For most of its history, mathematics was fairly constructive: • Euclidean geometry was based on geometric construction. • Algebra sought explicit solutions to equations. Analysis, probability, etc. were focused on calculations. Nineteenth century developments in analysis challenged this view. A sequence (an) in a metric space is said Cauchy if for every ε > 0, there is an m such that for every n, n ≥ m, d (a n , a n ) < ε.

This thesis is intended t0 help develop the theory 0f coalgebras by, Hrst, taking classic theorems in the theory 0f universal algebras amd dualizing them and, second, developing an interna] 10gic for categories 0f coalgebras. We begin with an introduction t0 the categorical approach t0 algebras and the dual 110tion 0f coalgebras. Following this, we discuss (c0)a,lg€bra.s for 2. (c0)monad and develop 2. theory 0f regular subcoalgebras which will be used in the interna] logic. We also prove that categories 0f (...) coalgebras are completc, under reasonably weak conditions, and simultaneously prove the wellknown dual result for categories 0f algebras. We dose the second chapter with 2. discussion 0f bisimulations in which we introduce a weaker 110tion 0f bisimulaticn than is current in the literature, but which is w€H—b€ha.v€d and reduces t0 the standard defmition under the assumption 0f choice. (shrink)

The theories of cultural anthropologist Ernest Becker arise from an existential and psychological analysis of the death terror/anxiety deep in the unconscious of every human. Becker details how this anxiety governs the ideologies and behaviors of our species—something now confirmed by thousands of experiments performed by psychologists engaged in contemporary terror management theory (TMT). Humans manage their anxiety through what Becker terms “hero systems”—concepts, beliefs, and myths we create to give us a sense of significance and meaning during, and even (...) beyond our mortal lives. Today, many dominant economic, technological, and religious hero systems seek to confirm our significance by denying that we are—like all other species—animals who must exist in a decaying, mortal body. Becker shows how this attempt to deny our “creatureliness” (basic biological nature) causes humans to stand against the natural world we are embedded in, leading to an assault on the planet and nonhuman animals. As a result, Becker believed pacifism was the only hero system capable of keeping humankind from destroying itself and the earth. Pacifism is the precursor to the more encompassing ethical concept of “reverence for life,” advocated by Dr. Albert Schweitzer. By respecting the will-to-live in all sentient beings, reverence for life transcends concern for humans alone and extends moral and physical safeguards to life as such. Confronting the fact that humans are increasingly alienated from their commodified world and their own being, reverence for life stands as a vital solution to many of our modern problems. And following contemporary TMT research, reverencing life can also expand one’s self-esteem, which research shows lowers death anxiety, reduces aggression, and offers authentic meaning to life itself. (shrink)

Although workplace bullying is common and has universally harmful effects on employees’ outcomes, little is known about workplace bullies. To address this gap in knowledge, we draw from the tenets of social exchange and displaced aggression theories in order to develop and test a model of workplace bullying that incorporates the effects of employees’ individual differences, perceptions of their work environments, and perceptions of supervisory treatment on their tendencies to bully coworkers. The results of mediated moderation analyses that examine responses (...) from two samples of working adults support our hypotheses. Specifically, we find evidence of an indirect relationship between entitlement and coworker bullying through perceptions of abusive supervision that is stronger for employees who report lower levels of felt accountability than employees who report higher levels of felt accountability. This study makes important theoretical and practical contributions to abusive supervision research, bullying research, and organizational efforts to promote ethical work environments devoid of interpersonal mistreatment by providing novel insight into how employees’ entitlement and felt accountability combine to influence their tendencies to perceive themselves as victims of abusive supervision and culprits of coworker bullying. (shrink)

We draw from ego depletion and leader–member exchange theories to provide nuanced insight into why abusive supervision is indirectly associated with supervisor-directed destructive voice. A multi-wave, multi-source field study demonstrates evidence that abusive supervision has a positive conditional indirect effect on supervisor-directed destructive voice through subordinates’ relational ego depletion with their supervisors that is stronger for higher LMX differentiation contexts than lower LMX differentiation contexts. We make novel theoretical, empirical, and practical contributions by providing a parsimonious explanation for why relational (...) aspects of supervisory treatment drain subordinates’ capacities for controlling their volitional actions during interactions with their supervisors and how this relationship impacts subordinates’ supervisor-directed destructive voice. Overall, our study extends the application of ego depletion and LMX theories to the examination of abusive supervision and destructive voice in order to meaningfully inform researchers’ attempts to build cohesive streams of research in these areas and practitioners’ attempts to promote ethical workplace environments. (shrink)

