Given an argumentation network with initial values to the arguments, we look for algorithms which can yield extensions compatible with such initial values. We find that the best way of tackling this problem is to offer an iteration formula that takes the initial values and the attack relation and iterates a sequence of intermediate values that eventually converges leading to an extension. The properties surrounding the application of the iteration formula and its connection with other numerical and non-numerical techniques proposed (...) by others are thoroughly investigated in this paper. (shrink)

Part IIb presents some of the most important theorems for stable equilibrium states that can be deduced from the four postulates of the unified theory presented in Part I. It is shown for the first time that the canonical and grand canonical distributions are the only distributions that are stable. Moreover, it is shown that reversible adiabatic processes exist which cannot be described by the dynamical equation of quantum mechanics. A number of conditions are discussed that must be (...) satisfied by the general equation of motion which is yet to be discovered. (shrink)

Ethical theory examines human action in general terms, whereas moral judgment takes place in particular situations. These situations often cannot be subsumed easily under general norms and call for a delicate balance of norms and circumstances. I describe situations where opposing courses of action seem morally reasonable and I call them states of deliberative equilibrium. I review Aristotle’s and Kant’s conceptions of moral judgment and I offer a rule for stepping from deliberation to judgment in many situations of (...) equilibrium. (shrink)

In this paper, the nonsmooth compound transmission control protocol with the gentle random early detection system with the state-dependent round-trip delay is investigated in detail. Uniqueness of the positive equilibrium is proved firstly. Then, the closed approximate periodic solutions in this state-dependent delayed nonsmooth compound TCP with the GRED model are obtained by employing the harmonic balance and alternating frequency/time domain method. Then, we compare the results generated by numerical simulations with those of the closed approximate expressions obtained by (...) HB-AFT. It indicates that HB-AFT is simple, correct, and powerful for state-dependent delayed nonsmooth dynamical systems. Finally, we find the complicated dynamic: chaos. It is a grazing chaos with a hybrid property, i.e., where usually w oscillates at a very low frequency and q oscillates at a very high frequency. And, the route to chaos is a very rare route, i.e., the instantaneous and local transition of stable equilibrium to chaos. So, to the end of stability and good performance, we should adjust the parameters carefully to avoid the periodic and chaotic oscillations. (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)

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)

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)

A review of the literature and ethnographic data from Australia, Canada, New Zealand, the United States, and the United Kingdom on the research ethics review process suggest that moral panics can become triggers for punctuated equilibrium in the review process at both the macro and microlevel, albeit with significantly different levels of magnitude and impact. These data suggest that neither the development of the ethics review process nor the process itself proceeds gradually, but both are characterized by periodic (...) major shifts evoked by particular events or situations that result in varying levels of moral panic. One way to deal with this moral panic is to increase the regulation of research and the depth or intensity of the scrutiny of applications under ethics review. Moral panics at the macrolevel influence those at the microlevel and, if the moral panic evoked at the local or microlevel is not satisfactorily resolved, it will evoke action at a higher level. Understanding the evolution of research ethics review processes from this perspective might help make actions by ethics committees and policy makers more understandable and help explain why attention to research ethics are heightened at particular points in time. It may also provide a basis for developing recommendations for adaptations to the ethics review process and policy at both the local and macrolevel. (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)

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)

Why do systems prepared in a non-equilibrium state approach, and eventually reach, equilibrium? An important contemporary version of the Boltzmannian approach to statistical mechanics answers this question by an appeal to the notion of typicality. The problem with this approach is that it comes in different versions, which are, however, not recognised as such, much less clearly distinguished, and we often find different arguments pursued side by side. The aim of this paper is to disentangle different versions of (...) typicality-based explanations of thermodynamic behaviour and evaluate their respective success. My conclusion will be that the boldest version fails for technical reasons, while more prudent versions leave unanswered essential questions. (shrink)

Reconsideration-proofness is a solution concept proposed by Kocherlakota :33–54, 1996) for infinite horizon single-player problems in which time inconsistency is important. Kocherlakota’s definition has a limitation: it is not applicable to environments with state variables. The limitation is important because many time-inconsistent problems have state variables. This paper displays a natural generalization of reconsideration-proofness to environments with state variables, and shows that it leads to nonexistence in three examples. Such nonexistence contrasts with the general existence theorem obtained in environments without (...) state variables in Kocherlakota. In the first two examples, existence can be recovered with a modification in the solution concept. In the last example, nonexistence occurs even with the modified solution concept. Insights about further research are derived from these nonexistence results. (shrink)

