximately counterbalanced by the burdens of size. At this equilibrium, imperial social institutions come under constant strain because of the high relative cost of security. Harsh taxation impoverishes peasant cultivators and leads to falling tax revenues. The ensuing decline in the number of free subjects makes military recruitment more difficult, and governments rely instead on barbarian auxiliaries, even for their main fighting forces. To save money, governments also give up active defense policies and try to keep hostile barbarians at bay through diplomacy, bribery, and settlement on imperial lands. The inevitable outcome is a weakened economic base, barbarization from within, and finally, partial or total collapse of the empire.[10] Elvin musters considerable evidence in support of his thesis, much of it from primary sources, but it is all in the way of illustration. Nowhere is he able to show that Chinese leaders followed any of the policies he describes for any of the reasons he attributes to them.

For the most part then, structural arguments build on a chain of inferences that use behavioral “principles” as anchor points. Empirical evidence, when available, may be exploited to suggest links between these principles and behavior. But even in the best of cases, these links are indirect and presumptive, and can be corroborated only obliquely and incompletely. Readers evaluate these arguments on the seeming “reasonableness” of the inferences, the quality and relevance of the evidence offered in support, and the extent to which that evidence permits or constrains alternative interpretations. Receptivity to arguments is significantly influenced by the appeal of the underlying political and behavioral “principles” in which the inferences are rooted. When these “principles” run counter to the reigning orthodoxy, the arguments may be dismissed out of hand regardless of the evidence.

Counterfactuals are frequently smuggled into so-called factual narratives. E. H. Carr, no friend of counterfactuals, does this in his treatment of the Soviet Union where he insists that the Bolshevik Revolution was hijacked by Stalin. The implication is that socialism would have developed differently without him.[11] After the Cuban missile crisis, former Kennedy administration officials and many scholars maintained that Khrushchev would not have deployed missiles in Cuba if Kennedy had behaved more decisively at the Bay of Pigs, the Vienna summit, and in Berlin. There was no evidence to support this interpretation, but it became the conventional wisdom and helped to shape a host of subsequent policy decisions, including the disastrous intervention in Vietnam. The evidence that had become available in the Gorbachev era suggests that Khrushchev had decided to send missiles to Cuba secretly because he overestimated Kennedy’s resolve; he feared that Kennedy was preparing to invade Cuba and would send the American navy to stop any ships carrying missiles to Cuba to deter that invasion.[12] Counterfactual arguments, like any historical argument, are only as compelling as the logic and “evidence” offered by the researcher to substantiate the links between the hypothesized antecedent and its expected consequences. Every good counterfactual thus rests on multiple “factuals,” just as every factual rests on counterfactual assumptions—and these assumptions too often go unexamined.

Any sharp distinction between factuals and counterfactuals rests on questionable ontological claims. Many of the scholars who dismiss counterfactual arguments do so because they do not believe they are based on facts. However, philosophers have long recognized that “facts” are social constructions. To say this is not to deny the existence of reality quite independently of any attempt to understand it by human beings, or that some understandings may transcend culture. Physical scientists may be correct in their claim that fundamental concepts like mass, volume, and temperature are essential to the study of nature and that extraterrestrial scientists would have to possess the same concepts to understand the universe, but this is not true of social concepts which vary across and within human cultures. There are many ways of describing social interactions, and the choice and utility of concepts depend largely on the purpose of the “knower.”[13] “Temperature” is undeniably a social construction, but it is a measure of something observable and real: changes in the energy levels of molecules. Social and political concepts do not describe anything so concrete. There is no such thing as a balance of power, a social class, or a tolerant society. Social “facts” are reflections of the concepts we use to describe social reality, not of reality itself. They are ideational and subjective, and even the existence of “precise” measures for them—something we only rarely have—would not make them any less arbitrary. In fact, as Quine has shown, theoretical concepts insinuate themselves into the “data language” of even the hardest sciences.[14] The construction of “factual” history is therefore imaginary, and its only claim to privilege is that the concepts and categories in terms of which it is constructed tell us something useful or interesting about the social world. The same is true for counterfactual history.

Why Counterfactuals?

Counterfactuals can combat the deeply rooted human propensity to see the future as being more contingent than the past, reveal contradictions in our belief systems, and highlight double standards in our moral judgments. Counterfactuals are an essential ingredient of scholarship. They help determine the research questions we deem important and the answers we find to them. They are essential teaching tools and critical to establishing claims of causation. They are equally necessary to evaluate real world outcomes.

Receptivity to contingency: There is a strong bias among scholars and students to recognize the contingency of important historical events. Two distinct but reinforcing processes may be at work here. R. H. Tawney observed that “historians give an appearance of inevitableness to an existing order by dragging into prominence the forces which have triumphed and thrusting into the background those which they have swallowed up.”[15] Historical interpretations, no matter how well-documented or convincingly presented, rarely achieve a consensus. They provoke critiques and contending interpretations, and the resulting controversy stimulates a search for additional documents. New evidence may require historians to reformulate their interpretations but it rarely discredits them outright. As the historiography of the First World War indicates, new evidence often provides the basis for still more interpretations. Decades of controversy, or even centuries of controversy about the French Revolution or the collapse of the Roman Empire, give rise to a plethora of interpretations that attribute these developments to a wide range of intellectual, social, economic and political causes.[16] Remove one or several putative causes and a half-dozen others remain. Nevertheless, historical debate encourages the belief that most major events and developments were massively “overdetermined.”[17]

The disciplinary tendency to privilege structural explanations is reinforced by the “certainty of hindsight bias.”[18] Baruch Fischoff has demonstrated that “outcome knowledge” affects our understanding of the past by making it difficult for us to recall that we were once unsure about what was going to happen. Events deemed improbable by experts (e.g., peace between Egypt and Israel, the end of the Cold War), are often considered “overdetermined” and all but inevitable after they have occurred.[19] By tracing the path that appears to have led to a known outcome, we diminish our sensitivity to alternative paths and outcomes. We may fail to recognize the uncertainty under which actors operated in the past and the possibility that they could have made different choices that might have led to different outcomes.

