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 . 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 , 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)
What counts as an intuitively plausible set theoretic content (notion, axiom or theorem) has been a matter of much debate in contemporary philosophy of mathematics. In this paper I develop a critical appraisal of the issue. I analyze first R. B. Jensen's positions on the epistemic status of the axiom of constructibility. I then formulate and discuss a view of intuitiveness in set theory that assumes it to hinge basically on mathematical success. At the same time, I present accounts of (...) set theoretic axioms and theorems formulated in non-strictly mathematical terms, e.g., by appealing to the iterative concept of set and/or to overall methodological principles, like unify and maximize, and investigate the relation of the latter to success in mathematics. (shrink)
We consider fine hierarchies in recursion theory, descriptive set theory, logic and complexity theory. The main results state that the sets of values of different Boolean terms coincide with the levels of suitable fine hierarchies. This gives new short descriptions of these hierarchies and shows that collections of sets of values of Boolean terms are almost well ordered by inclusion. For the sake of completeness we mention also some earlier results demonstrating the usefulness of fine hierarchies.
We review the history of the road to a manifestly covariant perturbative calculus within quantum electrodynamics from the early semi-classical results of the mid-twenties to the complete formalism of Stueckelberg in 1934. We choose as our case study the calculation of the cross-section of the Compton effect. We analyse Stueckelberg's paper extensively. This is our first contribution to a study of his fundamental contributions to the theoretical physics of the twentieth century.
The sources of the real conflict between science and various kinds of undertakings in occultism pretending to be science date back to the end of the 16th and beginning of the 17th centuries, when modern scientific method was barely taking shape. The natural philosophy of the 16th century, which put forth natural magic in place of divine magic, was the ideological antipode of the new science in process of formation. The pantheistic reinterpretation of monotheistic Christian creationism is a characteristic feature (...) of constructs in natural philosophy with their striving toward maximal substantialization of the nonmaterial. Thus, for example, the rationalist mystic of natural philosophy, Girolamo Cardano, returns in his work to the medieval notion of the world soul, but understands by it an entirely material substance which he identifies with light and heat. (shrink)
Taxometric analyses were applied to the construct of psychopathy (as measured by the Psychopathy Checklist) and to several variables reflecting antisocial childhood, adult criminality, and criminal recidivism. Subjects were 653 serious offenders assessed or treated in a maximum-security institution. Results supported the existence of a taxon underlying psychopathy. Childhood problem behaviors provided convergent evidence for the existence of the taxon. Adult criminal history variables were continuously distributed and were insufficient in themselves to detect the taxon.
Probabilistic local realism for two correlated systems as formulated by Clauser and Horne in 1974 is shown to be necessarily based on a perfect specification of the state and on an individual definition of probability. All known realistic formulations of probability calculus are instead defined in terms of relative frequencies, and perfect specifications of states are impossible. We reformulate probabilistic local realism by using the relative frequency definition only and show that the Einstein, Podolsky, and Rosen paradox still obtains.
Work on the methodology of natural science involves serious difficulties over and above those encountered in any other aspect of natural science or of philosophy. Reference is to the obvious fact that in discussing methodological questions of, for example, physics, so as to be precise, it is not enough to know physics: it is also necessary to familiarize oneself with certain branches of philosophy, the history of science, and so forth. Furthermore, a professional cannot limit himself to "general familiarity" with (...) the material. He has to know the details and, if possible, the entire literature on the question under discussion. However, the volume of literature on physics has, within the memory of the author alone — that is, over approximately forty years — multiplied dozens of times. I cannot say how great has been the increase in the quantity of information on the methodology of natural science and related disciplines. But what is important is that the amount of material that has accumulated to date is enormous. Some notion of the scale of the work may be gained from the abstract journal Obshchestvennye nauki za rubezhom. Seriia 8. Naukovedenie. For example, no. 1 for 1980 contained abstracts of 72 articles and books; this amounts to over 400 titles a year . When we add to this the Soviet literature and the need to include material from many years, we arrive at a figure of four digits. Naturally, only a very small portion of the literature is made use of in any particular piece of work, but it is impossible to know beforehand which items will be specifically needed. (shrink)
Language depth and complexity are comparable with the world reflected in its reality. The conceptual categories are formed by its means, allowing conceptualize ideas about the world, on the basis of which cognitive experience of man further develops. In all periods of its existence, the language is characterized by dynamism and synergy, the ability of self-development, improvement of socio-functional nature, taking care of maintaining its communicative suitability in the best condition. As a unique object of reality, as the most brilliant (...) creation of a human being, language deserves not only to be spoken, but also to get attention and be studied. Research experience proves that the language still holds many secrets and unrevealed laws of its being, development and functioning. Revealing these secrets and laws is possible on the basis of scientific and linguistic competence; the base substrate of it is communicative language competence, which itself can not get enough depth without the support of linguistic competence. Language is the most important means of formation and protection of ethnic and cultural consciousness and the identity of a man whose personal features begin to form on the base and with the help of language in early childhood. Historically, it is through the medium of the Russian language numerous peoples of Russia, the former Soviet Union, and abroad maintain and develop their culture in the broadest sense of the word connection, and it allows everyone to feel their place in the world and thus realize the dynamic integrity of mankind in the general context of space and time, rootedness in their limits, responsibility to them. Russian is the official language, and the state is obliged to develop and adopt measures linguoecological protective nature towards their language in the interests of Russian language and Russian-speaking communities abroad, and to ensure the preservation of its cultural and communicative power. The experience of Russian linguistics in formation of the theory of state language is invaluable in general sociolinguistic approach to language, based on the objective fact of ethnic, cultural and linguistic diversity of Russia. (shrink)