Relevance logics are a misunderstood lot. Despite being the subject of intense study for nearly a century, they remain maligned as too complicated, too abstruse, or too silly to be worth learning much about. This Element aims to dispel these misunderstandings. By focusing on the weak relevant logic B, the discussion provides an entry point into a rich and diverse family of logics. Also, it contains the first-ever textbook treatment of quantification in relevance logics, as well as an overview of (...) the cutting edge on variable sharing results and a guide to further topics in the field. (shrink)

In this paper, we examine a number of relevant logics’ variable sharing properties from the perspective of theories of topic or subject-matter. We take cues from Franz Berto’s recent work on topic to show an alignment between families of variable sharing properties and responses to the topic transparency of relevant implication and negation. We then introduce and defend novel variable sharing properties stronger than strong depth relevance—which we call cn-relevance and lossless cn-relevance—showing that the properties are satisfied by the weak (...) relevant logics and , respectively. We argue that such properties address a sort of semantic lossiness of strong depth relevance. (shrink)

Relevant logics infamously have the property that they only validate a conditional when some propositional variable is shared between its antecedent and consequent. This property has been strengthened in a variety of ways over the last half-century. Two of the more famous of these strengthenings are the strong variable sharing property and the depth relevance property. In this paper I demonstrate that an appropriate class of relevant logics has a property that might naturally be characterized as the supremum of these (...) two properties. I also show how to use this fact to demonstrate that these logics seem to be constructive in previously unknown ways. (shrink)

Formal symptoms of relevance usually concern the propositional variables shared between the antecedent and the consequent of provable conditionals. Among the most famous results about such symptoms are Belnap’s early results showing that for sublogics of the strong relevant logic R, provable conditionals share a signed variable between antecedent and consequent. For logics weaker than R stronger variable sharing results are available. In 1984, Ross Brady gave one well-known example of such a result. As a corollary to the main result (...) of the paper, we give a very simple proof of a related but strictly stronger result. (shrink)

Logic: the Basics is an accessible introduction to the core philosophy topic of standard logic. Focussing on traditional Classical Logic the book deals with topics such as mathematical preliminaries, propositional logic, monadic quantified logic, polyadic quantified logic, and English and standard ‘symbolic transitions’. With exercises and sample answers throughout this thoroughly revised new edition not only comprehensively covers the core topics at introductory level but also gives the reader an idea of how they can take their knowledge further and the (...) philosophical questions around logic. -/- Logic: the Basics is essential reading for first-year undergraduate philosophy students on standard introductory logic courses. (shrink)

In 1988, Kit Fine published a semantic theory for quantified relevant logics. He referred to this theory as stratified semantics. While it has received some attention in the literature, 1–20, 1992; Mares & Goldblatt, Journal of Symbolic Logic 71, 163–187, 2006), stratified semantics has overall received much less attention than it deserves. There are two plausible reasons for this. First, the only two dedicated treatments of stratified semantics available are, 27–59, 1988; Mares, Studia Logica 51, 1–20, 1992), both of which (...) are quite dense and technically challenging. Second, there are a number of prima facie reasons to be worried about stratified semantics. The purpose of this paper is to revitalize research on stratified semantics. I will do so by giving a ‘user friendly’ presentation of the semantics, and by giving reasons to think that the prima facie reasons to be worried about it are too simplistic. (shrink)

There is a natural story about what logic is that sees it as tied up with two operations: a ‘throw things into a bag’ operation and a ‘closure’ operation. In a pair of recent papers, Jc Beall has fleshed out the account of logic this leaves us with in more detail. Using Beall’s exposition as a guide, this paper points out some problems with taking the second operation to be closure in the usual sense. After pointing out these problems, I (...) then turn to fixing them in a restricted case and modulo a few simplifying assumptions. In a followup paper, the simplifications and restrictions will be removed. (shrink)

Weak enough relevant logics are often closed under depth substitutions. To determine the breadth of logics with this feature, we show there is a largest sublogic of R closed under depth substitutions and that this logic can be recursively axiomatized.

