This study explores the efficacy of a specific tool – the articulation of the ideal self – in job engagement, psychological well-being, and organizational citizenship behavior. We hypothesized that employees who can visualize their jobs as part of their ideal self – in particular how it helps in its development and realization – would feel higher levels of engagement and fulfillment in their lives, as well as engage in greater amounts of helping and voice OCB. A total of 239 full (...) time employees from five companies in Costa Rica filled out the ideal self questionnaire, the job engagement, and psychological well-being surveys, and were evaluated by their peers on task behavior and helping and voice OCB. Results of the SEM model showed that the ideal self was positively related to job engagement, psychological well-being and helping and voice. These findings contribute to the research on the impact and importance for organizations to help employees find meaningfulness in their work. (shrink)

In this article, we explore the implications of opposing domains theory for developing ethical leaders. Opposing domains theory highlights a neurological tension between analytic reasoning and socioemotional reasoning. Specifically, when we engage in analytic reasoning, we suppress our ability to engage in socioemotional reasoning and vice versa. In this article, we bring together the domains of neuroscience, psychology, and ethics, to inform our theorizing around ethical leadership. We propose that a key issue for ethical leadership is achieving a healthy balance (...) between analytic reasoning and socioemotional reasoning. We argue that organizational culture often encourages too heavy a reliance on nonemotional forms of reasoning to arrive at moral judgments. As a result, leaders run the risk of suppressing their ability to pay attention to the human side of moral dilemmas and, in doing so, dehumanize colleagues, particularly subordinates, and clients. (shrink)

Emotional, social, and cognitive intelligence competencies have been recognized as the most critical capabilities for organizations to acquire at all levels. For this reason, a wide body of research since the 1980s has demonstrated their positive impact on individual performance, career success, and wellbeing across sectors and professional roles, and a large number of theoretical contributions on how these competencies can be effectively developed has emerged over time. We focus attention on the developmental and learning processes of emotional, social, and (...) cognitive intelligence competencies that occur after formal training or educational courses provided by universities or certified organizations and directed to students or practitioners. Specifically, we conduct an exploratory literature review on the existing academic studies in order to identify the scholars and the pieces of research contributing most to the debate under investigation. This article aims at analyzing this body of research through a systematic review of the literature in order to: i) provide a comprehensive critical analysis of the distinctive features of the theoretical and methodological frameworks adopted to develop these competencies; ii) review the contexts in which the training initiatives analyzed by the literature have been delivered and the categories of learner involved; iii) discuss the learning outcomes of these educational programs and how they have been assessed; iv) identify gaps and inconsistencies in the current state of the literature, suggesting promising paths for future research; and v) stimulate insights for educators, human resource managers, executives, and policymakers by organizing and critically analyzing the extant contributions on competency development. This review represents the first attempt to systematize the methodologies of the educational programs for competency development and to assess their effectiveness in order to assist educators and executives in their ongoing efforts to equip students and employees with the relevant skills needed to achieve superior performance in the workplace. At the institutional level, policymakers should promote a dedicated agenda with concrete actions to equip people with emotional and social intelligence competencies. (shrink)

As organizational leaders worry about the appalling low percentage of people who feel engaged in their work, academics are trying to understand what causes an increase in engagement. We collected survey data from 231 team members from two organizations. We examined the impact of team members’ emotional intelligence (EI) and their perception of shared personal vision, shared positive mood, and perceived organizational support (POS) on the members’ degree of organizational engagement. We found shared vision, shared mood, and POS have a (...) direct, positive association with engagement. In addition, shared vision and POS interact with EI to positively influence engagement. Besides highlighting the importance of shared personal vision, positive mood, and POS, our study contributes to the emergent understanding of EI by revealing EI’s amplifying effect on shared vision and POS in relation to engagement. We conclude by discussing the research and practical implications of this study. (shrink)

