Rift Valley Fever is a vector-borne disease mainly transmitted by mosquito. To gain some quantitative insights into its dynamics, a deterministic model with mosquito, livestock, and human host is formulated as a system of nonlinear ordinary differential equations and analyzed. The disease threshold $$\mathcal{R}_0$$ is computed and used to investigate the local stability of the equilibria. A sensitivity analysis is performed and the most sensitive model parameters to the measure of initial disease transmission $$\mathcal{R}_0$$ and the endemic equilibrium (...) are determined. Both $$\mathcal{R}_0$$ and the disease prevalence in mosquitoes are more sensitive to the natural mosquito death rate, d m . The disease prevalence in livestock and humans are more sensitive to livestock and human recruitment rates, $$\Uppi_l$$ and $$\Uppi_h$$, respectively, suggesting isolation of livestock from humans is a viable preventive strategy during an outbreak. Numerical simulations support the analytical results in further exploring theoretically the long-term dynamics of the disease at the population level. (shrink)

A new multi-stage deterministic model for the transmission dynamics of syphilis, which incorporates disease transmission by individuals in the early latent stage of syphilis infection and the reversions of early latent syphilis to the primary and secondary stages, is formulated and rigorously analysed. The model is used to assess the population-level impact of preventive and therapeutic measures against the spread of the disease in a community. It is shown that the disease-free equilibrium of the model is globally-asymptotically stable whenever (...) the associated control reproduction number is less than unity. A special case of the model is shown to have a unique and globally-asymptotically stable endemic equilibrium whenever the associated reproduction number exceeds unity. Uncertainty and sensitivity analysis of the model, using parameter values and ranges relevant to syphilis transmission dynamics in Nigeria, show that the top three parameters that drive the syphilis infection are the disease transmission rate, compliance in condom use and efficacy of condom. Numerical simulations of the model show that the targeted treatment of secondary syphilis cases is more effective than the targeted treatment of individuals in the primary or early latent stage of syphilis infection. (shrink)

The public health benefits of herd immunity are often used as the justification for coercive vaccine policies. Yet, ‘herd immunity’ as a term has multiple referents, which can result in ambiguity, including regarding its role in ethical arguments. The term ‘herd immunity’ can refer to (1) the herd immunity threshold, at which models predict the decline of an epidemic; (2) the percentage of a population with immunity, whether it exceeds a given threshold or not; and/or (3) the indirect benefit afforded (...) by collective immunity to those who are less immune. Moreover, the accumulation of immune individuals in a population can lead to two different outcomes: elimination (for measles, smallpox, etc) or endemic equilibrium (for COVID-19, influenza, etc). We argue that the strength of a moral obligation for individuals to contribute to herd immunity through vaccination, and by extension the acceptability of coercion, will depend on how ‘herd immunity’ is interpreted as well as facts about a given disease or vaccine. Among other things, not all uses of ‘herd immunity’ are equally valid for all pathogens. The optimal conditions for herd immunity threshold effects, as illustrated by measles, notably do not apply to the many pathogens for which reinfections are ubiquitous (due to waning immunity and/or antigenic variation). For such pathogens, including SARS-CoV-2, mass vaccination can only be expected to delay rather than prevent new infections, in which case the obligation to contribute to herd immunity is much weaker, and coercive policies less justifiable. (shrink)

We formulate and analyze the dynamics of an influenza pandemic model with vaccination and treatment using two preventive scenarios: increase and decrease in vaccine uptake. Due to the seasonality of the influenza pandemic, the dynamics is studied in a finite time interval. We focus primarily on controlling the disease with a possible minimal cost and side effects using control theory which is therefore applied via the Pontryagin’s maximum principle, and it is observed that full treatment effort should be given while (...) increasing vaccination at the onset of the outbreak. Next, sensitivity analysis and simulations (using the fourth order Runge-Kutta scheme) are carried out in order to determine the relative importance of different factors responsible for disease transmission and prevalence. The most sensitive parameter of the various reproductive numbers apart from the death rate is the inflow rate, while the proportion of new recruits and the vaccine efficacy are the most sensitive parameters for the endemic equilibrium point. (shrink)

This paper describes a traditional SIR type epidemic model with saturated infection rate and treatment function. The dynamics of the model is studied from the point of view of stability and bifurcation. Basic reproduction number is obtained and it is shown that the model system may possess a backward bifurcation. The global asymptotic stability of the endemic equilibrium is studied with the help of a geometric approach. Optimal control problem is formulated and solved. Some numerical simulation works are (...) carried out to validate our analytical results. (shrink)

