Discrete Mathematics is designed to serve as a textbook for undergraduate engineering students of computer science and postgraduate students of computer applications. The book would also prove useful to post graduate students of mathematics. It seeks to provide a thorough understanding of the subject and present its practical applications to computer science.

This paper presents an integralist approach to Jaina logic. This is built around an analysis of the pivotal notion of antarvyāpti in Jaina logic. It is shown in this connection why antarvyāpti needs to be considered the ‘Core Perspective/problem’ of Jaina logic. Next, it is shown how all the salient features of Jaina logic (as viewed from its language-oriented perspective and the epistemic perspective respectively) stand intimately related to the so-called core perspective. In the remaining sections of the paper topics (...) like relationship of the core perspective i) to various non-standard systems of logic [DL, FL, NMR etc.,], ii) to the four pillars and to the eight MPC’s of Jaina philosophy, iii) to some bluntly unimaginative ways of looking at Jaina logic [e.g., Ducko-Rabbitism], iv) to the scheme of classification of propositions in Jaina logic, v) to the resulting conceptual economies related to methodology, and especially to a unified theory of Hetvābhāsa and, finally, vi) to a re-assessment of Frege-Husserl discord in the light of the significance of Jñānātmakatā vs Vākyātmakatā in Jaina logic, etc., have been discussed. (shrink)

Foreward by Pramod K. Nayar -- Prologue -- Acknowledgments -- Introduction -- The dys-abled players of Samuel Beckett's Endgame -- The circumcised body of Franz Kafka's select letters -- 'Connoisseurship ... of disease' and Thomas Mann's Death in Venice -- 'Undiscovered countries' with Virginia Woolf's On being ill -- 'Connect nothing with nothing' in T.S. Eliot's The wasteland -- Epilogue -- Pathography -- Index.

Hegel's treatment of the Sublime is both self-consistent and distinctive. He not only defines sublimity, but discovers and ranks its types or stages from one select point of view—the viewpoint of God-world relation; and the way he does this, on the one hand, distinguishes him from many others who have contributed to an understanding of the concept, and, on the other hand, enables him to suggest, if but implicitly, a criterion for distinguishing the sublime from allied concepts. Besides, he discusses (...) the matter in the wide context of diverse cultures, making quite a few insightful references to Eastern literature; and, consistently with his own conception of philosophy, also from the viewpoint of historical necessity, so that the sublime appears, in his Aesthetik, as a specific stage which the evolving story of art must in fact traverse. (shrink)

Although we believe the results reported below to have direct philosophical import, we shall for the most part confine our remarks to the realm of mathematics. The reader is referred to [4] for a philosophically oriented discussion, comprehensible to mathematicians, of tense logic.The “minimal” tense logicT0is the system having connectives ∼, →,F(“at some future time”), andP(“at some past time”); the following axioms:(whereGandHabbreviate ∼F∼ and ∼P∼ respectively); and the following rules:(8) fromαandα → β, inferβ,(9) fromα, infer any substitution instance ofα,(10) fromα, (...) inferGα,(11) fromα, inferHα.A tense logic is a systemTwhose language is that ofT0and whose axioms and rules include (1)–(11). The axioms and rules ofTother than (1)–(11) are calledproperaxioms and rules.We shall investigate three systems of semantics for tense logics, i.e. three notions ofstructureand three relations ⊧ which stand between structures and formulas. One reads⊧αas “αis valid in.” A structureis amodelof a tense logicTif every formula provable inTis valid in. A semantics isadequateforTif the set of models ofTin the semantics is characteristic forT, i.e. if wheneverT ∀ αthen there is a modelofTin the semantics such that∀ α. Two structuresand, possibly from different semantics, are calledequivalent(∼) if exactly the same formulas are valid inas in. (shrink)

