2.1. Rational thought

Hypothetical thought has been studied in many guises and one good illustration is conditional reasoning. Conditionals such as “if Alicia went to the stables then she rode Starlight” have been considered to be the key to how people make suppositions and conjecture relationships between events (Johnson-Laird & Byrne Reference Johnson-Laird and Byrne1991). One view is that the human ability to think rationally about hypothetical situations and conditional relations rests on the capacity to imagine possibilities (Johnson-Laird Reference Johnson-Laird1983). There are several principles that guide the possibilities that people consider when they understand a conditional (Johnson-Laird & Byrne Reference Johnson-Laird and Byrne2002). The first principle is that people tend to think about true possibilities, such as “Alicia went to the stables and she rode Starlight,” but they do not think about false possibilities, such as “Alicia went to the stables and she did not ride Starlight.” The second principle is that initially people think about just a few of the possibilities. There are several possibilities that are consistent with the conditional, such as “Alicia did not go to the stables and she did not ride Starlight” and “Alicia did not go to the stables and she rode Starlight” (perhaps because the pony was in a nearby field). But usually people mentally represent the conditional by thinking about just a single true possibility. Multiple possibilities tend to exceed working memory capacity. Of course, knowledge can help people to think about more possibilities, it can help them to enrich those possibilities, and it can also eliminate possibilities (Johnson-Laird & Byrne Reference Johnson-Laird and Byrne2002).

People can readily make some inferences based on the possibilities they have kept in mind, but they find other inferences more difficult to make. Suppose you know “if Mark left at 9 a.m. then he caught the airplane” and you are told, “Mark left at 9 a.m.” What, if anything, do you think follows from these premises? Most people find it easy to make the modus ponens inference, “he caught the airplane.” They have understood the conditional by envisaging the single true possibility, “Mark left at 9 a.m. and he caught the airplane.” Now suppose you are told “Mark did not catch the airplane.” What, if anything, follows from this premise and the conditional? Many people say nothing follows. They have difficulty making the inference to the conclusion, “he did not leave at 9 a.m.” To make this modus tollens inference, they need to remember that there are alternative possibilities and they must think through what they are. As a result, most people find the modus ponens inference easier than the modus tollens one. On this account, people make mistakes, and can appear irrational because of the limits to the possibilities they can consider (Johnson-Laird & Byrne Reference Johnson-Laird and Byrne1991). But they are rational, at least in principle, because they possess an underlying competence to think of all the relevant possibilities so that they can search for counterexamples.

2.2. Rational thought and imaginative thought

My claim in the book is that the principles for rational thought also guide imaginative thought. I suggest that a bridge from rationality to imagination can be built on counterfactual conditionals. Conditionals yield a good example of deductive rationality; counterfactual thoughts are a good example of everyday imagination. Counterfactual conditionals combine both rational and imaginative elements. Counterfactuals are special. Consider a counterfactual conditional in the subjunctive mood, “if Oswald had not killed Kennedy then someone else would have.” It seems to mean something very different from a factual conditional in the indicative mood, “if Oswald did not kill Kennedy then someone else did” (Lewis Reference Lewis1973). Attempts to understand counterfactuals have led to important developments in linguistics (Athanasiadou & Dirven Reference Athanasiadou and Dirven1997), artificial intelligence (Ginsberg Reference Ginsberg1986), and philosophy (Lewis Reference Lewis1973). A counterfactual such as “if only he had been handsome, I would have married him” evokes two possibilities: an imagined possibility in which the man is handsome and the speaker marries him, and a reality in which the man was not and she did not. The way that people interpret such assertions goes beyond the simple truth of their components (Quine Reference Quine1972). A counterfactual seems to presuppose that its antecedent is false, and so, according to a simple truth functional account, every counterfactual must be true. But people judge some counterfactuals to be plausible and others to be implausible. Philosophers have suggested instead that the truth of a counterfactual may depend on its truth in a “possible world” (Stalnaker Reference Stalnaker and Rescher1968).

The critical psychological difference between factual and counterfactual conditionals may lie in the possibilities that people think about. Consider the conditional, “if Iraq had weapons of mass destruction then the war was justified.” It is consistent with several possibilities: Iraq had weapons of mass destruction and the war was justified; Iraq did not have weapons of mass destruction and the war was not justified; and Iraq did not have weapons of mass destruction and the war was justified (for other reasons). Most people mentally represent the factual conditional initially by thinking about just the single possibility that Iraq had weapons of mass destruction and the war was justified. Now consider the counterfactual conditional, “if Iraq had had weapons of mass destruction then the war would have been justified.” It is consistent with essentially the same possibilities as the factual conditional. You might have understood the counterfactual by thinking about the conjecture, Iraq had weapons of mass destruction and the war was justified. But, you might also have thought about the facts that the speaker uttering the counterfactual is likely to have presupposed, that Iraq did not have weapons of mass destruction and the war was not justified. In other words, you might have thought about more than one possibility when you understood the counterfactual. The factual and counterfactual conditionals are consistent with essentially the same possibilities but a key difference between them is that people think about different possibilities when they understand them. The difference between factual and counterfactual conditionals illustrates a third principle underlying the possibilities that people think about: some ideas require people to think about dual possibilities, as Table 1 shows.

Table 1.

