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Directed Reflective Equilibrium: Thought Experiments and How to Use Them

In: Journal of Moral Philosophy
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Abstract

In this paper we develop a new methodology for normative theorising, which we call Directed Reflective Equilibrium. Directed Reflective Equilibrium is based on a taxonomy that distinguishes between a number of different functions of hypothetical cases, including two dimensions that we call representation and elicitation. Like its predecessor, Directed Reflective Equilibrium accepts that neither intuitions nor basic principles are immune to revision and that our commitments on various levels of philosophical enquiry should be brought into equilibrium. However, it also offers guidance about how different types of cases ought to be sequenced to achieve this result. We argue that this ‘directional’ approach improves, in various ways, upon the non-directional approach of traditional Reflective Equilibrium.

Abstract

In this paper we develop a new methodology for normative theorising, which we call Directed Reflective Equilibrium. Directed Reflective Equilibrium is based on a taxonomy that distinguishes between a number of different functions of hypothetical cases, including two dimensions that we call representation and elicitation. Like its predecessor, Directed Reflective Equilibrium accepts that neither intuitions nor basic principles are immune to revision and that our commitments on various levels of philosophical enquiry should be brought into equilibrium. However, it also offers guidance about how different types of cases ought to be sequenced to achieve this result. We argue that this ‘directional’ approach improves, in various ways, upon the non-directional approach of traditional Reflective Equilibrium.

A widely adopted method in philosophy is Reflective Equilibrium (hereafter re).1 According to this method, philosophers should aim to construct a theory that maximally coheres with considered moral judgments and general principles as well as a wide range of beliefs and facts.2 The theorist works back and forth between these commitments, discarding previous beliefs if necessary, to reach an equilibrium, the attainment of which provides justification for their theory. A central component in the method of re is the use of imaginary and real-world examples, thought experiments, and intuition pumps to test principles and elicit moral judgments. For simplicity, let us call these real or imagined realities cases.

The use of cases in normative theorizing has a long and illustrious history but has also been subject to a number of criticisms, which, in turn, threaten the validity of the method of reflective equilibrium. There are numerous criticisms, but here are two familiar ones. First, cases often simplify and abstract from real-world situations. Some worry that intuitions about fantastical cases warp our sense of morality; or that they encourage our moral thinking to become unrepresentative of, or detached from, real-world crises.3 A suspicion of abstractionism underpins much historical skepticism towards moral theory in general,4 and similar worries can be raised about hypothetical cases. Second, it is often said that re relies on a coherentist approach to justification: the idea that the coherence of a set of beliefs justifies these beliefs. But, if the re is read as an instance of coherentist justification, it faces a challenge about what to do in the event of inconsistency between our intuitions or between intuitions and basic principles.5 To be sure, there are theoretical resources to overcome this impasse: one could draw on the robustness of judgments, the vulnerability of intuitions to debunking, theoretical parsimony, and so on. However, what re is still lacking is a sense of how cases ought to be sequenced in theoretical enquiry, given their different uses. Distinguishing between different types of cases and developing a sensible model for sequencing them within theoretical enquiry helps to avoid some of the pitfalls of the case-based methodology, or so we will argue.

We aim to defend a revised version of re that we call Directed Reflective Equilibrium (hereafter dre). dre, like its predecessor, accepts that neither judgments about cases nor basic principles are immune to revision and that our commitments on various levels of philosophical enquiry should be brought into equilibrium. However, unlike re, it also offers guidance about how different types of cases ought to be used. With a clearer typology of cases in mind, a sequence of their usage suggests itself, which helps overcome the challenges faced by re. In referring to a ‘sequence,’ we mean using different cases for different purposes at different stages of a theoretical enquiry – engaging in directed rather that non-directed re in order to systematize the testing of principles and the elicitation of moral judgments. We do not suggest that the use of cases should be rigidly sequenced: some stages may be omitted, and dre accommodates a degree of movement back and forth between different stages of analysis in the manner of re. Nevertheless, we will argue that dre has a number of advantages over a non-directional approach to re.

The suggested sequence of dre proceeds as follows: first, philosophers should start from what we call “seed cases.” Seed cases are situations or dilemmas, usually from real life, that capture our moral attention and elicit strong, if unsystematized, intuitions. Second, these cases are “decomposed” into various moral factors that might affect our intuitions. Here, we understand moral factors as facts that have some weight or relevance in considering what an agent ought to do. Decomposition allows the philosopher to construct “controlled cases” that represent moral factors, independent of both the original context of the seed case and the other factors with which it previously coexisted. Testing different versions of these cases against each other, the philosopher then seeks to “organize” the elicited intuitions into principles. As in standard re, this organization will require going back and forth between principles and concrete judgments in representative cases. Third, to further test these principles, philosophers can create “argument cases” that elicit the recognition of reasons as well as intuitions, seeking to support principles on the one hand, and challenge biases, metaphysical beliefs, and underlying conceptual assumptions that may color our intuitions on the other. Fourth, principles that cohere with both intuitions and reasons can be “veiled” in the final type of case. “Construction cases” set up choice situations incorporating fundamental principles, making choices that do not accord with these principles impossible.

Various stages of our model will be familiar to many philosophers. Individuals, and philosophical debates more broadly, often employ cases in the ways we recommend. Our purpose here is not fundamentally to challenge the way that cases are currently used, or to suggest a radically different usage, but to systematize pre-existing elements of best practice and to highlight the advantages of a specifically directional approach. In the next two sections we explain our taxonomy and develop the model in greater detail. We then argue that the model improves on re by addressing some of the pitfalls of the case-based methodology mentioned above.

A Two-Dimensional Case Typology

An important distinction for understanding the case typology we introduce in the next section is between two dimensions of cases: representation and elicitation. We now explain these dimensions before showing how they structure the process of dre.