Despite several research on HIV/aids, it is still incumbent to investigate more effective control measures to mitigate its infection level. Therefore, we introduce an HIV/aids-resistant model with behavior change and study its basic properties. In order to determine the most sensitive parameters that are responsible for disease transmission with respect to the basic reproduction number and those responsible for disease prevalence with respect to the endemic equilibrium, the sensitivity analysis was established and it was confirmed that the influx (...) rate of people into the infected population and total abstinence from all risk practices and endemic areas are some of the most sensitive parameters for disease spread and disease eradication, respectively. Furthermore, by considering controls u1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$u_1$$\end{document} denoting the government’s intervention in promoting and encouraging behavior change, u2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$u_2$$\end{document} representing intake of balanced nutritional supplementation, and u3\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$u_3$$\end{document} connoting antiretroviral therapy (ART), an optimal control problem was developed and analyzed. Before the establishment of the necessary conditions of the optimal control using Pontryagin’s Maximum Principle, we proved the existence of the optimal control triplet (u1(t),u2(t),u3(t)∈Φ,\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$(u_1(t),u_2(t),u_3(t)\in \Phi,$$\end{document} where Φ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\Phi$$\end{document} is the control set at time t,) which has been neglected by many researchers in recent years. Using the Runge–Kutta scheme, the optimal control problem was solved to understand the best combination of control strategies. Using the demographic and epidemiological data for South Africa on HIV/aids, a numerical simulation was carried out and results are presented on 3D surface plots. The obtained results suggested that the combination of all the considered control measures is the best method to ensure disease eradication. (shrink)

In this study, for COVID-19, we divide people into four categories: susceptible S t, closely contacted C t, infective I t, and removed R t according to the current epidemic situation and then investigate two models: the SCIR models with immigration and without immigration. For the former, Model 1, we obtain the condition for global stability of its disease-free equilibrium. For the latter, Model 2, we establish the local asymptotic stability of its endemic equilibrium by constructing Lyapunov (...) function. Afterwards, by the bifurcation theory, we qualitatively analyze the properties of its Hopf bifurcations of the latter. Finally, numerical simulations are given to illustrate the obtained results of two models. The results imply the importance of finding closely contacted and overseas imports on epidemic control. It indicates that not only the incubation delay τ is crucial for the containment of the COVID-19 but also the scientific and rigorous containment measures are the key factors of the success of the containment. (shrink)

To mitigate the spread of schistosomiasis, a deterministic human-bovine mathematical model of its transmission dynamics accounting for contaminated water reservoirs, including treatment of bovines and humans and mollusciciding is formulated and theoretically analyzed. The disease-free equilibrium is locally and globally asymptotically stable whenever the basic reproduction number R0<1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$R_0<1$$\end{document}, while global stability of the endemic equilibrium is investigated by constructing a suitable Lyapunov function. To support the analytical results, parameter (...) values from published literature are used for numerical simulations and where applicable, uncertainty analysis on the non-dimensional system parameters is performed using the Latin Hypercube Sampling and Partial Rank Correlation Coefficient techniques. Sensitivity analysis to determine the relative importance of model parameters to disease transmission shows that the environment-related parameters namely, εs\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\varepsilon _s$$\end{document} (snails shedding rate of cercariae), ps\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$p_s$$\end{document} (probability that cercariae shed by snails survive), c (fraction of the contaminated environment sprayed by molluscicides) and μc\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mu _c$$\end{document} (mortality rate of cercariae) are the most significant to mitigate the spread of schistosomiasis. Mollusciciding, which directly impacts the contaminated environment as a single control strategy is more effective compared to treatment. However, concurrently applying mollusciciding and treatment will yield a better outcome. (shrink)

Schistosomiasis, a vector-borne chronically debilitating infectious disease, is a serious public health concern for humans and animals in the affected tropical and sub-tropical regions. We formulate and theoretically analyze a deterministic mathematical model with snail and bovine hosts. The basic reproduction number R0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$R_0$$\end{document} is computed and used to investigate the local stability of the model’s steady states. Global stability of the endemic equilibrium is carried out by constructing a suitable (...) Lyapunov function. Sensitivity analysis shows that the basic reproduction number is most sensitive to the model parameters related to the contaminated environment, namely: shedding rate of cercariae by snails, cercariae to miracidia survival probability, snails-miracidia effective contact rate and natural death rate of miracidia and cercariae. Numerical results show that when no intervention measures are implemented, there is an increase of the infected classes, and a rapid decline of the number of susceptible and exposed bovines and snails. Effects of the variation of some of the key sensitive model parameters on the schistosomiasis dynamics as well as on the initial disease transmission threshold parameter R0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$R_0$$\end{document} are graphically depicted. (shrink)

