This 2005 volume brings together twelve papers by many of the most prominent applied general equilibrium modelers honoring Herbert Scarf, the father of equilibrium computation in economics. It deals with developments in applied general equilibrium, a field which has broadened greatly since the 1980s. The contributors discuss some traditional as well as some modern topics in the field, including non-convexities in economy-wide models, tax policy, developmental modeling and energy modeling. The book also covers a range of distinct (...) approaches, conceptual issues and computational algorithms, such as calibration and areas of application such as macroeconomics of real business cycles and finance. An introductory chapter written by the editors maps out issues and scenarios for the future evolution of applied general equilibrium. (shrink)

How can we figure out what’s right or wrong, if moral truths are neither self-evident nor something we can perceive? Very roughly, the method of reflective equilibrium (RE) says that we should begin moral inquiry from what we already confidently think, seeking to find a a match between our initial convictions and general principles that are well-supported by background theories, mutually adjusting both until we reach a coherent outlook in which our beliefs are in harmony (the equilibrium part) (...) and we know why and how they support each other (the reflective part). It has been central to the self-understanding of normative ethics and other branches of philosophy in the last half a century. In this chapter, we examine the history of the idea of RE and introduce a schema for generating 256 variants. We explain why RE is subject to serious objections insofar as it purports to yield epistemic justification in virtue of achieving coherence. However, we also develop a new argument to the effect that RE is the best feasible method for us to achieve moral understanding and the ability to justify our judgments to others. It may thus be crucial for responsible moral inquiry, even if coherence among considered judgments and principles is neither sufficient nor necessary for justified moral belief. (shrink)

This article examines the method of reflective equilibrium (RE) and its role in philosophical inquiry. It begins with an overview of RE before discussing some of the subtleties involved in its interpretation, including challenges to the standard assumption that RE is a form of coherentism. It then evaluates some of the main objections to RE, in particular, the criticism that this method generates unreasonable beliefs. It concludes by considering how RE relates to recent debates about the role of intuitions (...) in philosophy. (shrink)

Reflective equilibrium ("RE", for short) is a method of justification which works roughly as follows: We start with our pre-theoretical judgements (about, e.g. moral issues) and try to explain them by a systematic theory. This leads to a process in which judgements and principles are mutually adjusted to each other until a state of equilibrium is reached. For more than half a century, RE has been very popular, as well as controversial, among philosophers of many persuasions. Given how (...) frequently the method is mentioned, embraced and attacked, it is surprising that only very few attempts have been made at analysing and developing RE in detail. This topical collection brings together papers that develop RE on a conceptual level, analyse it using formal methods or investigate applications of RE. (shrink)

In moral epistemology, the method of reflective equilibrium is often characterized in terms of intuitions or understood as a method for justifying intuitions. An analysis of reflective equilibrium and current theories of moral intuitions reveals that this picture is problematic. Reflective equilibrium cannot be adequately characterized in terms of intuitions. Although the method presupposes that we have initially credible commitments, it does not presuppose that they are intuitions. Nonetheless, intuitions can enter the process of developing a reflective (...) equilibrium and, if the process is successful, be justified. Since the method of reflective equilibrium does not essentially involve intuitions, it does not constitute a form of intuitionism in any substantial sense. It may be classified as intuitionist only in the minimal sense of not reducing justification to a matter of inference relations alone. (shrink)

Elgin has presented an extensive defence of reflective equilibrium embedded in an epistemology which focuses on objectual understanding rather than ordinary propositional knowledge. This paper has two goals: to suggest an account of reflective equilibrium which is sympathetic to Elgin’s but includes a range of further developments, and to analyse its role in an account of understanding. We first address the structure of reflective equilibrium as a target state and argue that reflective equilibrium requires more than (...) an equilibrium in the sense of a coherent position. On the one hand, the position also needs to be stable between a ‘conservative’ pull of input commitments and a ‘progressive’ pull of epistemic goals; on the other hand, reflective equilibrium requires that enough of the resulting commitments have some credibility independent of the coherence of the position. We then turn to the dynamics of reflective equilibrium, the process of mutual adjustment of commitments and theories. Here, the most pressing internal challenges for defenders of reflective equilibrium arise: to characterize this process more exactly and to explain its status in relation to reflective equilibrium as a target state. Finally, we investigate the role of reflective equilibrium in Elgin’s account of understanding and argue that objectual understanding cannot be explained in terms of reflective equilibrium alone. An epistemic agent who understands a subject matter by means of a theory also needs to be able to use this theory and the theory needs to meet some external rightness condition. (shrink)