Early life stress precedes alterations to neuro-immune activation, which may mediate an increased risk for stress-related psychiatric disorders, potentially through alterations of central kynurenine pathway metabolites, the latter being relatively unexplored. We hypothesized that ELS in a non-human primate model would lead to a reduction of neuroprotective and increases of neurotoxic KP metabolites. Twelve adult female bonnet macaques reared under conditions of maternal variable foraging demand were compared to 27 age- and weight-matched non-VFD-exposed female controls. Baseline behavioral observations of social (...) affiliation were taken over a 12-week period followed by the first cerebrospinal fluid sample. Subjects were then either exposed to a 12-week repeated separation paradigm or assigned to a “no-RSP” condition followed by a second CSF. We used high-performance liquid chromatography for kynurenine, tryptophan, 5-hydroxyindoleacetic acid, kynurenic acid, and anthranilic acid as a proxy for quinolinic acid determination. At baseline, social affiliation scores were reduced in VFD-reared versus control subjects. CSF log KYNA and log KYNA/KYN ratio were lower in VFD-reared versus control subjects. CSF log KYNA/KYN was positively correlated with CSF log ANTH in VFD only. Controlling for log KYNA/KYN, log ANTH was elevated in VFD-reared subjects versus controls. CSF log KYNA/KYN obtained post-RSP was positively correlated with mean social affiliation scores during RSP, specifically in VFD. ELS is associated with a reduced neuroprotective and increased neurotoxic pathway products. That the two contrasting processes are paradoxically correlated following ELS suggests a cross-talk between two opposing KP enzymatic systems. (shrink)

Zygon®, Volume 57, Issue 2, Page 344-367, June 2022.

The current two-sample investigation explores the role of enactment as a boundary condition in the relationship between experienced incivility and workplace outcomes. We integrate the tenets of the transactional model of stress and sensemaking theory to explain why enactment is a psychological sensemaking capability that can neutralize the adverse effects of experienced incivility on workplace outcomes. The results across two samples of data supported the study hypotheses by demonstrating that experienced incivility had stronger adverse effects on employees’ job satisfaction, OCBs, (...) and turnover intent for employees who reported lower levels of enactment than employees who reported higher levels of enactment. This study’s results make three important contributions to theory and research. First, we make an empirical contribution by examining enactment as a psychological sensemaking capability that can neutralize the adverse effects of experienced incivility on workplace outcomes. Second, we make a theoretical contribution by integrating the tenets of the transactional model of stress and sensemaking theory in a novel way that explains why enactment is a psychological sensemaking capability that can neutralize the adverse effects of stress on strain. Third, we demonstrate that enactment is the boundary condition that explains why incivility does not have universally adverse effects on employees’ outcomes. (shrink)

Research that examines unethical interpersonal treatment has received a great deal of attention from scholars and practitioners in recent years due to the remarkable impact of mistreatment in the workplace. However, the literature is incomplete because we have an inadequate understanding of insubordination, which we define as “subordinates’ disobedient behaviors that intentionally exhibit a defiant refusal of their supervisors’ authority.” In our study, we integrate social exchange theory and the advantageous comparison component of moral disengagement within the integrative model of (...) experiencing and responding to mistreatment at work. Then, we explain why subordinates disengage from moral control as they balance experiencing abusive supervision with perpetrating insubordination within negative supervisor–subordinate social exchange relationships. In Studies 1–4, we validate a five-item measure of insubordination and demonstrate its content, convergent, discriminant, criterion-related, and predictive validity. In Study 5, we demonstrate that there is a positive indirect effect of abusive supervision on insubordination through negative social exchange relationship quality that strengthens for subordinates who perceive higher levels of supervisors’ task performance than others. Overall, our study advances the conversation in the business ethics literature by creating a solid conceptual, empirical, and theoretical foundation for a cohesive program of insubordination research that meaningfully builds on prior findings in unethical interpersonal treatment research. (shrink)

