The complexity of equivalence relations has received much attention in the recent literature. The main tool for such endeavour is the following reducibility: given equivalence relations R and S on natural numbers, R is computably reducible to S if there is a computable function f:ω→ω that induces an injective map from R-equivalence classes to S-equivalence classes. In order to compare the complexity of equivalence relations which are computable, researchers considered also feasible variants of computable reducibility, such as the polynomial-time reducibility. (...) In this work, we explore Peq, the degree structure generated by primitive recursive reducibility on primitive recursive equivalence relations with infinitely many equivalence classes. In contrast with all other known degree structures on equivalence relations, we show that Peq has much more structure: e.g., we show that it is a dense distributive lattice. On the other hand, we also offer evidence of the intricacy of Peq, proving, e.g., that the structure is neither rigid nor homogeneous. (shrink)

We make some beginning observations about the category Eq of equivalence relations on the set of natural numbers, where a morphism between two equivalence relations R and S is a mapping from the set of R-equivalence classes to that of S-equivalence classes, which is induced by a computable function. We also consider some full subcategories of Eq, such as the category Eq(Σ01) of computably enumerable equivalence relations (called ceers), the category Eq(Π01) of co-computably enumerable equivalence relations, and the category Eq(Dark*) (...) whose objects are the so-called dark ceers plus the ceers with finitely many equivalence classes. Although in all these categories the monomorphisms coincide with the injective morphisms, we show that in Eq(Σ01) the epimorphisms coincide with the onto morphisms, but in Eq(Π01) there are epimorphisms that are not onto. Moreover, Eq, Eq(Σ01), and Eq(Dark*) are closed under finite products, binary coproducts, and coequalizers, but we give an example of two morphisms in Eq(Π01) whose coequalizer in Eq is not an object of Eq(Π01). (shrink)

It is prima facie uncontroversial that the justification of an assertion amounts to a collection of other (inferentially related) assertions. In this paper, we point at a class of assertions, i.e. mathematical assertions, that appear to systematically flout this principle. To justify a mathematical assertion (e.g. a theorem) is to provide a proof—and proofs are sequences of directives. The claim is backed up by linguistic data on the use of imperatives in proofs, and by a pragmatic analysis of theorems and (...) their proofs. Proofs, we argue, are sequences of instructions whose performance inevitably gets one to truth. It follows that a felicitous theorem, i.e. a theorem that has been correctly proven, is a persuasive theorem. When it comes to mathematical assertions, there is no sharp distinction between illocutionary and perlocutionary success. (shrink)

This note addresses the issue as to which ceers can be realized by word problems of computably enumerable (or, simply, c.e.) structures (such as c.e. semigroups, groups, and rings), where being realized means to fall in the same reducibility degree (under the notion of reducibility for equivalence relations usually called “computable reducibility”), or in the same isomorphism type (with the isomorphism induced by a computable function), or in the same strong isomorphism type (with the isomorphism induced by a computable permutation (...) of the natural numbers). We observe, e.g., that every ceer is isomorphic to the word problem of some c.e. semigroup, but (answering a question of Gao and Gerdes) not every ceer is in the same reducibility degree of the word problem of some finitely presented semigroup, nor is it in the same reducibility degree of some non‐periodic semigroup. We also show that the ceer provided by provable equivalence of Peano Arithmetic is in the same strong isomorphism type as the word problem of some non‐commutative and non‐Boolean c.e. ring. (shrink)

Computability theorists have introduced multiple hierarchies to measure the complexity of sets of natural numbers. The Kleene Hierarchy classifies sets according to the first-order complexity of their defining formulas. The Ershov Hierarchy classifies Δ20\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\varDelta ^0_2$$\end{document} sets with respect to the number of mistakes that are needed to approximate them. Biacino and Gerla extended the Kleene Hierarchy to the realm of fuzzy sets, whose membership functions range in a complete lattice L. In (...) this paper, we combine the Ershov Hierarchy and fuzzy set theory, by introducing and investigating the Fuzzy Ershov Hierarchy. In particular, we focus on the fuzzy n-c.e. sets which form the finite levels of this hierarchy. Intuitively, a fuzzy set is n-c.e. if its membership function can be approximated by changing monotonicity at most n-1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$n-1$$\end{document} times. We prove that the Fuzzy Ershov Hierarchy does not collapse; that, in analogy with the classical case, each fuzzy n-c.e. set can be represented as a Boolean combination of fuzzy c.e. sets; but that, contrary to the classical case, the Fuzzy Ershov Hierarchy does not exhaust the class of all Δ20\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\varDelta ^0_2$$\end{document} fuzzy sets. (shrink)

