Much forensic inference based upon DNA evidence is made assuming Hardy-Weinberg Equilibrium (HWE) for the genetic loci being used. Several statistical tests to detect and measure deviation from HWE have been devised, and their limitations become more obvious when testing for deviation within multiallelic DNA loci. The most popular methods-Chi-square and Likelihood-ratio tests-are based on asymptotic results and cannot guarantee a good performance in the presence of low frequency genotypes. Since the parameter space dimension increases at a quadratic rate (...) on the number of alleles, some authors suggest applying sequential methods, where the multiallelic case is reformulated as a sequence of “biallelic” tests. However, in this approach it is not obvious how to assess the general evidence of the original hypothesis; nor is it clear how to establish the significance level for its acceptance/rejection. In this work, we introduce a straightforward method for the multiallelic HWE test, which overcomes the aforementioned issues of sequential methods. The core theory for the proposed method is given by the Full Bayesian Significance Test (FBST), an intuitive Bayesian approach which does not assign positive probabilities to zero measure sets when testing sharp hypotheses. We compare FBST performance to Chi-square, Likelihood-ratio and Markov chain tests, in three numerical experiments. The results suggest that FBST is a robust and high performance method for the HWE test, even in the presence of several alleles and small sample sizes. (shrink)

This is a two-volume set that provides an introduction to non-cooperative Game Theory. Volume 1 covers the basic concepts, while Volume 2 is devoted to advanced topics. The book is richly illustrated with approximately 400 figures. It is suitable for both self-study and as the basis for an undergraduate course in game theory as well as a first-year graduate-level class. It is written to be accessible to anybody with high-school level knowledge of mathematics. At the end of each chapter there (...) is a collection of exercises accompanied by detailed answers. The book contains approximately 180 exercises. (shrink)

This thesis develops a detailed account of the emergence of for all practical purposes continuous, quasi-classical world histories from the discontinuous, stochastic micro dynamics of Minimal Bohmian Mechanics (MBM). MBM is a non-relativistic quantum theory. It results from excising the guiding equation from standard Bohmian Mechanics (BM) and reinterpreting the quantum equilibrium hypothesis as a stochastic guidance law for the random actualization of configurations of Bohmian particles. On MBM, there are no continuous trajectories linking up individual configurations. Instead, individual (...) configurations are actualized independently of each other, carving out the decoherence-induced branching structure of the universal wave function. Yet, by contrast to the Everett interpretation, branches of the universal wave function are not actualized in parallel, i.e. all at the same time. Rather, world branches, on MBM, are actualized sequentially. -/- For an introduction to MBM, the transition from BM to MBM is described, and their empirical equivalence is established. I present the conditions under which MBM can be classified as a primitive ontology (PO) theory, regarded as crucial for the acceptance of a theory as Bohmian by many proponents of BM. While rendering MBM compatible with the PO approach, it must not fall prey to the problem of communication, arising from the two-space reading of BM. -/- The issue of temporal solipsism, identified by Bell as a serious problem for his “Everett (?) theory” – the historic predecessor of MBM – is discussed. I argue that Barbour’s time capsule approach does not provide a satisfactory solution. In particular, his adopting a more than minimal psychophysical parallelism between brain processes and experience of macroscopic change is argued to be reasonable in light of our current best neuroscience, yet problematic for theories relying solely on time capsules, understood as highly structured, individual, internally static configurations. As a solution, I introduce worlds, and world histories, as key concepts in providing a link between MBM’s micro dynamics and macroscopic phenomena. Worlds, other than time capsules, are coarse-grained regions in phase- or configuration space, defined as sets of possible micro states satisfying a relation of sufficient similarity from a macroscopic perspective, with respect to a given micro state. Hence, worlds may overlap. -/- I argue that worlds thus construed are a reasonable option for replacing the disjoint macro regions of phase space, resulting from the usual way of partitioning phase space in the standard framework of Boltzmannian statistical mechanics. This move solves the issue of discontinuous change of macro variables upon the micro state crossing the boundary between different macro regions. -/- I adapt this move for MBM’s discontinuous micro dynamics in configuration space. Issues revolving around the microscopic-macroscopic distinction, particle identity, impenetrability and haecceity in light of the desideratum of particle number conservation, etc., are discussed. I provide a detailed explanation of how overlapping worlds in MBM form world histories, thereby linking up macroscopically distinct worlds. Thus, the problem of temporal solipsism is resolved in a way that is compatible with a more than minimal psychophysical parallelism. (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)

