Paraconsistent Weak Kleene logic is the 3-valued logic with two designated values defined through the weak Kleene tables. This paper is a first attempt to investigate PWK within the perspective and methods of abstract algebraic logic. We give a Hilbert-style system for PWK and prove a normal form theorem. We examine some algebraic structures for PWK, called involutive bisemilattices, showing that they are distributive as bisemilattices and that they form a variety, \, generated by the 3-element algebra WK; we also (...) prove that every involutive bisemilattice is representable as the Płonka sum over a direct system of Boolean algebras. We then study PWK from the viewpoint of AAL. We show that \ is not the equivalent algebraic semantics of any algebraisable logic and that PWK is neither protoalgebraic nor selfextensional, not assertional, but it is truth-equational. We fully characterise the deductive filters of PWK on members of \ and the reduced matrix models of PWK. Finally, we investigate PWK with the methods of second-order AAL—we describe the class \ of PWK-algebras, algebra reducts of basic full generalised matrix models of PWK, showing that they coincide with the quasivariety generated by WK—which differs from \—and explicitly providing a quasiequational basis for it. (shrink)

The paper studies the containment companion of a logic \. This consists of the consequence relation \ which satisfies all the inferences of \, where the variables of the conclusion are contained into those of the set of premises, in case this is not inconsistent. In accordance with the work started in [10], we show that a different generalization of the Płonka sum construction, adapted from algebras to logical matrices, allows to provide a matrix-based semantics for containment logics. In particular, (...) we provide an appropriate completeness theorem for a wide family of containment logics, and we show how to produce a complete Hilbert style axiomatization. (shrink)

We establish a duality between the category of involutive bisemilattices and the category of semilattice inverse systems of Stone spaces, using Stone duality from one side and the representation of involutive bisemilattices as Płonka sum of Boolean algebras, from the other. Furthermore, we show that the dual space of an involutive bisemilattice can be viewed as a GR space with involution, a generalization of the spaces introduced by Gierz and Romanowska equipped with an involution as additional operation.

Płonka sums consist of an algebraic construction similar, in some sense, to direct limits, which allows to represent classes of algebras defined by means of regular identities. Recently, Płonka sums have been connected to logic, as they provide algebraic semantics to logics obtained by imposing a syntactic filter to given logics. In this paper, I present a very general topological duality for classes of algebras admitting a Płonka sum representation in terms of dualisable algebras.

In the logical context, ignorance is traditionally defined recurring to epistemic logic. In particular, ignorance is essentially interpreted as “lack of knowledge”. This received view has - as we point out - some problems, in particular we will highlight how it does not allow to express a type of content-theoretic ignorance, i.e. an ignorance of φ that stems from an unfamiliarity with its meaning. Contrarily to this trend, in this paper, we introduce and investigate a modal logic having a primitive (...) epistemic operator I, modeling ignorance. Our modal logic is essentially constructed on the modal logics based on weak Kleene three-valued logic introduced by Segerberg (Theoria, 33(1):53–71, 1997). Such non-classical propositional basis allows to define a Kripke-style semantics with the following, very intuitive, interpretation: a formula φ is ignored by an agent if φ is neither true nor false in every world accessible to the agent. As a consequence of this choice, we obtain a type of content-theoretic notion of ignorance, which is essentially different from the traditional approach. We dub it severe ignorance. We axiomatize, prove completeness and decidability for the logic of reflexive (three-valued) Kripke frames, which we find the most suitable candidate for our novel proposal and, finally, compare our approach with the most traditional one. (shrink)

According to the so-called Lockean thesis, a rational agent believes a proposition just in case its probability is sufficiently high, i.e., greater than some suitably fixed threshold. The Preface paradox is usually taken to show that the Lockean thesis is untenable, if one also assumes that rational agents should believe the conjunction of their own beliefs: high probability and rational belief are in a sense incompatible. In this paper, we show that this is not the case in general. More precisely, (...) we consider two methods of computing how probable must each of a series of propositions be in order to rationally believe their conjunction under the Lockean thesis. The price one has to pay for the proposed solutions to the paradox is what we call “quasi-dogmatism”: the view that a rational agent should believe only those propositions which are “nearly certain” in a suitably defined sense. (shrink)