This thesis presents a novel theoretical framework for addressing one of the most pressing challenges in contemporary artificial intelligence: how fluctuational AI-driven decision systems can ethically balance epistemic uncertainty, human autonomy, and social equity in high-stakes environments. Current approaches to AI ethics treat these three dimensions as separate, static concerns to be optimized independently. However, this research demonstrates that in fluctuational AI systems operating in critical domains such as healthcare, criminal justice, and financial services, these elements exist in a state (...) of dynamic tension where changes in one dimension necessarily affect the others. -/- The central contribution of this work is the Dynamic Equilibrium Theory (DET), which introduces the concept of fluctuational ethics—the idea that ethical AI systems must be designed to handle not just uncertainty in data or predictions, but uncertainty in the ethical landscape itself. The framework proposes a triadic model where epistemic uncertainty, human autonomy, and social equity form an interconnected system that must maintain dynamic equilibrium rather than static optimization. -/- Through comprehensive analysis of empirical data from real-world AI deployments, including the COMPAS criminal justice algorithm and healthcare diagnostic systems, this research provides quantitative evidence for the interdependence of these ethical dimensions. The ProPublica analysis of COMPAS reveals that Black defendants were 1.96 times more likely to be falsely classified as high risk compared to White defendants, while White defendants were 1.71 times more likely to be incorrectly classified as low risk—demonstrating how epistemic uncertainty, human autonomy, and social equity interact in complex ways that current frameworks fail to address. -/- The thesis develops mathematical formalizations of the dynamic equilibrium using stochastic differential equations and tensor representations, providing a rigorous foundation for implementation. The framework is validated through case studies across multiple high-stakes domains, showing how different contexts require different equilibrium points while maintaining the fundamental integrity of all three dimensions. -/- This work represents a paradigm shift from static, rule-based ethical frameworks to dynamic, adaptive systems that recognize the inherent fluctuational nature of AI decision-making. The implications extend beyond technical implementation to policy and governance, suggesting new approaches to AI regulation that account for temporal ethical dynamics and contextual sensitivity. (shrink)

Ever since the introduction of reflective equilibrium in ethics, it has been argued that reflective equilibrium either leads to moral relativism, or that it turns out to be a form of intuitionism in disguise. Despite these criticisms, reflective equilibrium remains the most dominant method of moral justification in ethics. In this paper, I therefore critically examine the most recent attempts to defend the method of reflective equilibrium against these objections. Defenders of reflective equilibrium typically respond (...) to the objections by saying that either reflective equilibrium can in fact safeguard moral objectivity or alternatively, even if it cannot, that there simply are no reasonable alternatives. In this paper, I take issue with both responses. First, I argue that given the non-foundationalist aspirations of reflective equilibrium, moral objectivity cannot be maintained. Second, I argue that reflective equilibrium is not the only game in town once intuitionism has been discarded. I argue that given their own normative ambitions, combined with their rejection of intuitionism, proponents of reflective equilibrium have reason to take alternative methods of moral justification, and more specifically transcendental arguments, more seriously than they have done so far. I end by sketching the outlines of what this alternative methodology might look like. (shrink)

ABSTRACT In ethics, the use of empirical data has become more and more popular, leading to a distinct form of applied ethics, namely empirical ethics. This ‘empirical turn’ is especially visible in bioethics. There are various ways of combining empirical research and ethical reflection. In this paper we discuss the use of empirical data in a special form of Reflective Equilibrium (RE), namely the Network Model with Third Person Moral Experiences. In this model, the empirical data consist of the (...) moral experiences of people in a practice. Although inclusion of these moral experiences in this specific model of RE can be well defended, their use in the application of the model still raises important questions. What precisely are moral experiences? How to determine relevance of experiences, in other words: should there be a selection of the moral experiences that are eventually used in the RE? How much weight should the empirical data have in the RE? And the key question: can the use of RE by empirical ethicists really produce answers to practical moral questions? In this paper we start to answer the above questions by giving examples taken from our research project on understanding the norm of informed consent in the field of pediatric oncology. We especially emphasize that incorporation of empirical data in a network model can reduce the risk of self‐justification and bias and can increase the credibility of the RE reached. (shrink)

Equilibrium explanations use an equilibrium to represent and explain a system’s dynamic behavior. They provide a system with the property of global stability: a system will converge towards and remain in equilibrium regardless of its initial conditions and dynamic process. Thus, equilibrium explanations are generally treated as non-causal explanations. There are two claims subsumed under that comprehensive thesis. The first claim is that equilibrium explanations do not identify any causes because a system with global stability (...) resists manipulation. The second claim is that even if equilibrium explanations do identify causes by manipulation, those causes are embedded in a system’s deeper, underlying structural relationships, and those causes are irrelevant to explaining a system’s behavior. Only the system’s structural relationships are relevant. But equilibrium explanations are not monolithic. I compare dynamic systems with multiple, competing equilibria to systems with a globally stable equilibrium. Equilibrium explanations of the former use intervention on a system’s initial conditions and dynamic process to manipulate equilibria, which identifies causes. Furthermore, a system’s initial conditions and dynamic process are relevant to explaining why one equilibrium is selected instead of another. I then apply these lessons to systems with a globally stable equilibrium and discuss when their corresponding equilibrium explanations have a proper role in the parent sciences. (shrink)

