The paper is a contribution to intuitionistic reverse mathematics. We introduce a formal system called Basic Intuitionistic MathematicsBIM, and then search for statements that are, over BIM, equivalent to Brouwer’s Fan Theorem or to its positive denial, Kleene’s Alternative to the Fan Theorem. The Fan Theorem is true under the intended intuitionistic interpretation and Kleene’s Alternative is true in the model of BIM consisting of the Turing-computable functions. The task of finding equivalents of Kleene’s Alternative is, intuitionistically, a nontrivial extension (...) of the task of finding equivalents of the Fan Theorem, although there is a certain symmetry in the arguments that we shall try to make transparent. We introduce closed-and-separable subsets of Baire space N\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathcal{N}}$$\end{document} and of the set R\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathcal{R}}$$\end{document} of the real numbers. Such sets may be compact and also positively noncompact. The Fan Theorem is the statement that Cantor space C\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathcal{C}}$$\end{document}, or, equivalently, the unit interval [0, 1], is compact and Kleene’s Alternative is the statement that C\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathcal{C}}$$\end{document}, or, equivalently, [0, 1], is positively noncompact. The class of the compact closed-and-separable sets and also the class of the closed-and-separable sets that are positively noncompact are characterized in many different ways and a host of equivalents of both the Fan Theorem and Kleene’s Alternative is found. (shrink)

The author proved in his Ph.D. Thesis [W. Veldman, Investigations in intuitionistic hierarchy theory, Ph.D. Thesis, Katholieke Universiteit Nijmegen, 1981] that, in intuitionistic analysis, the positively Borel subsets of Baire space form a genuinely growing hierarchy: every level of the hierarchy contains sets that do not occur at any lower level. It follows from this result that there are natural examples of analytic and also of co-analytic sets that are not positively Borel. It turns out, however, that, in intuitionistic analysis, (...) one may give surprisingly different and, in some sense, much more simple examples of analytic and co-analytic sets that fail to be positively Borel. In the paper, two such examples are given. In proving them correct, one obtains new proofs of the Borel Hierarchy Theorem. Brouwer’s Continuity Principle plays a crucial role in arguments. (shrink)

L.E.J. Brouwer made a mistake in the formulation of his famous bar theorem, as was pointed out by S.C. Kleene. By repeating this mistake several times, Brouwer has caused confusion. We consider the assumption underlying his bar theorem, calling it Brouwer’s Thesis. This assumption is not refuted by Kleene’s example and we use it to obtain a conclusion different from Brouwer’s. Thus we come to support a view first expressed and defended by E. Martino and P. Giaretta in [Martino 1981]. (...) We also indicate that Brouwer’s Thesis has many more applications than Brouwer dreamt of. (shrink)

Despite changes in their representation and visibility, there are still serious concerns about the inclusion and day-to-day workplace challenges various groups face (e.g., women, ethnic and cultural minorities, LGBTQ+, people as they age, and those dealing with physical or mental disabilities). Men are also underrepresented in specific work fields, in particular those in HEED (Health care, Elementary Education and the Domestic sphere). Previous literature has shown that group stereotypes play an important role in maintaining these inequalities. We outline how insights (...) from research on stigma, social-identity, and self-regulation together increase our understanding of how targets are affected by and regulate negative stereotypes in the workplace. This approach starts from the basis that members of negatively-stereotyped groups are not just passive recipients of negative attitudes, stereotypes, and behaviors, but are active individuals pursuing multiple goals, such as goals for belonging and achievement. We argue that it is only by understanding stigma from the target’s perspective (e.g., how targets are affected and respond) that we can successfully address workplace inequality. Key in this understanding is that stereotypes, prejudice and discrimination have taken on much more subtle forms, with consequences for the way members of stigmatized-groups cope. These insights lead us to propose an approach to understanding barriers to workplace equality that highlights four key aspects: a) the different (often subtle) potential triggers of identity-threat in the workplace for members of stigmatized-groups, b) the ways in which members of stigmatized-groups cope with these threats, c) the role of supportive factors that mitigate potential threats and affect self-regulation, and d) potential hidden costs for the self or others of what appears at first to be effective self-regulation. The focus on threats, coping, support, and potential hidden costs helps us understand why current diversity efforts are not always successful in increasing and maintaining members of stigmatized-groups in organizations, and provides insight into how we can aid efforts to effectively lower barriers to workplace equality. (shrink)