Many psychologists regard the certainty of hindsight effect as deeply rooted and difficult to eliminate. But the experimental literature suggests that counterfactual intervention can assist people in retrieving and making explicit their massive but largely latent uncertainty about historical junctures, that is to recognize that they once thought, perhaps correctly, that events could easily have taken a different turn. Philip E. Tetlock and I conducted a series of experiments to test the extent to which counterfactual “unpacking” leads foreign policy experts to upgrade the contingency of international crises. In the first experiment, one group of experts was asked to assess the inevitability of the Cuban missile crisis. A second group was asked the same questions, but given three junctures at which the course of the crisis might have taken a different turn. A third group was given the same three junctures, and three arguments for why each of them was plausible. The resulting judgments of contingency varied in proportion to the degree of counterfactual unpacking.[20] There is every reason to expect that scholars exposed to counterfactuals, and better yet, forced to grapple with their theoretical consequences, will also become more open to the role of contingency in key decisions and events.

Testing and evaluation: Counterfactuals are fundamental to all theories and interpretations. If we hypothesize that x caused y, we assume that y would not have happened in the absence of x—ceteris paribus. Quantitative research attempts to get around this problem, and the contrapositive form of the fallacy of affirmation, by constructing a sample of comparable cases large enough to contain adequate variation on dependent (what is to be explained) and independent (what allegedly explains it) variables. In case studies and historical narratives, this is not possible.

Historians typically attempt to establish causation by process tracing. They try to document the links between a stated cause and a given outcome in lieu of establishing a statistical correlation. This works best at the individual level of analysis, but only when there is enough evidence to document the calculations and motives of actors. Even when such evidence is available, however, it may still not be possible to determine the relative weight of the several hypothesized causes, and which, if any, might have produced the outcome in the absence of others or in combination with other causes not at work in the case. To sustain causal inference, it is generally necessary to engage in comparative analysis. This is difficult to do because it requires extraordinary breadth on the part of the researcher, or a collaborative enterprise.

Counterfactual experiments can tease out the assumptions—often unarticulated—on which theories and historical interpretations rest. Apologists for the Soviet system insist that communism would have evolved differently if Lenin had lived longer or had been succeeded by someone other than Stalin.[21] Attempts to address this question have not resolved the controversy but have compelled historians to be more explicit about the underlying assumptions that guide and sustain contending interpretations of Stalin and the nature of the Communist Party and the Soviet state. Those assumptions have now become the focus of controversy, and scholars have looked for evidence with which to evaluate them. This process has encouraged a more sophisticated historical debate.

Because every causal argument has its associated counterfactual, critics have two generic strategies open to them. They can offer a different and more compelling theory or interpretation—far and away the most common strategy—or show that the outcome in question would have happened in the absence of the hypothesized causes. John Mueller’s study of the Cold War is a nice example of the second strategy. In contrast to the conventional wisdom that attributes the “long peace” between the superpowers to nuclear deterrence, Mueller argues that Moscow and Washington were restrained by their general satisfaction with the status, memories of World War II, and the human, economic, and social costs of large-scale, conventional warfare. He contends that the unheralded destructiveness of nuclear weapons was redundant and possibly counter-productive.[22] This Mueller strategy readily lends itself to simulation. Researchers can build a counterfactual world and look at how actors would behave under a wide range of conditions, including those that subtract putative causal factors.

Assessing outcomes: Counterfactuals are a key component of evaluation. Was the development of nuclear weapons a blessing or a curse for human kind? What about affirmative action, free trade, or the growing economic and political integration of Europe? Serious and thoughtful people can be found on all sides of these controversies. Their arguments share one thing in common: they use counterfactual benchmarks—most often, implicitly—to assess the merits of real world policies, outcomes, or trends. Proponents of nuclear weapons who claim that nuclear weapons had beneficial consequences during the Cold War imagine a superpower war, or at least a higher probability of one, in the absence of nuclear deterrence. Some critics of nuclear weapons, like John Mueller, argue that self-deterrence based on memories of the horrors of conventional war would have kept the peace. Other critics contend that nuclear weapons sustained the Cold War, and that it would have been less intense, and possibly resolved earlier, in their absence.

Assessment can be significantly influenced or even determined by the choice of counterfactual. The conventional wisdom holds that the allied victory in World War I was a good thing: it prevented an expansionist, continental power from achieving hegemony in continental Europe. This assessment represents the view of the world from the corporate boardrooms and corridors of power in London, New York, and Washington. From the perspective of say, Polish Jewry, the outcome was a disaster. If Germany had won, there almost certainly would have been no Hitler and no Holocaust. In this case, the choice of counterfactual reflects the different interests of the groups. As with historical analogies, the interesting and eminently researchable question becomes the extent to which counterfactuals guide evaluation or are chosen to justify positions that people have reached for quite different reasons.[23] An example of the latter is provided by Alessandro Portelli in his study of Italian communists. In interviews he conducted in the small city of Terni in Umbria, he found that workers often told stories of how history could and should have gone. These narratives describe a better world that workers believe might have come to pass if their leadership had caused specific events to occur differently between 1919 and 1925 and again between 1943 and 1953.[24]

Must counterfactuals be realistic? The several uses of counterfactuals I have described use both a “plausible” and a “miracle” world of counterfactuals. Plausible world counterfactuals are intended to impress readers as realistic; they cannot violate our understanding of what was technologically, culturally, temporally, or otherwise possible. In a recent study of the significance of World War I, I imagine a world in which Archduke Franz Ferdinand and his wife, Countess Sophie, returned alive from their visit to Sarajevo.[25] This counterfactual is eminently plausible because their assassination was such a near thing. Princip’s accomplice missed the royals en route to city hall, and Princip was lamenting his failure when the touring car carrying Franz Ferdinand and his wife came to a stop in front of him. This happened because the cars at the head of the procession had to back up because they had made a wrong turn. Princip stepped forward and fired two shots at point blank range into their touring car. With only a minimal rewrite of history—the procession was halted after the first attempted assassination, or that it subsequently stayed on the planned route—the assassination could easily have been averted.