In this paper, we focus on one controversial element of the method of reflective equilibrium, namely Rawls’s idea that the commitments that enter the justificatory procedure should be pre-selected or filtered: According to him, only considered judgements should be taken into account in moral philosophy. There are two camps of critics of this filtering process: 1) Critics of reflective equilibrium: They reject the Rawlsian filtering process as too weak and seek a more reliable one, which would actually constitute (...) a distinct epistemic method. 2) Proponents of reflective equilibrium: They reject the Rawlsian filtering process as too exclusionary. We defend RE against its critics, arguing that the method can secure reasonable commitments without depending on a strong external filtering process. However, we side with the critical proponents of reflective equilibrium and argue that without the Rawlsian weak filtering process, RE is more plausible both as a general method as well as in the context of moral philosophy. (shrink)

Philippe Huneman has recently questioned the widespread application of mechanistic models of scientific explanation based on the existence of structural explanations, i.e. explanations that account for the phenomenon to be explained in virtue of the mathematical properties of the system where the phenomenon obtains, rather than in terms of the mechanisms that causally produce the phenomenon. Structural explanations are very diverse, including cases like explanations in terms of bowtie structures, in terms of the topological properties of the system, or in (...) terms of equilibrium. The role of mathematics in bowtie structured systems and in topologically constrained systems has recently been examined in different papers. However, the specific role that mathematical properties play in equilibrium explanations requires further examination, as different authors defend different interpretations, some of them closer to the new-mechanistic approach than to the structural model advocated by Huneman. In this paper, we cover this gap by investigating the explanatory role that mathematics play in Blaser and Kirschner’s nested equilibrium model of the stability of persistent long-term human-microbe associations. We argue that their model is explanatory because: i) it provides a mathematical structure in the form of a set of differential equations that together satisfy an ESS; ii) that the nested nature of the ESSs makes the explanation of host-microbe persistent associations robust to any perturbation; iii) that this is so because the properties of the ESS directly mirror the properties of the biological system in a non-causal way. The combination of these three theses make equilibrium explanations look more similar to structural explanations than to causal-mechanistic explanation. (shrink)

The paper clarifies what is at stake in the theory/antitheory debate in ethics and articulates the distinctive core of the method of reflective equilibrium which distinguishes it from a generic coherence constraint. I call this distinctive core 'maieutic reflection'. The paper then argues that if she accepts constructivist views in metaethics, a proponent of the method of reflective equilibrium will be committed to the existence of a moral theory.

As Helen Longino's overview of Hypatia's engagement with feminist epistemology suggests, the last twenty-five years’ contributions to this field reveal a strong focus on the topic of knowledge. In her short outline, Longino questions this narrow focus on knowledge in epistemological inquiry. The main purpose of this article is to provide a framework for systematically taking up the questions raised by Longino, one that prevents us from running the risk of becoming unreflectively involved in sexist, racist, or otherwise problematic inquiry. (...) I argue that a specific form of the method of Reflective Equilibrium, as it is widely discussed in moral epistemology, logic, and theories of rationality, enables us to cope with the problems of traditional epistemology, which feminist theorizers such as Sally Haslanger have pointed to. With the account of Reflective Equilibrium I am offering—drawing in many respects on the model provided by Catherine Z. Elgin—we have an ameliorative method that allows us to rethink epistemological values, goals, and standards in a systematic way, and that largely avoids implicit and explicit biases in epistemology. (shrink)

This chapter contains sections titled: The Absence of the Ethical Reflective Equilibrium Straightness and Surprise Perception and Method Perception and Love Literary Theory and Ethical Theory.

The method of reflective equilibrium focuses on the relationship between principles and judgments. Principles are relatively general rules for comprehending the area of enquiry. Judgments are our intuitions or commitments, ‘at all levels of generality’ (Rawls 1975: 8), regarding the subject matter. The basic idea of reflective equilibrium is to bring principles and judgments into accord. This can be achieved by revising the principles and/or the judgments. -/- I first look at normative political judgments (Section 2) before considering (...) the role of principles, arguments, devices of representation and background theory in wide reflective equilibrium (Section 3). I then consider two of the main challenges to the method (Section 4), and show how to use it to deliberate about substantive political principles (Section 5). I conclude with an extended example of the method in action (Section 6). (shrink)

As a procedure, reflective equilibrium is simply a familiar kind of standard scientific method with a new name. A theory is constructed to account for a set of observations. Recalcitrant data may be rejected as noise or explained away as the effects of interference of some sort. Recalcitrant data that cannot be plausibly dismissed force emendations in theory. What counts as a plausible dismissal depends, among other things, on the going theory, as well as on background theory and on (...) knowledge that may be relevant to under-standing the experimental design that is generating the observations, including knowledge of the apparatus and observation conditions. This sort of mutual adjustment between theory and data is a familiar feature of scientific practice. Whatever authority RE seems to have comes, I think, from a tacit or explicit recognition that it has the same form as this familiar sort of scientific inference. One way to see the rationale underlying this procedure in science is to focus on prediction. Think of prediction as a matter of projecting what is known onto uncharted territory. To do this, you need a vehicle—a theory—that captures some invariant or pattern in what is known so that you can project it onto the unknown. How convincing the projection is depends on two factors: how sure one is of the observational base, and how sure one is that the theory gets the invariants right. The two factors are not independent, of course. One's confidence in the observational base will be affected by how persuasively the theory identifies and dismisses noise; one's confidence in the theory, on the other hand, will depend on one's confidence in the observations it takes seriously. Prediction is important as a test of theory precisely because verified predictions seem to show that the theory has correctly captured the general in the particular, that it has got the drift of the observational evidence in which our confidence is ultimately grounded. (shrink)

