Lindström’s theorem obviously fails as a characterization of first-order logic without identity ( $\mathcal {L}_{\omega \omega }^{-} $ ). In this note, we provide a fix: we show that $\mathcal {L}_{\omega \omega }^{-} $ is a maximal abstract logic satisfying a weak form of the isomorphism property (suitable for identity-free languages and studied in [11]), the Löwenheim–Skolem property, and compactness. Furthermore, we show that compactness can be replaced by being recursively enumerable for validity under certain conditions. In the proofs, we (...) use a form of strong upwards Löwenheim–Skolem theorem not available in the framework with identity. (shrink)

In this paper, we present a prenex form theorem for a version of Independence Friendly logic, a logic with imperfect information. Lifting classical results to such logics turns out not to be straightforward, because independence conditions make the formulas sensitive to signalling phenomena. In particular, nested quantification over the same variable is shown to cause problems. For instance, renaming of bound variables may change the interpretations of a formula, there are only restricted quantifier extraction theorems, and slashed connectives cannot be (...) so easily removed. Thus we correct some claims from Hintikka [8], Caicedo & Krynicki [3] and Hodges [11]. We refine definitions, in particular the notion of equivalence, and sharpen preconditions, allowing us to restore those claims, including the prenex form theorem of Caicedo & Krynicki [3], and, as a side result, we obtain an application to Skolem forms of classical formulas. It is a known fact that a complete calculus for IF-logic is impossible, but with our results we establish several quantifier rules that form a partial calculus of equivalence for a general version of IF-logic reflecting general properties of information flow in games. (shrink)

We prove strong completeness of the □-version and the ◊-version of a Gödel modal logic based on Kripke models where propositions at each world and the accessibility relation are both infinitely valued in the standard Gödel algebra [0,1]. Some asymmetries are revealed: validity in the first logic is reducible to the class of frames having two-valued accessibility relation and this logic does not enjoy the finite model property, while validity in the second logic requires truly fuzzy accessibility relations and this (...) logic has the finite model property. Analogues of the classical modal systems D, T, S4 and S5 are considered also, and the completeness results are extended to languages enriched with a discrete well ordered set of truth constants. (shrink)

It is shown that axiomatic extensions of intuitionistic propositional calculus defining univocally new connectives, including those proposed by Gabbay, are strongly complete with respect to valuations in Heyting algebras with additional operations. In all cases, the double negation of such a connective is equivalent to a formula of intuitionistic calculus. Thus, under the excluded third law it collapses to a classical formula, showing that this condition in Gabbay's definition is redundant. Moreover, such connectives can not be interpreted in all Heyting (...) algebras, unless they are already equivalent to a formula of intuitionistic calculus. These facts relativize to connectives over intermediate logics. In particular, the intermediate logic with values in the chain of length n may be "completed" conservatively by adding a single unary connective, so that the expanded system does not allow further axiomatic extensions by new connectives. (shrink)

We study a class of [0,1][0,1]-valued logics. The main result of the paper is a maximality theorem that characterizes these logics in terms of a model-theoretic property, namely, an extension of the omitting types theorem to uncountable languages.

It is shown that axiomatic extensions of intuitionistic propositional calculus defining univocally new connectives, including those proposed by Gabbay, are strongly complete with respect to valuations in Heyting algebras with additional operations. In all cases, the double negation of such a connective is equivalent to a formula of intuitionistic calculus. Thus, under the excluded third law it collapses to a classical formula, showing that this condition in Gabbay's definition is redundant. Moreover, such connectives can not be interpreted in all Heyting (...) algebras, unless they are already equivalent to a formula of intuitionistic calculus. These facts relativize to connectives over intermediate logics. In particular, the intermediate logic with values in the chain of length n may be "completed" conservatively by adding a single unary connective, so that the expanded system does not allow further axiomatic extensions by new connectives. (shrink)

An extensions by new axioms and rules of an algebraizable logic in the sense of Blok and Pigozzi is not necessarily algebraizable if it involves new connective symbols, or it may be algebraizable in an essentially different way than the original logic. However, extension whose axioms and rules define implicitly the new connectives are algebraizable, via the same equivalence formulas and defining equations of the original logic, by enriched algebras of its equivalente quasivariety semantics. For certain strongly algebraizable logics, all (...) connectives defined implicitly by axiomatic extensions of the logic are explicitly definable. (shrink)

