Before we can address the question of how to apply reflective equilibrium (RE) as a method, we have to be clear about how we understand RE and what we take its elements and criteria to be. Only then can we test the implications of this conception for its application as a method. This is expressed in desideratum (1), which was identified in Chap. 1:

Desideratum 1:

Reflective equilibrium should be spelled out as explicitly and precisely as possible, including: (i) its theoretical and methodological foundations, (ii) the aim of the method, and (iii) how RE can be specified for particular applications.

The present chapter describes the theoretical foundations of a specific conception of RE, that is, its elements and criteria. It thereby addresses part (i) of this desideratum. Parts (ii) and (iii) of the desideratum are addressed in Chap. 3, where I discuss how we can obtain a method from this theoretical conception.

I start by giving an overview of the main ideas of RE in Sect. 2.1, before focusing on the elements of RE and the relations between them. The relation of Agreement, i.e., the sought-after balance between commitments and a systematic account of these commitments, is addressed in Sect. 2.2. This relation is central for RE, and is predominantly associated with it. However, in the conception adopted here, RE does not reduce to coherence between commitments and a system: we do not only start from our commitments about the subject matter in question, but also have to respect them throughout the process. What this means is discussed in Sect. 2.3. Section 2.4 addresses the role of theoretical virtues for the system, while Sect. 2.5 explains what makes RE “wide”, that is, how the justificatory project in the foreground is situated in a broader context of background theories, background information, and background assumptions. Section 2.6 sums up the criteria of RE, and sketches the way ahead towards the case study.

2.1 The Idea of Reflective Equilibrium

Very roughly, the core idea of (so-called “wide”) RE is that we start from our existing judgments about relevant cases and search for fitting systematic principles, which, in turn, can be applied to new cases. When conflicts arise between judgments and principles, both sides are adjusted mutually in a process guided by epistemic goals and supported by accepted background theories. When a coherent state—an equilibrium—is reached as a result of this process, we can consider both our judgments and our principles to be justified.

In order to obtain a specific RE conception that can be tested in a case study, this rough idea needs to be spelled out. To do this, I draw on the most elaborate and fleshed-out conceptions that can be found in the literature, in particular on the works of Elgin (1996, 2017), Brun (2013, 2016, 2020), and Baumberger and Brun (2017, 2021). As we will see, this RE conception is more complex than just bringing particular judgments and general principles into coherence with each other: it requires an epistemic position to meet six criteria in order to be in a state of reflective equilibrium. In this section, I introduce the main ideas of this conception of reflective equilibrium, before spelling them out in more detail in the next sections.

Commitments vs. System

Standard accounts of RE typically see the difference between judgments and principles in terms of particular vs. general, but already Rawls (1974, 289) pointed out that judgments can also be general. Hence, Brun (2013, 240) argues that the main difference between principles and judgments has nothing to do with their content or their form, but that it is their function that is different. He argues that principles are part of a system, while judgments involve a certain degree of commitment—as minimal as it may be. This means that we can have parts of a system that are more or less a restatement of a commitment (cf. Knight 2017, 51–52), i.e., we can be committed to the judgment “one should not lie” while also using the principle “one should not lie” to systematically account for commitments. Thus, I will usually talk of commitments and (parts of) a system, where a system can be, e.g., a theory, a set of principles, or a model. Of course we can be committed to particular judgments, and general principles can be part of a system, but the relevant distinction is between the attitude of commitment on the one side, and the ability to provide a systematic account on the other. Together, the set of commitments and the system form a position; this is the object of the justification via RE. I say more on commitments, systems, and the relation between them in Sect. 2.2.

Agreement

Typically, the idea of reflective equilibrium is associated with bringing commitments and systems into agreement through mutual adjustments. This relation of agreement is normally understood as coherence, raising the question what coherence is, precisely. It is commonly agreed that coherence at the minimum requires consistency as a necessary condition, but also something more (Van Thiel and Van Delden 2009, 236). In the RE context, I take agreement between commitments and system to require at least that commitments and system are consistent, and that the commitments can be inferred from the system—although not necessarily in a strict deductive sense, and given relevant background information (Brun 2013, 241).

Given how central the search for agreement between systems and commitment is for RE, it is not surprising that it is often characterized as a coherentist account of justification: elements of an epistemic position are justified through being part of a coherent position, i.e., through their relations to other elements (Cath 2016, 216).

The RE Criteria: More than Coherence

However, the idea of RE involves more than coherence (see Baumberger and Brun 2021, 7931, as well as the references given there). As Brun (2020, 948–50) argues, there is a second reading of the “reflective equilibrium”-metaphor: namely, that the criterion (1) of agreement between commitments and system has to be established against the two further demands that (2) the resulting system has to do justice to theoretical virtues, and that (3) the resulting commitments have to (a) respect input commitments, and (b) at least some of them should have credibility that is independent of the current RE state (see also Baumberger and Brun 2021, 7931–35). The demands (2) and (3) are “pulling” from two sides on the relation between commitments and system, putting constraints on how the agreement can be reached: that the system has to be systematic in the sense of having theoretical virtues like simplicity or comprehensiveness blocks the conservative strategy of establishing consistency via the path of least resistance, i.e., avoiding adjustments of commitments whenever possible. And that resulting commitments have to have some independent credibility and also to respect input commitments, i.e., the commitments we have independently of the RE process, means that we cannot just formulate a very simple and comprehensive system, accepting everything that follows from it at the expense of rejecting all commitments that conflict with it.