The Emotional Competency Inventory framework of Daniel Goleman and Richard Boyatzis has gained significant impact in business leadership and management development. This paper considers the composition of the various versions of the ECI and its successor the Emotional and Social Competency Inventory to determine the nature of any appeal to ethics or moral competence within these frameworks. A series of concerns regarding the ethical limitations of the frameworks are presented with arguments supported by the relevant literature across the (...) Emotional Intelligence , competency theory and ethics fields. Based on a review of the ECI competencies in terms of their definitional constructs, it appears possible for an unethical manager or leader to demonstrate EI competence. Several cases involving high-profile business leaders, who were once lauded but later found to have acted unethically, are analysed. The authors consider the capacity of unethical leaders and managers to fulfil EI competence an issue of concern. The inclusion of an ethical management cluster and a number of competencies based on virtue ethics is proposed to meet this concern. Such an inclusion would address the critical issue of the purpose to which an EI competence is applied. Argument supporting the value of a virtue ethics approach as opposed to utilitarian or duty-based ethics approaches is also presented. Finally, a proposed exemplar of an ethically informed ECI framework is included for consideration. (shrink)

The relevance of the research topic is that the psychological aspects of leadership culture are formed under the influence of many factors - economic, organizational, philosophical, philosophical, emotional. The problem statement is the conceptualization of the psychological aspects of forming a leader's leadership culture that creates strategy and produces strong managerial ideas. A true leader should inspire, inspire enthusiasm, support people in motivation and form high-performing teams as a whole. Analysis of Recent Research and Publications - for analysis, we highlight (...) the work of Goleman, Daniel, Boyatzis, Richard and McKee, Annie. Primal Leadership Unleashing the Power of Emotional Intelligrnce. Boston · Massachusetts: Harvard Business Review Press, 2013. 288 pp., which presents the psychological foundations of a leader's emotional intelligence that allow us to substantiate the psychological aspects of forming a leadership culture for a high-performing team leader who maintains good relationships and positive expectations for the future. Methods are general and constructive methodology applied to the analysis of a leader's leadership culture in the context of a reflective paradigm. Selection of previously unresolved parts of the general problem addressed in the article. The basis of the research is the conceptualization of methodological foundations that allow penetrating into the psychological foundations of the formation of leadership culture, which shows that leaders are daily in the conditions of unstable economy, stochasticity and turbulence, frantic development of information technologies, aggravation of competition. Goal setting - an analysis of the methodological foundations of the psychological aspects of forming a leader's leadership culture, based on creative ideas and innovations. In the social-philosophical and psychological literature of recent years, the concept of "leadership of creation of leaders" of "management of creation of emotionally conscious organizations" has become widespread. The purpose of the article is to conceptualize the psychological aspects of forming a leader's leadership culture in the context of a reflexive paradigm. Objectives: 1) to explore the concept of "management creation leadership"; 2) to identify the most important attributes of managerial psychological culture aimed at forming the emotional intelligence of the cultural leader; 3) to formulate the concept of leadership management culture to fine-tune all processes, create strategy and produce strong ideas; It is proved what character traits are needed for a modern management culture to be a leader of high quality and to use the whole arsenal of positive leadership and mutual understanding in the organization. The conditions for creating leaders in the context of motivation to change and assessing the real self are revealed. Conditions for creating emotionally conscious leaders and organizations are revealed. The most important attributes of managerial psychological culture are directed to the formation of emotional intelligence of the cultural leader, directed to the culture of management, self-organization and reflexivity, which promote the interaction of culture and psychology, culture and intelligence, culture and creativity and innovations. Emotions, the ability to understand and empathize help a high-performing leader to lead the team, but to do so, one must develop the skills of emotional leadership in oneself. Conclusions. The use of psychological aspects of forming the emotional reflection of the leadership culture of the leader-reformer contributes to the formation of the concept of a culture of leadership management, to fine-tune all processes, create a strategy and produce strong ideas, reinforce the concept of individual leadership and promote the success of companies. Self-awareness and management skills span the focus on achievement, planning, initiative, honesty, self-control, and self-confidence. (shrink)

In set theory without the axiom of choice, we investigate the deductive strength of the principle “every topological space with the minimal cover property is compact”, and its relationship with certain notions of finite as well as with properties of linearly ordered sets and partially ordered sets.

