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 paper is to present a proof to the conclusion that is impossible to traverse an infinite series (in particular, an infinite series of past moments). This may also show (given additional assumptions) that the series of past moments cannot be infinite. In the first section I formulate five theses concerning traversing, successive addition and successive subtraction and I present the idea of the argument: if it were possible to traverse an infinite past, it should be in (...) principle possible to go back, which is, however, impossible. The main body of the paper is concerned with working out a simple mathematical representation of some structural features of processes like traversing and successive addition. I also make a crucial distinction between completion of a process at a particular time and its timeless "completion" in infinite time. In section V, I present the formal proof and defend it against a possible objection of question-begging. Finally, I suggest that my argume. (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.

First published in 1986, Knowledge, Belief, and Witchcraft remains the only analysis of indigenous discourse about an African belief system undertaken from within the framework of Anglo-American analytical philosophy. Taking as its point of departure W. V. O. Quine's thesis about the indeterminacy of translation, the book investigates questions of Yoruba epistemology and of how knowledge is conceived in an oral culture.

The New Evil Demon problem has been hotly debated since the case was introduced in the early 1980’s (e.g. Lehrer and Cohen 1983; Cohen 1984), and there seems to be recent increased interest in the topic. In a forthcoming collection of papers on the New Evil Demon problem (Dutant and Dorsch, forthcoming), at least two of the papers, both by prominent epistemologists, attempt to resist the problem by appealing to the distinction between justification and excuses. My primary aim here is (...) to critically evaluate this new excuse maneuver as a response to the New Evil Demon problem. -/- Their response attempts to give us reason to reject the idea that victims of the New Evil Demon have justification for believing as they do. I shall argue that this approach is ultimately unsuccessful, however much of value can be learned from these attempts. In particular, progress in the debate can be made by following those who advance the excuse maneuver and make explicit the connection between epistemic justification and epistemic norms. By doing so, the questions being debated are clarified, as is the methodology being used to attempt to answer them. (shrink)

There are various equivalent formulations of the Church-Turing thesis. A common one is that every effective computation can be carried out by a Turing machine. The Church-Turing thesis is often misunderstood, particularly in recent writing in the philosophy of mind.

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.

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)

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)

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)

This essay treats the problems, which appear at the present years in the relations of our common society and the communities of Christs, Mohammedians, Buddhists and groups of philosophical believers. This problem has rised when our state - in consequence of an decision of the Bundesverfassungsgericht - had given up his christian character and tries living in social connex with all groups of believers. We have no to discuss the requirements which are connected with tis relations.

BAT is a logic built to capture the inferential behavior of informal provability. Ultimately, the logic is meant to be used in an arithmetical setting. To reach this stage it has to be extended to a first-order version. In this paper we provide such an extension. We do so by constructing non-deterministic three-valued models that interpret quantifiers as some sorts of infinite disjunctions and conjunctions. We also elaborate on the semantical properties of the first-order system and consider a couple of (...) its strengthenings. It turns out that obtaining a sensible strengthening is not straightforward. We prove that most strategies commonly used for strengthening non-deterministic logics fail in our case. Nevertheless, we identify one method of extending the system which does not. (shrink)

The most‐critical point of reproductive development in all sexually reproducing species is the transition from mitotic to meiotic cell cycle. Studies in unicellular fungi have indicated that the decision to enter meiosis must be made before the beginning of the premeiotic S phase. Recent data from the mouse1 suggest that this timing of meiosis initiation is a universal feature shared also by multicellular eukaryotes. In contrast, the signaling cascade that leads to meiosis initiation shows great diversity among species. BioEssays 29:511–514, (...) 2007. © 2007 Wiley Periodicals, Inc. (shrink)