In this article, I provide Urquhart-style semilattice semantics for three connexive logics in an implication-negation language (I call these “pure theories of connexive implication”). The systems semantically characterized include the implication-negation fragment of a connexive logic of Wansing, a relevant connexive logic recently developed proof-theoretically by Francez, and an intermediate system that is novel to this article. Simple proofs of soundness and completeness are given and the semantics is used to establish various facts about the systems (e.g., that two of (...) the systems have the variable sharing property). I emphasize the intuitive content of the semantics and discuss how natural informational considerations underly each of the examined systems. (shrink)

A propositional logic has the variable sharing property if φ → ψ is a theorem only if φ and ψ share some propositional variable. In this note, I prove that positive semilattice relevance logic and its extension with an involution negation have the variable sharing property. Typical proofs of the variable sharing property rely on ad hoc, if clever, matrices. However, in this note, I exploit the properties of rather more intuitive arithmetical structures to establish the variable sharing property for (...) the systems discussed. (shrink)

The object of this paper is to examine half and full connexive extensions of the basic regular conditional logic CR. Extensions of this system are of interest because it is among the strongest well-known systems of conditional logic that can be augmented with connexive theses without inconsistency resulting. These connexive extensions are characterized axiomatically and their relations to one another are examined proof-theoretically. Subsequently, algebraic semantics are given and soundness, completeness, and decidability are proved for each system. The semantics is (...) also used to establish independence results. Finally, a deontic interpretation of one of the systems is examined and defended. (shrink)

In recent years, historians of science have increasingly turned their attention to the “print culture” of early modern science. These studies have revealed that printing, as both a technology and a social and economic system, structured the forms and meanings of natural knowledge. Yet in early modern Europe, naturalists, including John Aubrey, John Evelyn, and John Ray, whose work is discussed in this paper, often shared and read scientific texts in manuscript either before or in lieu of printing. Scribal exchange, (...) exemplified in the circulation of writings like commonplace books, marginalia, manuscript treatises, and correspondence, was the primary means by which communities of naturalists constructed scientific knowledge. Print and manuscript were necessary partners. Manuscript fostered close collaboration, and could be circulated relatively cheaply; but, unlike print, it could not reliably secure priority or survival for posterity. Naturalists approached scribal and print communication strategically, choosing the medium that best suited their goals at any given moment. As a result, print and scribal modes of disseminating information, constructing natural knowledge, and organizing communities developed in tandem. Practices typically associated with print culture manifested themselves in scribal texts and exchanges, and vice versa. “Print culture” cannot be hived off from “scribal culture.” Rather, in their daily jottings and exchanges, naturalists inhabited, and produced, one common culture of communication. (shrink)

Conditional logics have traditionally been intended to formalize various intuitively correct modes of reasoning involving conditional expressions in natural language. Although conditional logics have by now been thoroughly studied in a classical context, they have yet to be systematically examined in an intuitionistic context, despite compelling philosophical and technical reasons to do so. This paper addresses this gap by thoroughly examining the basic intuitionistic conditional logic ICK, the intuitionistic counterpart of Chellas’ important classical system CK. I give ICK both worlds (...) semantics and algebraic semantics, and prove that these are equivalent. I give a Gödel-type embedding of ICK into CK and a Glivenko-type embedding of CK into ICK. I axiomatize ICK and prove soundness, completeness, and decidability results. Finally, I discuss extending ICK. (shrink)