There are many plausible counterfactuals—historical near misses, if you like—that had they occurred probably would not have had any significance for the outcomes in question. Consequently, counterfactuals that are plausible must meet a second test: they must have a real probability of leading to the outcome the researcher intends to explore. To demonstrate this, the researcher must construct a logical path between the counterfactual change and the hypothesized outcome, and must meet other tests that are described in the last section of this article. Plausible world counterfactuals are thought by some researchers to be the only legitimate kind of counterfactual.[26]

“Miracle world” counterfactuals violate our understanding of what is plausible or may require a “slaughter” that even the West would not have allowed.”[27] Even Dr. Seuss might find a landlocked region of aquatic mammals with strong ethnic identities something of a stretch, but the analogy suggests a series of morally provocative counterfactuals. If the population of the southern Sudan were Caucasian and Christian, would the West have intervened earlier or more effectively? Miracle counterfactuals help us work through moral and scholarly problems. I might hypothesize that Europe achieved its military advantage because it was the only region of the world where no long-standing hegemony was established, and the resulting prolonged competition among its leading political units made them lean and mean, better-armed and more efficient in the use of large-scale violence.[28] To advance this hypothesis, I must have considered the counterfactual of a hegemonic Europe—perhaps achieved by a better organized and more astutely led Spain in the sixteenth century. To sustain the hypothesis, I need to consider what a hegemonic Europe would have been like and how it would have differed from historical Europe. My hypothesis is clearly not plausible and this is deemed a miracle counterfactual. Counterfactuals of this kind are, however, often particularly useful in evaluating existing interpretations and proposing new ones.

John Mueller’s world without nuclear weapons is a miracle counterfactual because it would require a massive rewrite of a century of scientific and political history to “uninvent” nuclear weapons, although the timing of their development might be altered by plausible world counterfactuals. The utility of miracle counterfactuals does not depend on their realism, but on the analytical utility of considering alternative worlds. Counterfactuals of this kind have a distinguished lineage. Euclid used one to prove that there are an infinite number of prime numbers, and Newton to demonstrate that the universe could not be infinite with regularly distributed and fixed stars. If these conditions held, Newton argued, the sky would not be blue.[29]

We might also distinguish between scholarly and folk counterfactuals. The former are those we invent and use in attached experimental way for any of the research purposes I have described. They may be plausible or miracle world counterfactuals. Folk counterfactuals are embedded in popular culture and often influence how people frame and respond to problems. They may provide pithy and powerful statements of widely-held beliefs that mobilize people for action. I recently heard a prominent religious leader proclaim on a television talk show that the Columbine shootings would never have happened if Hollywood and the other media had not produced so many violent movies, television shows, popular music, and video games. This is a good representative of the “where did we go wrong?” question, and assumes a prior turning point with a better counterfactual outcome if only we had chosen differently. Regret and desire appear to be the principal motivating agents of such counterfactuals, and the latter may reach its apotheosis in Andrew Marvell’s immortal lines: “Had we but World enough and time, This coyness, Lady, were no crime.”[30]

READ MORE: The history of Hollywood

Scholarly and folk counterfactuals can interact. Blaise Pascal invented the counterfactual of Cleopatra’s nose to illustrate the power of human vanity, and it has since become folk wisdom.[31] A volume of Astérix is devoted to Cleopatra and her nose, and there is even a Turkish saying, “to have a nose like Cleopatra’s.”[32] The counterfactual sensitizes and socializes listeners to a particular causal connection that we can state in the form of an English-language proverb, e.g. love makes the world go round. I noted earlier that the strategy of deterrence rests on the counterfactual (that we all would like to believe) that Hitler might have been overthrown, or at least made more cautious, if the democracies had stood firm earlier in the 1930s.

The discussion of scholarly and folk counterfactuals points to a broader truth about the relationship between counterfactuals and “factual” history. History consists of acts of labeling, and its core activity is framing hypotheses. Straight history and counterfactual history, popular and academic, are rhetorical strategies to get people to view the world and critical aspects of the present in particular ways. Counterfactual history can be a particularly powerful way of achieving this end in the classroom, and even those who do not accept its status as a scientific research tool can not afford to ignore it. This is all the more reason for introducing students to counterfactuals as early as possible.

Some Dangers in Attempting to Use
“Plausible World” Counterfactuals

Thoughtful historians and social scientists have pondered the problem of plausible world counterfactuals and appropriate criteria for using them. There is no consensus about what constitutes a good counterfactual, but there is a common recognition that it is extraordinarily difficult to construct a robust counterfactual —one whose antecedent we can assert with confidence will lead to the hypothesized consequent. There are three reasons for caution: 1) the statistical improbability of multi-step counterfactuals, 2) the interconnectedness of events, and 3) the unpredictable effects of second order counterfactuals.

Compound probability: The probability of a consequent is a multiple of the probability of each counterfactual linking the hypothesized antecedent to it. Suppose I contend that neither World War II nor the Holocaust would have happened if Mozart had lived to the age of sixty-five.[33] The argument would be that Mozart, having pushed classical form as far as it could go in the Jupiter Symphony, his last three operas and the Requiem, decided that his next dramatic works would have to be markedly different and that these became precursors of a new, “post-classicist” style. These works would then have created a viable alternative to Romanticism that would have been widely imitated by composers, writers and artists. The ensuing post-classicism would have kept enlightenment political ideas alive and held Romanticism in check. Nationalism would have been more restrained, and thus Austria-Hungary and Germany would have undergone very different political evolution. In order to postulate this alternative and vastly preferable world, however, my argument would have involved at least five counterfactual steps linking antecedent to consequent. These are: Mozart must survive to old age; develop a new style of artistic expression; subsequent composers, artists, and writers must imitate and elaborate it; Romanticism must become to some degree marginalized; and artistic developments must have important political ramifications. Even this last counterfactual presupposes numerous other enabling counterfactuals about the nature of the political changes that would lead to the hypothesized consequent (e.g., that there would be internal reforms that resolve or reduce the threat of internal dissolution of Austria-Hungary, German unification under different terms—or at least a Germany satisfied with the status quo, no First World War, and no Hitler and no Holocaust without Germany’s defeat in World War I). Even if every one of this long string of counterfactuals had a probability of at least fifty percent, the overall probability of the consequent would be a mere 0.03 for five steps and a frighteningly low 0.003 for eight steps. This particular counterfactual may appear far-fetched, but most of the interesting counterfactuals that might intrigue us are no less improbable statistically. They may start with a tiny and plausible alteration of the real world but then infer numerous follow-on developments to end up with a major change in reality.