Additionally, there is the demand that (4) the position should not only be internally but also externally coherent, meaning that the resulting system should be supported by background theories (Daniels 1979).

Weak Foundationalism

Because of criterion (3)—that commitments have to respect input commitments, and should have some credibility independent of the current RE state—I understand RE as a weakly foundationalist theory of justification (Brun 2013; Elgin 2014; Hansson 2007). This means that justification is not only derived from coherence alone: instead, a set of initially held commitments that have a minimal degree of credibility is revised in order to enhance their credibility by fitting them into a coherent account, which can also mean rejecting some of these initially credible commitments. Thus, justification via reflective equilibrium is not purely coherentist, because it requires that at least some of the resulting commitments have a degree of credibility that is independent of the coherence of the resulting position (Baumberger and Brun 2021, 7932). But it is only weakly foundationalist (BonJour 1985, 28–29), since a commitment can never be justified by independent credibility alone: for this, the commitment needs to be part of a coherent position that is in a state of reflective equilibrium. I say more on independent credibility below in Sect. 2.3.

Pragmatic-Epistemic Goals

Reaching a state of reflective equilibrium is a matter of degree—commitments and a system can be more or less in agreement, commitments can have more or less independent credibility, the system can exhibit virtues like simplicity or scope to a higher or a lower degree, and so on.Footnote 1 Because of the plurality of goals that a target position in RE should meet, there is no reason to think that all of them can be maximized at the same time: trade-offs are usually unavoidable.

[Doing] justice to a plurality of epistemic goals can involve trade-offs between any of them. Increasing the simplicity of a theory may only be feasible by discarding some independently credible commitments and thereby rejecting pieces of evidence. On the other hand, maintaining credibility blocks oversimplifications and sweeping generalizations one may be tempted to accept in the name of systematicity. That trade-offs are typically unavoidable is also a reason why we speak of “doing justice to” rather than “realizing” epistemic goals. Although justification calls for taking epistemic goals seriously, it would be unrealistic to insist on theories which effectively reach all those goals simultaneously. (Baumberger and Brun 2017, 178)

Which configuration of goals is relevant, and how much weight they should have, depends both on the subject matter and the specific pragmatic-epistemic objective that is pursued in the project of justification (Elgin 1996, 105; Baumberger and Brun 2017, 178; 2021, 7928). For example, for Rawls’ project with the pragmatic-epistemic objective of justifying principles of justice for a liberal society, Rawls (1999, 113–17) sees it as important that the principles should be general, universal, publicly acknowledged, impose an ordering on conflicting claims, and be accepted as final instances. Kuhn (1977, 322) names “accuracy, consistency, scope, simplicity, and fruitfulness” as some of the standard criteria for the evaluation of the adequacy of a theory, but depending on the specific objective, their importance will vary. For example, if we want to develop a regional weather model that makes exact predictions for mountain valleys, precision will be more important than if we want to develop a climate model for the purpose of understanding the basic mechanism of global climate change. In the latter case, however, simplicity and scope might be more important.

Justification and Pluralism in RE

Figure 2.1 gives a schematic overview of the main elements and requirements of RE. It shows how the position in the foreground is developed through adjusting commitments and a system both with respect to each other as well as with respect to the other constraints on a position in reflective equilibrium. We can thus distinguish between the process of searching for reflective equilibrium, and a state of being in reflective equilibrium. It is worth pointing out that, firstly, the RE criteria can be met to different degrees. This means that, secondly, it could be that there are several possible positions that, on balance, meet a configuration of these criteria equally well. There will often be different ways to resolve trade-offs between, e.g., theoretical virtues in the sense that there is no candidate system that is overall more virtuous than all other candidates, or between theoretical virtues of a system versus its ability to account for current commitments. This means that there can be a plurality of RE states that might be reached in different ways. But as long as they are equally plausible, i.e., overall meet the RE criteria to the same degree, choosing between them is a question of practicality, not of being justified. Equally plausible positions are justified to the same degree—but should of course be given up in favor of better justified positions (Elgin 1996, 107; 119; 2017, 66; 87–88). Thus, a fifth criterion for a position to be in a state of RE is (5) that it is at least as plausible with respect to the RE criteria as relevant alternatives.

Fig. 2.1
figure 1

A schematic overview of reflective equilibrium

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There is no guarantee that an RE state will be reached. RE gives us standards of justification, but there is no guarantee that by conducting a process of adjustments, we will automatically end up with a justified position. The justification RE provides is inherently provisional, and we always have to continue to assess our positions in order to review whether we can still reasonably claim to be justified (Elgin 1996, 12).

In the following sections, I address each of the RE criteria in turn, before summing them up and sketching the way ahead in Sect. 2.6.

2.2 Agreement between Commitments and System

The relation between commitments and a system is at the center of reflective equilibrium: we aim to arrive at justified commitments concerning a subject matter via supporting them with a system—e.g., one or more principle(s), a theory, or a model—where this system is, in turn, justified through being brought into agreement with our commitments. In the following, I elaborate in turn on commitments, the system, and the relation of agreement.