This serves as an introduction to a debate between Hans Kelsen and Otto Bauer concerning the nature and relative autonomy of the state, and the theories that informed the political practices of the Austro-Marxists and of the SDAP immediately after the fall of the monarchy and during the early years of the First Republic. Both pieces were published in Der Kampf, the SDAP’s theoretical journal, in which many key texts of Austro-Marxist thought appeared. The debate is of theoretical interest, particularly (...) with respect to Marxist state theory, but is potentially also of renewed relevance to an age of post-GFC austerity. Bauer’s distinction between functional oligarchy and functional democracy is identified as one such potential contribution to current debate and analysis. (shrink)

This serves as an introduction to a debate between Hans Kelsen and Otto Bauer concerning the nature and relative autonomy of the state, and the theories that informed the political practices of the Austro-Marxists and of the SDAP immediately after the fall of the monarchy and during the early years of the First Republic. Both pieces were published in Der Kampf, the SDAP’s theoretical journal, in which many key texts of Austro-Marxist thought appeared. The debate is of theoretical interest, particularly (...) with respect to Marxist state theory, but is potentially also of renewed relevance to an age of post-GFC austerity. Bauer’s distinction between functional oligarchy and functional democracy is identified as one such potential contribution to current debate and analysis. (shrink)

We present a definition of equilibrium for Boltzmannian statistical mechanics based on the long-run fraction of time a system spends in a state. We then formulate and prove an existence theorem which provides general criteria for the existence of an equilibrium state. We illustrate how the theorem works with toy example. 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. (shrink)

In 1916, Einstein rederived the blackbody radiation law of Planck that originated the idea of quantized energy one hundred years ago. For this purpose, Einstein introduced the concept of transition probability, which had a profound influence on the development of quantum theory. In this article, we adopt Einstein's assumptions with two exceptions and seek the statistical condition for the thermal equilibrium of matter without referring to the inner details of either statistical thermodynamics or quantum theory. It is shown that (...) the conditions of thermodynamic equilibrium of electromagnetic radiation and the energy balance of thermal radiation by the matter, between any of its two energy-states, not only result in Planck's radiation law and the Bohr frequency condition, but they remarkably yield the law of the statistical thermal equilibrium of matter: the Maxwell–Boltzmann distribution. Since the transition probabilities of the modern quantum theory of radiation coincide with their definition in Einstein's theory of blackbody radiation, the presented deduction of the Maxwell–Boltzmann distribution is equally valid within the bounds of modern quantum theory. Consequently, within the framework of the fundamental assumptions, the Maxwell–Boltzmann distribution of energy-states is not only a sufficient, but a necessary condition for thermal equilibrium between the matter and radiation. (shrink)

In a modern economy, “equilibrium” means that supply and demand is equal. It is at this point that the allocation of goods and services is at its most efficient, this being because the amount of goods and the amount of goods in demand are equally balanced. The market equilibrium therefore is determined by supply and demand. This paper looks at the concept of “equilibrium” in some of the early Confucian texts and its possible implications in economic activities. (...) In the Confucian context equilibrium, or what can be termed as the ultimate equilibrium, is to be understood in a broader sense where balances and harmony at different levels (e.g. individual and society) need to be sought in order to achieve a model of sustainable development. The ultimate equilibrium may provide an alternative approach to social welfare and economic prosperity creating universal harmony and better living for humans. In Confucian ideology, governing for the welfare of the people is not merely a question of increasing personal income and wealth; it requires implementation on a priority basis, taking into consideration the formation of an orderly society based on the enforcement of moral and ethical standards with the existence of a benevolent government which appropriates things according to the principles of harmony and order to achieve what can be termed as the “great equilibrium”—equilibrium that is not simply defined by balanced economic forces as in modern economic theory; but rather is used to suggest an ideal state of harmony in self fulfilment and socio-political order through incentives and by appropriate means. (shrink)

