Relevant logics are a family of non-classical logics characterized by the behavior of their implication connectives. Unlike some other non-classical logics, such as intuitionistic logic, there are multiple philosophical views motivating relevant logics. Further, different views seem to motivate different logics. In this article, we survey five major views motivating the adoption of relevant logics: Use Criterion, sufficiency, meaning containment, theory construction, and truthmaking. We highlight the philosophical differences as well as the different logics they support. We end with some (...) questions for future research. (shrink)

Justification logics provide frameworks for studying the fine structure of evidence and justification. Traditionally, these logics do not impose any closure requirements on justification. In this paper, we argue that for some applications they should subject justification to closure under some variety of logical consequence. Specifically, we argue, building on ideas from Beall, that the non-classical logic FDE offers a particularly attractive notion of consequence for this purpose and define a justification logic where justification is closed under FDE consequence. We (...) show the resulting logic to be sound and complete. Lastly, we discuss how the closure of justification under FDE ontrasts closure under related non-classical logics and how our approach contrasts with some alternatives. (shrink)

An advanced-level logic textbook that presents proof construction on equal footing with model building. Potentially relevant to students of mathematics and computer science as well.

In classically based modal logic, there are three common conceptions of necessity, the universal conception, the equivalence relation conception, and the axiomatic conception. They provide distinct presentations of the modal logic S5, all of which coincide in the basic modal language. We explore these different conceptions in the context of the relevant logic R, demonstrating where they come apart. This reveals that there are many options for being an S5-ish extension of R. It further reveals a divide between the universal (...) conception of necessity on the one hand, and the axiomatic conception on the other: The latter is consistent with motivations for relevant logics while the former is not. For the committed relevant logician, necessity cannot be the truth in all possible worlds. (shrink)

There appears to be few, if any, limits on what sorts of logical connectives can be added to a given logic. One source of potential limitations is the motivating ideology associated with a logic. While extraneous to the logic, the motivating ideology is often important for the development of formal and philosophical work on that logic, as is the case with intuitionistic logic. One family of logics for which the philosophical ideology is important is the family of relevant logics. In (...) this paper, I explore the limits of what a relevant connective is, showing how some basic criteria motivated by the ideology of relevant logicians provide robust limits on potential connectives. These criteria provide some plausible necessary conditions on being a relevant connective. (shrink)

In this paper, I motivate the addition of an actuality operator to relevant logics. Straightforward ways of doing this are in tension with standard motivations for relevant logics, but I show how to add the operator in a way that permits one to maintain the intuitions behind relevant logics. I close by exploring some of the philosophical consequences of the addition.

In relevant logics, necessary truths need not imply each other. In justification logic, necessary truths need not all be justified by the same reason. There is an affinity to these two approaches that suggests their pairing will provide good logics for tracking reasons in a fine-grained way. In this paper, I will show how to extend relevant logics with some of the basic operators of justification logic in order to track justifications or reasons. I will define and study three kinds (...) of frames for these logics. For the first kind of frame, I show soundness and highlight a difficulty in proving completeness. This motivates two alternative kinds of frames, with respect to which completeness results are obtained. Axioms to strengthen the justification logic portions of these logics are considered. I close by developing an analogy between the dot operator of justification logic and theory fusion in relevant logics. (shrink)

In this paper, an incompleteness theorem for modal extensions of relevant logics is proved. The proof uses elementary methods and builds upon the work of Fuhrmann.

Mares and Goldblatt, 163–187, 2006) provided an alternative frame semantics for two quantified extensions of the relevant logic R. In this paper, I show how to extend the Mares-Goldblatt frames to accommodate identity. Simpler frames are provided for two zero-order logics en route to the full logic in order to clarify what is needed for identity and substitution, as opposed to quantification. I close with a comparison of this work with the Fine-Mares models for relevant logics with identity and a (...) discussion of constant and variable domains. (shrink)

The operational semantics of Urquhart is a deep and important part of the development of relevant logics. In this paper, I present an overview of work on Urquhart’s operational semantics. I then present the basics of collection frames. Finally, I show how one kind of collection frame, namely, functional set frames, is equivalent to Urquhart’s semilattice semantics.

