An interesting positive theory is the GPK theory. The models of this theory include all hyperuniverses (see [5] for a definition of these ones). Here we add a form of the axiom of infinity and a new scheme to obtain GPK∞+. We show that in these conditions, we can interprete the Kelley‐Morse theory (KM) in GPK∞+ (Theorem 3.7). This needs a preliminary property which give an interpretation of the Zermelo‐Fraenkel set theory (ZF) in GPK∞+. (...) We also see what happens in the original GPK theory. Before doing this, we first need to study the basic properties of the theory. This is done in the first two sections. (shrink)

In this article I investigate the phenomenon of minimum and minimal models of second-order set theories, focusing on Kelley–Morse set theory KM, Gödel–Bernays set theory GB, and GB augmented with the principle of Elementary Transfinite Recursion. The main results are the following. (1) A countable model of ZFC has a minimum GBC-realization if and only if it admits a parametrically definable global well order. (2) Countable models of GBC admit minimal extensions with the same sets. (3) There is (...) no minimum transitive model of KM. (4) There is a minimum β-model of GB+ETR. The main question left unanswered by this article is whether there is a minimum transitive model of GB+ETR. (shrink)

This article studies three most basic systems of truth as well as their subsystems over set theory ZF possibly with AC or the axiom of global choice GC, and then correlates them with subsystems of Morse–Kelley class theory MK. The article aims at making an initial step towards the axiomatic study of truth in set theory in connection with class theory. Some new results on the side of class theory, such as conservativity, forcing and some (...) forms of the reflection principle, are also presented. The equivalence results among systems of truth and classes obtained in this article are summarized in Theorem 104 , Theorem 107 and Theorem 108. (shrink)

After reviewing various natural bi-interpretations in urelement set theory, including second-order set theories with urelements, we explore the strength of second-order reflection in these contexts. Ultimately, we prove, second-order reflection with the abundant atom axiom is bi-interpretable and hence also equiconsistent with the existence of a supercompact cardinal. The proof relies on a reflection characterization of supercompactness, namely, a cardinal κ is supercompact if and only if every Π11 sentence true in a structure M (of any size) containing κ (...) in a language of size less than κ is also true in a substructure m≺M of size less than κ with m∩κ∈κ. (shrink)

In this paper, we study when a set-continuous operator has a fixed-point that is the intersection of a directed family. The framework of our study is the Kelley-Morse theory KMC– and the Gödel-Bernays theory GBC–, both theories including an Axiom of Choice and excluding the Axiom of Foundation. On the one hand, we prove a result concerning monotone operators in KMC– that cannot be proved in GBC–. On the other hand, we study conditions on directed superclasses in GBC– (...) in order that their intersection is a fixed-point of a set-continuous operator. Finally, we illustrate our results with a solution to the liar paradox and a construction of maximal bisimulations. (shrink)

A structural (as opposed to Zadeh's quantitative) approach to fuzziness is given, based on the operator "very", which is added to the language of set theory together with some elementary axioms about it. Due to the axiom of foundation and to a lifting axiom, the operator is proved trivial on the cumulative hierarchy of ZF. So we have to drop either foundation or lifting. Since fuzziness concerns complemented predicates rather than sets, a class theory is needed for the (...) very operator. And of them the Kelley-Morse (KM) theory is more appropriate for reasons of class existence. Several definable realizations of the very-operator are presented in KM⁻. In the last section we consider the operator "very" without the lifting axiom on classes of urelements. To each structurally fuzzy set X a traditional quantitative fuzzy set X̄ is assigned -- its quantitative representation. This way we are able partly to recover ordinary fuzzy sets from the structurally fuzzy ones. (shrink)

In this paper I prove the following theorems which are the converses of some results of Judah and Laver (1983) and of Judah and Marshall (1993).-IfKM+ATW is not an extension by definition ofKM (and the model involved is well founded), then the existence of two inaccessible cardinals is consistent with ZF.-IfKM+ATW is not a conservative extension ofKM (and the model involved is well founded), then the existence of an inaccessible number of inaccessible cardinals is consistent with ZF.whereKM is Kelley Morse (...) theory andKM+ATW isKM with types of well-orders. (shrink)