Interconnectedness: Efforts to use counterfactuals not infrequently assume that one aspect of the past can be changed and everything else kept constant. John Mueller’s Cold War counterfactual is a case in point. He analyzes postwar history as it actually happened, including the Cuban missile crisis, to see if any major outcome would have been different in the absence of nuclear weapons. But what incentive would Khrushchev have had to deploy conventionally armed missiles in Cuba? The missiles could not have deterred an American invasion, and might well have invited one, and this was the very event Khrushchev hoped to prevent.[34] Without a Cuban missile crisis involving nuclear warheads, which had significant consequences for the future course of Soviet-American relations, the Cold War would have evolved differently, and the course of future superpower relations, benign or malign, is impossible to predict.

It might be thought that “surgical” counterfactuals can be realistic but they likely to be no more useful than surgical air strikes. Causes are interdependent and have important interaction effects. Even minimal rewrites of history may alter the context in such a way as to render the consequent moot or undercut the chain of events or logic leading to it. Consider another missile crisis counterfactual: postulate that if Richard Nixon had won the 1960 presidential election—and in reality, he lost by the narrowest of margins—he would have ordered an air strike against the Soviet missiles in Cuba. It is reasonable to assume that Nixon would have preferred an air strike to a blockade because he was more hawkish than Kennedy and would not have had a Secretary of Defense like Robert McNamara to make the case for restraint. But for these same reasons, Nixon might well have committed enough American forces to the faltering Bay of Pigs invasion in April 1961 for it to have been successful. If Castro had been overthrown there would have been no communist Cuba to which Khrushchev could send missiles a year later.

This Nixon example invokes a counterfactual arising from the antecedent, but outside the chain of logic leading from it to the consequent, to render the missile crisis moot. If Nixon had been elected president in 1960, the world would have been different in many ways, some of them with implications that are impossible to trace. He would have appointed a different defense secretary who in turn would have appointed a different chairman of the joint chiefs of staff. Personnel changes at the top would have had amplifying consequences for promotions and appointments further down the line. To the extent that the behavior of individual officers could have important foreign policy implications—and it certainly did during the Berlin and Cuban missile crises—all kinds of possibilities open up.

Second order counterfactuals: The problem of prediction is further complicated by the fact that the clock of history does not stop if and when the hypothesized consequent is reached. Subsequent developments can return history to the course from which the antecedent was intended to divert it. Colin Martin and Geoffrey Parker demonstrate that the defeat of the Spanish Armada was a near event. They suggest that better communication, different decisions by local commanders, or better weather might have allowed the Spanish to land an invasion force in England. If Spain had put an army ashore it almost certainly would have conquered the country. Martin and Parker go on to consider what would have happened next: Philip II was destined to be succeeded by Philip III, a far less capable ruler who would have had enormous difficulty maintaining an already over-extended empire. Because of this, they believe, England would have throne off the Spanish yoke in a relatively short time.[35]

Some counterfactuals, like the “butterfly effect,” may introduce small changes that have major, lasting, long-term effects. Others, like a Spanish victory in 1588, are big changes that appear to have big consequences, but the changes they introduce may be dampened down over time and end up having little lasting effect. It is also possible, however, that second counterfactuals arising from a Spanish occupation of England, no matter how brief that occupation, could have had dramatic and long-lasting changes for European politics or in other realms that Martin and Parker did not consider. None of these outcomes are predictable, and the “butterfly effect” might not be knowable in advance or even in retrospect.[36]

Looking for “Turning Points”: Unmaking the West

Having developed appropriate protocols for the use of counterfactual thought experiments, let us now turn to an interesting substantive problem: the development of Western civilization and its remarkable success in the modern era. How contingent were both developments? Could Western civilization or its political, economic, technological, and military primacy have been undone by a minimally rewritten history? At what point did the success of the West become difficult to prevent? What were the essential “turning points” in the development of the West? And what about the parallel development of other competitor civilizations—China, India, the Arabs, or the Ottomans? Could minimal rewrites of their histories have made them more successful competitors with the West? At what point did that become unlikely or impossible? The novelty of posing these problems and of inviting students to join in a counterfactual thought experiment could enable an instructor to add spice to a Western Civ or a world history class, and doing so might leave a deeper and more lasting understanding in students’ minds of what in fact did happen in history than more traditional teaching methods.

To ponder how contingent the development of Western civilization was in its remarkable success in the modern era was, we need to identify critical turning points of Western and non-Western history and ask “what if” through counterfactual experiments. To do this, we need protocols for assessing the contingency of each turning point and the aggregate implications of these experiments for the course of Western history. With this end in mind, I propose six tests, all of which take the form of questions:

1. What do we have to do to negate a turning point? Turning points are important because of their consequences. Constantine’s embrace of Christianity and victory at Milvian Bridge in 312 and subsequent victories over Licinius in 323–24 made him sole ruler of the Roman Empire and able to impose Christianity on the Empire and repress “heretical” sects. A common religion and political tradition may have been essential for the long-term development of Western civilization. Had Constantine been decisively defeated in any of these campaigns, the religious life of Rome would have developed differently and perhaps removed one of the foundation stones of Western culture. This clearly can be considered the negation of a turning point.

Some of the events that we consider turning points may not need to be prevented. It may only be necessary to alter them in minor ways that render them innocuous much the way small mutations in the genes of pathogens may decisively alter their virulence, one way or another. Suppose we allow the Greeks to win their crushing naval victory at Salamis in 480 BCE, but introduce a small change in the events that followed. Sparta was asked to name a general to lead the Greek alliance against the Persians, and nominated their King Pausanias for the position. They recalled him about a year later, tried him on charges of corruption, and decided to withdraw from the alliance for fear that exposure to the life of richer city states was too threatening to their way of life. Sparta’s withdrawal opened the way for Athens to assume leadership of the alliance, and ultimately to transform it into a powerful empire. A different and honest Spartan leader might have forestalled Athenian leadership of the Delian League, and with it the wealth and self-confidence that produced the fifth century cultural explosion that is widely acknowledged as another foundational stone of Western civilization.

