This paper deals with the question of the logicality of modal logics from a proof-theoretic perspective. It is argued that if Dos̆en’s analysis of logical constants as punctuation marks is embraced, it is possible to show that all the modalities in the cube of normal modal logics are indeed logical constants. It will be proved that the display calculus for each displayable modality admits a purely structural presentation based on double-line rules which, following Dos̆en’s analysis, allows us to claim that (...) the corresponding modal operators are logical constants. (shrink)

This article presents a sequent calculus for a negative free logic with identity, called N . The main theorem (in part 1) is the admissibility of the Cut-rule. The second part of this essay is devoted to proofs of soundness, compactness and completeness of N relative to a standard semantics for negative free logic.

We investigate incomplete symbols, i.e. definite descriptions with scope-operators. Russell famously introduced definite descriptions by contextual definitions; in this article definite descriptions are introduced by rules in a specific calculus that is very well suited for proof-theoretic investigations. That is to say, the phrase ‘incomplete symbols’ is formally interpreted as to the existence of an elimination procedure. The last section offers semantical tools for interpreting the phrase ‘no meaning in isolation’ in a formal way.

In this paper we apply proof theoretic methods used for classical systems in order to obtain upper bounds for systems in partial logic. We focus on a truth predicate interpreted in a Kripke style way via strong Kleene; whereas the aim is to connect harmoniously the partial version of Kripke–Feferman with its intended semantics. The method we apply is based on infinitary proof systems containing an ω\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\omega $$\end{document}-rule.

In this paper we use proof-theoretic methods, specifically sequent calculi, admissibility of cut within them and the resultant subformula property, to examine a range of philosophically-motivated deontic logics. We show that for all of those logics it is a (meta)theorem that the Special Hume Thesis holds, namely that no purely normative conclusion follows non-trivially from purely descriptive premises (nor vice versa). In addition to its interest on its own, this also illustrates one way in which proof theory sheds light on (...) philosophically substantial questions. (shrink)

This paper extends the investigations into logical properties of the quantified argument calculus (Quarc) by suggesting a series of proper subsystems which, although retaining the entire vocabulary of Quarc, restrict quantification in such a way as to make the result decidable. The proof of decidability is via a procedure that prunes the infinite branches of a derivation tree in what is a syntactic counterpart of semantic filtration. We demonstrate an application of one of these systems by showing that Aristotle’s assertoric (...) syllogistic is embeddable within, thus also providing another method of showing its decidability. (shrink)

Definite descriptions are in the focus of philosophical discussion at least since Russell's famous paper "On Denoting". We present in this paper a logic with descriptions in Russell's spirit. The formulation, however, is closely related to Schütte's development of predicate logic, i.e. the formulation of the calculus uses positive- and negative-parts. With respect to this slightly more sophisticated formulation it is possible to formalize Russell's convention that is originally stated in the metalanguage of his theory of descriptions within our calculus. (...) In this paper we prove an elimination theorem for this calculus. (shrink)

We study the logic of so-called lexicographic or priority merge for multi-agent plausibility models. We start with a systematic comparison between the logical behavior of priority merge and the more standard notion of pooling through intersection, used to define, for instance, distributed knowledge. We then provide a sound and complete axiomatization of the logic of priority merge, as well as a proof theory in labeled sequents that admits cut. We finally study Moorean phenomena and define a dynamic resolution operator for (...) priority merge for which we also provide a complete set of reduction axioms. (shrink)

Rudolf Carnap’s mature work on the logical reconstruction of scientific theories consists of two components. The first is the elimination of the theoretical vocabulary of a theory in terms of its Ramsification. The second is the reintroduction of the theoretical terms through explicit definitions in a language containing an epsilon operator. This paper investigates Carnap’s epsilon-reconstruction of theories in the context of pure mathematics. The main objective here is twofold: first, to specify the epsilon logic underlying his suggested definition of (...) theoretical terms and a suitable choice semantics for it. Second, to analyze whether Carnap’s approach is compatible with a structuralist conception of mathematics. (shrink)

This article investigates the proof theory of the Quantified Argument Calculus as developed and systematically studied by Hanoch Ben-Yami [3, 4]. Ben-Yami makes use of natural deduction, we, however, have chosen a sequent calculus presentation, which allows for the proofs of a multitude of significant meta-theoretic results with minor modifications to the Gentzen’s original framework, i.e., LK. As will be made clear in course of the article LK-Quarc will enjoy cut elimination and its corollaries.

