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)

يقدم المؤلف لنا قانونا اجتماعيًا لعلماء النفس والاجتماع السياسي صاغه كالآتي: (إذا زاد عدد الأفراد الذين يمارسون تصرّفًا يعدّ خزيًا، وتساهل القانون في محاسبة مرتكبيه، وعجز الناس عن إيقافه أو وجدوا له تبريرًا، تحوّل إلى ظاهرة ولم يعد خزيًا كما كان). و من هذه العبارة التقديمية يمكن أن نؤكد أن هذا الكتاب لا يمكن إيفاءه حقه بنبذة موجزة، فهو سفر فكري ممتع، حيث يتناول المؤلف فيه بشكل تحليلي وعلمي مقنع أهم الموضوعات التي تشغل العقل العربي، ما بين شخصيات سياسية كصدام (...) وسليماني، وما بين فكرة الموت والانتحار، والبغاء والجريمة، والالحاد والإيمان، واللاوعي الجمعي العربي وما يحمله من أمراض وانحرافات، والتحرش والكبت، والفساد والسلطة، واللغة العربية والحضارة. (shrink)

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)

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)

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)

It is difficult to understand the meaning of 'dignity' in human rights, bioethics and nursing literature because the word is used so vaguely. Unless dignity's meaning is spelt out it can disappear beneath more tangible priorities. In this article we define dignity and show how this can help health workers to maintain the dignity of people in their care.

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)

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)

There are doubtless many with personal experience of suffering, or of comforting others in distress, who would agree with Milton thus far that philosophic argument is powerless to satisfy those who in their anguish ask the question ‘Why did it happen to me?’ Yet to think so is to underestimate both the necessity and the power of reason: clarity of mind and the disposition to argue are commonly enhanced rather than diminished by suffering; and if reason is an essential part (...) of man's nature, it should serve him, if anywhere, in the trials of life. We have every justification, therefore, despite common opinion, for seeking a rational answer to the question proposed. It must, however, be admitted at the outset that there is no direct answer to the question which can both withstand critical scrutiny and bring genuine comfort to the afflicted, an answer, that is, which accepts the question as it stands with its attendant presuppositions; but there is an indirect answer, which, precisely by rejecting one or more of these presuppositions and restating the question, can indeed satisfy these two requirements. Before such an answer can be outlined, however, the question in its traditional form must be examined and the traditional answers to it critically reviewed. (shrink)

IntroductionBisphenol A is highly debated and studied in relation to a variety of health outcomes. This large variation in the literature makes BPA a topic that is prone to selective use of literature, in order to underpin one’s own findings and opinion. Over time, selective use of literature, by means of citations, can lead to a skewed knowledge development and a biased scientific consensus. In this study, we assess which factors drive citation and whether this results in the overrepresentation of (...) harmful health effects of BPA.MethodsA citation network analysis was performed to test various determinants of citation. A systematic search identified all relevant publications on the human health effect of BPA. Data were extracted on potential determinants of selective citation, such as study outcome, study design, sample size, journal impact factor, authority of the author, self-citation, and funding source. We applied random effect logistic regression to assess whether these determinants influence the likelihood of citation.ResultsOne hundred sixty-nine publications on BPA were identified, with 12,432 potential citation pathways of which 808 citations occurred. The network consisted of 63 cross-sectional studies, 34 cohort studies, 29 case-control studies, 35 narrative reviews, and 8 systematic reviews. Positive studies have a 1.5 times greater chance of being cited compared to negative studies. Additionally, the authority of the author and self-citation are consistently found to be positively associated with the likelihood of being cited. Overall, the network seems to be highly influenced by two highly cited publications, whereas 60 out of 169 publications received no citations.ConclusionIn the literature on BPA, citation is mostly driven by positive study outcome and author-related factors, such as high authority within the network. Interpreting the impact of these factors and the big influence of a few highly cited publications, it can be questioned to which extent the knowledge development in human literature on BPA is actually evidence-based. (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.