For a sufficiently large class of formal systems a duality theorem is proved. We consider such formal set theories $\widetilde{\scr{T}}$ [2] which, at least, satisfy the following conditions: 1. The theory $\widetilde{\scr{T}}$ contains its own (either bounded or introduced by a definition) substantive constant U, for which $\vdash \forall x[x\in U]$ or $\vdash \forall x[x\subset U]$ . 2. The operation of "complement", denoted by C, is defined with respect to U. 3. For any formula (resp. a term), A ⊦ A (...) ↔ ⅂⅂ A (resp. ⊦ CCA = A), and some basic conclusions follow. (shrink)

Collection of Buddhist philosophical texts written by Mongolian monks and scholars.

In the article the issue of singling out some systemic criteria of differentiation between the fundamental and applied terminologies is considered. The authors point at the fact that each terminology has its own individual peculiarities, which mark it out against a general background of the terminological fund of a certain language. It is asserted that one of the most important and effective criteria that can be the basis of the approach to the study of sublanguages for special purposes is a (...) fundamental or applied character of the sphere of professional or scientific knowledge verbalized by a certain terminology. Such terms, as ‘fundamental terminology‘, ‘applied terminology‘ and ‘terminology of transition type‘, are introduced for scientific use. The fundamental terminology is understood as a sublanguage for special purposes that verbalizes the notions, forming the totality of fundamental knowledge, serving for the description of phenomena and processes in reality and in science, in the framework of which the fundamental research is carried out. The applied terminology is the name for the sublanguage for special purposes representing the notions, in which the results of human being’s practical scientific-industrial activity for changing the reality, forming the artificial habitat, are conceptualized. The terminology of transition type is the terminology that verbalizes the fragments of the field of scientific knowledge in which the research can have both a fundamental and applied character. The authors come to the conclusion that pure applied or fundamental terminologies are quite rare, that it is rational to speak about the degree of manifestation of the applied or fundamental character within the limits of this or that terminological system. (shrink)

There is no unique way to generalize the mass operator 0 2 −p · p to curved spacetimes. The possible generalizations using either an analytic or an algebraic (group-theoretic) approach are discussed. We investigate in detail three possibilities: (i) the generalized D'Alembertian $$- \tilde \square = - (1/\sqrt { - g} )(\partial /\partial x^v )(\sqrt { - g} g^{\mu v} {\text{ }}\partial /\partial x^\mu$$ (ii) the operator ( $- (\tilde \square + \tfrac{1}{6}{\text{R)}}$ , which is conformally invariant in the massless (...) case, and (iii) an operator suggested by Meggs for Robertson-Walker spacetimes. A criterion for choosing among the different possibilities is proposed. It is used to eliminate the Meggs operator, but is not stringent enough to decide between the other two. (shrink)

في كتابه من نقد العقل إلى هيرمينوطيقا الرموز: بحث في فلسفة الثقافة عند إرنست كاسيرر، الصادر عن المركز العربي للأبحاث ودراسة السياسات، يحاول فؤاد مخوخ التركيز على فلسفة كاسيرر، ساعيًا لإثبات أصالتها وجِدَّتِها في مجال نقد الثقافة. فـ "قراءة كاسيرر فلسفة كانط"، كما يقول مخوخ، "متميزة وأصيلة، ويتجلى ذلك في مشروع تطوير نقد العقل وتمديده إلى نقد الثقافة الذي تجسد في فلسفة الأشكال الرمزية باعتبارها فلسفةً للثقافة، وتقعيدًا نظريًا لإبيستمولوجيا علوم الثقافة، وهيرمينوطيقا لتأويل عالَم الإنسان وفهمه".

Within the framework of the Kershaw approach and of a hypothesis on spatial stochasticity, the relativistic equations of Lehr and Park, Guerra and Ruggiero, and Vigier for stochastic Nelson mechanics are obtained. In our model there is another set of equations of the hydrodynamical type for the drift velocityv i(x j,t) and stochastic velocityu i(x j,t) of a particle. Taking into account quadratic terms in l, the universal length, we obtain from these equations the Sivashinsky equations forv i(x j,t) in (...) the caseu i →0. In the limit l →0, these equations acquire the Newtonian form. (shrink)

Drawing on fiqh al-aqalliyyat, this article introduces a Muslim minorities curriculum and negotiates the notion of diasporicity as a process that signifies a community’s readiness to respond to its own cultural, religious and literacy practices. More specifically, first, I propose a Muslim minorities curriculum that is informed by diasporicity and fiqh al-aqalliyyat. Second, the article makes a distinction between diaspora and diasporicity. In what ways can diasporicity itself be conceptualized to advance Muslim education and what are the pedagogical implications? Third, (...) it identifies what I call dialectical constructs within fiqh al-aqalliyyat that are conducive to diasporicity, namely, qiyas, ijtihad, istihsan, and taysir. Additionally, this article explores contingency as an overlooked philosophical and pedagogical dimension, which advances intercultural and critical thinking skills. It conceptualizes a Muslim education that is attuned to the “curriculum-as-lived”; hence it develops an educational theory that validates diasporicity. (shrink)

