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 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.

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)

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)

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)

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.

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)

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)

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)

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)

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)

In this article Roberto Balzani, the mayor of Forlì, remembers Roberto Ruffilli, 25 years after his murder. The remembrance reconstructs the steps of his academic career and of his political commitment. Ruffilli graduated at the Catholic University of Milan; his researches in contemporary history placed him in an original position if compared with the Italian studies of the time. The constant attention towards the history of administration and the transformations of the state is the basis on which Ruffilli (...) built his proposals concerning the reform of the insitutional and political system. Balzani concludes the article by affirming that the problems of today aren't any different, that is why Ruffilli's proposals still demonstrate their modernity. (shrink)

The book reviewed here, Roberto Frega’s Practice, Judgment, and the Challenge of Moral and Political Disagreement, is an important and ambitious book. It is ambitious because it addresses the problems at stake in contemporary philosophical debates without any kind of awkwardness and shyness. Frega believes pragmatism to be a theoretically viable option, and tries to prove its soundness by adopting it as the conceptual framework of a theory of moral objectivity alternative to the ones formulat...

The subject of this paper is objectivity from Kant's point of view: or better, my own perspective on Kant's perspective on objectivity. More precisely, I want to draw attention to some aspects of the latter, which I believe are too narrow and must be widened before we can benefit from a Kantian approach today.

A discussion with Roberto Andorno about global bioethics and biolaw, the Coronavirus pandemic, and its impact on human dignity and rights. Can we foresee the emerging new profile of global bioethics and biolaw in the post-Coronavirus era? How significant are they going to be in the future, after the enormous pressure that the Coronavirus pandemic has exercised on key political, legal, and ethical values? Must the voice of bioethicists -compared to the ‘hard’ scientific data- be louder in the future (...) concerning decisions about emergency social and medical measures? Is there a hope that public empowerment will support robust, global public engagement and meaningful deliberation? How much does Roberto Andorno’s view on human dignity reveal a supposed commitment to moral realism? The massive deaths of elderly people living in hospices of Sweden, Spain, and Italy, based on an implicit ‘fair innings’ view, has recently posed certain questions on the moral unacceptability of such practices. The same questions arise in the case of the legalization of euthanasia grounded on the implicit acceptance of the view that life is not worth living under certain circumstances. Is it possible that the human rights bodies worldwide will acquire executive power, and how could this become possible? How influential the ‘precautionary principle’ can become regarding clinical and research ethics in the future? How urgent is the importance of the introduction of bioethical education in the curricula of ‘hard’ empirical studies? Roberto Andorno discusses with us all these controversial and under heated public debate issues, giving sometimes provocative answers. (shrink)

Fr. Roberto Busa was an Italian Jesuit. In this article his biography will briefly be presented, and some issues raised by his philosophy analyzed. Busa was known as a pioneer of computerized research in the humanities. With the support of IBM he constructed the Index Thomisticus, containing all the works of St. Thomas Aquinas. He believed that expressions of the human can be mathematically modeled. He was the originator of a specific conception of hypertext, in which logically structured programs (...) are able to challenge the general linguistic mode of thinking, in order to make better communication and understanding possible. However, Busa was also con- scious of the general ethical problems involved (Babel), and he hoped that the basic logic of objects could progress towards the truth of being. (shrink)

Roberto Esposito is one of the most prolific and important exponents of contemporary Italian political theory.

This book by Roberto Esposito - a leading Italian political philosopher - is a highly original exploration of the relationship between human bodies and societies. The original function of law, even before it was codified, was to preserve peaceful cohabitation between people who were exposed to the risk of destructive conflict. Just as the human body's immune system protects the organism from deadly incursions by viruses and other threats, law also ensures the survival of the community in a life-threatening (...) situation. It protects and prolongs life. But the function of law as a form of immunization points to a more disturbing consideration. Like the individual body, the collective body can be immunized from the perceived danger only by allowing a little of what threatens it to enter its protective boundaries. This means that in order to escape the clutches of death, life is forced to incorporate within itself the lethal principle. Starting from this reflection on the nature of immunization, Esposito offers a wide-ranging analysis of contemporary biopolitics. Never more than at present has the demand for immunization come to characterize all aspects of our existence. The more we feel at risk of being infiltrated and infected by foreign elements, the more the life of the individual and society closes off within its protective boundaries, forcing us to choose between a self-destructive outcome and a more radical alternative based on a new conception of community. (shrink)