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)

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)

Causal Decision Theory reckons the choice-worthiness of an option to be completely independent of its evidential bearing on its non-effects. But after one has made a choice this bearing is relevant to future decisions. Therefore it is possible to construct problems of sequential choice in which Causal Decision Theory makes a guaranteed loss. So Causal Decision Theory is wrong. The source of the problem is the idea that agents have a special perspective on their own contemplated actions, from which (...) evidential connections that observers can see are either irrelevant or invisible. (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)

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)

John Rawls’ “reflective equilibrium” ranges amongst the most popular conceptions in contemporary ethics when it comes to the basic methodological question of how to justify and trade off different normative positions and attitudes. Even where Rawls’ specific contractualist account is not adhered to, “reflective equilibrium” is readily adopted as the guiding idea of coherentist approaches, seeking moral justification not in a purely deductive or inductive manner, but in some balancing procedure that will eventually procure a stable adjustment of (...) relevant doctrines and standpoints. However, it appears that the widespread use of this idea has led to some considerable deviations from its meaning within Rawls’ original framework and to a critical loss of conceptual cogency as an ethico-hermeneutical tool. This contribution identifies three kinds of “balancing” constellations that are frequently, but inadequately brought forth under the heading of Rawlsian “reflective equilibrium”: (a) balancing theoretical accounts against intuitive convictions; (b) balancing general principles against particular judgements; (c) balancing opposite ethical conceptions or divergent moral statements, respectively. It is argued that each of these applications departs from Rawls’ original construction of “reflective equilibrium” and also deprives the idea of its reliability in clarifying and weighing moral stances. (shrink)

This article argues that, suitably modified, the method of reflective equilibrium is a plausible way of selecting moral principles. The appropriate conception of the method is wide and radical, admitting consideration of a full range of moral principles and arguments, and requiring the enquiring individual to consider others' views and undergo experiences that may offset any formative biases. The individual is not bound by his initial considered judgments, and may revise his view in any way whatsoever. It is appropriate (...) to describe the method as a balance between coherentism and fallibilist foundationalism. With these points in mind, various criticisms, including the claims that considered judgments are not initially credible and are shaped by prejudice, and that the method itself fails to determine principle selection, are challenged. (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)

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)

This paper aims to flesh out the celebrated notion of reflective equilibrium within a probabilistic framework for epistemic rationality. On the account developed here, an agent's attitudes are in reflective equilibrium when there is a certain sort of harmony between the agent's credences, on the one hand, and what the agent accepts, on the other hand. Somewhat more precisely, reflective equilibrium is taken to consist in the agent accepting, or being prepared to accept, all and only claims (...) that follow from a maximally comprehensive theory that is more probable than any other such theory. Drawing on previous work, the paper shows that when an agent is in reflective equilibrium in this sense, the set of claims they accept or are prepared to accept is bound to be logically consistent and closed under logical implication. The paper also argues that this account can explain various features of philosophical argumentation in which the notion of reflective equilibrium features centrally, such as the emphasis on evaluating philosophical theories holistically rather than in a piecemeal fashion. (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)

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)

We associate the method of reflective equilibrium with developing principles of social justice, but it can also be used on a literary canon, with the aim of identifying principles of inclusion and exclusion. But I note three risks of doing so, using the American literary canon as an example.

T.H. Irwin characterizes the reflective equilibrium procedure as one which should not involve ruthless surgery, in a metaphorical sense. I argue that many people will find avoiding this difficult, because they do not conceive or go in for subtle options.