According to Cantor (Mathematische Annalen 21:545–586, 1883 ; Cantor’s letter to Dedekind, 1899 ) a set is any multitude which can be thought of as one (“jedes Viele, welches sich als Eines denken läßt”) without contradiction—a consistent multitude. Other multitudes are inconsistent or paradoxical. Set theoretical paradoxes have common root—lack of understanding why some multitudes are not sets. Why some multitudes of objects of thought cannot themselves be objects of thought? Moreover, it is a logical truth that such multitudes do (...) exist. However we do not understand this logical truth so well as we understand, for example, the logical truth $${\forall x \, x = x}$$ . In this paper we formulate a logical truth which we call the productivity principle. Rusell (Proc Lond Math Soc 4(2):29–53, 1906 ) was the first one to formulate this principle, but in a restricted form and with a different purpose. The principle explicates a logical mechanism that lies behind paradoxical multitudes, and is understandable as well as any simple logical truth. However, it does not explain the concept of set. It only sets logical bounds of the concept within the framework of the classical two valued $${\in}$$ -language. The principle behaves as a logical regulator of any theory we formulate to explain and describe sets. It provides tools to identify paradoxical classes inside the theory. We show how the known paradoxical classes follow from the productivity principle and how the principle gives us a uniform way to generate new paradoxical classes. In the case of ZFC set theory the productivity principle shows that the limitation of size principles are of a restrictive nature and that they do not explain which classes are sets. The productivity principle, as a logical regulator, can have a definite heuristic role in the development of a consistent set theory. We sketch such a theory—the cumulative cardinal theory of sets. The theory is based on the idea of cardinality of collecting objects into sets. Its development is guided by means of the productivity principle in such a way that its consistency seems plausible. Moreover, the theory inherits good properties from cardinal conception and from cumulative conception of sets. Because of the cardinality principle it can easily justify the replacement axiom, and because of the cumulative property it can easily justify the power set axiom and the union axiom. It would be possible to prove that the cumulative cardinal theory of sets is equivalent to the Morse–Kelley set theory. In this way we provide a natural and plausibly consistent axiomatization for the Morse–Kelley set theory. (shrink)

We study reflection principles in Kelley-Morse set theory with urelements (KMU). We first show that First-Order Reflection Principle is not provable in KMU with Global Choice. We then show that KMU + Limitation of Size + Second-Order Reflection Principle is mutually interpretable with KM + Second-Order Reflection Principle. Furthermore, these two theories are also shown to be bi-interpretable with parameters. Finally, assuming the existence of a κ+-supercompact cardinal κ in KMU, we construct a model of KMU + Second-Order Reflection (...) Principle where Limitation of Size fails. (shrink)

The class forcing theorem, which asserts that every class forcing notion ${\mathbb {P}}$ admits a forcing relation $\Vdash _{\mathbb {P}}$, that is, a relation satisfying the forcing relation recursion—it follows that statements true in the corresponding forcing extensions are forced and forced statements are true—is equivalent over Gödel–Bernays set theory $\text {GBC}$ to the principle of elementary transfinite recursion $\text {ETR}_{\text {Ord}}$ for class recursions of length $\text {Ord}$. It is also equivalent to the existence of truth predicates for (...) the infinitary languages $\mathcal {L}_{\text {Ord},\omega }$, allowing any class parameter A; to the existence of truth predicates for the language $\mathcal {L}_{\text {Ord},\text {Ord}}$ ; to the existence of $\text {Ord}$ -iterated truth predicates for first-order set theory $\mathcal {L}_{\omega,\omega }$ ; to the assertion that every separative class partial order ${\mathbb {P}}$ has a set-complete class Boolean completion; to a class-join separation principle; and to the principle of determinacy for clopen class games of rank at most $\text {Ord}+1$. Unlike set forcing, if every class forcing notion ${\mathbb {P}}$ has a forcing relation merely for atomic formulas, then every such ${\mathbb {P}}$ has a uniform forcing relation applicable simultaneously to all formulas. Our results situate the class forcing theorem in the rich hierarchy of theories between $\text {GBC}$ and Kelley–Morse set theory $\text {KM}$. (shrink)