In set theory without the Axiom of Choice ( $\mathsf {AC}$ ), we investigate the open problem of the deductive strength of statements which concern the existence of almost disjoint and maximal almost disjoint (MAD) families of infinite-dimensional subspaces of a given infinite-dimensional vector space, as well as the extension of almost disjoint families in infinite-dimensional vector spaces to MAD families.

We show that the Boolean Prime Ideal Theorem () does not imply the Nielsen‐Schreier Theorem () in, thus strengthening the result of Kleppmann from “Nielsen‐Schreier and the Axiom of Choice” that the (strictly weaker than ) Ordering Principle () does not imply in. We also show that is false in Mostowski's Linearly Ordered Model of. The above two results also settle the corresponding open problems from Howard and Rubin's “Consequences of the Axiom of Choice”.

In set theory without the axiom of choice (AC), we study the relative strength of the principle “No decreasing sequence of cardinals,” that is, “There is no function f on ω such that |f(n+1)|<|f(n)| for all n∈ω” (NDS) with regard to its position in the hierarchy of weak choice principles. We establish the following results: (1) The Boolean prime ideal theorem plus countable choice does not imply NDS in ZF; (2) “Every non-well-orderable set has a well-orderable partition into denumerable sets” (...) (Dℵ0) plus the axiom of choice for well-ordered families of nonempty finite sets does not imply NDS ∨ “The axiom of choice for countable families of nonempty countable sets” in ZFA; and (3) The axiom of choice for well-ordered families of nonempty sets, each of cardinality not greater than or equal to 2ℵ0, does not imply NDS ∨ “countable union theorem” in ZFA. The above results answer corresponding questions left open in works by Howard and Rubin (1998) and Howard and Tachtsis (2016). We also show the following: (4) “Every non-well-orderable set has a well-orderable partition into infinite well-orderable sets” (Dw) is strictly weaker than D ℵ0 in ZFA. This resolves an open problem from Keremedis and Tachtsis (2003). (shrink)

It is a long standing open problem whether or not the Axiom of Countable Choice implies the fragment of Martin's Axiom either in or in. In this direction, we provide a partial answer by establishing that the Boolean Prime Ideal Theorem in conjunction with the Countable Union Theorem does not imply restricted to complete Boolean algebras in. Furthermore, we prove that the latter (formally) weaker form of and the Δ‐system Lemma are independent of each other in.We also answer open questions (...) from Tachtsis [16] which concern the status of restricted to complete Boolean algebras in certain Fraenkel–Mostowski permutation models of and we strengthen some results from the above paper. (shrink)

In $\mathsf {ZF}$ (i.e., Zermelo–Fraenkel set theory minus the axiom of choice ( $\mathsf {AC}$ )), we investigate the open problem of the deductive strength of the principle UFwob(ω): “There exists a free ultrafilter on ω with a well-orderable base”, which was introduced by Herzberg, Kanovei, Katz, and Lyubetsky [(2018), Journal of Symbolic Logic, 83(1), 385–391]. Typical results are: (1) “ $\aleph _{1}\leq 2^{\aleph _{0}}$ ” is strictly weaker than $\mathsf {UF_{wob}}(\omega )$ in $\mathsf {ZF}$. (2) “There exists a free (...) ultrafilter on $\omega $ ” does not imply “ $\aleph _{1}\leq 2^{\aleph _{0}}$ ” in $\mathsf {ZF}$, and thus (by (1)) neither does it imply $\mathsf {UF_{wob}}(\omega )$ in $\mathsf {ZF}$. This fills the gap in information in Howard and Rubin [Mathematical Surveys and Monographs, American Mathematical Society, 1998], as well as in Herzberg et al. (2018). (3) Martin’s Axiom ( $\mathsf {MA}$ ) implies “no free ultrafilter on $\omega $ has a well-orderable base of cardinality $<2^{\aleph _{0}}$ ”, and the latter principle is not implied by $\aleph _{0}$ -Martin’s Axiom ( $\mathsf {MA}(\aleph _{0})$ ) in $\mathsf {ZF}$. (4) $\mathsf {MA} + \mathsf {UF_{wob}}(\omega )$ implies $\mathsf {AC}(\mathbb {R})$ (the axiom of choice for non-empty sets of reals), which in turn implies $\mathsf {UF_{wob}}(\omega )$. Furthermore, $\mathsf {MA}$ and $\mathsf {UF_{wob}}(\omega )$ are mutually independent in $\mathsf {ZF}$. (5) For any infinite linearly orderable set X, each of “every filter base on X can be well ordered” and “every filter on X has a well-orderable base” is equivalent to “ $\wp (X)$ can be well ordered”. This yields novel characterizations of the principle “every linearly ordered set can be well ordered” in $\mathsf {ZFA}$ (i.e., Zermelo–Fraenkel set theory with atoms), and of $\mathsf {AC}$ in $\mathsf {ZF}$. (6) “Every filter on $\mathbb {R}$ has a well-orderable base” implies “every filter on $\omega $ has a well-orderable base”, which in turn implies $\mathsf {UF_{wob}}(\omega )$, and none of these implications are reversible in $\mathsf {ZF}$. (7) “Every filter on $\omega $ can be extended to an ultrafilter with a well-orderable base” is equivalent to $\mathsf {AC}(\mathbb {R}),$ and thus is strictly stronger than $\mathsf {UF_{wob}}(\omega )$ in $\mathsf {ZF}$. (8) “Every filter on $\omega $ can be extended to an ultrafilter” implies “there exists a free ultrafilter on $\omega $ which has no well-orderable base of cardinality ${<2^{\aleph _{0}}}$ ”. The former principle does not imply “there exists a free ultrafilter on $\omega $ which has no well-orderable base” in $\mathsf {ZF}$, and the latter principle is true in the Basic Cohen Model. (shrink)