A manifestly covariant relativistic statistical mechanics of a system of N indistinguishable events with motion in space-time parametrized by an invariant “historical time” τ is considered. The relativistic mass distribution for such a system is obtained from the equilibrium solution of the generalized relativistic Boltzmann equation by integration over angular and hyperangular variables. All the characteristic averages are calculated. Expressions for the pressure and the energy density are found, and the relativistic equation of state is obtained. Validity criteria are (...) defined. The Galilean limit is considered; the theory is shown to pass over to the usual nonrelativistic statistical mechanics of indistinguishable particles. Anti-events are introduced; for an event-anti-event system the equation of state p, ρ ∝ T 6 is found, which gives the value of the sound velocity c 2 = 0.20, in agreement with the “realistic” equation of state suggested by Shuryak for hot hadronic matter. (shrink)

Influential neoclassical economist Lionel McKenzie has made major contributions to postwar economic thought in the fields of equilibrium, trade, and capital accumulation. This selection of his papers traces the development of his thinking in these three crucial areas.McKenzie's early academic life took him to Duke, Princeton, Oxford, the University of Chicago, and the Cowles Commission. In 1957, he went to the University of Rochester to head the economics department there, and he remains at Rochester, now Wilson Professor Emeritus of (...) Economics. McKenzie's most significant research was undertaken during a period that saw the development of the major themes of neoclassical economics and the use of fundamental mathematical methods to do so. McKenzie contributed to both aspects of this research program. He helped shape the direction of the field and, at Rochester, influenced generations of future scholars. In 2002, The MIT Press published McKenzie's Classical General Equilibrium Theory, a detailed summary of the model and methodology. This book, collecting his most important papers in the form in which they were originally published, can be seen as a companion to that one. The many state-of-the-art results achieved in McKenzie's original papers present sophisticated theoretical work that will continue to be important to future developments in the discipline. (shrink)

The aim of the paper is the construction of a distributional model which enables the study of the evolutionary dynamics that arise for symmetric games, and the equilibrium selection mechanisms that originate from such processes. The evolution of probability distributions over the state variables is studied using the Fokker-Planck diffusion equation. Equilibrium selection using the ’’basin of attraction’’ approach, and a selection process suggested by Pontryagin are contrasted. Examples are provided for all generic 2-person symmetric binary choice games. (...) JEL Classification: C78.. (shrink)

As our understanding of biological evolution continues to deepen, tension still surrounds the relationship between competition and cooperation in the evolution of the biosphere, with rival viewpoints often associated with the Red Queen and Black Queen hypotheses respectively. This essay seeks to reconcile these viewpoints by integrating observations of some general trends in biosphere evolution with concepts from game theory. It is here argued that biodiversity and ecological cooperation are intimately related, and that both tend to cyclically increase over biological (...) history; this is likely due to the greater relative stability of cooperation over competition as a means of long-term conflict resolution within ecosystems. By integrating this view of the biosphere with existing models such as Niche Game Theory, it may be argued that competition and cooperation in ecosystems coexist at equilibria which shift preferentially towards increasing cooperation over biological history. This potentially points to a state of “cooperative equilibrium” as a limit or endpoint in long-term biosphere evolution, such that Black Queen and Red Queen behavior dominate different phases in an evolutionary movement towards optimal cooperative stability in ecological networks. This concept, if accepted, may also bear implications for developing future mathematical models in evolutionary biology, as well as for resolving the perennial debate regarding the relative roles of conflict and harmony in nature. (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)

The wide reflective equilibrium (WRE) is considered the most important method of ethical justification and is intensively discussed in the scientific community. However, it is unclear to what extent it is actually applied in the ethical literature. The objective of this paper is to fill this gap by providing a critical overview of its explicit applications. Explicit application refers to studies that, following Daniels’ definition, contain three levels, name their elements, and provide a connection between the levels. Philosophers Index, (...) ProQuest, PubMed, Web of Science, and Scopus were searched for studies that explicitly used the WRE method and were written in German or English. All topics, disciplines, and publication forms were considered. Nineteen studies were found in which the WRE was applied 23 times. In the 23 applications, 50 equilibria were discussed, and 19 times it was reported that an equilibrium state was reached. The authors applied the WRE in various disciplines, for different purposes, and to diverse topics. The applications themselves differed considerably regarding the application procedure and the scope. Differences can be seen in particular with regard to the presentation of the adjustment process and the WRE criteria used. The results indicate that the WRE can be successfully applied, but the number of explicit applications is still very low. Further research is needed to develop the WRE into an established method of justification. In particular, standards are needed for adjustment and for WRE criteria. (shrink)