Several authors have recently argued that the excessive focus on equilibrium models in mainstream economic analysis prevents economists from providing accurate representations of the complex and dynamic nature of real economic systems. In response, this paper argues the following. Many economic systems are the products of deliberate and centralized human design. People can and do build and support structures, such as social institutions, aiming to enhance the predictability of economic systems, and thus to move them toward being equilibrium (...) systems. This provides a reason to think that many economic systems can be represented by equilibrium models. (shrink)

This book offers a comprehensive account of logic that addresses fundamental issues concerning the nature and foundations of the discipline. The authors claim that these foundations can not only be established without the need for strong metaphysical assumptions, but also without hypostasizing logical forms as specific entities. They present a systematic argument that the primary subject matter of logic is our linguistic interaction rather than our private reasoning and it is thus misleading to see logic as revealing "the laws of (...) thought". In this sense, fundamental logical laws are implicit to our "language games" and are thus more similar to social norms than to the laws of nature. Peregrin and Svoboda also show that logical theories, despite the fact that they rely on rules implicit to our actual linguistic practice, firm up these rules and make them explicit. By carefully scrutinizing the project of logical analysis, the authors demonstrate that logical rules can be best seen as products of the so called reflective equilibrium. They suggest that we can profit from viewing languages as "inferential landscapes" and logicians as "geographers" who map them and try to pave safe routes through them. This book is an essential resource for scholars and researchers engaged with the foundations of logical theories and the philosophy of language. (shrink)

An explanation and defense of the use of reflective equilibrium in ethics.

This open access book provides the first explicit case study for an application of the method of reflective equilibrium (RE), using it to develop and defend a precautionary principle. It thereby makes an important and original contribution to questions of philosophical method and methodology. The book shows step-by-step how RE is applied, and develops a methodological framework which will be useful for everyone who wishes to use reflective equilibrium. With respect to precautionary principles, the book demonstrates how a (...) rights-based precautionary principle can be constructed and defended. The case study succeeds in demonstrating that RE can be successfully applied and puts real constraints on the justification process. This is all the more remarkable as the case study was designed as an open-ended process, without presupposing any specific results. This book will be highly relevant both to people interested in philosophical methodology and epistemology, as well as to researchers who are interested in using philosophical methods and tools and applying them to practical problems. (shrink)

According to the free energy principle, life is an “inevitable and emergent property of any random dynamical system at non-equilibrium steady state that possesses a Markov blanket” :20130475, 2013). Formulating a principle for the life sciences in terms of concepts from statistical physics, such as random dynamical system, non-equilibrium steady state and ergodicity, places substantial constraints on the theoretical and empirical study of biological systems. Thus far, however, the physics foundations of the free energy principle have received hardly (...) any attention. Here, we start to fill this gap and analyse some of the challenges raised by applications of statistical physics for modelling biological targets. Based on our analysis, we conclude that model-building grounded in the free energy principle exacerbates a trade-off between generality and realism, because of a fundamental mismatch between its physics assumptions and the properties of actual biological targets. (shrink)

Equilibrium is a central concept of statistical mechanics. In previous work we introduced the notions of a Boltzmannian alpha-epsilon-equilibrium and a Boltzmannian gamma-epsilon-equilibrium. This was done in a deterministic context. We now consider systems with a stochastic micro-dynamics and transfer these notions from the deterministic to the stochastic context. We then prove stochastic equivalents of the Dominance Theorem and the Prevalence Theorem. This establishes that also in stochastic systems equilibrium macro-regions are large in requisite sense.

This paper contains a survey of the main definitions and results obtained to date related to Temporal Equilibrium Logic, a nonmonotonic hybrid approach that combines Equilibrium Logic (the best-known logical characterisation for the stable models semantics of logic programs) with Linear-Time Temporal Logic.