In set theory without the Axiom of Choice (), we investigate the problem of the placement of Łoś's Theorem () in the hierarchy of weak choice principles, and answer several open questions from the book Consequences of the Axiom of Choice by Howard and Rubin, as well as an open question by Brunner. We prove a number of results summarised in § 3.

Charles Taber and Milton Lodge provide compelling evidence that people's minds may be closed to information that is inconsistent with their prior beliefs. This type of inconsistency has often been termed ?irrational.? However, recent research suggests that being open or closed minded is not an unchanging variable but depends on one's goals, including one's need for closure, which vary from person to person and situation to situation. In this vein, as Taber and Lodge suggest, those who have more political information (...) may, after having been open minded enough to acquire the information, become closed minded by virtue of having acquired it. At the same time, being more open minded to inaccurate information might lead one in the wrong direction; hence, open mindedness does not necessarily enhance the accuracy of one's judgments or the quality of one's decisions. We may need to rethink the concept of an enlightened, well-informed electorate, to the extent that it assumes the unqualified benefits of open mindedness. (shrink)

For an integer \, Ramsey Choice\ is the weak choice principle “every infinite setxhas an infinite subset y such that\ has a choice function”, and \ is the weak choice principle “every infinite family of n-element sets has an infinite subfamily with a choice function”. In 1995, Montenegro showed that for \, \. However, the question of whether or not \ for \ is still open. In general, for distinct \, not even the status of “\” or “\” is known. (...) In this paper, we provide partial answers to the above open problems and among other results, we establish the following:1.For every integer \, if \ is true for all integers i with \, then \ is true for all integers i with \.2.If \ are any integers such that for some prime p we have \ and \, then in \: \ and \.3.For \, \\\ implies \, and \ implies neither \ nor \ in \.4.For every integer \, \ implies “every infinite linearly orderable family of k-element sets has a partial Kinna–Wagner selection function” and the latter implication is not reversible in \ ). In particular, \ strictly implies “every infinite linearly orderable family of 3-element sets has a partial choice function”.5.The Chain-AntiChain Principle implies neither \ nor \ in \, for every integer \. (shrink)