Summary of principles that guide the possibilities that people envisage

Of course another critical difference between factual and counterfactual conditionals is that the possibilities correspond to the putative facts for the factual conditional, whereas they correspond not only to putative facts but also to counterfactual possibilities for the counterfactual conditional. People keep track of the status of different possibilities. They think about two possibilities when they understand a counterfactual conditional, and they note one as the “facts” and the other as “imagined” possibilities (Johnson-Laird & Byrne Reference Johnson-Laird and Byrne2002). A fourth principle is that even though people tend to keep in mind just true possibilities, they can think about what might have been because they can envisage possibilities that once were true but are so no longer. Often in everyday thoughts, people temporarily suppose something to be true even when they know it is false. They keep track of what is actually true and what is imagined. They can think about entirely imaginary situations, for example, to understand and create fantasy and fiction, in daydreams as well as in theatre, film, and literature. They can think about what is true in these imagined situations and what is false in them.

People tend to think about two possibilities for some ideas and this factor has significant consequences for how they imagine what might have been. It helps to explain why people mentally change only some aspects of their mental representation of reality. A basic principle of mutability is that an event can be readily changed if it brings to mind an alternative. For example, suppose you go to a concert and you sit in seat 426. You change seats after a while to seat 739 to get a better view. At the interval, an announcement is made that there is a prize of a trip around the world for the person seated in seat 426 (Johnson Reference Johnson1986). You may wish you had not changed seats. The prize seems to have been almost in your grasp. But suppose instead you had gone to the concert and you sat in seat 739 from the outset. At the interval, an announcement is made that there is a prize of a trip around the world for the person seated in seat 426. You may wish you had won, but you are unlikely to believe that the prize was almost in your grasp. In the first scenario, there is a ready-made alternative and people are influenced by the availability of alternatives. They may base their judgments on the ease with which instances can be brought to mind (Kahneman & Tversky Reference Kahneman, Tversky, Kahneman, Slovic and Tversky1982). The fifth principle is that people readily imagine a counterfactual alternative to a possibility if it is mentally represented from the outset with a second possibility. The possibility can be mutated easily; for example, it can be deleted from the mental representation and replaced with the second possibility as its counterfactual alternative.

The principles that guide the possibilities that people envisage when they reason help to explain how people imagine alternatives to reality. In Chapters 3 to 7 of The Rational Imagination I show how the application of these principles explains the regularities people exhibit in their imagination of counterfactual alternatives. I begin in Chapter 3 by showing how these principles explain why most people imagine counterfactual alternatives to an action more than to a failure to act in many situations.

3.1. Clues from reasoning: Counterfactual conditionals

A key principle is that people think about some ideas by keeping in mind two possibilities. The two possibilities they envisage affect the way people think in many situations; for example, the two possibilities affect the way they reason about counterfactual conditionals. Suppose you are told: “if Mark had left at 9 a.m. then he would have caught the airplane.” You may interpret the subjunctive conditional as a counterfactual and think initially about two possibilities: the conjecture, Mark left at 9 a.m. and he caught the airplane, and the presupposed facts, Mark did not leave at 9 a.m. and he did not catch the airplane. Suppose you then discover that Mark did not catch the airplane. What would you conclude? People are able to infer readily that Mark did not leave at 9 a.m. (Byrne & Tasso Reference Byrne and Tasso1999). The modus tollens inference is difficult to make from a factual conditional “if Mark left at 9 a.m. then he caught the airplane,” because people think about just a single possibility initially: Mark left at 9 a.m. and he caught the airplane. But as the theory predicts, the inference is easier to make from the counterfactual because of the enriched representation.

Suppose you discover that, in fact, Mark left at 9 a.m. What would you conclude from this premise and the counterfactual conditional? People are able to infer readily that Mark caught the airplane. These data for modus tollens and modus ponens support the suggestion that people think about both possibilities: the conjecture, Mark left at 9 a.m. and he caught the airplane, and also the presupposed facts, Mark did not leave at 9 a.m. and he did not catch the airplane. The evidence that people understand counterfactual conditionals by keeping in mind two possibilities provides an important clue to solve the puzzle of why people imagine counterfactual alternatives to their actions more than their inactions.

3.2. The rational imagination: Why people imagine alternatives to actions

People think about two possibilities when they understand an action. When you understand the decision to act you think about the situation before the action and the situation after the action. Consider the scenario in which two individuals, Mary and Laura, consider their stock options. Mary owns shares in company A. During the past year she considered switching to stock in company B, but she decided against it. She now finds out that she would have been better off by $1,000 if she had switched to the stock of company B. Laura owned shares in company B. During the past year she switched to stock in company A. She now finds out that she would have been better off by $1,000 if she had kept her stock in company B (Kahneman & Tversky Reference Kahneman, Tversky, Kahneman, Slovic and Tversky1982). When people think about Laura's action they think about both the pre-action situation, Laura owned shares in company B, and the post-action situation, Laura owns shares in company A:

However, when they think about Mary's inaction, they think only about one situation – the shares that she owns in company A:

They do not need to think about two possibilities for an inaction – the situation before the decision and the situation after the decision – because these two situations are the same. An important corollary to the principles that guide the possibilities that people think about is that people keep in mind two possibilities when they understand an action. Inactions are mentally represented more economically than actions (Byrne & McEleney Reference Byrne and McEleney2000). This difference may underlie the perception that actions are a departure from the status quo (Kahneman & Miller Reference Kahneman and Miller1986). Because people envisage more information for actions than for inactions, they can mentally change actions more easily than inactions.