Conditional logics were originally developed for the purpose of modeling intuitively correct modes of reasoning involving conditional—especially counterfactual—expressions in natural language. While the debate over the logic of conditionals is as old as propositional logic, it was the development of worlds semantics for modal logic in the past century that catalyzed the rapid maturation of the field. Moreover, like modal logic, conditional logic has subsequently found a wide array of uses, from the traditional (e.g. counterfactuals) to the exotic (e.g. conditional (...) obligation). Despite the close connections between conditional and modal logic, both the technical development and philosophical exploitation of the latter has outstripped that of the former, with the result that noticeable lacunae exist in the literature on conditional logic. My dissertation addresses a number of these underdeveloped frontiers, producing new technical insights and philosophical applications. -/- I contribute to the solution of a problem posed by Priest of finding sound and complete labeled tableaux for systems of conditional logic from Lewis' V-family. To develop these tableaux, I draw on previous work on labeled tableaux for modal and conditional logic; errors and shortcomings in recent work on this problem are identified and corrected. While modal logic has by now been thoroughly studied in non-classical contexts, e.g. intuitionistic and relevant logic, the literature on conditional logic is still overwhelmingly classical. Another contribution of my dissertation is a thorough analysis of intuitionistic conditional logic, in which I utilize both algebraic and worlds semantics, and investigate how several novel embedding results might shed light on the philosophical interpretation of both intuitionistic logic and conditional logic extensions thereof. -/- My dissertation examines deontic and connexive conditional logic as well as the underappreciated history of connexive notions in the analysis of conditional obligation. The possibility of interpreting deontic modal logics in such systems (via embedding results) serves as an important theoretical guide. A philosophically motivated proscription on impossible obligations is shown to correspond to, and justify, certain (weak) connexive theses. Finally, I contribute to the intensifying debate over counterpossibles, counterfactuals with impossible antecedents, and take—in contrast to Lewis and Williamson—a non-vacuous line. Thus, in my view, a counterpossible like "If there had been a counterexample to the law of the excluded middle, Brouwer would not have been vindicated" is false, not (vacuously) true, although it has an impossible antecedent. I exploit impossible (non-normal) worlds—originally developed to model non-normal modal logics—to provide non-vacuous semantics for counterpossibles. I buttress the case for non-vacuous semantics by making recourse to both novel technical results and theoretical considerations. (shrink)

The current ethical-legal consensus — prohibiting assisted suicide and euthanasia, but (1) allowing patients to forgo all life-saving treatment, and (2) permitting pain relief that increases the risk of death — is a means of having it both ways. This is how we often make “tragic choices.”.

Since McCall (1966), the heterodox principle of propositional logic that it is impossible for a proposition to be entailed by its own negation—in symbols, ¬(¬φ→φ)—has gone by the name of Aristotle’s thesis, since Aristotle apparently endorses it in Prior Analytics 2.4, 57b3–14. Scholars have contested whether Aristotle did endorse his eponymous thesis, whether he could do so consistently, and for what purpose he endorsed it if he did. In this article, I reconstruct Aristotle’s argument from this passage and show that (...) he accepts this thesis. Further, I show that the argument he gives is, making plausible assumptions, a correct proof in a consistent fragmentary nonclassical metalogic for a metatheorem he previously states concerning his assertoric syllogistic. In this way, Aristotle’s argument emerges as a fascinating case study in the use of a nonclassical metalogic to prove a result about a nonclassical object system. (shrink)

The Supreme Court, reluctant to find constitutional rights in areas marked by divisive social and legal debate, is not likely to constitutionalize a right to assisted suicide. The Court should cleave to the tradition of discouraging suicide and criminalizing its assistance.

The object of this paper is to examine two approaches to giving non-vacuous truth conditions for counterpossibles, counterfactuals with impossible antecedents. I first develop modifications of a Lewis-style sphere semantics with impossible worlds. I argue that this approach sanctions intuitively invalid inferences and is supported by philosophically problematic foundations. I then develop modifications of certain ceteris paribus conditional logics with impossible worlds. Tableaux are given for each of these in an appendix and soundness and completeness results are proved. While certain (...) of the latter systems are shown to have similar problems to logics from the first approach, at least one relatively weak system appears to offer an adequate uniform semantics for counterpossibles and counterfactuals. (shrink)