Jc Beall has made several contributions to the theory of restricted quantification in relevant logics. This paper examines these contributions and proposes an alternative account of restricted universals. The alternative is not, however, a theory of relevant restricted universals in any real sense. It is, however, a theory of restricted universals phrased in the most plausible general quantificational theory for relevant logics—Kit Fine’s stratified semantics. The motivation both for choosing this semantic framework and for choosing the particular theory of restricted (...) quantification we use is because they are the best way of dealing with these topics from Beall’s theory-building theory picture of logic, establishing a second point of contact with Beall’s work. (shrink)

Abstractionism in the philosophy of mathematics aims at deriving large fragments of mathematics by combining abstraction principles (i.e. the abstract objects $\S e_1, \S e_2$, are identical if, and only if, an equivalence relation $Eq_\S$ holds between the entities $e_1, e_2$) with logic. Still, as highlighted in work on the semantics for relevant logics, there are different ways theories might be combined. In exactly what ways must logic and abstraction be combined in order to get interesting mathematics? In this paper, (...) we investigate the matter by deriving the axioms of second-order Peano Arithmetic from Frege's Basic Law V (the extension of $F$ is identical with the extension of $G$ if, and only if, $F$ and $G$ are extensionally equivalent) in the presence of a relevant higher-order logic. The results are interesting. Not only must we take on logic as true, and not only must we apply our logic to abstraction principles, but also we have to apply our theory of abstraction back to the logic in order to arrive at arithmetic. Thus, what Abstractionism gives us is not simply what we get from abstraction via logic, but also what we get from logic via abstraction. (shrink)

Here's the thing: when you look at it from just the right angle, it's entirely obvious how semantics for second-order relevant logics ought to go. Or at least, if you've understood how semantics for first-order relevant logics ought to go, there are perspectives like this. What's more is that from any such angle, the metatheory that needs doing can be summed up in one line: everything is just as in the first-order case, but with more indices. Of course, it's no (...) small matter finding the magical angle from which everything becomes obvious. And even having found this perspective, one cannot assume one's audience will find things as obvious as oneself. All that to say this: if the results in the paper below strike you as obvious, pay attention to the perspective that makes that possible. And if they don't, feel free to ignore this preamble in its entirety. (shrink)

This paper presents a new semantics for the weak relevant logic DW that makes the role of the infamous Routley star more explicable. Central to this rewriting is combining aspects of both the American and Australian plan for understanding negations in relevance logics.

I present a version of Kit Fine's stratified semantics for the logic RWQ and define a natural family of related structures called RW hyperdoctrines. After proving that RWQ is sound with respect to RW hyperdoctrines, we show how to construct, for each stratified model, a hyperdoctrine that verifies precisely the same sentences. Completeness of RWQ for hyperdoctrinal semantics then follows from completeness for stratified semantics, which is proved in an appendix. By examining the base category of RW hyperdoctrines, we find (...) reason to be worried about the ontology of stratified models. (shrink)

In this paper, we provide a semantics for a range of positive substructural logics, including both logics with and logics without modal connectives. The semantics is novel insofar as it is meant to explicitly capture the computational flavor of these logics, and to do so in a way that builds in both nondeterministic and nonconcurrent computational processes.

In this paper we introduce a novel way of building arithmetics whose background logic is R. The purpose of doing this is to point in the direction of a novel family of systems that could be candidates for being the infamous R#1/2 that Meyer suggested we look for.

Linnebo and Pettigrew present some objections to category theory as an autonomous foundation. They do a commendable job making clear several distinct senses of ‘autonomous’ as it occurs in the phrase ‘autonomous foundation’. Unfortunately, their paper seems to treat the ‘categorist’ perspective rather unfairly. Several infelicities of this sort were addressed by McLarty. In this note I address yet another apparent infelicity.

Abstraction principles provide implicit definitions of mathematical objects. In this paper, an abstraction principle defining categories is proposed. It is unsatisfiable and inconsistent in the expected ways. Two restricted versions of the principle which are consistent are presented.

Categorial logic, as its name suggests, applies the techniques and machinery of category theory to topics traditionally classified as part of logic. We claim that these tools deserve attention from a greater range of philosophers than just the mathematical logicians. We support this claim with an example. In this paper we show how one particular tool from categorial logic---hyperdoctrines---suggests interesting metaphysics. Hyperdoctrines can provide semantics for quantified languages, but this account of quantification suggests a metaphysical picture quite different from the (...) one suggested by standard model-theoretic semantics. (shrink)