In this paper we apply proof theoretic methods used for classical systems in order to obtain upper bounds for systems in partial logic. We focus on a truth predicate interpreted in a Kripke style way via strong Kleene; whereas the aim is to connect harmoniously the partial version of Kripke–Feferman with its intended semantics. The method we apply is based on infinitary proof systems containing an ω-rule.

Free logics is a family of first-order logics which came about as a result of examining the existence assumptions of classical logic. What those assumptions are varies, but the central ones are that the domain of interpretation is not empty, every name denotes exactly one object in the domain and the quantifiers have existential import. Free logics usually reject the claim that names need to denote in, and of the systems considered in this paper, the positive free logic concedes that (...) some atomic formulas containing non-denoting names are true, while negative free logic rejects even the latter claim. Inclusive logics, which reject, are likewise considered. These logics have complex and varied axiomatizations and semantics, and the goal of this paper is to present an orderly examination of the various systems and their mutual relations. This is done by first offering a formalization, using sequent calculi which possess all the desired structural properties of a good proof system, including admissibility of contraction and cut, while streamlining free logics in a way no other approach has. We then present a simple and unified system of abstract semantics, which allows for a straightforward demonstration of the meta-theoretical properties, and offers insights into the relationship between different logics. The final part of this paper is dedicated to extending the system with modalities by using a labeled sequent calculus, and here we are again able to map out the different approaches and their mutual relations using the same framework. (shrink)

The Quantified argument calculus (Quarc) has received a lot of attention recently as an interesting system of quantified logic which eschews the use of variables and unrestricted quantification, but nonetheless achieves results similar to the Predicate calculus (PC) by employing quantifiers applied directly to predicates instead. Despite this noted similarity, the issue of the relationship between Quarc and PC has so far not been definitively resolved. We address this question in the present paper, and then expand upon that result. Utilizing (...) recent developments in structural proof theory, we develop a G3-style sequent calculus for Quarc and briefly demonstrate its structural properties. We put these properties to use immediately to construct direct proofs of the meta-theoretical properties of the system. We then incorporate an abstract (and, as we shall see, logical) predicate into the system in a way that preserves all the structural properties. This allows us to identify a system of Quarc which is deductively equivalent to PC, and also yields a constructive method of demonstrating the Craig interpolation theorem (which speaks in favor of the aforementioned predicate being logical). We further generalize this extension to develop a bivalent system of Quarc with defining clauses that still maintains all the desirable properties of a good proof system. (shrink)

We study two logics of knowledge and belief stemming from the work of Stalnaker, omitting positive introspection for knowledge. The two systems are equivalent with positive introspection, but not without. We show that while the logic of beliefs remains unaffected by omitting introspection for knowledge in one system, it brings significant changes to the other. The resulting logic of belief is non-normal, and its complete axiomatization uses an infinite hierarchy of coherence constraints. We conclude by returning to the philosophical interpretation (...) underlying both models of belief, showing that neither is strong enough to support a probabilistic interpretation, nor an interpretation in terms of certainty or the “mental component” of knowledge. (shrink)

We study two logics of knowledge and belief stemming from the work of Stalnaker, omitting positive introspection for knowledge. The two systems are equivalent with positive introspection, but not without. We show that while the logic of beliefs remains unaffected by omitting introspection for knowledge in one system, it brings significant changes to the other. The resulting logic of belief is non-normal, and its complete axiomatization uses an infinite hierarchy of coherence constraints. We conclude by returning to the philosophical interpretation (...) underlying both models of belief, showing that neither is strong enough to support a probabilistic interpretation, nor an interpretation in terms of certainty or the “mental component” of knowledge. (shrink)