The Representation Dimension

We explain the representation dimension of cases by borrowing from the discussion of models in the philosophy of science.6 In a nutshell, a model is a representation of a target system, and the relevant relation between target system and model is a similarity relation. We can think of most models as structures that are relevantly similar to their respective target systems. For example, the drawing of a cell in a biology textbook is relevantly similar to many different cells in the real world. It is, of course, an idealized exemplar of real cells,7 but what makes it similar is that certain structural features are alike.8

The sciences use models in the form of equations, computer code, or scale models. In normative theory, however, most models are “word models,” stated purely in narrative form.9 However, this should not detract from the fact that the function is very similar: to represent a target system in a way that makes it more amenable to analysis than the real-world cases it represents. In physics, for example, frictionless planes are easier to analyze than real imperfect planes, but the former still reveal something important about the latter. In normative theory, fictional cases are (arguably) easier to analyze than complex real-world problems. Take Peter Singer’s famous example, Drowning Child,10 in which it is possible to save the life of a child – but only by getting an expensive pair of shoes wet. This case helps us approach issues of global poverty, even though the subject is obviously much more complex than the hypothetical case and has various empirical complications. The hypothetical case has a narrow but important purpose: to explore one relevant normative factor at play in the real-world case (we will discuss concerns with the representativeness of cases such as Drowning Child later).

Cases used as models are really idealized exemplars: models of a larger class of real-world cases. Just like the drawing of the cell, the models are unrealistic due to high idealization. But they are unrealistic for a purpose: to single out structural aspects that they would share with all the real-world cases they represent. This, then, sets up the real-world representation dimension: cases are either representative or non-representative of normative factors that we must incorporate into our deliberation when facing real-world situations. As we will see when we introduce our sequence, the representativeness of cases informs how they should be constructed and selected.

The Elicitation Dimension

Cases can be used for different purposes. In particular, they can be used to trigger different responses. On the one hand, cases can be used to elicit intuitions; on the other hand, there are cases that are not, or not primarily, used to elicit intuitions but rather to elicit the recognition of reasons. Sometimes the case models an argument to the reader and tries to convince them of its correctness; then the response is the acceptance (or rejection) of the argument. Sometimes the case is constructed to encourage the reader to reason towards an argument. Either way, after the case has been presented, the reader is supposed to relate to reasons, not just report an intuition. Consider, for example, Derek Parfit’s case of the 14-year-old girl.11 In this case, a 14-year-old girl becomes pregnant, and a common initial reaction is that a child born into such circumstances will not have the best start in life and that the girl would, therefore, harm or wrong the child by bringing them into the world. However, on closer inspection, this particular child cannot be born at any other time, and so one cannot appeal to the wellbeing of the child to justify why the girl ought not to give birth to it. This case might produce an intuitive response, but its primary aim is to elicit the recognition of a particular argument: the non-identity problem.

Having specified these two central dimensions upon which cases used in normative theorizing differ, we can now flesh out how these dimensions figure in the process of dre.

A Typology of Cases

Figure 1 shows the case taxonomy we are proposing, with the two dimensions indicated at the top and left of the figure, setting up a 2x2 typology. The four types of cases we distinguish all have a role to play in dre. In the next section we explain these case types and their function in terms of representation and elicitation. The ideal sequence of dre is indicated by gray arrows, showing that, in the most complete dre process, one starts with seed cases, proceeds to controlled cases and argument cases, and ends with construction cases. Finally, Figure 1 also points to the central role of principles. All but the seed cases have a function related to the formulation, testing, support, and systematization of principles.

Figure 1
Figure 1

Directed Reflective Equilibrium Case Use

Citation: Journal of Moral Philosophy 18, 1 (2021) ; 10.1163/17455243_20203008

Seed Cases and Decomposition

The first stage of our model employs what we call seed cases. These are cases that capture the moral phenomenon which we wish to investigate, without making any initial effort to decide what factors are morally salient, or to separate relevant from irrelevant factors. Many debates in moral philosophy have been inspired by real cases that seem to capture something important about the normative landscape. For example, decisions in war may inspire discussions of principles in just war theory,12 cases of famine or other humanitarian crises may inspire discussion of the duty of rescue,13 and acts of terrorism and political torture may prompt discussions of harming others as a means to an end. As well as being taken from real scenarios, good seed cases also frequently elicit strong, but conflicting or conflated intuitions. Cases of famine, for example, may raise complex moral problems involving, among other things, the distinction between positive and negative duties, the stringency of assistive duties, the historical and contemporaneous responsibility of wealthy countries for poverty-related hardship, and many more. The same is true of harming in war, terrorism, and many other common seed cases in moral philosophy. These cases often capture important but multi-faceted moral problems. They pull our intuitions in different directions, perhaps in accordance with pre-existing moral or political sensibilities, and almost always involve a complex intersection of different morally salient facts. In our case typology, seed cases are intuition-eliciting and non-representative: they provide the basis for constructing other, simpler cases, which either represent elements of the seed case or elicit normative responses to factors drawn from the seed case.

The complexity or “murkiness” of seed cases can be daunting. The purpose of the next stage, decomposition, is to identify a range of factors that have potential moral salience and extract them from the seed case. Once we have extracted as many of these factors as possible, they can be formulated into their own cases and thereby separated from factors with which they coexist in the seed case. Let’s take the example of harming in war to demonstrate this process. Suppose we take as our seed case a report of a soldier killing an unarmed combatant in war. We then break the case down into a list of factors that might have moral salience. There may be many such factors, including: (1) orders within a military hierarchy, (2) the chaotic context of war, (3) epistemic uncertainty, (4) the status of the victim (combatant or non-combatant), (5) whether the victim was armed, (6) the culpability of the decision to kill, (7) whether wrongdoing was foreseeable, (8) the moral significance of causation, and perhaps more. Each of these factors can then be separated from the others and formulated into further cases. Many revisionists in just war theory, for example, compare situations in war to structurally similar cases of interpersonal harm, to isolate relevant factors from, say, the chaotic context of war or the epistemic uncertainty that pervades decisions in war.14

Controlled Cases

Building on the output of decomposition, philosophers can systematically integrate the different factors into hypothetical cases. In our previous example we saw how we might separate factors like culpability and causation, consider self-defense outside the context of war entirely, stipulate epistemic certainty, and so on. Such cases are made possible through decomposition by separating and isolating the different normative factors at play in a seed case. We will refer to cases used in this stage of the process of dre as controlled cases to emphasize their use in separating factors.15 Unlike seed cases, which are singular, however, these cases aim to represent a particular factor that is present in many real-life situations. To demonstrate how controlled cases work, consider the famous trolley case (Trolley). In this case, we must decide whether to do nothing and allow a runaway trolley to kill five people, or to divert the trolley onto a side track where it will kill one person. Trolley is an interesting moral dilemma in itself, but the feature we highlight here is that Trolley aims to represent a factor that is present in a wider class of cases. When debating Trolley and its variations, we’re clearly not interested in railways, trolleys, people tied to tracks, and the like. Rather, we are interested in a large class of cases in which killing or letting some die can save a larger group of others. This normative factor is what Trolley seeks to bring to the fore, and the numerous variations of Trolley do the same with other factors. In other words, trolley cases serve as a stand-in for many real-world cases with similar structures and the factor emphasized in Trolley is representative of a larger class of cases that are of genuine real-world interest.