This essay will examine some rather serious trouble confronting claims that mathematicalia might be social constructs. Because of the clarity with which he makes the case and the philosophical rigor he applies to his analysis, our exemplar of a social constructivist in this sense is Julian Cole, especially the work in his 2009 and 2013 papers on the topic. In a 2010 paper, Jill Dieterle criticized the view in Cole’s 2009 paper for being unable to account for the atemporality of (...) mathematical existents. Cole’s 2013 paper addresses this objection, providing a modification of his 2009 paper allowing for atemporal mathematicalia. An unusual consequence of Cole’s account is that at least some existential claims about mathematicalia used to be false but now have always been true. By examining the semantics of such claims, we demonstrate that social constructivism is in fact, despite Cole’s attempts to rectify matters, incompatible with atemporal mathematicalia. In the course of examining these semantic details, however, an alternative hybrid view of fictionalism and social constructivism emerges. Those tempted by social constructivism, while perhaps disappointed by the negative results of the paper, may be encouraged by how much of their view can be recovered in this alternative account. (shrink)

In this chapter, Logan Paul Gage examines the only real attempt to disprove God’s existence by a New Atheist: Richard Dawkins’s “Ultimate 747 Gambit.” Central to Dawkins’s argument is the claim that God is more complex than what he is invoked to explain. Gage evaluates this claim using the main extant notions of simplicity in the literature. Gage concludes that on no reading does this claim survive scrutiny. Along the way, Dawkins claims that there are no good positive arguments (...) for God’s existence. Gage attempts to show that Dawkins’s argument depends upon distinctively philosophical assumptions that do not appear to withstand scrutiny. (shrink)

To contribute to the continuing challenge of explaining how managers identify stakeholders and assess their salience, in this article, we chronicle the history, assess the impact, and evaluate the possibilities opened by Mitchell, Agle, and Wood (MAW-1997). We do so through two types of qualitative analysis, and also through utilizing a quantitative network analysis tool. The first qualitative analysis categorizes the major contributions of the most influential papers succeeding MAW-1997; the second identifies and compares the relevant issues with MAW-1997 at (...) the time of initial publication and today. We apply main path analysis, a quantitative tool, to map how this scholarly domain has evolved. These three analyses robustly depict the impact of MAW-1997 and the ensuing scholarly conversation, and they enable us to illustrate the current state and trajectory of stakeholder identification and salience scholarship. We close by discussing pressing topics related to the broader body of stakeholder theory literature. (shrink)

Emphasizing the creative nature of mathematics, this conversational textbook guides students through the process of discovering a proof as they transition to advanced mathematics. Using several strategies, students will develop the thinking skills needed to tackle mathematics when there is no clear algorithm or recipe to follow.

Excerpt“We have invented happiness,” said the last men, and they blinked. Friedrich Nietzsche, Thus Spoke Zarathustra1Introduction One of the key issues in the Marxist sociopolitical theory of the critique of capitalism regards the idea of “domination” or “control.” Webster's Dictionary defines domination as: (1) supremacy or preeminence over another; (2) exercise of mastery or ruling power; (3) exercise of preponderant, governing, or controlling influence.2 From a sociopolitical perspective, domination can be addressed using two different approaches. The first, a traditional approach, (...) views domination as external to the individual or the group…. (shrink)

An analysis is made of Pope Francis’ Encyclical Laudato Si from a general systems approach. A call is made for a dialogue between theologians and environmental scientist. A parallel is found between the Pope’s identification of rapidification as a root cause of global warming and McLuhan’s notion of the speedup of modern life due to the emergence of electric technology. An analysis of Hebrew Scriptures is made, suggesting that rather than subduing the earth, the translation of Gen 1:28 seems to (...) indicate that the intention was to occupy and tend the land. The Jewish notion of Bal Tashchit one of the 613 mitzvos or commandments from Scripture, supports this interpretation as it calls for stewardship of G-d’s gifts. (shrink)

Prominent atheists claim the Bible is a racist text. Yet Dr. Martin Luther King Jr. read it daily. Then again, so did many ardent segregationists. Some atheists claim religion serves to oppress the masses. Yet the classic text of the French Revolution, What is the Third Estate?, was written by a priest. On the other hand, the revolutionaries ended up banning religion. What do we make of religion's confusing role in history? And what of religion's relationship to science? Some scientists (...) claim that we have no free will. Others argue that advances in neurobiology and physics disprove determinism. As for whispering to the universe, an absurd habit say the skeptics. Yet prayer is a transformative practice for millions. This book explores the most common atheist critiques of the Bible and religion, incorporating Jewish, Christian, and Muslim voices. The result is a fresh, modern re-evaluation of religion and of atheism. (shrink)

