A natural deduction formulation is given for the intermediate logic called MH by Gabbay in [4]. Proof-theoretic methods are used to show that every deduction can be normalized, that MH is the weakest intermediate logic for which the Glivenko theorem holds, and that the Craig-Lyndon interpolation theorem holds for it.

The usual rule used to obtain natural deduction formulations of classical logic from intuitionistic logic, namely.

In 1939, Curry proposed a philosophy of mathematics he called formalism. He made this proposal in two works originally written then, although one of them was not published until 1951. These are the two philosophical works for which Curry is known, and they have left a false impression of his views. In this article, I propose to clarify Curry’s views by referring to some of his later writings on the subject. I claim that Curry’s philosophy was not what is now (...) usually called formalism, but is really a form of structuralism. (shrink)

Evidence is given that implication (and its special case, negation) carry the logical strength of a system of formal logic. This is done by proving normalization and cut elimination for a system based on combinatory logic or λ-calculus with logical constants for and, or, all, and exists, but with none for either implication or negation. The proof is strictly finitary, showing that this system is very weak. The results can be extended to a "classical" version of the system. They can (...) also be extended to a system with a restricted set of rules for implication: the result is a system of intuitionistic higher-order BCK logic with unrestricted comprehension and without restriction on the rules for disjunction elimination and existential elimination. The result does not extend to the classical version of the BCK logic. (shrink)

Because the main difference between combinatory weak equality and λβ-equality is that the rule \begin{equation*}\tag{\xi} X = Y \vdash \lambda x.X = \lambda x.Y\end{equation*} is valid for the latter but not the former, it is easy to assume that another way of defining combinatory β-equality is to add rule (ξ) to the postulates for weak equality. However, to make this true, one must choose the definition of combinatory abstraction in (ξ) very carefully. If one tries to use one of the (...) more common abstraction algorithms, the result will be an equality, = ξ , that is either equivalent to βη-equality (and so strictly stronger than β-equality) or else strictly weaker than β-equality. This paper will study the relations = ξ for several commonly used abstraction algorithms, distinguish between them, and axiomatize them. (shrink)

The role of responsible leadership—for each leader and as part of a leader’s collective actions—is essential to global competitive success (Doh and Stumpf, Handbook on responsible leadership and governance in global business, 2005 ; Maak and Pless, Responsible leadership, 2006a . Failures in leadership have stimulated interest in understanding “responsible leadership” by researchers and practitioners. Research on responsible leadership draws on stakeholder theory, with employees viewed as a primary stakeholder for the responsible organization (Donaldson and Preston, Acad Manag Rev 20(1):65–91, (...) 1995 ; Freeman, Strategic management: a stakeholder approach, 1984 ; Mitchell et al., Acad Manag Rev 22:853–886, 1997 ; Phillips and Freeman, Stakeholder theory and organizational ethics, 2003 . We define and operationalize responsible leadership from the perspective of employees and their views of the actions of their leaders. Drawing on a comprehensive survey of 28 Indian and global organizations operating in India, we report the results from 4,352 employees on the relationship between responsible leadership, their pride in and satisfaction with their organization, and retention 1 year later. Strong associations were found among these variables suggesting that responsible leadership—employee perceptions of the support they receive from managers, the HR practices, and corporate socially responsible actions—may be an overarching construct that connects them to the organization. (shrink)

This article argues that Cicero laid down his imperium in Brundisium in September 47 after Caesar had, in a meeting between the two men, granted Cicero permission to retain his imperium and title of imperator for as long as Cicero wished to do so. Instead of accepting Caesar’s offer, Cicero instead immediately repudiated it, laid down his imperium in the city of Brundisium, and went immediately to Tusculum to begin a second period of political retirement. Caesar’s offer and his return (...) to Italy in the autumn of 47 gave Cicero an excuse to consider expired the SCU of 7 January 49 and, by immediately renouncing his imperium, perform, under the cover of his now-fulfilled obligation to the Pompeians, a calculated personal statement of political independence. (shrink)

How can computer professionals shape the future of new computing technologies? Using the recent history of handheld computers as an example, this paper investigates how computer professionals can shape the future by helping to define what new technologies should be. Computer professionals can play a variety of roles in creating, maintaining, and questioning problem framings, or the basic assumptions about what problem a new technology is trying to solve. In addition to political activism and professional ethics, computer professionals need to (...) reflect on the process of defining new technological directions, and how they can help shape technology development into outcomes they believe in. (shrink)

This paper examines the intricate relationship between De Senectute and the Second Philippic, arguing that De Senectute is an important lens through which to read the Second Philippic. When Cicero decided on irrevocable opposition to Antony, the moral and political theorizing about the role of senes (literally, ‘old men/elders’) in the state found in De Senectute provided a convenient and topical framework for synthesizing the invective of the Second Philippic. A close reading of De Senectute with the Second Philippic demonstrates (...) that the philosophical thinking of De Senectute informed Cicero’s political persona in the Second Philippic and establishes the Second Philippic as the intellectual successor to De Senectute. (shrink)

