This paper presents a semantical analysis of the Weak Kleene Logics Kw3 and PWK from the tradition of Bochvar and Halldén. These are three-valued logics in which a formula takes the third value if at least one of its components does. The paper establishes two main results: a characterisation result for the relation of logical con- sequence in PWK – that is, we individuate necessary and sufficient conditions for a set.

A wide family of many-valued logics—for instance, those based on the weak Kleene algebra—includes a non-classical truth-value that is ‘contaminating’ in the sense that whenever the value is assigned to a formula φ⁠, any complex formula in which φ appears is assigned that value as well. In such systems, the contaminating value enjoys a wide range of interpretations, suggesting scenarios in which more than one of these interpretations are called for. This calls for an evaluation of systems with multiple contaminating (...) values. In this paper, we consider the countably infinite family of multiple-conclusion consequence relations in which classical logic is enriched with one or more contaminating values whose behavior is determined by a linear ordering between them. We consider some motivations and applications for such systems and provide general characterizations for all consequence relations in this family. Finally, we provide sequent calculi for a pair of four-valued logics including two linearly ordered contaminating values before defining two-sided sequent calculi corresponding to each of the infinite family of many-valued logics studied in this paper. (shrink)

This paper discusses three relevant logics that obey Component Homogeneity - a principle that Goddard and Routley introduce in their project of a logic of significance. The paper establishes two main results. First, it establishes a general characterization result for two families of logic that obey Component Homogeneity - that is, we provide a set of necessary and sufficient conditions for their consequence relations. From this, we derive characterization results for S*fde, dS*fde, crossS*fde. Second, the paper establishes complete sequent calculi (...) for S*fde, dS*fde, crossS*fde. Among the other accomplishments of the paper, we generalize the semantics from Bochvar, Hallden, Deutsch and Daniels, we provide a general recipe to define containment logics, we explore the single-premise/single-conclusion fragment of S*fde, dS*fde, crossS*fdeand the connections between crossS*fde and the logic Eq of equality by Epstein. Also, we present S*fde as a relevant logic of meaninglessness that follows the main philosophical tenets of Goddard and Routley, and we briefly examine three further systems that are closely related to our main logics. Finally, we discuss Routley's criticism to containment logic in light of our results, and overview some open issues. (shrink)

This volume presents recent advances in philosophical logic with chapters focusing on non-classical logics, including paraconsistent logics, substructural logics, modal logics of agency and other modal logics. The authors cover themes such as the knowability paradox, tableaux and sequent calculi, natural deduction, definite descriptions, identity, truth, dialetheism and possible worlds semantics. The developments presented here focus on challenging problems in the specification of fundamental philosophical notions, as well as presenting new techniques and tools, thereby contributing to the development of the (...) field. Each chapter contains a bibliography, to assist the reader in making connections in the specific areas covered. Thus this work provides both a starting point for further investigations into philosophical logic and an update on advances, techniques and applications in a dynamic field. The chapters originate from papers presented during the Trends in Logic XI conference at the Ruhr University Bochum, June 2012. (shrink)

The book is divided into three parts. The first, containing three papers, focuses on the characterization of the central tenets of previii sentism (by Neil McKinnon) and eternalism (by Samuel Baron and Kristie Miller), and on the ‘sceptical stance’ (by Ulrich Meyer), a view to the effect that there is no substantial difference between presentism and eternalism. The second and main section of the book contains three pairs of papers that bring the main problems with presentism to the fore and (...) outlines its defence strategy. Each pair of papers in this section can be read as a discussion between presentists and eternalists, wherein each directly responds to the arguments and objections offered by the other. This is a discussion that is sometimes absent in the literature, or which is at best carried out in a fragmented way. The first two papers of the section deal with the problem of the compatibility of Special Relativity Theory (SRT) and presentism. SRT is often considered to be a theory that contradicts the main tenet of presentism, thereby rendering presentism at odds with one of our most solid scientific theories. Christian Wüthrich’s paper presents arguments for the incompatibility of the two theories (SRT and presentism) within a new framework that includes a discussion of further complications arising from the theory of Qauantum Mechanics. Jonathan Lowe’s paper, by contrast, develops new general arguments against the incompatibility thesis and replies to Wüthrich’s paper. The second pair of papers focuses on the problem that presentists face, in providing grounds for past tensed truths. In the first (by Matthew Davidson), new arguments are provided to defend the idea that the presentist cannot adequately explain how what is now true about the past is grounded, since for the presentist the past is completely devoid of ontological ground. The second paper (by Brian Kierland) takes up the challenge of developing a presentist explanation of past truths, beginning by outlining some existing views in the literature before advancing an original proposal. (shrink)