I sometimes wonder whether some proponents of physician-assisted suicide or physician-assisted death think they own the copyright to such catchy phrases as “death with dignity” and “a good death” so that if you are against PAS or PAD, thenyou must be againsta dignified death or a good death. If one removes the quotation marks around phrases like “aid-in-dying” or “compassionate care for the dying,” I am not opposed to such end-of-life care either. Indeed, how couldanybodybe against this type of care?I (...) do not want to abandon dying patients anymore than Dr. Timothy Quill does. Although, unfortunately, it will not always be easy to achieve the desired result, I agree with him that it ought to be a goal of medicine “to help people die well, to help them receive a good death” — or at least “the best possible” death under the circumstances. I part company with Professor Quill, however, when he urges us to change the law in the majority of our states so that in some circumstances patients may achieve a “good death” or a “dignified” one by means of lethal drugs. (shrink)

Gerald Sykes -- Aldous Huxley -- Gerald Heard -- Christopher Isherwood -- John van Druten -- Marianna Masin -- J. Crawford Lewis -- Dorothy F. Mercer -- Kurt Friedrichs -- Swami Atulananda -- Jane Molard -- The Countess of Sandwich -- John Yale -- Joan Rayne -- Durgacharan -- Pravrajika Saradaprana.

In his Outlines of Pyrrhonism 2.110–113, Sextus Empiricus presents four different accounts of the conditional, presumably all from the Hellenistic period, in increasing logical strength. While the interpretation and provenance of the first three accounts is relatively secure, the fourth account has perplexed and frustrated interpreters for decades or longer. Most interpreters have ultimately taken a dismissive attitude towards the fourth account and discounted it as being of both little historical and logical interest. We argue that this attitude is unwarranted (...) and demonstrate that the conditional expressed in the fourth account can profitably be understood as a precursor of analytic entailment, familiar from containment logics such as those developed by Parry and Angell. Exploiting recent work by Fine, we present a formal truthmaker semantics for this conditional and show how it sheds light on a number of longstanding issues in the interpretation of this passage. (shrink)

In On the Trinity 15.12.21, Augustine appears to endorse the KK principle (that if one knows that φ, then one knows that one knows that φ) in the course of giving an argument – the Multiplicity Argument – against the Academic skeptics. Gareth Matthews has disputed Augustine’s endorsement of the KK principle and presented a different reading of the Multiplicity Argument. In this note, I show that Matthews’s construal of the Multiplicity Argument is both interpretively and technically defective and defend (...) the attribution of some form of the KK principle to Augustine. (shrink)

This work has been selected by scholars as being culturally important and is part of the knowledge base of civilization as we know it. This work is in the public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work. Scholars believe, and we concur, that this work is important enough to be (...) preserved, reproduced, and made generally available to the public. To ensure a quality reading experience, this work has been proofread and republished using a format that seamlessly blends the original graphical elements with text in an easy-to-read typeface. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant. (shrink)

As schizotypal personality disorder increasingly prevails in the general population, a rapid and comprehensive measurement instrument is imperative to screen individuals at risk for SPD. To address this issue, we aimed to develop a computerized adaptive testing for SPD using a non-clinical Chinese sample, consisting of a calibration sample and a validation sample. The item pool of SPD was constructed from several widely used SPD scales and statistical analyses based on the item response theory via a calibration sample using a (...) graded response model. Finally, 90 items, which measured at least one symptom of diagnostic criteria of SPD in the fifth edition of the Diagnostic and Statistical Manual of Mental Disorders and had local independence, good item fit, high slope, and no differential item functioning, composed the final item pool for the CAT-SPD. In addition, a simulated CAT was conducted in an independent validation sample to assess the performance of the CAT-SPD. Results showed that the CAT-SPD not only had acceptable reliability, validity, and predictive utility but also had shorter but efficient assessment of SPD which can save significant time and reduce the test burden of individuals with less information loss. (shrink)

