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.

Under the influence of Hilary Putnam’s collapse of the fact/value dichotomy, a resurging approach that challenges the movements of American pragmatism and discourse ethics, I tease out in the first section of my paper the demand for the warranted assertibility hypothesis in Putnam’s sense that may be possible, relying on moral realism to get rid of ‘rampant Platonism’. Tracing back to ‘communicative action’ or the Habermasian way that puts forward the reciprocal understanding of discourse instigates the idea of life-world as (...) composed of ‘culturally transmitted and linguistically organized stock of interpretative patterns’, this section looks for whether Habermas’ psychoanalysis of prolonged discussion can accord with Putnam’s thick ethical terms or not. The last section of the paper pitfalls Putnam’s stance to accepting Habermas’ ‘discourse ethics’ that centers around the context of entangling ‘rational thoughts’ to ‘communication’, but he introduces the idea of fallibilism in a rational query that also attacks the Habermasian metaphysical idea of the validity of ethical statements that goes towards the truth. My next attempt is to see whether Putnam’s objective dictum towards morality that resonates the collapse of fact/value dichotomy from a universalistic stand can successfully evade Rorty’s naive realism and Habermas’ ‘sociologism about values’ respectively. This sort of claim insists on a universalizable pattern of culture-relative value. I consider that the idea of a fact/value dichotomy engages with the inextricable entanglement between the normative and descriptive content, besides the epistemic values having exclusively intertwined with the structure of factual discourse that intends towards collapsing the fact/value dichotomy, a subjective universalizability predilection. (shrink)

This paper discusses Kant’s prospect of ‘hope’ that entangles with interrelated epistemic terms like belief, faith, knowledge, etc. The first part of the paper illustrates the boundary of knowing in the light of a Platonic analysis to highlight the distinction between empiricism and rationalism. Kant’s notion of ‘transcendent metaphysical knowledge’, a path-breaking way to look at the metaphysical thought, can fit with the regulative principle that seems favoruable to the experience-centric knowledge. The second part of the paper defines ‘hope’ as (...) an interwoven part of belief, besides ‘hope’ as a component of ‘happiness' can persuade the future behaviours of the individuals. Revisiting Kant’s three categorizations of hopes (eschatological hope, political hope, and hope for the kingdom of ends), the paper traces out Kant’s good will as a ‘hope’ and his conception of humanity. (shrink)

Rough Sets were introduced by Z. Pawlak in the year 1982 with the intention to address knowledge representation and data processing from the angle of computation and decision making. The main idea...

This fictionalized script traces the contours of the conversation that seeks to fathom the crisis unleashed by the outbreak and global spread of the coronavirus and the ensuing anxieties created in our current social living. The scenario of deepened isolation of the self from the other is considered, and it is proposed that isolation, while an unavoidable requirement, does not mean it is some mental lassitude but rather may be seen as an enthusiastic concern toward recovering physical and mental wellbeing (...) of the larger communities concerned to control the possible avenues of transmission of the contagion. The conversation meanders around the issue of quarantine, its attraction or otherwise, and who benefits from this restriction, its effects on one’s mental constitution, etc. Philosophers have been known to isolate themselves in other contexts and situations give us a taste of what is to come in the dialogue to resist the calamity of the coronavirus and its grim effects that engulf the entire humanity. (shrink)

Consumer complaining behavior (CCB) is an important stream of research and practice, as it links the domains of service failure and service recovery. CCB research, although extensive and temporally wide, exhibits a lack of concern for the underlying assumptions of scholarly inquiry. Researchers neither explicitly mention, nor consciously indicate their ontological, epistemological, and methodological assumptions. We systematically identify the extant CCB literature and map it to two well-accepted paradigmatic classifications (Burrell and Morgan 1979; Deetz Organization Science 7(2): 191–207, 1996). Normative (...) or functionalist paradigm with the assumptions of an objective external reality, a positivist epistemology, a determinist view of human nature, and nomothetic methodology emerges as the dominant CCB research paradigm. The implications of this dominance are discussed as a barometer of the future of CCB research and practice. (shrink)

This book introduces the theory of graded consequence and its mathematical formulation. It also compares the notion of graded consequence with other notions of consequence in fuzzy logics, and discusses possible applications of the theory in approximate reasoning and decision-support systems. One of the main points where this book emphasizes on is that GCT maintains the distinction between the three different levels of languages of a logic, namely object language, metalanguage and metametalanguage, and thus avoids the problem of violation of (...) the principle of use and mention; it also shows, gathering evidences from existing fuzzy logics, that the problem of category mistake may arise as a result of not maintaining distinction between levels. (shrink)