2.2.1 Commitments

Given a certain subject matter—e.g., fairness—we have various commitments about how actions and outcomes should be evaluated, or how we should or should not act. These can be explicit, i.e., statements which we openly endorse, or implicit, e.g., commitments that get expressed in our actions, or that we would endorse if they were presented to us. For example, as an only child, I might never have considered whether it is unfair if always only one of two siblings gets gifts, but will assert it as soon as presented with the situation. The status of being a commitment comes from being held, as Elgin (1996, 160) puts it, not from being aware that one holds it.

We can be committed to intuitions (Brun 2013), beliefs, judgments, or (what we take to be) considered judgments, but also to non-propositional content like pictorial representations or emotions (Elgin 1996, chapter V). Commitment comes in different degrees, and it can also be “minimal or feeble” (Brun 2013, 240), as long as it is considered to have something speaking favor of it or to be at least a starting point at which we find ourselves (Baumberger and Brun 2021, 7930). We can be committed to a broad range of propositions, both particular and general (Elgin 1996, 102)—the difference between commitments about a subject matter and parts of a system is therefore neither one of content nor of form, but a functional distinction (Baumberger and Brun 2017, 172).

We start from our initial commitments about a subject matter, but to make progress we need to develop a systematic account of said subject matter. And merely listing the commitments we initially hold will not meet this purpose (Elgin 1996, 103; Baumberger and Brun 2021, 7930). Our commitments are apt to be inconsistent with each other; or their relationship might be unclear altogether (Elgin 1996, 106).

For example, if I judge that situation a is unfair and situation b fair, it might not directly be clear whether or not the situations are similar in a way that makes it inconsistent to hold both these judgments at the same time. Some of what seems like an initially credible commitment might turn out to be based on prejudice. Or there might be inferences between them that we did not consider so far, e.g., a subset of commitments where each one seems plausible on its own, but that might together commit us to something that we actually do not want to accept. In short, our initial commitments do not allow us to meet our pragmatic-epistemic goals, and this is why we start a process of inquiry and justification in the first place.

Merely collecting and writing down our commitments in a list does not enable us to directly infer anything for new cases, as we cannot be clear what exactly the relevant features are that make us classify an act as, e.g., fair or unfair. And neither will it allow us to distinguish between justified commitments and those based on prejudice, bias, or misinformation. To identify and test (candidates for) relevant features, we have to formulate a system that is in agreement with our commitments, i.e., that names relevant features and can account for the commitments. This system is formulated through a process that will also transform our commitments.Footnote 2

We can distinguish between input, current, and resulting commitments, meaning the commitments we have independently of the RE process, the ones we have at a given point during the process, and the ones that result at the end of the process. These distinctions are due to the nature of the RE process, during which some of the commitments that we started out with will be adjusted or rejected, while additional commitments can be accepted. Thus, the input and the resulting commitments might differ significantly.

Among input commitments, the additional distinction between initial and emerging commitments can be made (Baumberger and Brun 2021, 7932). Initial commitments are a sub-class of the input commitments, namely the input commitments the RE process initially starts out with. Emerging commitments are another subclass of the input commitments. They are commitments which are made explicit during the RE process but neither because they are inferred from the system nor as a direct result of an adjustment to the position. This might happen because during the RE process we can be confronted with new considerations that never occurred to us before. Thus, like the initial commitments, those emerging commitments enter the process as input. Emerging commitments need to be distinguished from what Baumberger and Brun (2021, 7932) call “purely inferential” commitments, that is commitments which the epistemic agent accepts purely because she inferred them from the system currently under construction. As we will see in Sect. 2.3, this difference is important for the constraint that resulting commitments should respect input commitments.

2.2.2 System

The set of commitments that we have before we start the RE process expresses our commitments concerning a subject matter. The system is constructed for the purpose of clarifying and systematizing our commitments in order to do justice to the pragmatic-epistemic goals that drive the process of justification. It fulfills a different function than the commitments and expresses a change in perspective on the subject matter, aiming to grasp it from a theoretical point of view. This functional distinction remains true even when a reflective equilibrium is reached and we are also committed to the system in the indirect sense of being committed to everything that can be inferred from the system.

That this distinction is purely functional, and not fixed on content or form, is illustrated by Brun (2020) with the example of modus ponens: On the one hand, we can see the inference rule ϕ → ψ;ϕ ⊢ ψ as a principle, i.e., a part of a logical system that, e.g., characterizes valid logical inferences. On the other hand, we can be committed to accept all inferences of this form as valid. If an RE was reached, both will be the case.

The system can include elements such as principles, theories, models, or category schemes (for a discussion of category schemes, see Elgin 1996, 136). Parts of the system can be law-like or general, but they do not need to be (see, e.g., Gertken 2014): the important part is that the system is in agreement with the commitments while also doing justice to theoretical virtues.