The received wisdom in statistical mechanics is that isolated systems, when left to themselves, approach equilibrium. But under what circumstances does an equilibrium state exist and an approach to equilibrium take place? In this paper we address these questions from the vantage point of the long-run fraction of time definition of Boltzmannian equilibrium that we developed in two recent papers. After a short summary of Boltzmannian statistical mechanics and our definition of equilibrium, we state an (...) existence theorem which provides general criteria for the existence of an equilibrium state. We first illustrate how the theorem works with a toy example, which allows us to illustrate the various elements of the theorem in a simple setting. After a look at the ergodic programme, we discuss equilibria in a number of different gas systems: the ideal gas, the dilute gas, the Kac gas, the stadium gas, the mushroom gas and the multi-mushroom gas. In the conclusion we briefly summarise the main points and highlight open questions. (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)

Although the controversy between Malthus and Ricardo has long been considered to be an important source for the history of economic thought, it has hardly been the object of a careful study qua controversy, i.e. as a polemical dialogical exchange. We have undertaken to fill this gap, within the framework of a more ambitious project that places controversies at the center of an account of the history of ideas, in science and elsewhere. It is our contention that the dialogical co-text (...) is essential for reconstructing the meaning and the evolution of science. In the present paper we try to substantiate this contention by means of a pragma-rhetorical study of this particular controversy. First, we reconstruct, through an analysis of a chunk of the correspondence, a micro-level of specific moves and countermoves which constitute a sequential structure within which also meta-scientific and meta-controversial considerations play a role. We then move to a macro-level of analysis, looking for recurrent patterns of argumentation. Finally, we draw epistemological conclusions on the nature of rationality and progress as manifested in actual scientific controversies. (shrink)

Prioritarianism is a variant of utilitarianism. It differs from utilitarianism in that benefiting individuals matters more the worse off these individuals are. On this view, there are two standard ways of handling risky prospects: Ex-Post Prioritarianism adjusts for prioritizing the worse off in final outcomes and then values prospects by the expectation of the sum total of those adjusted values, whereas Ex-Ante Prioritarianism adjusts for prioritizing the worse off on each individual's expectation and then values prospects by the sum total (...) of those adjusted expectations. A standard objection to Ex-Post Prioritarianism is that it violates Ex-Ante Pareto, that is, it prescribes choices that worsen the expectations for everyone. In this article, I argue that Ex-Ante Prioritarianism suffers from much the same problem: it violates a sequential version of Ex-Ante Pareto, that is, it prescribes sequences of choices that worsen the expectations for everyone. (shrink)

Psychological Sequentialism holds that no causal constraint is necessary for the preservation of what matters in survival; rather, it is sufficient for preservation if two groups of mental states are similar enough and temporally close enough. Suppose that one’s body is instantaneously dematerialized and subsequently, by an amazing coincidence, a collection of molecules is configured to form a qualitatively identical human body. According to Psychological Sequentialism, these events preserve what matters in survival. In this article, I examine some of the (...) main arguments for the view and argue that they fail to establish that no causal constraint is necessary. I also argue that Psychological Sequentialism yields implausible consequences that render it hard to accept the view. (shrink)

In previous work, I have sought to show that the basic argument for epistemic relativism derives from the problem of the criterion that stems from ancient Pyrrhonian scepticism. Because epistemic relativism depends upon a sceptical strategy, it is possible to respond to relativism on the basis of an anti-sceptical strategy. I argue that the particularist response to scepticism proposed by Roderick Chisholm may be combined with a naturalistic and reliabilist conception of epistemic warrant as the basis for a satisfactory response (...) to epistemic relativism. In this paper, I outline this particularist response to relativism, and provide further commentary on the relationship between naturalism and particularism. In addition, I set the approach in contrast with reflective equilibrium approaches in epistemology. I also briefly explore the connection between the particularist response to relativism and G. E. Moore’s defense of an external world. (shrink)

Which moral judgments should one pay attention to in building a moral philosophy? Thomas Kelly and Sarah McGrath object to John Rawls’s suggestion to not rely on judgments heavily bound up with one’s own interests. I propose a solution in response to the objection.