An extensions by new axioms and rules of an algebraizable logic in the sense of Blok and Pigozzi is not necessarily algebraizable if it involves new connective symbols, or it may be algebraizable in an essentially different way than the original logic. However, extension whose axioms and rules define implicitly the new connectives are algebraizable, via the same equivalence formulas and defining equations of the original logic, by enriched algebras of its equivalente quasivariety semantics. For certain strongly algebraizable logics, all (...) connectives defined implicitly by axiomatic extensions of the logic are explicitly definable. (shrink)

We generalize a theorem of Mundici relating compactness of a regular logic L to a strong form of normality of the associated spaces of models. Moreover, it is shown that compactness is in fact equivalent to ordinary normality of the model spaces when L has uniform reduction for infinite disjoint sums of structures. Some applications follow. For example, a countably generated logic is countably compact if and only if every clopen class in the model spaces is elementary. The model spaces (...) of L are not normal for vocabularies of uncountable power ωα. It also follows that first-order logic is the only finite-dependence logic having normal model spaces and satisfying at the same time the downward Löwenheim-Skolem theorem and uniform reduction for pairs. (shrink)

It is shown that Friedman's problem, whether there exists a proper extension of first order logic satisfying the compactness and interpolation theorems, has extremely simple positive solutions if one considers extensions by generalized (finitary) propositional connectives. This does not solve, however, the problem of whether such extensions exist which are also closed under relativization of formulas.

Este trabajo se encuadra dentro de una nueva visión de la lógica de Leibniz, la cual pretende mostrar que sus escritos fueron ricos no solamente en proyectos ambiciosos sino también en desarrollos lógico-matematicos concretos. Se demuestra que su “Caracteristica Numerica” que asigna pares de números a las proposiciones categóricas es una semántiea para la cual la silogística aristotélica es correcta y completa, y que el sistema algebraico presentado en Fundamentos de un Cálculo Lógico es una lógica algebraica similar a la (...) de Boole.This work is a contribution to a new view of Leibniz’s logic, pretending to show that his writings were not only rich in projects, but also in concrete logico-mathematical developments. We prove that his “Numerical Characteristic” assigning pairs of numbers to terms of categorical propositions, is a complete and correct semantics for aristotelian syllogistic, and the algebraic system presented in Fundamentals of Logical Calculus is essentially a complete version of boolean algebraic logic. (shrink)

In any model theoretic logic, Beth’s definability property together with Feferman-Vaught’s uniform reduction property for pairs imply recursive compactness, and the existence of models with infinitely many automorphisms for sentences having infinite models. The stronger Craig’s interpolation property plus the uniform reduction property for pairs yield a recursive version of Ehrenfeucht-Mostowski’s theorem. Adding compactness, we obtain the full version of this theorem. Various combinations of definability and uniform reduction relative to other logics yield corresponding results on the existence of non-rigid (...) models. (shrink)

We introduce a natural class of quantifiersTh containing all monadic type quantifiers, all quantifiers for linear orders, quantifiers for isomorphism, Ramsey type quantifiers, and plenty more, showing that no sublogic ofL ωω (Th) or countably compact regular sublogic ofL ∞ω (Th), properly extendingL ωω , satisfies the uniform reduction property for quotients. As a consequence, none of these logics satisfies eitherΔ-interpolation or Beth's definability theorem when closed under relativizations. We also show the failure of both properties for any sublogic ofL (...) ∞ω (Th) in which Chang's quantifier or some cardinality quantifierQ α, with α≧1, is definable. (shrink)

"Contains a balanced account of recent advances in set theory, model theory, algebraic logic, and proof theory, originally presented at the Tenth Latin American Symposium on Mathematical Logic held in Bogata, Columbia. Traces new interactions among logic, mathematics, and computer science. Features original research from over 30 well-known experts worldwide.".

El adiós a las escuelas -- El capitalismo, motor de la modernidad tardía.

