Equivalents of Mingle and Positive Paradox

Relevant logic is a proper subset of classical logic. It does not include among its theorems any ofpositive paradox A (B A)mingle A (A A)linear order (A B) (B A)unrelated extremes (A ) (B B¯)This article shows that those four formulas have different effects when added to relevant logic, and then lists many formulas that have the same effect as positive paradox or mingle.     

Algebras of Intervals and a Logic of Conditional Assertions

Intervals in boolean algebras enter into the study of conditional assertions (or events) in two ways: directly, either from intuitive arguments or from Goodman, Nguyen and Walker's representation theorem, as suitable mathematical entities to bear conditional probabilities, or indirectly, via a representation theorem for the family of algebras associated with de Finetti's three-valued logic of conditional assertions/events. Further representation theorems forge a connection with rough sets. The representation theorems and an equivalent of the boolean prime ideal theorem yield an algebraic completeness theorem for the three-valued logic. This in turn leads to a Henkin-style completeness theorem. Adequacy with respect to a family of Kripke models for de Finetti's logic, ukasiewicz's three-valued logic and Priest's Logic of Paradox is demonstrated. The extension to first-order yields a short proof of adequacy for Körner's logic of inexact predicates.     

A Revenge-Immune Solution to the Semantic Paradoxes

The paper offers a solution to the semantic paradoxes, one in which (1) we keep the unrestricted truth schema True(A)A, and (2) the object language can include its own metalanguage. Because of the first feature, classical logic must be restricted, but full classical reasoning applies in ordinary contexts, including standard set theory. The more general logic that replaces classical logic includes a principle of substitutivity of equivalents, which with the truth schema leads to the general intersubstitutivity of True(A) with A within the language.The logic is also shown to have the resources required to represent the way in which sentences (like the Liar sentence and the Curry sentence) that lead to paradox in classical logic are defective. We can in fact define a hierarchy of defectiveness predicates within the language. Contrary to claims that any solution to the paradoxes just breeds further paradoxes (revenge problems) involving defectiveness predicates, there is a general consistency/conservativeness proof that shows that talk of truth and the various levels of defectiveness can all be made coherent together within a single object language.     

Confidentiality and paradox: the location of ethical space

Implicit in Jung's alchemical metaphor of the vas bene clausum is the idea of an analytic frame with a space inside it for something vital, a relationship between two selves, to develop. For this to happen, analysts must respect their patients' rights to confidentiality. The paper explores the analyst's state of mind and the intrapsychic processes that are constellated when struggling with ethical dilemmas about issues of confidentiality in analytic work. The author suggests that at times when analysts consider breaking confidentiality, there is often a disturbing inner conflict between their moral principles (codes of ethics) and their internal personal ethical attitude. At these difficult moments, the mutuality of the work and the vas bene clausum can be significantly disrupted. The analyst tries to find a third position, a mental and emotional ethical space where the subjective and the objective, the ethical and the unethical can become more companionable bedfellows.     

The Logic of Instance Ontology

An ontology's theory of ontic predication has implications for the concomitant predicate logic. Remarkable in its analytic power for both ontology and logic is the here developed Particularized Predicate Logic (PPL), the logic inherent in the realist version of the doctrine of unit or individuated predicates. PPL, as axiomatized and proven consistent below, is a three-sorted impredicative intensional logic with identity, having variables ranging over individuals x, intensions R, and instances of intensions Ri. The power of PPL is illustrated by its clarification of the self-referential nature of impredicative definitions and its distinguishing between legitimate and illegitimate forms. With a well-motivated refinement on the axiom of comprehension, PPL is, in effect, a higher-order logic without a forced stratification of predicates into types or the use of other ad hoc restrictions. The Russell–Priest characterization of the classic self-referential paradoxes is used to show how PPL diagnosis and solves these antimonies. A direct application of PPL is made to Grelling's Paradox. Also shown is how PPL can distinguish between identity and indiscernibility.     

What the Liar Taught Achilles

Zeno's paradoxes of motion and the semantic paradoxes of the Liar have long been thought to have metaphorical affinities. There are, in fact, isomorphisms between variations of Zeno's paradoxes and variations of the Liar paradox in infinite-valued logic. Representing these paradoxes in dynamical systems theory reveals fractal images and provides other geometric ways of visualizing and conceptualizing the paradoxes.     

Two Envelopes and Binding

This paper describes a way of defending a modification of Eckhardt's [2013] solution to the Two Envelopes Paradox. The defence is based on ideas from Arntzenius, Elga, and Hawthorne [2004].     

Better than ever? Employee reactions to ethical failures in organizations,and the ethical recovery paradox

This research examines organizational attempts to recover internally from ethical failures witnessed by employees. Drawing on research on service failure recovery, relationship repair, and behavioral ethics, we investigate how witnessing unethical acts in an organization impacts employees and their relationship with their organization. In two studies—one in the lab and one in the field—we examine the extent to which it is possible for organizations to recover fully from these ethical lapses. Results reveal an ethical recovery paradox, in which exemplary organizational efforts to recover internally from ethical failure may enhance employee perceptions of the organization to a more positive level than if no ethical failure had occurred.     

IN PRAISE OF A LOGIC OF DEFINITIONS THAT TOLERATES Ω‐INCONSISTENCY

I argue that a general logic of definitions must tolerate ω‐inconsistency. I present a semantical scheme, , under which some definitions imply ω‐inconsistent sets of sentences. I draw attention to attractive features of this scheme, and I argue that yields the minimal general logic of definitions. I conclude that any acceptable general logic should permit definitions that generate ω‐inconsistency. This conclusion gains support from the application of to the theory of truth.     

On Quantitative and Qualitative Parsimony

The distinction between quantitative and qualitative parsimony is supposed to allow David Lewis to dismiss one of the charges against his modal realism: that is, the charge of bloated ontology. The aim of this paper is to undermine Lewis's response to this objection. In order to do this, a distinction between multipliable and nonmultipliable objects is introduced. Based on this it is argued that the acceptance of Lewis's response requires one to believe in modal realism in the first place—that is, one has to believe in the view that the existence of nonactual spatiotemporal worlds does not affect the quality of the ontological commitment. Although the paper focuses on the problem of the metaphysics of possible worlds, this should be regarded merely as a case study. Accordingly, the results of this analysis should find applications in other metaphysical debates as well.