Bohmian mechanics is arguably the most naively obvious embedding imaginable of Schr¨ odinger’s equation into a completely coherent physical theory. It describes a world in which particles move in a highly non-Newtonian sort of way, one which may at first appear to have little to do with the spectrum of predictions of quantum mechanics. It turns out, however, that as a consequence of the defining dynamical equations of Bohmian mechanics, when a system has wave function ψ its configuration is typically (...) random, with probability density ρ given by |ψ|2, the quantum equilibrium distribution. It also turns out that the entire quantum formalism, operators as observables and all the rest, naturally emerges in Bohmian mechanics from the analysis of “measurements.” This analysis reveals the status of operators as observables in the description of quantum phenomena, and facilitates a clear view of the range of applicability of the usual quantum mechanical formulas. (shrink)

Among the areas of knowledge that the method of reflective equilibrium (RE) has been applied to is that of logical validity. According to RE in logic, we come to be justified in believing a (deductive) logical theory in virtue of establishing some state of equilibrium between our initial judgements over the validity of specific (natural language) arguments and the logical principles which constitute our logical theory. Unfortunately, however, while relatively popular, RE with regards to logical theorizing is underspecified. (...) In particular, it’s unclear what constitute: (1) the relevant logical “data”, (2) logical theories, so that they can be suitably tested, and (3) the mechanisms under which such theories are tested. Considering the various options for how to interpret the position, we argue that in order to be workable the advocate of RE about logic must embrace what we call an _operationalised_, _wide_ and _communal_ version of RE with a _rich_ understanding of logical theories. Fortunately for the advocate of RE, there is an available account of logic’s epistemology which possesses just these properties, _logical predictivism_. However, equally unfortunately, logical predictivism commits the advocate of RE to certain further claims that they have historically been weary of holding. Consequently, it is unclear whether RE about logic itself is a viable proposal, or rather a similar but distinct epistemology of logic. (shrink)

ABSTRACT In ethics, the use of empirical data has become more and more popular, leading to a distinct form of applied ethics, namely empirical ethics. This ‘empirical turn’ is especially visible in bioethics. There are various ways of combining empirical research and ethical reflection. In this paper we discuss the use of empirical data in a special form of Reflective Equilibrium (RE), namely the Network Model with Third Person Moral Experiences. In this model, the empirical data consist of the (...) moral experiences of people in a practice. Although inclusion of these moral experiences in this specific model of RE can be well defended, their use in the application of the model still raises important questions. What precisely are moral experiences? How to determine relevance of experiences, in other words: should there be a selection of the moral experiences that are eventually used in the RE? How much weight should the empirical data have in the RE? And the key question: can the use of RE by empirical ethicists really produce answers to practical moral questions? In this paper we start to answer the above questions by giving examples taken from our research project on understanding the norm of informed consent in the field of pediatric oncology. We especially emphasize that incorporation of empirical data in a network model can reduce the risk of self‐justification and bias and can increase the credibility of the RE reached. (shrink)

Consider a general equilibrium model in which information is an indivisible differentiated commodity for which satiation occurs at one unit. Suppose that uncountably many types of information are possible which can be costlessly combined by agents who desire information only because it helps them to maximize state dependent utilities under uncertainty. Similarity of information is expressed by a metric which reflects substitution possibilities among different information structures. Such a large pure exchange economy in which prices for (differentiated) information structures (...) and (finitely many) ordinary commodities are determined simultaneously is consistent - equilibrium distributions exist. (shrink)

I argue that the conception of reflective equilibrium that is generally accepted in contemporary philosophy is defective and should be replaced with a conception of fruitful reflective disequilibrium which prohibits ad hoc manoeuvres, encourages new approaches, and eschews all justification in favour of continuous improvement. I suggest how the conception of fruitful disequilibrium can be applied more effectively to moral enquiry, to encourage genuine progress in moral knowledge, if we make moral theory empirically testable by adopting a meta-ethical postulate (...) which is independently plausible. (shrink)

Reflective equilibrium, as a methodology for the “formation of logics,” fails on the fringe, where intricate details can make or break a logical theory. On the fringe, the process of theorification cannot be methodologically governed by anything like reflective equilibrium. When logical theorising gets tricky, there is nothing on the pre-theoretical side on which our theoretical claims can reflect of—at least not in any meaningful way. Indeed, the fringe is exclusively the domain of theoretical negotiations and the methodological (...) power of reflective equilibrium is merely nominal. (shrink)

We generalize the concept of Nash equilibrium in mixed strategies for strategic form games to allow for ambiguity in the players' expectations. In contrast to other contributions, we model ambiguity by means of so-called lower probability measures or belief functions, which makes it possible to distinguish between a player's assessment of ambiguity and his attitude towards ambiguity. We also generalize the concept of trembling hand perfect equilibrium. Finally, we demonstrate that for certain attitudes towards ambiguity it is possible (...) to explain cooperation in the one-shot Prisoner's Dilemma in a way that is in accordance with some recent experimental findings. (shrink)

In this paper, we investigate how data about public preferences may be used to inform policy around the use of controversial novel technologies, using public preferences about autonomous vehicles (AVs) as a case study. We first summarize the recent ‘Moral Machine’ study, which generated preference data from millions of people regarding how they think AVs should respond to emergency situations. We argue that while such preferences cannot be used to directly inform policy, they should not be disregarded. We defend an (...) approach that we call ‘Collective Reflective Equilibrium in Practice’ (CREP). In CREP, data on public attitudes function as an input into a deliberative process that looks for coherence between attitudes, behaviours and competing ethical principles. We argue that in cases of reasonable moral disagreement, data on public attitudes should play a much greater role in shaping policies than in areas of ethical consensus. We apply CREP to some of the global preferences about AVs uncovered by the Moral Machines study. We intend this discussion both as a substantive contribution to the debate about the programming of ethical AVs, and as an illustration of how CREP works. We argue that CREP provides a principled way of using some public preferences as an input for policy, while justifiably disregarding others. (shrink)