Testing and Supporting Principles

Controlled cases can then be used to test principles. A principle is a statement that generalizes to more than one case.16 Because principles generalize, they enable philosophers to think about cases more systematically. Formulating principles naturally follows from decomposition: while the exercise of decomposition shows which factors might be relevant for the assessment of a case, well-formulated principles provide an account of how the different factors can be used to reach a normative or evaluative assessment.

One can think of a principle as a function, mapping each element of the domain (the set to which the principle is applicable) to one element of the codomain (the set of all possible assessments provided by the principle). Consider, for instance, a principle aiming to tell us which instances of defensive harming are permissible or even required. The domain may consist of all possible instances in which a person engages in defensive harm. The codomain consists of the three elements (impermissible, permissible, required). The principle, thought of as a function, determines for each possible instance whether this form of defensive harming is permissible, impermissible, or required.

A principle needs to pick up on patterns to be useful. To see this, think first of a maximally verbose and therefore not very useful principle: for each element in the domain it explicitly states which assessment from the codomain applies. This would result in a gigantic, potentially infinitely large lookup-table (“if this, then that …”) that provides an entry for every possible situation and the assessment of that situation. Needless to say, such a “principle” barely deserves the title. This is why the controlled cases described in the previous sections are so useful – if successful, they have already identified which properties can make a difference in the assessment, and which do not. The decomposed relevant factors allow the philosopher to set aside most of the descriptive richness of the domain elements and instead focus on the small number of factors that make a difference. But most principles go further than that: instead of listing all possible combinations of factor instantiations, they give us a simple heuristic or formula, telling us which patterns of factors lead to which judgment.

In the seed case and decomposition stages, cases are used for exploratory purposes. But a key goal of moral theorizing is to formulate principles or sets of principles that constitute theories. This leads us to two new functions of controlled cases: principle testing and principle support. We first address the role of principle testing, which is closely related to the question of case selection, then turn to principle support in the next section. Because a principle states a general relation between relevant factors and assessment, testing it requires that we choose cases systematically, mapping out the space of possible factor constellations. With unlimited time, we would want to map out the space systematically with a large sample of cases at many different locations. With more limited time, moral philosophers tend to select up to three different types of cases.

First, “corner cases” are situations in which one or more factors take a (near) minimum or maximum value to test how the principle fares in the most extreme settings and assess its robustness. For an example of a corner case, take Nozick’s Utility Monster, which creates near infinite amounts of wellbeing from each unit of resources given to it.17 Utilitarianism seems to imply, therefore, that we should always give resources to the utility monster, rather than those who are much worse off, because this will maximize utility. Though unrealistic, the Utility Monster tests our judgments in a situation where the maximization of utility is in extreme conflict with other possible values, such as equality or priority for the worst off. Corner cases give us an opportunity to test our commitments against extreme, even unrealistic pressure, in the same way plane wings are bent nearly 90 degrees in a stress test, even if they are unlikely to be subject to such pressure during flight. We should be interested in the robustness of a principle’s plausibility, rather than just its plausibility in the range of cases we are most likely to confront.

Corner cases can also be counterexamples – the second type of controlled case often used for testing principles. Counterexamples put moral judgments under pressure, but more generally they challenge principles by intuitions in the opposite direction. The Utility Monster is a corner case, but it is also a counterexample because the intuitive judgment is that resources should go to the worst off rather than the monster, and thus the case suggests that Act-Utilitarianism is false.

Argument Cases

Supporting Principles

Argument cases are not employed in a purely exploratory mode – they also have an argumentative function. We draw attention to two important argumentative purposes: for supporting principles and for testing metaphysical assumptions. Take supporting principles first. Cases can lend support to principles in two ways: in exposition, by illustrating the application of the principles, or substantively, by demonstrating reasons that support the principles, though these two strategies of support often blend into each other. Cases of the former type are pedagogical devices for the benefit of the reader: stating the principle precisely would suffice to state the view, but an example of its application can support understanding, without necessarily supporting the content of the principle. For example, Trolley may be used to illustrate the difference between Act-Utilitarianism and the Principle of Doing and Allowing by pointing to their different implications with respect to permissibly diverting the trolley.

Cases that aim to provide substantive support for a principle go beyond mere illustration – they are also supposed to incline the reader to accept the principle. Of course, there is no rigid distinction between controlled cases and argument cases, or between exploration and argument. Two types of cases mentioned above – corner cases and counterexamples – have an important role to play in arguing against or in favor of principles. But argument cases have other functions, too. For example, GA Cohen argues for his version of egalitarianism, and, more specifically, his interpretation of the difference principle, by providing an example. In his “kidnapper” case, Cohen asks us to imagine a criminal who has abducted a child and now tries to convince the parents to pay a ransom to him by insisting that children should be with their parents. Cohen points out that while this statement is generally true, the kidnapper is not in a position to appeal to it as a premise of his argument. After all, the kidnapper is the cause of the child not being with their parents.18

The kidnapper case is interesting because not only does it elicit an intuition, it also encourages the reader to reason about the argument the kidnapper gives and why it fails. This demonstrates a different general function of cases that we described earlier: apart from eliciting intuitions, some cases can also be used to elicit the recognition of reasons to support an argument, marking the next dimensional shift in our typology. When a case elicits the recognition of a pattern of reasoning, it typically also elicits an intuition, but the intuition is not necessarily the goal of the exercise. In the kidnapper case, for example, it is entirely unsurprising that we have the intuition that kidnapping is wrong, or that the reasoning provided by the kidnapper is preposterous. But the point of the kidnapper case is to make the reader reason about the standing a speaker needs to have to make certain arguments. This insight is then transposed to a different context and used to criticize certain incentive-based arguments for demanding higher salaries.

