This book offers current international initiatives, developed for working with children from "Birth to Eight" by a diverse group of noted professional authors. Their readings present an overview of early education as it evolved from the Froebelian kindergarten to today's practices in various Early Education settings around the globe. The international voices of the authors represent a balanced perspective of happenings in various nations and lend a conversational approach to each chapter. The chapters analyze the Universal Preschool Education movement promoted (...) by various countries, states, and agencies; examine model curriculum programs in a variety of teaching/learning settings; and identify directions the community can take in promoting effective early education programs. Particular attention is given to key issues and concerns faced by practitioners and families world-wide. Studies reveal successful approaches to bilingual education in a Chilean kindergarten, research findings on gender differences in primary school girls for learning science in Wales, literacy development strategies for teaching in UK multicultural classrooms and childhood centres, the process of integration special education with early childhood practices in China, and exemplars of community outreach to improve the well being of children through advocacy for governmental changes in early education policies and professional development. This book is for everyone interested in the well being of young children moving forward in a global age to meet the challenges of early citizenship in their world. (shrink)

Paul Edwards' October 1989 essay, ‘Heidegger's Quest for Being’ illustrates the wisdom of the dictum that the only legitimate criticism of a philosopher's position is a constructive criticism. His negative critique amounts to no more than expressions of distaste, dislike, and displeasure, and nothing of philosophical interest follows from his assertions, as the discourse is primarily an argument ad hominem . He grossly misinterprets Heidegger on some elemental and fundamental matters as well. In particular, he sorely misinterprets what he refers (...) to as the ‘Quest for Being’, which only further contributes to the objectionable character of the essay. (shrink)

We prove that if the Mathias forcing is followed by a forcing with the Laver Property, then any V\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathsf {V}$$\end{document}-q\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathsf {q}$$\end{document}-point is isomorphic via a ground model bijection to the canonical V\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathsf {V}$$\end{document}-Ramsey ultrafilter added by the Mathias real. This improves a result of Shelah and Spinas.

We examine the notion of primitive satisfaction in logical matrices. Theorem II. 1, being the matrix counterpart of Baker's well-known result for congruently distributive varieties of algebras (cf [1], Thm. 1.5), links the notions of primitive and standard satisfaction. As a corollary we give the matrix version of Jónsson's Lemma, proved earlier in [4]. Then we investigate propositional logics with disjunction. The main result, Theorem III. 2, states a necessary and sufficient condition for such logics to be finitely based.

The class Matr(C) of all matrices for a prepositional logic (, C) is investigated. The paper contains general results with no special reference to particular logics. The main theorem (Th. (5.1)) which gives the algebraic characterization of the class Matr(C) states the following. Assume C to be the consequence operation on a prepositional language induced by a class K of matrices. Let m be a regular cardinal not less than the cardinality of C. Then Matr (C) is the least class (...) of matrices containing K and closed under m-reduced products, submatrices, matrix homomorphisms, and matrix homomorphic counter-images. (shrink)

W tym artykule zaproponuję konstrukcję trójwartościowej logiki przekonań, którą nazywam: LSB3_1. Podam również i udowodnię kompletność LSB3_1 w odniesieniu do danej semantyki. LSB3_1 opiera się na preformalnych założeniach i intuicjach, które przedstawiono w sekcji 1. Sekcja 2 zawiera składnię i podział instrukcji LSB3_1 na wewnętrzne i zewnętrzne. Rozdział 3 przedstawia semantykę LSB3_1, a także szereg tautologii i formuł nietautologicznych w LSB3_1 wraz z ich intuicyjną interpretacją. System aksjomatyczny dla LSB3_1 i jego porównanie z silną logiką Kleene'a są przedstawione w sekcji (...) 4. Twierdzenie o kompletności dla LSB3_1 jest przedstawione w rozdziale 5. Zdefiniuję termin koniunkcyjna forma normalna i przedstawię lematy, które prowadzą do udowodnienia redukcji języka LSB3_1 wzory przed udowodnieniem twierdzenia o zupełności. (shrink)