Advances in life-saving technologies in the past few decades have challenged our traditional understandings of death. Traditionally, death was understood to occur when a person stops breathing, their heart stops beating and they are cold to the touch. Today, physicians determine death by relying on a diagnosis of ‘total brain failure’ or by waiting a short while after circulation stops. Evidence has emerged, however, that the conceptual bases for these approaches to determining death are fundamentally flawed and depart substantially from (...) the established biological conception of death. We argue that the current approach to determining death consists of two different types of unacknowledged legal fictions. These legal fictions were developed for practices that are largely ethically legitimate but need to be reconciled with the law. The considerable debate over the determination of death in the medical and scientific literature has not informed the public that vital organs are being procured from still-living donors and it seems unlikely that this information can remain hidden for long. Given the instability of the status quo and the difficulty of making the substantial legal changes required by complete transparency, we argue for a second-best policy solution: acknowledging the legal fictions involved in determining death to move in the direction of greater transparency. This may someday result in more substantial legal change to directly confront the challenges raised by life-sustaining and life-preserving technologies without the need for fictions. (shrink)

This essay seeks to clarify Gandhi's logic of self-suffering. Its inner accents have not received the attention they deserve. So I propose to emphasize them, though the context of such suffering and its impact on men too must be given due regard.

An interpretation of Aristotle's modal syllogistic is proposed which is intuitively graspable, if only formally correst. The individuals to which a term applies, and possibly-applies, are supposed to be determined in a uniform way by the set of individuals to which the term necessarily-applies.

In verse twelve of the Tao Te Ching, Lao Tzu makes a curious claim about the five flavors; namely that they cause people not to taste or that they jade the palate. The five flavors are: sweet, sour, salt, bitter and spicy or hot as in 'heat'. To the Western mind, the claim, 'The five flavors cause them [persons] to not taste,' is counterintuitive; on the contrary, the presence of the five flavors in a dish or in a meal would (...) expand or enhance the senses and the palate, i.e., taste would be augmented by the five flavors. So what is the plausible meaning of the Taoistic claim? To answer this question, I look very briefly at the history of the doctrine of the five flavors and the history of Chinese cuisine. Lao Tzu probably has Confucian feasts in mind in making such a claim, but other interpretations are discussed. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Hume Studies Volume XX, Number 2, November 1994, pp. 261-287 Collingwood's Understanding of Hume S. K. WERTZ What was David Hume's reception in the British idealistic tradition? In this paper, I shall contribute a short chapter on this question by examining Hume's place in R. G. Collingwood's thought.1 Such an examination has been lacking in the literature, so what follows is a comprehensive study of Collingwood's use of Hume (...) throughout all of R.G.'s writings. I shall mainly focus on two main, unrelated discussions of Hume: first is the theory of the imagination which primarily occurs in The Principles of Art, and second is the set of relations between human nature and human history which is principally found in The Idea of History. These sections will be followed by a section on minor discussions and omissions and a conclusion. It is a common misconception that Collingwood (1889-1943) has little to offer Hume scholarship, and I wish to amend that here. Actually, Collingwood has good insights into the nature of the imagination and its role in human understanding, besides instructive thoughts on Hume on human nature and history, even though his discussion of the latter is flawed. This essay serves both historical and philosophical purposes. It is to sample Hume's place in early twentieth century British idealism at a time when he began to emerge as an important philosophical figure worthy of careful study. (By "idealism," I mean the philosophical movement which takes ideas to be an irreducible part of the world and whose program is opposed to both materialism and realism.) So Collingwood's portrait is historically interesting. But over and above this, it carries significant philosophical amendments, S. K. Wertz is at the Department of Philosophy, Texas Christian University, Box 30781, Fort Worth, TX 76129 USA. e-mail: [email protected] 262 S. K. Wertz criticisms, and suggestions about Hume's thought and the eighteenth century intellectual climate. Collingwood has mostly been studied as a philosopher of history or as an aesthetician, but not in toto from the perspective of one of the historical figures to whom he is deeply indebted. Such a view affords a portrait of Hume that is instructive and rewarding. The comparison of Hume and Collingwood lead us to finer appreciation of both philosophers. Let us first look at Collingwood's positive contribution. Imagination Collingwood begins his analysis by declaring his intentions: I shall...try to show that there are such things, to be with what Hume (whose account of them I shall take as my starting-point) called 'ideas' as distinct from 'impressions'. I shall try to show that there is a special activity of mind correlative to them, and that this is what we generally call imagination, as distinct from sensation on the one hand and intellect on the other. (PA 170-71, emphasis added) Why would Collingwood start with Hume's distinction between impressions and ideas? Undoubtedly, this means that Collingwood is willing to accept the validity of the distinction and to build on it. Isn't this a strange place for an idealist to begin? Not really. When we look at British philosophy at the turn of this century, we find idealists preoccupied with the distinction,2 so it is not extraordinary to find Collingwood utilizing it to some extent. Like most Oxford students of the time, Collingwood read Locke, Berkeley, and Hume in his undergraduate program. Consequently we find them in the problems he addresses. "It was Hume who first perceived the [Lockean] problem [of confusing sensation with imagination]," Collingwood attributes, "and tried to solve it by distinguishing ideas from impressions" (PA 200). In detail: He [Hume] was right when he laid it down that the immediate concern of thought is not with impressions but with ideas; that it is ideas, not impressions, that are associated with one another and thus built up into the fabric of knowledge; and that ideas, though 'derived' from impressions, are not mere relics of them like an after-taste of onions or an after-image of the sun (as Lockeans like Condillac supposed), but something different in kind: different, if not in what he... (shrink)

