We apply Benacerraf’s distinction between mathematical ontology and mathematical practice to examine contrasting interpretations of infinitesimal mathematics of the seventeenth and eighteenth century, in the work of Bos, Ferraro, Laugwitz, and others. We detect Weierstrass’s ghost behind some of the received historiography on Euler’s infinitesimal mathematics, as when Ferraro proposes to understand Euler in terms of a Weierstrassian notion of limit and Fraser declares classical analysis to be a “primary point of reference for understanding the eighteenth-century theories.” Meanwhile, scholars like (...) Bos and Laugwitz seek to explore Eulerian methodology, practice, and procedures in a way more faithful to Euler’s own. Euler’s use of infinite integers and the associated infinite products are analyzed in the context of his infinite product decomposition for the sine function. Euler’s principle of cancellation is compared to the Leibnizian transcendental law of homogeneity. The Leibnizian law of continuity similarly finds echoes in Euler. We argue that Ferraro’s assumption that Euler worked with a classical notion of quantity is symptomatic of a post-Weierstrassian placement of Euler in the Archimedean track for the development of analysis, as well as a blurring of the distinction between the dual tracks noted by Bos. Interpreting Euler in an Archimedean conceptual framework obscures important aspects of Euler’s work. Such a framework is profitably replaced by a syntactically more versatile modern infinitesimal framework that provides better proxies for his inferential moves. (shrink)

Can visual interaction with artwork prompt healing? Can the brain recover from traumatic experiences and help heal the whole body? Since the 1940s, art therapists have claimed that the production of art can help heal past traumas. Similarly, occupational therapists have employed techniques from arts and crafts since the end of World War II to retrain soldiers helping them recover from the trauma of war. The global Covid-19 pandemic has caused health-related and psychological problems--isolation, increased anxiety, and fear--for people of (...) all ages, with the rates of such traumas affecting children tripling over the past two years. According to the Nebraska-based quilting company, Accuquilt, during the first six months of pandemic isolation in 2020, sales more than doubled as new customers showed a desire to participate in arts and crafts from home. This essay explores various approaches to the arts to determine how art may restore dignity and health following traumatic experiences. (shrink)

Abraham’s “leadership by example” provides a template for business leaders to implement a tone at the top based on a balance of tzedek (righteousness) and mishpat (legal judgement). The former expresses the generosity of spirit required of leaders, while the latter expresses the sound judgement in conformity with both ethics and enacted law. We relate the two constructs to several contemporary theories of justice and jurisprudence. We also relate the development of Abrahamic Justice in the Jewish tradition from antiquity through (...) Maimonides in the middle ages. We draw insight from this tradition to answer a contemporary business ethics question: Do corporate managers violate their fiduciary duty to shareholders if they refuse to engage in legal tax avoidance? (shrink)

Many scholars believe that traditional courses in ethics (especially business ethics) have not been successful in making students ethical. The best that educators can hope is that these courses will help build ethical awareness. It is thus apparent that the apparatus used to teach ethics does not inspire the intellectual leap needed between the abstract awareness of ethical issues to the functional changes in behavior and decision-making. This paper posits that the creative arts, including literature, poetry, music, pictorial art, and (...) film, may provide the tools to help bridge that gap. The creative arts can profoundly impact individuals and cause social change by gradually implanting values and changing beliefs. They can instill morals by using stories, sounds, and images and arouse the passion needed to change behaviors. (shrink)

The contention of this paper is that the marketing concept is but one aspect of a philosophy of business referred to by the authors as the framework for organizational success. This framework maintains that the marketing concept must work together with good management approaches and with ethical business practices in order to satisfy the needs and wants of the various publics of the organization — customers, employees, suppliers, society — and, in the long run, ensure the satisfaction of the needs (...) of the organization itself. The authors propose that focusing on one concept, and ignoring the other two aspects, is not likely to promote organizational success. (shrink)

Ethical violations are becoming common in the business world. Teaching proper ethical behavior can begin in college. In this study, we surveyed 350 students to determine what affects students’ perceptions of the ethics of professors and to determine whether or not taking a course in ethics changes this perception. The most important factor in determining whether or not a professor is ethical is “fairness in grading.” Surprisingly, there was no statistically significant difference between students who took a course in ethics (...) and those who did not in their perception of what makes a professor ethical or unethical. There were some differences, however, between males and females in these perceptions. By learning ethical principle at the college-level, there may be an impact on ethical behavior when in the business world. (shrink)

The goal of this paper is to define and analyze systems which exhibit brittle behavior. This behavior is characterized by a sudden and steep decline in performance as the system approaches the limits of tolerance. This can be due to input parameters which exceed a specified input, or environmental conditions which exceed specified operating boundaries. An analogy is made between brittle commmunication systems in particular and materials science.