I understand the system as the organizing element which is constructed in order to identify which features of the commitments are the relevant ones, how the different commitments relate to each other, and to make explicit what further considerations are relevant and should be added. Going back to the fairness case, we could, e.g., compare a system that picks out equality as the relevant feature with one that identifies desert as the main consideration for fairness. Which of them turns out to be more plausible will depend on how well it can account for the current commitments, whether we are willing to commit to the implications of the system for situations we did not consider before, and whether or not we can use this system for the purpose we had in mind. For example, a system that is restricted to fairness in interpersonal relations will most likely not be suitable as an account for fairness in jurisprudence.

2.2.3 Agreement between System and Commitments

The sought-after relation of agreement between commitments and system is often identified with coherence. To be in agreement, commitments and system have to be consistent with each other, but this is only a necessary, not a sufficient condition: also completely unrelated propositions can also be consistent with each other. What else is needed on top of consistency to count as agreement will differ depending on the specific project of justification one pursues. One sensible proposal for a minimal characterization of agreement is that (a) the commitments are consistent in themselves, (b) the system is consistent in itself, (c) commitments and system are consistent with each other, and (d) the system accounts for the commitment in the sense that the latter can be inferred from the former (given relevant background information). “Inference” includes, but does not reduce to, deductively valid arguments. Requiring that epistemic coherence always rests on logical inferences would be too demanding. Weaker relations, e.g., “increases the probability that” or “makes it more reasonable to believe that” can form the basis for coherence (Hansson 2006, 100).

Arguably, the agreement criterion is a necessary requirement for a position to be in a full state of reflective equilibrium. There is no guarantee that it can be reached, though: maybe the best position that we can reach still includes conflicts between commitments and a system. Justification in the form of reflective equilibrium is not trivial to reach.

However, agreement is not sufficient for RE, either: agreement could be reached, e.g., by only making the most minimal adjustments to the commitments in order to resolve inconsistencies, and then writing the list of the commitments down as a “system”—which would of course be able to account for the commitments since it would be identical with them. If we can consistently commit to everything that can be inferred from this “system”, agreement would have been reached.Footnote 3 However, we would not be willing to call this cleaned up list a “system”, nor would it meet the goals that motivated us to start revising our commitments. On the other hand, it seems that too-drastic revisions of commitments have to be blocked, too: we should not simply abandon the subject matter and start pursuing another project of inquiry. The latter might seem dubious and carry the danger of making RE too conservative (cf. Dutilh Novaes 2020, n. 5)—could it not, e.g., result in us staying committed to biases and prejudices?

In the next section, I distinguish two senses of how input commitments should be respected—and argue that, if understood in the right way, this “respect” does not make RE too conservative, but actually contributes to its justificatory power.

2.3 Respecting Input Commitments and the Criterion of Independent Credibility

There are (at least) three demands on commitments: As we have already seen, (i) commitments should be in agreement with the system, which also requires that they are consistent. Additionally, (ii) they should have independent credibility, i.e., some credibility that is independent of the current RE process, and (iii) resulting commitments should respect input commitments adequately (see Baumberger and Brun 2021; Brun 2020, for arguments in favor of making these distinctions). In this section, I focus on the demands that are particular to the commitments, i.e., independent credibility and respecting input commitments in order not to abandon the subject.

2.3.1 Independent Credibility

Reflective equilibrium never starts completely from scratch (Scheffler 1954, 188): we always have some sentences that we hold as acceptable or plausible, even if we are lacking the justification via RE. These are the input commitments that we have independently, or before, the RE process. We are committed to these sentences (or acts, or values, etc.) because we ascribe some independent credibility to them, i.e., credibility they have independently of being justified via RE.

Reasons for ascribing independent credibility to a commitment can be because (a) it accommodates some evidence, which for empirical projects might mean observations or testimony, and for non-empirical projects could, e.g., refer to intuitions (Baumberger and Brun 2017, 177). Another reason for ascribing some minimal degree of independent credibility to a commitment is simply (b) that so far nothing speaks against holding this commitment. Such very minimal commitments might for example play the role of working hypotheses that help us to develop our position. Lastly, commitments can have credibility that is independent from the current RE process if (c) background theories support them (Baumberger and Brun 2017, 177), for example, in the context of justifying a theory of distributive justice, a commitment to help people who are much less well-off may be supported by a moral background theory which includes a requirement to help the poor.

As point (b) shows, a minimal degree of commitment is enough to qualify an input commitment to enter the process. That is, if we are committed to a consideration, this is enough to ascribe it some independent credibility and to let this commitment enter the process of adjustments. We do not need to identify additional (e.g., inferential) support for this commitment. In case of conflicts, these weak commitments will often be discarded most easily; however, it can also be that a number of weak commitments together outweigh a more “weighty” one (cf. Scheffler 1954, 182). Thus, admitting also very weak commitments—for example, based on a mere hunch—is one of the ways that opens the possibility for innovation in reflective equilibrium, while insisting that a consideration has to have a particular “pedigree” to be independently credible may lead to conservatism and entrench bias.

Consequently, even having a very high degree of independent credibility is not enough for the justification of a commitment (Elgin 1996, 102): it also has to be part of a position in which it and the rest of the relevant commitments are accounted for by a system that does justice to theoretical virtues—that is, in order to be justified, a commitment needs to be part of a position that is in reflective equilibrium.