How we can reliably draw inferences from data, evidence and/or experience has been and continues to be a pressing question in everyday life, the sciences, politics and a number of branches in philosophy (traditional epistemology, social epistemology, formal epistemology, logic and philosophy of the sciences). In a world in which we can now longer fully rely on our experiences, interlocutors, measurement instruments, data collection and storage systems and even news outlets to draw reliable inferences, the issue becomes even more pressing. (...) While we were working on this question using a formal epistemology approach Landes and Osimani (2020); De Pretis et al. (2019); Osimani and Landes (2020); Osimani (2020), we realised that the width of current active interests in the notion of reliability was much broader than we initially thought. Given the breadth of approaches and angles present in philosophy (even in this journal Schubert 2012; Avigad 2021; Claveau and Grenier 2019; Kummerfeld and Danks 2014; Landes 2021; Trpin et al. 2021; Schippers 2014; Schindler 2011; Kelly et al. 2016; Mayo-Wilson 2014; Olsson and Schubert 2007; Pittard 2017), we thought that it would be beneficial to provide a forum for an open exchange of ideas, in which philosophers working in different paradigms could come together. Our call for expression of interest received a great variety of promised manuscripts, the variety is reflected in the published papers. They range from fields far away from our own interests such as quantum probabilities de Ronde et al. (2021), evolvable software systems Primiero et al. (2021), to topics closer to our own research in the philosophy of medicine Lalumera et al. (2020), psychology Dutilh et al. (2021), traditional epistemology Dunn (2021); Tolly (2021) to finally close shared interests in formal epistemology Romero and Sprenger (2021) even within our own department Merdes et al. (2021). Our job is now to reliably inform you about all the contributions in the papers in this special issue. Unfortunately, that task is beyond our capabilities. What we can and instead do is to summarise the contributed papers to inform your reliable inference to read them all in great detail. (shrink)

In this contribution we will present a generalization of de Finetti's betting game in which a gambler is allowed to buy and sell unknown events' betting odds from more than one bookmaker. In such a framework, the sole coherence of the books the gambler can play with is not sucient, as in the original de Finetti's frame, to bar the gambler from a sure-win opportunity. The notion of joint coherence which we will introduce in this paper characterizes those coherent books (...) on which sure- win is impossible. Our main results provide geometric characterizations of the space of all books which are jointly coherent with a xed one. As a consequence we will also show that joint coherence is decidable. (shrink)

In this paper we propose a semantic analysis of Lewis' counterfactuals. By exploiting the structural properties of the recently introduced boolean algebras of conditionals, we show that counterfactuals can be expressed as formal combinations of a conditional object and a normal necessity modal operator. Specifically, we introduce a class of algebras that serve as modal expansions of boolean algebras of conditionals, together with their dual relational structures. Moreover, we show that Lewis' semantics based on sphere models can be reconstructed in (...) this framework. As a consequence, we establish the soundness and completeness of a slightly stronger variant of Lewis' logic for counterfactuals with respect to our algebraic models. In the second part of the paper, we present a novel approach to the probability of counterfactuals showing that it aligns with the uncertainty degree assigned by a belief function, as per Dempster-Shafer theory, to its associated conditional formula. Furthermore, we characterize the probability of a counterfactual in terms of Gärdenfors' imaging rule for the probabilistic update. (shrink)

Individuating the logic of scientific discovery appears a hopeless enterprise. Less hopeless is trying to figure out a logical way to model the epistemic attitude distinguishing the practice of scientists. In this paper, we claim that classical logic cannot play such a descriptive role. We propose, instead, one of the three-valued logics in the Kleene family that is often classified as the less attractive one, namely Hallden’s logic. By providing it with an appropriate epistemic interpretation, we can informally model the (...) scientific attitude. (shrink)

The aim of the paper is to shed light on some of the most original elements of Fichte’s conception of morality as expressed in his account of specific obligations. After some remarks on Fichte’s original classification of ethical duties, the paper focuses on the prohibition of lying, the duty to communicate our true knowledge, and the duty to set a good example. Fichte’s account of those duties not only goes beyond the mere justification of universally acknowledged demands, but also deploys (...) different arguments than his contemporaries, most notably Kant. Fichte thereby sketches a conception of morality in which the agent is crucially required to contribute to the morality of others. The chapter explores the contrast between Fichte’s view and Kant’s thought of an end in itself and suggests that Fichte’s view of morality amounts to a form of normative perfectionism that is qualified by the underlying claim of the agent-neutral character of moral demands. (shrink)

The paper aims at studying, in full generality, logics defined by imposing a variable inclusion condition on a given logic \. We prove that the description of the algebraic counterpart of the left variable inclusion companion of a given logic \ is related to the construction of Płonka sums of the matrix models of \. This observation allows to obtain a Hilbert-style axiomatization of the logics of left variable inclusion, to describe the structure of their reduced models, and to locate (...) them in the Leibniz hierarchy. (shrink)