This manuscript considers the transmission dynamics of lymphatic filariasis with some intervention strategies in place. Unlike previously developed models, our model takes into account both the exposed and infected classes in both the human and mosquito populations, respectively. We also consider vaccinated, treated and recovered humans in the presented model. The global dynamics of the proposed model are completely determined by the basic and effective reproduction numbers. We then use Lyapunov function theory to find the sufficient conditions for global stability (...) of both the disease-free equilibrium and endemic equilibrium. The Lyapunov functions show that when the basic reproduction number is less than or equal to unity, the disease-free equilibrium is globally asymptotically stable, and when it is greater than unity then the endemic equilibrium is also globally asymptotically stable. Finally, numerical simulations are carried out to investigate the effects of the intervention strategies and key parameters to the spread of lymphatic filariasis. The numerical simulations support the analytical results and illustrate possible model behavioral scenarios. (shrink)

In this article, we investigated a deterministic model of pneumonia-meningitis coinfection. Employing the Atangana–Baleanu fractional derivative operator in the Caputo framework, we analyze a seven-component approach based on ordinary differential equations. Furthermore, the invariant domain, disease-free as well as endemic equilibria, and the validity of the model’s potential results are all investigated. According to controller design evaluation and modelling, the modulation technique devised is effective in diminishing the proportion of incidences in various compartments. A fundamental reproducing value is generated (...) by exploiting the next generation matrix to assess the properties of the equilibrium. The system’s reliability is further evaluated. Sensitivity analysis is used to classify the impact of each component on the spread or prevention of illness. Using simulation studies, the impacts of providing therapy have been determined. Additionally, modelling the appropriate configuration demonstrated that lowering the fractional order from 1 necessitates a rapid initiation of the specified control technique at the largest intensity achievable and retaining it for the bulk of the pandemic’s duration. (shrink)

A two strain HIV/AIDS model with treatment which allows AIDS patients with sensitive HIV-strain to undergo amelioration is presented as a system of non-linear ordinary differential equations. The disease-free equilibrium is shown to be globally asymptotically stable when the associated epidemic threshold known as the basic reproduction number for the model is less than unity. The centre manifold theory is used to show that the sensitive HIV-strain only and resistant HIV-strain only endemic equilibria are locally asymptotically stable when (...) the associated reproduction numbers are greater than unity. Qualitative analysis of the model including positivity, boundedness and persistence of solutions are presented. The model is numerically analysed to assess the effects of treatment with amelioration on the dynamics of a two strain HIV/AIDS model. Numerical simulations of the model show that the two strains co-exist whenever the reproduction numbers exceed unity. Further, treatment with amelioration may result in an increase in the total number of infective individuals (asymptomatic) but results in a decrease in the number of AIDS patients. Further, analysis of the reproduction numbers show that antiretroviral resistance increases with increase in antiretroviral use. (shrink)

This commentary on Philip Kitcher’s Ethical Project compares his theory of the evolution of morality with my less ambitious theory of the evolution of fairness norms that seeks to flesh out John Mackie’s insight that one should use game theory as a framework within which to assess anthropological data. It lays particular stress on the importance of the folk theorem of repeated game theory, which provides a template for the set of stable social contracts that were available to ancestral hunter-gatherer (...) communities. It continues by drawing attention to the relevance of Harsanyi’s theory of empathetic preferences in structuring the fairness criteria that evolved as one response to the equilibrium selection problem that the folk theorem demonstrates is endemic in our species. (shrink)

To date, our knowledge of Rift Valley fever disease spread and maintenance is still limited, as flooding, humid weather and presence of biting insects such as mosquitoes, have not completely explained RVF outbreaks. We propose a model that includes livestock, mosquitoes and ticks compartments structured according to their questing and feeding behaviour in order to study the possible role of ticks on the dynamics of RVF. To quantify disease transmission at the initial stage of the epidemic, we derive an explicit (...) formula of the basic reproductive number, $$R_0$$ R 0. Using the concept of Metzler matrix, we state necessary conditions for global asymptotic stability of the disease-free equilibrium. Results suggest that although host-ticks interactions may serve as disease reservoirs or disease amplifiers, the Aedes reproductive number should be kept under unity if disease post-epizootics activities are to be controlled. Results of both local and global sensitivity analysis of selected model parameters indicate that $$R_0$$ R 0 is more sensitive to the ticks attachment and detachment rates, probability of transmission from ticks to host and from host to ticks, length of infection in livestock and ticks death rate. Furthermore, when comparing the mean value of $$R_0$$ R 0 with that from previous studies which did not include ticks we found that our $$R_0$$ R 0 is very much larger resulting in an increase in the exponential phase of an outbreak. These findings suggest that if ticks are capable of transmitting the virus, they may be contributing to disease outbreaks and endemicity. (shrink)