Mere postponement of a turning point may sometimes deprive it of its most important effects. In my discussion of the origins of the First World War, I have argued that it, or any conflict like it, might have been prevented if Franz Ferdinand’s assassination could have been forestalled for as little as three years. The underlying conditions that moved Europe toward war were rapidly evolving, and any one of a number of changes might have made Austria, Germany, or Russia—or all three—war averse. In the interim, it is unlikely that any other event could have served as catalyst for war because Sarajevo met an unusual set of conditions without which neither Austrians nor Germans would have been prepared to risk war.[37]

Our first task, therefore, is to determine what kinds of changes we have to make in the events identified as turning points. Once we know whether they need to be prevented, altered, or merely forestalled, we can search for minimal rewrites capable of achieving these ends.

2. How many credible minimal rewrites can be found that might prevent, alter or stall the turning point? Earlier I noted how easy it would have been to avert Franz Ferdinand’s assassination if only his cavalcade had followed the planned route. Numerous other minimal rewrites could also have kept the archduke and his wife alive. Princip might have obeyed the order to abort the assassination sent to him by the military conspirators in Belgrade; Austrian authorities in Bosnia might have taken security as seriously as they had the menu and music for the banquets they planned in the archduke’s honor; Franz Ferdinand might have cancelled his trip in response to multiple warnings and his wife’s fears; he might have followed the advice of his advisors and left Sarajevo directly after the ceremony at city hall or have raced down Appel Quay past Princip. These minimal rewrites suggest contingency by virtue of their variety. The first counterfactual removes the assassins, two others remove the target, and two more leave him on the scene but make him much more difficult to kill. As a general rule, the more different components of a turning point there are that can be removed by minimal rewrite counterfactuals, the more contingent the turning point and more unlikely the consequent.

3. How far back must we go to find credible minimal rewrites? We should try to avoid the conjunction fallacy and the best way to do this is to keep the intervening step between antecedent and consequent to a minimum. Temporal proximity, while not the same thing, is a good rough measure. Most of the minimal rewrites I suggest in the example above meet this test. They would have prevented Franz Ferdinand’s assassination with few intervening steps, and this is one reason why they appear plausible. The further back in time we go to find a minimal rewrite counterfactual, the more steps there are likely to be between antecedent and consequent, and we must remember that the probability of any counterfactual is the multiple of the probabilities of every step in the chain.

Minimal rewrite counterfactuals at temporal remove invite a second problem: they allow more parallel chains of causation, one or more of which may lead by alternative routes to the outcome the minimal rewrite is intended to prevent. Early public cancellation of the archduke’s visit to Sarajevo might have encouraged dedicated assassins to find some way of getting close to him during the army maneuvers scheduled outside the city. This would have been difficult but not impossible given the poor state of Austrian military security.

4. At what level of analysis are our minimal rewrites? Minimal rewrites of history require small, plausible changes in reality, likely to have big consequences. Surgical interventions at close proximity to the hypothesized consequent are hard to devise and this seriously constrains the choice of counterfactuals. For these reason, practitioners of counterfactual history most often invoke changes in personnel involving assassinations (Hinkley kills Reagan), failed assassinations (Franz Ferdinand lives), the fortunes of war (William of Orange or Hitler die in battle), disease (Pericles survives the plague), and accidents (Alexander the Great lives to a ripe old age). Equally popular are changes in policy where the chosen course of action was a near thing (Greek naval strategy at Salamis), where another strategy appears just as feasible as the one chosen (the Ottomans make an all-out effort to capture Vienna), or unintended deviations from plans arising from what Carl von Clausewitz called “friction”—the “countless minor incidents” including undelivered, garbled or misinterpreted messages, the failure of key players or equipment to appear on time and a host of other problems that degrade performance.[38]

To help assess contingency it is useful to introduce the concept of level of analysis. This is where we look for explanations—or counterfactuals in this instance—and it may be at a system, unit, sub-unit, or individual level, or the environment in which the system functions. The latter may be the easiest place to look for minimal rewrite counterfactuals. It includes such things as the weather, timing, and much of what comes under the rubric of fiction. This is followed by the level of leaders, and here too, there are often relatively simple and plausible ways of changing, or at least removing, critical personnel. Almost all of the counterfactuals in the paragraph above are at one of these last two levels. Changes in strategies may require intervention at the higher level of elites, bureaucracies, or domestic politics, and thus more elaborate arguments linking antecedents to consequences.

However, when we change ideas, state structures, or the balance of power, all requiring intervention at the system level, minimal rewrites are out of the question unless we go back to a point in time when those ideas, structures, and balances had not jelled and might be significantly affected by small, plausible changes at lower levels one and two. We could readily imagine a very different balance of power and set of alliances in seventeenth- or eighteenth-century Europe if we prevented or rearranged some of the marriages that Habsburgs, Bourbons, and other royal families used to extend or consolidate their influence. But the further back we introduce changes, the less plausible the consequent because our antecedent is likely to introduce other changes with unknown interaction effects and consequences. So for our purposes, a turning point should be considered contingent to the extent that it can be untracked by numerous, plausible counterfactuals which are minimal and close in time (see numbers 1 and 2 above).

5. How redundant is the turning point? Different causal paths have different implications for contingency. A turning point described by the simple, linear pathway of A B C (and only A B C) might be prevented by severing any link in the three step chain. If A and B are themselves the products of other chains of causation, there may be many possible ways of using minimal rewrite counterfactuals to prevent the turning point by preventing preconditions A and B. There are few turnings that are the outcomes of simple linear chains. Others are likely to have one or more paths leading to them. If we prevent A B C, the possibility G H C, and perhaps of M N C, remain. To prevent turning point C we need to know all the chains leading to it, and something about their probability. In situations of equifinality, where multiple paths lead to the same outcome, estimates of probability are likely to be complicated by interaction effects. The removal of any causal chain may significantly change the probability (in either direction) of other paths. Death is an extreme example of this phenomenon. If we eradicate child diseases or inoculate people against them, reduce the incidence of other infectious diseases through public health measures, and gain the upper hand in the struggles against heart disease and cancer, the likelihood of dying from other causes (e.g., accidents, stroke, kidney failure), including new ailments (e.g., HIV) will increase. One way or the other, the grim reaper will come for all of us.