Intriguingly, in certain circumstances people imagine a counterfactual alternative to an inaction. People usually think about a single state of affairs when they understand an inaction. But, of course, they can switch from thinking about one possibility to thinking about two possibilities. In The Rational Imagination I consider several ways in which this switch to thinking about two possibilities for an inaction occurs. For example, people think about two possibilities to mentally represent a failure to act when they know that there were good reasons to act (Zeelenberg et al. Reference Zeelenberg, van der Bos, van Dijk and Pieters2002; Zhang et al. Reference Zhang, Bonnefon and Deng2004). They also think about two possibilities when they consider the consequences of a failure to act from a long-term perspective (Gilovich & Medvec Reference Gilovich and Medvec1995). When most people look back over their lives, it is their inactions that they tend to regret, the things they failed to do, such as failing to spend time with family and friends, failing to avail of educational opportunities, or failing to pursue hobbies. I outline in the book how people switch to thinking “if only” about a failure to act from a long-term perspective when they can imagine a better outcome (e.g., if he had switched to a different college, he would have been happy), compared to the outcome they imagine when they think “if only” about an action (e.g., if he had stayed in his original college, he would have remained unhappy) (Byrne & McEleney Reference Byrne and McEleney2000). People can think of the good that may have resulted had more time been spent with family and friends, had educational opportunities been availed of, or had hobbies been pursued. In these situations, if only the person had acted, a better outcome might have occurred than the outcome that did in fact occur. A second corollary to the principles that guide the possibilities that people think about is that people can switch from thinking about one possibility to thinking about two possibilities in some circumstances. The impact of an imagined better outcome is illustrated in the example of Jane who went to a travel agency to look for holidays in the Caribbean. There was a wonderful package deal at a very affordable price. She wondered whether to book it immediately but she decided to think about it overnight. The next day when she returned to the travel agency the holiday had been sold and there were no other deals that looked as attractive. Jane is likely to regret her inaction. If she had acted, she would have been able to go on a fabulous holiday.

People tend to focus on actions when they think about what could have happened. Even more strikingly, they tend to focus on forbidden actions. In Chapter 4 of The Rational Imagination, I offer an account of how people think about what should have happened and what should not have happened.

4.1. Clues from reasoning: Inferences about obligations

Knowledge of a regulation – for example, “hard-hats must be worn on the building site” – ensures that most people think about not only what is obligatory, such as wearing a hard hat, but also what is not permissible, such as not wearing a hard hat. A sixth principle about the possibilities that people envisage is that they think about the forbidden possibility as well as the permitted possibility when they understand an obligation. For the obligation, “if Jack's parents are elderly, he should look after them,” people keep in mind two possibilities: (1) Jack's parents are elderly and he looks after them, and (2) Jack's parents are elderly and he does not look after them. They note that the status of this second possibility is that it is forbidden. People usually think about true possibilities. Even when they understand a counterfactual conjecture that contradicts known facts, they may temporarily suppose the conjecture to be true. But obligations are different. Their understanding requires people to think about a forbidden possibility. Obligations are unique in that they require people to consider the possibility that is explicitly ruled out by the conditional. The forbidden possibility influences the inferences they make and the counterfactual alternatives they imagine.

Most people reason well about obligations (Bucciarelli & Johnson-Laird Reference Bucciarelli and Johnson-Laird2005; Cheng & Holyoak Reference Cheng and Holyoak1985; Cosmides Reference Cosmides1989; Sperber et al. Reference Sperber, Cara and Girotto1995). Because people think about the permitted possibility and the forbidden possibility, they can make certain inferences readily. When reasoners are told “if Paul rides a motorbike, he must wear a helmet,” and are also told that “Paul is not wearing a helmet,” they can infer that Paul is not permitted to ride a motorbike. In other words, they readily make the otherwise difficult modus tollens inference from a conditional with obligation content. The ease with which they make the inference highlights an important feature of reasoning. There is more than one way to make an inference. A common route to making the modus tollens inference is by thinking about the true possibilities, as we have seen earlier. But reasoning about obligations illustrates a second route for the inference, by thinking about what is forbidden. For the conditional, “if Paul rides his motorbike, he must wear a helmet,” people think about two possibilities: (1) Paul rides his motorbike and he wears a helmet, and (2) Paul rides his motorbike and he does not wear a helmet (forbidden). When they are told that Paul did not wear a helmet, they can match this information to the forbidden possibility, and infer that it is forbidden for him to ride his motorbike. The theory accurately predicts that people can make more modus tollens inferences from obligation conditionals compared to conditionals with other sorts of content (Quelhas & Byrne Reference Quelhas and Byrne2003).

Counterfactual obligations communicate, through shared knowledge or context, information about what was once obligatory and what was once forbidden; and they also communicate that what was once unacceptable is no longer so. Suppose, for example, that it used to be obligatory to pay a property tax on houses which increased with increasing house size, but that the tax was abolished some years ago. Suppose your friend buys a large house. You might say, “if you had bought that house 10 years ago, you would have had to pay a very large tax bill.” For a counterfactual obligation, people may think about one of the permitted possibilities conjectured by the counterfactual: your friend bought the house 10 years ago and paid a large tax bill. They may also think about the forbidden possibility: your friend bought the house 10 years ago and did not pay a large tax bill. And they may also think about the presupposed facts: your friend did not buy the house 10 years ago and did not pay a large tax bill. These insights from how people reason about obligations and forbidden events help to explain why people are drawn to forbidden events when they imagine counterfactual alternatives.

4.2. The rational imagination: Why people focus on forbidden fruit

When you learn that manufacturers in Europe must identify genetically modified constituents in food, you understand what is forbidden: they are not allowed to conceal genetically modified constituents. When you know that scientists are obliged to restrict cloning attempts to nonhuman species, you understand what is forbidden: they are not allowed to clone humans. A conditional obligation is understood by thinking about one of the permitted possibilities, and also what is forbidden. This ready access to the forbidden possibility has a large impact on how people imagine events turning out differently.