In 1970, K. Kunen, working in the context of Kelley–Morse set theory, showed that the existence of a nontrivial elementary embedding j:V→V is inconsistent. In this paper, we give a finer analysis of the implications of his result for embeddings V→V relative to models of ZFC. We do this by working in the extended language , using as axioms all the usual axioms of ZFC , along with an axiom schema that asserts that j is a nontrivial elementary embedding. (...) Without additional axiomatic assumptions on j, we show that that the resulting theory is weaker than an ω-Erdös cardinal, but stronger than n-ineffables. We show that natural models of ZFC+BTEE give rise to Schindler’s remarkable cardinals. The approach to inconsistency from ZFC+BTEE forks into two paths: extensions of ZFC+BTEE+Cofinal Axiom and ZFC+BTEE+¬Cofinal Axiom, where Cofinal Axiom asserts that the critical sequence is cofinal in the ordinals. We describe near-minimal inconsistent extensions of each of these theories. The path toward inconsistency from ZFC+BTEE+¬Cofinal Axiom is paved with a sequence of theories of increasing large cardinal strength. Indeed, the extensions of the theory ZFC +“j is a nontrivial elementary embedding” form a hierarchy of axioms, ranging in strength from Con to the existence of a cardinal that is super-n-huge for every n, to inconsistency. This hierarchy is parallel to the usual hierarchy of large cardinal axioms, and can be used in the same way. We also isolate several intermediate-strength axioms which, when added to ZFC+BTEE, produce theories having strengths in the vicinity of a measurable cardinal of high Mitchell order, a strong cardinal, ω Woodin cardinals, and n-huge cardinals. We also determine precisely which combinations of axioms, of the form result in inconsistency. (shrink)

Assuming the consistency ofZF + “There is an inaccessible number of inaccessibles”, we prove that Kelley Morse theory plus types is not a conservative extension of Kelley-Morse theory.

Acute care nurse practitioner roles have been introduced in many countries. The acute care nurse practitioner provides nursing and medical care to meet the complex needs of patients and their families using a holistic, health‐centred approach. There are many pressures to adopt a performance framework and execute activities and tasks. Little time may be left to explore domains of advanced practice nursing and develop other forms of knowledge. The primary objective of praxis is to integrate theory, practice and art, (...) and facilitate the recognition and valuing of different types of knowledge through reflection. With this framework, the acute care nurse practitioner assumes the role of clinician and researcher. Praxis can be used to develop the acute care nurse practitioner role as an advanced practice nursing role. A praxis framework permeates all aspects of the acute care nurse practitioner's practice. Praxis influences how relationships are structured with patients, families and colleagues in the work setting. Decision‐makers at different levels need to recognize the contribution of praxis in the full development of the acute care nurse practitioner role. Different strategies can be used by educators to assist students and practitioners to develop a praxis framework. (shrink)

"Ontology and the Foundations of Mathematics" consists of three papers concerned with ontological issues in the foundations of mathematics. Chapter 1, "Numbers and Persons," confronts the problem of the inscrutability of numerical reference and argues that, even if inscrutable, the reference of the numerals, as we ordinarily use them, is determined much more precisely than up to isomorphism. We argue that the truth conditions of a variety of numerical modal and counterfactual sentences place serious constraints on the sorts of items (...) to which numerals, as we ordinarily use them, can be taken to refer: Numerals cannot be taken to refer to objects that exist contingently such as people, mountains, or rivers, but rather must be taken to refer to objects that exist necessarily such as abstracta. ;Chapter 2, "Modern Set Theory and Replacement," takes up a challenge to explain the reasons one should accept the axiom of replacement of Zermelo-Fraenkel set theory, when its applications within ordinary mathematics and the rest of science are often described as rare and recondite. We argue that this is not a question one should be interested in; replacement is required to ensure that the element-set relation is well-founded as well as to ensure that the cumulation of sets described by set theory reaches and proceeds beyond the level o of the cumulative hierarchy. A more interesting question is whether we should accept instances of replacement on uncountable sets, for these are indeed rarely used outside higher set theory. We argue that the best case for replacement comes not from direct, intuitive considerations, but from the role replacement plays in the formulation of transfinite recursion and the theory of ordinals, and from the fact that it permits us to express and assert the content of the modern cumulative view of the set-theoretic universe as arrayed in a cumulative hierarchy of levels. ;Chapter 3, "A No-Class Theory of Classes," makes use of the apparatus of plural quantification to construe talk of classes as plural talk about sets, and thus provide an interpretation of both one- and two-sorted versions of first-order Morse-Kelley set theory, an impredicative theory of classes. We argue that the plural interpretation of impredicative theories of classes has a number of advantages over more traditional interpretations of the language of classes as involving singular reference to gigantic set-like entities, only too encompassing to be sets, the most important of these being perhaps that it makes the machinery of classes available for the formalization of much recent and very interesting work in set theory without threatening the universality of the theory as the most comprehensive theory of collections, when these are understood as objects. (shrink)