Although it became customary to warn against confusing postmodernism with deconstructionism, it seems plausible to suggest that their central agendas are not dissimilar. Moreover, from the philosophical point of view, it is the idea of the 'deconstruction of meaning' that can be said to constitute the foundation of postmodernism understood here as an intellectual movement. It is true that grounded in the poststructuralist language analysis, deconstructionism seeks primarily to challenge the attempts inherent in the Western philosophical tradition to establish ultimate (...) meaning in a text. However, as one might have anticipated, the deconstruction of meaning of texts provided a basis for a large scale project leading to deconstruction of all 'truths', as conceived in the mainstream philosophical tradition. And it did it by questioning the coherence of the very concept of 'truth'. Eclectic as postmodernism is, it can be recognized by the fundamental assumption that there is no common denominator that guarantees the one-ness of the world, or the possibility of objective or neutral thought. This assumption would suffice to make one expect that postmodernism will challenge the very foundations of any metaphysical or religious system of beliefs. And so it does. In this paper I would like to ellucidate just one way this challange may be construed, poiting to the example of Don Cupitt, the leading exponent of the 'antirealist' critique of the discourse of theism. (shrink)

Dear Readers,After a long break caused, on the one hand, by staff changes in the Editorial Board and, on the other, by the lingering coronavirus pandemic, another issue of the Ignatianum Philosophical Yearbook is coming out. The new editorial team has decided to expand the journal’s formula to include texts from the general humanities; thus, there will be articles not only on philosophy, but also on history, cultural and religious studies, and theology, on top of Polish and foreign literature. The (...) journal is also open to a wide range of issues that take into account the mission of the Jesuit University Ignatianum as a Catholic research center. An important element of this approach is the issue of the Mediterranean civilizational tradition and cultural heritage, which in our understanding are the most important sources of knowledge and inspiration for the study of contemporary problems of individual people, societies and states as well. (shrink)

In the paper we study the class of weakly algebraizable logics, characterized by the monotonicity and injectivity of the Leibniz operator on the theories of the logic. This class forms a new level in the non-linear hierarchy of protoalgebraic logics.

Any finite support iteration of posets with precalibre ℵ 1 which has the length of cofinality greater than ω 1 yields a model for the dual Borel conjecture in which the real line is covered by ℵ 1 strong measure zero sets.

In 1948, Stanis aw Ja kowski defined a logical system D2 of a discursive 1 sentential calculus. The aim of this paper is to introduce the reader to the basic ideas of the discursive logic and to show, in a historical perspective, its development originating from the two germ papers [19] and [20]. We intend to present some problems connected with it and outline the solutions they have received up to the present day.

An explanation is given of why, after adding to a model M of ZFC first a Solovay real r and next a Cohen real c, in M[ r][ c] a Cohen real over M[ c] is produced. It is also shown that a Solovay algebra iterated with a Cohen algebra can be embedded into a Cohen algebra iterated with a Solovay algebra.

This book makes a significant contribution to the standard decision theory, that is, the theory of choice built around the principle of maximizing expected utility, both to its causal version and to the more traditional noncausal approach. The author’s success in clarifying the foundations of the standard decision theory in general, and causal decision theory in particular, also makes the book uniquely suitable for a person whose research in philosophy has led her to want to learn about contemporary decision theory. (...) The book presupposes some mathematical sophistication, and it contains more philosophical and mathematical argumentation per page than may be suitable for an undergraduate level course; but it stands out as an ideal textbook for a graduate-level course focused on the foundations of the standard decision theory. (shrink)

This article attempts to answer the question: what has the current migration crisis revealed in relations between Christianity and Islam, two religions with common Abrahamic roots? What conclusions can be drawn about the state of these relations, particularly with regard to ordinary members of the two religions? How should we assess the reaction of Christians in Europe to the inflow of refugees from Muslim countries in the light of the Gospel, the Second Vatican Council and the teaching of Pope Francis?The (...) article consists of four parts. Part I briefly presents Christian-Muslim relationships over the centuries. Part II focuses on the sense of danger occurring in European societies in connection with the influx of Muslims during the migration crisis. Part III presents the teachings of the Second Vatican Council about Islam and Part IV describes Pope Francis’s attitude towards refugees from Muslim countries. (shrink)