Free logics are a family of first-order logics which came about as a result of examining the existence assumptions of classical logic (Hintikka _The Journal of Philosophy_, _56_, 125–137 1959 ; Lambert _Notre Dame Journal of Formal Logic_, _8_, 133–144 1967, 1997, 2001 ). What those assumptions are varies, but the central ones are that (i) the domain of interpretation is not empty, (ii) every name denotes exactly one object in the domain and (iii) the quantifiers have existential import. Free (...) logics reject the claim that names need to denote in (ii). _Positive_ free logic concedes that some atomic formulas containing non-denoting names (including self-identity) are true, _negative_ free logic treats them as uniformly false, and _neutral_ free logic as taking a third value. There has been a renewed interest in analyzing proof theory of free logic in recent years, based on intuitionistic logic in Maffezioli and Orlandelli (_Bulletin of the Section of Logic_, _48_(2), 137–158 2019 ) as well as classical logic in Pavlović and Gratzl (_Journal of Philosophical Logic_, _50_, 117–148 2021 ), there for the positive and negative variants. While the latter streamlines the presentation of free logics and offers a more unified approach to the variants under consideration, it does not cover neutral free logic, since there is some lack of both clear formal intuitions on the semantic status of formulas with empty names, as well as a satisfying account of the conditional in this context. We discuss extending the results to this third major variant of free logics. We present a series of G3 sequent calculi adapted from Fjellstad (_Studia Logica_, _105_(1), 93–119 2017, _Journal of Applied Non-Classical Logics_, _30_(3), 272–289 2020 ), which possess all the desired structural properties of a good proof system, including admissibility of contraction and all versions of the cut rule. At the same time, we maintain the unified approach to free logics and moreover argue that greater clarity of intuitions is achieved once neutral free logic is conceptualized as consisting of two sub-varieties. (shrink)

The aim of this paper is to introduce and explain display calculi for a variety of logics. We provide a survey of key results concerning such calculi, though we focus mainly on the global cut elimination theorem. Propositional, first-order, and modal display calculi are considered and their properties detailed.

Die Frage nach Gott war seit Platon – und verstärkt im Denken Augustins – ein Hauptpunkt des philosophischen Fragens überhaupt. Noch Kant zählte sie zu den »Kardinalsätzen der reinen Vernunft«, zu den Fragen, an denen »die Vernunft ihr größtes Interesse hat«. Martin Heidegger, dessen Denken weithin von der Gottesfrage angeregt ist und um sie kreist, hat dagegen erwogen, »von Gott im Bereich des Denkens zu schweigen« – nicht weil er diese Frage für belanglos hielt, sondern weil das Denken sich für (...) diese Frage erst neu öffnen und vorbereiten müsse. In die von Kant und Heidegger bestimmte Situation hinein hat Emmanuel Levinas ein Denken entfaltet, das – im Wissen um die Schwierigkeiten – einen neuen Zugang zur Gottes- frage eröffnet. Der aus einem Symposion entstandene Band enthält Beiträge von Levinas-Interpreten der ›ersten Stunde‹ (Bernhard Casper, Jean Greisch und Ludwig Wenzler), aber auch Beiträge, die Levinas in Verbindung mit Autoren der abendländischen Philosophie sehen (Johannes Brachtendorf, Norbert Fischer und Eduard Zwierlein), und schließlich Beiträge, die sich der immanenten Auslegung von Aspekten seines Werks zuwenden (Sarah Allen, Reinhold Esterbauer, Branko Klun und Jakub Sirovátka). (shrink)