John Rawls’ method of reflective equilibrium is the most influential methodology in contemporary ethics.This paper argues that this influence is undeserved, for two reasons. First, reflective equilibrium fails to accomplish two tasks that give us reason to care about methodology. On the one hand, it fails to explain how (or whether) moral knowledge is possible.This is because the method is explicitly oriented towards the distinct (and less interesting) task of characterizing our moral sensibilities. On the other hand, the (...) method fails to provide an informative way of adjudicating central methodological debates in ethics. Second, where Rawls’ method –and the background methodology he uses to motivate it –do have substance, that substance is implausible. The role of dispositions in the method entails that it endorses obviously irrational inferences. Further, the method makes substantively implausible distinctions between the dispositions that are allowed to play a methodological role. Rawls' background methodology appeals to the idea of a psychology in ‘wide reflective equilibrium’. However, both formal and empirical path-dependence considerations strongly suggest that there is nothing even minimally determinate that is someone’s psychology in ‘wide reflective equilibrium’. I close by exploring salient attempts to salvage the spirit of reflective equilibrium by abandoning elements of Rawls’ approach. I argue that none of these attempts succeed. I conclude that appeal to the method of reflective equilibrium is not a helpful means of addressing pressing methodological questions in ethics. In a slogan, reflective equilibrium is methodologically irrelevant. (shrink)

This paper proposes a Rawlsian conception of moral justification as a social activity. Through a close reading, Rawls’ view of ethical justification is shown to be significantly more dialogical and deliberative than is commonly appreciated. The result is a view that emphasizes the social nature of ethical justification and identifies information sharing between persons as the crux of justification in metaethics, in contrast to normative ethics. I call it Rawlsian reflective equilibrium to distinguish it from other varieties.

I argue against the claim that it is trivial to state that Sidgwick used the method of wide reflective equilibrium. This claim is based on what could be called the Triviality Charge, which is pressed against the method of wide reflective equilibrium by Peter Singer. According to this charge, there is no alternative to using the method if it is interpreted as involving all relevant philosophical background arguments. The main argument against the Triviality Charge is that although the (...) method of wide reflective equilibrium is compatible with coherentism (understood as a form of weak foundationalism) as well as moderate foundationalism, it is not compatible with strong foundationalism. Hence, the claim that a philosopher uses the method of wide reflective equilibrium is informative. In particular, this is true with regard to Sidgwick. (shrink)

In this paper, I present a problem for regarding the reflective equilibrium and original position methods as consistent. I do not prove that there is an inconsistency, but there is a puzzle of how the two methods can be made consistent. The concern about inconsistency is because the former method allows for a kind of historical bias, as noted by T.H. Irwin, whereas the latter method seeks to guard against historical bias.

Standard models in epistemic game theory make strong assumptions about agents’ knowledge of their own beliefs. Agents are typically assumed to be introspectively omniscient: if an agent believes an event with probability p, she is certain that she believes it with probability p. This paper investigates the extent to which this assumption can be relaxed while preserving some standard epistemic results. Geanakoplos (1989) claims to provide an Agreement Theorem using the “truth” axiom, together with the property of balancedness, a significant (...) relaxation of introspective omniscience. I provide an example which shows that Geanakoplos’s statement is incorrect. I then introduce a new property, local balancedness, which allows us both to correct Geanakoplos’s result, and to extend it to cases where the truth axiom may fail. I exploit this general Agreement Theorem to provide novel epistemic conditions for correlated and Nash equilibrium, both of which relax the assumption of introspective omniscience. In all three cases, the results are also extended to infinite state spaces. (This is Chapter 5 of my 2014 Oxford DPhil (PhD) thesis.). (shrink)

In Being Realistic About Reasons,T.M. Scanlon develops a non-naturalistic realist account of normative reasons. A crucial part of that account is Scanlon’s contention that there is no deep epistemological problem for non-naturalistic realists, and that the method of reflective equilibrium suffices to explain the possibility of normative knowledge. In this critical notice we argue that this is not so: on a realist picture, normative knowledge presupposes a significant correlation between distinct entities, namely between normative beliefs and normative facts. This (...) correlation calls for an explanation. We show that Scanlon does not have the resources to offer such an explanation. (shrink)

