Tarski characterized logical notions as invariant under permutations of the domain. The outcome, according to Tarski, is that our logic, which is commonly said to be a logic of extension rather than intension, is not even a logic of extension—it is a logic of cardinality. In this paper, I make this idea precise. We look at a scale inspired by Ruth Barcan Marcus of various levels of meaning: extensions, intensions and hyperintensions. On this scale, the lower the level of meaning, (...) the more coarse-grained and less “intensional” it is. I propose to extend this scale to accommodate a level of meaning appropriate for logic. Thus, below the level of extension, we will have a more coarse-grained level of form. I employ a semantic conception of form, adopted from Sher, where forms are features of things “in the world”. Each expression in the language embodies a form, and by the definition we give, forms will be invariant under permutations and thus Tarskian logical notions. I then define the logical terms of a language as those terms whose extension can be determined by their form. Logicality will be shown to be a lower level analogue of rigidity. Using Barcan Marcus’s principles of explicit and implicit extensionality, we are able to characterize purely logical languages as “sub-extensional”, namely, as concerned only with form, and we thus obtain a wider perspective on both logicality and extensionality. (shrink)

When considering m-sequents, it is always possible to obtain an m-sequent calculus VL for every m-valued logic (defined from an arbitrary finite algebra L of cardinality m) following for instance the works of the Vienna Group for Multiple-valued Logics. The Gentzen relations associated with the calculi VL are always finitely equivalential but might not be algebraizable. In this paper we associate an algebraizable 2-Gentzen relation with every sequent calculus VL in a uniform way, provided the original algebra L has a (...) reduct that is a distributive lattice or a pseudocomplemented distributive lattice. We also show that the sentential logic naturally associated with the provable sequents of this algebraizable Gentzen relation is the logic that preserves degrees of truth with respect to the original algebra (in contrast with the more common logic that merely preserves truth). Finally, for some particular logics we obtain 2-sequent calculi that axiomatize the algebraizable Gentzen relations obtained so far. (shrink)

Les trois dialogues composés par le cardinal Nicolas de Cues pendant l'été 1450 ne résument pas toute la pensée de cet auteur, mais ils éclairent d'un jour relativement nouveau sa réflexion sur le lien entre sagesse et savoir. Proche en cela des Anciens, Nicolas de Cues pense leur unité dans la lumière de l'Un - de la Déité, écrit-il parfois - réfléchie par la puissance de l'esprit humain. Cet esprit est compris comme imago dei, non pas image de Dieu, (...) car tout ce qui est image de Dieu, mais plutôt copie de Dieu, reprise de la toute-puissance divine dans les limites que lui impose, toutefois, le fait d'être finie. La vérité étant en elle-même inaccessible ici-bas - inattingible, écrit Nicolas de Cues - reste le développement de cette vérité ou de l'Un, c'est à dire ce monde que l'esprit a pour tâche de mesurer, de reprendre, de recréer. Savoir pour inventer un monde à venir, avec humilité et ouverture à l'Etranger : cela s'accorde précisément avec ce que certains historiens nomment l'Humanisme. (shrink)

Real-life stories from teachers who share their passion for shaping the lives of young people today.

Cardinal Mercier’s Manual of Modern Scholastic Philosophy is a standard work, prepared at the Higher Institute of Philosophy, Louvain, mainly for the use of clerical students in Catholic Seminaries. Though undoubtedly elementary, it contains a clear, simple, and methodological exposition of the principles and problems of every department of philosophy, and its appeal is not to any particular class, but broadly human and universal. Volume I includes a general introduction to philosophy and sections on cosmology, psychology, criteriology, and metaphysics (...) or ontology. (shrink)

Nicholas of Cusa (1401-1464), a student of canon law who became a Catholic cardinal, was widely considered the most important original philosopher of the Renaissance. He wrote principally on theology, philosophy, and church politics. This volume makes most of Nicholas's other writings on Church and reform available in English for the first time.