A nonlinear differential equation model is proposed to study the dynamics of HIV/AIDS and its effects on workforce productivity. The disease-free equilibrium point of the model is shown to be locally asymptotically stable when the associated basic reproduction number $$\mathcal{{R}}_{0}$$ is less than unity. The model is also shown to exhibit multiple endemic states for some parameter values when $$\mathcal{{R}}_{0} 1$$. Global asymptotic stability of the disease-free equilibrium is guaranteed only when the fractions of the Susceptible subclass (...) populations are within some bounds. Optimal control analysis of the model revealed that the most cost effective strategy that should be adopted in the fight against HIV/AIDS spread within the workforce is one that seeks to prevent infections and the treatment of infected individuals. (shrink)

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

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)

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)

Most documented extinctions of vertebrates in the last 400 years have been island endemics. In this paper, we focus on the need to develop a historical framework to establish conservation priorities for insular faunas and, in particular, to test the validity of nominal endemics. We use the example of the islands of the North Pacific Coast of North America, a region that includes approximately one-half of all mammals endemic to North American islands north of Mexico. Few of these endemics (...) have been re-evaluated since their original descriptions, although many of these islands have been heavily impacted by habitat conversion, species introductions, over-exploitation, and secondary ripple effects. Evidence from molecular genetics and paleontology suggests that many taxa arrived in the region since the last glacial advance. Some of these nominal endemics show minimal differentiation, while others comprise multiple evolutionary lineages. The NPC may also have played an important role in the in situ diversification of some taxa during the Pleistocene. Evidence, such as new fossil discoveries and numerous described endemics, lends support for refugia hypotheses. However, these ideas cannot be tested until a better understanding of geographic variation and the evolutionary relationships of the fauna and flora of the North Pacific Coast is developed. This framework would provide significant insight into the dynamic biogeographic history of the region and help prioritize conservation efforts. (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 moral epistemology, the method of reflective equilibrium is often characterized in terms of intuitions or understood as a method for justifying intuitions. An analysis of reflective equilibrium and current theories of moral intuitions reveals that this picture is problematic. Reflective equilibrium cannot be adequately characterized in terms of intuitions. Although the method presupposes that we have initially credible commitments, it does not presuppose that they are intuitions. Nonetheless, intuitions can enter the process of developing a reflective (...) equilibrium and, if the process is successful, be justified. Since the method of reflective equilibrium does not essentially involve intuitions, it does not constitute a form of intuitionism in any substantial sense. It may be classified as intuitionist only in the minimal sense of not reducing justification to a matter of inference relations alone. (shrink)

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

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

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)

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

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)

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

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

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

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

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)

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)

반성적 평형은 도덕철학 및 정치철학의 영역에서 가장 유력한 정당화 방법론으로 평가받고 있지만, 롤스의 공정으로서의 정의의 최종 형태에서 반성적 평형의 전체 구조가 어떻게 파악되고 있는지는 아직 충분히 이해되지 못하고 있다. 이러한 불충분한 이해는 반성적 평형이 정당화 방법론으로서 심각한 결함을 갖고 있다는 비판들이 제기되는 근본적인 원인이 된다. 본 논문은 롤스의 넓은 반성적 평형을 이유(reason)에 의한 정당화 및 이성의 공적 사용을 중심으로 해명하고 이를 기초로 반성적 평형의 전체 구조를 제시하는 것을 목적으로 한다. ‘모두의 대화(omnilogue)’로서 복합적인 구조를 갖는 이러한 반성적 평형 모델은 기존의 비판들을 (...) 극복할 수 있을 뿐만 아니라 롤스의 본래 의도에 가장 충실하다는 강점을 갖는다. (shrink)

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

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)

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)

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

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

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)

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

In this article, we develop an approach for the moral assessment of research and development networks on the basis of the reflective equilibrium approach proposed by Rawls and Daniels. The reflective equilibrium approach aims at coherence between moral judgments, principles, and background theories. We use this approach because it takes seriously the moral judgments of the actors involved in R & D, whereas it also leaves room for critical reflection about these judgments. It is shown that two norms, (...) namely reflective learning and openness and inclusiveness, which are used in the literature on policy and technological networks, contribute to achieving a justified overlapping consensus. We apply the approach to a case study about the development of an innovative sewage treatment technology and show how in this case the two norms are or could be instrumental in achieving a justified overlapping consensus on relevant moral issues. (shrink)

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

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

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

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