COVID-19 has affected millions of people around the globe. People's mental health, especially those of nurses, has been primarily affected by the fear of this virus. More focus has been paid to vaccination and treatment of the virus, but less attestation has been given to addressing the mental health of people affected by the virus. Empirical studies show that different external factors are not easily manageable and controllable by the individual. This study preliminarily explores the connection between fear of COVID-19 (...) and secondary traumatic stress in nurses. Further, it examines the moderating effects of occupational self-efficacy on the relationship between fear of COVID-19 and secondary traumatic stress. Data for the study was collected from the nurses of six large hospitals in Karachi, Pakistan. The final analysis was performed on 243 samples. Studies on COVID-19 suggest that increased occupational self-efficacy decreases fear and its impact. This study offers insights for managers to develop stress management programs and provide proper training and counseling sessions to the nurses to motivate them emotionally. Theoretically, this study broadens the understanding of the theory of emotions by using the pandemic as a stressor. Future studies may explore different roles of occupational self-efficacy and study its influential role in managing different kinds of emotions explained by the theory of emotions. Managers at the workplace could design different self-efficacy training for nurses to increase their self-motivation to fight different types of stress they face at the workplace. (shrink)

With the development of positive psychology, prosocial behavior has received widespread attention from researchers. Some studies have shown that emotion has a significant influence on individual prosocial behavior, but little research has studied the effect of different types of empathy on college students’ prosocial behaviors. The current study examined the mediating effects of gratitude among the associations between different types of empathy and prosocial behavior among Chinese college students. For the study, we used the Prosocial Tendency Measurement questionnaire, the Hebrew (...) version of Interpersonal Reactivity Index-C, and The Gratitude Questionnaire that investigated 1,037 participants. The results indicated that gratitude played a mediating role between perspective-taking and prosocial behavior, fantasy and prosocial behavior, empathic concern and prosocial behavior, and personal distress and prosocial behavior, respectively. The current study contributes to a better understanding of the relationship between empathy and prosocial behavior. (shrink)

I show that the lattice of the positive integers ordered by division is characteristic for Urquhart’s positive semilattice relevance logic; that is, a formula is valid in positive semilattice relevance logic if and only if it is valid in all models over the positive integers ordered by division. I show that the same frame is characteristic for positive intuitionistic logic, where the class of models over it is restricted to those satisfying a heredity condition. The results of this article highlight (...) deep connections between intuitionistic and semilattice relevance logic. (shrink)

In this article, I present a semantically natural conservative extension of Urquhart’s positive semilattice logic with a sort of constructive negation. A subscripted sequent calculus is given for this logic and proofs of its soundness and completeness are sketched. It is shown that the logic lacks the finite model property. I discuss certain questions Urquhart has raised concerning the decision problem for the positive semilattice logic in the context of this logic and pose some problems for further research.

A number of philosophers deny that contradictions can be believed. Are they correct? In this note, I show that even in quite weak logics, on pain of inconsistency, if there are false beliefs, either there are propositions which are true but unbelievable or contradictions are believable. Since the antecedent clearly holds, I offer some considerations in favor of the latter disjunct. Objections and variants of the main argument are considered.

In this article, I consider the positive logic of Boolean groups (i.e. Abelian groups where every non-identity element has order 2), where these are taken as frames for an operational semantics à la Urquhart. I call this logic BG. It is shown that the logic over the smallest nontrivial Boolean group, taken as a frame, is identical to the positive fragment of a quasi-relevance logic that was developed by Robles and Méndez (an extension of this result where negation is included (...) is also discussed). It is proved that BG satisfies the variable sharing property and is Halldén complete, while failing to satisfy the disjunction property. Sound and complete subscripted tableaux are presented for BG. An axiomatization (in the positive language extended with fusion) is presented, which is sound with respect to BG and, with respect to a related ternary relational semantics, complete; the problem of identifying a complete axiomatization for BG itself is left open. Connections between BG and the quasi-relevance logic KR are also discussed. (shrink)

