The connections between mathematical logic and combinatorics have a rich history. This paper focuses on one aspect of this relationship: understanding the strength, measured using the tools of computability theory and reverse mathematics, of various partition theorems. To set the stage, recall two of the most fundamental combinatorial principles, König's Lemma and Ramsey's Theorem. We denote the set of natural numbers by ω and the set of finite sequences of natural numbers by ω<ω. We also identify each n ∈ ω (...) with its set of predecessors, so n = {0, 1, 2, …, n − 1}. (shrink)

The Rainbow Ramsey Theorem is essentially an "anti-Ramsey" theorem which states that certain types of colorings must be injective on a large subset (rather than constant on a large subset). Surprisingly, this version follows easily from Ramsey's Theorem, even in the weak system RCA₀ of reverse mathematics. We answer the question of the converse implication for pairs, showing that the Rainbow Ramsey Theorem for pairs is in fact strictly weaker than Ramsey's Theorem for pairs over RCA₀. The separation involves techniques (...) from the theory of randomness by showing that every 2-random bounds an ω-model of the Rainbow Ramsey Theorem for pairs. These results also provide as a corollary a new proof of Martin's theorem that the hyperimmune degrees have measure one. (shrink)

In many simple integral domains, such as Z or Z[i], there is a straightforward procedure to determine if an element is prime by simply reducing to a direct check of finitely many potential divisors. Despite the fact that such a naive approach does not immediately translate to integral domains like Z[x] or the ring of integers in an algebraic number field, there still exist computational procedures that work to determine the prime elements in these cases. In contrast, we will show (...) how to computably extend Z in such a way that we can control the ordinary integer primes in any Π20 way, all while maintaining unique factorization. As a corollary, we establish the existence of a computable unique factorization domain such that the set of primes is Π20-complete in every computable presentation. (shrink)

We show, relative to the base theory RCA₀: A nontrivial tree satisfies Ramsey's Theorem only if it is biembeddable with the complete binary tree. There is a class of partial orderings for which Ramsey's Theorem for pairs is equivalent to ACA₀. Ramsey's Theorem for singletons for the complete binary tree is stronger than $B\sum_{2}^{0}$ , hence stronger than Ramsey's Theorem for singletons for ω. These results lead to extensions of results, or answers to questions, of Chubb, Hirst, and McNicholl [3].

8.3 The consistency proof -- 8.4 Applications of the consistency proof -- 8.5 Second-order arithmetic -- Problems -- Chapter 9: Set Theory -- 9.1 Axioms for sets -- 9.2 Development of set theory -- 9.3 Ordinals -- 9.4 Cardinals -- 9.5 Interpretations of set theory -- 9.6 Constructible sets -- 9.7 The axiom of constructibility -- 9.8 Forcing -- 9.9 The independence proofs -- 9.10 Large cardinals -- Problems -- Appendix The Word Problem -- Index.

CONTEMPORARY ISSUES IN BUSINESS ETHICS, 6E introduces readers to business ethics by focusing on the influence of market mechanisms and social values on workplace norms. And because business is increasingly a global enterprise, this edition emphasizes the role of ethics both at home and abroad.

The overarching goal in the seventh edition of this text remains what it was for the first edition: "to provide a clear, concise, and reasonably comprehensive introductory survey of the ethical choices available to us in business." This book arose from the challenges encountered in my own teaching of business ethics. Over the years I have taught business ethics in many settings and with many formats. I sometimes relied on an anthology of readings, other times I emphasized case studies.