Computability theorists have introduced multiple hierarchies to measure the complexity of sets of natural numbers. The Kleene Hierarchy classifies sets according to the first-order complexity of their defining formulas. The Ershov Hierarchy classifies limit computable sets with respect to the number of mistakes that are needed to approximate them. Biacino and Gerla extended the Kleene Hierarchy to the realm of fuzzy sets, whose membership functions range in a complete lattice. In this paper, we combine the Ershov Hierarchy and fuzzy set (...) theory, by introducing and investigating the Fuzzy Ershov Hierarchy. (shrink)

We investigate the complexity of embeddings between bi-embeddable structures. In analogy with categoricity spectra, we define the bi-embeddable categoricity spectrum of a structure A as the family of Turing degrees that compute embeddings between any computable bi-embeddable copies of A; the degree of bi-embeddable categoricity of A is the least degree in this spectrum (if it exists). We extend many known results about categoricity spectra to the case of bi-embeddability. In particular, we exhibit structures without degree of bi-embeddable categoricity, and (...) we show that every degree d.c.e above 0(α) for α a computable successor ordinal and 0(λ) for λ a computable limit ordinal is a degree of bi-embeddable categoricity. We also give examples of families of degrees that are not bi-embeddable categoricity spectra. (shrink)

In this paper we argue, against a somewhat standard view, that pragmatic phenomena occur in mathematical language. We provide concrete examples supporting this thesis.

This paper is part of a project that is based on the notion of a dialectical system, introduced by Magari as a way of capturing trial and error mathematics. In Amidei et al. (2016, Rev. Symb. Logic, 9, 1–26) and Amidei et al. (2016, Rev. Symb. Logic, 9, 299–324), we investigated the expressive and computational power of dialectical systems, and we compared them to a new class of systems, that of quasi-dialectical systems, that enrich Magari’s systems with a natural mechanism (...) of revision. In the present paper we consider a third class of systems, that of p-dialectical systems, that naturally combine features coming from the two other cases. We prove several results about p-dialectical systems and the sets that they represent. Then we focus on the completions of first-order theories. In doing so, we consider systems with connectives, i.e. systems that encode the rules of classical logic. We show that any consistent system with connectives represents the completion of a given theory. We prove that dialectical and q-dialectical systems coincide with respect to the completions that they can represent. Yet, p-dialectical systems are more powerful; we exhibit a p-dialectical system representing a completion of Peano Arithmetic that is neither dialectical nor q-dialectical. (shrink)

We study the algorithmic complexity of isomorphic embeddings between computable structures.

We study degree spectra of structures with respect to the bi-embeddability relation. The bi-embeddability spectrum of a structure is the family of Turing degrees of its bi-embeddable copies. To facilitate our study we introduce the notions of bi-embeddable triviality and basis of a spectrum. Using bi-embeddable triviality we show that several known families of degrees are bi-embeddability spectra of structures. We then characterize the bi-embeddability spectra of linear orderings and study bases of bi-embeddability spectra of strongly locally finite graphs.

We aim at providing a philosophical analysis of the notion of “proof by Church’s Thesis”, which is – in a nutshell – the conceptual device that permits to rely on informal methods when working in Computability Theory. This notion allows, in most cases, to not specify the background model of computation in which a given algorithm – or a construction – is framed. In pursuing such analysis, we carefully reconstruct the development of this notion (from Post to Rogers, to the (...) present days), and we focus on some classical constructions of the field, such as the construction of a simple set. Then, we make use of this focus in order to support the following encompassing claim (which opposes to a somehow commonly received view): the informal side of Computability, consisting of the large class of methods typically employed in the proofs of the field, is not fully reducible to its formal counterpart. (shrink)

This paper studies algorithmic learning theory applied to algebraic structures. In previous papers, we have defined our framework, where a learner, given a family of structures, receives larger and larger pieces of an arbitrary copy of a structure in the family and, at each stage, is required to output a conjecture about the isomorphism type of such a structure. The learning is successful if there is a learner that eventually stabilizes to a correct conjecture. Here, we analyze the number of (...) mind changes that are needed to learn a given family K. We give a descriptive set-theoretic interpretation of such mind change complexity. We also study how bounding the Turing degree of learners affects the mind change complexity of a given family of algebraic structures. (shrink)