People keep in mind both the permitted possibility and the forbidden possibility, and so they can readily imagine a counterfactual alternative to the forbidden possibility. Steven, who did not return home in time to save his wife, is judged to say “if only …” most often about his decision to visit a bar for a drink. A third corollary to the principles that guide the possibilities that people think about is that they envisage two possibilities when they understand controllable events, as Table 2 shows. People imagine alternatives to socially unacceptable actions, such as stopping at a bar for a beer in the context of an ill spouse waiting at home, because they think about two possibilities – stopping for a beer and not stopping for a beer – and they note that one of the possibilities is unacceptable (stopping for a beer), and the other is acceptable (not stopping for a beer). They imagine an alternative by mentally changing the unacceptable possibility and they say, “if only Steven had not stopped for a beer …” The unacceptable possibility brings to mind its acceptable counterpart, just as an event that is exceptional for an individual brings to mind its normal counterpart (Kahneman & Miller Reference Kahneman and Miller1986).

Table 2.

Summary of some corollaries to the principles that guide the possibilities that people think about when they imagine counterfactual alternatives

If you do what you should do socially, people do not tend to wish you had not done it. Consider a situation in which a friend of yours, Bernard, is disappointed: he had an important performance at a concert in front of thousands of people and it was not well received. You know he stayed out late at a pre-concert party the night before, something he rarely does. He tells you he went to the party because he wanted to meet one of his orchestral heroes. You may believe that his poor performance was his own fault and he should not have gone to the party (Klauer et al. Reference Klauer, Jacobsen and Migulla1995). But suppose, instead, your friend tells you he went to the party because it was a fund-raiser for his orchestra. You understand his obligation by keeping in mind two possibilities: “he went to the party” is acceptable in this case, and “he did not go to the party” is unacceptable. Would you think he should not have gone to the party? Would you think his poor performance was his own fault? When participants described Bernard's thoughts, they generated reliably fewer “if only …” sentence completions that focused on the party when they were told he was obliged to go to it, compared to when they were not given a reason (Walsh & Byrne 2007).

Some theorists believe that the ease with which people reason about certain permissions or obligations shows that the mind evolved to store knowledge about social regulations in specialised modules (Cosmides Reference Cosmides1989). The modules contain rules that are specific to reasoning about certain content, such as the domains of obligation and permission (Cheng & Holyoak Reference Cheng and Holyoak1985), and they are operated on by specialised procedures (Gigerenzer & Hug Reference Gigerenzer and Hug1992). An alternative view is that people reason about permissions and obligations rather than give fixed responses to them (Sperber & Girotto Reference Sperber, Girotto, Fitness and Sterelny2003). Their reasoning depends on their ability to think about permitted possibilities and especially about possibilities that are forbidden. Human beings evolved but it is not known yet which aspects of the brain resulted from selective pressures. In Chapter 4, I suggest that what evolved is the ability to understand obligations by thinking about not only the permitted possibility but also the forbidden possibility.

People tend to focus on controllable actions, especially controllable actions that are socially unacceptable. But intriguingly, people often imagine a counterfactual alternative to a controllable event even when the controllable event was not the cause of the outcome. In Chapter 5 of The Rational Imagination I explore the vagaries in the relationship between causal and counterfactual thoughts.

5.1. The causal chicken and the counterfactual egg

Causal thoughts can influence the counterfactual alternatives that people imagine. Causal knowledge affects judgments about the plausibility of a counterfactual speculation. Experts committed to a causal law perceive less “wiggle room for re-writing history” (Tetlock & Lebow Reference Tetlock and Lebow2001, p. 838). And the relation is reciprocal: People sometimes imagine counterfactual alternatives to help them to work out causal relations. Consider for example, what caused the rise of the West? If Islamic armies had conquered France and Italy in the 8th century, would later European development have been side-tracked? Such counterfactual thoughts are an essential ingredient in historical reasoning, even if they are considered controversial (Tetlock & Lebow Reference Tetlock and Lebow2001).

The counterfactual thought that if an antecedent had not happened, then the outcome would not have happened, increases the judgment that the antecedent has a causal relation to the outcome. Consider a taxi driver who refused to give a couple a lift and the couple were subsequently killed in an accident in their own car as they drove across a bridge that collapsed (Wells & Gavanski Reference Wells and Gavanski1989). Most people judge the driver's decision not to give the couple a lift to have had some causal role in the couple's death when they are told that the taxi driver crossed the bridge safely. But they tend to judge the driver's decision to have had little causal role when they are told that he was also killed as he drove across the collapsing bridge. When the driver was also killed, they cannot say “if only he had given them a lift, they would still be alive” (Wells & Gavanski Reference Wells and Gavanski1989). Causal thoughts can influence counterfactual thoughts, and vice versa. But causal thoughts and counterfactual thoughts can diverge. An important clue to explain why people imagine counterfactual alternatives to events within their control, even though they know these events were not the cause of the outcome, comes from the study of different sorts of causal relations.

5.2. Clues from reasoning: Strong causal and enabling relations

The observation that people sometimes focus on different events in their counterfactual and causal thoughts can be explained by the possibilities that people think about. The explanation has two main components. The first part of the explanation as to why the focus of counterfactual and causal thoughts differs is that people mentally represent a causal claim and a counterfactual one by thinking about different possibilities. A causal claim can be readily paraphrased as a counterfactual; for example, “Heating the water to 100 degrees centigrade caused it to boil” can be paraphrased by “if the water had not been heated to 100 degrees centigrade it would not have boiled.” Many philosophers have supposed that to think counterfactually is to think causally (Hume Reference Hume, Norton and Norton1739/2000; Mill Reference Mill1872/1956). The strong causal relation is consistent with the possibility, “water was heated to 100 degrees and it boiled,” as well as the possibility, “water was not heated to 100 degrees and it did not boil.” The counterfactual is consistent with the same two possibilities. However, people mentally represent a causal relation and a counterfactual in different ways. For example, they keep in mind just a single possibility initially when they understand the strong causal relation. But they keep in mind both possibilities when they understand the counterfactual, one corresponding to the conjecture and the other to the presupposed facts. As a result, the counterfactual makes more information readily available to them from the outset than does the causal assertion.

