The ternary, not binary, Kripke-type relation on a set of possible worlds is an essential part of the semantics of entailment by Routley-Meyer [2]. The unpopularity of such approach among many logicians is due to its intuitive vague content and complexity. An attempt is made to use not one ternary relation but two binary relations and necessity of bibinarness is demonstrated. It is shown that both semantics are equal hence the soundness and completeness of the system R of entailment can (...) be established with the respect to the bibinary semantics. Furthermore, the ternary semantic with discrete matrix for Lukasiewicz system Lℵ0 , which was proposed in [3], could be transformed into the bibinary one and it leads to the conclusion of the completeness and soundness of Lℵ0 with the respect to the bibinary semantic. The brief consideration of the bibinary semantic intuitive content is added, which further logical study could be based on. (shrink)

We show that the first order theory of the lattice $\mathscr{L}^{ (S) of finite dimensional closed subsets of any nontrivial infinite dimensional Steinitz Exhange System S has logical complexity at least that of first order number theory and that the first order theory of the lattice L(S ∞ ) of computably enumerable closed subsets of any nontrivial infinite dimensional computable Steinitz Exchange System S ∞ has logical complexity exactly that of first order number theory. Thus, for example, the lattice of (...) finite dimensional subspaces of a standard copy of $\bigoplus_\omega$ Q interprets first order arithmetic and is therefore as complicated as possible. In particular, our results show that the first order theories of the lattice L(V ∞ ) of c.e. subspaces of a fully effective ℵ 0 -dimensional vector space V∞ and the lattice of c.e. algebraically closed subfields of a fully effective algebraically closed field F ∞ of countably infinite transcendence degree each have logical complexity that of first order number theory. (shrink)

‘Biochromatology’ can be defined as the study of the relationships between colours, and between colours and design in nature. Certain laws concerning biochromatics can be formulated in the terminology of the Colour Circle. One of them is that planes in warm colours and planes in cold colours never adjoin. Another law is that design is never polychromatic. It seems that the observed biochromatical facts can be explained with the help of the principle “optimal manifestation of colour”, which in turn is (...) based on the formative principles of matter itself. (shrink)

Commentary on Montero, B. (2020) What experience doesn’t teach: Pain-amnesia and a new paradigm for memory research, Journal of Consciousness Studies, 27 (11–12).

In what follows I examine the following question: does it make a difference in moral psychology whether one adopts Aristotle's ordinary or Kant's revisionist definition of virtue as habit? Points of commensurability and critical comparison are provided by Kant's attempt to refute Aristotle's definition of virtue as a mean and by the moral problems of ignorance and weakness. These two problems are essential topics for moral psychology. I show two things. First, Kant's definition is revisionist because he excludes from moral (...) habit-formation what Aristotle includes, that is, practice in prudential calculation of a mean, and habit-formation by repetition. This follows from Kant's insistence that an act is virtuous only if the moral agent is willing freely and universally. Secondly, Aristotle's virtues modify behavior directly, whereas Kant's virtues modify behavior indirectly by creating moral feeling which, in turn, represses the temptations of the natural inclination. I suggest, thirdly, that as one approximates Kant's ideal of perfect virtue, entailed by the broad duties of beneficence and self-perfection, the difference in kind invented by Kant between virtue and prudence, as a morally neutral rational skill, erodes and becomes a difference in degree. I conclude that Aristotle's ordinary definition of virtue is better able to modify human behavior and solve these two moral problems. (shrink)

This book analyses Eriugena’s Christian Platonic ideas on theology, cosmology, anthropology, epistemology, and ethics, and their sources in Patristic philosophical theology and ancient philosophy. The first part is devoted to Eriugena’s theology: thus, it focusses on God from a variety of perspectives, some of them also comparative in their nature. The second part consists in research into Eriugena's cosmology, anthropology, and ethics, including virtue ethics. The two large sections are interrelated by an exploration of Eriugena's concepts of apokatastasis and epistrophé, (...) in his great theory of the movement of all "from God to God". (shrink)

Stephen Hagiochristophorites a été haut fonctionnaire des finances dans le gouvernement d'Andronikos I Komnenos. Ses opposants l'ont appelé antichristophorites car pour eux, il s'est éloigné des voies tracées par Dieu. Il est devenu un des acolytes les plus loyaux d'Andronikos Komnenos. Son efficacité dans son poste de haut fonctionnaire l'a fait aimé par l'empereur et de l'autre côté a contribué à son impopularité.

Here are the answers to questions Man has sought through the ages; here are practical answers you hoped could be found somewhere; here are answers that work. ...

Includes text of Gommaṭasāra Jīva-Kāṇḍa in Prakrit with English and Hindi translation.