Even multiple chains may be inadequate to capture the causal complexity of some of the events that have at times been identified as turning points. Another model to consider is confluence, where a stream of independent causal chains come together to make an outcome possible. A house goes up in smoke. Investigation reveals that the fire spread from a lighted candle that was left unattended on a window sill. The window was not completely sealed, and a draft blew one of the curtains close enough to the flame for it to catch fire. The smoke alarm connected to the house security system did not function because its battery was dead and the fire department failed to receive the timely warning that might have permitted it to save the dwelling. What caused the house to burn down? The candle was the source of the fire, but it would not have been lit or placed on the window sill if it had not been the holiday season and had its owners not been following a neighborhood custom. If the window had not been warped, or the insulation around it had provided a better seal, the candle would not have started a fire. If the owners had been home, or if smoke alarm had a charged battery, the house would not have burned down. No single factor was responsible for this disaster; it took a combination of them interacting in a particular way.[39]

However, some outcomes, like the fire in the house, requiring the confluence of many independent causes which could have been prevented or transformed in magnitude by removing or changing any one of them with a minimal rewrite are highly contingent. By contrast, other confluences may have multiple pathways that lead to them—and require multiple interventions to prevent. By way of illustrating this we can cite the fact that historians do not attribute Western industrialization to any single cause, but to complex interactions among a confluence of factors, most or all of which were necessary for this turning point. Their contingency would depend on how many minimal rewrites were necessary to halt or deflect each possible pathway.

6. What about second order counterfactuals? Up to this point we have tried to prevent, alter, or stall turning points. But we must also think about how they might come to pass despite our best efforts. Second order counterfactuals, either by themselves or in interaction with one another, might produce the turning point, or some variant of it at a later date. Ross Hassig reasons that, in some circumstances, Cortés’ defeat might have well just served as the catalyst for a renewed Spanish attempt at conquest. If in the interval disease had decimated the Aztec population, the Spanish might have easily succeeded the second time around, and the history of Meso-America might have evolved along strikingly similar lines.[40]

There are two other counterfactual routes to preventing turning points in the rise of the West. Enabling counterfactuals necessary to bring about the antecedent can be set in motion by a chain of events that leads to the turning point, as can events arising from the antecedent itself. A rigorous attempt to assess contingency compels us to work though these possible pathways in search of the most likely ways that turning points could still have come about. If secondary routes to turning points can be found, researchers need to find ways to stop them with additional counterfactuals. Roughly speaking, the more alternatives that are found, and the more likely they appear, the less contingent the turning point.

In this imaginary exercise, I have broken down the development and rise of the West into a set of smaller, more manageable problems through the use of turning points. By factoring our two big questions about the rise of the West in this way a more fine-grained analysis of key components of a causal chain is possible. When we work back to the larger picture, we confront the same set of problems we did with the individual turning points. There is no reason to suppose that Western civilization and its remarkable success in the modern era was the result of a single causal chain and could have been stopped by preventing any of its component turning points. It seems likely that outcomes so complex and with so many attributes were the result of multiple chains and obviously are at least in part equifinal.

The inescapable conclusion is that counterfactuals are like fractals. The defining characteristic of a fractal is that its structure is the same at every level of magnification. So it is with counterfactuals. Enabling counterfactuals, turning point counterfactuals, and the use of turning points to prevent a larger outcome involve the same set of problems and require the same set of procedures to address them. And like fractals, the chain of connections could be extended further (but not infinitely as in the case of fractals) in either the micro or macro direction. We could look at levels beneath enabling counterfactuals, or beyond the success of the West if we made it an antecedent to some other consequent.

Kasparov vs. Deep Blue

It is interesting to note that historical counterfactual research confronts two fundamental problems that, in engineering and the sciences, can often be solved or finessed. Unlike in these fields, in historical counterfactual thought experiments, there is no rigorous way to establish probability or to track reasonably the long-term consequences of counterfactuals. In the course of this article, I have made casual use of the concept of probability, largely for heuristic purposes. Probability is the frequency of a particular outcome when all outcomes are known. This can be determined logically, as in the case of a coin toss. If there are no imperfections in the coin and the height and trajectory of each toss varies randomly, the probability of either a head or a tail should be fifty percent. Probability can also be determined empirically; we can observe a large number of the same class of event and keep track of the frequency of different outcomes. If the sample is large enough, and the events fully comparable but independent, we can make a good estimate of the probability of any given outcome. Empirical tests of this kind can sometimes be carried out in laboratories, or in real world in the case of some kinds of iterative processes. Simulations are sometimes also possible. For better or worse, history is a one-time event. The tape of time cannot be rewound and run again and again. The best we can do is assess probability and contingency by means of counterfactual experimentation, and here we encounter a Catch-22. Estimates of contingency require some knowledge of the range of possible outcomes, real and counterfactual, and of the probability of each. But in history, probability cannot be measured. If we could form good estimates we would not need counterfactual experiments.

The protocols for counterfactual experimentation and those for assessing the contingency of turning points put extraordinary demands on historians. They must determine the best strategy for negating a turning point, and this involves consideration of numerous possible counterfactuals. Even the most promising counterfactuals may require additional, enabling counterfactuals, and researchers must then consider the most important consequences of all of these counterfactuals. They must also ask if the turning point could be produced by some other set of causal chains and, if so, find ways of preventing this from happening. They must then direct their attention to second order counterfactuals, and search for and untrack any that might lead to the turning point at some future time. Thorough execution of each of these tasks would make for more convincing counterfactuals but it is simply not feasible given the time and effort it would take.