This means that while the independent credibility of a commitment plays a role for justification, and has to be respected, it is not determinate. The question is not only how strongly we are committed to each of our individual commitments, but also how willing we are to commit to the whole set taken together—and this might sometimes speak against upholding one or more individual commitments. Compare the following quote by Scheffler (1954):

The justification for accepting [a sentence] A at a given time may now be made not on the grounds of its own initial credibility, nor of some unspecified coherence, but on the basis of its coherence with the system which maximizes initial [i.e., in the terminology used here: independent; T.R.] credibility at that time, while, together with its sister sentences, A indirectly controls the choice of this standard system. (Scheffler 1954, 182)

Respecting input commitments and their independent credibility can indeed be a reason to reject specific input commitments, even those that have a high independent credibility: while the independent credibility of a commitment speaks in its favor, the independent credibility of other commitments can—in case of conflicts—speak against it (mediated through a system that accounts for some, but conflicts with other, commitments).

When adjusting commitments, we thus have to make plausible that the independent credibility of a commitment was not simply discarded, but in fact outweighed by other relevant considerations, i.e., to argue that independent credibility was respected adequately. Another way to put this is that adjusting the commitment in question should increase the credibility of the epistemic position as a whole more than the independent credibility of the commitment would contribute to it. Maximizing the credibility of the position as a whole is not the same as minimizing deviation from the independently credible starting positions (cf. Elgin 1996, 109).

Brun (2013, 241) gives the example of a supporter of gay marriage who appeals to a ‘between consenting adults’ principle and realizes that this conflicts with his commitment to the wrongness of polygamy. He can then, e.g., argue that the latter “was feeble anyway in comparison to the principle which covers many commitments he firmly holds”. This would be an instance of referring to the relative weights of commitments and system, i.e., the other commitments outweigh the polygamy-commitment via the ‘between consenting adults’ principle. The epistemic position as a whole is more plausible without the commitment.

Alternatively, or additionally, he could argue that his views on polygamy were merely a cultural prejudice. This would mean that the independent credibility of the commitment cannot withstand scrutiny, and that he is actually lacking positive reasons to uphold the commitment. If his commitment turns out to be grounded only in cultural prejudices, he has no valid reasons that could explain why there should be a relevant difference between gay marriage and polygamy, if we are upholding a ‘between consenting adults’ principle. The independent credibility of the commitment is in this case not only outweighed, but lost.Footnote 4

The criterion of independent credibility means that RE does not create justification “ex nihilo” (Baumberger and Brun 2017, 176)—instead of “pure” coherentism, it makes RE a combination of (weak) foundationalism and (weak) coherentism (cf. Hansson 2007). Justification by reflective equilibrium requires that the resulting position includes at least some commitments which also have some degree of credibility independently of the position. As Elgin (1996, 107) puts it, “For reflective equilibrium, independently motivated, initially tenable commitments must underwrite coherence.”

One reason why a resulting commitment has independent credibility might be that it is an independently credible input commitment which survived the process of adjustments. But not only input commitments can have independent credibility: it is possible that commitments that are the result of adjusting an input commitment have some credibility that is independent of their coherence with the current position. Consequently, respecting independent credibility does not only refer to the independent credibility of input commitments. Following Baumberger and Brun (2021, 7934), we can distinguish independent credibility, the credibility a commitment has independent of the coherence of the current position, from initial credibility, the credibility a commitment had at the initial stage.

Since not only input commitments can have independent credibility, and because independent credibility can vary and change over time, adequately taking independent credibility of commitments into account does not automatically ensure that we do not change the subject. The subject matter is constrained by our input commitments, and those are what have to be respected in order not to abandon the subject.

2.3.2 Not Abandoning the Subject

When we start a project of inquiry in order to search for a justified answer, we do this because we want to learn something about a particular problem, or particular subject matter. Thus, simply abandoning the subject and focusing on another problem will not be an adequate answer. Strawson (1963) has expressed the worry that we might be tempted to simply change the subject in the following way:

[We] may be diverted from the wish to understand what we are doing, by encouragement to do something else; and [...] if the wish seems futile, the diversion may seem desirable; and then the complaint that the wish is not thereby satisfied will, not doubt, seem futile too. (Strawson 1963, 509)

Baumberger and Brun (2017) give two examples for how a process of reflective equilibrium could go astray and abandon the subject:

If a course of reflection leads to a theory which merely underwrites might is right, it will not count as providing a moral theory since it would force us to give up too much of our most important moral commitments. Similarly, if a model turns out to describe only short-term conditions of meteorological variables such as temperature and precipitation in a given region, it will not count as a climate (in contrast to weather) model. (Baumberger and Brun 2017, 179)

However, even if we do not want to change the subject in this radical sense of abandoning it and ending up with a theory or systematization of another subject, it still has to be possible that the subject undergoes significant changes in the sense of alterations and elaborations (Elgin 1996, 130): we want to be able to get rid of prejudices and biases, we want to be able to include further relevant considerations, and we want to be able to explicate concepts so that they are more suitable for our epistemic objectives—even if this conceptual change can change the extension of our concepts (compare the famous example of explicating “fish” so that it excludes whales).