Cardinal Mercier's A Manual of Modern Scholastic Philosophy is a standard work, prepared at the Higher Institute of Philosophy, Louvain, mainly for the use of clerical students in Catholic seminaries. Though undoubtedly elementary, it contains a clear, simple, and methodological exposition of the principles and problems of every department of philosophy, and its appeal is not to any particular class, but broadly human and universal. Volume I includes a general introduction to philosophy and sections on cosmology, psychology, criteriology, and (...) metaphysics or ontology. Volume II contains sections on natural theology, logic, ethics, and outlines of the history of philosophy. (shrink)

Cardinal Mercier’s Manual of Modern Scholastic Philosophy is a standard work, prepared at the Higher Institute of Philosophy, Louvain, mainly for the use of clerical students in Catholic Seminaries. Though undoubtedly elementary, it contains a clear, simple, and methodological exposition of the principles and problems of every department of philosophy, and its appeal is not to any particular class, but broadly human and universal. Volume II contains sections on natural theology, logic, ethics and outlines of the history of philosophy.

In lieu of an abstract, here is a brief excerpt of the content:THE IMPACT OF VER/TATIS SPLENDOR ON CATHOLIC EDUCATION AT THE UNIVERSITY AND SECONDARY LEVELS* CARDINAL PIO LAGHI Prefect of the Sacred Congregationfor Catholic Education INTRODUCTION T HE TOPIC which has been proposed to me, "The Impact of Veritatis Splendor on Catholic Education at the University and Secondary Levels,'' requires a note of clarification with regard to the word impact. When this Encyclical Letter of Pope John Paul II (...) appeared, it was received with much comment, both positive and negative, on the part of the press and the other media. This is one aspect of the topic proposed : to trace in a synthetic way a picture of the reactions which the document stirred. Such would certainly be an interesting study, but I would perhaps be led to traverse much terrain before arriving at the nucleus of what I feel is my duty to say to you. I shall limit myself, therefore, to commenting on two positive reactions appearing in Italian newspapers immediately after the publication of the Encyclical. The first was in the well-known Roman newspaper, Il Tempo, under the title, "An Act of Consistency in an Epoch of Doubt." It states: "If lighthouses had been moved every month, the sailors in the night would have seen the ships of history dashed against the rocks; and no voyager would have reached his homeland again if the North Star, within the Zodiac, had to obey vacillating positions of fashions and ideologies.... The papal document stirs discussions.... Nevertheless it is very much of current interest. While many ships finish on the rocks because they have * This paper was originally presented at the Forum on Catholic University Education at Duquesne University in Pittsburgh, 3 November 1995. 1 2 CARDINAL PIO LAGHI sailed following fireflies instead of lighthouses and while the ruling classes have shipwrecked for having chosen compasses that lie, there is abroad a need to see the permanence of certain values recognized in the midst of all that changes, the necessity of an ethical nucleus linked to principles of the human person, honesty, freedom and responsibility." This is a positive reaction, then, which welcomes the Encyclical as a text which says things that have to be said, giving basic directions for a journey, and stating the things no one dares to speak but of which everyone knows the necessity in daily living. This is also the substance of another comment on the Encyclical that I think it would be useful to cite. Carlo Bo, a university professor and a well-known figure in Italian intellectual life, writes: "Modern culture no longer has objective criteria for distinguishing good from evil,'' and he adds, "John Paul II has fought against Communism in defense of freedom; now he criticizes Western culture, which makes of freedom an absolute value.... The exaltation of freedom leads to ethical relativism, against which the Pope raises his voice." Agreement and basic approval are transparent in these lines, but the title under which they appear is "A Call to Order." Immediately the image is evoked-negative to the sensitivities of our times-of a commander intent on imposing order on his soldiers. The heart of the problem perhaps, at least with regard to the teaching of moral theology in the Catholic context, is in the clear perception of the need for an unchanging point of reference, of a lighthouse for the voyage, and at the same time the fear of speaking of this need, of making it the subject of reflection, communication, and teaching. There is a kind of widespread fear which keeps us at a distance from the truth, from the permanent foundations of human acting, from the objective and the universal; a fear which is perhaps the principal cause on account of which so great a part of contemporary humanity risks dying of thirst while standing before a spring of cool water. In order not to appear authoritarian or negative, one keeps silent, does not speak, expresses oneself in a partial or even an erroneous way with regard to all that is most necessary for life. It would be difficult not to see in this a problem which is typically an educa- THE IMPACT OF VERITATIS SPLENDOR 3... (shrink)