Three frames of reference for engineering ethics are discussed—individual, professional and social—which can be further broken down into “microethics” concerned with individuals and the internal relations of the engineering profession and “macroethics” referring to the collective social responsibility of the engineering profession and to societal decisions about technology. Few attempts have been made at integrating microethical and macroethical approaches to engineering ethics. The approach suggested here is to focus on the role of professional engineering societies in linking individual and professional (...) ethics and in linking professional and social ethics. A research program is outlined using ethics support as an example of the former, and the issuance of position statements on product liability as an example of the latter. (shrink)

In California Dental Association v. FTC, 119 S. Ct. 1604, the U.S. Supreme Court reviewed a decision by the U.S. Court of Appeals for the Ninth Circuit that a nonprofit affiliation of dentists violated section 5 of the Federal Trade Commission Act, 15 U.S.C.A. § 45, which prohibits unfair competition. The Court examined two issues: the Federal Trade Commission's jurisdiction over the California Dental Association ; and the proper scope of antitrust analysis. The Court unanimously held that CDA was subject (...) to FTC's jurisdiction, but split 5-4 in its finding that the district court's use of abbreviated rule-of-reason analysis was inappropriate.CDA is a voluntary, nonprofit association of local dental societies. It boasts approximately 19,000 members, who constitute roughly threequarters of the dentists practicing in California. Although a nonprofit, CDA includes for-profit subsidiaries that financially benefit CDA members. CDA gives its members access to insurance and business financing, and lobbies and litigates on their behalf. Members also benefit from CDA marketing and public relations campaigns. (shrink)

LetCbe an axiom system formalized within the first order functional calculus, and letC′ be related toCas the Bernays-Gödel set theory is related to the Zermelo-Fraenkel set theory. Ilse Novak [5] and Mostowski [8] have shown that, ifCis consistent, thenC′ is consistent. Mostowski has also proved the stronger result that any theorem ofC′ which can be formalized inCis a theorem ofC.The proofs of Novak and Mostowski do not provide a direct method for obtaining a contradiction inCfrom a contradiction inC′. We could, (...) of course, obtain such a contradiction by proving the theorems ofCone by one; the above result assures us that we must eventually obtain a contradiction. A similar process is necessary to obtain the proof of a theorem inCfrom its proof inC′. The purpose of this paper is to give a new proof of these theorems which provides a direct method of obtaining the desired contradiction or proof.The advantage of the proof may be stated more specifically by arithmetizing the syntax ofCandC′. (shrink)

Specialists and primary care physicians play an integral role in treating the twin epidemics of pain and addiction. But inadequate access to specialists causes much of the treatment burden to fall on primary physicians. This article chronicles the differences between treatment contexts for both pain and addiction — in the specialty and primary care contexts — and derives a series of reforms that would empower primary care physicians and better leverage specialists.

The Problem of Virtue The shortest and surest way of making men happy is not to adorn their cities, nor even to enrich them, but to make them good. ...

This paper discusses collaborative learning and its use in an elective course on ethics in engineering. Collaborative learning is a form of active learning in which students learn with and from one another in small groups. The benefits of collaborative learning include improved student performance and enthusiasm for learning, development of communication skills, and greater student appreciation of the importance of judgment and collaboration in solving real-world problems such as those encountered in engineering ethics. Collaborative learning strategies employed in the (...) course include informal small group discussions/problem solving, role-playing exercises, and cooperative student group projects, including peer grading. Student response to these techniques has been highly favorable. Realizing the benefits of collaborative learning is a challenge to both teachers, who must give up some control in the classroom, and students, who must be willing to take greater responsibility for their learning. (shrink)

The evolutionary neurological foundations of religious experience are detailed. Human beings have been burying and preparing their dead for the Hereafter for more than 100,000 years. These behaviors and beliefs are related to activation of the amygdala, hippocampus, and temporal lobe, which are responsible for religious, spiritual, and mystical trancelike states, dreaming, astral projection, near‐death and out‐of‐body experiences, and the hallucination of ghosts, demons, angels, and gods. Abraham, Moses, Muhammad, and Jesus Christ, and others who have communed with angels or (...) gods display limbic system hyperactivity, whereas patients report religious hallucinations or out‐of‐body experiences when limbic structures are stimulated or excessively activated. It is postulated that limbic and temporal lobe structures account for the sexual and violent aspects of religious behavior and also serve as a “transmitter to God,” and that the evolution of these structures made spiritual experience possible. (shrink)