Cases that elicit reasons will normally come with a richer logical structure than cases that elicit intuitions only. In Cohen’s kidnapper case, the case itself contained an argument that provokes the reader into resisting the argument. Cohen also invites the reader to reason by structural analogy when comparing the kidnapper with the case of a doctor who only works when they get a higher-than-average salary: a common way to elicit reasons from cases is to compare two cases and analyze the differences between them.19

The distinction between cases for testing and for supporting principles allows us to state another principle of case use: testing and supporting cases must be chosen according to different criteria. Cases that illustrate, or support by eliciting reasons, should be chosen for their ability to enable explanation, understanding, and reasoning. They will be cases for which the application of the principle is most plausible, and they are chosen to make the assessment of the principle intuitive. The opposite holds for testing cases: they should be chosen to find out how robust the principle is in less paradigmatic case applications. That may involve exploring extreme assumptions or pro-actively scanning for counterexamples. Moreover, a meaningful test ought to be conducted by confrontation with several (and typically diverse) cases. Thus, the supporting and testing role should typically be fulfilled by different cases; running these two functions together would be a mistake.

Querying Metaphysical Assumptions

The use of cases is not restricted to evaluative and normative investigations – it is equally important in conceptual analysis and metaphysics. Since ethical theory often depends on conceptual analysis or metaphysical assumptions, cases are often employed to test or query such assumptions. The use of cases for conceptual analysis has been analyzed in detail elsewhere,20 so we set it aside in the interest of space. We will, however, briefly demonstrate the use of cases for the analysis of metaphysical assumptions by looking at the metaphysics of causation and the metaphysical assumptions related to different conceptions of harm. Cases of this type are often counter-intuitive: rather than being used to elicit intuitions, they show us that our intuitions and our background assumptions are in tension.

For an example of how ethics is influenced by the metaphysics of causation, consider overdetermination cases such as Derek Parfit’s two assassins:

“X and Y simultaneously shoot and kill me. Either shot, by itself, would have killed.”21

This raises questions about causation: whether X (or Y) has caused the death. And entangled with this is the question whether and why X or Y act wrongly, and whether X or Y are individually responsible for Derek’s death. At the minimum, the case illustrates the questions to be discussed, but it also triggers judgments about both the causal and ethical claims. The two assassins make us question common background assumptions about causation. For instance, a common assumption about causation is that the cause is necessary for the effect. But that assumption (together with some further auxiliary assumptions) leads to counterintuitive judgments about wrongfulness and responsibility in overdetermination cases, challenging the reader to revise either the background assumption about causation or the judgments about these cases.

For an example of how the metaphysical assumptions concerning harm influence ethical theory, consider Warren S. Quinn’s puzzle of the self-torturer.22 A patient can increase the electric current flowing through their body in tiny steps, such that the effect of each tiny increase is imperceptible, but comes with a payment of $10,000. The patient therefore prefers to nudge up the current at each step. However, once increased the current cannot be reduced, and once many steps have been taken, the pain becomes so unbearable that the patient would give up all his money to make it stop. This raises important questions about the analysis of harms that fall below the threshold of perceptibility. For instance, a common assumption about harm is that it must be directly perceptible. Another common assumption is that a relationship like “is as harmful as” is transitive, such that if A is as harmful as B and B is as harmful as C then A is as harmful as C. But these two assumptions (together with some further auxiliary assumptions) lead to the counterintuitive result that the lowest setting harms the self-torturer just as much as the highest setting, which is absurd. Either the assumptions or (less likely) the judgment must be revised.23

What makes the cases for testing metaphysical assumptions so powerful is that they also have a representative role: our interest lies not in synchronized assassins, confused self-torturers, and so on. Our interest arises because these cases represent larger classes of realistic cases and it is this power to represent that makes these cases relevant: they make us realize that some of the conventional thinking about applied, real-world cases might rest on muddled or at least questionable assumptions.

Cases for testing metaphysical assumptions typically play an auxiliary role in applied ethics and political philosophy by helping to investigate, clarify, or revise background assumptions, though they can take center stage in more theoretical projects. In the normal sequence of case use they are most effective after principles have been formulated. This is because they can serve as a check on the metaphysical assumptions made in the principle formulation. But in more theoretical projects, the case may be needed right at the start: to set up the puzzle and frame the debate. Which order works best depends on the context of the investigation and the division of labor between theoretical and applied ethics. Interestingly, the debate about case use has largely overlooked this function of cases even though this category contains some of the most influential thought experiments appealed to in ethics.

Construction Cases

Some of the most famous hypothetical cases in normative theory play a role that we have not yet described. Construction cases, as we will call them, are used infrequently but often take center stage in grand theories. One of the most famous construction cases is Rawls’s original position. Like argument cases, they seek to elicit the recognition of reasons, guiding the reader to understand, follow and accept arguments – albeit through a more complex modeling function. But unlike the cases in the last two categories, construction cases are specifically non-representative. They set out frameworks that constrain our reasoning and our judgments in particular ways, asking us to imagine a hypothetical, idealized choice situation – one that decidedly does not represent real-life choice situations – and to determine which outcomes would be accepted under such conditions.24 The point of the construction case, then, is not to represent real choice situations, but to represent a plausible theoretical starting point that provides a focus for further normative theorizing. Construction cases fill the last remaining cell of our typology.

Construction cases can be understood as the final step, following the process of decomposing factors, organizing the factors into principles, and testing these principles against metaphysical and folk psychological assumptions. At this point, there will sometimes be factors, the salience of which a theorist is very confident about, but which people are generally likely to misjudge in their normative evaluations. Consider, for example, Rawls’ original position. People are asked to imagine themselves behind a veil of ignorance that blinds them to their current position, privilege, and talents in society and decide upon principles for the societal distribution of benefits and burdens without such knowledge. The original position is “modelling the way in which the citizens in a well-ordered society, viewed as moral persons, would ideally select first principles of justice for their society.”25 Rawls calls the original position a “device of representation,”26 but he means representation in a specifically normative sense – quite different from what philosophers of science have in mind when they think about models.27 When justifying the original position, Rawls states that it aims to ensure that “no one should be advantaged or disadvantaged by natural fortune or social circumstances in the choice of principles.”28 The case accounts for these considerations, in other words, by incorporating into our reasoning a combination of factors, the normative significance of which Rawls is confident about, namely equal concern for people’s claims regardless of background and abilities, or fairness.