Jones's (1991) issue-contingent model of ethical decision making posits that six dimensions of moral intensity influence decision markers' recognition of an issue as a moral problem and subsequent behavior. He notes that "organizational settings present special challenges to moral agents" (1991, p. 390) and that organizational factors affect "moral decision making and behavior at two points: establishing moral intent and engaging in moral behavior" (1991, p. 391). This model, however, minimizes both the impact of organizational setting and organizational factors on (...) these experiences of ethical issues. In this theory, context is modeled as affecting the moral intent and behavior of the actor rather than directly affecting the issue's moral intensity. Here we look specifically at the effect of context on the moral intensity of ethical issues through a phenomenological study. Our results indicate that in certain environments, context may be critical in affecting the moral intensity of ethical issues. Thus, researchers should consider it more fully when assessing these issues' moral intensity. (shrink)

In Arrovian social choice theory assuming the independence of irrelevant alternatives, Murakami (1968) proved two theorems about complete and transitive collective choice rules that satisfy strict non-imposition (citizens’ sovereignty), one being a dichotomy theorem about Paretian or anti-Paretian rules and the other a dictator-or-inverse-dictator impossibility theorem without the Pareto principle. It has been claimed in the later literature that a theorem of Malawski and Zhou (1994) is a generalization of Murakami’s dichotomy theorem and that Wilson’s (1972) impossibility theorem is (...) stronger than Murakami’s impossibility theorem, both by virtue of replacing Murakami’s assumption of strict non-imposition with the assumptions of non-imposition and non-nullness. In this note, we first point out that these claims are incorrect: non-imposition and non-nullness are together equivalent to strict non-imposition for all transitive collective choice rules. We then generalize Murakami’s dichotomy and impossibility theorems to the setting of incomplete social preference. We prove that if one drops completeness from Murakami’s assumptions, his remaining assumptions imply (i) that a collective choice rule is either Paretian, anti-Paretian, or dis-Paretian (unanimous individual preference implies noncomparability) and (ii) that adding proposed constraints on noncomparability, such as the regularity axiom of Eliaz and Ok (2006), restores Murakami’s dictator-or-inverse-dictator result. (shrink)

Despite advances in theory, often driven by feminist ethicists, research ethics struggles in practice to adequately account for and respond to the agency and autonomy of people considered vulnerable in the research context. We argue that shifts within feminist research ethics scholarship to better characterise and respond to autonomy and agency can be bolstered by further grounding in discourses from the social sciences, in work that confirms the complex nature of human agency in contexts of structural and other sources (...) of vulnerability. We discuss some of the core concepts and critiques emerging from the literature on women and children's agency in under‐resourced settings, highlighting calls to move from individualistic to relational models of agency, and to recognise the ambiguous, value‐laden, and heterogeneous nature of the concept. We then draw out what these conceptual shifts might mean for research ethics obligations and guidance, illustrating our analysis using a case vignette based on research ethics work conducted in South Africa. We conclude that if research practices are to be supportive of agency, it will be crucial to scrutinise the moral judgements which underpin accounts of agency, derive more situated definitions of and responses to agency, and enable people and participants to influence these based on their own experiences and self‐perceptions. (shrink)

In positive theories, we have an axiom scheme of comprehension for positive formulas. We study here the “generalized positive” theory GPK∞+. Natural models of this theory are hyperuniverses. The author has shown in [2] that GPK∞+ interprets the Kelley Morse class theory. Here we prove that GPK∞+ + ACWF and the Kelley-Morse class theory with the axiom of global choice and the axiom “On is ramifiable” are mutually interpretable. This shows that GPK∞+ + ACWF is a (...) “strong” theory since “On is ramifiable” implies the existence of a proper class of inaccessible cardinals. (shrink)

We will present an elementary theory in which we can speak of mereological sets composed of distributive classes. Besides the concept of a distributive class and the membership relation , it will possess the notion of a mereological set and the relation of being a mereological part. In this theory we will interpret Morse’s elementary set theory (cf. Morse [11]). We will show that our theory has a model, if only Morse’s theory has one.