My chapter deals with an important part of how Wolff pursued the normative ambitions of his ethics in giving practical guidance with regard to specific moral issues. I first consider how Wolff’s ethics tackles the duties to others, which traditionally represent a difficult issue for moral perfectionism. In this regard, I argue that Wolff’s strategy combines two aspects: (a) he includes in perfection non-active aspects and (b) operates with an agent-neutral notion of perfection, in spite of important passages that might (...) suggest differently. I then focus on Wolff’s treatment of the duties concerning veracity and lying, and show how it follows that general strategy. Combining its two aspects, Wolff examines specific moral issues by adopting a non-welfarist notion of benefit and harm as the standard that can give guidance about practical cases. (shrink)

I present a novel explanation of the apparent truth of certain remarks about fiction, such as an utterance of ''Salieri commissioned the Requiem'' during a discussion of the movie Amadeus. I criticize the traditional view, which alleges that the uttered sentence abbreviates the longer sentence ''it is true in the movie Amadeus that Salieri commissioned the Requiem''. I propose a solution which appeals to some independently motivated results concerning the contexts relevant for the semantic evaluation of indexical expressions.

The concern of this book is to see whether the phenomenological effervescence of politics is still possible to retrace the nucleolus of the political in its archetypical form.

This book argues against the widely celebrated utopia of -transparency- by showing, across a panorama of postwar French thought, how attempts to show the perils of transparency in politics, ethics, and knowledge led to major conceptual inventions, many of which we now take for granted.

Die vorliegende Arbeit zielt darauf ab, Momente der Husserlschen Phänomenologie hervorzuheben, in denen diese an ihre Grenzen stößt. Der Ausweis dieser Grenzphänomene, die in der Husserl-Literatur bisher noch nicht systematisch untersucht worden sind, steht im Zentrum der Arbeit. Der Autor hat sich systematisch mit phänomenologisch orientierten Autoren zeitgenössischer Philosophie auseinandergesetzt u. a. mit der Absicht, die Fruchtbarkeit der Husserlschen Analysen für die zeitgenössische Philosophie hervorzuheben.

Die Epitome physica des Nikephoros Blemmydes (1197 – nach 1269) gilt als eines der meistverbreiteten Lehrbücher aristotelischer Naturphilosophie in der byzantinischen und nachbyzantinischen Welt. Dennoch blieb die handschriftliche Überlieferung bisher gänzlich unerforscht und der Text wurde nie in Form einer kritischen Edition zugänglich gemacht. Die Epitome physica stellt das zweite Buch der Εἰσαγωγικὴ ἐπιτομή (Einführendes Kompendium) dar, deren erstes Buch der Logik gewidmet ist. Als Grundlage dienten Blemmydes im Wesentlichen Aristoteles und seine Kommentatoren (sowie für den astronomischen Teil den Stoiker (...) Kleomedes), wobei er versuchte, eine Synthese der antiken Naturphilosophie mit der christlichen Weltanschauung zu erreichen. Von den über 120 erhaltenen Manuskripten der Epitome, die vom 13. bis ins 19 Jh. datieren, werden im vorliegenden Buch die Handschriften aus der Palaiologenzeit sowie die Mehrheit derjenigen aus der Renaissance manuskriptologisch und philologisch untersucht sowie ihre textgeschichtlichen Beziehungen rekonstruiert. Daneben kommen auch die Verbreitung und der kulturelle Stellenwert der Epitome physica in der byzantinischen Welt und in der europäischen Renaissance zur Darstellung. (shrink)

1. Sviluppi critici della fenomenologia.--2. Fenomenologia e sapere scientifico.

The five-volume set Kant and Philosophy in a Cosmopolitan Sense contains the proceedings of the Eleventh International Kant Congress, which took place in Pisa in 2010. The proceedings consist of 25 plenary talks and 341 papers selected by a team of international referees from over 700 submissions. The contributions span 14 sections: Kant’s Concept of Philosophy; Theory of Cognition and Logic; Ontology and Metaphysics; Ethics; Law and Justice; Religion and Theology; Aesthetics; Anthropology and Psychology; Politics and History; Science, Mathematics, and (...) the Philosophy of Nature; Kant and the Leibnizian Tradition; Kant and the Philosophical Tradition; Kant and Schopenhauer; and Kant’s Heritage. Thanks to cooperation from the Schopenhauer Gesellschaft, the 2010 conference was the first in the history of the International Kant Congress to include a session on Kant and Schopenhauer. -/- . (shrink)

The set of unary functions of complexity classes defined by using bounded primitive recursion is inductively characterized by means of bounded iteration. Elementary unary functions, linear space computable unary functions and polynomial space computable unary functions are then inductively characterized using only composition and bounded iteration.