Logics based on weak Kleene algebra (WKA) and related structures have been recently proposed as a tool for reasoning about flaws in computer programs. The key element of this proposal is the presence, in WKA and related structures, of a non-classical truth-value that is “contaminating” in the sense that whenever the value is assigned to a formula ϕ, any complex formula in which ϕ appears is assigned that value as well. Under such interpretations, the contaminating states represent occurrences of a (...) flaw. However, since different programs and machines can interact with (or be nested into) one another, we need to account for different kind of errors, and this calls for an evaluation of systems with multiple contaminating values. In this paper, we make steps toward these evaluation systems by considering two logics, HYB1 and HYB2, whose semantic interpretations account for two contaminating values beside classical values 0 and 1. In particular, we provide two main formal contributions. First, we give a characterization of their relations of (multiple-conclusion) logical consequence—that is, necessary and sufficient conditions for a set Δ of formulas to logically follow from a set Γ of formulas in HYB1 or HYB2 . Second, we provide sound and complete sequent calculi for the two logics. (shrink)

In this paper we present BTC, which is a complete logic for branchingtime whose modal operator quantifies over histories and whose temporal operators involve a restricted quantification over histories in a given possible choice. This is a technical novelty, since the operators of the usual logics for branching-time such as CTL express an unrestricted quantification over histories and moments. The value of the apparatus we introduce is connected to those logics of agency that are interpreted on branching-time, as for instance (...) Stit Logics. (shrink)

Supervaluationism holds that the future is undetermined, and as a consequence of this, statements about the future may be neither true nor false. In the present paper, we explore the novel and quite different view that the future is abundant: statements about the future do not lack truth-value, but may instead be glutty, that is both true and false. We will show that (1) the logic resulting from this “abundance of the future” is a non-adjunctive paraconsistent formalism based on subvaluations, (...) which has the virtue that all classical laws are valid in it, while no formula like φ ∧ ¬φ is satisfiable (though both φ and ¬φ may be true in a model); (2) The peculiar behaviour of abundant logical consequence has an illuminating analogy in probability logic; (3) abundance preserves some important features of classical logic (not preserved in supervaluationism) when it comes to express those important retrogradations of truth which are presupposed by the argument de praesenti ad praeteritum. (shrink)

In this paper, we use a ‘normality operator’ in order to generate logics of formal inconsistency and logics of formal undeterminedness from any subclassical many-valued logic that enjoys a truth-functional semantics. Normality operators express, in any many-valued logic, that a given formula has a classical truth value. In the first part of the paper we provide some setup and focus on many-valued logics that satisfy some of the three properties, namely subclassicality and two properties that we call fixed-point negation property (...) and conservativeness. In the second part of the paper, we introduce normality operators and explore their formal behaviour. In the third and final part of the paper, we establish a number of classical recapture results for systems of formal inconsistency and formal undeterminedness that satisfy some or all the properties above. These are the main formal results of the paper. Also, we illustrate concrete cases of recapture by discussing the logics $\mathsf{K}^{\circledast }_{3}$, $\mathsf{LP}^{\circledast }$, $\mathsf{K}^{w\circledast }_{3}$, $\mathsf{PWK}^{\circledast }$ and $\mathsf{E_{fde}}^{\circledast }$, that are in turn extensions of $\mathsf{{K}_{3}}$, $\mathsf{LP}$, $\mathsf{K}^{w}_{3}$, $\mathsf{PWK}$ and $\mathsf{E_{fde}}$, respectively. (shrink)