In February 1996 and May 1997, world chess champion Gary Kasparov played two matches against Deep Blue, a bank of refrigerator-sized IBM SP 2 computers. Kasparov won the first match 4–2, but lost the second 3.5–2.5 in what was hailed as a dramatic victory for artificial intelligence. The idea of a chess playing machine dates back to the 1760s, when Wolfgang von Kempelen exhibited the Maezal Chess Automaton throughout Europe. His machine infuriated Napoleon when it beat him in nineteen moves. The emperor never guessed the nature of its mechanism: a diminutive Turkish chess master hidden in a cabinet inside who operated the turbaned and mustachioed marionette, who moved the pieces on the board above. Modern computers rely on elaborate algorithms to identify possible moves and the most likely responses of opponents, work through each line of play for a given number of turns, and evaluate all the outcomes to reach an informed choice.[41]

The principal advantage that all computers have over people is their awesome ability to crunch numbers. Deep Blue works through a billion positions a second and this is why it can explore so many variations over so many turns. Counterfactual research in history demands a search pattern similar to chess. Historians must identify the most promising “moves,” look at how reality might respond and how the interaction of counterfactuals and existing context might play out even beyond the hypothesized consequent. The game of counterfactuals may even be more complicated than chess. In the latter, two players engage in move and countermove. Each new move in the branching tree of analysis encompasses roughly thirty-eight times as many positions. In counterfactuals, there can be multiple interactions at every move, as antecedents, enabling counterfactuals, and the chains they set in motion interact with one another. In chess, the definition of a move is clear; each player moves a piece in turn. In counterfactuals, chains of consequence unfold simultaneously and continually.

Supercomputers are routinely used to conduct counterfactual simulations in the sciences. Until such time as the programmers of Deep Blue turn their attention to historical counterfactuals, however, historians must behave more like chess masters than computers. Gary Kasparov has the merest fraction of the processing speed and capability of the simplest computer, but beat Deep Blue in their first tournament and lost the second by only one game. The most challenging task in chess is determination of which of the multitudinous branching points are most worth examining because no computer can analyze them all. Deep Blue was an improvement on its predecessors and made use of more sophisticated tuning mechanisms to select promising lines of play. Human beings, especially chess masters, still have a considerable comparative advantage in this respect. They use their intuition and judgment to select one or two possible moves and project their likely consequences out to a limit of about eight turns ahead. At each turn, they are ruthless in eliminating possibilities, and thus stay within the limiting data processing capabilities of the human mind by tracking only a few chains of moves. The best computer algorithm is crude in comparison to the still uncanny human ability to zero in on promising lines of play.

Historians have no recourse but to follow the strategy of Gary Kasparov and substitute judgment for computing power. They can learn much about what really happened in history by using their imaginations to invent counterfactuals they think capable of preventing or adding turning points in historical chains of events. They must use their professional judgment to select a few chains of counterfactual interaction to analyze in detail and estimate the probabilities associated with each. In chess, there is a straight-forward way to estimate performance. Players either win, lose, or draw their games. In counterfactual research this is not possible. The best players can do is to be persuasive by making absolutely explicit the logic connecting antecedent and consequent and the assumptions on which all the chains of causation they consider are based. Such an exercise makes no pretense to be a science, only to harness human intelligence with the goal of making informed individual and collective judgments about interesting and important problems. This is no different from the claims made by more conventional forms of history.


1. See Raymond E. Wolfinger and Benjamin Highton, “Can More Efficient Purging Boost Turnout,” paper presented at the 1994 annual meeting of the American Political Science Association; Ruy A. Teixeira, The Disappearing American Voter (Washington, D.C.: Brookings Institution, 1992); Steven J. Rosenstone and John Mark Hansen, Mobilization, Participation, and Democracy in America (New York: Macmillan, 1993); Richard J. Timpone, “Past History Reverses: Counterfactuals and the Impact of Registration Reform on Participation and Representation,” unpublished paper.

2. According to A. J. P. Taylor, The Struggle for the Mastery in Europe, 1848–1918 (London: Oxford University Press, 1954), “a historian should never deal in speculation about what did not happen.” E. H. Carr, What is History? (London: Macmillan, 1961), 127; E. P. Thompson, The Poverty of Theory and Other Essays (New York: Monthly Review Press, 1978), 300. M. M. Postan writes: “The might-have beens of history are not a profitable subject of discussion,” quoted in J. D. Gould, “Hypothetical History,” Economic History Review, 2nd ser. 22 (August 1969), 195–207; see also David Hackett Fischer, Historians’ Fallacies (New York: Harper Colophon Books, 1970), 15–21; Peter McClelland, Casual Explanation and Model-Building in History, Economics, and the New Economic History (Ithaca: Cornell University Press, 1975).

3. Private communication to the author.

4. Yuen Foong Khong, “Confronting Hitler and Its Consequences,” in Counterfactual Thought Experiments in World Politics: Logical, Methodological, and Psychological Perspectives, ed. Philip E. Tetlock and Aaron Belkin (Princeton: Princeton University Press, 1996), 95–118.

5. Jay M. Winter, The Great War and the British People (London: Macmillan, 1986), 76–83.

6. Tin-bor Victoria Hui, Rethinking War, State Formation, and System Formation: A Historical Comparison of Ancient China (659–221 BC) and Early Modern Europe (1495–1815 AD), Ph. D. dissertation, Columbia University, 2000. See also R. Bin Wong, China Transformed: Historical Change and the Limits of the European Experience (Ithaca: Cornell University Press, 1997).

7. Kenneth Pomeranz, “China, Europe and Industrialization,” in Unmaking the West: “What-If” Scenarios that Rewrite World History, ed. Philip E. Tetlock, Richard Ned Lebow, and Geoffrey Parker (Ann Arbor: University of Michigan Press, 2006).

8. Jon Elster, Political Psychology (New York: Cambridge University Press, 1993), 5; Sidney Tarrow, “Expanding Paired Comparison: A Modest Proposal,” American Political Science Association, Comparative Politics Newsletter, (Summer 1999), 9–12; Doug McAdam, Sidney Tarrow and Charles Tilly, “Comparisons, Mechanisms and Episodes,” in Dynamics of Contention, forthcoming.

9. Richard Ned Lebow and Janice Gross Stein, We All Lost the Cold War (Princeton: Princeton University Press, 1994).

10. Mark Elvin, The Pattern of the Chinese Past: A Social and Economic Interpretation (Stanford: Stanford University Press, 1973).

11. E. H. Carr, Socialism in One Country, 1924–1926, 3 vols. (New York: Macmillan, 1958–1964), vol. 1, 151.

12. Lebow and Stein, We All Lost the Cold War, ch. 4 reviews this argument and the new evidence.

13. John R. Searle, The Construction of Social Reality (New York: Free Press, 1995).

14. Donald Davidson and Jaakko Hintikka, eds., Words and Objections. Essays on the Work of W. V. Quinei (Dordrecht, Holland: D. Reidel, 1969).