As scientific and engineering efforts become increasingly global in nature, the need to understand differences in perceptions of research ethics issues across countries and cultures is imperative. However, investigations into the connection between nationality and ethical decision-making in the sciences have largely generated mixed results. In Study 1 of this paper, a measure of biases and compensatory strategies that could influence ethical decisions was administered. Results from this study indicated that graduate students from the United States and international graduate students (...) studying in the US are prone to different biases. Based on these findings, recommendations are made for developing ethics education interventions to target these decision-making biases. In Study 2, we employed an ethics training intervention based on ethical sensemaking and used a well-established measure of ethical decision-making that more fully captures the content of ethical judgment. Similar to Study 1, the results obtained in this study suggest differences do exist between graduate students from the US and international graduate students in ethical decision-making prior to taking the research ethics training. However, similar effects were observed for both groups following the completion of the ethics training intervention. (shrink)

Given the growing public concern and attention placed on cases of research misconduct, government agencies and research institutions have increased their efforts to develop and improve ethics education programs for scientists. The present study sought to assess the impact of these increased efforts by sampling empirical studies published since the year 2000. Studies published prior to 2000 examined in other meta-analytic work were also included to provide a baseline for assessing gains in ethics training effectiveness over time. In total, this (...) quantitative review consisted of 66 empirical studies, 106 ethics courses, 150 effect sizes, and 10,069 training participants. Overall, the findings indicated that ethics instruction resulted in sizable benefits to participants and has improved considerably within the last decade. A number of specific findings also emerged regarding moderators of instructional effectiveness. Recommendations are discussed for improving the development, delivery, and evaluation of ethics instruction in the sciences. (shrink)

This paper argues that international development research should be submitted to the oversight of research ethics committees from the countries where data will be collected. This includes research conducted by individuals who may fall outside the jurisdictions of most ethics guidelines or policies, such as individuals contracted by non-governmental organizations. The argument is grounded in an understanding of social justice that recognizes that not seeking local ethics approval can be an affront to the decolonization movement, and may lead to significant (...) direct harms to participants. Local ethics oversight can help ensure projects appropriately take into consideration local laws, regulations, priorities and context. For example, a local research ethics committee may be in a better position than a foreign one to assess whether any given proposed project carries context-specific risks. In addition, submitting to a local research ethics committee is to acknowledge the legitimacy of local authorities, thereby taking a stance against the history of colonizing disempowerment. Local oversight is a mechanism to increase the accountability of researchers working abroad: if respect for local authority and tailoring to local context are to be upheld, there must be mechanisms to ensure that research that does not meet these requirements does not proceed. Objections based on the limited oversight capacity in some countries and on concerns related to the politicization of the review process are discussed. Finally, the roles and responsibilities of the various stakeholders in the implementation of greater local ethics oversight are laid out. (shrink)

This book investigates the phenomenological ways that dance choreographing and dance performance exemplify both Truth and meaning-making within Native American epistemology, from an analytic philosophical perspective. Given that within Native American communities dance is regarded both as an integral cultural conduit and “a doorway to a powerful wisdom,” Shay Welch argues that dance and dancing can both create and communicate knowledge. She explains that dance—as a form of oral, narrative storytelling—has the power to communicate knowledge of beliefs and histories, (...) and that dance is a form of embodied narrative storytelling. Welch provides analytic clarity on how this happens, what conditions are required for it to succeed, and how dance can satisfy the relational and ethical facets of Native epistemology. (shrink)

An Insiders¿ Style Guide to Mind and Spirit ¿ Every Decade Should Be the Best Decade of Your Life by Natalie Logan is a fun and entertaining short read. Miami Florida ¿ Miami has long been a premier tourist destination, acclaimed for its physical beauty and its excellent climate. Year round, the fabled white-sand beaches and clear blue waters lapping Miami Beach have beckoned visitors to America¿s 'Riviera¿. Others are lured by Miami¿s world-class shopping and cosmopolitan dining and its (...) international culture. Mind and Spirit content:Personal Life CoachQuiet Your Inner CriticConfidence ¿ Keep Your Head High and Own Everything You Do and Do It BigBeauty and Happiness Feel Fabulous Tricks Must HavesWell Read Commit Random Acts of KindnessRe-Claim Your WeekendsManage Stress Aauvi Insiders¿ Style Guide Series ¿ There is something great about A-list living and Mind and Spirit, the ninth book of a twenty-one book series, is another step to achieving such an extraordinary life. You should be bursting with energy, and feeling you have an incredible motor inside you. There¿s still so much you want to do. You live more passionately now and savor every second. You think that¿s what happens when you grow up. (shrink)