The problem of future contingents is one of the most ancient and debated puzzles in Western philosophy, and Supervaluationism is, today, one of the most prominent solutions to the problem. Recently, John MacFarlane has carried a well-known criticism to Supervaluationism and put forward a new solution of the problem of future contingents, which is known as Double Time Reference Theory. Here, we compare DTRT with Supervaluationist semantics, and we show that the success of MacFarlane's criticism crucially depends on the expressivity (...) of the language adopted. Once a reasonable expressive power is granted, however, MacFarlane's criticism no longer applies. (shrink)

In this paper, we extend the expressive power of the logics K3, LP and FDE with anormality operator, which is able to express whether a for-mula is assigned a classical truth value or not. We then establish classical recapture theorems for the resulting logics. Finally, we compare the approach via normality operator with the classical collapse approach devisedby Jc Beall.

This paper makes first steps toward a systematic investigation of how pertinence to topic contributes to determine deductively valid reasoning along with preservation of designated values. I start from the interpretation of Weak Kleene Logic WKL as a reasoning tool that preserves truth and topic pertinence, which is offered by Jc Beall. I keep Beall’s motivations and I argue that WKL cannot meet them in a satisfying way. In light of this, I propose an informal definition of a topic-sensitive logic (...) and I proceed to turn it into a formal one by deploying the topic-algebraic framework from the Topic-Sensitive Intentional Modalities project by Francesco Berto. I apply the framework in order to define semantically a ‘classical topic-sensitive logic’ CTSL that meets Beall’s motivations and proves topic-sensitive. Then, I prove results that connect CTSL and any possible topic-sensitive logic to the tradition of containment logics and provide a unification tool for a wide range of recent proposals in philosophical logic. A topic-theoretical interpretation of WKL is then offered without prejudice to the fact that the logic is not topic-sensitive. Finally, the paper discusses some conceptual issues and research perspectives. (shrink)

L’esistenza non è logica è un libro estremamente interessante e di grande qualità, e Francesco Berto ha il pregio di accostare un’esposizione sempre accessibile alla solidità teorica della sua proposta e alla padronanza dei temi che affronta. Il titolo riassume una delle idee principali del volume: l’esistenza è una proprietà, e – soprattutto – è una proprietà che non va definita in termini di una nozione logica come – per esempio – quella espressa dal quantificatore esistenziale. Nel libro,...

Temporal aspects dwell both in the world around us and at the core of our experience of it. Reality, thought, and language all seem to be imbibed in temporality at some level or another. It is thus not surprising that philosophers who have to face the problems of understanding time have resorted to tools from different spheres of investigation, and often at the points of overlap of these areas. Metaphysics, philosophy of physics and science in general, philosophy of language, phenomenology, (...) philosophy of mind, the study of perception and cognition, but also anthropology, sociology, and history of culture, art, and ideas all contain theories and reflections that are crucial to our understanding and experience of time. Many recent debates in analytic philosophy have tackled in different ways the question of whether the sensation of the passage of time that seems to characterise our ordinary experience should be understood as reflecting some obje .. (shrink)

In this paper, we discuss the notion of inevitable ignorance that the Italian Constitutional Court has introduced in justifying a restriction of the legal maxim Ignorantia legis non excusat. In particular, we argue that the epistemic flavor of the notion extends to the notion of inevitability beside that of ignorance, and we offer an epistemic analysis of the notion. This analysis is based both on the legal-theoretical framework defined by the justification of the restriction of the maxim, and on a (...) discussion of some paradigmatic Italian cases where the standard of excusability involving inevitable ignorance is applied. The analysis reveals that the notion of inevitable ignorance is closely connected to a number of notions also used in formal epistemology, such as belief, evidence, rationality, and trust. (shrink)

The paper introduces a probabilistic semantics for the paraconsistent temporal logic Ab presented by the authors in a previous work on future contingents. Probabilistic concepts help framing two possible interpretations of the logic in question - a `subjective' and an `objective' one - and explaining the rationale behind both of them. We also sketch a proof-method for Ab and address some considerations regarding the conceptual appeal of our proposal and its possible future developments.