Les musées contemporains sont en pleine mutation, ils passent du statut de « temples de l’art et de la culture » à celui de pourvoyeurs d’activités culturelles et ludiques. Censés instruire, ils s’engagent dans la voie controversée de plaire en vue d’exister, le but ultime étant de drainer le plus de « clients » possible pour assurer la continuation. Et dans la mouvance, ils n’hésitent pas à s’exporter au même titre que les enseignes commerciales vers des cités-nations à la recherche (...) d’une « présence » sur la mappemonde globalisée. Le Louvre-Abou Dabi est un exemple saillant de cette tendance mondialisée, tout comme Guggenheim, il devient un jalon mobile de l’art et de la culture. Dans cette phénoménologie de « l’existence par l’architecture », les œuvres architecturales deviennent des objets-outils de notoriété et de communication, plus inhérents au marketing qu’à la culture. Mais quelle part d’intérêt va pour les collections dans ce nouveau statut du musée ou le bâtiment est à lui seul un gage d’existence et de contemporanéité ? Et dans quelle mesure, la part de responsabilité publique qui incombe aux musées dans le développement culturel de la collectivité, risque-t-elle d’être compromise par les lois du marché?Contemporary museums are rapidly evolving from “temples of art and culture” to providers of cultural and recreational activities. Although supposed to be instructive, they are embarking on a controversial policy of pleasing the public in order to exist, the ultimate aim being to draw as many “customers” as possible to secure their future. And in pursuing these aims, they have been exporting themselves, just like any commercial brand, to nation-cities seeking a “place” on the globalised map. The Abu Dhabi Louvre is a striking example of this global trend, as is the Guggenheim, which has now become a movable landmark in the arts and culture landscape. This phenomenon of “existence through architecture” is turning architectural works into objects as well as tools to enhance communication and notoriety, a development that has more to do with marketing than with culture. But given this new status, where the building itself guarantees the museum’s existence and contemporaneity, how much interest is there in its collections? And to what extent is every museum’s share of public responsibility for collective cultural development likely to compromised by “market forces”? (shrink)

Mainstream science, technology, and society scholars have shown little interest in engineering ethics, one going so far as to label engineering ethics activists as “shit shovelers.” Detachment from engineering ethics on the part of most STS scholars is related to a broader and long-standing split between the scholar-oriented and activist-oriented wings of STS. This article discusses the various STS “subcultures” and argues that the much-maligned activist STS subculture is far more likely than the mainstream scholar subculture to have a significant (...) impact on engineering ethics education and practice. (shrink)

In 1792, Thomas Paine sounded a cautionary note about the economics of empire: The most unprofitable of all commerce is that connected with foreign dominion. To a few individuals it may be beneficial, merely because it is commerce; but to the nation it is a loss. The expense of maintaining dominion more than absorbs the profit of any trade.1 Had Americans consistently heeded Paine’s advice, the United States might have avoided much of the overseas bloodshed, as well as domestic bureaucratization, (...) which have accompanied the creation of the American empire. (shrink)

The monarchic, and aristocratical, and popular partisans have been jointly laying their axes to the root of all government, and have in their turns proved each other absurd and inconvenient. In vain you tell me that artificial government is good, but that I fall out only with the abuse. The thing! the thing itself is the abuse! ~ Edmund Burke, 1756..

What knowledge enables Cyrus to rule easily over multitudes? Why does Xenophon convey it in a novel? Cyrus possesses knowledge of ambition’s effects in the honour-loving soul. He perceives that honour-loving men can be ensnared into abject dependence if they can be made to accept any one individual’s will as the sole source of honour; easier still is the task of ruling those far more numerous men whose love of honour is infused with or subordinated to the love of the (...) material rewards that accompany victory. Cyrus creates a hierarchy of dependence, with himself at the apex, and he rules his honour-loving followers easily, creating the institutions of an empire that endured to Xenophon’s own day. Xenophon depicts this arrangement in a historical romance, rather than describe it in a treatise, in ordermore effectively to inspire the love of virtue in his readers. (shrink)

This chapter contains sections titled: Responsibility for environmental harm to humans Responsibilities to the natural world Business ethics in the age of sustainable economics.