We provide a general criterion for Fraenkel–Mostowski models of $${\textsf{ZFA}}$$ (i.e. Zermelo–Fraenkel set theory weakened to permit the existence of atoms) which implies “every linearly ordered set can be well ordered” ( $${\textsf{LW}}$$ ), and look at six models for $${\textsf{ZFA}}$$ which satisfy this criterion (and thus $${\textsf{LW}}$$ is true in these models) and “every Dedekind finite set is finite” ( $${\textsf{DF}}={\textsf{F}}$$ ) is true, and also consider various forms of choice for well-ordered families of well orderable sets in these (...) models. In Model 1, the axiom of multiple choice for countably infinite families of countably infinite sets ( $${\textsf{MC}}_{\aleph _{0}}^{\aleph _{0}}$$ ) is false. It was the open question of whether or not such a model exists (from Howard and Tachtsis “On metrizability and compactness of certain products without the Axiom of Choice”) that provided the motivation for this paper. In Model 2, which is constructed by first choosing an uncountable regular cardinal in the ground model, a strong form of Dependent choice is true, while the axiom of choice for well-ordered families of finite sets ( $${\textsf{AC}}^{{\textsf{WO}}}_{{\textsf{fin}}}$$ ) is false. Also in this model the axiom of multiple choice for well-ordered families of well orderable sets fails. Model 3 is similar to Model 2 except for the status of $${\textsf{AC}}^{{\textsf{WO}}}_{{\textsf{fin}}}$$ which is unknown. Models 4 and 5 are variations of Model 3. In Model 4 $${\textsf{AC}}_{\textrm{fin}}^{{\textsf{WO}}}$$ is true. The construction of Model 5 begins by choosing a regular successor cardinal in the ground model. Model 6 is the only one in which $$2{\mathfrak {m}} = {\mathfrak {m}}$$ for every infinite cardinal number $${\mathfrak {m}}$$. We show that the union of a well-ordered family of well orderable sets is well orderable in Model 6 and that the axiom of multiple countable choice is false. (shrink)

We establish the following results: 1. In ZF (i.e., Zermelo-Fraenkel set theory minus the Axiom of Choice AC), for every set I and for every ordinal number α ≥ ω, the following statements are equivalent: (a) The Tychonoff product of| α| many non-empty finite discrete subsets of I is compact. (b) The union of| α| many non-empty finite subsets of I is well orderable. 2. The statement: For every infinite set I, every closed subset of the Tychonoff product [0, 1] (...) I which consists of functions with finite support is compact, is not provable in ZF set theory. 3. The statement: For every set I, the principle of dependent choices relativised to I implies the Tychonoff product of countably many non-empty finite discrete subsets of I is compact, is not provable in ZF⁰ (i.e., ZF minus the Axiom of Regularity). 4. The statement: For every set I, every ℵ₀-sized family of non-empty finite subsets of I has a choice function implies the Tychonoff product of ℵ₀ many non-empty finite discrete subsets of I is compact, is not provable in ZF⁰. (shrink)

In set theory without the Axiom of Choice, we investigate the set-theoretic strength of the principle NDS which states that there is no function f on the set ω of natural numbers such that for everyn ∈ ω, f ≺ f, where for sets x and y, x ≺ y means that there is a one-to-one map g : x → y, but no one-to-one map h : y → x. It is a long standing open problem whether NDS implies (...) AC. In this paper, among other results, we show that NDS is a strong axiom by establishing that ACLO ↛ NDS in ZFA set theory. The latter result provides a strongly negative answer to the question of whether “every Dedekind-finite set is finite” implies NDS addressed in G. H. Moore “Zermelo’s Axiom of Choice. Its Origins, Development, and Influence” and in P. Howard–J. E. Rubin “Consequences of the Axiom of Choice”. We also prove that ACWO ↛ NDS in ZF and that “for all infinite cardinals m, m + m = m” ↛ NDS in ZFA. (shrink)

We show that the property of sequential compactness for subspaces of.

