The aim of this paper is to study a particular family of non-deterministic semantics for modal logics that has eight truth-values. These eight-valued semantics can be traced back to Omori and Skurt (2016), where a particular member of this family was used to characterize the normal modal logic K. The truth-values in these semantics convey information about a proposition’s truth/falsity, whether the proposition is necessary/not necessary, and whether it is possible/not possible. Each of these triples is represented by a unique (...) value. In this paper we will study which modal logics can be obtained by changing the interpretation of the $$\Box $$ modality, assuming that the interpretation of other connectives stays constant. We will show what axioms are responsible for a particular interpretations of $$\Box $$. Furthermore, we will study subsets of these axioms. We show that some of the combinations of the axioms are equivalent to well-known modal axioms. We apply the level-valuation technique to all of the systems to regain the closure under the rule of necessitation. We also point out that some of the resulting logics are not sublogics of S5 and comment briefly on the corresponding frame conditions that are forced by these axioms. Ultimately, we sketch a proof of meta-completeness for all of these systems. (shrink)

The aim of this article was to prepare a basis for further quantitative research concerning the nutritional knowledge of medical professionals (doctors) and dieticians in view of the accuracy of dietary recommendations given to patients. For this purpose, a review of literature data in this area was performed and logical fallacies were proposed as the ‘tool’ that doctors rely on in cases when they lack the proper knowledge required to be able give an informed and beneficial recommendation. In the course (...) of the study, it was found that nutritional education is neglected in medical curricula, while dieticians are underused as professionals in clinical settings. Furthermore, numerous characteristics of the medical profession and the doctor–patient relationship are conducive to committing several types of logical fallacies, prompted mainly by the need for providing advice without delay and the infallibility traditionally expected from doctors. Hence, the gaps in nutritional knowledge and the fallacious character of recommendations, in addition to the re-valuation of the role of the nutritionist, need to be further investigated in order to improve the quality of patient advice in the area of dietary requirements as well as to propose the necessary changes in curricula. (shrink)

What would it look like for researchers to take non-human animal rights seriously? Recent discussions foster the impression that scientific practice needs to be reformed to make animal research ethical: just as there is ethically rigorous human research, so there can be ethically rigorous animal research. We argue that practically little existing animal research would be ethical and that ethical animal research is not scalable. Since animal research is integral to the existing scientific paradigm, taking animal rights seriously requires a (...) radical, wholesale reimagining of science.Trial registration: ClinicalTrials.gov identifier: NCT05340426. (shrink)

Provability logics are, roughly speaking, modal logics meant to capture the formal principles of various provability operators or predicates.

The main goal of this paper is to provide an abstract framework for constructing proof systems for various many-valued logics. Using the framework it is possible to generate strongly complete proof systems with respect to any finitely valued deterministic and non-deterministic logic. I provide a couple of examples of proof systems for well-known many-valued logics and prove the completeness of proof systems generated by the framework.

This paper critically examines and evaluates Yacin Hamami’s reconstruction of the standard view of mathematical rigor. We will argue that the reconstruction offered by Hamami is premised on a strong and controversial epistemological thesis and a strong and controversial thesis in the philosophy of mind. Secondly, we will argue that Hamami’s reconstruction of the standard view robs it of its original philosophical rationale, i.e. making sense of the notion of rigor in mathematical practice.

Festschrift volume to K. Ramakrishna Rao, Indian psychologist, philosopher and educationist; contributed articles.

A Higgsless model for strong, electroweak and gravitational interactions is proposed. This model is based on the local symmetry group SU(3)×SU(2)L×U(1)×C,where C is the local conformal symmetry group. The natural minimal conformally invariant form of total Lagrangian is postulated. It contains all standard model fields and gravitational interaction. Using the unitary gauge and the conformal scale fixing conditions, we can eliminate all four real components of the Higgs doublet in this model. However, the masses of vector mesons, leptons, and quarks (...) are automatically generated and are given by the same formulas as in the conventional standard model. In this manner one gets the mass generation without the mechanism of spontaneous symmetry breaking and without the remaining real dynamical Higgs field. The gravitational sector is analyzed, and it is shown that the model admits in the classical limit the Einsteinian form of gravitational interactions. (shrink)

Inhalt: Vorwort von H.-M. Pawlowski / S. Smid / R. Specht - H.-M. Pawlowski: Probleme der Rechtsbegrundung im Staat der Glaubensfreiheit - V. Gerhardt: Selbstandigkeit und Selbstbestimmung. Freiheit bei Kant und Schelling - H. Folkers: Die durch Freiheit gebaute Stadt Gottes - W. E. Ehrhardt: Mythologie und Offenbarung der Freiheit - W. Bartuschat: Uber Spinozismus und menschliche Freiheit beim fruhen Schelling - C. Cesa: Schellings Kritik des Naturrechts - H. J. Sandkuhler: F. W. J. Schelling - Philosophie als (...) Seinsgeschichte und Anti-Politik - D. Losurdo: Von Louis Philippe bis Louis Bonaparte - R. Pettoello: Die Dialektik der menschlichen Freiheit als Emanzipation und als Abfall von Gott - H. Klenner: Schelling und die Rechtsphilosophie - S. Smid: Freiheit als Keim des Rechts - W. Schmied-Kowarzik: Freiheit - Recht - Geschichte - J. Simon: Die Wirklichkeit der Freiheit (Kant, Schelling, Hegel) - W. Schild: Die verstandlichen Schwierigkeiten des Rechtsdenkens mit dem Freiheitsbegriff - Personenregister. (shrink)