The veil of ignorance makes vivid the underlying idea that the choice of principles should not be affected by arbitrary factors like unearned natural properties or pre-existing biases. Importantly, however, it also takes into account that people are likely to be affected by such factors and thus misjudge the fairness of potential principles of justice in ways that reflect their position and power in society. But as Rawls notes: “it should be impossible to tailor principles to the circumstances of one’s own case.”29 The original position constrains our ability to do so. In principle, of course, we could appeal directly to fairness to argue in favor of Rawls’ principles. However, using fairness as a constraint on rational choice instead, inhibiting our ability to tailor principles to our own circumstances, captures the force of the argument in a different way – not least, by encouraging the reader to reach these conclusions from a first-person perspective.

Other examples of construction cases include: Ronald Dworkin’s auction, in which we are asked to imagine a group of shipwreck survivors washed up on an island and faced with the task of dividing the island’s land and resources in a just manner among themselves through an auction which is meant to leave everyone content with their post-auction bundle;30 Adam Smith’s impartial spectator, which asks us to evaluate the moral sentiments of ourselves and others from the point of view of a well-informed and impartial spectator;31 Dworkin’s judge Hercules, which asks how an ideal judge with unlimited time and knowledge would rule on constitutional cases;32 Chandran Kukathas’ ‘liberal archipelago,’ which considers society as a collection of co-existing but separate societies and asks which rules should guide such diversity;33 and Thomas Hobbes’ state of nature, which highlights the dangers of living without (and the difficulties of achieving) stability. All of the mentioned cases function by using factors as input to constrain our reasoning, ensuring, for example, that we take into account the dangers of societal instability or the opportunity costs of our choices, or that we disregard partiality towards our own situation. By incorporating factors in this way, construction cases exclude certain normative conclusions from being reached. This can help explain that such cases are used so rarely – because excluding certain conclusions requires an extraordinarily high level of confidence in the relevant, excluding factor.

Importantly, construction cases play a dual role in shaping our thinking by facilitating the strengthening of certain factors in our reasoning (e.g. fairness and opportunity costs) and helping to justify the principles and judgments reached via these cases by lending them added support. Thus, the hypothetical agreement itself constitutes an argument in favor of some principles (e.g. Rawls’ principles of justice) because the principles have been agreed upon in a choice situation that excludes partiality and ensures equal consideration of claims. Usually, discussions of construction cases focus solely on this principle-supporting output.34 In dre, however, we emphasize the double role that construction cases play in the process of justification: first, by using input from the previous stages to determine how our reasoning should be constrained, and second, by providing an additional, distinct underpinning for normative principles due to the controlled choice-situation into which the chooser is placed.

Some Advantages of Directed Reflective Equilibrium

In this section we outline some of the specific advantages of dre over non-sequenced approaches. The first advantage was made evident, we hope, in the course of laying out the model. Cases have a multitude of purposes in normative theory, and though these are often recognised implicitly, it pays to have a more explicit and comprehensive taxonomy. This allows us to construct cases in accordance with their specific purpose, and, as previously noted, the criteria for case selection vary depending on the type of case being constructed.

dre is not merely a taxonomy of cases, however: it also recommends a specific progression of case-use in normative theory. Having outlined the various functions of cases, we can see how, overall, the use of cases moves from an exploratory mode to an argumentative mode. Many cases in philosophical writing have an argumentative purpose: they aim to pump intuitions, provide counterexamples, and so on. By contrast, dre encourages us to make use of cases just as much in our early exploratory phase as in our later argumentative phase. And having distinguished between the various functions of cases, we are now better placed to see how the use of cases can go wrong when the two phases are mixed.

When philosophers move to the testing of principles too quickly, this narrows the inquiry in two ways. First, skipping the exploratory seed case and decomposition phase increases the risk of missing important factors and fixating too quickly on existing principles. Reducing the list of candidate factors for principle formulation narrows the scope of the search for new principles, especially those principles that are not easily identified due to bias or inertia. This danger is particularly relevant in applied ethics, and especially when investigating new or philosophically under-explored phenomena. But even in well-established areas of philosophical research it is important not to rule out overlooked factors too early. One may be tempted to select a factor that leaps out at us from a seed case and consider this in more detail. Philosophical debate often operates in this way, where one thinker will highlight a factor that appears important and another will criticize this and highlight a different factor. Decomposition encourages us to begin by simulating this dialectical process intrapersonally before defending any one factor, by breaking down the seed case into as many relevant factors as possible.

It is worth noting that we are describing a process of philosophical thinking rather than writing, and some or even all of the early stages may not be incorporated into written output. However, there are a number of benefits of making this process explicit and, in particular, of performing it early in the reflective equilibrium process. First, decomposition is a more neutral way to capture the variety of factors with potential moral relevance. A common criticism of appeal to moral intuition is that our intuitions are shaped by biases and pre-existing theoretical commitments. Decomposition offers a way to mitigate this worry by extracting as many moral factors as possible from a seed case and formulating them into cases of their own. Of course, no methodology can eliminate bias entirely, but engaging in thorough decomposition before using argument cases is one way to guard against selection bias.

Second, if relevant factors are not identified in the exploratory phase, the preconceived principles are unlikely to be tested with cases that present variations on these factors, either separately or in interaction. Moving on to testing principles before a careful exploratory phase has the counter-productive effect that the testing will be less comprehensive because alternative hypotheses are not explored. The appropriate use of argument cases to test metaphysical and conceptual assumptions also helps the directional approach to avoid path-dependency problems, as the conclusions arising from normative theory depend, in part, on the metaphysical assumptions we adopt at the start of our investigation. These cases ensure that the results of our theorizing are more likely to determine whether intuitive disagreement is based on genuine normative disagreement or disagreement about metaphysical or conceptual assumptions.

An Anchor in the Real World

One common criticism of hypothetical cases, which we sketched at the outset, is that they are abstract or fantastical and therefore not relevant to real-world problems. There are plenty of responses available to this charge;35 here we add one more. dre recommends beginning enquiry with a seed case. Such cases, however complex or “murky” from an analytical perspective, help us focus on the salient moral factors that we find in real-world scenarios and therefore “anchor” the ensuing enquiry. Or, as Susanne Burri puts it in a recent article, starting from real-world seed cases helps ensure “practical applicability.”36 This can help to ensure that the results of philosophical enquiry have implications for what we (as individuals, groups, or states) ought to do with regard to these problems, as long as subsequent stages of theorizing are also performed with care, e.g. ensuring that controlled cases maintain their representativeness with the seed case, even if they transpose a factor into a very different context.