Despite global and local attempts to end genital mutilation, in their various forms, whether of males or females, the practice has persisted throughout human history in most parts of the world. Various medical, scientific, hygienic, aesthetic, religious, and cultural reasons have been used to justify it. In this symposium on circumcision, against the background of the other articles by Hutson, Short, and Viens, the practice is set by the author within a wider, global context by discussing a range of rationalisations (...) used to support different types of genital mutilation throughout time and across the globe. It is argued that in most cases the rationalisations invented to provide support for continuing the practice of genital mutilation—whether male or female—within various cultural and religious settings have very little to do with finding a critical and reflective moral justification for these practices. In order to question the ethical acceptability of the practice in its non-therapeutic forms, we need to focus on child rights protection. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Art's DetourA Clash of Aesthetic TheoriesS. K. Wertz (bio)Both John Dewey1 and Martin Heidegger2 thought that art's audience had to take a detour in order to appreciate or understand a work of art. They wrote about this around the same time (mid-1930s) and independently of one another, so this similar circumstance in the history of aesthetics is unusual since they come from very different philosophical traditions. What was it (...) about the climate of the times that led them to such an idea? Is it still viable today? Both philosophers thought that art's audience is not in a position to immediately appreciate works of art—that we are missing something for a direct appreciation or apprehension—so we must take a detour. Why the detours and what are they? Are the detours similar? And are Dewey and Heidegger right about this? The essay that unfolds below attempts to answer these questions.First a definition is in order so we know what the term "detour" means when I use it. What is a detour? It is a deviation from a direct course or the usual procedure; a roundabout way temporarily replacing part of a route; in other words, a bypass or a roundabout way to some destination. The Little Oxford Dictionary adds a different twist on my characterization: "a course that leaves and rejoins [the] direct route."3 Applying this idea to art, we can say that a detour describes an audience who ordinarily perceives an artwork is a legitimate beginning for an appreciation of it, but that course must be bypassed for another (conception) before it can rejoin the direct route (perception). In other words, perceptions in the aesthetic experience must be aided by conceptions—a decidedly Kantian stance taken by Dewey and Heidegger. Their illustrations make my interpretation plausible.One of Heidegger's examples is Van Gogh's painting of a pair of peasant boots.4 He selects this painting to illustrate his metaphysics, which centers around the notion of "equipment." Peasant boots are equipment in [End Page 100] the sense that they are worn or used; the mere thing (like shoes or boots in a store [exhibited] or a closet [in storage]) disappears in use and becomes equipment. Between equipment and mere things—these two categories of being—are artworks. They are pictorial representations of equipment (in Heidegger's illustration; a pair of shoes as mere things could be a pictorial representation, like an advertisement, but it wouldn't be the same). Through the painted boots, a world comes into focus—a network of meaning. The world Heidegger sees in the Van Gogh painting is captured in the following descriptions: "In the vicinity of the [art]work we were suddenly somewhere else than we usually tend to be…. The art work let us know what shoes are in truth" (ATCR 233). So the nature of art is still a question about the nature of representation for Heidegger: it is what the shoes disclose to us about human existence. As he says, it is not just merely a pair of shoes portrayed but shoes "from the dark opening of the worn insides … the toilsome tread of the worker stares forth" (ATCR 232). In other words, we see the difficult labor that this particular owner toiled with in her daily chores.In Tralbaut's book, he quotes Heidegger in a caption alongside the painting: "Engraving in the intimate obscurity of the hollow of a boot is the weariness of the steps of work. The rough and solid weight of the clog tells of the slow and obstinate trudge across the fields."5 Heidegger continues in the same vein:In the stiffly rugged heaviness of the shoes there is the accumulated tenacity of her slow trudge through the far-spreading and ever-uniform furrows of the field swept by a raw wind. On the leather lie the dampness and richness of the soil. Under the soles slides the loneliness of the field-path as evening falls. In the shoes vibrates the silent call of the earth, its quiet gift of the ripening grain and its unexplained self-refusal in the fallow desolation of... (shrink)