According to the dialetheist argument from the inconsistency of informal mathematics, the informal version of the Gödelian argument leads us to a true contradiction. On one hand, the dialetheist argues, we can prove that there is a mathematical claim that is neither provable nor refutable in informal mathematics. On the other, the proof of its unprovability is given in informal mathematics and proves that very sentence. We argue that the argument fails, because it relies on the unjustified and unlikely assumption (...) that the informal Gödel sentence is informally provable. (shrink)

Study of rationalism in Urdu literature.

Classical logic of formal provability includes Löb’s theorem, but not reflection. In contrast, intuitions about the inferential behavior of informal provability (in informal mathematics) seem to invalidate Löb’s theorem and validate reflection (after all, the intuition is, whatever mathematicians prove holds!). We employ a non-deterministic many-valued semantics and develop a modal logic T-BAT of an informal provability operator, which indeed does validate reflection and invalidates Löb’s theorem. We study its properties and its relation to known provability-related paradoxical arguments. We also (...) argue that T-BAT is a fairly sensible candidate for a formal logic of informal provability. (shrink)

Constitutional and judicial law-making is increasingly beginning to find its reflection not only in the Anglo-Saxon, but also in the Romano-Germanic legal family. However, the prerequisites for the use of this legal instrument are different, which determines the relevance of conducting a comparative analysis regarding the provision of such a mechanism in the USA and Kazakhstan. The purpose of the research is to identify common and distinctive features in the process of implementation of constitutional and judicial law-making in countries belonging (...) to different legal systems. The article uses the methods of analysis, synthesis, comparison, deduction and generalization. As a result, the specificity of ensuring the mechanism of constitutional law-making in the USA was expressed, taking into account various forms of law-making activity. It has been established that the development of constitutional provisions in the United States takes place with the help of the constitutional doctrines of the Supreme Court of the United States, which provide for the introduction of amendments to constitutional provisions without a formal procedure. As a result of the study of the experience of Kazakhstan, it was established that special priority was given to the role of precedent, in particular, the decision of the Supreme Court of the Republic of Kazakhstan. This is explained by the integrative nature of the Romano-Germanic legal system, which allows effective development of national legislation as a whole and its provisions. The obtained results can be used during the professional training of judges in the Republic of Kazakhstan. (shrink)

The paper deals with the issue of some Aristotelian motives and categories in the Didaskalikos of Alcinous, one of the most important works of Middle Platonism. They are particularly evident in the chapters in which Alcinous discusses issues related to Platonic theology and theory of Ideas. A special place here is the motif of God as Intellect who thinks of Ideas (of absolute Forms, in the Platonic sense) and at the same time thinks of Himself (in the Aristotelian sense). In (...) connection with these Aristotelian motives, the question arises: do these motives have a substantive significance here, that is, do they really express Aristotle’s metaphysical views, or are they only a literary framework, in which the Platonic content is clothed? (shrink)

The image of a ball rolling along a series of hills and valleys is an effective heuristic by which to communicate stability concepts in ecology. However, the dynamics of this landscape model have little to do with ecological systems. Other landscape representations, however, are possible. These include the particle on an energy landscape, the potential landscape, and the Lyapunov function landscape. I discuss the dynamics that these representations admit, and the application of each to ecological modeling and the analysis and (...) representation of stability. (shrink)

Recently, Gao et al. and Chappie et al. elucidated the crystal structures of the polytetrameric stalk domain of the dynamin‐like virus resistance protein, MxA, and of the G‐domain dimer of the large, membrane‐deforming GTPase, dynamin, respectively. Combined, they provide a hypothetical oligomeric structure for the complete dynamin protein. Here, it is discussed how the oligomers are expected to form and how they participate in dynamin mediated vesicle fission during the process of endocytosis. The proposed oligomeric structure is compared with the (...) novel mechanochemical model of dynamin function recently proposed by Bashkirov et al. and Pucadyil and Schmid. In conclusion, the new model of the dynamin oligomer has the potential to explain how short self‐limiting fissogenic dynamin assemblies are formed and how concerted GTP hydrolysis is achieved. The oligomerisation of two other dynamin superfamily proteins, the guanylate binding proteins (GBPs) and the immunity‐related GTPases (IRGs), is addressed briefly. (shrink)