Cornell realism (CR), a prominent meta-ethical position that has emerged since the last decades of the twentieth century, proposes a non-reductionist naturalistic account of moral properties and facts. This paper argues that the best version of CR’s chosen methodology for arriving at justified moral beliefs must be seen as a variant of reflective equilibrium. In comparison to the traditional versions, our proposal offers a ‘social’ reinterpretation of reflective equilibrium in delineating CR’s epistemology. We argue that it satisfactorily accounts (...) for objectivity and calls for the inclusion of the social nature of both moral and scientific inquiries. Emphasising the social dimension of their epistemological account also nudges debates in metaethics into incorporating the much-needed social dimension while dealing with questions of moral beliefs and facts that have been of CR’s concern. (shrink)

Real-world economies are open-ended dynamic systems consisting of heterogeneous interacting participants. Human participants are decision-makers who strategically take into account the past actions and potential future actions of other participants. All participants are forced to be locally constructive, meaning their actions at any given time must be based on their local states; and participant actions at any given time affect future local states. Taken together, these essential properties imply real-world economies are locally-constructive sequential games. This paper discusses a modeling (...) approach, Agent-based Computational Economics, that permits researchers to study economic systems from this point of view. ACE modeling principles and objectives are first concisely presented and explained. The remainder of the paper then highlights challenging issues and edgier explorations that ACE researchers are currently pursuing. (shrink)

This paper responds to Thomas Kelly and Sarah McGrath’s worry that there can be evil reflective equilibrium. I propose that some of John Rawls’s restrictions on moral judgments we can enter into the procedure serve to protect against evil reflective equilibrium.

We discuss the social-epistemic aspects of Catherine Elgin’s theory of reflective equilibrium and understanding and argue that it yields an argument for the view that a crucial social-epistemic function of epistemic authorities is to foster understanding in their communities. We explore the competences that enable epistemic authorities to fulfil this role and argue that among them is an epistemic virtue we call “epistemic empathy”.

I consider Timothy Williamson’s objection that we do not have any reason to regard reflective equilibrium as a philosophical method. I present what I think a Rawlsian advocate of the method would say, or could say.

Consider a gas confined to the left half of a container. Then remove the wall separating the two parts. The gas will start spreading and soon be evenly distributed over the entire available space. The gas has approached equilibrium. Why does the gas behave in this way? The canonical answer to this question, originally proffered by Boltzmann, is that the system has to be ergodic for the approach to equilibrium to take place. This answer has been criticised on (...) different grounds and is now widely regarded as flawed. In this paper we argue that these criticisms have dismissed Boltzmann’s answer too quickly and that something almost like Boltzmann’s answer is true: the approach to equilibrium takes place if the system is epsilon-ergodic, i.e. ergodic on the entire accessible phase space except for a small region of measure epsilon. We introduce epsilon-ergodicity and argue that relevant systems in statistical mechanics are indeed espsilon-ergodic. (shrink)

In this paper, I present an objection to the reflective equilibrium method based on land purchases and trespassing. I then propose a solution, which involves a change to how we regard the method.