The past decade has seen a burgeoning of scholarly interest in conscientious objection in healthcare. While the literature to date has focused primarily on individual healthcare practitioners who object to participation in morally controversial procedures, in this article we consider a different albeit related issue, namely, whether publicly funded healthcare institutions should be required to provide morally controversial services such as abortions, emergency contraception, voluntary sterilizations, and voluntary euthanasia. Substantive debates about institutional responsibility have remained largely at the level of (...) first-order ethical debate over medical practices which institutions have refused to offer; in this article, we argue that more fundamental questions about the metaphysics of institutions provide a neglected avenue for understanding the basis of institutional conscientious objection. To do so, we articulate a metaphysical model of institutional conscience, and consider three well-known arguments for undermining institutional conscientious objection in light of this model. We show how our metaphysical analysis of institutions creates difficulties for justifying sanctions on institutions that conscientiously object. Thus, we argue, questions about the metaphysics of institutions are deserving of serious attention from both critics and defenders of institutional conscientious objection. (shrink)

Malgré le nombre et la valeur des traductions, et malgré maintes études parues au cours des dernières années, le nom de Schelling est encore largement inconnu en France, et sa philosophie méconnue. Or, il s'agit d'un génie philosophique de premier ordre. Xavier Tilliette a entrepris de raconter une vie qui éclaire singulièrement une œuvre " en devenir ", épousant toujours le mouvement de l'existence. Schelling, éternel commençant, s'il n'a pu achever son grand projet des Ages du monde, a parcouru (...) dans leur diversité les âges de la vie, " de la belle aube au triste soir ", traversant la Révolution, l'Empire, le romantisme, la Restauration et 1848, pour finir dans un oubli relatif et dans l'isolement. (shrink)

This text rebukes and amplifies a study published under the title "L'auguste vieillard à la Constituante : un révélateur d'idéologie révolutionnaire," published in "Sedes Sapientiae," volume 109, September 2009.

In this work, Xavier Lakshmanan argues for a textual linguistic approach to Christian theology. The book takes its shape in conversation with Paul Ricoeur’s philosophical thought, demonstrating how Ricoeur’s hermeneutic philosophy can inform the way Christians interpret and appropriate biblical narratives without delimiting the potential of the text or eroding the distinctiveness of its language. The text can be appropriated in ways that address the fundamental questions of life. New meanings are constantly generated from the same text in order (...) to describe and redescribe existence, and form human identity. The self is linked inseparably with narrative; every interpretation of narrative is at the same time a reinterpretation of the self and of its possibilities. In such interpretative processes, the reader interprets the text and the text interprets the reader at the same time through an interactive reading. Accordingly, the aim of interpreting the narratives is to open up the world of the text in front of the text and in front of the reader. Here what the text uncovers is the «textual» structure of existence itself. The reality that unfolds through language discloses the possibilities of existence, and in this way the text creates a future. A revised identity emerges against the horizon of that future to give a coherent and dynamic account of the self against a horizon of hope. (shrink)

Este nuevo volumen de las obras de Xavier Zubiri recoge de forma íntegra tres cursos, que hasta ahora se encontraban inéditos, o de los que sólo se conocían algunos fragmentos. Se trata de los cursos que Zubiri impartió sobre “El problema filosófico de la historia de las religiones” (Madrid, 1965), “El problema de Dios en la historia de las religiones” (Barcelona, 1965), y “El hombre y el problema de Dios” (Madrid, 1968). Las religiones y su historia constituyen uno de (...) los grandes intereses de Xavier Zubiri como filósofo. A diferencia de otros planteamientos, que abordan lo religioso a partir de la vivencia de lo sagrado, o del discurso sobre lo divino, Zubiri entendió que el tratamiento filosófico de la religión debe partir de un hecho más elemental, que él llamaba “religación”. La religación sería un dato básico e ineludible, inseparable de la aprehensión primordial de la realidad, que nos constituye como humanos. Para Zubiri, las religiones, su diversidad, y su historia, serían más bien la plasmación ulterior de ese hecho radical. Al análisis de ese hecho, y al estudio de su despliegue histórico, incluyendo el cristianismo, están dedicados estos tres importantes cursos. Su lectura nos pone en contacto directo con el surgimiento de una de las filosofías más originales de nuestro tiempo. (Fuente: Alianza). (shrink)

In the absence of Woodin cardinals, fine structural inner models for mild large cardinal hypotheses admit forcing extensions where bounded forcing axioms hold and yet the reals are projectively well-ordered.