In this work, S.K. Chakraborty develops the themes propounded in his earlier work to provide a systematic presentation of the relevant vedantic and allied principles in a conceptual and empirical framework. From an overall perspective of vedantic ethical vision and its application to managerial and corporate ethical morality, the book examines what the Vedantic ethical system, and great thinkers like Tagore, Gandhi, Burobindo and others, can teach us about such questions as individual leadership, transformation of the work ethos, ethics and (...) productivity, and others. Throughout, the conceptual and the empirical are closely intertwined, and substantial graphic appendices on the Tata leadership crisis of 1991 and the securities scam of 1991-92 give an immediacy and relevance to the analysis. (shrink)

Some may be of the opinion that one event can begin before another only by virtue of the existence of some event (a “witness”) which wholly precedes the other and does not wholly precede the one (and similarly for “ends before” and “does not abut”). Those would prefer $\mathbb{F}$ 0 to $\mathbb{F}$ as a model for observers' apprehensions of events. Since G is a functor from $\mathbb{M}$ to $\mathbb{F}$ 0, the current construction (restricted to $\mathbb{F}$ 0) remains applicable.This work supports (...) a claim that the psychologically fundamental temporal relationships are “wholly precedes”, “begins before”, “ends before” and “abuts”. But only in a very weak sense. Any other set of relationships which is interdefinable with this one, using only quantifier-free formulas in the definitions, could be used to define a category $\mathbb{F}$ ′ which is indistinguishable from $\mathbb{F}$ (because the same functions preserve and reflect the new relationships). This work equally supports the claim that those relationships are the psychologically fundamental ones, or the claim that it is just “wholly precedes” which is fundamental, and that we perceive “begins before” just by virtue of witnesses. But it refutes the claim that only “wholly precedes” is fundamental, and that we understand “begins before” only because we understand time as a linear ordering. (shrink)