Normative theory that begins with discussion of abstract principles may still have practical implications: utilitarianism, for example, has many practical implications. But practical implications are not the same as practical applicability, or, in our terms, anchorage in real-world problems. The use of seed cases helps to focus our attention on moral phenomena that are pertinent to real-world moral issues, beyond ensuring that the results of theorizing have practical implications. This enables the directional approach to address one of the problems which we previously noted with regard to re. re does not prescribe any specific starting point for moral theory. A theorist might start from a specific case but might equally start from an abstract principle.37 The use of seed cases in dre, by contrast, represents an attractive middle ground between fixating on specific real-world problems and pursuing highly abstract theory.38

On the standard approach to reflective equilibrium, intuitions drawn from hypothetical examples can, in principle, be entirely unconnected to real-life situations. This gives rise to the worry that such intuitions have little bearing on actual moral and political dilemmas. Thus, while intuitions elicited by hypothetical cases better track individual normative factors, the guidance such intuitions provide for moral and political agency is limited, if the hypotheticals are not grounded in real life. If one begins from a seed case, after the following steps are completed, there is a higher likelihood that resulting principles will maintain their representative connection to the real moral phenomena.

Distilling Clarity from Complexity

Although seed cases may have intuitive pull, the intuitions they elicit are frequently muddled and obscured by being bundled up in complex ways. Multiple normative factors often coexist, making it difficult to appreciate which judgments or reasons, if any, are supported by which factors. Because of this, it is often valuable to analyze cases in which moral considerations that typically coexist are separated to see how they function independently. This often requires unrealistic cases since in most realistic scenarios the considerations that we wish to pull apart are found together. Decomposition and controlled cases are useful tools for achieving this. Including decomposition as an explicit stage of the enquiry models something that often emerges dialectically: an itemization of the various moral factors that may play a role in the seed case. Controlled cases then offer a useful analytical tool to separate factors from their original context to see how they operate independently. When faced with a complex, perhaps real-world, moral case, we are presented with a choice: we can either evaluate the case in all its complexity, attempting to discuss relevant considerations without comparison with other cases. Alternatively, we can tease apart different factors by considering other cases where these factors are present, but others that co-existed with it in the original case are absent. Thus, a single complex case can become a family tree of cases.

Controlled cases like Drowning Child or Trolley thus deliberately aim to test or support the importance of specific factors by isolating their intuitive pull and suppressing the effect of other factors. Factors are explored, then, by eliciting intuitions about them individually (or, if necessary, in deliberate interaction with other factors) and good hypothetical cases are ones that both represent factors present in a number of real-life cases and elicit clear intuitive responses. Drowning Child, for example, is inspired by an actual famine in South Asia. Alleviating actual famines by donating money to charities, of course, does not happen as straightforwardly as does saving the child in Singer’s example, and many have criticized the case on this basis, raising worries about factors which are relevant when considering charitable donations that are not present in Drowning Child. Some worry, for example, that, unlike saving the drowning child, charitable donations are often ineffective, create and uphold relations of dependency, help sustain corrupt governments, and do not suffice to remedy global poverty and injustice.39

In the role that controlled cases are meant to play in dre, however, Drowning Child is not meant to include these factors because it is not meant to replicate the normative complexity of an actual famine. Rather, it is meant to isolate and foreground the intuitive pull of one factor – being able to help others greatly at little cost to oneself. In this particular example, the case is also meant to suppress another factor, which is present and which is often given exaggerated importance in cases of actual charitable donations – geographical distance. Drowning Child does not tell us what to do when faced with an actual famine, but it helps us untangle the complexity of the situation by highlighting factors that we are liable to underappreciate and subduing other factors, the importance of which we are liable to overestimate (such as geographical distance). More generally, then, hypothetical cases representing decomposed factors can help provide clarity about the real-life dilemmas of seed cases, in which factors are intertwined and obscured.

It is important that controlled cases properly represent the factors they draw from the seed case. However, we must also be clear that controlled cases represent a factor, not the seed case itself. As mentioned, Drowning Child represents the ability to save life at low cost, and thus excludes other (perhaps important) factors from real famines such as inefficiency or sustaining corrupt governments. According to dre, it is irrelevant for critics to focus on the various ways a controlled case is unlike the real phenomena in which the theorist is interested. It is far more important to conduct the process of decomposition thoroughly, ensuring that factors are properly articulated, to maintain representativeness with the seed case.

Once we understand the rationale behind decomposition and controlled cases, we can be clearer about the criteria for case construction. We should begin by considering how best to separate a factor from a seed case with minimal distraction. No more contextual information should be added to the controlled case than is necessary to maintain representativeness with the relevant factor from the seed case. We should then ask whether the benefit of representing this factor outweighs the distraction.

Controlled cases will sometimes require an unrealistic setup in order to isolate the relevant factors,40 but this should always be balanced against the benefit of representation and isolation. Consider Thomson’s ‘people-seeds’ example in this regard.41 In this case, people-seeds drift about in the air like pollen, and despite the mesh screens erected to prevent their entry, they take root in the carpet and start to grow, eventually turning into human beings. Though this example is absurd, it is intended to be analogous to pregnancy via intercourse that one has taken reasonable steps to avoid. Since there are no realistic cases of this kind (except actual pregnancies that cannot function as analogies) the analogy is necessarily fantastical. Again, the case does not give us conclusive evidence about the real-life issue from which the factor is drawn – the permissibility of abortion. It does, however, provide information about one important question: whether we can incur demanding, individual obligations to sustain potential human life when we have taken all reasonable steps to avoid this potentiality. Our discussion shows how the people seeds case, despite its fantastical nature, does precisely what controlled cases ought to do. The case isolates a particular variable and puts it into a context that can properly function as an analogy. The fantastical elements are excused since it is difficult to see how cases that capture the relevant factor could be more realistic without involving actual pregnancies. Perhaps there are cases that successfully represent the same factors whilst being less mired in fantastical detail. We do not know what such cases would look like, but our present purpose is to articulate the criteria that should govern the construction of such cases: maintaining representativeness with the factor taken from the seed case with minimal possible distraction through fantastical detail.

Spotting Interaction Effects

Decomposition is effective for identifying interaction effects. Frances Kamm sums up the general phenomenon of interaction effects with her Principle of Contextual Interaction. According to this principle, a factor’s moral salience may differ with its context. If a factor seems irrelevant in one case, it doesn’t follow that it is irrelevant in others, and vice versa.42 One worry about re is that it has no inbuilt mechanism to detect interaction effects. A principle may be consistent with one intuition about a specific factor and thus be in re, but the Principle of Contextual Interaction suggests that equilibrium may yet be threatened if the intuitive judgment about that factor changes when it is transposed to a different context.