The propositional calculus AoC, “Algebra of Classes”,and the extended propositional calculus EAC, “Extended Algebra ofClasses” are introduced in this paper. They are extensions, by additionalpropositional functions which are not invariant under the biconditional,of the corresponding classical propositional systems. Theirorigin lies in an analysis, motivated by Cantor’s concept of the cardinalnumbers, of A. P. Morse’s impredicative, polysynthetic set theory.

We describe a first-order theory of generalized sets intended to allow a similar treatment of sets and proper classes. The theory is motivated by the iterative conception of set. It has a ternary membership symbol interpreted as membership relative to a set-building step. Set and proper class are defined notions. We prove that sets and proper classes with a defined membership form an inner model of Bernays-Morse class theory. We extend ordinal and cardinal notions to generalized sets (...) and prove ordinal and cardinal results in the theory. We prove that the theory is consistent relative to ZFC + (∃ x) [ x is a strongly inaccessible cardinal]. (shrink)

Higher types can readily be added to set theory, Bernays-Morse set theory being an example. A type for each ordinal is added in [2]. Adding higher types to set theory provides a neat solution to the problem of how to handle higher type categories. We give the basic definitions, and prove cocompleteness of some higher type categories. MSC: 14A15.

In this article we show that Morse-Kelley class theory provides us with an adequate framework for class forcing. We give a rigorous definition of class forcing in a model \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$$$ \end{document} of MK, the main result being that the Definability Lemma can be proven without restricting the notion of forcing. Furthermore we show under which conditions the axioms are preserved. We conclude by proving that Laver’s Theorem does not hold (...) for class forcings. (shrink)

Foundations of a General Theory of Manifolds [Cantor, 1883], which I will refer to as the Grundlagen, is Cantor’s first work on the general theory of sets. It was a separate printing, with a preface and some footnotes added, of the fifth in a series of six papers under the title of “On infinite linear point manifolds”. I want to briefly describe some of the achievements of this great work. But at the same time, I want to discuss (...) its connection with the so-called paradoxes in set theory. There seems to be some agreement now that Cantor’s own understanding of the theory of transfinite numbers in that monograph did not contain an implicit contradiction; but there is less agreement about exactly why this is so and about the content of the theory itself. For various reasons, both historical and internal, the Grundlagen seems not to have been widely read compared to later works of Cantor, and to have been even less well understood. But even some of the more recent discussions of the work, while recognizing to some degree its unique character, misunderstand it on crucial points and fail to convey its true worth. (shrink)

One of the central problems in the philosophy of action is to spell out the distinction between action and what merely happens, e.g., a wink versus an eye twitch. This essay proposes a theory of action offering an account of this distinction. The central claim of the theory is that action is movement that is controlled by the mover, where movement is understood capaciously and control is characterized by a trio of conditions consisting of an aim condition, a (...) modal condition, and an explanatory condition. Importantly, being controlled is shown to be a determinable property of movements, and its determination dimensions are isolated. Paired with the claim that action is movement that is controlled by the mover, this account of control as a determinable illuminates the diversity within the category of action. (shrink)

In this highly original of realism, David Kelley argues that perception is the discrimination of objects as entities, that the awareness of these objects is direct, and that perception is a reliable foundation for empirical knowledge. His argument relies on the basic principle of the 'primacy of existence, ' in opposition to Cartesian representationalism and Kantian idealism.

There is a well-known equivalence between avoiding accuracy dominance and having probabilistically coherent credences (see, e.g., de Finetti 1974, Joyce 2009, Predd et al. 2009, Pettigrew 2016). However, this equivalence has been established only when the set of propositions on which credence functions are defined is finite. In this paper, I establish connections between accuracy dominance and coherence when credence functions are defined on an infinite set of propositions. In particular, I establish the necessary results to extend the classic accuracy (...) argument for probabilism to certain classes of infinite sets of propositions including countably infinite partitions. (shrink)

This is an introduction to set theory and logic that starts completely from scratch. The text is accompanied by many methodological remarks and explanations.