15. R. H. Tawney, The Agrarian Problem in the Sixteenth Century (London: Longmans, Green, and Co., 1912), 177.

16. Alexander Demandt, Der Fall Roms: die Auflosung des romischen Reiches im Urteil der Nachwelt (Munich, Germany: Beck, 1984), 695, found two hundred and ten causes for the fall of Rome in the historical literature since 1600.

17. Paul W. Schroeder, “World War I as Galloping Gertie: A Reply to Joachim Remak,” Journal of Modern History 44 (1972): 319–345, reasons: “The fact that so many plausible explanations for the outbreak of war have been advanced over the years indicates on the one hand that it was massively overdetermined.”

18. This point is also made by Philip E. Tetlock and Aaron Belkin, “Counterfactual Thought Experiments in World Politics: Logical, Methodological, and Psychological Perspectives,” in Tetlock and Belkin, Counterfactual Thought Experiments in World Politics, 15–16.

19. Baruch Fischoff, “Hindsight is not Equal to Foresight: The Effect of Outcome Knowledge on Judgment under Uncertainty,” Journal of Experimental Psychology: Human Perception and Performance 1, no.2 (1975): 288–99; S. A. Hawkins and R. Hastie, “Hindsight: Biased Judgments of Past Events after the Outcomes are Known,” Psychological Bulletin 107, no. 3 (1990): 311–27.

20. Philip E. Tetlock and Richard Ned Lebow, “Poking Counterfactual Holes in Covering Laws: Cognitive Styles and Political Learning,” American Political Science Review 95 (2001): 829–43.

21. George W. Breslauer, “Counterfactuals Reasoning in Western Studies of Soviet Politics and Foreign Relations,” in Tetlock and Belkin, Counterfactual Thought Experiments in World Politics, 69–94.

22. John Mueller, Retreat from Doomsday: The Obsolescence of Major War (New York: Basic Books, 1989).

23. Yuen Foong Khong, Analogies at War: Korea, Munich, Dien Bien Phu, and the Vietnam Decisions of 1965 (Princeton: Princeton University Press, 1992), for a strong statement of the former position with regard to historical analogies.

24. Alessandro Portelli, “Uchronic Dreams: Working-Class Memory and Possible Worlds,” in The Death of Luigi Trastulli and Other Stories: Form and Meaning in Oral History (Albany: State University of New York Press, 1991), 99–116.

25. Richard Ned Lebow, Unmaking the West and Richard Ned Lebow, “Contingency, Catalysts and International System Change,” Political Science Quarterly 115 (Winter 2000–01): 591–616.

26. John Elster, Logic and Society: Contradictions and Possible Worlds (New York: John Wiley, 1978); G. Hawthorn, Plausible Worlds: Possibility and Understanding in History and the Social Sciences (New York: Cambridge University Press, 1991), 31–60.

27. Tetlock and Belkin, Counterfactual Thought Experiments in World Politics (fn 23), p. 14.

28. Ludwig Dehio, The Precarious Balance: Four Centuries of the European Power Struggle (New York: Knopf, 1995), argues that competition among many independent units produced “fertile friction” among Greek city states and in modern Europe.

29. Newton reasoned that the energy reaching us from an individual star is E/r^2, where r is the distance of the star, and E is the average energy radiated by each star, and if the density (d) of stars in the universe is constant, the number of stars would be d r^3. The total energy produced by these stars would grow in a linear fashion with r, and rise to infinity in a infinite universe—neither we nor the earth would exist. Hence, the density of stars must decrease or the universe must be finite.

30. Andrew Marvell, “To His Coy Mistress,” in Andrew Marvell, ed. Hug MacDonald (London: Routledge & Kegan Paul, 1952), 21–22.

31. Francis Kaplan, ed., Les Pensées de Pascali (Paris: Les Éditions du Cerf, 1982), 209.

32. René de Goscinny and Albert de Uderzo, Astérix et Cleopatre (Neuilly-sur-Seine, France: Dargaud, 1965). Is it a coincidence that this publishing house is located at 12, rue Blaise-Pascal? The Turkish saying was brought to my attention by Prof. Orhan Tekelioglu of Bilkent University.

33. Richard Ned Lebow, “If Mozart Had Died at Your Age: Psychologic vs. Statistical Inference,” Political Psychology 27 (March 2006).

34. Cederman, “Rerunning History,” in Tetlock and Belkin, Counterfactual Experiments in World Politics, 253, 255, for this criticism of Mueller.

35. Parker, The Grand Strategy of Philip II, 281–96.

36. M. Maruyama, “The Second Cybernetics: Deviation-amplifying Mutual Causal Processes,” American Scientist 51, no. 2 (1963): 164–79, contends that the very essence of the “butterfly effect” is that it cannot be discovered. He offers the example of a city built on the American plains because the first white settler awoke on an especially beautiful morning and took it as a sign to put down his stakes here rather than somewhere else. The coincidence of weather and intent was unpredictable, and would be invisible as a cause to researchers a century later attempting to discover why the city grew up where it did.

37. Lebow, “Contingency, Catalysts and International System Change.”

38. Carl von Clausewitz, On War, trans. Michael Howard and Peter Paret (Princeton: Princeton University Press, 1976), 119–21.

39. J. L. Mackie, “Causes and Conditions,” in The Nature of Causation, ed. Myles Brand (Urbana: University of Illinois Press, 1976), 308–44; Roy Bhaskar, The Possibility of Naturalism: A Philosophical Critique of the Contemporary Human Science (Brighton: Harvester Press, 1979); Rom Harré and Peter Secord, The Explanation of Social Behaviour (Oxford: Basil Blackwell, 1973); Heikki Patomäki, “How to Tell Better Stories about World Politics,” European Journal of International Relations 2 (March 1996): 105–34.

40. Ross Hassig, “Over Cortés’s Dead Body: The Triumph of the Aztec Empire,” in Tetlock, Lebow, and Parker, Unmaking the West.

41. Feng-husing Hsu, Thomas Anantharaman, Murray Campbell, and Andrew Nowatzyk, “A Grandmaster Chess Machine,” Scientific American 263 (October 1990), 44–50; “The Deep Blue Team Plots Its Next Move,” available at <>, a web site that includes more articles, the games, and commentary on the play.

By: Richard Ned Lebow