L.E.J. Brouwer made a mistake in the formulation of his famous bar theorem, as was pointed out by S.C. Kleene. By repeating this mistake several times, Brouwer has caused confusion. We consider the assumption underlying his bar theorem, calling it Brouwer’s Thesis. This assumption is not refuted by Kleene’s example and we use it to obtain a conclusion different from Brouwer’s. Thus we come to support a view first expressed and defended by E. Martino and P. Giaretta in [Martino 1981]. (...) We also indicate that Brouwer’s Thesis has many more applications than Brouwer dreamt of. (shrink)

In this article we discuss the political and economic consequences of the contemporary legal theory of incorporation. We argue that incorporation has developed historically in a way that makes it internally inconsistent, but that this inconsistency is useful for the powerful because of its legal and economic effects. The corporation can “shape shift,” which is very helpful for claiming some rights and disavowing certain responsibilities. Of course this flexibility comes at the expense of consistent concepts and this leads to the (...) creation of what we term an “ideal‐type reified singular representation.” We go on to show the far‐reaching effects of this representation for legal studies, economics, and political theory, and show it worked in the pro‐corporate decision in the recent Citizens United case. We conclude by providing several alternative ways to think about the nature of corporate organization. (shrink)

In intuitionistic analysis, "Brouwer's Continuity Principle" implies, together with an "Axiom of Countable Choice", that the positively Borel sets form a genuinely growing hierarchy: every level of the hierarchy contains sets that do not occur at any lower level.

Corporate governance (CG) is a key area of management with important implications for business ethics. The interface of CG and business ethics is populated with rich intellectual debates on the role of ethics in governance from a multi-disciplinary perspective. Within these debates, the relationship between CG and outcomes for business and society, and the role of CG structures and processes and their comparative aspects across institutional settings are discussed. Despite a proliferation of research at the interface of CG and ethics, (...) we observe that an engagement with topics, methodologies, and expected outcomes drawing on established frames and theories of CG tends to the ignoring or even the preclusion of an explicit engagement with debates in business ethics. Through this VSI, we as section editors showcase previously published papers in the Journal that proactively explore the explicit linkages and interfaces between CG and ethical societal challenges, with the aim of inspiring further such CG research. (shrink)

Teacher discipline strategies are well documented when it comes to its effects on students and the working climate in the classroom. Although it is commonly acknowledged that for student teachers classroom management is a major concern, student teachers? use of discipline strategies is largely unknown. In this paper, we examine student teachers? beliefs in relation to their discipline strategies. Three clusters of discipline strategies are distinguished: sensitive, directive and aggressive discipline strategies. Beliefs that were taken into account are self-images on (...) control and affiliation, control orientation and anticipated student responses on control and affiliation. All participants were student teachers of a one-year teacher education programme for secondary education in the Netherlands. Student questionnaires were used to measure discipline strategies (n?=?2506). Student teachers? (n?=?104) self-images, control orientation and anticipated student responses were measured with student teacher questionnaires. Results of the multiple regression analyses showed that student teachers? sensitive and directive discipline strategies are explained best by self-images on control; aggressive discipline strategies are explained best by self-images on affiliation and by control orientation. Apart from the possible academic interest in these particular findings, results are believed to be useful in a practical sense, in particular for teacher education programmes. (shrink)

MartinoEnrico.* * Intuitionistic Proof Versus Classical Truth, The Role of Brouwer’s Creative Subject in Intuitionistic Mathematics. Logic, Methodology and the Unity of Science; 42. Springer, 2018. ISBN: 978-3-319-74356-1 ; 978-3-030-08971-9, 978-3-319-74357-8. Pp. xiii + 170.