We present an extension of the basic revision theory of circular definitions with a unary operator, □. We present a Fitch-style proof system that is sound and complete with respect to the extended semantics. The logic of the box gives rise to a simple modal logic, and we relate provability in the extended proof system to this modal logic via a completeness theorem, using interpretations over circular definitions, analogous to Solovay’s completeness theorem forGLusing arithmetical interpretations. We adapt our proof to (...) a special class of circular definitions as well as to the first-order case. (shrink)

This paper will develop ideas from [44]. We will generalize their work in two directions. First, we provide axioms for justification logics over the base logic B and show that the logic permits a proof of the internalization theorem. Second, we provide alternative frames that more closely resemble the standard versions of the ternary relational frames, as well as a more general approach to the completeness proof. We prove that soundness and completeness hold for justification logics over a wide variety (...) of base logics. Finally, we will strengthen Belnap’s variable sharing for the justification logic context, demonstrating that the justifications are properly relevant justifications. (shrink)

An important question for proponents of non-contractive approaches to paradox is why contraction fails. Zardini offers an answer, namely that paradoxical sentences exhibit a kind of instability. I elaborate this idea using revision theory, and I argue that while instability does motivate failures of contraction, it equally motivates failure of many principles that non-contractive theorists want to maintain.

We present a new frame semantics for positive relevant and substructural propositional logics. This frame semantics is both a generalisation of Routley–Meyer ternary frames and a simplification of them. The key innovation of this semantics is the use of a single accessibility relation to relate collections of points to points. Different logics are modeled by varying the kinds of collections used: they can be sets, multisets, lists or trees. We show that collection frames on trees are sound and complete for (...) the basic positive distributive substructural logic $\mathsf {B}^+$, that collection frames on multisets are sound and complete for $\mathsf {RW}^+$ (the relevant logic $\mathsf {R}^+$, without contraction, or equivalently, positive multiplicative and additive linear logic with distribution for the additive connectives), and that collection frames on sets are sound for the positive relevant logic $\mathsf {R}^+$. The completeness of set frames for $\mathsf {R}^+$ is, currently, an open question. (shrink)

In this paper, we build on earlier work by Standefer (Logic J IGPL 27(4):543–569, 2019) in investigating extensions of substructural logics, particularly relevant logics, with the machinery of justification logics. We strengthen a negative result from the earlier work showing a limitation with the canonical model method of proving completeness. We then show how to enrich the language with an additional operator for implicit commitment to circumvent these problems. We then extend the logics with axioms for D, 4, and (...) 5, which requires additional justification term operators, following the work of Pacuit (in proceedings of the fifth panhellenic logic symposium, 2005) and Rubtsova (in Grigoriev D, Harrison J (eds) Computer science—theory and applications, CSR 2006; J Logic Comput 16(5):671–684, 2006), and present the required modifications to the frame semantics. We present a simplification of the neighborhood frames from the earlier work and we close by investigating the distinctive contribution of the + operator to the logic. (shrink)

We present some proof-theoretic results for the normal modal logic whose characteristic axiom is \. We present a sequent system for this logic and a hypersequent system for its first-order form and show that these are equivalent to Hilbert-style axiomatizations. We show that the question of validity for these logics reduces to that of classical tautologyhood and first-order logical truth, respectively. We close by proving equivalences with a Fitch-style proof system for revision theory.

In this article, we present a definition of a hyperintensionality appropriate to relevant logics. We then show that relevant logics are hyperintensional in this sense, drawing consequences for other non-classical logics, including HYPE and some substructural logics. We further prove results concerning extensionality in relevant logics. We close by discussing related concepts for classifying formula contexts and potential applications of these results.

In Saving Truth from Paradox, Hartry Field presents and defends a theory of truth with a new conditional. In this paper, I present two criticisms of this theory, one concerning its assessments of validity and one concerning its treatment of truth-preservation claims. One way of adjusting the theory adequately responds to the truth-preservation criticism, at the cost of making the validity criticism worse. I show that in a restricted setting, Field has a way to respond to the validity criticism. I (...) close with some general considerations on the use of revision-theoretic methods in theories of truth. (shrink)

We argue that distinct conditionals—conditionals that are governed by different logics—are needed to formalize the rules of Truth Introduction and Truth Elimination. We show that revision theory, when enriched with the new conditionals, yields an attractive theory of truth. We go on to compare this theory with one recently proposed by Hartry Field.