We combine computable structure theory and algorithmic learning theory to study learning of families of algebraic structures. Our main result is a model-theoretic characterization of the learning type InfEx_\iso, consisting of the structures whose isomorphism types can be learned in the limit. We show that a family of structures is InfEx_\iso-learnable if and only if the structures can be distinguished in terms of their \Sigma^2_inf-theories. We apply this characterization to familiar cases and we show the following: there is an infinite (...) learnable family of distributive lattices; no pair of Boolean algebras is learnable; no infinite family of linear orders is learnable. (shrink)

Computable reducibility is a well-established notion that allows to compare the complexity of various equivalence relations over the natural numbers. We generalize computable reducibility by introducing degree spectra of reducibility and bi-reducibility. These spectra provide a natural way of measuring the complexity of reductions between equivalence relations. We prove that any upward closed collection of Turing degrees with a countable basis can be realised as a reducibility spectrum or as a bi-reducibility spectrum. We show also that there is a reducibility (...) spectrum of computably enumerable equivalence relations with no countable basis and a reducibility spectrum of computably enumerable equivalence relations which is downward dense, thus has no basis. (shrink)

In previous work, we have combined computable structure theory and algorithmic learning theory to study which families of algebraic structures are learnable in the limit (up to isomorphism). In this paper, we measure the computational power that is needed to learn finite families of structures. In particular, we prove that, if a family of structures is both finite and learnable, then any oracle which computes the Halting set is able to achieve such a learning. On the other hand, we construct (...) a pair of structures which is learnable but no computable learner can learn it. (shrink)

In this paper we focus on the logicality of language, i.e. the idea that the language system contains a deductive device to exclude analytic constructions. Puzzling evidence for the logicality of language comes from acceptable contradictions and tautologies. The standard response in the literature involves assuming that the language system only accesses analyticities that are due to skeletons as opposed to standard logical forms. In this paper we submit evidence in support of alternative accounts of logicality, which reject the stipulation (...) of a natural logic and assume instead the meaning modulation of nonlogical terms. (shrink)

We offer a novel picture of mathematical language from the perspective of speech act theory. There are distinct speech acts within mathematics, and, as we intend to show, distinct illocutionary force indicators as well. Even mathematics in its most formalized version cannot do without some such indicators. This goes against a certain orthodoxy both in contemporary philosophy of mathematics and in speech act theory. As we will comment, the recognition of distinct illocutionary acts within logic and mathematics and the incorporation (...) of illocutionary force indicators in the formal language for both goes back to Frege’s conception of these topics. We are, therefore, going back to a Fregean perspective. This paper is part of a larger project of applying contemporary speech act theory to the scientific language of mathematics in order to uncover the varieties and regular combinations of illocutionary acts present in it. For reasons of space, we here concentrate only on assertive and declarative acts within mathematics, leaving the investigation of other kinds of acts for a future occasion. (shrink)

In this short paper, we analyse whether assuming that mathematical objects are “thin” in Linnebo's sense simplifies the epistemology of mathematics. Towards this end, we introduce the notion of transparency and show that not all thin objects are transparent. We end by arguing that, far from being a weakness of thin objects, the lack of transparency of some thin objects is a fruitful characteristic mark of abstract mathematics.

Computably enumerable equivalence relations received a lot of attention in the literature. The standard tool to classify ceers is provided by the computable reducibility \. This gives rise to a rich degree structure. In this paper, we lift the study of c-degrees to the \ case. In doing so, we rely on the Ershov hierarchy. For any notation a for a non-zero computable ordinal, we prove several algebraic properties of the degree structure induced by \ on the \ equivalence relations. (...) A special focus of our work is on the existence of infima and suprema of c-degrees. (shrink)

The Friedman–Stanley jump, extensively studied by descriptive set theorists, is a fundamental tool for gauging the complexity of Borel isomorphism relations. This paper focuses on a natural computable analog of this jump operator for equivalence relations on $\omega $, written ${\dotplus }$, recently introduced by Clemens, Coskey, and Krakoff. We offer a thorough analysis of the computable Friedman–Stanley jump and its connections with the hierarchy of countable equivalence relations under the computable reducibility $\leq _c$. In particular, we show that this (...) jump gives benchmark equivalence relations going up the hyperarithmetic hierarchy and we unveil the complicated highness hierarchy that arises from ${\dotplus }$. (shrink)