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)

This article brings together two different topics: reflective equilibrium (RE) and belief revision theory (BRT). RE is a popular method of justification in many areas of philosophy, it involves a process of mutual adjustments striving for a state of coherence, but it lacks formally rigorous elaborations and faces severe criticism. To elucidate core elements of RE and provide a solid basis to address objections, a formal model of RE within BRT is presented. A fruitful starting point to the formalization (...) of RE is Olsson’s coherentist interpretation of semi-revision, but it does not come with a comparative notion of stability. This paper develops an account of comparative stability in an RE setting for belief changing operations. The operations are useful to characterize RE states as well as processes, and they are shown to satisfy postulates of rational belief change. (shrink)

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)

This book synthesizes the game-theoretic modeling of decision-making processes and an ancient moral requirement, called the Golden Rule of ethics (GR). This rule states, "Behave to others as you would like them to behave to you." The GR is one of the oldest, most widespread and specific moral requirements that appear in Christianity, Islam, Judaism, Buddhism, and Confucianism. The book constructs and justifies mathematical models of dynamic socio-economic processes and phenomena that reveal the mechanism of the GR and are (...) based on the concept of Berge equilibrium. The GR can be naturally used for resolving or balancing conflicts, and its "altruistic character" obviously excludes wars, blood-letting, and armed clashes. The previous book of the authors, The Berge Equilibrium: A Game-Theoretic Framework for the Golden Rule of Ethics, covers the static case of the GR. In this book, the dynamic case of the GR is investigated using the altruistic concept of Berge equilibrium and three factors as follows: a) a modification of N.N. Krasovskii's mathematical formalization of differential positional games (DPGs), in view of the counterexamples given by A.I. Subbotin and A.F. Kononenko; b) the method of guiding control, proposed by N.N. Krasovskii; c) the Germeier convolution of the payoff functions of different players. Additionally, the book features exercises, problems, and solution tips collected together in Appendix 1, as well as new approaches to conflict resolution as presented in Appendices 2-4. The book will be of use to undergraduate and graduate students and experts in the field of decision-making in complex control and management systems, as well as anyone interested in game theory and applications. (shrink)

Although democratic innovations are spread all over the world, there is little research on the institutional outcomes of implementing such innovations in governmental organisations. To remedy this, it is important to focus on cases where DIs have been implemented and formally connected to the policymaking process over a longer period. Reykjavik provides such a case. Drawing on observations and interviews with key stakeholders over a period of three years, this study analyses how the institutional logic of DIs influenced the local (...) government in Reykjavik. The study presents two conclusions: First, it is clear that one equilibrium has not been replaced by another. Second, there is no peaceful co-existence between the two, but instead the outcome is an organisation in ‘a state of flux’. There are several factors contributing to this outcome, but three stand out: a populist power-shift, dissatisfaction with theworking of the implemented DIs and deliberative ambiguity. In the final part of the article, the institutional outcome is discussed in relation to overall consequences for the political system. (shrink)

There has been a recent surge of interest among economists in developing models of doxastic states that can account for some aspects of human cognitive limitations that are ignored by standard formal models, such as awareness. Epistemologists purport to have a principled reason for ignoring the question of awareness: under the equilibrium conception of doxastic states they favour, a doxastic state comprises the doxastic commitments an agent would recognise were he fully aware, so the question of awareness (...) plays no role. The objective of this paper is to scrutinize this argument. A thesis underlying the argument, which we call the independence of doxastic commitments with respect to awareness, is identified, and examples are given where it appears to be violated. By considering these examples, one can get an idea of the price of accepting this thesis. On the one hand, one can escape the conclusion that the thesis is violated, but only at the expense of another principle espoused by all major formal models of belief, which we call constant doxastic rest; and abandoning this principle necessitates extensive revision of current models of belief. On the other hand, there are epistemologically valid reasons for thinking that the thesis fails to hold in the examples, which have to be rebutted if the thesis, and the equilibrium justification for ignoring the issue of awareness, are to be retained. (shrink)

Why do systems prepared in a non-equilibrium state approach, and eventually reach, equilibrium? An important contemporary version of the Boltzmannian approach to statistical mechanics answers this question by an appeal to the notion of typicality. The problem with this approach is that it comes in different versions, which are, however, not recognised as such, much less clearly distinguished, and we often find different arguments pursued side by side. The aim of this paper is to disentangle different versions of (...) typicality-based explanations of thermodynamic behaviour and evaluate their respective success. My conclusion will be that the boldest version fails for technical reasons, while more prudent versions leave unanswered essential questions. (shrink)