This study examines the Foucauldian notion of “parrhesia” within the context of curricular practices through a renewal of scholarly interest in Islamic metaphysics as represented by the Avicennean modalities of reality: necessity, contingency, and possibility. It explores the role of contingency in advancing educational practices that generate inclusive dissemination of knowledge that captures the language of Tajdeed (legitimate renovation) in Islamic education. This article argues that contingency, as a causality-oriented modality, determines whether meaning is relative or absolute, while necessity, as (...) an acknowledgment of universal truth, slips into demagoguery that can be used to canonize strict textualism and absolutism. Contingency is defined here as a practice that stimulates synthesis and dialogical understanding of knowledge. Accordingly, the study asks the following questions: How does infusing the Avicennean concept of contingency into curriculum practices offer opportunities for inclusivity and free speech? How can revisiting Islamic cosmological modalities help Muslim educators and curriculum writers move into the broader path of inclusive pedagogies? From an educational position, the article introduces a curriculum of metaphysics that advocates the implementation of contingency, which is considered essential to parrhesia and democracy. It also draws attention to an anti-metaphysical attitude that is generally present in curriculum theorizing. Accordingly, Metaphysics is invoked to challenge a state of flux or hegemonized assumptions; hence, metaphysics validates parrhesia. (shrink)

A cornerstone of physics, Maxwell‘s theory of electromagnetism, apparently contains a fatal flaw. The standard expressions for the electromagnetic field energy and the self-mass of an electron of finite extension do not obey Einstein‘s famous equation, \, but instead fulfill this relation with a factor 4/3 on the left-hand side. Furthermore, the energy and momentum of the electromagnetic field associated with the charge fail to transform as a four-vector. Many famous physicists have contributed to the debate of this so-called 4/3-problem (...) without arriving at a complete solution. It has generally been assumed that, as originally suggested by Poincaré, the problems are connected to the question of stability of the charge distribution, and that relativistic equivalence between energy and self-mass can only be restored by inclusion of stabilizing forces. Alternative solutions to the problems have also been proposed. Nearly a century ago Fermi suggested a covariant definition of the electromagnetic energy and momentum, and sixty years later Kalckar et al. argued that the 4/3 problem is caused by omission of a relativistic correction in the standard evaluation of the self-force from Coulomb self-interaction. However, the relation between these suggestions has not been clear. We show that the relativistic correction implies that the mechanical momentum of an accelerated rigid body must be defined as the sum of the momenta of its parts for fixed time in the momentary rest frame of the body. For the total momentum of particles and field to be conserved, the total energy–momentum tensor must be divergence free, and this then requires that the momentum of the associated electromagnetic field be defined in the same way, consistent with the suggestion by Fermi. This comprehensive solution of the 4/3-problem demonstrates that there is no conflict of Maxwell‘s theory with special relativity and the questions of equivalence of electromagnetic energy and self-mass and of stability of a classical charge distribution are independent. In appendices we discuss the relations of our treatment with Fermi‘s seminal paper and with a classic paper by Dirac where he evaluated the damping self-force on a point electron from transport of energy and momentum in the electromagnetic field. (shrink)

The topic of our discussion is extremely complex by virtue of the diversity of problems it covers, their contradictions, and their many layers. An objective analysis is complicated by the fact that we are "by origin from there," that we were all drawn into the process, and that it is difficult, if not impossible, for us to distance ourselves from this fact. Being involved in what happened is, on the one hand, a positive factor: it gives access to occurring events (...) through a knowledge of facts and details that is difficult, if not impossible, to obtain for an investigator of the events many years later. But such involvement not only discloses the truth, it also creates the illusion that one possesses the truth, because a participant in events often makes his personal beliefs about them the basis of theoretical generalizations. A participant and a witness are very different categories in terms of their objective relation to actual facts. (shrink)

Artykuł dotyczy treści oraz perspektyw rozwoju filozofii języka, zawierającej metodologiczne zasady badań nad językiem. Autorka przedstawia przegląd formacji lingwistyczno-filozoficznych w historii filozofii, jak również w dziejach językoznawstwa, wskazuje źródła współczesnych teorii lingwistyczno-filozoficznych. Analizuje ponadto właściwości języka jako systemu postrzegania świata, co znajduje wyraz przede wszystkim w jego funkcji kultywującej. System gramatyczny i leksykalny akumuluje bowiem zdobyte w procesie rozwoju kulturowo – historycznego doświadczenia określonej wspólnoty etniczno-kulturowej. Możliwość badania języka w z punktu widzenia filozofii jest uwarunkowana tym, że język ma istotę (...) znakową, służy jako narzędzie działalności poznawczej człowieka, a jednocześnie jako narzędzie komunikacji. Autorka wyraża przekonanie, że struktura, treść i funkcje języka w społeczeństwie są uwarunkowane jego rozwojem historycznym zgodnie z prawami dialektyki, obowiązującymi także w świecie rzeczy materialnych. W zastosowaniu tych. (shrink)