L'ouvrage Quelles doctrines constitutionnelles pour quel(s) droit(s) constitutionel(s) réuni les contributions des plus éminents spécialistes du droit constitutionnel français, mais aussi étrangers, dans le but de dresser un état des lieux scientifiques de cette discipline : qu'est-ce le droit constitutionnel aujourd'hui? Quellle est son utilité? Et quelles sont ses méthodes, ses évolutuons? Les différentes contributions ici proposées se penchent sur la possible formalisation (ou pas) d'une discipline scientifique autour d'une ou différentes écoles, ainsi que les évolutions qui travaillent les objets, (...) ou encore les domaines politiques et juridiques, mais aussi économiques, sociaux et culturels qu'il se propose d'appréhender. Cet ouvrage se révèle donc un outil précieux pour tous les juristes, mais plus largement, pour tous les citoyens qui s'intéressent aux questions de l'organisation constitutionnelle du Pouvoir au sein des Etats modernes. (shrink)

En un diálogo continuo con la tradición filosófica, Zubiri va página a página describiendo el acto de la intelección humana y desmontando el cúmulo de hipótesis y teorías que subyacen al llamado «problema del conocimiento». Zubiri consigue descubrir, mediante el recurso a un procedimiento puramente descriptivo, en qué consiste el acto humano por excelencia, la intelección. La intelección humana, dice Zubiri, no es una síntesis trascendental, sino algo más simple a la vez que más radical, la mera actualización de lo (...) real en la inteligencia sentiente. (shrink)

Features of threatening cues and the associated context influence the perceived imminence of threat and the defensive responses evoked. To provide additional knowledge about how the directionality of a threat (i.e. directed-towards or away from the viewer) might impact defensive responses in humans, participants were shown pictures of a man carrying a gun (threat) or nonlethal object (neutral) directed-away from or towards the participant. Cardiac and electrodermal responses were collected. Compared to neutral images, threatening images depicting a gun directed-towards the (...) participant induced sustained bradycardia and an increased electrodermal response, interpreted as immobility under attack. This defensive immobility reaction is evoked by high perceived threat and inescapable situations and indicates intense action preparation. Pictures of guns directed-away from the participant induced shorter bradycardia and no significant modulation of the electrodermal response compared to neutral pictures, which might be consistent with the perception of a less threatening situation. The results show that the directionality of threat stimuli is a key factor that prompts different patterns of defensive responses. (shrink)

We introduce and consider the inner-model reflection principle, which asserts that whenever a statement \varphi(a) in the first-order language of set theory is true in the set-theoretic universe V, then it is also true in a proper inner model W \subset A. A stronger principle, the ground-model reflection principle, asserts that any such \varphi(a) true in V is also true in some non-trivial ground model of the universe with respect to set forcing. These principles each express a form of width (...) reflection in contrast to the usual height reflection of the Lévy–Montague reflection theorem. They are each equiconsistent with ZFC and indeed \Pi_2-conservative over ZFC, being forceable by class forcing while preserving any desired rank-initial segment of the universe. Furthermore, the inner-model reflection principle is a consequence of the existence of sufficient large cardinals, and lightface formulations of the reflection principles follow from the maximality principle MP and from the inner-model hypothesis IMH. We also consider some questions concerning the expressibility of the principles. (shrink)

Est-ce un hasard si Jean-Marc Ferry, d'un côté du Rhin, Jürgen Habermas, de l'autre, entrouvrent aujourd'hui la porte de la République au discours religieux? Si la raison publique faite de liberté et d'égalité semblait suffire pour régir le champ économique et social de notre Modernité première, elle s'avère trop courte lorsqu'il s'agit de formuler la norme commune applicable aux fondamentaux de l'existence tels que la vie, le corps, l'amour, la mort... D'où l'appel de nos deux auteurs aux ressources de sens (...) qu'ont accumulées les religions et, singulièrement, le christianisme. Pour prendre cette requête au sérieux, il fallait revisiter les grands axes de la tradition chrétienne (création, faute, incarnation, salut, trinité, eucharistie) pour en dégager les enseignements qui enrichiraient la raison publique d'aujourd'hui. Mais la foi se laissera-t-elle ainsi arraisonner? Et la raison s'ouvrira-t-elle à ce discours qui vient de plus loin qu'elle? La partie est loin d'être gagnée. Xavier Dijon la mène avec grand talent. (shrink)