The Hardy–Weinberg equilibrium has been argued by Sober, Stephens and others to represent the zero-force state for evolutionary biology understood as a theory of forces. I investigate what it means for a model to involve forces, developing an explicit account by defining what the zero-force state is in a general theoretical context. I use this account to show that Hardy–Weinberg equilibrium is not the zero-force state in biology even in the contexts in which it applies, and argue based (...) on this that drift should not be understood as an evolutionary force. (shrink)

We introduce a deductive system Bal which models the logic of balance of opposing forces or of balance between conflicting evidence or influences. ‘‘Truth values’’ are interpreted as deviations from a state of equilibrium, so in this sense, the theorems of Bal are to be interpreted as balanced statements, for which reason there is only one distinguished truth value, namely the one that represents equilibrium. The main results are that the system Bal is algebraizable in the sense of (...) [5] and its equivalent algebraic semantics BAL is definitionally equivalent to the variety of abelian lattice ordered groups, that is, the categories of the algebras in BAL and of ℓ–groups are isomorphic (see [10], Ch.4, 4). We also prove the deduction theorem for Bal and we study different kinds of semantic consequence associated to Bal. Finally, we prove the co-NP-completeness of the tautology problem of Bal. (shrink)

We study the equilibrium behavior of informed traders interacting with market scoring rule (MSR) market makers. One attractive feature of MSR is that it is myopically incentive compatible: it is optimal for traders to report their true beliefs about the likelihood of an event outcome provided that they ignore the impact of their reports on the profit they might garner from future trades. In this paper, we analyze non-myopic strategies and examine what information structures lead to truthful betting by (...) traders. Specifically, we analyze the behavior of risk-neutral traders with incomplete information playing in a dynamic game. We consider finite-stage and infinite-stage game models. For each model, we study the logarithmic market scoring rule (LMSR) with two different information structures: conditionally independent signals and (unconditionally) independent signals. In the finite-stage model, when signals of traders are independent conditional on the state of the world, truthful betting is a Perfect Bayesian Equilibrium (PBE). Moreover, it is the unique Weak Perfect Bayesian Equilibrium (WPBE) of the game. In contrast, when signals of traders are unconditionally independent, truthful betting is not a WPBE. In the infinite-stage model with unconditionally independent signals, there does not exist an equilibrium in which all information is revealed in a finite amount of time. We propose a simple discounted market scoring rule that reduces the opportunity for bluffing strategies. We show that in any WPBE for.. (shrink)

The word “sustainable” débuted in 1987 but has since become a hot topic issue, both for scientific research and wider society. Although sustainability may appear to be a thoroughly twenty-first century goal, sustainability science concepts and goals such as balance, endurance, order and change, reach back at least as far as the proto-scientific investigations of alchemy. Both alchemy and sustainability science can be understood as systems or strategies which individuals and societies can use to organise and manage themselves in a (...) complex world filled with dynamic problems. Alchemy never created a panacea or transmuted base metals into gold because those goals proved to be based on fundamentally flawed theories and premises. Nevertheless, alchemy did succeed in helping adherents manage themselves and their societies in advantageous ways. Alchemy also positively and significantly influenced subsequent scientific development. Likewise, science helps humanity manage itself on multiple scales, from the individual to the international, and will certainly contribute to further scientific research and development. However, it is not yet known whether carbon neutrality, entirely renewable energy and other sustainability goals will be achieved or whether these goals will also come to be seen as based on flawed understandings and theories. For this reason, this article explores key features of alchemy, traces how they persisted through Enlightenment-era science and how they continue to be present and influential within scientific efforts today. The article goes on to reflect on how the history, development and continued use of concepts such as balance, endurance, order and change may be useful portents of how humans and human society will manage themselves in the future. Such reflections may also temper the zeal with which individuals that accept or reject sustainability goals treat each other, thereby offering a way for divergent groups to manage their interactions. Flawed theories prevented alchemy from achieving many of its primary stated goals. However, alchemy was very beneficial, both during its period of use and subsequently through its influence on subsequent development. This article identifies ideas from alchemy that were originally beneficial and that have persisted through Enlightenment-era science and into contemporary science. The article also explores how those ideas continue to influence scientific and sustainability goals today. Understanding and reflecting on alchemy’s successes and failures facilitates reflection on the potential successes and failures of sustainability and the human consequences of trying to manage a sustainable future. (shrink)