We study the algorithmic complexity of embeddings between bi-embeddable equivalence structures. We define the notions of computable bi-embeddable categoricity, \ bi-embeddable categoricity, and degrees of bi-embeddable categoricity. These notions mirror the classical notions used to study the complexity of isomorphisms between structures. We show that the notions of \ bi-embeddable categoricity and relative \ bi-embeddable categoricity coincide for equivalence structures for \. We also prove that computable equivalence structures have degree of bi-embeddable categoricity \, or \. We furthermore obtain results (...) on the index set complexity of computable equivalence structure with respect to bi-embeddability. (shrink)

We examine the degree structure $\operatorname {\mathrm {\mathbf {ER}}}$ of equivalence relations on $\omega $ under computable reducibility. We examine when pairs of degrees have a least upper bound. In particular, we show that sufficiently incomparable pairs of degrees do not have a least upper bound but that some incomparable degrees do, and we characterize the degrees which have a least upper bound with every finite equivalence relation. We show that the natural classes of finite, light, and dark degrees are (...) definable in $\operatorname {\mathrm {\mathbf {ER}}}$. We show that every equivalence relation has continuum many self-full strong minimal covers, and that $\mathbf {d}\oplus \mathbf {\operatorname {\mathrm {\mathbf {Id}}}_1}$ needn’t be a strong minimal cover of a self-full degree $\mathbf {d}$. Finally, we show that the theory of the degree structure $\operatorname {\mathrm {\mathbf {ER}}}$ as well as the theories of the substructures of light degrees and of dark degrees are each computably isomorphic with second-order arithmetic. (shrink)

Mauro Basaure Cet article cherche à innover dans le cadre de la controverse sur le musée de la Mémoire et des Droits de l’homme du Chili : devrait-il ou non intégrer dans sa muséographie la période antérieure au 11 septembre 1973, c’est-à-dire le contexte du coup d’État? Je défends la thèse selon laquelle le MMDH peut intégrer une dimension contextuelle sans trahir sa mission, sa vision et sa fonction, tant qu’il répond à une approche de la notion de contexte-sans-causalité. (...) Selon moi, le grand problème de la critique venant de la droite politique – qui accuse le musée de ne pas remplir sa mission pédagogique, car il décontextualise le coup d’État – est que cette critique répond à une vision causale de la notion de contexte, ce qui la conduit à des contradictions insurmontables. Si, grâce à une muséographie bien réfléchie, le concept de contextualisation non causale était mis en oeuvre avec succès, ceci n’engendrerait pas une contradiction au sein du musée mais pourrait même le favoriser. La conviction que le coup d’État et ses atrocités n’ont ni causes ni antécédents et ne peuvent en avoir renforce la mission pédagogique du MMDH. (shrink)