The paper highlights the alienation and separation produced by science—technology between man and nature, and between man and man. The principal thesis in this paper is that such separative mentality is the root cause of the deterioration in ethics even in unexpected quarters. Warnings about this were foreseen by a number of Indian livers and thinkers during the early twentieth century. Their prophecies seem to be unfortunately coming true. After sharing this sample of opinions, several recent cases of vicious unethicalities (...) all over the world have been presented. This is followed by a brief survey of Western thought over the past six decades which too was mature enough to caution us about the blind onslaught of technology. The paper concludes by arguing for a complete overhaul of the vocabulary of modern discourse from the objective to the subjective. (shrink)

About this book Hilary Whitehall Putnam was one of the leading philosophers of the second half of the 20th century. As student of Rudolph Carnap's and Hans Reichenbach's, he went on to become not only a major figure in North American analytic philosophy, who made significant contributions to the philosophy of mind, language, mathematics, and physics but also to the disciplines of logic, number theory, and computer science. He passed away on March 13, 2016. The present volume is a memorial (...) to his extraordinary intellectual contributions, honoring his contributions as a philosopher, a thinker, and a public intellectual. It features essays by an international team of leading philosophers, covering all aspects of Hilary Putnam's philosophy from his work in ethics and the history of philosophy to his contributions to the philosophy of science, logic, and mathematics. Each essay is an original contribution. -/- Author information James Conant, Univ. of Chicago/Univ. of Leipzig, USA/Germany; Sanjit Chakraborty, IISER Kolkata/VIT-AP University, India. (shrink)

A collective understanding that traces a debate between ‘what is science?’ and ‘what is a science about?’ has an extraction to the notion of scientific knowledge. The debate undertakes the pursuit of science that hardly extravagance the dogma of pseudo-science. Scientific conjectures invoke science as an intellectual activity poured by experiences and repetition of the objects that look independent of any idealist views (believes in the consensus of mind-dependence reality). The realistic machinery employs in an empiricist exposition of the objective (...) phenomenon by synchronizing the general method to make observational predictions that cover all the phenomena of the particular entity without any exception. The formation of science encloses several epistemological purviews and a succession of conjectures cum refutation that a newer theorem could reinstate. My attempt is to advocate a holistic plea of scientific conjectures that outruns the restricted regulation of experience or testable hypothesis to render the validity of a chain of logical reasoning (deductive or inductive) of basic scientific statements. The milieu of scientific intensification integrates speculation that loads efficiency towards a new experimental dimension where the reality is not itself objective or observers relative; in fact the observed phenomenon divulges in the constructive progression of preferred methods of falsifiability and uncertainty. (shrink)

Increasing global competition has intensified the use of informal sector workforce worldwide. This phenomenon is true with regard to India, where 92% of the workers hold precarious jobs. Our study examines the dynamics of workplace dignity in the context of Indian security guards deployed as contract labour by private suppliers, recognising that security guards’ jobs were marked by easy access, low status, disrespect and precariousness. The experiences of guards serving bank ATMs were compared with those working in large reputed organisations. (...) The former reported loss of dignity though their inherent self-worth remained partially intact, whereas the latter reclaimed dignity despite the precarious working conditions and the absence of unions. Guards from large reputed organisations evolved strategies by which they took advantage of the client’s vulnerabilities, developed ‘thick’ relationships at work and immersed themselves in 'doing dignity work' to ensure that they are not disposable. ‘Doing dignity work’ was a visible device which involved actions that met or went beyond the norms laid down by the client and was used by security guards to limit the extent of their precariousness. Since the opportunity to reclaim dignity was facilitated by large reputed clients’ adherence to legal regulations, we see implications of the study for the moral economy. (shrink)

Venn diagram system has been extended by introducing names of individuals and their absence. Absence gives a kind of negation of singular propositions. We have offered here a non-classical interpretation of this negation. Soundness and completeness of the present diagram system have been established with respect to this interpretation.