There exist different kinds of averaging of the differences of the energy–momentum and angular momentum in normal coordinates NC(P) which give tensorial quantities. The obtained averaged quantities are equivalent mathematically because they differ only by constant scalar dimensional factors. One of these averaging was used in our papers [J. Garecki, Rep. Math. Phys. 33, 57 (1993); Int. J. Theor. Phys. 35, 2195 (1996); Rep. Math. Phys. 40, 485 (1997); J. Math. Phys. 40, 4035 (1999); Rep. Math. Phys. 43, 397 (1999); (...) Rep. Math. Phys. 44, 95 (1999); Ann. Phys. (Leipzig) 11, 441 (2002); M.P. Dabrowski and J. Garecki, Class. Quantum. Grar. 19, 1 (2002)] giving the canonical superenergy and angular supermomentum tensors. In this paper we present another averaging of the differences of the energy–momentum and angular momentum which gives tensorial quantities with proper dimensions of the energy–momentum and angular momentum densities. We have called these tensorial quantities “the averaged relative energy–momentum and angular momentum tensors”. These tensors are very closely related to the canonical superenergy and angular supermomentum tensors and they depend on some fundamental length L > 0. The averaged relative energy–momentum and angular momentum tensors of the gravitational field obtained in the paper can be applied, like the canonical superenergy and angular supermomentum tensors, to coordinate independent analysis (local and in special cases also global) of this field. Up to now we have applied the averaged relative energy–momentum tensors to analyze vacuum gravitational energy and momentum and to analyze energy and momentum of the Friedman (and also more general, only homogeneous) universes. The obtained results are interesting, e.g., the averaged relative energy density is positive definite for the all Friedman and other universes which have been considered in this paper. (shrink)

Does the alleged religious experience of a mystic constitute a reliable source of knowledge about the object of his or her experience? Or does it rationally justify a move from such experience to meaningful beliefs about God or the Absolute which is supposed to be the object of that experience? And are religious beliefs in need of being grounded in religious experience in order to be rationally justified? Although it seems pretty obvious that a great many adherents of all religions (...) find reasons for their beliefs in their religious traditions rather than in their personal religious experiences, one could note that usually these traditions present religious experiences of their founder figures as constituting evidence for their authenticity and truthfulness ; the supposed mystical experiences of some adherents of a given religious tradition are often treated by their co-believers as an important evidence which increases credibility of their own religious convictions. (shrink)

Does the alleged religious experience of a mystic constitute a reliable source of knowledge about the object of his or her experience? Or does it rationally justify a move from such experience to meaningful beliefs about God or the Absolute which is supposed to be the object of that experience? And are religious beliefs in need of being grounded in religious experience in order to be rationally justified? Although it seems pretty obvious that a great many adherents of all religions (...) find reasons for their beliefs in their religious traditions rather than in their personal religious experiences, one could note that usually these traditions present religious experiences of their founder figures as constituting evidence for their authenticity and truthfulness ; the supposed mystical experiences of some adherents of a given religious tradition are often treated by their co-believers as an important evidence which increases credibility of their own religious convictions. (shrink)

We are facing a crisis of trust in expertise today. Fewer and fewer people trust experts, and more and more politicians openly ignore expert consensus. 'Democracy in the Post-Truth Era' asks what might happen to democracy if we reject the fundamental liberal assumption that people are capable of making informed choices. The book explores the potential impact on society if people, including politicians, never appreciate the relevance of expert opinions. What if people cannot choose between supporters and opponents of key (...) issues such as the causes of climate change, effectiveness of vaccines and ways of combating economic and social crises? Applying social epistemology to these questions, the book considers whether democracy can be defended in the post-truth era. (shrink)

This book is both suitable for logically and algebraically minded graduate and advanced graduate students of mathematics, computer science and philosophy, and ...