The second part of the explanation for why the focus of counterfactual and causal thoughts differs is that there are different sorts of causes and people think about different possibilities when they understand them. A strong causal relation, such as the one about water boiling, is consistent with two possibilities – although people initially think about just one of them (Goldvarg & Johnson-Laird Reference Goldvarg and Johnson-Laird2001). An enabling relation, such as “dry leaves made it possible for the forest fire to spread” is consistent with three possibilities: “dry leaves and the forest fire,” “no dry leaves and no forest fire,” and “dry leaves and no forest fire” (Goldvarg & Johnson-Laird Reference Goldvarg and Johnson-Laird2001). People can distinguish between strong causal relations and enabling relations (Cheng Reference Cheng1997; Goldvarg & Johnson-Laird Reference Goldvarg and Johnson-Laird2001). Moreover, they make different inferences from strong causal relations and enabling relations (Byrne et al. Reference Byrne, Espino and Santamaria1999).

People mentally represent the enabling relation by initially thinking about the possibility, “dry leaves and the forest fire,” and they can readily access a second possibility, “no dry leaves and no forest fire.” An important corollary to the principles that guide the possibilities people consider is that they think about a single possibility when they understand a strong causal relation; they are able to think readily about a second possibility when they understand an enabling relation. This second possibility provides a ready-made counterfactual alternative. They can imagine the situation turning out differently if the enabling condition had not occurred. Consequently, people tend to focus more often on enabling relations than on strong causal relations in their counterfactual thoughts.

5.3. The rational imagination: Why counterfactual and causal thoughts differ

The clue from reasoning about causes that helps solve the puzzle is the crucial distinction between a strong causal relation and an enabling relation. Counterfactual thoughts often focus on enabling conditions, for example, “if only I had taken a different route home, I would not have had the crash,” whereas causal thoughts often focus on strong causes, for example, “the drunk driver caused the crash.” Causes can seem immutable because people keep in mind just a single possibility. Enabling conditions seem mutable because they require people to think about two possibilities. Enablers can be mentally deleted from an imagined alternative – dry leaves removed, alternative routes home taken, airport security improved. Wishing that whatever could have been done had been done to prevent the outcome or promote a better one may be a plausible alternative.

It is easier to think about one possibility than about several possibilities. The theory predicts that people should produce more causal thoughts than counterfactual thoughts, because they mentally represent a strong causal relation by thinking about a single possibility, and they mentally represent a counterfactual by thinking about two possibilities. The data support the hypothesis: Most people tend to think spontaneously more often about why a situation turned out the way it did, than about how it might have turned out differently (McEleney & Byrne Reference McEleney and Byrne2006). Further support comes from the observation that causal assertions are made earlier by children than counterfactual assertions (Harris Reference Harris2000). An important development of childhood cognition is the ability to keep more information in working memory (Oakhill & Johnson-Laird Reference Oakhill and Johnson-Laird1985). As a result, children should be able to think about a strong causal relation, for which they need think about only a single possibility, before they can imagine a counterfactual alternative, for which they must think about two possibilities. Two-year-olds can engage in pretend play, for example, they can climb into a large brown box and pretend it is a boat at sea (Riggs & Peterson Reference Riggs, Peterson, Mitchell and Riggs2000). Counterfactual thinking is similar to pretence but it requires a comparison of the facts with the imagined alternative (Harris Reference Harris2000). By age 2 or 3 years, children can use “nearly” and “almost” (Harris et al. Reference Harris, German and Mills1996). By age 3 or 4 years, they can answer questions about what should have been done so that a bad outcome would not have happened (Laura should have used the pencil so her fingers would not have got ink on them). Children are able to make hypothetical inferences, for example, “If I draw on this piece of paper, which box will it go in?” (in a situation in which blank sheets go in a different box from used sheets), before they can make counterfactual inferences such as “If I had not drawn on the paper, which box would it go in?” (Riggs et al. Reference Riggs, Peterson, Robinson and Mitchell1998).

When people imagine how an outcome could have turned out differently, their “if only …” thoughts about an antecedent increase their judgment that it is causally related to the outcome. Intriguingly, when they imagine how the outcome might have turned out the same, their “even if …” thoughts about the antecedent decrease their judgment that it is causally related to the outcome. I address this other side of the causal coin in Chapter 6 of The Rational Imagination.

6.1. Clues from reasoning: “Even if …” conditionals and inferences

People think about a semi-factual conditional such as, “even if the airplane crash victim had made it to the village, he still would have died” by thinking initially about two possibilities. They envisage the conjecture, “he made it to the village and he died” and the presupposed facts, “he did not make it to the village and he died.” A corollary to the principles that guide the possibilities that people think about is that they mentally represent an “even if …” conditional by thinking about two possibilities, one in which the antecedent and the outcome both occur, and one in which the antecedent does not occur but the outcome occurs.

There is clear evidence that people think about two possibilities when they understand a semi-factual “even if …” conditional. A semi-factual conditional such as “even if there had been lilies there would still have been roses” primes you to read the conjunction “there were no lilies and there were roses” very rapidly. You understand the semi-factual by mentally representing two possibilities from the outset: “there were lilies and there were roses” and “there were no lilies and there were roses” When you are subsequently told that in fact “there were no lilies and there were roses” you can process this information rapidly. It matches one of the possibilities you have thought about from the outset. The theory accurately predicts that people are able to read the conjunction “there were no lilies and there were roses” more quickly after they have understood an “even if” conditional compared to after they have understood a factual “if” conditional (Santamaria et al. Reference Santamaria, Espino and Byrne2005; See also Moreno-Rios et al., in press). The evidence shows that people understand semi-factual conditionals by keeping in mind two possibilities, one in which the antecedent and outcome both occur and one in which the antecedent does not occur but the outcome occurs. It provides an important clue to solve the puzzle of why people do not tend to think an antecedent caused the outcome when they can imagine a semi-factual alternative.