Review by A. Kanamori, Boston University (author of The Higher Infinite), review in The Bulletin of Symbolic Logic: “Notwithstanding and braving the daunting complexities of this labyrinth, José Ferreirós has written a magisterial account of the history of set theory which is panoramic, balanced and engaging. Not only does this book synthesize much previous work and provide fresh insights and points of view, but it also features a major innovation, a full-fledged treatment of the emergence of the set-theoretic approach (...) in mathematics from the early nineteenth century. Much of history is in the details, and much of good history is in tone, emphasis, and the drawing together of different strands. Without being Whiggish, Ferreirós is never far from major synthetic themes, themes that in the main work toward balance and pull back from excesses of emphasis of some recent histories. The main criticism of the book would have to be on matters of broad interpretation. Yet, Ferreirós brings a considerable mathematical acuity and expertise to his enterprise, and this makes his viewpoints the more compelling.” . (shrink)

According to subjectivism about ill-being, the token states of affairs that are basically bad for you must be suitably connected, under the proper conditions, to your negative attitudes. This article explores the prospects for this family of theories and addresses some of its challenges. This article (i) shows that subjectivism about ill-being can be derived from a more general doctrine that requires a negatively valenced relationship between any welfare subject and the token states that are of basic harm to that (...) subject and (ii) responds to some objections, including the objection that subjectivists about ill-being cannot plausibly explain the badness of pain. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:How Policies and Practices in Medical Settings Impact Communication Access with Deaf Patients and CaregiversKelley Cooper, Maggie Russell, Debra Chaiken, Michael W. Mazzaroppi, and Gretchen RomanIntroductionWe are a group of Deaf community members, sign language interpreters, organizational leaders, and academic partners. We have a collective point of view about how policies and practices in medical settings impact communication access with Deaf patients and caregivers. Here, we account multiple stories (...) from our respective experiences in an effort to improve healthcare institutions' awareness of the recommended modalities when communicating with Deaf patients accessing care. Our stories clarify any misunderstandings about communication with Deaf patients who expressively use spoken language and receptively use sign language. We convey that it is imperative to use visual language when explaining discharge paperwork and emphasize that it is critical for a Deaf caregiver to be fully aware of the plan of care when offering support to their loved one. We illustrate the importance of honoring the requests for in-person sign language interpreting versus video remote interpreting (VRI) as well as requests for Deaf-Hearing sign language interpreter teams. Deaf interpreters bring formative cultural, linguistic, and life experiences and work in partnership with a hearing interpreter to provide a more nuanced communication exchange across a wide range of visual languages.Maggie Russell: Anecdote 1The hospital recidivism rate for a Deaf Nepali male patient continues to increase. As the Interpreter Referral Service Director, I am aware of this patient because he receives care management services from our organization. He has several life-threatening conditions, attends dialysis, is on multiple medications, and is frequently in and out of the local hospital. The hospital considers him as someone who identifies as an oral Deaf person, as he has severe to profound hearing loss with little or no residual hearing and visually receives signed language but expressively uses spoken language. Three interpreters, a spoken Nepalese interpreter, a Deaf Nepali Sign Language (NSL) interpreter, and a hearing American Sign Language (ASL) interpreter, working together as a team are recommended for effective communication with this patient and the medical team of providers. However, interpreting services at the hospital provide only one interpreter, a spoken Nepalese interpreter, which [End Page E3] does not satisfy the necessary accommodations for access. A plethora of prescriptions were added to his regimen to counter the condition that caused a recent inpatient stay. The patient's wife is his primary caregiver. She communicates receptively and expressively using NSL. A Deaf NSL and hearing ASL interpreter team creates effective communication with his wife and the medical team of providers. Since she is expected to follow the doctor's recommendations as explained in the discharge instructions, she also requires accommodations for communication access. Neither the patient nor his wife received a formal education, and they do not read or write English or the language of their country of origin. Therefore, information in English or Nepalese conveyed in the printed discharge paperwork is inaccessible. The new medications were not incorporated into his already established monthly "pill pack," and the couple was unable to read the information on the pill bottles that were delivered to their home. Subsequently, incorrect use of the newly prescribed medications significantly delayed the patient's course of recovery. This couple also had minimal exposure to medical information and medical processes prior to living in the United States; the medical services in the refugee camps in Nepal were typically non-existent. Utilizing a hearing ASL interpreter alone does not constitute barrier-free access for either of these individuals. Interpreting medical documents in a visual format is so critical for providing access, but it doesn't necessarily guarantee comprehension because of their limited health literacy. In addition to employing the recommended interpreting team, using teach-back methods during an encounter is a good way for medical providers to ensure the patient and caregiver's understanding of the plan of care.Maggie Russell: Anecdote 2As the Interpreter Referral Service Director at our organization, I served as the hearing interpreter on a Deaf-Hearing ASL interpreter team at a follow-up gastrointestinal appointment from a gall bladder biopsy for a Deaf male patient, along with his Deaf... (shrink)