Corruption involves greed, money, and risky decision-making. We explore the love of money, pay satisfaction, probability of risk, and dishonesty across cultures. Avaricious monetary aspiration breeds unethicality. Prospect theory frames decisions in the gains-losses domain and high-low probability. Pay dissatisfaction (in the losses domain) incites dishonesty in the name of justice at the individual level. The Corruption Perceptions Index, CPI, signals a high-low probability of getting caught for dishonesty at the country level. We theorize that decision-makers adopt avaricious love-of-money aspiration (...) as a lens and frame dishonesty in the gains-losses domain (pay satisfaction-dissatisfaction, Level 1) and high-low probability (CPI, Level 2) to maximize expected utility and ultimate serenity. We challenge the myth: Pay satisfaction mitigates dishonesty across nations consistently. Based on 6500 managers in 32 countries, our cross-level three-dimensional visualization offers the following discoveries. Under high aspiration conditions, pay dissatisfaction excites the highest- (third-highest) avaricious justice-seeking dishonesty in high (medium) CPI nations, supporting the certainty effect. However, pay satisfaction provokes the second-highest avaricious opportunity-seizing dishonesty in low CPI entities, sustaining the possibility effect—maximizing expected utility. Under low aspiration conditions, high pay satisfaction consistently leads to low dishonesty, demonstrating risk aversion—achieving ultimate serenity. We expand prospect theory from a micro and individual-level theory to a cross-level theory of monetary wisdom across 32 nations. We enhance the S-shaped Curve to three 3-D corruption surfaces across three levels of the global economic pyramid, providing novel insights into behavioral economics, business ethics, the environment, and responsibility. (shrink)

Background: There are intriguing and challenging ethical dilemmas in the practice of palliative care in a traditional developing society.Objective: To review the different ethical issues involved in cancer and palliative care in developing countries, with special reference to India.Methods: Published literature on pain relief and palliative care in the developing countries was reviewed to identify ethical issues and dilemmas related to these, and ways in which ethical principles could be observed in delivery of palliative care in such countries are discussed.Results: (...) The literature review revealed a number of ethical dilemmas and challenges that professionals, cancer patients and their families encountered during palliative care. It was noted that patients’ preferences and decisions are influenced by family members. Dilemmas leave the professionals and families confused about how ethical their actions have been. Specific ethical issues were noted in relation to the availability and use of oral morphine for pain relief, spiritual care, lack of adequate palliative care services, and palliative care education.Conclusions: The four principles of ethics posed difficulties in understanding the complex ethical issues in a developing country with a traditional background. Ethical issues need to be handled delicately and sensitively in palliative care settings, within the framework of the traditions and culture of the society and financial constraints. The possible role of ethics committees in palliative care settings to help decision-making needs to be studied and discussed. (shrink)

THIS ESSAY DEALS WITH D F NORTON’S INTERPRETATION OF HUME’S METHODOLOGY IN THE LATTER’S FAMOUS DISCUSSION OF MIRACLES IN THE FIRST INQUIRY. NORTON CONSTRUES "EXPERIENCE" TO MEAN PERSONAL, INDIVIDUAL EXPERIENCE. THE AUTHOR SHOWS THAT THERE IS ANOTHER SENSE OF THE WORD WHICH IS MORE COSMOPOLITAN AND ONE WHICH SQUARES MORE WITH THE USES OF EVIDENCE FOUND IN THE "HISTORY OF ENGLAND". ALTERNATIVE INTERPRETATIONS OF THE HUME PASSAGE ARE GIVEN AND HUME’S METHOD IS COMPARED WITH R G COLLINGWOOD’S IMAGINATIVE RECONSTRUCTIONIST IDEA (...) OF HISTORY. (shrink)

The notion of a harmonious universe was taught by Pythagoras as early as the sixth century BC, and remained a basic premise in Western philosophy, science, and art almost to our own day. In Touches of Sweet Harmony, S. K. Heninger first recounts the legendary life of Pythagoras, describes his school at Croton, and discusses the materials from which the Renaissance drew its information about Pythagorean doctrine. The second section of the book reconstructs the many facets of this doctrine, and (...) the final section shows its influence on Renaissance poetics. Professor Heninger's magisterial work introduces the reader not only to Pythagoras but to a host of other classical, medieval, and Renaissance figures as well--from Plato and Aristotle through St. Augustine and Macrobius down to Sidney and Spenser. (shrink)

This volume is a collection of S.K. Chakraborty's papers on the east-west distinction in worldviews. The essays are reflective and deliberate upon philosophical diferences and attitudes of thinkers that have shaped the behavior of the common man, both in and out of the workplace.

We show that the join of two classical [respectively, regular, normal] modal logics employing distinct modal operators is a conservative extension of each of them.