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.

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 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 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)

The ArgumentCassirer's analyses of twentieth-century physics from the perspective of the philosophy of science focuses on the concept of the object of scientific experience. Within his concept of functional knowledge, he takes a structural stance and claims that it is specifically this concept of the object that has paved the way for modern science. This article aims, first, to show that Cassirer's interpretation of Felix Klein's “Erlanger Programm” provided the impetus for this view. Then, it analyzes Kant's conception of objectivity (...) in order to examine whether Cassirer can rightfully claim that his view is a further development of transcendental principles. Finally, it is argued that it is Cassirer's concept of the object that enables him to integrate one decisive feature of scientific progress, namely, the increasinggeneralizationof the basic concepts of a science, into his conception of knowledge. This is illustrated in more detail through the example of the progression from Newton's mechanics to relativity theory. (shrink)

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 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.

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)

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)

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)

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.

Betrachtet man den Gebrauch der Worte ‘Moral’ und ‘Vernunft’ etwas genauer, so stellt man fest, dass nicht klar ist, was sie bezeichnen bzw. wie Moral und Vernunft zusammenhängen. In dem Buch ‘Rationalität in der Angewandten Ethik’, in dem sich verschiedene Autoren die Aufgabe gestellt haben, diese Umstände in das Licht der Betrachtung zu rücken, finden wir Fragen darüber, wie “Moral”, “Angewandte Ethik” und “Vernunft” (auch in der Anwendung) zu verstehen und zu vereinen sind.

Although not explicitly stated, Nobert Elias’s Civilizing Process provides a theoretical framework for Prolegomenon Toward a Primate Rights Bill. The core tenets of Elias’s work, including interdependency, habitus, and privatization, are common threads throughout the book. The book depicts a utopian ideal whereby the transformation in societal attitudes to nonhuman primates reaches a level wherein all primates come within the protection of the law. This will require the metamorphosis of attitudes and approaches, including state involvement and intervention, in order (...) to ensure the proposed bill of rights is enforced. Whether this will continue as an ideal or, in the future, form the basis of federal legislation akin to the European Convention on Human Rights or the Universal Declaration of Human Rights remains to be seen; nevertheless, the book raises some compelling arguments. (shrink)

A new type of formalization of classical first-order logic with equality is introduced on the basis of the sequent calculus. It serves to justify the claim that equality is a logical constant characterised by well-behaved rules satisfying properties usually regarded as essential. The main feature of this approach is the application of sequents built not only from formulae but also from terms. Two variants of sequent calculus are examined, a structural and a logical one. The former is defined in accordance (...) with Dos̆en’s criteria for logical constants. The latter is a standard Gentzen’s sequent calculus and satisfies Hacking’s criteria for logicality, including cut elimination. It is also shown that provided rules are harmonious in the sense advocated by Gratzl and Orlandelli. (shrink)

SummaryDiffraction gratings have contributed enormously to modern science. Although some historians have written about them, there is much more to be brought to light. This paper discusses their development and use in the period up to about 1880 before Rowland began to produce them. Rittenhouse described the action of a diffraction grating in 1786, but no explanation was possible until the wave theory of light was developed. Fraunhofer discovered the dark lines in the solar spectrum in 1814, and then investigated (...) diffraction, producing the first ruled gratings, making detailed measurements and calculating the wavelengths of prominent spectral lines. After Bunsen and Kirchhoff showed the association between spectral lines and chemical elements there was an upsurge of interest in measuring wavelengths. The gratings used in this work almost all came from one source, a relatively unknown instrument maker called Nobert, who made them by an extremely laborious process using a machine he had built himself. The most significant wavelength measurements were made by Ångström, but Mascart, Van der Willigen, Stefan, Ditscheiner and Cornu also did important work. Nobert gratings were investigated by Quincke, copied photographically by Rayleigh, and were known and discussed in the USA. Nobert's work helped to advance spectroscopy much more than has been acknowledged. (shrink)

After World War II, quite a few mathematicians, including Mark Kac, John von Neumann, and Nobert Wiener, worked on the physical problem of phase transitions, i.e. changes in the state of matter caused by gradual changes of physical parameters such as the condensation of a gas to a liquid and the loss of magnetization of a ferromagnet above a certain temperature. The significance of these mathematicians was not so much that they brought mathematical rigor to the theoretical description of (...) the phenomena,1 but that they applied their mathematical skills and tools to solve concrete mathematical problems encountered in the microscopic modeling of phase transitions. The present paper deals... (shrink)

In a interview concerning the Internet and cyberculture, communications professor Nobert Bolz was asked how he prepares his children for a world in which the authority of experts is in competition with emerging lay communities of knowledge production, such as Wikipedia. Bolz replied: “I try to constantly hammer in that they should read books. I just always say, read books, otherwise you'll belong to the losers. This is the only objective for educating my own children that I've given myself—with (...) only modest success.” With regard to his students, however, Bolz added: “On the other hand, when I see my own…. (shrink)

Im zweiten Buch seiner rechtstheologischen Summe De legibus ac Deo legislatore aus dem Jahre 1612 entwickelt Francisco Suárez seine Theorie des Naturrechts. Dabei gelingt Suárez die kritische Überarbeitung der lex-naturalis-Theorien des Augustinus und Thomas von Aquin und damit eine kritische Kontinuität mittelalterlicher Rechtstheologie. Suárez formuliert aber darüber hinaus eine für das frühe 17. Jahrhundert eigenständige Konzeption, die als innovatives Modell von Naturrecht mit den Entwürfen Hugo Grotius’ und Thomas Hobbes’ zu konkurrieren vermag. Die Einflüsse dieses genuin politisch-theologischen Naturrechtskonzepts reichen bis (...) zu Pufendorf und Wolff. Der Band erschließt diesen Schlüsseltext des frühneuzeitlichen Naturrechts im Sinne eine kooperativen Kommentars. Mit Beiträgen von Oliver Bach, Nobert Brieskorn, Simon Eultgen, Holger Glinka, Frank Grunert, Dominik Recknagel, Stefan Schweighöfer, Kurt Seelmann und Gideon Stiening. (shrink)

O artigo, num primeiro momento, busca contextualizar as condições de surgimento do ensaio Dois poemas de Friedrich Hölderlin, de Benjamin, recorrendo a alguns fatos históricos, como a morte de seu amigo Fritz Heinle e Nobert von Hellingrath. Ligadas ao estopim da Primeira Guerra Mundial, tais mortes representam para Benjamin a morte de toda uma geração de jovens, na qual ele havia depositado toda a esperança de renascimento da cultura alemã. A leitura que faz de Hölderlin, nesse sentido, tem um (...) fim político, ao procurar combater uma interpretação esteticizante de seus poemas, influenciada pelo círculo de Stefan George. Num segundo momento, o artigo aprofunda a leitura do ensaio de Benjamin sobre Hölderlin, buscando definir o conceito de “poetificado” como conceito central de sua crítica de arte, evidenciando em que medida esse conceito lhe serve como contraposição às leituras provenientes do círculo de George, entre elas, a do próprio Hellingrath. (shrink)