It is shown that AC, the axiom of choice for families of non-empty subsets of the real line ℝ, does not imply the statement PW, the powerset of ℝ can be well ordered. It is also shown that the statement “the set of all denumerable subsets of ℝ has size 2math image” is strictly weaker than AC and each of the statements “if every member of an infinite set of cardinality 2math image has power 2math image, then the union has (...) power 2math image” and “ℵ ≠ ℵω” is Hartogs' aleph, the least ℵ not ≤ 2math image), is strictly weaker than the full axiom of choice AC. (shrink)

We study theorems from Functional Analysis with regard to their relationship with various weak choice principles and prove several results about them: “Every infinite‐dimensional Banach space has a well‐orderable Hamel basis” is equivalent to ; “ can be well‐ordered” implies “no infinite‐dimensional Banach space has a Hamel basis of cardinality ”, thus the latter statement is true in every Fraenkel‐Mostowski model of ; “No infinite‐dimensional Banach space has a Hamel basis of cardinality ” is not provable in ; “No infinite‐dimensional (...) Banach space has a well‐orderable Hamel basis of cardinality ” is provable in ; (the Axiom of Choice for denumerable families of non‐empty finite sets) is equivalent to “no infinite‐dimensional Banach space has a Hamel basis which can be written as a denumerable union of finite sets”; Mazur's Lemma (“If X is an infinite‐dimensional Banach space, Y is a finite‐dimensional vector subspace of X, and, then there is a unit vector such that for all and all scalars α”) is provable in ; “A real normed vector space X is finite‐dimensional if and only if its closed unit ball is compact” is provable in ; (Principle of Dependent Choices) + “ can be well‐ordered” does not imply the Hahn‐Banach Theorem () in ; and “no infinite‐dimensional Banach space has a Hamel basis of cardinality ” are independent from each other in ; “No infinite‐dimensional Banach space can be written as a denumerable union of finite‐dimensional subspaces” lies in strength between (the Axiom of Countable Choice) and ; implies “No infinite‐dimensional Banach space can be written as a denumerable union of closed proper subspaces” which in turn implies ; “Every infinite‐dimensional Banach space has a denumerable linearly independent subset” is a theorem of, but not a theorem of ; and “Every infinite‐dimensional Banach space has a linearly independent subset of cardinality ” implies “every Dedekind‐finite set is finite”. (shrink)

In the setting of ZF, i.e., Zermelo–Fraenkel set theory without the Axiom of Choice , we study partitions of Russell-sets into sets each with exactly n elements , for some integer n. We show that if n is odd, then a Russell-set X has an n -ary partition if and only if |X | is divisible by n. Furthermore, we establish that it is relative consistent with ZF that there exists a Russell-set X such that |X | is not divisible (...) by any finite cardinal n > 1. (shrink)

We show that none of the following statements is provable in Zermelo-Fraenkel set theory (ZF) answering the corresponding open questions from Brunner in ``The axiom of choice in topology'':(i) For every T2 topological space (X, T) if X is well-ordered, then X has a well-ordered base,(ii) For every T2 topological space (X, T), if X is well-ordered, then there exists a function f : X × W T such that W is a well-ordered set and f ({x} × W) is (...) a neighborhood base at x for each x X,(iii) For every T2 topological space (X, T), if X has a well-ordered dense subset, then there exists a function f : X × W T such that W is a well-ordered set and {x} = f ({x} × W) for each x X. (shrink)

A Hausdorff space is called effectively Hausdorff if there exists a function F—called a Hausdorff operator—such that, for every with,, where U and V are disjoint open neighborhoods of x and y, respectively. Among other results, we establish the following in, i.e., in Zermelo–Fraenkel set theory without the Axiom of Choice (): is equivalent to “For every set X, the Cantor cube is effectively Hausdorff”. This enhances the result of Howard, Keremedis, Rubin and Rubin [13] that is equivalent to “Hausdorff (...) spaces are effectively Hausdorff” in. The Boolean Prime Ideal Theorem and the statement “For every infinite set X, the Stone space of the Boolean algebra is effectively Hausdorff” are mutually independent. In particular, the latter statement is not provable in. The Axiom of Choice for non‐empty subsets of () is equivalent to each of “Separable Hausdorff spaces are effectively Hausdorff” and “The Cantor cube is effectively Hausdorff”. The Principle of Dependent Choices in conjunction with the Axiom of Choice for continuum sized families of non‐empty subsets of does not imply the axiom of choice for partitions of. The latter independence result fills the gap in information in Howard and Rubin's book “Consequences of the Axiom of Choice”. The axiom of countable choice for non‐empty subsets of is equivalent to each of “Denumerable Hausdorff spaces are effectively Hausdorff”, “Denumerable T3 spaces are completely normal” and “Denumerable Tychonoff spaces are Urysohn”. (shrink)