I address the worry that reflective equilibrium is too weak as an account of justification because it fails to let differing views converge. I take up informal aspects of convergence and operationalise them in a formal model of reflective equilibrium. This allows for exploration by the means of computer simulation. Findings show that the formal model does not yield unique outputs, but still boosts agreement. I conclude from this that reflective equilibrium is best seen as a pluralist (...) account of justification that cannot be accused of resulting in an “anything goes” relativism. (shrink)

Donald Capps (2009: 145) suggested the hypothesis that “the Nash equilibrium is descriptive of the normal brain, whereas the game theory formulated by John van Neumann, which Nash’s theory challenges, is descriptive of the schizophrenic brain”. The paper offers arguments in its favor. They are from psychiatry, game theory, set theory, philosophy and theology. The Nash equilibrium corresponds to wholeness, stable emergent properties as well as to representing actual infinity on a material, limited and finite organ as a (...) human brain. (shrink)

The paper explores whether the method of reflective equilibrium (RE) in ethics and political philosophy should be individual or public in character. I defend a modestly public conception of RE, in which public opinion is used specifically as a source of considered judgments about cases. Public opinion is superior to philosophical opinion in delivering judgments that are untainted by principled commitments. A case-based approach also mitigates the methodological problems that commonly confront efforts to integrate philosophy with the investigation of (...) popular attitudes. This conception of RE is situated in relation to alternative accounts, including those of Daniels, Rawls, and Wolff and de-Shalit. (shrink)

In Boltzmannian statistical mechanics macro-states supervene on micro-states. This leads to a partitioning of the state space of a system into regions of macroscopically indistinguishable micro-states. The largest of these regions is singled out as the equilibrium region of the system. What justifies this association? We review currently available answers to this question and find them wanting both for conceptual and for technical reasons. We propose a new conception of equilibrium and prove a mathematical theorem which establishes in (...) full generality -- i.e. without making any assumptions about the system's dynamics or the nature of the interactions between its components -- that the equilibrium macro-region is the largest macro-region. We then turn to the question of the approach to equilibrium, of which there exists no satisfactory general answer so far. In our account, this question is replaced by the question when an equilibrium state exists. We prove another -- again fully general -- theorem providing necessary and sufficient conditions for the existence of an equilibrium state. This theorem changes the way in which the question of the approach to equilibrium should be discussed: rather than launching a search for a crucial factor, the focus should be on finding triplets of macro-variables, dynamical conditions, and effective state spaces that satisfy the conditions of the theorem. (shrink)

Discussions of the foundations of Classical Equilibrium Statistical Mechanics (SM) typically focus on the problem of justifying the use of a certain probability measure (the microcanonical measure) to compute average values of certain functions. One would like to be able to explain why the equilibrium behavior of a wide variety of distinct systems (different sorts of molecules interacting with different potentials) can be described by the same averaging procedure. A standard approach is to appeal to ergodic theory to (...) justify this choice of measure. A different approach, eschewing ergodicity, was initiated by A. I. Khinchin. Both explanatory programs have been subjected to severe criticisms. This paper argues that the Khinchin type program deserves further attention in light of relatively recent results in understanding the physics of universal behavior. (shrink)

In this paper, we study the introduction of modal past temporal operators in Temporal Equilibrium Logic, an hybrid formalism that mixes linear-time modalities and logic programs interpreted under stable models and their characterisation in terms of Equilibrium Logic. We show that Kamp’s translation can also be used to translate the new extension of TEL with past operators into Quantified Equilibrium Logic. Additionally, we provide a method for removing past operators that consists in replacing past-time subformulas by fresh (...) auxiliary atoms, obtaining an equivalent formula, modulo the original alphabet. (shrink)

Recent years have seen a rekindling of interest in the method of reflective equilibrium. Most of this attention has been suspicious, however. Critics have alleged that the method is nothing more than a high-minded brand of navel-gazing, that it suffers from all the classic problems of inward-looking coherence theories, and that it overestimates the usefulness of self-scrutiny. In this paper I argue that these criticisms miss their mark because they labor under crucial misconceptions about the method of reflective (...) class='Hi'>equilibrium. In defending reflective equilibrium I put forward a handful of theses about the nature of inquiry (or, more generally, norm-governed enterprises) that form the backdrop to the method. The critics’ objections fall short, I argue, because they do not recognize reflective equilibrium’s embrace of these theses. Confronting these objections and understanding why they fail brings us to a better understanding what, exactly, the method of reflective equilibrium is. The answer I come to in the final section of the paper is that the method of reflective equilibrium is not, exactly, anything. It is a mistake to try to give a positive characterization of the view, to identify it with a concern with a particular species of data, particular procedures and methods, or even a particular conception of normative success. Instead, it should be understood as the denial of essentialism about just these matters—as a form of anti-essentialism about our epistemic inputs, methods, and goals. (shrink)