The word “sustainable” débuted in 1987 but has since become a hot topic issue, both for scientific research and wider society. Although sustainability may appear to be a thoroughly twenty-first century goal, sustainability science concepts and goals such as balance, endurance, order and change, reach back at least as far as the proto-scientific investigations of alchemy. Both alchemy and sustainability science can be understood as systems or strategies which individuals and societies can use to organise and manage themselves in a (...) complex world filled with dynamic problems. Alchemy never created a panacea or transmuted base metals into gold because those goals proved to be based on fundamentally flawed theories and premises. Nevertheless, alchemy did succeed in helping adherents manage themselves and their societies in advantageous ways. Alchemy also positively and significantly influenced subsequent scientific development. Likewise, science helps humanity manage itself on multiple scales, from the individual to the international, and will certainly contribute to further scientific research and development. However, it is not yet known whether carbon neutrality, entirely renewable energy and other sustainability goals will be achieved or whether these goals will also come to be seen as based on flawed understandings and theories. For this reason, this article explores key features of alchemy, traces how they persisted through Enlightenment-era science and how they continue to be present and influential within scientific efforts today. The article goes on to reflect on how the history, development and continued use of concepts such as balance, endurance, order and change may be useful portents of how humans and human society will manage themselves in the future. Such reflections may also temper the zeal with which individuals that accept or reject sustainability goals treat each other, thereby offering a way for divergent groups to manage their interactions. Flawed theories prevented alchemy from achieving many of its primary stated goals. However, alchemy was very beneficial, both during its period of use and subsequently through its influence on subsequent development. This article identifies ideas from alchemy that were originally beneficial and that have persisted through Enlightenment-era science and into contemporary science. The article also explores how those ideas continue to influence scientific and sustainability goals today. Understanding and reflecting on alchemy’s successes and failures facilitates reflection on the potential successes and failures of sustainability and the human consequences of trying to manage a sustainable future. (shrink)

The word “sustainable” débuted in 1987 but has since become a hot topic issue, both for scientific research and wider society. Although sustainability may appear to be a thoroughly twenty-first century goal, sustainability science concepts and goals such as balance, endurance, order and change, reach back at least as far as the proto-scientific investigations of alchemy. Both alchemy and sustainability science can be understood as systems or strategies which individuals and societies can use to organise and manage themselves in a (...) complex world filled with dynamic problems. Alchemy never created a panacea or transmuted base metals into gold because those goals proved to be based on fundamentally flawed theories and premises. Nevertheless, alchemy did succeed in helping adherents manage themselves and their societies in advantageous ways. Alchemy also positively and significantly influenced subsequent scientific development. Likewise, science helps humanity manage itself on multiple scales, from the individual to the international, and will certainly contribute to further scientific research and development. However, it is not yet known whether carbon neutrality, entirely renewable energy and other sustainability goals will be achieved or whether these goals will also come to be seen as based on flawed understandings and theories. For this reason, this article explores key features of alchemy, traces how they persisted through Enlightenment-era science and how they continue to be present and influential within scientific efforts today. The article goes on to reflect on how the history, development and continued use of concepts such as balance, endurance, order and change may be useful portents of how humans and human society will manage themselves in the future. Such reflections may also temper the zeal with which individuals that accept or reject sustainability goals treat each other, thereby offering a way for divergent groups to manage their interactions. Flawed theories prevented alchemy from achieving many of its primary stated goals. However, alchemy was very beneficial, both during its period of use and subsequently through its influence on subsequent development. This article identifies ideas from alchemy that were originally beneficial and that have persisted through Enlightenment-era science and into contemporary science. The article also explores how those ideas continue to influence scientific and sustainability goals today. Understanding and reflecting on alchemy’s successes and failures facilitates reflection on the potential successes and failures of sustainability and the human consequences of trying to manage a sustainable future. (shrink)