6.2. The rational imagination: Imagined semi-factuals and causality

Consider a scenario about a runner competing in the Olympics (based on Boninger et al. Reference Boninger, Gleicher and Strathman1994):

In the days after the race the runner thought “even if …” How do you think she completed this thought? People completed the “even if …” sentence by saying, for example, “even if I had taken the newer drug, I still would have lost the race.” They think about two possibilities: the conjecture, “she took the newer drug and she lost the race,” and the presupposed facts, “she did not take the newer drug and she lost the race.” To what extent do you think the runner's decision to take the older well-known drug led to her failure to obtain an Olympic medal in the 400 metre race? In The Rational Imagination I propose that the two possibilities imagined for the semi-factual alternative emphasize that the antecedent, taking the well-known drug, was not necessary for the outcome. They correspond to the possibilities that people consider initially for a weak causal relation. The theory accurately predicts that judgments of the strength of the causal relation between the antecedent and the outcome are weaker when people imagine a semi-factual alternative (McCloy & Byrne Reference McCloy and Byrne2002).

When people imagine an alternative to reality in which the outcome turns out the same even though they acted differently, the outcome can seem inevitable (Sanna et al. Reference Sanna, Schwarz and Stocker2002b). The idea that an outcome was inevitable can be comforting and can even appear to absolve people of blame and responsibility. Some religions and cultures value the related ideas of fate and destiny. Given that the ideas of individual progress and perfection gained currency just a few hundred years ago, we can speculate that our ancestors may not have been so inclined to perceive fault-lines in reality and to imagine alternatives that are better than reality. In Chapter 7 of The Rational Imagination I consider one last perceived fault-line of reality. I examine the tendency people show to imagine alternatives in which they change the last event in a simple sequence of events.

7.1. Clues from reasoning: The case of “only if” conditionals

People think about possibilities in a way that preserves a record of the temporal order of the events in the world. Consider an “only if” conditional “Alicia went swimming only if she slept well.” You may be surprised to find that an “if” conditional, such as “if Alicia went swimming, she slept well,” and an “only if” conditional, such as “Alicia went swimming only if she slept well,” are usually logically equivalent. The equivalence can be illustrated by thinking about what possibility is ruled out by “Alicia went swimming only if she slept well.” Most people judge accurately that it rules out the possibility that Alicia went swimming and she did not sleep well, which is the same possibility ruled out by the “if” conditional (Jeffrey Reference Jeffrey1981). But the two conditionals are not psychologically equivalent (Evans Reference Evans1977). When you know that “Alicia went swimming only if she slept well,” which event do you believe occurs first, Alicia went swimming, or, she slept well? The “only if” conditional seems to work best when its second clause, “Alicia slept well,” refers to a state of affairs that holds prior to the state referred to in its first clause, “Alicia went swimming” (Marcus & Rips Reference Marcus and Rips1979).

People make different inferences from “only if” and “if” conditionals. Suppose you know that “Alicia went swimming only if she slept well” and then you find out that “Alicia did not sleep well.” What would you conclude? Many people conclude readily that, “Alicia did not go swimming.” The modus tollens inference, which is difficult to make from an “if” conditional, is made readily from the “only if” conditional. Why is the inference so easy from the “only if” conditional? The answer is that “only if” requires people to think about more possibilities from the outset than “if” (Johnson-Laird & Byrne Reference Johnson-Laird and Byrne1989). People understand “Alicia went swimming only if she slept well” by thinking about the possibility in which both events occurred and they also think about the possibility in which neither event occurred. As a result, they can readily make the inference. But there is more to the mental representation of “only if” than keeping in mind two possibilities.

Temporal information is conveyed implicitly by many “only if” conditionals, such as “Alicia went swimming only if she slept well.” People understand the order in which the events occurred in the world and so they think about the possibility “Alicia sleeps well and she goes swimming” rather than the opposite order, “Alicia goes swimming and she sleeps well.” Likewise, they think about the second possibility “Alicia does not sleep well and she does not go swimming.” When they read an “only if” conditional, “A only if B,” they are primed to read quickly the conjunction, “B and A” (with the clauses in the reversed order of mention to their order in the “only if” conditional). They are also primed to read quickly the conjunction “not-B and not-A.” They read “not-B and not-A” reliably faster after they read “A only if B” compared to “if A, then B.” The result supports the view that people think about two possibilities when they understand “only if.” Equally tellingly, they do not read “A and B” more quickly after they read “A only if B” compared to “if A then B” (Santamaría & Espino Reference Santamaria and Espino2002). A seventh principle about the possibilities people consider is that the possibilities encode the temporal order of events in the world. The evidence shows that people understand “only if” conditionals by keeping in mind two possibilities which preserve the temporal order of the events in the world. It provides an important clue to solve the puzzle of why people imagine a counterfactual alternative that changes the most recent event in a sequence of events.