THIS PAPER IS THE CO-WINNER OF THE FRED BERGER PRIZE IN PHILOSOPHY OF LAW FOR THE 1999 AMERICAN PHILOSOPHICAL ASSOCIATION FOR THE BEST PUBLISHED PAPER IN THE PREVIOUS TWO YEARS. -/- The conflict between liberal legal theory and critical legal studies (CLS) is often framed as a matter of whether there is a theory of justice that the law should embody which all rational people could or must accept. In a divided society, the CLS critique of this view is overwhelming: (...) there is no such justice that can command universal assent. But the liberal critique of CLS, that it degenerates into an unpalatable moral relativism on which there is no non-arbitrary basis between a justice that underwrites forms of domination such as slavery and a justice that condemns such forms of domination is equally powerful and compelling. I show that there is a way to harmonize both views that is subject to empirical test. -/- First I show that the most widely accepted and influential formulation of liberal justice, John Rawls' Justice as Fairness, in. e.g, A Theory of Justice, cannot avoid the relativistic challenge because it would not be accepted, as a matter of sociological fact, by real people in a divided society once the "veil of Ignorance" is removed and real people step out from the Original Position. To put it differently, different reflective equilibria are inevitable in a divided society. Given the weight that Rawls properly puts on the realizability of a conception of justice and its stability in practice, this is a fatal objection. There can be no divided society that is "well ordered" in Rawls' sense, governed by a shared conception of justice and known to be so governed. -/- I then turn to the most powerful statement of the CLS view, Milton's Fisk's relativistic account in The State and Justice. For Fisk, justice is a compromise between what the dominant groups can compel and what the the subordinate groups will acquiesce to., There is no one such compromise in any given situation, so the account is in that sense relativistic, but more deeply, it is relativistic in that it offers no non-arbitrary, non-question begging way to choose between the official justice of, e.g., a slaveholding society and and the radical justice of the slaves, which has no place for slaveholders as a group or slavery as an institution.All that Fisk can offer is an arbitrary existential choice: I'm with the slaves. (Or the slaveowners.) Most of us would find this disconcerting or even unacceptable. -/- I show that Fisk's general sort of account can be modified to allow for an non-arbitrary choice. Given general facts about human nature, societies based on domination will produce resistance that over the long run will diminish or eliminate various forms of domination. Through a sort of ratchet effect, rights won will be hard if not impossible to reverse. Societies embodying forms of domination can therefore be compared on dimensions of stability: the more domination, the more resistance, and the less stability. Such societies are inferior on the dimension of justice to more emancipatory society on the terms of both kinds of justice, official and radical. -/- This is not question begging because regimes of domination incorporate stability no less than more emancipatory social orders. The choice between official justice embodying domination and radical justice that does not is not arbitrary because it is based on a shared commitment to long term stability. This offers an empirical test of which social orders are more justice, and a prediction that over time, domination will tend to decrease. (shrink)

Why does classical equilibrium statistical mechanics work? Malament and Zabell (1980) noticed that, for ergodic dynamical systems, the unique absolutely continuous invariant probability measure is the microcanonical. Earman and Rédei (1996) replied that systems of interest are very probably not ergodic, so that absolutely continuous invariant probability measures very distant from the microcanonical exist. In response I define the generalized properties of epsilon-ergodicity and epsilon-continuity, I review computational evidence indicating that systems of interest are epsilon-ergodic, I adapt Malament and (...) Zabell’s defense of absolute continuity to support epsilon-continuity, and I prove that, for epsilon-ergodic systems, every epsilon-continuous invariant probability measure is very close to the microcanonical. (shrink)

It seems that intuitions are indispensable in philosophical theorizing. Yet, there is evidence that our intuitions are heavily influenced by biases. This generates a puzzle: we must use our intuitions, but we seemingly cannot fully trust those very intuitions. In this paper, I develop a methodology for philosophical theorizing which attempts to avoid this puzzle. Specifically, I develop and defend a methodology that I call Extra-Wide Reflective Equilibrium. I argue that this method allows us to use intuitions, while also (...) providing a mechanism to check the influence of bias on our intuitions. In section I, defend the claim that intuitions are indispensable in philosophical theorizing. In section II, I outline recent arguments against the reliability of intuitions. In section III, I explain and defend my account of Extra-Wide Reflective Equilibrium. (shrink)

John Rawls recommends a reflective equilibrium method for evaluating which principles institutions should abide by. In this paper, I identify and challenge three assumptions that he makes.

In this paper it is argued that functional role semantics can be saved from criticisms, such as those raised by Putnam and Fodor and Lepore, by indicating which beliefs and inferences are more constitutive in determining mental content. The Scylla is not to use vague expressions; the Charybdis is not to endorse the analytic/synthetic distinction. The core idea is to use reflective equilibrium as a strategy to pinpoint which are the beliefs and the inferences that constitute the content of (...) a mental state. The beliefs and the inferences that are constitutive are those that are in reflective equilibrium in the process of attributing mental states to others. (shrink)

In this paper, I attempt to synthesize the two most influential contemporary ethical approaches that appeal to moral intuitions, viz., Rawlsian reflective equilibrium and Audi’s moderate intuitionism. This paper has two parts. First, building upon the work of Audi and Gaut, I provide a more detailed and nuanced account of how these two approaches are compatible. Second, I show how this novel synthesis can both (1) fully address the main objections to reflective equilibrium, viz., that it provides neither (...) necessary nor sufficient conditions for the justification of our moral beliefs and (2) help ethical intuitionism to deal with the fundamental problem of peer disagreement over our basic moral intuitions. In doing so, I sketch out a novel and attractive diachronic way of thinking about peer disagreement more generally. (shrink)