Circular denitions have primarily been studied in revision theory in the classical scheme. I present systems of circular denitions in the Strong Kleene and supervaluation schemes and provide complete proof systems for them. One class of denitions, the intrinsic denitions, naturally arises in both schemes. I survey some of the features of this class of denitions.

This paper has two aims. First, it sets out an interpretation of the relevant logic E of relevant entailment based on the theory of situated inference. Second, it uses this interpretation, together with Anderson and Belnap’s natural deduc- tion system for E, to generalise E to a range of other systems of strict relevant implication. Routley–Meyer ternary relation semantics for these systems are produced and completeness theorems are proven. -/- .

Two common forms of natural deduction proof systems are found in the Gentzen–Prawitz and Jaśkowski–Fitch systems. In this paper, I provide translations between proofs in these systems, pointing out the ways in which the translations highlight the structural rules implicit in the systems. These translations work for classical, intuitionistic, and minimal logic. I then provide translations for classical S4 proofs.

Anderson and Belnap presented indexed Fitch-style natural deduction systems for the relevant logics R, E, and T. This work was extended by Brady to cover a range of relevant logics. In this paper I present indexed tree natural deduction systems for the Anderson–Belnap–Brady systems and show how to translate proofs in one format into proofs in the other, which establishes the adequacy of the tree systems.

We offer a defense of one aspect of Paul Horwich’s response to the Liar paradox—more specifically, of his move to preserve classical logic. Horwich’s response requires that the full intersubstitutivity of ‘ ‘A’ is true’ and A be abandoned. It is thus open to the objection, due to Hartry Field, that it undermines the generalization function of truth. We defend Horwich’s move by isolating the grade of intersubstitutivity required by the generalization function and by providing a new reading of the (...) biconditionals of the form “ ‘A’ is true iff A.”. (shrink)

ABSTRACT In our response Field's ‘Properties, Propositions and Conditionals’, we explore the methodology of Field's program. We begin by contrasting it with a proof-theoretic approach and then commenting on some of the particular choices made in the development of Field's theory. Then, we look at issues of property identity in connection with different notions of equivalence. We close with some comments relating our discussion to Field's response to Restall’s [2010] ‘What Are We to Accept, and What Are We to Reject, (...) While Saving Truth from Paradox?’. (shrink)

Few debates in environmental philosophy have been more heated than the one over the nature of wilderness. And yet, when one surveys the present scene, one finds that a variety of different conceptions of wilderness are still quite popular – some more so in certain professions than others. In this paper, I look at three popular conceptions of wilderness with an eye toward sussing out the good and the bad them. I look at what I call (1) the folk view (...) of wilderness, (2) Leopold’s conception of wilderness, and (3) the legal conception of wilderness (as found in the Wilderness Act of 1964). In the final part of the paper, I sketch out a sort of spectrum account of wilderness, one that I argue allows us to capture more cases of wilderness and might serve as a useful tool in future conservation efforts. (shrink)

Environmental philosophy plays an important role, directly and indirectly, in many parts of society, including land and wildlife management (Leopold, 1949; Minteer, 2015), political activism (Abbey, 1968; Malm, 2020),and technological research and development (Baum & Owe, 2022; Donhauser et al., 2021). Environmental philosophy uncovers the ethical relationships existing between humans and the living and non-living world. It reveals the nuances of our scientific ecological concepts. And it tries to tell us how we might act – individually or collectively – to (...) better achieve our environmental goals. The aim of this special issue is to explore the limits and ever-expanding outer edges of this increasingly important area of philosophical thought. (shrink)

