Here, an epidemiological model considering pro and anti-vaccination groups is proposed and analyzed. In this model, susceptible individuals can migrate between these two groups due to the influence of false and true news about safety and efficacy of vaccines. From this model, written as a set of three ordinary differential equations, analytical expressions for the disease-free steady state, the endemic steady state, and the basic reproduction number are derived. It is analytically shown that low vaccination rate and no influx to (...) the pro-vaccination group have similar impacts on the long-term amount of infected individuals. Numerical simulations are performed with parameter values of the COVID-19 pandemic to illustrate the analytical results. The possible relevance of this work is discussed from a public health perspective. (shrink)

We show that arbitrary tautologies of Johansson’s minimal propositional logic are provable by “small” polynomial-size dag-like natural deductions in Prawitz’s system for minimal propositional logic. These “small” deductions arise from standard “large” tree-like inputs by horizontal dag-like compression that is obtained by merging distinct nodes labeled with identical formulas occurring in horizontal sections of deductions involved. The underlying geometric idea: if the height, h(∂), and the total number of distinct formulas, ϕ(∂), of a given tree-like deduction ∂ of a minimal (...) tautology ρ are both polynomial in the length of ρ, |ρ|, then the size of the horizontal dag-like compression ∂ᶜ is at most h(∂)×ϕ(∂), and hence polynomial in |ρ|. That minimal tautologies ρ are provable by tree-like natural deductions ∂ with |ρ|-polynomial h(∂) and ϕ(∂) follows via embedding from Hudelmaier’s result that there are analogous sequent calculus deductions of sequent ⇒ρ. The notion of dag-like provability involved is more sophisticated than Prawitz’s tree-like one and its complexity is not clear yet. Our approach nevertheless provides a convergent sequence of NP lower approximations of PSPACE-complete validity of minimal logic. (shrink)

Currently living people cannot be said to be wronged because of the wrongless emissons of greenhouse gases by past people. According to the usual subjunctive-historical understanding of harm, currently living people cannot be said to be harmed by the impact of greenhouse emissions on their well-being. By relying on a subjunctive-threshold notion of harm we can justify conclusions about both the present generation’s duties not to violate the rights of future generations, and the present generation’s duties to compensate currently living (...) people for the harms inflicted upon them through the lasting impact of wrongless past harms. This interpretation supports a forward-looking understanding of the grounds of our relating to wrongless past harms. The significance of past harms lies in their consequences for the well-being of currently living and future people. The subjunctive-threshold notion of harm lends support to a standard of minimal, general, and universal justice. Those actors who are in a position to fulfill its requirements are under a duty to do so. Especially the rich and powerful countries ought to counteract the harmful impact of past greenhouse emissions. (shrink)

Context: Second-order cybernetics and its implications have been understood within the cybernetics community for some time. These implications are important for understanding the structure of scientific endeavor, and for researchers in other fields to see the reflexive nature of scientific research. This article is about the role of context in the creation and exploration of our experience. Problem: The purpose of this article is to point out the fundamental nature of the circularity in cybernetics and in scientific work in general. (...) I give a point of view on the nature of objective knowledge by placing it in the context of reflexivity and eigenform. Method: The approach to the topic is based on logical analysis of the nature of circularity. Mathematics and cybernetics are both fundamentally concerned with the structure of distinctions, but there can be no definition of a distinction without circularity, since such a definition would itself be a distinction. The article proceeds by explicating the structure of reflexive domains D where the transformations of the domain are in one-to-one correspondence with the domain itself. Results: I show that every element of a reflexive domain has a fixed point. This means that eigenforms arise naturally in reflexive domains. Furthermore, a reflexive domain is itself an eigenform (at a higher level. This supports the context of a second-order science that would study domains of science as part of a larger cybernetic landscape. Implications: The value of the article is in its concise reformulation of the scientific endeavor as a search for eigenforms in reflexive domains. This new view of science is promising in that it includes the former worlds of apparent objectivity and it embraces those newer worlds of science where the theories and theorists become active participants in the ongoing process of creating knowledge. Constructivist content: I argue that the perspective of reflexive domains constitutes a new way to think about the practice of science, with observers deeply imbedded, and objectivity understood as the mutual search for eigenforms. (shrink)

In this chapter, we integrate three distinct strands of thought to argue that the concept of “fairness” varies significantly across cultures. As a result, ensuring that human-AI interactions meet relevant fairness standards requires a deep understanding of the cultural contexts in which AI-enabled systems are deployed. Failure to do so will not only result in the generation of unfair outcomes by an AI-enabled system, but it will also degrade legitimacy of and trust in the system. The first strand concerns the (...) dominant approach taken in the technology industry to ensure that AI-enabled systems are fair. This approach is to reduce fairness to some mathematical formalism that can be applied universally, a quintessentially Western conception of fairness. The second strand concerns alternative conceptions of fairness that have their roots in philosophical traditions of the East, namely Confucian virtue ethics. Understanding how individuals from diverse cultural backgrounds perceive fairness—particularly their beliefs about fairness in human-to-human interactions—is crucial for understanding how they will interpret fairness in human-AI interactions. Building on these philosophical and behavioral differences, as highlighted by empirical research, the third strand integrates insights from political science and interdisciplinary studies. This perspective offers valuable guidance on designing AI-enabled systems to align with contextually relevant standards of fairness. Examining existing beliefs about fairness within the context of institutional decision-making provides valuable insights into what people expect from AI-generated decisions. These expectations often include key elements such as a sufficient degree of transparency, clear lines of accountability, and mechanisms to contest decisions made by the system—all of which are essential components of procedural fairness. Rather than adopting a one-size-fits-all approach to ensuring fairness, the design and deployment of AI systems must carefully account for the operating environment, including the socio-political and cultural context, to ensure that the system aligns with the relevant standards of fairness. (shrink)