We establish that, in ZF, the statementRLT: Given a setIand a non-empty setF\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathcal{F}}$$\end{document}of non-empty elementary closed subsets of 2Isatisfying the fip, ifF\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathcal{F}}$$\end{document}has a choice function, then⋂F≠∅\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\bigcap\mathcal{F} \ne \emptyset}$$\end{document},which was introduced in Morillon :739–749, 2012), is equivalent to the Boolean Prime Ideal Theorem. The result provides, on one hand, an affirmative answer to Morillon’s corresponding (...) question in Morillon and, on the other hand, a negative answer—in the setting of ZFA —to the question in Morillon of whether RLT is equivalent to Rado’s selection lemma. (shrink)

We study the role that the axiom of choice plays in Tychonoff's product theorem restricted to countable families of compact, as well as, Lindelöf metric spaces, and in disjoint topological unions of countably many such spaces.

We show that the countable axiom of choice CAC strictly implies the statements “Lindelöf metric spaces are second countable” “Lindelöf metric spaces are separable”. We also show that CAC is equivalent to the statement: “If is a Lindelöf topological space with respect to the base ℬ, then is Lindelöf”.

Despite advancements in human research ethics and the growing significance of Research Ethics Board (REB) members, educational opportunities specifically tailored to their needs remain lacking in many countries. In response to this gap, our research aims to understand the demographics, needs, and preferences for educational opportunities of REB members in Canada. We conducted a survey that found REB demographics to be diverse and have different perceptions of their roles on topics such as the evaluation of the scientific merit of studies (...) and responsibilities to stakeholders. We found that REB members in general prefer online tutorials and webinars for their education. Educators interested in facilitating the development of future training programs should consider the needs and preferences of REB members outlined in this publication. (shrink)

We investigate, within the framework of Zermelo-Fraenkel set theory ZF, the interrelations between weak forms of the Axiom of Choice AC restricted to sets of reals.

Let X be an infinite set and let and denote the propositions “every filter on X can be extended to an ultrafilter” and “X has a free ultrafilter”, respectively. We denote by the Stone space of the Boolean algebra of all subsets of X. We show: For every well‐ordered cardinal number ℵ, (ℵ) iff (2ℵ). iff “ is a continuous image of ” iff “ has a free open ultrafilter ” iff “every countably infinite subset of has a limit point”. (...) implies “every open filter on extends to an open ultrafilter” implies “has an open ultrafilter” implies It is relatively consistent with that (ω) holds, whereas (ω) fails. In particular, none of the statements given in (2) implies (ω). (shrink)

We study properties of certain subclasses of the Dedekind finite sets in set theory without the axiom of choice with respect to the comparability of their elements and to the boundedness of such classes, and we answer related open problems from Herrlich’s “The Finite and the Infinite.” The main results are as follows: 1. It is relatively consistent with ZF that the class of all finite sets is not the only finiteness class such that any two of its elements are (...) comparable. 2. The principle “Small Violations of Choice” —introduced by A. Blass—implies that the class of all Dedekind finite sets is bounded above. 3. “The class of all Dedekind finite sets is bounded above” is true in every permutation model of ZFA in which the class of atoms is a set, and in every symmetric model of ZF. 4. There exists a model of ZFA set theory in which the class of all atoms is a proper class and in which the class of all infinite Dedekind finite sets is not bounded above. 5. There exists a model of ZF in which the class of all infinite Dedekind finite sets is not bounded above. (shrink)