In this paper, we approach the problem of classical recapture for LP and K3 by using normality operators. These generalize the consistency and determinedness operators from Logics of Formal Inconsistency and Underterminedness, by expressing, in any many-valued logic, that a given formula has a classical truth value (0 or 1). In particular, in the rst part of the paper we introduce the logics LPe and Ke3 , which extends LP and K3 with normality operators, and we establish a classical recapture (...) result based on the two logics. In the second part of the paper, we compare the approach in terms of normality operators with an established approach to classical recapture, namely minimal inconsistency. Finally, we discuss technical issues connecting LPe and Ke3 to the tradition of Logics of Formal Inconsistency and Underterminedness. (shrink)

Supervaluationism holds that the future is undetermined, and as a consequence of this, statements about the future may be neither true nor false. In the present paper, we explore the novel and quite different view that the future is abundant: statements about the future do not lack truth-value, but may instead be glutty, that is both true and false. We will show that the logic resulting from this “abundance of the future” is a non-adjunctive paraconsistent formalism based on subvaluations, which (...) has the virtue that all classical laws are valid in it, while no formula like φ ∧ ¬φ is satisfiable ; The peculiar behaviour of abundant logical consequence has an illuminating analogy in probability logic; abundance preserves some important features of classical logic when it comes to express those important retrogradations of truth which are presupposed by the argument de praesenti ad praeteritum. (shrink)

Introduction -- Inquiry as the logic of practical reasoning -- From reasoning to judgment -- Expressive inquiry -- The public sphere -- Pragmatism, pluralism, and the fact of relativism -- A pragmatic theory of objectivity -- Why justification matters? -- Pragmatism as an epistemology of practice.

El artículo analiza el vínculo entre derecho y violencia en Walter Benjamin y Franz Rosenzweig. Primero, se estudia la relación entre Benjamin, Rosenzweig y Carl Schmitt, y, a continuación, la proximidad entre las concepciones benjaminiana y rosenzweiguiana de la historia y de la temporalidad mesiánica, así como la relación entre justicia, derecho y eternidad. Finalmente, se presenta la propuesta derridiana de una deconstrucción de la crítica benjaminiana de la violencia y su antecedente en _La estrella de la redención_.

In this article I examine the main conceptions of public reason in contemporary political philosophy in order to set the frame for appreciating the novelty of the pragmatist understanding of public reason as based upon the notion of consequences and upon a theory of rationality as inquiry. The approach is inspired by Dewey but is free from any concern with history of philosophy. The aim is to propose a different understanding of the nature of public reason aimed at overcoming the (...) limitations of the existing approaches. Public reason is presented as the proper basis for discussing contested issues in the broad frame of deep democracy. (shrink)

I examine some accounts that articulate the content of perception that occurs by means of a mirror. The defended account entails that a right hand seen in the mirror does not "become" a left hand.

From Antiquity to the 19th century it was very common to explain natural phenomena (especially biological ones) through final causes. This paper analyses one of the periods of development of this concept, in Antiquity, with special emphasis upon the contributions of Socrates and Plato. They introduced the idea of an intelligent and beneficial god, who plans the structure of the universe and of all beings in the best possible way. This concept was strongly influential in later periods. RESUMO: Da Antiguidade (...) até o século XIX foi muito comum procurar-se entender os fenômenos naturais (especialmente os biológicos) através de causas finais. Este artigo analisa um dos períodos de formação dessas concepções, na Antiguidade, dando especial atenção às contribuições de Sócrates e Platão. Estes introduzem a ideia de uma divindade inteligente e bondosa, que planeja a estrutura do universo e de todos os seres da melhor forma possível. Essa concepção teve grande influência, no período posterior. (shrink)