7.2. The rational imagination: Why people change recent events

In the coin toss game in which Lisa tossed heads and Jenny tossed tails, most people believe the players could have won if only Jenny had tossed heads. There are three counterfactual possibilities for this game but people tend to think about just one of them, the possibility that “Lisa tossed heads and Jenny tossed heads and they win.” They do not think about the possibility that “Lisa tossed tails and Jenny tossed heads and they lose” because it is not an effective counterfactual alternative; that is, it does not change the outcome (Byrne Reference Byrne and Medin1997). But why do they not think about the possibility, “Lisa tossed tails and Jenny tossed tails and they win?” The answer lies in the final corollary to the principles of possibilities: people encode the first part of a possibility as immutable. When they imagine a counterfactual alternative to the coin toss, they hold constant the first player's selection, “Lisa tossed heads,” and they change the second player's selection, “Jenny tossed tails.” The first player's selection is presupposed (Miller & Gunasegaram Reference Miller and Gunasegaram1990). It provides the background against which later events are perceived (Sherman & McConnell Reference Sherman and McConnell1996).

Suppose you wanted a computer program to behave like a person who participated in the coin toss game. The program must generate the same sorts of counterfactual alternatives as people do and so it must focus on the most recent event. To carry out the task in the way that the theory proposes people do, the program needs to keep a record of possibilities and make changes to them. A computer program written in the programming language LISP to simulate the theory takes as input a description of the coin toss game, “if the two coins are of the same face (both heads or both tails), each player wins $1,000” (Walsh & Byrne Reference Walsh and Byrne2004). It produces as output a counterfactual about how the events could have turned out differently: “if Jenny had tossed heads, they would have won.” The program makes a record of the facts described in the story, “Lisa tossed heads and Jenny tossed tails and they both lost.” It also makes a record of the set of counterfactual possibilities suggested by the story, that is, the possibilities in which the players would have won. The program compares its record of the facts to the two possibilities in which the players would have won. It generates a counterfactual alternative by changing parts of its record of the facts to be like parts of its record of the possibilities in which the players would have won. The program relies on a simple algorithm based on the key principle: Because Lisa is the first player mentioned in the facts, her selection is the anchor and it is held constant.

People do not readily think of an alternative to an anchored idea. But just as people can sometimes switch to thinking about two possibilities in situations in which they usually think about a single possibility, so too an anchored idea can be transformed into a more mutable one. The theory predicts that people should be able to imagine a counterfactual alternative even to an anchor such as the first player's selection, when they have thought about two possibilities rather than a single possibility. Imagine a television game show based on the coin toss game in which a technical hitch occurs:

The first event, Lisa tosses heads, is the anchor but the technical hitch provides an alternative to it: Lisa tosses tails. People think about two possibilities, the pre-hitch and post-hitch plays. They can imagine a counterfactual alternative in which they mentally change the first event. The theory accurately predicts that people say, “if only Lisa had tossed heads” as often as “if only Jenny had tossed tails” (Byrne et al. Reference Byrne, Segura, Culhane, Tasso and Berrocal2000).

The idea of a “last chance” is a powerful one. When people try to understand why someone carried out a shocking act, such as a school massacre, they often focus on the events that occurred immediately before it. Their focus reflects the belief that the bad outcome was precipitated by the event that immediately preceded it.

In Chapters 3 to 7 of The Rational Imagination I explain the perceived fault-lines of reality that people focus on in their imagination of counterfactual alternatives, such as actions, forbidden actions, strong and weak causes and enabling conditions, and recent events. The explanation depends on the idea that people think about possibilities, and the possibilities they think about are guided by a set of principles. In the penultimate chapter, Chapter 8, I consider some implications of this view of the imagination.

8.1. Individual differences in imaginative thoughts

Cognitive differences underlie many differences between individuals in thinking and reasoning (Sternberg Reference Sternberg1997). People may create different counterfactual alternatives because of differences in their ability to think about possibilities of various sorts (Barrouillet & Lecas Reference Barrouillet and Lecas1999; Torrens et al. Reference Torrens, Thompson and Cramer1999). Some individuals may tend to focus more on the facts and others on the imagined possibility. For example, what two shapes do you think would best fit the counterfactual, “if there had been a circle on the blackboard then there would have been a triangle?” People consider two possibilities when they understand the counterfactual, the imagined possibility of a circle and a triangle, and the presupposed facts of no circle and no triangle. The theory accurately predicts that people are torn between these two possibilities (Byrne & Tasso Reference Byrne and Tasso1999). Some people say that the two shapes that would best fit the counterfactual are the circle and the triangle, whereas others say that the best two shapes would be shapes that are not the circle or the triangle. People were similarly torn when their task was to say what two shapes would definitely go against the description.

There may be even more fundamental differences in the way different individuals interpret counterfactuals (Thompson & Byrne Reference Thompson and Byrne2002). A minority of individuals seem to think about just a single possibility. About three-quarters of participants envisaged two possibilities when they understood a counterfactual such as “if Mark had gone to Moose Jaw then Karl would have gone to Medicine Hat.” They thought about the conjecture, “Mark went to Moose Jaw and Karl went to Medicine Hat,” and they also thought about the presupposed facts, “Mark did not go to Moose Jaw and Karl did not go to Medicine Hat.” We established that they thought about these two possibilities by their answers to two tasks. First, when these individuals judged what someone who uttered the counterfactual meant to imply, they interpreted the intended implication as: “Mark did not go to Moose Jaw” or “Karl did not go to Medicine Hat,” or both. Second, when they judged whether different situations were consistent or inconsistent with the counterfactual, they judged the situation, “Mark went to Moose Jaw and Karl went to Medicine Hat” to be consistent with it.