General Equilibrium Theory: An Introduction treats the classic Arrow-Debreu general equilibrium model in a form accessible to graduate students and advanced undergraduates in economics and mathematics. Topics covered include mathematical preliminaries, households and firms, existence of general equilibrium, Pareto efficiency of general equilibrium, the First and Second Fundamental Theorems of Welfare Economics, the core and core convergences, future markets over time and contingent commodity markets under uncertainty. Demand, supply, and excess demand appear first as functions, then (...) optionally as correspondences. The mathematics presented includes a real analysis, the Brouwer fixed point theorem, and separating and supporting hyperplane theorems. Optional chapters introduce the existence of equilibrium with set-valued supply and demand, the mathematics of upper and lower hemicontinuous correspondences, and the Kakutani fixed point theorem. The treatment emphasizes clarity and accessibility to the student through use of examples and intuition. (shrink)

The purpose of this paper is to make progress on the theoretical discussions about marketing systems in relation to the construction of the concept of equilibrium. An argumentative basis was developed in relation to the service-dominant logic, as well as propositions based on the theory of stakeholders, on distributive justice and on the discussion of externalities to consider the product as an agent of the marketing system. In addition, a product typology that sees life as a material basis for (...) delivering a performance developed, arguing that systems based on this kind of materiality require a different moral consideration. (shrink)

The model of congestion games is widely used to analyze games related to traffic and communication. A central property of these games is that they are potential games and hence posses a pure Nash equilibrium. In reality, it is often the case that some players cooperatively decide on their joint action in order to maximize the coalition’s total utility. This is modeled by Coalitional Congestion Games. Typical settings include truck drivers who work for the same shipping company, or routers (...) that belong to the same ISP. The formation of coalitions will typically imply that the resulting coalitional congestion game will no longer posses a pure Nash equilibrium. In this paper, we provide conditions under which such games are potential games and posses a pure Nash equilibrium. (shrink)

There are two general classes of social conventions: conventions of coordination, and conventions of partial conflict. In coordination problems, the interests of the agents coincide, while in partial conflict problems, some agents stand to gain only if other agents unilaterally make certain sacrifices. Lewis' (1969) pathbreaking analysis of convention in terms of game theory focuses on coordination problems, and cannot accommodate partial conflict problems. In this paper, I propose a new game-theoretic definition of convention which generalizes previous game-theoretic definitions (Lewis (...) 1969, Vanderschraaf 1995), and which can be used to characterize norms of justice in partial conflict situations. I argue that the key structural property necessary for a social arrangement to be a convention is that it be conditionally self-enforcing, in the sense that: (i) each agent has a decisive reason to follow her end of the arrangement given that she expects all to do likewise, (ii) given a different set of expectations, some agents would have had a decisive reason to deviate, and (iii) these facts are common knowledge. This leads to a definition of convention as a strict correlated equilibrium (Aumann 1974) together with appropriate common knowledge conditions. Examples are given in which it is shown how this more general account of convention can be used to analyze norms of justice as well as coordination problems. It is only a general sense of common interest; which sense all the members of the society express to one another, and which induces them to regulate their conduct by certain rules. I observe, that it will be for my interest to leave another in the possession of his goods, provided he will act in the same manner with regard to me. He is sensible of a like interest in the regulation of his conduct. When this common sense of interest is mutually express'd, and is known to both, it produces a suitable resolution and behavior. And this may properly be call'd a convention or agreement betwixt us,.. (shrink)

Boltzmannian statistical mechanics partitions the phase space of a sys- tem into macro-regions, and the largest of these is identified with equilibrium. What justifies this identification? Common answers focus on Boltzmann’s combinatorial argument, the Maxwell-Boltzmann distribution, and maxi- mum entropy considerations. We argue that they fail and present a new answer. We characterise equilibrium as the macrostate in which a system spends most of its time and prove a new theorem establishing that equilib- rium thus defined corresponds to (...) the largest macro-region. Our derivation is completely general in that it does not rely on assumptions about a system’s dynamics or internal interactions. (shrink)