ABSTRACT Populism raises questions about the extent to which public opinion should be a legitimate foundation for executive power. In the United States, it is often thought, such a foundation was established at the beginning of the twentieth century through the creation of a newly “representative” modern presidency. This new presidency, it is held, acts as an agent of populist majorities to undermine constitutional and legal norms. In fact, however, the argument for presidential representation is a long-standing element of politics (...) in the United States. It is appealed to, recurrently, by what might be called the party of opinion against its natural opponent, the party of law. (shrink)

The presidency of Donald Trump saw the rise of a new kind of conspiracy in QAnon. The internet-assembled meta-conspiracy has grown to include elements of other growing conspiracies such as the anti-mask movement and anti-vaxxers. As it has grown, QAnon has attracted significant support for its beliefs from white evangelicals who also supported Trump in huge numbers in both 2016 and 2020. In this integrative review of literature, I explore the reasons that QAnon has performed so well so quickly, finding (...) justification for conspiracy theory support among evangelicals in the theory of cognitive dissonance. QAnon has found a foothold in evangelical circles during worldwide pandemic, which has left many evangelicals unmoored from their spiritual family and susceptible to other realms of community online. The conspiracy theory has infiltrated evangelicalism by using the language and concerns of Christianity in its messaging and by attempting to justify evangelical support of Donald Trump. Although traditional media are quick to point out the theory’s inconsistencies and failed prophecies, this paper finds that the harm QAnon has done to the evangelical community may only be undone through spiritual connection and practice. (shrink)

Cet article examine les enjeux des théories de la Bildung chez Kant et Schiller, et leur confrontation mutuelle avec la philosophie de l’autre. On propose une voie interprétative médiane qui ne part pas de l’opposition trop réductrice entre la morale et l’esthétique, ni ne lit Schiller comme étant foncièrement opposé à Kant pour des raisons soit morales, soit éducatives, mais situe plutôt la principale contribution de Schiller dans la sphère de la moralisation. Cette approche éclaire plus adéquatement la manière dont (...) la théorie schillérienne de la Bildung répond aux questions fondamentales laissées ouvertes par les conceptions de Kant. (shrink)

John F. X. Knasas has issued a series of philosophical and exegetical critiques of what he presents as the Cartesian subjectivism of “transcendental Thomism” in general and Bernard Lonergan in particular. But Professor Knasas’s spontaneous assumptions about knowing, objectivity, and reality are those of Descartes and Kant, not St. Thomas. He thus misinterprets St. Thomas and Fr. Lonergan and misconstrues the nature of knowing. The roots of the differences between Professor Knasas and Fr. Lonergan are exposed by contrasting two radically (...) opposed accounts of knowing, two correlative meanings of the term ‘real’, and two correspondingly divergent interpretations of St. Thomas. In the process, Professor Knasas’s repeated misrepresentation of Fr. Lonergan is corrected. (shrink)

Gaven Kerr argues that Lonergan is a metaphysical realist but follows an inherently idealist method. Furthermore, Kerr claims, Lonergan’s isomorphism of cognitional and ontological elements does not hold, because ontological act is not parallel to cognitional judgment. In so arguing, however, Kerr conflates ontological act with efficient causality, misunderstands the nature of the parallel asserted by Lonergan’s isomorphism, and involves himself in a priori speculation about the implications of Lonergan’s method. An efficient cause is an extrinsic principle, whereas “act” names (...) an intrinsic constituent of contingent being. The parallel between ontological and cognitional composition, moreover, and the isomorphism of ontological and cognitional elements, are subtler than Kerr appreciates. The suspicion, finally, that Lonergan’s method is somehow inherently idealist is idle and not borne out by the facts. (shrink)

In this article I propose to do five things. First, I describe the present confusion disturbing the tranquility of the American polity. Next, I hypothesize that an important source of civil confusion is that American civildiscourse is generally conducted in two different moral languages. Neither of these is adequate to the reality of the human good, and their speakers are, perhaps increasingly, given to misunderstanding one another. Third, I propose some reasons why not only misunderstanding but even outright hostility seems (...) to be growing. Fourth, I suggest that if we Christians are to be of genuine service to our fellow citizens, we have to begin by emancipating ourselves from inadequate moral languages and renew our capacity to function in a more properly Christian language. Finally, I suggest a possible contribution Christians might make to the renewal of civil discourse. (shrink)

In this paper, I shall discuss some claims about selves McTaggart makes in The Nature of Existence.