In this paper I will defend the incapacity of the informational frameworks in thermal physics, mainly those that historically and conceptually derive from the work of Brillouin (1962) and Jaynes (1957a), to robustly explain the approach of certain gaseous systems to their state of thermal equilibrium from the dynamics of their molecular components. I will further argue that, since their various interpretative, conceptual and technical-formal resources (e.g. epistemic interpretations of probabilities and entropy measures, identification of thermal entropy as Shannon (...) information, and so on) are shown to be somehow incoherent, inconsistent or inaccurate, these informational proposals need to 'epistemically parasitize' the manifold of theoretical resources of Boltzmann's and Gibbs' statistical mechanics, respectively, in order to properly account for the equilibration process of an ideal gas from its microscopic properties. Finally, our conclusion leads us to adopt a sort of constructive skepticism regarding the explanatory value of the main informationalist trends in statistical thermophysics. (shrink)

Boltzmannian statistical mechanics (BSM) partitions a system’s space of micro-states into cells and refers to these cells as ‘macro-states’. One of these cells is singled out as the equilibrium macro-state while the others are non-equilibrium macro-states. It remains unclear, however, how these states are characterised at the macro-level as long as only real-valued macro-variables are available. We argue that physical quantities like pressure and temperature should be treated as field-variables and show how field variables (...) fit into the framework of our own version of BSM, the long-run residence time account of BSM. The introduction of field variables into the theory makes it possible to give a full macroscopic characterisation of the approach to equilibrium. (shrink)

Here, we analyze how the set of nucleotides in the cell is equilibrated and how this generates simple rules that help the cell to organize itself via maintenance of a stable non‐equilibrium state. A major mechanism operating to achieve this state is thermodynamic buffering via high activities of equilibrating enzymes such as adenylate kinase. Under stable non‐equilibrium, the ratios of free and Mg‐bound adenylates, Mg2+ and membrane potentials are interdependent and can be computed. The adenylate status is balanced (...) with the levels of reduced and oxidized pyridine nucleotides through regulated uncoupling of the pyridine nucleotide pool from ATP production in mitochondria, and through oxidation of substrates non‐coupled to NAD+ reduction in peroxisomes. The set of adenylates and pyridine nucleotides constitutes a generalized cell energy status and determines rates of major metabolic fluxes. As the result, fluxes of energy and information become organized spatially and temporally, providing conditions for self‐maintenance of metabolism. (shrink)

It is shown that the traditional formalism of equilibrium quantum statistical mechanics may fully be incorporated into a general macro-observable approach to quantum statistical mechanics recently proposed by the same author. (1,2) In particular, the partition functions which in the traditional approach are assumed to connect nonnormalized density operators with thermodynamic functions are reinterpreted as functions connecting so-called quantum mechanical effect operators with state parameters. It is argued that these functions although only part of a much richer internal structure (...) of the macro-observable are sufficient to cope with all problems one usually encounters in equilibrium quantum statistical mechanics. p]Denn eigentlich unternehmen wir umsonst, das Wesen eines Dinges auszudrücken. Wirkungen werden wir gewahr, und eine vollständige Geschichte dieser Wirkungen umfaßte wohl allenfalls das Wesen jenes Dinges.Johann W. v. Goethe Farbenlehre. (shrink)

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 political economy, the seminal contribution of the Baron–Ferejohn bargaining model constitutes an important milestone for the study of legislative policy making. In this paper, we analyze a particular equilibrium characteristic of this model, equilibrium uniqueness. The Baron–Ferejohn model yields a class of payoff-unique stationary subgame perfect equilibria in which players’ equilibrium strategies are not uniquely determined. We first provide a formal proof of the multiplicity of equilibrium strategies. This also enables us to establish some important (...) properties of SSPE. We then introduce veto players into the original Baron–Ferejohn model. We state the conditions under which the new model has a unique SSPE not only in terms of payoffs but also in terms of players’ equilibrium strategies. (shrink)

This book presents a collection of articles on applied general equilibrium analysis by major contributors to this field. This rapidly expanding method of analysis involves the use of computers to study entire economies and the interrelationships among firms, households and governments in these economies. There are also articles on the particular computational techniques involved in the numerical estimation of these equilibrium models and on several particular applications. Papers deal with the United States, Mexican and Australian economies. Other (...) chapters provide an analysis of long-run energy problems, fiscal federalism and economic planning. (shrink)

For strategic communication games à la Crawford and Sobel the paper shows that under some prior beliefs different equilibrium partitions of the state space can have equal cardinality. Hence, there can be different equilibrium action profiles with the same size.