O conceito de pseudo-ciência procura identificar propostas que têm uma aparência científica mas que não satisfazem critérios rigorosos de cientificidade. Alguns exemplos muito citados de pseudo-fenômenos estão os fatos alegados pela parapsicologia e pela astrologia. Para caracterizar a pseudo-ciência alguns autores propuseram critérios psicológicos, sociológicos ou metodológicos. O objetivo básico de uma caracterização metodológica dos pseudo-fenômenos é permitir identificar aquilo que parece existir, mas não existe. Trata-se, portanto, de uma distinção essencialmente ontológica. Este trabalho irá descrever várias tentativas de estabelecer (...) critérios desse tipo e mostrará que nenhuma delas é satisfatória. Será apresentada uma abordagem alternativa, compatível com o caráter provisório do conhecimento científico, que permite avaliar a proposta de existência de um novo fenômeno e guiar a pesquisa, sem no entanto permitir concluir se o fenômeno existe ou não. (shrink)

Any formalization of legal texts requires not only a syntactical and semantical analysis, but also a pragmatical approach. There are some difficulties in the formalization of legal pragmatics. Legal theory acknowledges that legal languages are contaminated with value expressions and their ideological linguistic context. The theoretical categories introduced by legal scientist according to traditional, but also culturally variable criteria, are necessary for the construction of legal text (in their prescriptive version), but nearly always they are implicitly used and not explicitly (...) mentioned. Kelsenian and Hohfeldian categories are exempIes of not equivalent classificatory criteria. The problem, for any attempted automated analysis of legal languages, is also how to introduce in the logical and algorithmic schemes used in computation, symbolic eIements taking into account those not explicit categorial-forms. (shrink)

Este artículo trata sobre los horizontes de la eficacia histórica y la comprensión en la fenomenología de Husserl. El autor comienza considerando el marco que ofrece el análisis de Gadamer de los tres modos de llegar a un acuerdo con las tradiciones, es decir, la metodología generalizadora, la conciencia histórica singularizadora, y la exposición de la conciencia efectiva de la historia. A continuación pasa a describir cómo Husserl se basa en las ideas de Dilthey, y argumenta que el punto principal (...) de partida se encuentra en el concepto de nexo de eficacia. Por último, se realiza un intento por mostrar el punto de vista de Husserl sobre los tres niveles en el camino hacia la experiencia hermenéutica. Se recuerda que Gadamer se refiere a una línea clara que va desde los conceptos de la síntesis pasiva y la intencionalidad anónima hasta la experiencia hermenéutica. Al examinar lo que está involucrado en los horizontes de la eficacia, los horizontes de comprensión, las tipicidades de acceso, las fusiones de mundos familiares y extraños, y los movimientos en zigzag a lo largo de las tradiciones, el trabajo concluye que Husserl se ha preocupado mucho por la noción de una conciencia expuesta ante la eficacia de la historia. This paper deals with the horizons of historical effectiveness and understanding in Husserl’s phenomenology. The author begins by considering the framework afforded by Gadamer’s analyses of the three modes of coming to terms with traditions, i.e., generalizing methodology, singularizing historical consciousness, and exposure of consciousness to effective-history. He then goes on to outline how Husserl draws on Dilthey’s ideas, and argues that a main point of departure is to be found in the notion of nexus of effectiveness. Finally, an attempt is made to show Husserl’s views on the three levels in the way to hermeneutic experience. It is recalled that Gadamer refers to a clear line that leads from the concepts of pasive synthesis and anonymous intentionality to hermeneutic experience. By examining what is involved in horizons of effectiveness, horizons of understanding, access-typicalities, fusions of homeworlds and alienworlds, and zigzag movements throughout traditions, the paper concludes that Husserl has concerned himself a great deal with the notion of a consciousness exposed to the effectiveness of history. (shrink)