In contrast, about one-quarter of participants focused on a single possibility: the facts, “Mark did not go to Moose Jaw and Karl did not go to Medicine Hat.” First, when these individuals were asked what someone who uttered the counterfactual meant to imply, they judged the person meant to imply that “Mark did not go to Moose Jaw” or “Karl did not go to Medicine Hat,” or both – like the first group. But, unlike the first group, when they were asked to judge whether different situations were consistent or inconsistent with the counterfactual, this second group judged the situation “Mark went to Moose Jaw and Karl went to Medicine Hat” to be inconsistent with the counterfactual. Importantly, the two groups reasoned differently. For example, the single-possibility group who understood the counterfactual by thinking about just the single possibility, “Mark did not go to Moose Jaw and Karl did not go to Medicine Hat,” tended not to make the modus ponens inference from “Mark went to Moose Jaw” to “therefore, Karl went to Medicine Hat.” These differences in the imagination of possibilities may have consequences for the impact of counterfactual thoughts. Someone who understands a counterfactual “if Bert had driven fast, he would have been injured,” by thinking only about the facts “Bert was not driving fast and he was not injured” may not benefit from the preparatory effects of the counterfactual alternative (Bert should not drive fast in the future). They also may not gain any solace from its emotional amplification (Bert feels relieved at his lucky escape this time).

8.2. Creative thoughts

My interest in The Rational Imagination is in the creation of counterfactual alternatives to reality. But an understanding of the counterfactual imagination may have implications for understanding other sorts of creative thoughts. Creative thoughts are relied upon to write a poem, paint a picture, compose a piece of music, design an experiment, or invent a new product. These sorts of activities can seem very different from the imagination of a counterfactual alternative to reality. But counterfactual imaginative thoughts may share some similarities with other sorts of creative thoughts, such as category expansion, concept combination, and insight.

One sort of creative thought is inventing new instances of a category, such as designing a new coffee mug, a better car, or a fashionable “new look.” Take a moment to imagine a new alien life form. The results are typically diverse, from the giant plants in “The day of the triffids,” to the fluid metal of the robots in “Terminator 2.” When people draw a creature from a planet somewhere else in the universe, their drawings differ very widely (Ward et al. Reference Ward, Patterson and Sifonis2004). But they also show some very informative regularities. For example, people tended to make sure that their alien creature had sensory organs, most commonly eyes, and functional appendages, most commonly legs. People may think of possibilities corresponding to true instances of the category, and they may not think about possibilities that are not instances of the category. They may imagine an alternative creature by making a minimal change to their representation of the exemplar they have in mind. They can readily think of alternative possibilities for the size, shape, and color of creatures; for example, known birds come in many different sizes. They may be able mentally to alter these aspects of the category more readily than other aspects. They may think of just a single possibility to mentally represent other aspects, such as the presence of the sensory organ of eyes. These aspects of reality seem immutable because people do not mentally represent them from the outset by thinking about alternative possibilities.

A second sort of creative thought is concept combination. One way that people come up with new ideas is by combining several existing concepts to form a new one. Suppose you hear for the first time the combination “corn oil.” What do you think it means? You may decide it is oil made from corn. Now imagine you hear for the first time, “baby oil.” What does it mean? You are unlikely to decide it is oil made from babies. It is more likely you will conclude it is oil to rub on babies' skin. Now, what is “lamp oil?” It is unlikely you will say it is oil made from lamps, or oil to rub on lamps. Instead you might say it is oil to fuel lamps (Wisniewski Reference Wisniewski1996). When people combine two concepts they often transfer aspects of the first concept to change something about the second concept. What do you think a “robin snake” is? You might think it is a snake with a red breast. Alternatively, you might decide that it is a snake that eats robins. What is a “cactus fish?” You might consider that it is a fish that has prickly spines. Prickly spines are diagnostic of cactii, there are few other plants that have them (Costello & Keane Reference Costello and Keane2001). People may combine concepts by identifying the most immutable aspect of the first concept and the most mutable aspect of the second concept. They may think about what snakes eat, or the shapes and colors of fish, by thinking about several possibilities from the outset. The perceived fault-lines of the concept correspond to the aspects for which people can readily think of several possibilities. Because they mentally represent some aspects of a concept, for example, what snakes eat, by more than a single possibility, they can alter those aspects readily.

A third sort of creative thought is insight. In the sciences and arts, individuals sometimes report experiencing a moment of “insight” in which a new idea “pops” into mind. Suppose you are asked to describe how to throw a ping-pong ball so that it will go a short distance, come to a dead stop, and then reverse itself. You are not allowed to bounce the ball against any object or attach anything to it (Ansburg & Dominowski Reference Ansburg and Dominowski2000). What solution would you suggest? Most people suggest throwing the ball so that it curves back to them (but this solution violates the constraint that the ball comes to a dead stop). Others suggest throwing the ball against a wall or to another person (but this solution violates the constraint not to bounce the ball against any object). Few people reach the correct solution, to throw the ball up into the air. People may think about problems such as the ping-pong one by thinking about possibilities that are limited by their previous experience with similar situations (Galinsky & Moscowitz Reference Galinsky and Moskowitz2000; Keane Reference Keane1997). They may add the usual horizontal trajectory of a ping-pong ball in play to their mental representation of the problem. But they may not add the horizontal trajectory assumption to their mental representation of other sorts of ball in play. In a basketball version of the problem, the trajectory of the ball should become a fault-line in the mental representation of reality, that is, an aspect of the facts for which people can think of alternative possibilities. This account accurately predicts that people can solve a basketball version more readily than a ping-pong version of the same problem (Murray & Byrne Reference Murray and Byrne2007). Moments of insight may be moments of mutability, when a previously immutable aspect of the mental representation of reality is transformed into a fault-line. In Chapter 8 of The Rational Imagination I suggest that the idea that the imagination depends on thinking about possibilities has implications for understanding individual differences and for understanding other sorts of creative thoughts. In Chapter 9, I consider what it means for the counterfactual imagination to be rational.