It seems plausible that making progress in understanding and theory-development can also consist in the insight that our original delimitation of the subject matter was not helpful or misled. Systematizing our commitments about a specific subject often requires considerable re-thinking and re-categorizing—potentially going so far that we will speak of “paradigm changes” (Baumberger and Brun 2021, 7934). Take the following example: using your moral commitments you decide that a course of action is impermissible because it conflicts with the principle that one ought not inflict gratuitous pain on people. You then notice that in that principle the term ‘on people’ does no work. The principle should be ‘one ought not inflict gratuitous pain’. This immediately extends your moral theory to all animals capable of experiencing pain. Have you changed the subject of your moral theory? You have definitely massively extended its scope.Footnote 5 But arguably, you also made substantial progress by recognizing the moral value of non-human animals.

How, then, can the criterion of not abandoning the subject be spelled out in a way that still allows us to make progress? What we want to do is to improve upon our initial commitments (see, e.g., Elgin 2017, 66) with a specific (set of) goals, or questions, in mind. This means that in order to ensure that we stay on topic, it is necessary that we can trace how the resulting commitments were obtained from the input commitments. But this is not enough: we also have to be able to give reasons, or arguments, for why these adjustments consist in improvements of our original grasp of the subject matter. In short, we need to be able to give arguments that can explain why the input commitments seemed plausible, but still needed to be revised.

This “tie” back to the input commitments ensures that even if our position has substantially changed, we can still see how it is connected back to our initial understanding of the subject, and the initial problems we started out with. This requirement thus highlights the importance of the process of adjustments in RE: it is not just enough to describe the initial and the resulting position, but rather we need to be able to reasonably trace how the latter was constructed based on the former. We can read the following quotation from Strawson (1963) as an expression of this:

[If] the clear mode of functioning of the constructed concepts is to cast light on problems and difficulties rooted in the unclear mode of functioning of the unconstructed concepts, then precisely the ways in which the constructed concepts are connected with and depart from the unconstructed concepts must be plainly shown. (Strawson 1963, 513)

This process can be a reconstruction and does not need to be a description of how we did actually proceed, but it needs to allow us to see how the resulting position can be reached starting from the input commitments. After all, we want to learn something about the commitments that we start out with, and to improve upon them—and learning why we should revise them is one way in which we might achieve this goal.

Which changes of input commitments are compatible with addressing the relevant subject matter is not a question that has a clear-cut answer, however. Instead, it has to be answered based on arguments referring to input commitments, the overall pragmatic-epistemic objective, and background theories (Baumberger and Brun 2021, 7933). In the example from Baumberger and Brun (2017) above, we did fail to formulate a moral theory, and we did construct a weather and not a climate model. These failures become apparent not only because we made too-drastic changes to the input commitments, but especially because we can argue that these projects missed their objective: our background expectations for a moral theory speak against the might is right principle, and background theories about the distinction between climate and weather allow us to argue that the constructed model fails to be a climate model.

Thus, it seems illusory to expect that there is one precise yet generally applicable criterion for whether or not the subject was changed. Generally, we should expect that there will still be some overlap between input and resulting commitments, that resulting commitments will accommodate some of the same evidence as input commitments did, or that the theory will still be applicable to the same cases and questions as the input commitments intended to answer. For example, when constructing a moral theory, we might accept that we were wrong in our judgment about whether or not a specific action is permissible, but we will still want to know what we should do in this situation. And we will expect that the answer stands in an appropriate relation to our input commitments about relevant factors for moral evaluation (cf. Brun 2020, 937–38).

The criterion of respecting input commitments in order to ensure that the subject is not abandoned is thus a different criterion than the one that commitments should have independent credibility. The independent credibility of a commitment—e.g., how it is supported by evidence or background theories—will of course typically play a role in the arguments for whether or not an adjustment, or series of adjustments, amounts to abandoning the subject. But it is not only the input commitments that can have independent credibility, and the not-abandoning-the-subject requirement is specific to input commitments (initial and emerging). Purely inferential commitments, that is, commitments the agent adopts solely because she inferred them from the system currently under construction, do not have independent credibility. Another way to say this is that the system cannot be a source of credibility that is independent of how well the commitment fits into the position under construction, as the system is itself a part of this position. What starts as a purely inferential commitment can gain independent credibility later, e.g., if it turns out that it can be supported by background theories. But even then, those commitments do not play a role for providing understanding of the original subject matter and consequently do not need to be respected like input commitments (Baumberger and Brun 2021, 7932; compare also the status of “merely derived beliefs” in Hansson 2006).

One last point, before we move on to theoretical virtues of the system: of course, not switching the subject is not an ultimate epistemological demand. An agent may very well abandon a subject and start to pursue other goals, if, e.g., she continues to fail to reach reflective equilibrium. However, if we do abandon the original subject, we should do so consciously. We start to speak about other problems if we are no longer able to show how our current inquiry ties back to the input commitments of the original problem. Consequently, our results will have no direct authority or justificatory power on the abandoned subject.

2.4 Theoretical Virtues

There are some epistemic goals that commitments and the system both should fulfill qua them being parts of the position, that is, the position should be internally and externally consistent. Additionally, as discussed in the section above, commitments should have independent credibility. In this section, I focus on the epistemic goals that are specific to the system, i.e., theoretical virtues.