To demonstrate, consider again the case of killing a combatant in war. We might reason that culpably causing a threat to another is a ground for liability to defensive harm. But it would be too hasty to conclude from this anything about the relevance of causing a threat and being culpable independently. It may be that causation on its own is relevant, or perhaps not: perhaps it is only relevant when combined with culpable action. And perhaps the same is true for culpability. Until we have separated these factors and formulated them into their own cases systematically, we run a greater risk of drawing conclusions without taking into account interaction effects. Using decomposition to separate factors from seed cases, and therefore from their original context, helps to isolate those factors. And once this isolation is achieved, it is possible to conceive of controlled cases that deliberately vary a select number of factors to pick up interaction effects early.

Different Forms of Elicitation

Reading many philosophical debates, one might be forgiven for thinking that the primary argumentative purpose of cases is to pump intuitions.43 This is, indeed, an important function, but as our earlier discussion of the elicitation dimension shows, dre employs cases for various forms of elicitation beyond intuition pumping. Cases can either trigger intuitive responses, or they can be used for argumentative purposes, perhaps as presumptive support for a philosophical claim or to explore the implications of different principles. Such reason-eliciting cases can also be employed to query assumptions and refine principles. These different purposes are part of the basis for distinguishing between various argument cases. And as our discussion of Rawls’ original position shows, construction cases also elicit patterns of reasoning.

We do not have a great deal to add here beyond our discussion of the elicitation function in the course of outlining the model. We hope our account of dre highlights the benefit of these different forms of elicitation, and the importance of distinguishing between them. Of course, re might also make use of these cases, and in this respect, they are not exclusive to a directional approach. Nevertheless, we suggest that they are best placed after the exploratory process of decomposition, and the investigation of moral factors in independent controlled cases. The different forms of elicitation reflect cases in their argumentative mode: used for pumping intuitions; encouraging the recognition of patterns of reasoning; challenging metaphysical assumption; and finally, theory building using construction cases.

Conclusion

In this paper we have argued that, once we distinguish the multifarious functions of cases, we can make best use of them through a specific sequence, which we call dre. Though we think it has various advantages over traditional re, we should emphasize that we do not see the model as rigid, but fluid. For some problems or enquiries, some of these stages may be omitted (most obviously, construction cases may not be appropriate). Moreover, some movement back and forth between different stages in dre is encouraged. For example, in the argumentative stage, movement back and forth between principles and argument cases (such as counterexamples or corner cases) may proceed in much the same manner as in re.

Central to our development and defense of dre has been a taxonomy of different cases and their functions. Oftentimes these different functions are already evident in the literature, even if they have not been identified explicitly. Some of these functions are also independent of the directional approach and can be employed in the course of re or other case-based methodologies. Our aim has been to deepen, clarify, and extend our understanding of these cases, rather then fully supplant previous methods. That said, we have also argued that, once the various functions of cases are properly distinguished, they fit neatly into and complement our directional approach.

Acknowledgements

For helpful comments on drafts of this paper we would like to thank Clare Bergum, Mohammed Azizul, Keith Dowding, Eva Erman, and many audiences to whom we have presented the paper.

Biographical Note

Adam Slavny is an Associate Professor in the School of Law at the University of Warwick.

Kai Spiekermann is Professor of Political Philosophy in the Department of Government at the London School of Economics.

Holly Lawford-Smith is a Senior Lecturer in Political Philosophy at the University of Melbourne.

David V. Axelsen is a Lecturer in the Department of Government at the University of Essex.

1

See John Rawls, A Theory of Justice, Rev. edn (Oxford: Oxford University Press, 1999 [1971]), p. 18. for the introduction of the terminology.

2

See Rawls, A Theory of Justice and Norman Daniels, Justice and Justification: Reflective Equilibrium in Theory and Practice (Cambridge: Cambridge University Press, 1996), Ch. 1.

3

Allen Wood, ‘Humanity as an End in Itself’ in Derek Parfit, On What Matters, Volume 2 (Oxford: Oxford University Press, 2011) and Mathias Thaler, ‘Unhinged Frames: Assessing Thought Experiments in Normative Political Theory,’ British Journal of Political Science 48 (2016), pp. 1119–1141.

4

Onora O’Neill, ‘Abstraction Idealization and Ideology in Ethics,’ Royal Institute of Philosophy Supplements 22 (1987), pp. 55–69.

5

For similar queries about reflective equilibrium, see J. Arras, ‘The Way We Reason Now: Reflective Equilibrium in Bioethics’, in B. Steinbock (ed.) The Oxford Handbook of Bioethics (New York: Oxford University Press, 2007), pp. 46–71 and T. Kelly and S. McGrath, ‘Is Reflective Equilibrium Enough?’ Philosophical Perspectives 24(1) (2010), pp. 325–359.

6

Ronald Giere, Explaining Science: A Cognitive Approach (Chicago: University of Chicago Press, 1988), Peter Godfrey-Smith, ‘The Strategy of Model-Based Science,’ Biology and Philosophy 21 (2006), pp. 725–40; ‘Models and Fictions in Science,’ Philosophical Studies 143(1) (2009), pp. 101–16 and Michael Weisberg, Simulation and Similarity: Using Models to Understand the World (Oxford and New York: Oxford University Press, 2013).

7

Weisberg, Simulation and Similarity, p. 18 and Stephen Downes, ‘The Importance of Models in Theorizing: A Deflationary Semantic View,’ PSA: Proceedings of the Biennial Meeting of the Philosophy of Science Association, 1(January) (1992), pp. 142–53.

8

One popular approach in the sciences has a “hub-and-spoke” structure, as Peter Godfrey-Smith, ‘Models and Fictions in Science,’ p. 107, points out: “In these cases, what scientists do is give an exact description of one case of the target phenomenon, which acts as a ‘‘hub’’ that anchors a large number of other cases. The ‘‘other’’ cases include all the actual-world ones; the hub is a fiction. The central models of both evolutionary change and population growth within modern biology work like this, for example.”

9

The occasional formalized game-theoretical model can be found but remains the exception rather than the norm.

10

Peter Singer ‘Famine, affluence, and morality’, Philosophy & Public Affairs 1(3) (1972), pp. 229–243.