This essay explores the phenomenon of common sense through a contextual analysis of Hannah Arendt’s political application of Kant’s Critique of Judgment. I begin by tracing the development of Arendt’s thinking on judgment and common sense during the 1950s which led her to turn to the third Critique. I then consider the justification of her move by examining the philosophical context and political applications of the third Critique, arguing that within it Kant made an original and profound discovery: that the (...) phenomenon of common sense contains a hidden faculty that may anchor moral and political judgments. I conclude by arguing that Arendt was on firmer ground than is often thought in adapting Kantian common sense to politics, a fact that may afford new possibilities for the practice of moral and political thought. (shrink)

Shortly after the Vandals took Carthage in 439, the city's Catholic bishop, Quodvultdeus, and a large number of his clergy were said to have been placed “naked and despoiled on broken ships” and put to sea, banished from Africa. By God's mercy, the exiles made their way safely to Naples, where Quodvultdeus quickly came to be regarded as a saint: a fifth-century mosaic from the catacombs of St. Januarius in Capodimonte seems to depict the African bishop, and by the middle (...) of the ninth century his feast day was celebrated in the local liturgical calendar. A similar story could be told of Gaudiosus of Abitina, another fifth-century African bishop who was said to have fled the Vandals and who also achieved sainthood in Campania. The flight of refugees like Quodvultdeus and Gaudiosus from the political turmoil that wracked North Africa between the fifth and the eighth centuries, however, has long been seen as having a far greater significance than the reinvention of exiled African bishops as southern Italian holy men. In late antiquity and the early Middle Ages, the cults of numerous saints who had been martyred in Africa and whose cults had originally developed there spread beyond the shores of the southern Mediterranean to the rest of the Christian world. In seeking to explain the diffusion of these cults, historians have long focused on the movements of refugees—and, above all, those who fled the Vandals' conquest of Africa and their subsequent persecution of the region's Catholic population—as displaced Africans such as Quodvultdeus are thought to have brought the relics of their local saints with them into foreign exile. (shrink)

Modernist philosophy and psychology have pursued a variety of methods and models for understanding the universal inclination of human persons toward moral self-deception. We tend, as the Scriptures reveal and as recent empirical studies have confirmed, to think more highly of ourselves and our personal moral caliber than we ought. Whereas, Freud, Sartre, and others have offered solutions to the “paradox” of self-deception—that is, how one can be both deceiver and deceived—their solutions ultimately fall short in terms of both coherence (...) and explanatory power. From a Christian perspective, secular frameworks are bound to falter because they do not account for humanity’s status as fallen and sinful before a holy God. The gospel of Jesus Christ, on the other hand, offers means not only of understanding, but overcoming, moral self-deception. Historically, no movement of Christian spirituality has been more rigorously skeptical of the human ability to “know thyself” truly than the Puritans. This analysis of Puritan pastoral theology provides a helpful lens through which to view, and undermine, the deceitfulness of the human heart. (shrink)

Empirical evidence suggests that fishes, as a whole, are emotional and possess intelligence comparable to that of mammals. Furthermore, although data are sparse, recent studies suggest that representatives from the two major “fish” taxa—bony fish (e.g., groupers and cleaner wrasses) and cartilaginous fish (e.g., giant mantas)—may possess self-awareness and a theory of mind. These capacities indicate that a fish could be capable of the emotion of betrayal. Modern, small-scale aquaculture operations present preconditions in which betrayal might be felt by a (...) fish. (shrink)

We argue that differences in the institutional setting of Europe and the US is the critical factor in understanding policymaking in Europe and the United States, and particularly the influence of nongovernmental organizations (NGOs). To test this relationship between institutional differences, corporate social responsibility (CSR), and NGO activism, we investigate 12 cases involving US and European companies in each of three industries. We conclude that different institutional structures and political legacies in the US and Europe are important factors in explaining (...) the influence of NGOs on business and in the policymaking process, regardless of the timeliness of corporate strategy or NGO influence. (shrink)

Regional market integration in Europe and North America has grown increasingly extensive. This integration has created institutions and structures to guide pancontinental political, economic, and social policies. At the same time, both regions are experiencing pressures of decentralization. These competing trends are transforming relationships between and among business, society, and government. This article compares and contrasts integration in North America and Europe, and discusses the implications of political, economic, and institutional changes in these two regions for business-government relations and the (...) structure and strategic orientation of the corporate public affairs (PA) function. This article reviews recent literature on comparative political economy, business and public policy, and corporate PA, and it presents a conceptual model and research propositions, supported by case illustrations, of how integration and decentralization affect business-government relations and corporate PA in Europe and North America. (shrink)