As I have already mentioned in Sect. 2.1, the system should do justice to a number of theoretical virtues. Virtues such as accuracy, scope, simplicity, and fruitfulness will be relevant in most contexts (at least to some degree, and most likely in different interpretations). There are also more specific virtues, which will be relevant only in some contexts, e.g., visualizability for purposes of scientific modeling, or the ability to be action-guiding for moral principles.

These virtues will sometimes pull in different directions, for example, it might only be possible to gain simplicity at the cost of accuracy, or vice versa. Thus, they will also have to be weighed against each other—and against the criteria of respecting input commitments and the independent credibility of commitments. The specific pragmatic-epistemic objective that we pursue in the RE process in question informs which specific configuration of virtues is relevant (Baumberger and Brun 2021, 7928). For example, if we want to justify an approach to decision-making under uncertainty for public policy-making, other theoretical virtues (or at least another weighting of them) might be relevant than if our goal were a purely formal decision theory. In the second case, mathematical precision may be paramount, whereas in the first case, the ability to be action-guiding will be much more important.

Demanding that the system has theoretical virtues ensures its systematicity, since it blocks the strategy of writing down the list of commitments, calling it a system, and claiming to have reached a position in reflective equilibrium (Baumberger and Brun 2017, 177–78). Striving for theoretical virtues in order to be able to meet a certain pragmatic-epistemic objective is what drives the process of adjustments forward against the more conservative “pull” from the demands to respect input commitments and their independent credibility. The criterion that the system should have theoretical virtues thereby also contributes to the coherence of the position, for example, because it asks for a system that can categorize commitments, identify relevant features, and relate them to each other. Having theoretical virtues is thus a part of what makes a system systematic.

The idea that it is a pressure for systematization that drives us to move away from what we were initially committed to about the subject matter, that is, what drives us to make progress, is expressed nicely in the following quote by Scheffler (1954):

[Justification] is the systematic rechanneling of initial commitments in such a way that each act is judged in terms of all others. We do not start from scratch, but always with initial commitments of some degree; but neither do we rest content with the latter. We modify and transform them into derived commitments of various sorts by systematic pressure which is channeled through principles of congruence. (Scheffler 1954, 188, italics added by T.R.)

There are two reasons why the RE criterion demands that the system should do justice to a configuration of theoretical virtues, and not realize them exactly. Firstly, as already mentioned in Sect. 2.1, theoretical virtues can pull in different directions, and sometimes trade-offs will be unavoidable. Demanding that a system reaches all the goals at the same time would thus be unrealistic.

Secondly, the exact characteristics of the configuration of epistemic goals, e.g., which virtues are relevant, how much weight they should have, and how they are exactly interpreted, is a result of the process and not a precondition for it (Baumberger and Brun, 2021, 7929; Elgin, 2017, 89). The configuration of theoretical virtues that we start out with is also a form of higher-order commitment to the standards that we employ in our inquiry. Like first-order commitments about the subject matter, they can change during the process. And like first-order commitments, theoretical virtues can be supported or undermined by background theories about specific theoretical virtues and their cognitive merits (Baumberger and Brun 2021, 7929; Elgin 1996, 105). Thus, like first-order commitments about the subject matter, our higher-order commitments in the form of theoretical virtues and other standards of inquiry are open to revision, but have to be respected during the process.

2.5 Background Elements and Social Dimensions

We have already seen that it is central for RE to reach a state of agreement between commitments and a systematic account of them. However, to be justified, it is not enough for a position of commitments and a system to be internally in agreement. The position should also be externally coherent, that is, with related theories and otherwise accepted and justified theories and conceptions (cf. Kuhn 1977, 323). Instead of settling for the best “fit” between commitments and system candidates, we should also refer to background theories in order to bring forward arguments for or against possible adjustments. The justification of a current position in the foreground thus takes place against a background that is relatively fixed and—at the given time—not called into question. This background necessarily will include epistemic achievements of others, as a single epistemic agent is not able to justify everything on their own.

2.5.1 Background Theories, Background Information, and Background Assumptions

Within the background, three rough distinctions can be made: firstly, there are accepted background theories which are vindicated in a way relatively independent of the foreground, that is, their justification should be relatively independent from the current project of inquiry. During the RE process, they will also guide the process of adjustments by providing additional support or constraints on the foreground system.

Secondly, often additional background information is needed to relate the system and the commitments to each other, e.g., in order to infer something from a moral principle on a specific action, factual information on the relevant situation in which the action takes place needs to be added:

Moral beliefs often explain, entail or conflict with other beliefs only if some context of nonmoral assumptions is presupposed. For instance, hedonistic utilitarianism does not by itself conflict with, or entail, the view that it was wrong of USA to wage war against Iraq, but only in conjunction with claims about the consequences of USA’s war. (Tersman 1993, 54)

Thirdly, in practice we will often have to make background assumptions, because we cannot investigate everything at the same time and will have to make some stipulations in order to get the process going. As long as these assumptions don’t do the “real work” of systematizing the commitments, this seems relatively unproblematic, but it requires paying close attention to it while actually carrying out (or reconstructing) an RE process.