A dual-processing model of moral whistleblowing in organizations is proposed. In this theory paper, moral whistleblowing is described as a unique type of whistleblowing that is undertaken by individuals that see themselves as moral agents and are primarily motivated to blow the whistle by a sense of moral duty. At the individual level, the model expands on traditional, rational models of whistleblowing by exploring how moral intuition and deliberative reasoning processes might interact to influence the whistleblowing behavior of moral agents. (...) The model combines individual variables, organizational variables, and external, societal variables to explain the moral whistleblowing process and the impact of moral agents on organizations and society. (shrink)

This Article proposes a thought-experiment with regard to the administration of class actions. It is almost axiomatic that class actions are determined through a single “certification.” However, class actions can be certified through a tiered certification, e.g., a preliminary certification on a more lenient standard, followed by a full certification. Flattening the certification process allows a richer set of solutions to familiar dilemmas. Currently, a noncertified class does not bar subsequent certification attempts. Focusing on this problem, this Article demonstrates that (...) tiered certification is a superior solution — members of a class that passed the first certification but not the second receive at least minimal procedural protection and thus could be precluded from serial certification attempts. More generally, tiered certification can better handle several species of collective litigation, which can be referred to as semi-class actions. Collective proceedings, whose certification costs are greater than their social benefit, do not justify a comprehensive class treatment. But to the extent that these cases entail some modest social value, they deserve to pass a less onerous, preliminary certification. The Article discusses cases that fit this pattern, for instance prospective, class-wide relief for technical regulatory violations. (shrink)

King develops a syntax-based account of propositions based on the idea that propositional unity is grounded in the syntactic structure of the sentence. This account faces two objections: a Benacerraf objection and a grain-size objection. I argue that the syntax-based account survives both objections, as they have been put forward in the existing literature. I go on to show, however, that King equivocates between two distinct notions of ‘propositional structure ’ when explaining his account. Once the confusion is resolved, it (...) is clear that the syntax-based account suffers from both Benacerraf and grain-size problems after all. I conclude by showing that King's account can be revised to avoid these problems, but only if it abandons its motivating idea that it is syntax that unifies the proposition. (shrink)

Predictive modeling in education draws on data from past courses to forecast the effectiveness of future courses. The present effort sought to identify such a model of instructional effectiveness in scientific ethics. Drawing on data from 235 courses in the responsible conduct of research, structural equation modeling techniques were used to test a predictive model of RCR course effectiveness. Fit statistics indicated the model fit the data well, with the instructional characteristics included in the model explaining approximately 85% of the (...) variance in RCR instructional effectiveness. Implications for using the model to develop and improve future RCR courses are discussed. (shrink)

BackgroundSleep, physical activity, and diet have been associated with mental health and well-being individually in young adults. However, which of these “big three” health behaviors most strongly predicts mental health and well-being, and their higher-order relationships in predictive models, is less known. This study investigated the differential and higher-order associations between sleep, physical activity, and dietary factors as predictors of mental health and well-being in young adults.MethodIn a cross-sectional survey design, 1,111 young adults ages 18–25 from New Zealand and the (...) United States answered an online survey measuring typical sleep quantity and quality; physical activity; and consumption of raw and processed fruit and vegetables, fast food, sweets, and soda, along with extensive covariates and the outcome measures of depressive symptoms [measured by the Center for Epidemiological Depression Scale ] and well-being.ResultsControlling for covariates, sleep quality was the strongest predictor of depressive symptoms and well-being, followed by sleep quantity and physical activity. Only one dietary factor—raw fruit and vegetable consumption—predicted greater well-being but not depressive symptoms when controlling for covariates. There were some higher-order interactions among health behaviors in predicting the outcomes, but these did not survive cross-validation.ConclusionSleep quality is an important predictor of mental health and well-being in young adults, whereas physical activity and diet are secondary but still significant factors. Although strictly correlational, these patterns suggest that future interventions could prioritize sleep quality to maximize mental health and well-being in young adults. (shrink)

Practical reasoners are resource-bounded—in particular they require time to derive consequences of their knowledge. Building on the Timed Reasoning Logics (TRL) framework introduced in [1], we show how to represent the time required by an agent to reach a given conclusion. TRL allows us to model the kinds of rule application and conflict resolution strategies commonly found in rule-based agents, and we show how the choice of strategy can influence the information an agent can take into account when making decisions (...) at a particular point in time. We prove general completeness and decidability results for TRL, and analyse the impact of communication in an example system consisting of two agents which use different conflict resolution strategies. (shrink)