An “insightful” and in-depth look at anti-science politics and its deadly results (Maria Konnikova, New York Times–bestselling author of The Biggest Bluff). Thomas Jefferson said, “Wherever the people are well informed, they can be trusted with their own government.” But what happens when they aren’t? From climate change to vaccinations, transportation to technology, health care to defense, we are in the midst of an unprecedented expansion of scientific progress—and a simultaneous expansion of danger. At the very time we need them (...) most, scientists and the very idea of objective knowledge are being bombarded by a vast, well-funded war on science, and the results are deadly. Whether it’s driven by identity politics, ideology, or industry, the result is an unprecedented erosion of thought in Western democracies as voters, policymakers, and justices actively ignore scientific evidence, leaving major policy decisions to be based more on the demands of the most strident voices. This compelling book investigates the historical, social, philosophical, political, and emotional reasons why evidence-based politics are in decline and authoritarian politics are once again on the rise on both left and right—and provides some compelling solutions to bring us to our collective senses, before it's too late. “If you care about attacks on climate science and the rise of authoritarianism, if you care about biased media coverage and shake-your-head political tomfoolery, this book is for you.”—The Guardian. (shrink)

This interdisciplinary analysis presents an innovative examination of the nature of pride and humility, including all their slippery nuances and points of connection. By combining insights from visual art, literature, philosophy, religious studies, and psychology, this volume adapts a complementary rather than an oppositional approach to examine how pride and humility reinforce and inform one another. This method produces a robust, substantial, and meaningful description of these important concepts. The analysis takes into account key elements of pride and humility, including (...) self-esteem and self-confidence, human interconnectedness, power's function and limitations, and the role of fear. Shawn R. Tucker explores the many inflections of these terms, inflections that cast them by turns as positive or negative, emboldening or discouraging, and salubrious or vicious depending upon the context and manner in which they are used. (shrink)

In Steve Jobs and Philosophy, sixteen philosophers take a close look at the inspiring yet often baffling world of Steve Jobs. What can we learn about business ethics from the example of Jobs? What are the major virtues of a creative innovator? How could Jobs successfully defy and challenge conventional business practices? How did Jobs combine values and attitudes previously believed to be unmixable? What does it really mean to “think different”? Can entrepreneurs be made or are they just born? (...) If Jobs didn’t make any major inventions, just what was his contribution? How is Jobs’s life illuminated by Buddhism? How does a counter-culture transform mainstream culture? What does Jobs teach us about the notions of simplicity and functionality in design? How do Jobs’s achievements alter the way we think about technology in relation to human life? (shrink)

Growth in CSR-washing claims in recent decades has been dramatic in numerous academic and activist contexts. The discourse, however, has been fragmented, and still lacks an integrated framework of the conditions necessary for successful CSR-washing. Theorizing successful CSR-washing as the joint occurrence of five conditions, this paper undertakes a literature review of the empirical evidence for and against each condition. The literature review finds that many of the conditions are either highly contingent, rendering CSR-washing as a complex and fragile outcome. (...) This finding runs counter to the dominant perception in the general public, among activists, and among a vocal contingent of academics that successful CSR-washing is rampant. (shrink)

Attention to care in modern society has fallen out of view as an ethos of personal responsibility, free markets, and individualism has been in the ascendant. The Liberalism of Care argues that contemporary liberalism is suffering from a crisis of care, manifest in a decaying sense of collective political responsibility for citizens' well- being and for the most vulnerable members of our communities. The book maintains that this practical crisis stems from a theoretical one. We have lost the political language (...) of care, which, prior the 19th century, was commonly used to express these dimensions of political life. To recover that language, Shawn C. Fraistat turns to three prominent philosophers-Plato, Jean-Jacques Rousseau, and William Godwin-who illuminate the varied ways caring language and caring values have structured core debates in the history of Western political thought about the proper role of government, as well as the rights and responsibilities of citizens. The Liberalism of Care presents a distinctive vision for our liberal politics where political communities and citizens can utilize the ethic and practices of care to face practical challenges. (shrink)

Various theorists have endorsed the “communication argument”: communicative capacities are necessary for morally responsible agency because blame aims at a distinctive kind of moral communication. I contend that existing versions of the argument, including those defended by Gary Watson and Coleen Macnamara, face a pluralist challenge: they do not seem to sit well with the plausible view that blame has multiple aims. I then examine three possible rejoinders to the challenge, suggesting that a context-specific, function-based approach constitutes the most promising (...) modification of the communication argument. (shrink)

The equivocal contours of arielismo-one of the most influential anti-imperialist ideologies, spiritual movements, cultural models, and utopian pedagogies for Latin American youth in an epoch of rampant US interventionism.