11

Derek Parfit, Reasons and Persons (Oxford: Clarendon, 1984), §122.

12

For example, military acts designed to terrorize a population into surrender provide the foundation for the comparison between ‘terror bomber’ and ‘tactical bomber’ cases. See, for example, Michael Walzer, ‘World War ii: Why Was This War Different?’ Philosophy & Public Affairs 1(1) (1971), pp. 3–21.

13

Singer, ‘Famine, affluence, and morality.’ Mollie Gerver, The Ethics and Practice of Refugee Repatriation (Edinburgh: Edinburgh University Press, 2018).

14

For a key text in revisionist just war theory that takes this approach, see Jeff McMahan, Killing in War (Oxford: Oxford University Press, 2009).

15

A similar, but more minimalistic way of depicting this use of thought experiments (termed “heuristic thought experiments”) can be found in Georg Brun, ‘Thought Experiments in Ethics’, in Michael T Stuart, Yiftach Fehige, and James Robert Brown (eds.), The Routledge Companion to Thought Experiments (Abingdon: Routledge, 2017), pp. 195–210.

16

Christian List and Laura Valentini, ‘The Methodology of Political Theory’, in Herman Cappelen, Tamar Szabo Gendler, and John Hawthorne (eds.), The Oxford Handbook of Philosophical Methodology (Oxford: Oxford University Press, 2016), pp. 525–553. Our understanding of principles is consistent with treating principles as summaries of normative facts rather than grounds of normative facts. See Selim Berker, ‘The Explanatory Ambitions of Moral Principles’, Noûs 53(4), pp,. 904–936.

17

Robert Nozick, Anarchy, State and Utopia (New York: Basic Books, 1974).

18

G.A. Cohen, ‘Incentives, Inequality, and Community’, in Tanner Lectures on Human Value (1991).

19

Kimberley Brownlee and Zofia Stemplowska, ‘Thought Experiments’ in Adrian Blau (ed.), Methods in Analytical Political Theory (Cambridge: Cambridge University Press, 2017).

20

See, for instance, List and Valentini, ‘The Methodology of Political Theory.’

21

Parfit, Reasons and Persons, p. 10.

22

Warren S. Quinn, ‘The Puzzle of the Self-Torturer’, Philosophical Studies 59(1) (1990), pp. 79–90.

23

Other examples of argument cases for querying metaphysical assumptions include the bean-stealing bandits in Jonathan Glover, ‘It Makes No Difference Whether or Not I Do It’, Proceedings of the Aristotelian Society, Supplementary Volumes 49 (1975), pp. 171–209 and the pregnant 14-year old girl in Parfit, Reasons and Persons §122.

24

Carla Bagnoli, ‘Constructivism in Metaethics’, in Edward N. Zalta (ed.), Stanford Encyclopedia of Philosophy (2020). Available at https://plato.stanford.edu/archives/sum2020/entries/constructivism-metaethics/.

25

John Rawls, ‘Kantian Constructivism in Moral Theory’, The Journal of Philosophy 77(9) (1980), pp. 515–572, p. 520.

26

John Rawls, Political Liberalism (New York: Columbia University Press, 1993), p. 27.

27

James Johnson, ‘Models Among the Political Theorists’, American Journal of Political Science 58(3) (2014), pp. 547–60, misses this important distinction in his discussion of models within political theory.

28

Rawls, Theory of Justice, p. 18

29

Ibid.

30

Ronald Dworkin, ‘What is Equality? Part 2: Equality of Resources’, Philosophy & Public Affairs 10(4) (1981), pp. 283–345.

31

Samuel Fleischacker, ‘Adam Smith’s Moral and Political Philosophy’, in Edward N. Zalta (ed.), The Stanford Encyclopedia of Philosophy (2017). Available at: https://plato.stanford.edu/archives/spr2017/entries/smith-moral-political. This notion is also used in the construction and justification of Roger Crisp’s account of sufficiency. See, Roger Crisp, ‘Equality, priority, and compassion’, Ethics 113(4) (2003), pp. 745–763.

32

Ronald Dworkin, Law’s Empire (Cambridge MA: Harvard University Press, 1986).

33

Chandran Kukathas, The Liberal Archipelago: A Theory of Diversity and Freedom. (Oxford: Oxford University Press, 2003).

34

E.g. Brownlee and Stemplowska, ‘Thought Experiments’, Brun, ‘Thought Experiments’ and Carl Knight, ‘Reflective Equilibrium’, in Adrian Blau (ed.), Methods in Analytical Political Theory (Cambridge: Cambridge University Press, 2017), pp. 46–64.

35

See, for example, Brownlee and Stemplowska, ‘Thought Experiments’ For a moderate defense of thought experiments, see Adrian Walsh, ‘A Moderate Defence of the Use of Thought Experiments in Applied Ethics’, Ethical Theory and Moral Practice14(4) (2011), pp. 467–481.

36

Susanne Burri, ‘Why Moral Theorizing Needs Real Cases: The Redirection of V‐Weapons during the Second World War’, Journal of Political Philosophy 28(2) (2020), pp. 247–269.

37

As Eva Erman and Niklas Möller put it in ‘Practices and principles: On the methodological turn in political theory’, Philosophy Compass 10(8) (2015), pp. 533–546, reflective equilibrium “is completely neutral with regard to where we start our normative endeavour – we may start with abstract principles or with local norms and contextual claims.”

38

Very recently, Eric Brandstedt and Johan Brännmark have suggested a way of making reflective equilibrium more practical by combining it with Rawlsian Constructivism in ‘Rawlsian Constructivism: A Practical Guide to Reflective Equilibrium’, Journal of Ethics (2020). Our approach adds more specification to the role played by cases and the sequencing of different stages of the method, but otherwise we take the two approaches to be compatible.

39

David Miller, National Responsibility and Global Justice (Oxford: Oxford University Press, 2007), chapter 9; Peter K Unger, (1996), Living High and Letting Die: Our Illusion of Innocence (Oxford: Oxford University Press, 1996).

40

Brownlee and Stemplowska, ‘Thought Experiments’.

41

J. J. Thomson, ‘A Defence of Abortion,’ Philosophy & Public Affairs 1(1) (1971), pp. 47–66.

42

See Francis Kamm, Morality and Mortality Vol. 2 (Oxford: Oxford University Press, 1996), p. 51.

43

The term “intuition pump” was coined by Daniel Dennett, Consciousness Explained (London: Penguin, 1991).

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