The method of reflective equilibrium starts with a set of initial judgments about some subject matter and refines that set to arrive at an improved philosophical worldview. However, the method faces two, trenchant objections. The Garbage-In, Garbage-Out Objection argues that reflective equilibrium fails because it has no principled reason to rely on some inputs to the method rather than others and putting garbage-in assures you of getting garbage-out. The Circularity Objection argues that reflective equilibrium fails because it (...) has no principled, non-circular way of sorting whatever is put into the method. The moves required to avoid both objections are instructive. Reflective equilibrium requires a meta-justification, and we offer one that appeals to the epistemic goods that underwrite a view known as phenomenal conservatism. Reflective equilibrium calls on us to start with what seems most likely to be true and to alter that collection of judgments in the ways that seem most likely to get us to the truth. Proceeding in this way is epistemically defensible and unavoidable. Hence, reflective equilibrium is not just good, it’s phenomenal. (shrink)

A model of brain function is presented that is consistently based on the biological principle of equilibrium. The neuronal modules of the cerebral cortex are proposed as units in which equilibrium between incoming signals and the synaptic structure is determined or established. Because of the electromagnetic activity of the brain, the electromagnetic properties of thecells are brought into focus. Due to the synaptic changes of the modules -essentially during sleep -an electromagnetic resting balance between the modules is established. (...) Incoming signals during the day, disturb the electromagnetic resting equilibrium and are detected and understood by this. The connecting nodes within the neuronal network are given by the equilibrium modules. Incoming information is represented in the form of the specific pathway of the network, while recognized information is represented by the equilibrium states within the modules. The paper leads to an understanding of information storage and processing in the brain. It even provides a hypothesis for understanding the emergence of the "self". Finally, the consideration of electromagnetic wave properties of neurons opens up a biophysical starting point to understanding conscious perceptions. In neuroscience, we lack a unifying theory of the brain. The reason for this may be an important detail –a missing link –that we do not yet see. Following the "track of biological equilibrium" in this paper leads to the hypothesis that the electromagnetic properties of the neurons are potential candidates to fill that gap. A hypothesis is developed describing their physiological significance in the processing of neurological information. (shrink)

Feynman's sum-over-histories formulation of quantum mechanics has been considered a useful calculational tool in which virtual Feynman histories entering into a coherent quantum superposition cannot be individually measured. Here we show that sequential weak values, inferred by consecutive weak measurements of projectors, allow direct experimental probing of individual virtual Feynman histories, thereby revealing the exact nature of quantum interference of coherently superposed histories. Because the total sum of sequential weak values of multitime projection operators for a complete set (...) of orthogonal quantum histories is unity, complete sets of weak values could be interpreted in agreement with the standard quantum mechanical picture. We also elucidate the relationship between sequential weak values of quantum histories with different coarse graining in time and establish the incompatibility of weak values for nonorthogonal quantum histories in history Hilbert space. Bridging theory and experiment, the presented results may enhance our understanding of both weak values and quantum histories. (shrink)

It is an ongoing controversy whether natural selection is a cause of population change, or a mere statistical description of how individual births and deaths accumulate. In this paper I restate the problem in terms of the reference class problem, and propose how the structure of stable equilibrium can provide a solution in continuity with biological practice. Insofar natural selection can be understood as a tendency towards equilibrium, key statisticalist criticisms are avoided. Further, in a modification of the (...) Newtonian-force analogy, it can be suggested that a better metaphor for natural selection is that of an emergent force, similar in nature to entropic forces: with magnitude and direction, but lacking a spatiotemporal origin or point of application. (shrink)

H.L.A. Hart objects to John Rawls’s liberty principle by drawing attention to how our legal system accepts the restriction of liberty to protect against other harms than liberty-deprivation, such as by laws against slander, libel, and publications which grossly infringe privacy. What is the solution for John Rawls, faced with this criticism? One solution is, by the reflective equilibrium method, to justify abandoning the judgment that these actions are immoral.