BackgroundRecent advancements in neuroscientific techniques have allowed us to make huge progress in our understanding of memories, and in turn has paved the way for new memory modification technologies that can modulate memories with a degree of precision, which was not previously possible. With advancements in such techniques, new and critical ethical questions have emerged. Understanding and framing these ethical questions within the current philosophical theories is crucial in order to systematically examine them as we translate these techniques to the (...) clinic.Main bodyIn this paper, we discuss the ethical implications of modern neuroscience techniques that aim to disrupt or enhance memories. We attempt to frame the MMTs in the context of existing ethical philosophical theories to provide a cohesive analysis of the myriad of ethical quagmires that might emerge from such technologies. We argue the application of Aristotle’s Golden Mean and multiple accounts of authenticity are useful in approaching the ethical questions surrounding MMTs. We then propose a framework in which ethical considerations can be systematically examined. Lastly, we provide caveats and considerations for the use of this framework. Overall, we provide a practical approach for the ethical use of MMTs depending on the situation.ConclusionWhile at face value, our model appears to put severe limitations on the application of MMTs, we are not completely opposed to their use, but rather our framework guides the agent to consider the implications before making any decisions. Most importantly, we argue that the use of MMTs does not reduce the responsibility of the initial decision, and the agent must accept the post-MMT self as the new “true self” regardless of the outcome. As the developmental trajectory of MMTs suggests we are getting closer to practical clinical applications, ethical concerns across a wide range of disciplines need to be addressed to develop best strategies and policies when dealing with MMTs. If this can be achieved, we believe the ethical use of MMTs is not only possible but would also be of tremendous benefit to many people suffering from memory-related mental disorders. (shrink)

It is widely agreed that reactive attitudes play a central role in our practices concerned with holding people responsible. However, it remains controversial which emotional attitudes count as reactive attitudes such that they are eligible for this central role. Specifically, though theorists near universally agree that guilt is a reactive attitude, they are much more hesitant on whether to also include shame. This paper presents novel arguments for the view that shame is a reactive attitude. The arguments also support the (...) view that shame is a reactive attitude in the sense that concerns moral accountability. The discussion thereby challenges both the view that shame is not a reactive attitude at all, suggested by philosophers such as R. Jay Wallace and Stephen Darwall, and the view that shame is a reactive attitude but does not concern moral accountability, recently defended by Andreas Carlsson and Douglas Portmore. (shrink)

A common refrain in and outside academia is that prominent sports figures ought to engage more in the public discourse about political issues. This idea parallels the idea that athletes ought to be role models in general. This paper first examines and critiques the “athlete as role model” argument and then applies this critique to the “athlete as political activist” argument. Appealing to the empirical political psychological literature, the paper sketches an argument that athlete activism might actually do more harm (...) than good. (shrink)

One of the many claims about the value of local food is that local food exchanges generate trust between producers and consumers. To what degree is this actually the case and how does such trust develop? Drawing on interview and fieldwork data in one local food system in the Northeastern U.S., I show how local food participants build trust and reciprocity with one another in order to mitigate the challenges imposed by the conventional system. This trust and reciprocity builds primarily (...) through three mechanisms: reliable, positive relationships; demonstrations of good will toward one another; and a shared understanding of the value of locally-oriented food. Through these mechanisms, local food operators are able to build a healthy, stable local food system, able to better resist the pressures of the conventional system in which it must continually operate. (shrink)

One of the many claims about the value of local food is that local food exchanges generate trust between producers and consumers. To what degree is this actually the case and how does such trust develop? Drawing on interview and fieldwork data in one local food system in the Northeastern U.S., I show how local food participants build trust and reciprocity with one another in order to mitigate the challenges imposed by the conventional system. This trust and reciprocity builds primarily (...) through three mechanisms: reliable, positive relationships; demonstrations of good will toward one another; and a shared understanding of the value of locally-oriented food. Through these mechanisms, local food operators are able to build a healthy, stable local food system, able to better resist the pressures of the conventional system in which it must continually operate. (shrink)