Die Erforschung Kants ist langst zu einem weltumspannenden Unternehmen geworden. Welch reiche Frucht der Wissenschaft dadurch zufallt, zeigen die Beitrage dieser Festschrift, die dem Nestor der deutschen Kantforschung, Norbert Hinske, gewidmet ist. Bekannte Vertreter der italienischen, japanischen, russischen und deutschen Kantforschung kommen zu Wort. Von besonderer Bedeutung fur die - in diesem Punkt ganzlich neu zu schreibende - Lebens- und Entwicklungsgeschichte Kants ist ein neu entdeckter, erstmals im Faksimile abgedruckter Brief von J. E. Biester an J. N. Tetens, der (...) belegt, dass der preussische Kultusminister v. Zedlitz zunachst nicht etwa Kant, sondern Tetens nach Halle berufen hat. Hinskes vollstandige Bibliographie rundet den Band ab - und zeigt eindrucksvoll, wie viel die Kantforschung weltweit gerade ihm zu verdanken hat. The study of Kant has long been a global undertaking. The articles in this Festschrift for the leading German expert on Kant, Norbert Hinske, show how richly productive this has been for scholars. Leading Italian, Japanese, Russian and German representatives of research on Kant have provided contributions to it. What is particular significant for the history of Kant's life and development, which has to be completely rewritten in this regard, is a newly discovered letter, reprinted in facsimile for the first time, from J. E. Biester to J. N. Tetens, which proves that Prussian Minister of Culture v. Zedlitz initially did not appoint Kant but rather Tetens to the position in Halle. Hinske's complete bibliography is included in the volume and is impressive evidence of how much Kant research worldwide owes to him. (shrink)

Quelle est la portée significative du lien entre connaissance rationnelle et théorie du fondement des sciences dans l'épistémologie contemporaine? En reprenant à nouveaux frais le débat séculaire sur la théorie du fondement des sciences et en apportant de nouveaux éclairages, cet ouvrage définit le rôle de la critique philosophique et ses tâches nouvelles imposées par ce débat. Professeur d'épistémologie et de méthodologie de la recherche scientifique à l'Université de Kisangani et à l'Université catholique du Congo.

We introduce a new understanding of deontic modals that we callobligations as weakest permissions. We argue for its philosophical plausibility, study its expressive power in neighborhood models, provide a complete Hilbert-style axiom system for it and show that it can be extended and applied to practical norms in decision and game theory.

Das Handbuch gewährt einen umfassenden Überblick über Tocquevilles Leben, Werk und Wirkung auf dem aktuellen Stand der historischen, philosophischen und sozialwissenschaftlichen Forschung. Dem äußerst facettenreichen, in Deutschland aber nach wie vor unterschätzten Autor widmet dieser Band eine ebenso kompakte wie systematische Darstellung, die auf der Basis eines strukturierten Zugriffs und unter Berücksichtigung aller seiner Schriften verschiedene Aspekte seines Denkens erfasst. Deutschsprachige Leserinnen und Leser können sich schnell und zielführend fundierte Informationen über Tocquevilles Theorien, seine zentralen Begriffe sowie die wichtigsten Einflüsse (...) verschaffen. Zugleich dient das Handbuch als Kompass zur Einordnung von Tocquevilles Analysen in gegenwärtige Debatten und Themengebiete und gibt anschlussfähige Hinweise für die Konzeption von Projekten in Forschung und Lehre. (shrink)

Levinas entfaltet seine ethischen Uberlegungen von der konkreten Begegnung mit dem Anderen her, der in seiner radikalen Andersheit einen ethischen Anspruch an das Ich stellt. Dieser Anspruch zeigt sich insbesondere im Antlitz und im Blick des Anderen. Somit gehort das Antlitz des Anderen zu den zentralen Denkfiguren der Philosophie Levinas. Der vorliegende Sammelband entfaltet das Kernmotiv des Antlitzes in unterschiedlichen Richtungen (etwa im Gesprach mit der philosophischen Tradition) und zeigt zugleich seine Wirkung auf verschiedenen Feldern: in der Kunst oder im (...) Politischen. (shrink)

Kant war uberzeugt, dass er das "Wissen aufheben" musste, "um zum Glauben Platz zu bekommen". Wie sich der philosophisch begrundete "Vernunftglaube" aber zum Offenbarungsglauben verhalt, ist eine Frage, die bis heute Nachdenkens bedarf. Der Band vergegenwartigt Uberlegungen von der Stoa bis in unsere Zeit. Er verdeutlicht: Wo Philosophie die Fragen der Religion vergisst oder missachtet, verliert sie Rang und Tiefe. Wo religioser Glaube die Beziehung zum philosophischen Fragen vernachlassigt, wird er verlieren und scheitern. Wo jedoch etwas philosophisch gedachtes Absolutes die (...) Beziehung zur Geschichtlichkeit des menschlichen Lebens aus dem Blick verliert und die faktische Absolutheit im Geschichtlichen nicht zu verstehen versucht, verliert die Philosophie ihre Kernaufgaben aus dem Blick. (shrink)