The use of the nomer ‘corporate’ is hardly an issue in contemporary scholarship on corporate governance. I will argue that this nomer is important for two main reasons. First, the corporate form distinguishes itself from any other form of business representation. In this sense, it is important to know exactly how this form is different to understand how conceptions of ‘corporate governance’ relate to different forms of representation. Second, it is my contention that the use of a particular understanding of (...) incorporation directly informs the concept of internal governance in terms of constituency, structure, ownership and the locus of corporate agency. It is in this sense that I argue that the identification of corporate constituencies and the allocation of agency and ownership is a precondition of business ethics. With this aim in mind, I explore the governance in corporations as the result of the legal understanding of incorporation and the separate legal entity. I explore two historical positions from which five legal positions on the separate legal entity can be derived. These five positions provide reference points for the attribution of ownership and agency between the separate legal entity and the aggregation of individuals that together make up the corporation. Incorporation, as the legal act that constitutes the corporation, can then be shown to adopt multiple and mutually exclusive positions. These positions are central to the debate on the respective claims to agency and ownership between the separate legal entity and the aggregation of individuals. I then end the article by arguing that all concepts of incorporation create legal and economic issues regarding the allocation of ownership and agency, which makes their understanding and the choice behind them important for theories of governance. (shrink)

The use of the nomer ‘corporate’ is hardly an issue in contemporary scholarship on corporate governance. I will argue that this nomer is important for two main reasons. First, the corporate form distinguishes itself from any other form of business representation. In this sense, it is important to know exactly how this form is different to understand how conceptions of ‘corporate governance’ relate to different forms of representation. Second, it is my contention that the use of a particular understanding of (...) incorporation directly informs the concept of internal governance in terms of constituency, structure, ownership and the locus of corporate agency. It is in this sense that I argue that the identification of corporate constituencies and the allocation of agency and ownership is a precondition of business ethics. With this aim in mind, I explore the governance in corporations as the result of the legal understanding of incorporation and the separate legal entity. I explore two historical positions from which five legal positions on the separate legal entity can be derived. These five positions provide reference points for the attribution of ownership and agency between the separate legal entity and the aggregation of individuals that together make up the corporation. Incorporation, as the legal act that constitutes the corporation, can then be shown to adopt multiple and mutually exclusive positions. These positions are central to the debate on the respective claims to agency and ownership between the separate legal entity and the aggregation of individuals. I then end the article by arguing that all concepts of incorporation create legal and economic issues regarding the allocation of ownership and agency, which makes their understanding and the choice behind them important for theories of governance. (shrink)

Often assumed to induce fatalism, empirical evidence shows that environmental apocalypticism is frequently associated with activism. I suggest this is the case because the notion of imminent catastrophe reveals a moral to the environmental story, and in so doing furnishes a point of view from which people can determine what constitutes environmentally ethical behavior. Insofar as it guides behavior, this apocalyptic moral reasoning can be usefully understood as a folk version of consequentialism. Further research on how people put environmental ethics (...) into practice would complement the significant advances environmental ethicists have made in the areas of normative and meta-ethics over the past several decades. (shrink)

We establish constructive refinements of several well-known theorems in elementary model theory. The additive group of the real numbers may be embedded elementarily into the additive group of pairs of real numbers, constructively as well as classically.

In intuitionistic analysis, a subset of a Polish space like or is called positively Borel if and only if it is an open subset of the space or a closed subset of the space or the result of forming either the countable union or the countable intersection of an infinite sequence of (earlier constructed) positively Borel subsets of the space. The operation of taking the complement is absent from this inductive definition, and, in fact, the complement of a positively Borel (...) set is not always positively Borel itself (see Veldman, 2008a). The main result of Veldman (2008a) is that, assuming Brouwer's Continuity Principle and an Axiom of Countable Choice, one may prove that the hierarchy formed by the positively Borel sets is genuinely growing: every level of the hierarchy contains sets that do not occur at any lower level. The purpose of the present paper is a different one: we want to explore the truly remarkable fine structure of the hierarchy. Brouwer's Continuity Principle again is our main tool. A second axiom proposed by Brouwer, his Thesis on Bars is also used, but only incidentally. (shrink)