Sometimes, the background is seen as another element of the process of adjustments, which is to be adjusted mutually with the commitments and the system.Footnote 6 However, while I agree that nothing is, in principle, safe from revision in RE, I think the background should not be seen as one of the primary elements to be adjusted in a given project of justification. What is accepted as background also partly constrains the subject matter, and if we start to change the background too drastically, we will also change the subject. Another way to put it is to say that by not including what is in the background in our input commitments, we also express a sort of higher-order commitment about the subject matter in question.

Thus understood, the distinction between foreground and background is not an absolute distinction, but a matter of perspective: it depends on the specific pragmatic-epistemic project that we are pursuing. During an RE process, parts of the background can be called into question and become part of the foreground, but this will typically mean that we are changing our epistemic project: for example, because we might have noticed that our delimitation of the subject matter rested on problematic assumptions in the background, and that we just cannot make progress in our original project without addressing these problems.Footnote 7 Background theories that are justified by their own RE process are more likely to remain fixed through the process than background assumptions, since their status as being part of a justified position of their own gives us strong reasons not to revise them easily. In general, it might be a good strategy to try to hold the background constant for as long as possible. But this does not change that there are no absolute, once-and-for-all fixed points.

2.5.2 Going Public

When taking background elements into account, we typically have to rely on theories, distinctions, or claims that we cannot directly prove or justify ourselves in order to continue to pursue our current pragmatic-epistemic project. Having to justify all that for ourselves before coming back to the question we are concerned with would mean that we never arrive there.

As Elgin (1996, 116) argues, relying on others in RE amounts to more than calling on experts to “patch holes” in our position, e.g., in situations where we are lacking the expertise to estimate the independent credibility of a commitment. Ultimately, we have to rely on the “resources of the community” for even trivial facts:

My tenable belief that trash is collected on Tuesdays needs no support from the experts. My own experience bears it out. Still, to have that belief, and to have experiences that count as evidence for or against it, requires knowing what trash is, what trash collection is, what Tuesdays are. Such facts are socially constituted and are imparted through socialization. Without the resources the community provides, I could neither formulate nor justify the belief in question. (Elgin 1996, 116)

Not all of these background resources have to be made explicit by an agent engaging in a pragmatic-epistemic project by employing RE, of course (nor would this be possible). But we have to keep in mind that we can justify our positions only with, and against, the broader background of the relevant epistemic communities, without being able to review everything for ourselves. This is not in itself something RE specific. However, through the background–foreground distinction, RE makes the point of relying on background resources especially salient.

Not only do we have to rely on the resources of others because we cannot justify everything on our own, we should also do so in order to “broaden the base” so as to control “for perspective and for eccentricity” (Elgin 1996, 117). The social-epistemological elements of RE do not only concern background theories and background information, but agents should also consider the commitments of others, in particular commitments of experts or people whose opinion on the subject matter is otherwise relevant (maybe because they are practitioners, e.g., the commitments of nurses and patients should be considered when developing principles of ethics for care in nursing homes).

RE is thus inherently holistic, which also explains why the justification it provides is preliminary: we should cast the net as wide as possible, and include as many relevant considerations as possible, but there is always the possibility that new information arises that unbalances our equilibrium.

2.6 Summing Up: Criteria of Reflective Equilibrium

To sum up, we may list the following conditions for reaching a position that is in a state of reflective equilibrium:

  1. 1.

    The resulting commitments and the system are in agreement;

  2. 2.

    The resulting commitments and the system are supported by background theories;

  3. 3.

    The system does justice to the relevant theoretical virtues;

  4. 4.

    The resulting commitments respect the input commitments adequately;

  5. 5.

    The resulting commitments have independent credibility; and

  6. 6.

    The resulting position is at least as plausible as all available alternatives.

Criterion (6) is important because the criteria (1)–(5) can be met to different degrees, and trade-offs among them are possible. Thus, through following different pathways and exploring different ways of systematization and adjustment, multiple, equally plausible positions might be achieved that are in reflective equilibrium to the same degree, i.e., overall meeting the criteria equally well. As Elgin (1996, 119) argues, this is not a problem for justification, but rather a question of practicability: as long as my position is at least as plausible as yours, none of us has a good reason to abandon our position and adopt the other. However, simply because there might be more than one maximally plausible position which is acceptable, it does not follow that a position which is less than maximally plausible—which is inferior to another relevant alternative—is acceptable (Elgin 1996, 143–145).

And even though it is possible that more than one justified position results, it is also possible that none is reached. Following Elgin (1996), I see reflective equilibrium as an imperfect procedural epistemology. There is no guarantee that an equilibrium is reached, and we may with reason believe that a system is in equilibrium when it is not (Elgin 1996, 14). The consequence of this, however, is not skepticism, but fallibilism: justification is inherently provisional, but no less reasonable (Elgin 1996, 15).

The Way Ahead

In this chapter, I described the theoretical foundations of reflective equilibrium as an imperfect procedural epistemology that is weakly foundationalist and holistic. However, this theoretical conception needs to be specified in various ways in order to become applicable in the form of a method. In the next Chap. 3, I identify the various methodological decisions and challenges that need to be made in order to get from this theoretical conception to an applicable method. In particular, I will suggest ways in which the initial position can be described, and in which the process of adjustments and the evaluation of its results can be structured.