The first half of the 17th century was a time of intellectual ferment when wars of natural philosophy were echoes of religious wars, as we illustrate by a case study of an apparently innocuous mathematical technique called adequality pioneered by the honorable judge Pierre de Fermat, its relation to indivisibles, as well as to other hocus-pocus. André Weil noted that simple applications of adequality involving polynomials can be treated purely algebraically but more general problems like the cycloid curve cannot be (...) so treated and involve additional tools–leading the mathematician Fermat potentially into troubled waters. Breger attacks Tannery for tampering with Fermat’s manuscript but it is Breger who tampers with Fermat’s procedure by moving all terms to the left-hand side so as to accord better with Breger’s own interpretation emphasizing the double root idea. We provide modern proxies for Fermat’s procedures in terms of relations of infinite proximity as well as the standard part function. (shrink)

In the biblical Book of Ruth, Boaz instructs his workers not to molest Ruth. We draw insights on the problem of workplace sexual harassment in the family-firm setting from the Book of Ruth. We then integrate these insights with several discrete findings in the literatures on workplace sexual harassment and family firms: First, family firms are relatively strong when it comes to a culture of fairness and respect. Second, family firms sometimes lack formal codes of ethics, which could hamper integrity. (...) Third, religious exemplars can reinforce the positive culture of family firms and even substitute for a formal code of ethics. Fourth, religious exemplars can also attenuate excessive risk-taking behavior in family firms. (shrink)

Classically, an osculating circle at a point of a planar curve is introduced technically, often with formula giving its radius and the coordinates of its center. In this note, we propose a new and intuitive definition of this concept: among all the circles which have, on the considered point, the same tangent as the studied curve and thus seem equal to the curve through a microscope, the osculating circle is this that seems equal to the curve through a microscope within (...) microscope. (shrink)

In this paper, we show that God is portrayed in the Hebrew Bible and in the Rabbinic literature—some of the very Hebrew texts that have influenced the three major world religions of Judaism, Christianity, and Islam—as One who can be argued with and even changes his mind. Contrary to fundamentalist positions, in the Hebrew Bible and other Jewish texts God is omniscient but enjoys good, playful argumentation, broadening the possibilities for reasoning and reasonability. Arguing with God has also had a (...) profound influence upon Jewish humor, demonstrating that humans can joke with God. More specifically, we find in Jewish literature that humor’s capacity to bisociate between different domains of human experience can share a symbiotic relationship with argumentation’s emphasis on producing multiple, contested perspectives. Overall, once mortals realize that figures such as God can accept many perspectives through humor, teasing, arguing, criticism, and in at least one case, even lawsuits, a critical point emerges: citizens should learn to live, laugh, and reason with others with whom they disagree. (shrink)

A core value of Judaism is leading an ethical life. The Talmud, an authoritative source on Jewish law and tradition, has a number of discussions that deal with honesty in business and decision-making. One motive that can cause individuals to be unscrupulous is the presence of a conflict of interest. This paper will define, discuss, and review five Talmudic concepts relevant to conflict of interest. They are (1) Nogea B’Davar (being an interested party), (2) V’hiyitem N’keyim (behaving to ensure that (...) one is above suspicion) (3) Lifnei Iver (placing a stumbling block before the blind), (4) Shokhad (accepting a bribe), and (5) Geneivat Da’at (deception and undeserved goodwill). Case examples will be used to apply these Talmudic principles to contemporary business practice. This will include discussion of these Talmudic concepts as it applies to specific contemporary business examples relevant to the boardroom, accounting firms, investment banking, politics, and government. It may be impossible to eliminate all conflicts of interest. However, knowledge and awareness of these Talmudic principles can help individuals in business settings better address the ethical issues that they confront. (shrink)

The following reviews recent developments in the cognitive and evolutionary psychology of religion, and argues for an adaptationist stance.

The Talmud, the compilation of Jewish oral law, is over 1500 years old and includes extensive discussions of business ethics. This paper presents four levels of ethical behavior in business gleaned from the words of the Talmud. At the lowest level, an individual is just barely inside the law; the highest level is the way of the pious. The author has attempted to relate the ethics in ancient business situations to business practices today.

Belief storage is often modeled as having the structure of a single, unified web. This model of belief storage is attractive and widely assumed because it appears to provide an explanation of the flexibility of cognition and the complicated dynamics of belief revision. However, when one scrutinizes human cognition, one finds strong evidence against a unified web of belief and for a fragmented model of belief storage. Using the best available evidence from cognitive science, we develop this fragmented model into (...) a nascent theory of the cognitive architecture of belief storage. (shrink)

Eminent political theorist Joseph Carens tests the limits of democratic theory in the realm of immigration, arguing that any acceptable immigration policy must be based on moral principles even if it conflicts with the will of the majority.

Eminent political theorist Joseph Carens tests the limits of democratic theory in the realm of immigration, arguing that any acceptable immigration policy must be based on moral principles even if it conflicts with the will of the majority.

We present a simple distributed concept that appears to insinuate SWARM behavior in a collection of mobile platforms. The control is based on the inter-mobile platform communication links’ signal-to-noise ratio. This double use of communications is a natural linkage for SWARM behavior.

Public health emergencies, including infectious disease outbreaks and natural disasters, are issues faced by every community. To address these threats, it is critical for all jurisdictions to understand how law can be used to enhance public health preparedness, as well as improve coordination and collaboration across jurisdictions. As sovereign entities, Tribal governments have the authority to create their own laws and take the necessary steps to prepare for, respond to, and recover from disasters and emergencies. Legal preparedness is a key (...) component of public health preparedness. This article first explains legal preparedness and Tribal sovereignty and then describes the relationship between Tribal Nations, the US government, and states. Specific Tribal concerns with respect to emergency preparedness and the importance of coordination and collaboration across jurisdictions for emergency preparedness are discussed. Examples of collaborative efforts between Tribal and other governments to enhance legal preparedness are described. (shrink)