Aconvention is a state in which agents coordinate their activity, not as the result of an explicit agreement, but because their expectations are aligned so that each individual believes that all will act so as to achieve coordination for mutual benefit. Since agents are said to follow a convention if they coordinate without explicit agreement, the notion raises fundamental questions: (1) Why do certain conventions remain stable over time?, and (2) How does a convention emerge in the first place? In (...) a pioneering study, Lewis (1969) addresses these questions by applyingnoncooperative game theory. Lewis defines a convention as aNash coordination equilibrium of a noncooperative game that issalient, that is, it is somehow conspicuous to the agents so that all expect one another to conform with the equilibrium. This paper presents a new game theoretic definition of conventions, which formalizes the notion of salience and which also generalizes the class of conventions Lewis discusses in his work. I define a convention as acorrelated equilibrium (Aumann 1974, 1987) satisfying apublic intentions criterion: Every agent wants his intended action to becommon knowledge. I argue that many conventions correspond to correlated equilibria that are not Nash equilibria, and that this is consistent with Lewis' general viewpoint. Finally, I argue that game theoretic characterizations of convention, such as Lewis' and my own, help to explain a convention's stability, but that a fully satisfactory account of the emergence of convention requires a theory of equilibrium selection beyond the scope of Lewis' work. (shrink)

Practical equilibrium, like reflective equilibrium, is a way of deciding what to think about morality. It shares with reflective equilibrium the general thesis that there is some way in which a moral theory must, in order to be acceptable, answer to one’s moral intuitions, but it differs from reflective equilibrium in its specification of exactly how a moral theory must answer to one’s intuitions. Whereas reflective equilibrium focuses on a theory’s consistency with those intuitions, practical (...) equilibrium also gives weight to a theory’s approval of one’s having those intuitions. (shrink)

I distinguish two ways of developing anti-exceptionalist approaches to logical revision. The first emphasizes comparing the theoretical virtuousness of developed bodies of logical theories, such as classical and intuitionistic logic. I'll call this whole theory comparison. The second attempts local repairs to problematic bits of our logical theories, such as dropping excluded middle to deal with intuitions about vagueness. I'll call this the piecemeal approach. I then briefly discuss a problem I've developed elsewhere for comparisons of logical theories. Essentially, the (...) problem is that a pair of logics may each evaluate the alternative as superior to themselves, resulting in oscillation between logical options. The piecemeal approach offers a way out of this problem andthereby might seem a preferable to whole theory comparisons. I go on to show that reflective equilibrium, the best known piecemeal method, has deep problems of its own when applied to logic. (shrink)

What is the nature of the intellectual enterprise - general equilibrium analysis - that so many economists regard as the centerpiece of their discipline? In this book, Roy Weintraub considers both the modern history of the analysis, and the methodological puzzles that it, and mathematical economic theory in general, pose. Professor Weintraub argues that previous writings on the history and method of general equilibrium theory have been curiously biased and misleading. He provides a clear and careful presentation of (...) the development of the theory from the 1930s through to the Arrow-Debreu work of the 1950s. This historical analysis is the centre of the book: a case study which permits the author to justify the status of general equilibrium theory in economics and the activity in which economic theorists engage. He argues that previous methodological investigations have been distorted by their use of inappropriate models taken from the philosophy of science that were developed to appraise work in the physical sciences. (shrink)

In political philosophy, reflective equilibrium is a standard method used to systematically reconcile intuitive judgments with theoretical principles. In this paper, we propose that survey experiments and a model selection method—i.e., the Akaike Information Criterion (AIC)-based model selection method—can be viewed together as a methodological means of satisfying the epistemic desiderata implicit in reflective equilibrium. To show this, we conduct a survey experiment on two theories of distributive justice, prioritarianism and sufficientarianism. Our experimental test case and AIC-based model (...) selection method demonstrate that the refined sufficientarian principle, a widely accepted principle of distributive justice, is no more plausible than the prioritarian principle. This tells us that some changes of certain intuitions revolving around sufficientarianism should be examined (separately) based on the findings of the survey experiment and AIC model selection. This shows the potential of our approach—both practically and methodologically—as a novel way of applying reflective equilibrium in political philosophy. (shrink)

It is more than a half-century since Nelson Goodman [1955] applied what we call the Reflective Equilibrium model of justification to the problem of justifying induction, and more than three decades since Rawls [1971] and Daniels [1979] applied celebrated extensions of this model to the problem of justifying principles of social justice. The resulting Wide Reflective Equilibrium model (WRE) is generally thought to capture an acceptable way to reconcile inconsistency between an intuitively plausible general principle and an intuitively (...) plausible judgment about a particular case. Recently a different model for reconciling moral inconsistency has emerged: Moral Consistency Reasoning [Campbell and Kumar 2012, 2013a; Kumar and Campbell 2012; Campbell 2009: 86?7; Campbell and Woodrow 2003; Wong 2002]. MCR applies when two moral judgments give opposing assessments of (what appear to be) relevantly similar particular cases. Though WRE and MCR are strikingly different, each arguably captures a rationally acceptable method for reconciling moral inconsistency. Moreover, as will be shown, they function in complementary ways. Are they parts of a more comprehensive model of moral reasoning in the face of inconsistency that would explain the attractions of each? This essay first spells out the relevant differences between the models and then formulates a more general model of moral reasoning in the face of inconsistency.?1 reviews the emergence of Goodman's model that he offers in the spirit of epistemology naturalized, almost a decade before Quine coined the term [1969a].?2 analyses six salient features of WRE to be compared with six contrasting features of MCR in?3.?4 presents the general model. (shrink)