The reception of Avicenna by medieval Jewish readers presents an underappreciated enigma. Despite the philosophical and scientific stature of Avicenna, his philosophical writings were relatively little studied in Jewish milieus, be it in Arabic or in Hebrew. In particular, Avicenna's philosophical writings are not among the “Hebräische Übersetzungen des Mittelalters” – only very few of them were translated into Hebrew. As an author associated with a definite corpus of writings, Avicenna hardly existed in Jewish philosophy in Hebrew. Paradoxically, however, some (...) of Avicenna's most distinctive ideas were widely known and embraced by Jewish philosophers. This is the phenomenon that we dub Avicennian knowledge without Avicenna. In contrast with the philosophical treatises, Avicenna's medical writings were widely and intensively studied by Jews, especially in Hebrew, and remained influential until at least the seventeenth century. The present article presents a comprehensive picture of Avicenna's reception within medieval Jewish cultures in both Arabic and Hebrew and tries to explain the Jews’ complex attitude to Avicenna.La réception d'Avicenne par les érudits juifs médiévaux présente une énigme dont on n'a pas encore pris toute la mesure. Malgré la grande stature scientifique et philosophique d'Avicenne, ses écrits philosophiques ont été peu connus des savants juifs, que ce soit en arabe ou en hébreu. Ils n'ont guère fait partie des “Hebräische Übersetzungen des Mittelalters” – peu seulement ont été traduits en hébreu. En tant qu’auteur associé à un corpus de textes, Avicenne n'existe presque pas dans la philosophie juive en hébreu. Paradoxalement cependant, certaines des idées les plus caractéristiques d'Avicenne étaient bien connues et acceptées par des philosophes juifs. Nous appelons ce phénomène savoir avicennien sans Avicenne. Contrairement aux écrits philosophiques, les ouvrages médicaux d'Avicenne, eux, étaient lus et utilisés par les juifs, notamment en traductions hébraïques, et ce jusqu'au xviie siècle. Cet article présente un tableau général de la réception d'Avicenne, en arabe et en hébreu, dans les différentes cultures juives et il tente d'expliquer l'attitude complexe des savants juifs vis-à-vis d'Avicenne.Send article to KindleTo send this article to your Kindle, first ensure [email protected] is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about sending to your Kindle. Find out more about sending to your Kindle. Note you can select to send to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be sent to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply. Find out more about the Kindle Personal Document Service.AVICENNA AMONG MEDIEVAL JEWS THE RECEPTION OF AVICENNA'S PHILOSOPHICAL, SCIENTIFIC AND MEDICAL WRITINGS IN JEWISH CULTURES, EAST AND WESTVolume 22, Issue 2Gad Freudenthal and Mauro Zonta DOI: https://doi.org/10.1017/S0957423912000033Your Kindle email address Please provide your Kindle [email protected]@kindle.com Available formats PDF Please select a format to send. By using this service, you agree that you will only keep articles for personal use, and will not openly distribute them via Dropbox, Google Drive or other file sharing services. Please confirm that you accept the terms of use. Cancel Send ×Send article to Dropbox To send this article to your Dropbox account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about sending content to Dropbox. AVICENNA AMONG MEDIEVAL JEWS THE RECEPTION OF AVICENNA'S PHILOSOPHICAL, SCIENTIFIC AND MEDICAL WRITINGS IN JEWISH CULTURES, EAST AND WESTVolume 22, Issue 2Gad Freudenthal and Mauro Zonta DOI: https://doi.org/10.1017/S0957423912000033Available formats PDF Please select a format to send. By using this service, you agree that you will only keep articles for personal use, and will not openly distribute them via Dropbox, Google Drive or other file sharing services. Please confirm that you accept the terms of use. Cancel Send ×Send article to Google Drive To send this article to your Google Drive account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about sending content to Google Drive. AVICENNA AMONG MEDIEVAL JEWS THE RECEPTION OF AVICENNA'S PHILOSOPHICAL, SCIENTIFIC AND MEDICAL WRITINGS IN JEWISH CULTURES, EAST AND WESTVolume 22, Issue 2Gad Freudenthal and Mauro Zonta DOI: https://doi.org/10.1017/S0957423912000033Available formats PDF Please select a format to send. By using this service, you agree that you will only keep articles for personal use, and will not openly distribute them via Dropbox, Google Drive or other file sharing services. Please confirm that you accept the terms of use. Cancel Send ×Export citation Request permission. (shrink)

Economic and sanitary crises have great repercussions on access to food and the health of the population. In this context, austerity policies can have devastating effects on social rights. The purpose of this essay is to reflect on the impact of various types of crises on the Human Right to Adequate Food and Nutrition (DHANA) and on Food and Nutritional Security (SAN) of vulnerable populations and to identify of public policies, programs and actions developed based on the relief of the (...) damage caused by the COVID-19 pandemic. From the collection of information carried out in a non-systematic way on government websites and scientific databases, documents were read in full, categorized, and critically analyzed. Three different contexts, Africa, Latin America, and Portugal, are presented by the authors who work in these realities, with the intention of contributing to mitigate the food problems that worsen and are derived from the pandemic situation. (shrink)

On Kant's view, the feeling of respect is the mark of moral agency, and is peculiar to us, animals endowed with reason. Unlike any other feeling, respect originates in the contemplation of the moral law, that is, the idea of lawful activity. This idea works as a constraint on our deliberation by discounting the pretenses of our natural desires and demoting our selfish maxims. We experience its workings in the guise of respect. Respect shows that from the agent's subjective perspective, (...) morality is the experience of being bound and necessitated, but also of being free and emancipated from inclinations. (shrink)

On Kant's view, the feeling of respect is the mark of moral agency, and is peculiar to us, animals endowed with reason. Unlike any other feeling, respect originates in the contemplation of the moral law, that is, the idea of lawful activity. This idea works as a constraint on our deliberation by discounting the pretenses of our natural desires and demoting our selfish maxims. We experience its workings in the guise of respect. Respect shows that from the agent's subjective perspective, (...) morality is the experience of being bound and necessitated, but also of being free and emancipated from inclinations.Respect is a feeling that is generated by the agent's reflection on the nature of her own agency. It is not directed to anybody in particular, but to the very idea of rational agency, which is characterized by self-mastery and self-legislation. Contrary to animals, we do not derive our ends from nature, but we are capable of setting ends of our own, by exercising practical reason, that is, by engaging in the activity of law making. (shrink)