On retrouve dans la construction des connaissances scientifiques un projet initial dont la portée met un accent particulier sur le rapport indéfectible entre l'exigence critique, la rationalité et la méthodologie des sciences. Ce projet trouve une véritable mise en oeuvre dans l'épistémologie critique de Jean Ladrière, qui s'inscrit dans la tradition du rationalisme critique, à la lumière du projet plus global d'une critique de la raison théorique.

Le terme d'athéisme produit un sentiment trompeur de familiarité. Car l'athéisme ne s'arrête pas à la négation de Dieu et les Dieux ont cette propension à ressusciter sous d'autres formes, à quitter le royaume de la religion et de la théologie pour se réfugier dans le quotidien de nos vies. C'est ce que Marx dénomme la " religion quotidienne " qui déifie des réalités sociales et économiques comme la valeur, le capital, la marchandise, transformant celles-ci en puissances tutélaires et transcendantes (...) face auxquelles les hommes seraient à la fois impuissants et irrémédiablement soumis. Trois textes de Marx permettent ici de saisir le passage de l'opium du peuple au fétichisme de la marchandise, et le type de subversion politique que produit l'athéisme. Véritable " sport de combat ", l'athéisme consiste alors en une pensée de l'émancipation et de la démocratie par et pour un peuple qui se constitue par la critique toujours renouvelée des pouvoirs. Cette critique est le legs précieux de Marx : toutes les religions scellent la croyance que l'Histoire serait commandée par des forces sur lesquelles les hommes n'auraient pas de prise, et c'est pourquoi il faut les combattre. L'athéisme conséquent n'appelle pas à la réforme, mais à la révolution. (shrink)

The objective of this article is to analyse and compare four methods of ethical case deliberation. These include Clinical Pragmatism, The Nijmegen Method of ethical case deliberation, Hermeneutic dialogue, and Socratic dialogue. The origin of each method will be briefly sketched. Furthermore, the methods as well as the related protocols will be presented. Each method will then be evaluated against the background of those situations in which it is being used. The article aims to show that there is not one (...) ideal method of ethical case deliberation, which fits to all possible kinds of moral problems. Rather, as each of the methods highlights a limited number of morally relevant aspects, each method has its strengths and weaknesses as well. These strengths and weaknesses should be evaluated in relation to different types of situations, for instance moral problems in treatment decisions, moral uneasiness and residue, and the like. The suggestion arrived at on the basis of the findings of this paper is a reasonable methodological plurality. This means that a method can be chosen depending on the type of moral problem to be deliberated upon. At the same time it means, that by means of a method, deliberation should be facilitated. (shrink)

Approaches to legal pluralism vary widely across the spectrum of different disciplines. They comprise normative and descriptive perspectives, focus both on legal pluralist realities as well as public debates, and address legal pluralism in a range of different societies with varying political, institutional and historical conditions. Emphasising an empirical research to contemporary legal pluralist settings in Muslim contexts, the present collected volume contributes to a deepened understanding of legal pluralist issues and realities through comparative examination. This approach reveals some common (...) features, such as the relevance of Islamic law in power struggles and in the construction of (state or national) identities, strategies of coping with coexisting sets of legal norms by the respective agents, or public debates about the risks induced by the recognition of religious institutions in migrant societies. At the same time, the studies contained in this volume reveal that legal pluralist settings often reflect very specific historical and social constellations, which demands caution towards any generalisation. The volume is based on papers presented at a conference in Münster (Germany) in 2016 and comprises contributions by Judith Koschorke, Karen Meeschaut, Yvonne Prief, Ulrike Qubaja, Werner de Saeger, Ido Shahar, Katrin Seidel, Konstantinos Tsitselikis, Vishal Vora and Ihsan Yilmaz. (shrink)