After reporting in detail Aristotle’s texts and comments on the well-known motion paradoxes Arrow, Dichotomy, Achilles and Stadium, tracking back to the 5th century BCE and credited by Aristotle to Zeno of Elea, we next explain and dis-cuss traditional continuous solutions of the paradoxes, based on Cauchy’s limit concept. Afterward, the heated philosophical debate on supertasks and infinity machines is reported before the paradoxes are examined within the context of modern quantum theory. Already in 1905, Einstein concluded that matter could (...) not be a continuous thing. Classical continuous spacetime is replaced by ‘granular’ spacetime, and the concept of distance in granular spacetime is discussed. This is followed by a detailed presentation of modern discrete solutions in granular spacetime, several of which are published here for the first time. Finally, a procedure is presented to determine when traditional continuous methods suffice instead of discrete methods, and the handling of discrete versus continuous in physics is briefly reported. (shrink)

Upshot: Eigenform is a precondition for distinction and distinction is a precondition for eigenform. While my target article discussed eigenform and reflexivity, it could just as well have discussed distinctions and the emergence of distinctions. This theme was implicit in many of the comments. We make this circularity explicit for the sake of a deeper understanding.

Open peer commentary on the article “The Circular Conditions of Second-order Science Sporadically Illustrated with Agent-based Experiments at the Roots of Observation” by Manfred Füllsack. Upshot: The aim of my commentary is to reflect on fundamental issues related to circularity, distinction and the properties of observers.

Let the individuals of a population be divided into two groups with different personal habits. The core group is associated with health risk behaviors; the non-core group avoids unhealthy activities. Assume that the infected individuals of the core group can spread a contagious disease to the whole population. Also, assume that cure does not confer immunity. Here, an epidemiological model written as a set of ordinary differential equations is proposed to investigate the infection propagation in this population. In the model, (...) migrations between these two groups are allowed; however, the transitions from the non-core group into the core group prevail. These migrations can be either spontaneous or stimulated by social pressure. It is analytically shown that, in the scenario of spontaneous migration, the disease is either naturally eradicated or chronically persists at a constant level. In the scenario of stimulated migration, in addition to eradication and constant persistence, self-sustained oscillations in the number of sick individuals can also be found. These analytical results are illustrated by numerical simulations and discussed from a public health perspective. (shrink)

The relationship between the United Kingdom and the United States seems to embody most fully the type of the ‘special relationship’ today. It is a relationship founded ultimately on biological kinship, structured by mutual economic and strategic interests and cemented by a sense of political and ‘spiritual’ affinity. At least the broad contours of such contemporary ‘special relationships’ are sufficiently clear. This is far from being the case with those of the Archaic and Classical Greek world, for two main reasons. (...) First, and more decisively, our sources for the history of that world – literary, epigraphical, archaeological – are normally scrappy, discontinuous and variously slanted. Second, and only in part because of the nature of the evidence, the workings of all ancient Greek interstate relationships, whether ‘special’ or not, are in principle controversial. For in the absence of governments and parties in the modern sense it is frequently impossible to explain confidently a particular foreign policy decision taken by a Greek state. A fortiori it is in principle even more difficult to describe and account for ‘special’ relationships between states that apparently transcended purely immediate, local and narrowly self-interested considerations. (shrink)

Background: The Taiwan Nursing Accreditation Council has proposed eight core professional nursing qualities including ethical literacy. Consequently, nursing ethics education is a required course for student nurses. These courses are intended to improve the ethical literacy. Moral sensitivity is the cornerstone of ethical literacy, and learning moral sensitivity is the initial step towards developing ethical literacy. Objectives: To explore the effect of nursing ethics educational interventions based on multiple teaching strategies on student nurses moral sensitivity. Based on the visual, auditory (...) and kinaesthetic model, three strategies were developed for determining the programme components and corresponding learning styles. Research design: This was a quasi-experimental study. Participants: A total of 234 junior-college student nurses participated in this study. All participants were aged 18–19 years. Ethical considerations: The study protocol was approved by the institutional review boards of Kaohsiung Veterans General Hospital. Only the participants who signed an informed consent form took part in the study. The participants were permitted to withdraw from the study at any point if they wished to do so without affecting their academic score. Results: The scores of Modified Moral Sensitivity Questionnaire for Student Nurses were significantly improved after the intervention of integrating multiple teaching strategies ( p =.042). Significant relationships were observed between the satisfaction scores of two teaching strategies and moral sensitivity. The results indicated that using multiple teaching strategies is effective for promoting nursing ethics learning. Conclusion: This strategy was consistent with the student nurses’ preferred learning style and was used to correct their erroneous ethical conceptions, assisting in developing their ethical knowledge. (shrink)