La dotta ignoranza -- Le congetture -- Il Dio nascosto -- La ricerca di Dio -- La filiazione di Dio -- Il dono del Padre dei lumi -- Congettura sugli ultimi giorni -- Dialogo sulla Genesi -- Difesa della dotta ignoranza -- La sapienza -- La mente -- Gli esperimenti con la bilancia -- La visione di Dio -- Il berillo -- L'ugaglianza -- Il principio -- Il potere che è -- il non-altro -- La caccia della sapienza -- Il (...) gioco della palla -- Compendio -- Il vertice della contemplazione -- La quadratura del cerchio -- I complementi matematici -- La perfezione matematica. (shrink)

This paper concerns late 1920 s attempts to construct unitary theories of gravity and electromagnetism. A first attempt using a non-standard connection—with torsion and zero-curvature—was carried out by Albert Einstein in a number of publications that appeared between 1928 and 1931. In 1929, Tullio Levi-Civita discussed Einstein’s geometric structure and deduced a new system of differential equations in a Riemannian manifold endowed with what is nowadays known as Levi-Civita connection. He attained an important result: Maxwell’s electromagnetic equations and the gravitational (...) equations were obtained exactly, while Einstein had deduced them only as a first order approximation. A main feature of Levi-Civita’s theory is the essential use of the Ricci’s rotation coefficients, introduced by Gregorio Ricci Curbastro many years before. We trace the history of Ricci’s coefficients that are still used today, and highlight their geometric and mechanical meaning. (shrink)

'ground-breaking anthology... wide array of perspectives on WW1, from both sides of the fighting' -B. Adler, Choice 'a very fine anthology' -Times Literary SupplementThe First World War inspired a huge outpouring of writing that, until recently, was thought to be almost the exclusive preserve of men. Yet the war also acted as a catalyst which enabled women writers to find a literary and political voice. This anthology bears witness to the great variety and scope of women's writing about the war. (...) Covering the years 1914-1930, the book brings together little-known writing from across the world, drawing on a wide spectrum of genres from letters and diary entries to essays, novels, and short stories. Among the celebrated writers featured in this anthology are: Radclyffe Hall, Sylvia Pankhurst, Maud Gonne, Rebecca West, May Sinclair, Olive Schreiner, Colette, Vera Brittain, Gertrude Stein, Katherine Mansfield, HD, and Virginia Woolf. (shrink)

Quelles politiques linguistiques vont le mieux permettre de mettre en valeur les avantages du bilinguisme et l'apprentissage des langues tout en favorisant la pérennité des langues minoritaires à l'ère de la mondialisation? Cet article tente de répondre à la question en basant son propos sur l'exemple des politiques d'aménagement linguistique du Canada et du Québec. Il montre que la mondialisation linguistique exerce une pression supplémentaire sur un équilibre déjà fragile entre les francophones et les anglophones au Canada et il suggère (...) de réviser les principes actuels afin d'assurer la pérennité du français, notamment au Québec.What language policies will best help highlight the benefits of bilingualism and language learning while promoting the sustainability of minority languages ​​in the era of globalization? This article attempts to answer the question, basing his remarks on the example of language planning policies of Canada and Quebec. It shows that linguistic globalization puts additional pressure on already fragile balance between Francophones and Anglophones in Canada and suggested revising the current principles in order to ensure the sustainability of the French, especially in Quebec. (shrink)

Thus emerges the paradox of All Israel's destiny. Some of the children of Israel gathered in a state like all others—no more and no less and this is legitimate and necessary. This state was founded by the children of the People whom God called not to be like the others, but, rather for the others, because of His design for universal salvation. What is true for the people who have settled in this state which was recreated for the Jews, is (...) true for the members, of the Jewish people who are dispersed throughout the Diaspora as citizens of various countries. But this vocation to testify is in the hands of God, and not in the power of man. The destiny of Israel is that its destiny overtakes it over and over. (shrink)