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)

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)

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)

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)

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.

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.

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)

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)

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.

Originally published in 1985, this is a short meditation by a great old man on people relating to other people who are dying, and the need for all of us to open ...

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.

Anwander questions "the role that Pogge assigns to benefiting from injustice in the determination of our duties toward the victims of injustice... challenging his claim that there is a negative duty not to benefit from injustice.".

This paper discusses “impartiality thought experiments”, i.e., thought experiments that attempt to generate intuitions which are unaffected by personal characteristics such as age, gender or race. We focus on the most prominent impartiality thought experiment, the Veil of Ignorance (VOI), and show that both in its original Rawlsian version and in a more generic version, empirical investigations can be normatively relevant in two ways: First, on the assumption that the VOI is effective and robust, if subjects dominantly favor a certain (...) normative judgment behind the VOI this provides evidence in favor of that judgment; if, on the other hand, they do not dominantly favor a judgment this reduces our justification for it. Second, empirical investigations can also contribute to assessing the effectiveness and robustness of the VOI in the first place, thereby supporting or undermining its applications across the board. (shrink)

Michel Foucault entwickelt sich gegenwartig zweifellos zu einer der neuen Bezugsgrossen des padagogischen Diskurses: Nach einer langen Phase grosser Widerstande innerhalb der deutschsprachigen Erziehungswissenschaft werden jetzt die ...

Walter Benjamin was one of the most intriguing and original Marxist cultural theorists of the twentieth-century. He made a precarious living in Berlin as a literary journalist and, partly under the influence of Ernst Bloch and Lukacs, turned toward the Critical Theory of the Frankfurt School. In the late 1920's, he became a close friend of Brecht, championing his revolutionary "epic theater". Driven from Germany in 1933 by the rise of Nazism, Benjamin settled in Paris where he had close associations (...) with the surrealists. When the Nazis invaded France, Benjamin fled to the Spanish frontier where on being denied entry, he committed suicide rather than risk being delivered to the SS. Benjamin's writings are a curious mixture of esoteric, sometimes mystical Jewish thought, artistic modernism, and unorthodox Marxism. He united an apocalyptic vision of history with a concern for the material, productive basis of art. Fascinated by tradition, yet a radical spokesman for the new technological media, steeped in high German philosophy, but a champion of the proletariat, Benjamin was in turn philologist, literary critic, political commentator, and philosopher of history. Bolz and van Reijen proceed from the standpoint that Benjamin's thought was shaped by his attempt to connect extremes—to make the theological idea of salvation fruitful for political thought. Then, they go on to structure Benjamin's important clusters of themes in light of the radical consequences of this intention. (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)

Carey's book on conceptual change and the accompanying argument that children's biology initially is organized in terms of naïve psychology has sparked a great detail of research and debate. This body of research on children's biology has, however, been almost exclusively been based on urban, majority culture children in the US or in other industrialized nations. The development of folkbiological knowledge may depend on cultural and experiential background. If this is the case, then urban majority culture children may prove to (...) be the exception rather than the rule, because plants and animals do not play a significant role in their everyday life. Urban majority culture children, rural majority culture children, and rural Native American children were given a property projection task based on Carey's original paradigm. Each group produced a unique profile of development. Only urban children showed evidence for early anthropocentrism, suggesting that the co-mingling of psychology and biology may be a product of an impoverished experience with nature. In comparison to urban majority culture children even the youngest rural children generalized in terms of biological affinity. In addition, all ages of Native American children and the older rural majority culture children gave clear evidence of ecological reasoning. These results show that both culture and expertise play a role in the development of folkbiological thought. (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)

This paper explores the relevance of the debate about ethical expertise for the practice of clinical ethics. We present definitions, explain three theories of ethical expertise, and identify arguments that have been brought up to either support the concept of ethical expertise or call it into question. Finally, we discuss four theses: the debate is relevant for the practice of clinical ethics in that it (1) improves and specifies clinical ethicists' perception of their expertise; (2) contributes to improving the perception (...) of moral competence of non-ethicists; (3) gives insight into complementary styles of argumentation of ethicists and non-ethicists; and (4) contributes to the awareness of the problem of profession-building of (clinical) ethicists. (shrink)

This is a new release of the original 1949 edition.