A review of Abbey-Anne Smith's book "Animals in Tillich's Philosophical Theology.".

Stanovich & West's dual-system represents a major development in an understanding of reasoning and rationality. Their notion of System 1 functioning as a computational escape hatch during the processing of complex tasks may deserve a more central role in explanations of reasoning performance. We describe examples of apparent escape-hatch processing from the reasoning and judgement literature.

As idealized descriptions of mathematical language, there is a sense in which formal systems specify too little, and there is a sense in which they specify too much. On the one hand, formal languages fail to account for a number of features of informal mathematical language that are essential to the communicative and inferential goals of the subject. On the other hand, many of these features are independent of the choice of a formal foundation, so grounding their analysis on a (...) particular choice of a formal system introduces unnecessary specificity. This chapter begins to map out the design features of mathematical language without descending to the level of formal implementation, drawing on examples from the mathematical literature and insights from the design of computational proof assistants and their libraries. (shrink)

The early twentieth century was a lively time for the foundations of mathematics. This ensuing debates were, in large part, a reaction to the settheoretic and nonconstructive methods that had begun making their way into mathematical practice around the turn of the twentieth century. The controversy was exacerbated by the discovery that overly na¨ıve formulations of the fundamental principles governing the use of sets could result in contradictions. Many of the leading mathematicians of the day, including Hilbert, Henri Poincar´e, ´.

Of all the demands that mathematics imposes on its practitioners, one of the most fundamental is that proofs ought to be correct. It has been common since the turn of the twentieth century to take correctness to be underwritten by the existence of formal derivations in a suitable axiomatic foundation, but then it is hard to see how this normative standard can be met, given the differences between informal proofs and formal derivations, and given the inherent fragility and complexity of (...) the latter. This essay describes some of the ways that mathematical practice makes it possible to reliably and robustly meet the formal standard, preserving the standard normative account while doing justice to epistemically important features of informal mathematical justification. (shrink)

Philosophical concerns rarely force their way into the average mathematician’s workday. But, in extreme circumstances, fundamental questions can arise as to the legitimacy of a certain manner of proceeding, say, as to whether a particular object should be granted ontological status, or whether a certain conclusion is epistemologically warranted. There are then two distinct views as to the role that philosophy should play in such a situation.

In a wide range of fields, the word “modular” is used to describe complex systems that can be decomposed into smaller systems with limited interactions between them. This essay argues that mathematical knowledge can fruitfully be understood as having a modular structure and explores the ways in which modularity in mathematics is epistemically advantageous.

At the turn of the nineteenth century, mathematics exhibited a style of argumentation that was more explicitly computational than is common today. Over the course of the century, the introduction of abstract algebraic methods helped unify developments in analysis, number theory, geometry, and the theory of equations; and work by mathematicians like Dedekind, Cantor, and Hilbert towards the end of the century introduced set-theoretic language and infinitary methods that served to downplay or suppress computational content. This shift in emphasis away (...) from calculation gave rise to concerns as to whether such methods were meaningful, or appropriate to mathematics. The discovery of paradoxes stemming from overly naive use of set-theoretic language and methods led to even more pressing concerns as to whether the modern methods were even consistent. This led to heated debates in the early twentieth century and what is sometimes called the “crisis of foundations.” In lectures presented in 1922, David Hilbert launched his Beweistheorie, or Proof Theory, which aimed to justify the use of modern methods and settle the problem of foundations once and for all. This, Hilbert argued, could be achieved as follows. (shrink)

On a traditional view, the primary role of a mathematical proof is to warrant the truth of the resulting theorem. This view fails to explain why it is very often the case that a new proof of a theorem is deemed important. Three case studies from elementary arithmetic show, informally, that there are many criteria by which ordinary proofs are valued. I argue that at least some of these criteria depend on the methods of inference the proofs employ, and that (...) standard models of formal deduction are not well-equipped to support such evaluations. I discuss a model of proof that is used in the automated deduction community, and show that this model does better in that respect. (shrink)