ABSTRACT Theories of sets such as Zermelo Fraenkel set theory are usually presented as the combination of two distinct kinds of principles: logical and set-theoretic principles. The set-theoretic principles are imposed ‘on top’ of first-order logic. This is in agreement with a traditional view of logic as universally applicable and topic neutral. Such a view of logic has been rejected by the intuitionists, on the ground that quantification over infinite domains requires the use of intuitionistic rather than classical logic. (...) In the following, I consider constructive set theories, which use intuitionistic rather than classical logic, and argue that they manifest a distinctive interdependence or an entanglement between sets and logic. In fact, Martin-Löf type theory identifies fundamental logical and set-theoretic notions. Remarkably, one of the motivations for this identification is the thought that classical quantification over infinite domains is problematic, while intuitionistic quantification is not. The approach to quantification adopted in Martin-Löf’s type theory is subtly interconnected with its predicativity. I conclude by recalling key aspects of an approach to predicativity inspired by Poincaré, which focuses on the issue of correct quantification over infinite domains and relate it back to Martin-Löf type theory. (shrink)

This study examines employee perceptions on the effective adoption of artificial intelligence principles in their organizations. 49 interviews were conducted with employees of 24 organizations across 11 countries. Participants worked directly with AI across a range of positions, from junior data scientist to Chief Analytics Officer. The study found that there are eleven components that could impact the effective adoption of AI principles in organizations: communication, management support, training, an ethics office, a reporting mechanism, enforcement, measurement, accompanying technical processes, a (...) sufficient technical infrastructure, organizational structure, and an interdisciplinary approach. The components are discussed in the context of business code adoption theory. The findings offer a first step in understanding potential methods for the effective adoption of AI principles in organizations. (shrink)

The 'history of ideas', better known these days as intellectual history, is a flourishing field of study which has been the object of much controversy but hardly any historical exploration. This major new work from Donald R. Kelley is the first comprehensive history of intellectual history, tracing the study of the history of thought from ancient, medieval and early modern times, its emergence as the 'history of ideas' in the 18th century, and its subsequent expansion. The point of departure for (...) this study is the perspective opened up by Victor Cousin in the early 19th-century on 'Eclecticism' and its association with the history of philosophy established by Renaissance scholars. Kelley considers a broad range of topics, including the rivalry between 'ideas' and language, the rise of cultural history, the contributions of certain 19th- and 20th-century practitioners of the history of ideas in interdisciplinary areas of philosophy, literature and the sciences, and finally the current state of intellectual history. The central theme of the book is the interplay between the canon of philosophical thought and the tradition of language and textual study, the divergence of the latter marking the 'descent of ideas' into the realm of cultural history. (shrink)

This article addresses the question of fundamental entities in set theory. It takes up J. Hamkins’ claim that models of set theory are such fundamental entities and investigates it using the methodology of P. Maddy’s naturalism, Second Philosophy. In accordance with this methodology, I investigate the historical case study of the use of models in the introduction of forcing, compare this case to contemporary practice and give a systematic account of how set-theoretic practice can be said to introduce (...) models as new entities. In conclusion, I argue for a view that takes both sets and models to be fundamental entities in set theory. (shrink)

In arguing against the view that the ethical standards for business are separate from normal interpersonal standards, virtue theory has been applied to business ethics in a limited manner. Previous virtue theorists have argued that this separation need not occur because the virtues for succeeding in business are congruent with civic and personal virtues. However, they have neglected the fact that virtue theory stresses that virtues are formed to fulfil certain desires, ends, and purposes of the person. Since (...) ends are formed within a community, business and corporations should view themselves as members of the community which contributes to the ethical development of its individuals. Hence, I argue that business cannot have a separate standard of ethical behaviour than that of its community, because its goals are means which are subordinate to the ultimate goal of individual and community flourishing. (shrink)

John Burgess in a 2004 paper combined plural logic and a new version of the idea of limitation of size to give an elegant motivation of the axioms of ZFC set theory. His proposal is meant to improve on earlier work by Paul Bernays in two ways. I argue that both attempted improvements fail. I am grateful to Philip Welch, two anonymous referees, and especially Ignacio Jané for written comments on earlier versions of this paper, which have led to (...) substantial improvements. Thanks also to the participants in a discussion group at the University of Bristol, where an earlier version was presented. (shrink)