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.

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)

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)

BackgroundReducing the number of animals used in experiments has become a priority for the governments of many countries. For these reductions to occur, animal-free alternatives must be made more available and, crucially, must be embraced by researchers.MethodsWe conducted an international online survey for academics in the field of animal science (N = 367) to explore researchers’ attitudes towards the implementation of animal-free innovations. Through this survey, we address three key questions. The first question is whether scientists who use animals in (...) their research consider governmental goals for animal-free innovations achievable and whether they would support such goals. Secondly, responders were asked to rank the importance of ten roadblocks that could hamper the implementation of animal-free innovations. Finally, responders were asked whether they would migrate (either themselves or their research) if increased animal research regulations in their country of residence restricted their research.ResultsWhile nearly half (40%) of the responders support governmental goals, the majority (71%) of researchers did not consider such goals achievable in their field within the near future. In terms of roadblocks for implementation of animal-free methods, ~ 80% of the responders considered ‘reliability’ as important, making it the most highly ranked roadblock. However, all other roadblocks were reported by most responders as somewhat important, suggesting that they must also be considered when addressing animal-free innovations. Importantly, a majority reported that they would consider migration to another country in response to a restrictive animal research policy. Thus, governments must consider the risk of researchers migrating to other institutes, states or countries, leading to a ‘brain-drain’ if policies are too strict or suitable animal-free alternatives are not available.ConclusionOur findings suggest that development and implementation of animal-free innovations are hampered by multiple factors. We outline three pillars concerning education, governmental influence and data sharing, the implementation of which may help to overcome these roadblocks to animal-free innovations. (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)

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)

A summary view of the main evidence at our disposal may be soon obtained. Three traditions appear at the outset. The first depends on a MS. once at Mainz, and now no longer extant, but of which part, at any rate, still existed in the sixteenth century; the second on an eleventh century MS. at Bamberg; and the third on a number of later MSS. in Rome, Florence, Paris, the British Museum, Oxford, Holkham, and other places. The fact that these (...) three traditions must be regarded as separate may be seen first from the parts of the decade which they each omit. (shrink)

Central to Kuhn’s notion of incommensurability are the ideas of meaning variance and lexicon, and the impossibility of translation of terms across different theories. Such a notion of incommensurability is based on a particular understanding of what a scientific language is. In this paper we first attempt to understand this notion of scientific language in the context of incommensurability. We consider the consequences of the essential multisemiotic character of scientific theories and show how this leads to even a single theory (...) being potentially ‘internally incommensurable’. We then discuss Kuhn’s lexicon‐based approach to incommensurability and the problems associated with it. Finally we argue that this approach by Kuhn has interesting overlaps with the problem of meaning associated with multisemiosis, particularly the challenge of understanding the process of symbolization in scientific theories. (shrink)

Our fascination with artificial intelligence (AI), robots and sentient machines has a long history, and references to such humanoids are present even in ancient myths and folklore. The advancements in digital and computational technology have turned this fascination into apprehension, with the machines often being depicted as a binary to the human. However, the recent domains of academic enquiry such as transhumanism and posthumanism have produced many a literature in the genre of science fiction (SF) that endeavours to alter this (...) antagonistic notion of AI. In his novel Klara and the Sun, Kazuo Ishiguro explores this notion of AI as a caring machine capable of nursing an ailing young girl back to health. Through this portrayal of AI as a sentient being capable of empathy and cognition, Ishiguro is attempting to usher in a new perception of AI: a posthuman perception that challenges the conventional notions of AI as a machine devoid of emotions. The novel further expands on the idea of self, soul and human consciousness and ponders on the question, what makes humans human, and if it is possible to imbibe these qualities onto an AI. Owing to the novelty of this notion, an unexplored avenue that deserves further exploration, this paper examines the plausibility of this new notion of AI through a careful exegesis of the novel. The paper also attempts to chart the impact of SF in society and culture. The study reveals a positive shift in perception towards AI, and there seems to be much scope for interdisciplinary and transdisciplinary research. (shrink)

The persons who adapt to changes as may be necessary in the course of their existence not only survive in the struggle for existence but also thrive and enjoy their lives in the best possible way under the given circumstances. For, life consists in various relationships, which are in constant movement and change.Therefore dealing with change or change-management has got pivotal importance in all walks of humans’ lives. In order to facilitate smooth change all big and small inheritances have to (...) be shed off. Adaptation to change involves some amount of give and take. Before stepping into new shoes one has to remove old ones. Sticking to good or bad things of the past in some cases spoils the present. One should, therefore, be in a position to come out of the situation of status quoor inertia. In some cases our ego does not allow us to change. It forces us to remain in the state that we have been enjoying hitherto. If we are untouched by sense of exuberance and live a life of simplicity, we can break the fetters of ego. The crux of the problem lies in affecting the change of attitude towards the present state of affairs and performance of corresponding duty. The persons should realize that change in power, position, strength etc. is inevitable. So,they should be mentally and physically prepared for it. This can be conveniently achieved by developing adaptability to and management of change. (shrink)