Moral thinking pervades our practical lives, but where did this way of thinking come from, and what purpose does it serve? Is it to be explained by environmental pressures on our ancestors a million years ago, or is it a cultural invention of more recent origin? In The Evolution of Morality, Richard Joyce takes up these controversial questions, finding that the evidence supports an innate basis to human morality. As a moral philosopher, Joyce is interested in whether any implications (...) follow from this hypothesis. Might the fact that the human brain has been biologically prepared by natural selection to engage in moral judgment serve in some sense to vindicate this way of thinking--staving off the threat of moral skepticism, or even undergirding some version of moral realism? Or if morality has an adaptive explanation in genetic terms--if it is, as Joyce writes, "just something that helped our ancestors make more babies"--might such an explanation actually undermine morality's central role in our lives? He carefully examines both the evolutionary "vindication of morality" and the evolutionary "debunking of morality," considering the skeptical view more seriously than have others who have treated the subject.Interdisciplinary and combining the latest results from the empirical sciences with philosophical discussion, The Evolution of Morality is one of the few books in this area written from the perspective of moral philosophy. Concise and without technical jargon, the arguments are rigorous but accessible to readers from different academic backgrounds. Joyce discusses complex issues in plain language while advocating subtle and sometimes radical views. The Evolution of Morality lays the philosophical foundations for further research into the biological understanding of human morality. (shrink)

In The Myth of Morality, Richard Joyce argues that moral discourse is hopelessly flawed. At the heart of ordinary moral judgements is a notion of moral inescapability, or practical authority, which, upon investigation, cannot be reasonably defended. Joyce argues that natural selection is to blame, in that it has provided us with a tendency to invest the world with values that it does not contain, and demands that it does not make. Should we therefore do away with morality, as (...) we did away with other faulty notions such as witches? Possibly not. We may be able to carry on with morality as a 'useful fiction' - allowing it to have a regulative influence on our lives and decisions, perhaps even playing a central role - while not committing ourselves to believing or asserting falsehoods, and thus not being subject to accusations of 'error'. (shrink)

One way in which the characteristic gestures of philosophy and criticism differ from each other lies in their involvements with disillusionment, with the undoing of our naivete, especially regarding what we take ourselves to know about the meaning of what we say. Philosophy will often find less than we thought was there, perhaps nothing at all, in what we say about the “external” world, or in our judgments of value, or in our ordinary psychological talk. The work of criticism, on (...) the other hand, frequently disillusions by finding disturbingly more in what is said than we precritically thought was there. In our relation to the meaningfulness of what we say, there is a disillusionment of plentitude as well as of emptiness. And no doubt what is “less” for one discipline may be “more” of what someone else is looking for.In recent years, metaphor has attracted more than its share of both philosophical and critical attention, including philosophical denials of the obvious, as well as critical challenges to the obviousness of the ways we talk about metaphor. In this paper I discuss a problem of each sort and suggest a complex of relations between them. The particular denial of the obvious that I’m interested in is the claim recently made by Donald Davidson that “a metaphor doesn’t say anything beyond its literal meaning ,” nor is it even correct to speak of metaphor as a form of communication.1 There’s disillusionment with a vengeance; and even if not strictly believable, it is still not without its therapeutic value, as we shall see. 1. Donald Davidson, “What Metaphors Mean,” in On Metaphor, ed. Sheldon Sacks , p. 30; hereafter abbreviated “WMM.” Davidson’s view has found supporters among both philosophers and literary theorists. It is, for example, important to the early argument of Richard Rorty’s recent book. See his Contingency, Irony, and Solidarity , p. 18. Richard Moran is an assistant professor of philosophy at Princeton University. He is currently working on a book on subjectivity and contemporary concepts of personhood. (shrink)

This anthology is a significant contribution to the debate over the relevance of Martin Heidegger's Nazi ties to the interpretation and evaluation of his philosophical work. Included are a selection of basic documents by Heidegger, essays and letters by Heidegger's colleagues that offer contemporary context and testimony, and interpretive evaluations by Heidegger's heirs and critics in France and Germany.In his new introduction, "Note on a Missing Text," Richard Wolin uses the absence from this edition of an interview with Jacques (...) Derrida as a springboard for examining questions about the nature of authorship and personal responsibility that are at the heart of the book.Richard Wolin is Professor of Modern European Intellectual History and Humanities at Rice University. He is the author of Walter Benjamin, The Politics of Being: The Political Thought of Martin Heidegger, and The Terms of Cultural Criticism: The Frankfurt School, Existentialism and Poststructuralism. (shrink)