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.

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)

This article investigates whether acts of plagiarism are predictable. Through a deductive, quantitative method, this study examines 517 students and their motivation and intention to plagiarize. More specifically, this study uses an ethical theoretical framework called the Theory of Reasoned Action and Planned Behavior to proffer five hypotheses about cognitive, relational, and social processing relevant to ethical decision making. Data results indicate that although most respondents reported that plagiarism was wrong, students with strong intentions to plagiarize had a more positive (...) attitude toward plagiarizing, believed that it was important that family and friends think plagiarizing is acceptable, and perceived that plagiarizing would be an easy task. However, participants in the current study with less intention to plagiarize hold negative views about plagiarism, do not believe that plagiarism is acceptable to family, friends or peers, and perceive that the act of plagiarizing would prove difficult. Based on these findings, this study considers implications important for faculty, librarians, and student support staff in preventing plagiarism through collaborations and outreach programming. (shrink)

By focusing on the known details of Laonikos Chalkokondyles’ biography, on his relation to Byzantine historiographical tradition, by comparing his historical work to that of contemporary intellectuals living under the Ottomans as well as those in the west, examining his portrayal of Mehmed II, his adoption of a Herodotean model, the revival of Herodotus in the Renaissance more generally, and the reception of the ᾿Aπόδειξις in the fifteenth and sixteenth centuries, I argue that Laonikos was writing for an elite circle (...) of Byzantine émigrés and other intellectuals with access to classical Greek in the west, rather than for the post- Byzantine intellectuals associated with the Ottoman court. (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)

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)

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)

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.

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)

Is the existence of God a question of fact? To the majority of theists, both now and in the past, I think it has seemed clear that, if the phrase ‘God exists’ is to be meaningful, then it is a fact, either that God exists or that he does not. This assertion may even seem trivially true; and yet it has evidently been denied, in recent years, by many theologians. The reasons for such a denial are, in part, to be (...) found in the general reaction against metaphysical philosophy, which was characteristic of the early years of this century, and which is, in Britain, epitomised by A. J. Ayer's stipulation that no proposition can be factually significant unless it is verifiable; unless, in principle at least, some series of observations could conceivably show it to be true. By restricting ‘observation’ to the senses of the physical body, and by emphasising the fact that God, as transcendent by definition, was not a possible object of the senses, some philosophically sensitive theologians were startled into denying that ‘God’ was, even in principle, verifiable; and consequently into denying that propositions purporting to assert his existence were factual. (shrink)

Unethical business in India became a recognized phenomenon during the second World War. Academic/journalistic/legal concern with ethics has become visible only during the nineties. Corruption-of-the-poor and corruption-of-the-rich need to be distinguished - especially in the context of globalization. The danger of attributing unethical practices to system failure is recognized. It is also important to bring to bear on intellectual property rights the more fundamental principle of natural property rights. Consciousness ethics will be more crucial than just intellectual ethics.

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.

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.

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)

Recently David Best has advanced the claim that sport is not an art form, and that although sport may be aesthetic, it is not artistic. Such a claim is false and runs counter to ordinary usage and sport practice. On behalf of sport practice, let me cite as an example the world-class Canadian skater, Toller Cranston, who thinks there are such things as ‘artistic sports, those being gymnastics, diving, figure skating’. Best claims that athletes like Cranston are conceptually confused and (...) that they endow sport with greater respectability than should be allowed. Ascribing the predicate ‘artistic’ to sport performances reflects ‘barbarous usage’. Why does Best exclude the artistic from the realm of sport? Upon examination of his argument, one finds that this exclusion derives mainly from his concepts of art and sport. He thinks that art has a subject-matter, a content, and that sport does not. Sport is contentless, so ‘sport’ and ‘art’ are two logically distinct regions. But is this so? Are we to accept Best's argument or are we to listen to accomplished, reflective athletes in the area of artistic sports? It seems the most reasonable analytic procedure would be to listen to Cranston's case and decide whether such a piece of intentionalist criticism5 should override Best's premises. (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)

There seems to exist a dilemma in the literature as to the correct relativistic formula for the Sagnac phase-shift. The paper addresses this issue in the light of a novel, kinematically equivalent linear Sagnac-type thought experiment, which provides a vantage point from which the effect of rotation in the usual Sagnac effect can be analyzed. The question is shown to be related to the so-called rotating disc problem known as the Ehrenfest paradox. The relativistic formula for the Sagnac phase-shift seems (...) to depend on the way the paradox is resolved. Kinematic resolution of the Ehrenfest paradox proposed by some authors predicts the usually quoted formula for the Sagnac delay but the resolution itself is shown to be based upon some implicit assumptions regarding the behaviour of solid bodies under acceleration. In order to have a greater insight into the problem, a second version of the thought experiment involving linear motion of a “special type” of a non-rigid frame of reference is discussed. It is shown by analogy that the usually quoted special relativistic formula for the Sagnac delay follows, provided the material of the disc matches the “special type.”. (shrink)

Горобец К. В. Аксиосфера права: философский и юридический дискурс : моногр. / К. В. Горобец. – Одесса : Фенікс, 2013. – 218 с. Монография посвящена философско-правовым аспектам аксиосферы права, которая предстает в качестве структурного компонента права и выражается в виде центрированной системы правовых ценностей и иерархизированной системы ценностей права. Правовые ценности рассматриваются как феномены, являющиеся одновременно компонентами права и способом его постижения. Ценности права понимаются как блага, которые защищаются и обеспечиваются правом в силу их значимости для человека и общества. Доказывается, (...) что аксиосфера права существует наряду с нормосферой права. При этом их целостность обеспечивается посредством особого феномена – верховенства права. Монография будет полезна специалистам в сфере философии права, общетеоретической юриспруденции, отраслевых юридических наук, а также всем, кто интересуется проблемами развития современного права. (shrink)