Among Dunn’s many important contributions to relevance logic was his work on the system RM (R-mingle). Although RM is an interesting system in its own right, it is widely considered to be too strong. In this chapter, I revisit a closely related system, RM0 (sometimes known as ‘constructive mingle’), which includes the mingle axiom while not degenerating in the way that RM itself does. My main interest will be in examining this logic from two related semantical perspectives. First, I give (...) a purely operational bisemilattice semantics for it by adapting previous work of Humberstone. Second, I examine a more conventional algebraic semantics for it and discuss how this relates to the operational semantics. A novel operational semantics for J (intuitionistic logic) as well as its conventional Heyting algebraic semantics emerge as special cases of the corresponding semantics for RM0. The results of this chapter suggest that RM0 is a more interesting logic than has been appreciated and that Humberstone’s operational semantic framework similarly deserves more attention than it has received. (shrink)

In the early 1970s, Alasdair Urquhart proposed a semilattice semantics for relevance logic which he provided with an influential informational interpretation. In this article, I propose a BHK-inspired reinterpretation of the semantics which is related to Kit Fine’s truthmaker semantics. I discuss and compare Urquhart’s and Fine’s semantics and show how simple modifications of Urquhart’s semantics can be used to characterize both full propositional intuitionistic logic and Jankov’s logic. I then present (quasi-)relevant companions for both of these systems. Finally, I (...) provide sound and complete labelled sequent calculi for all of the systems discussed. (shrink)

The main object of this article is to give two novel proofs of the admissibility of Ackermann’s rule (γ) for the propositional relevant logic R. The results are established as corollaries of cut elimination for systems of tableaux for R. Cut elimination, in turn, is established both nonconstructively (as a corollary of completeness) and constructively (using Gentzen-like methods). The extensibility of the techniques is demonstrated by showing that (γ) is admissible for RQ* (R with constant domain quantifiers). The status of (...) the admissibility of (γ) for RQ* was, to the best of the author’s knowledge, an open problem. Further extensions of these results will be explored in the sequel(s). (shrink)

This commentary examines the interpretation of Parmenides developed by Rose Cherubin in her paper, “Parmenides, Liars, and Mortal Incompleteness.” First, I discuss the tensions Cherubin identifies between the definitions and presuppositions of justice, necessity, fate, and the other requisites of inquiry. Second, I critically assess Cherubin’s attribution of a sort of liar paradox to Parmenides. Finally, I argue that Cherubin’s handling of the Doxa, the section of Parmenides’ poem that deals with mortal opinion and cosmology, is unsatisfactory. I suggest that (...) her reading may contradict the text in denying that the Doxa contains truths. (shrink)

Given the centrality of learners’ individual differences in their academic achievement, a plethora of research has been done on various individual difference variables and their associations with learners’ increased achievement. Yet, the role of creativity and self-efficacy in EFL learners’ academic achievement has not been extensively studied. Further, no review inquiry has simultaneously probed into the consequences of these two individual difference variables for learners’ academic achievement. This study strives to fill this underappreciated gap by addressing the positive consequences of (...) creativity and self-efficacy for EFL learners’ academic achievement. The desirable consequences of creativity and self-efficacy beliefs were clarified using the available evidence. Finally, the conclusions and consequences of the findings are discussed. (shrink)

According to current interpretations of Parmenides, he either embraces a token-monism of things, or a type-monism of the nature of each kind of thing, or a generous monism, accepting a token-monism of things of a specific type, necessary being. These interpretations share a common flaw: they fail to secure commensurability between Parmenides’ alētheia and doxa. We effect this by arguing that Parmenides champions a metaphysically refined form of material monism, a type-monism of things; that light and night are allomorphs of (...) what-is ; and that the key features of what-is are entailed by the theory of material monism. (shrink)