Comme ailleurs dans le monde, les courants évangéliques et pentecôtistes ont tenté dès les années 1980 de s’imposer dans l’espace public de l’Afrique de l’Ouest. Bien qu’apparus au début du XX e siècle, ce n’est que dans la deuxième moitié du siècle que l’on observe un changement dans l’engagement évangélique vis-à-vis de la société : d’un retrait du monde à une « ouverture vers l’activité politique », marquée par le thème du combat spirituel pour les territoires. En Afrique de l’Ouest, (...) cette nouvelle visibilité dans l’espace public s’est concrétisée par l’élection de présidents évangéliques, comme Matthieu Kérékou au Bénin en 1996, ou Laurent Gbagbo en Côte d’Ivoire en 2000. Mais au sein d’une même société, les relations entre évangélismes et politique peuvent ainsi être multiples. Pour les saisir, il est nécessaire d’adopter différents points de vue, depuis les instances de pouvoir jusqu’aux relations interpersonnelles de la vie quotidienne. (shrink)

Some contemporary philosophers, notably B. Williams and S. Wolf, argue that moral perfection is not just an unsustainable ideal, but also an unreasonable one in that it thwarts and demotes all the various elements that contribute to personal well-being. More importantly, moral perfection seems to imply the denial of an identifiable personal self; hence the paradox of moral perfection. I argue that this alleged paradox arises because of a misunderstanding of the role of moral ideals, of their overridingness, and of (...) the way they relate to well-being. (shrink)

This publication features the stories and experiences of pharmacy professionals who identify as members of historically underrepresented groups. This collection of personal essays presents significant events in the lives of those in the pharmacy community whose experiences have been shaped by their race, ethnicity, gender or gender presentation, sexual orientation, ability, language, mental health, or other factors. The perspectives from the narratives highlight the importance of diversity, equity, and inclusion in the healthcare sector. The authors of the narratives also reflect (...) on their experience to consider what they wish would have happened in the experience, to offer advice for others that may be faced with similar situations. Access to these stories will deepen the collective understanding among pharmacy colleagues, patients, and society of the experiences that individuals from historically underrepresented groups within pharmacy have experienced. (shrink)

This paper argues that Deonna and Teroni's attitudinal theory of emotions faces two serious problems. The first is that their master argument fails to establish the central tenet of the theory, namely, that the formal objects of emotions do not feature in the content of emotions. The second is that the attitudinal theory itself is vulnerable to a dilemma. By pointing out these problems, our paper provides indirect support to the main competitor of the attitudinal theory, namely, the perceptual theory (...) of emotions. (shrink)

Background Ethical decision making in intensive care is a demanding task. The need to proceed to ethical decision is considered to be a stress factor that may lead to burnout. The aim of this study is to explore the ethical problems that may increase burnout levels among physicians and nurses working in Portuguese intensive care units . A quantitative, multicentre, correlational study was conducted among 300 professionals.Results The most crucial ethical decisions made by professionals working in ICU were related to (...) communication, withholding or withdrawing treatments and terminal sedation. A positive relation was found between ethical decision making and burnout in nurses, namely, between burnout and the need to withdraw treatments , to withhold treatments and to proceed to terminal sedation . This did not apply to physicians. Emotional exhaustion was the burnout subdimension most affected by the ethical decision. The nurses' lack of involvement in ethical decision making was identified as a risk factor. Nevertheless, in comparison with nurses , it was the physicians who more keenly felt the need to proceed to ethical decisions in ICU.Conclusions Ethical problems were reported at different levels by physicians and nurses. The type of ethical decisions made by nurses working in Portuguese ICUs had an impact on burnout levels. This did not apply to physicians. This study highlights the need for education in the field of ethics in ICUs and the need to foster inter-disciplinary discussion so as to encourage ethical team deliberation in order to prevent burnout. (shrink)

Ludwig Wittgenstein’s practical incursions on the domain of art were many and well known. It is worth drawing attention to the design that he did together with Paul Engelmann for his sister Margarethe Stonborough-Wittgenstein’s house and the bust he made for, and was inspired by, the sculptor Michael Drobil. To attribute just an anecdotal character to Wittgenstein’s few artistic projects is a misunderstanding. The Austrian philosopher devoted himself to them with the fervor and rigor that characterize his philosophical writings. He (...) took care of every detail in his sister’s house, which sometimes ended up in difficult changes, although quite minimal (as when he had the ceilings lowered a few centimeters just before .. (shrink)