O "Plano para o `Sistema de filosofia fenomenológica' de Edmund Husserl" inclui uma fenomenologia da proto-intencionalidade que, ao mesmo tempo, compreende os proto-impulsos, o inconsciente e a associação como temas de uma fenomenologia progressiva. Enquanto a fenomenologia regressiva parte do dado com o fim de realizar uma análise desconstrutiva, este tipo alternativo de fenomenologia implica uma análise construtiva em relação com o que não é dado na intuição. O artigo procura desenvolver essas questões em quatro passos, seguindo um fio condutor (...) proporcionado pela noção de tensão. Em primeiro lugar, considera-se a fusão associativa enquanto implica uma tensão no sujeito e dá lugar à constituição de objetos. Em segundo lugar, mostram-se as raízes da tensão numa intencionalidade instintiva. Em terceiro lugar, examina-se a relação entre instinto e protogeneratividade. Em quarto lugar, coloca-se em relevo a significação desses temas para as noções de patência e latência. Por último, intenta-se vincular os conceitos husserlianos de tensão e intencionalidade com as noções heideggerianas de carga e ser-no-mundo.El "Plan para el `Sistema de filosofía fenomenológica' de Edmund Husserl" incluye una fenomenología de la protointencionalidad que a su vez comprende los protoimpulsos, lo inconsciente y la asociación como temas de una fenomenología progresiva. Mientras que la fenomenología regresiva parte de lo dado a fin de realizar un análisis desconstructivo, este tipo alternativo de fenomenología implica un análisis constructivo en relación con lo que no es dado en la intuición. El artículo procura desarrollar estas cuestiones en cuatro pasos, siguiendo un hilo conductor proporcionado por la noción de tensión. En primer lugar, se considera la fusión asociativa en tanto implica una tensión en el sujeto y da lugar a la constitución de objetos. En segundo lugar, se muestran las raíces de la tensión en una intencionalidad instintiva. En tercer lugar, se examina la relación entre instinto y protogeneratividad. En cuarto lugar, se pone de relieve la significación de estos temas para las nociones de patencia y latencia. Por último, se intenta vincular los conceptos husserlianos de tensión e intencionalidad con las nociones heideggerianas de carga y ser-en-el-mundo.The "Plan for Edmund Husserl's `System of Phenomenological Philosophy'" encompasses a phenomenology of primal intentionality that in turn comprises primal impulses, the unconscious and association as themes of a progressive phenomenology. Whereas regressive phenomenology starts from the given in order to accomplish a deconstructive analysis, this alternative type of phenomenology entails a constructive analysis with regard to what is not given in intuition. The article attempts to develop these problems in four steps following a main thread afforded by the notion of tension. First, associative fusion is considered insofar as it implies a tension in the subject and brings forth the genesis of objects. Secondly, the roots of tension in an instinctive intentionality are shown. Thirdly, the relationship between instinct and primal generativity is examined. Fourthly, the import of these themes for the notions of patency and latency is disclosed. Finally, an attempt is made to link the Husserlian concepts of tension and intentionality to the Heideggerian notions of burden and being-in-the-world. (shrink)

A first aspect has to do with the non-intentional and primal praxis of the living body. To this is added its status as a support for the sensuous values of comfort and health and a springboard for spiritual values, the highest level of which lies in the ethical values of the person. These Husserlian views find new developments in phenomenology: M. Henry highlights a pre-intentional “I can”, M. Scheler analyzes the relationship between hedonistic, vital, and spiritual values, and P. Ricoeur (...) describes the living body both as the “source” of its own proper values and the “affective resonator” of all values, and also outlines a view on happiness that encompasses particular bodily attunements. Finally, Husserl considers the offering of the living body to spiritual values in sacrifice as the positive assertion of humankind’s life. J. Patočka and E. Levinas have developed this line of thought. (shrink)