Scientific realism does not view theoretical terms as mere instruments of experimental predictions; it grants referential status to natural kind terms with 'epistemic access' and view scientific theories and terms as corresponding to physical phenomena and entities which exist independently of observation, and as thereby being the source of objective -approximate and not absolute- knowledge of the physical realm. As a result, scientific realism is accused of ontologising the unobservables. Against this charge, scientific realism posits the idea of the dialectical (...) relation between theoretical terms referring to the unobservables and scientific methods. The second argument made by realism is the ‘no miracle’ thesis. These arguments stand challenged by the Copenhagen interpretation of quantum mechanics. The aim of the paper is to examine the relevance of the two arguments of scientific realism in countering the idea that the existence of quantum states in the microphysical world renders realism obsolete. (shrink)

This paper establishes that the contemporary figures of organizational leadership are at best excellent examples of 'dealership' characterized by high skills-competence and low values-commitment. The author points out that managerial and organizational psychology for leadership is yet to grapple with the most fundamental of all the themes: the complete model of man which places the spirit-core of SELF in the centre. The paper upholds the classical Indian concept of wisdom leadership and introduces the rajarshi model of the leader as the (...) very embodiment of satya and rita. The author then dwells on the nature of'rishi-consciousness' and elaborates on the 'rishi' process which leads to the unfoldment of unitive SELF-awareness or ekatmanubhuti. Speaking on behalf of one of the most enduring civilizations of the world, the author asserts that wisdom leadership comes from the ability to perceive the indivisible whole and this ability is not a function of the thinking, reasoning mind but of the intuitive, spiritual mind. (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.

This article takes a close look at the nature offeminine values in congruence with natural law. The thoughts of Tagore primarily and to a lesser degree of Vivekananda, Gandhi and Nivedita on this most momentous area of social-psychological well-beingfor humans are highlighted. Trendy and shallow modernism seems to be aiming at cheap goals in the name of women's liberation, and the long-term damage to humanity is becoming incalculable. The tragic and bizarre events occurring across the whole spectrum, from homes and (...) schools to business and politics, can be traced in a big way to the hot pace of centrifugalized breaking up of stable family values woven around natural, centripetal feminine values. (shrink)

This paper argues that Zika virus infection has its ethical implications beyond the reproductive health of women. It claims that Zika virus infection like public health emergency exposes the underlying health determinants and health status of women. Therefore, ethical mitigation of Zika like public health emergencies should consider these underlying health determinants and health status of women. For, undermining and overlooking these underlying determinants and health status of women, during the public health emergencies, enhance the health inequities. The recent Zika (...) virus infection in Brazil has triggered different ethics consultation and has prompted to outline ethical recommendations. However, the recommendations have either focused on the reproductive health of women or on the core strategies of public health emergency. Considering this as a gap in perspective to prepare for Zika like public health emergencies, this paper argues that it is the underlying holistic health of women, precisely, health capability, which should be given due ethical consideration. Finally, the paper concludes highlighting the fact that focusing on the holistic health of the women during Zika like public health emergencies and beyond can bring in long-term benefits for global health equity. (shrink)

The concept of morality underpins the moral responsibility that not only depends on the outward practices (or ‘output,’ in the case of humanoid robots) of the agents but on the internal attitudes (‘input’) that rational and responsible intentioned beings generate. The primary question that has initiated the extensive debate, i.e., ‘Can humanoid robots be moral?’, stems from the normative outlook where morality includes human conscience and socio-linguistic background. This paper advances the thesis that the conceptions of morality and creativity interplay (...) with linguistic human beings instead of non-linguistic humanoid robots, as humanoid robots are indeed docile automata that cannot be responsible for their actions. To eradicate human ethics in order to make way for humanoid robot ethics highlights the moral actions and adequacy that hinges the myth of creative agency and self-dependency, which a humanoid robot can scarcely express. (shrink)

The concept of morality underpins the moral responsibility that not only depends on the outward practices (or ‘output’, in the case of humanoid robots) of the agents but on the internal attitudes (‘input’) that rational and responsible intentioned beings generate. The primary question that has initiated extensive debate, i.e. ‘Can humanoid robots be moral?’, stems from the normative outlook where morality includes human conscience and socio-linguistic background. This paper advances the thesis that the conceptions of morality and creativity interplay with (...) linguistic human beings instead of non-linguistic humanoid robots, as humanoid robots are indeed docile automata that cannot be responsible for their actions. To eradicate human ethics in order to make way for humanoid robot ethics highlights the moral actions and adequacy that hinges the myth of creative agency and self-dependency, which a humanoid robot can scarcely express. -/- . (shrink)

Does there exist any equivalence between the notions of inconsistency and consequence in paraconsistent logics as is present in the classical two valued logic? This is the key issue of this paper. Starting with a language where negation ( ${\neg}$ ) is the only connective, two sets of axioms for consequence and inconsistency of paraconsistent logics are presented. During this study two points have come out. The first one is that the notion of inconsistency of paraconsistent logics turns out to (...) be a formula-dependent notion and the second one is that the characterization (i.e. equivalence) appears to be pertinent to a class of paraconsistent logics which have double negation property. (shrink)

Abstract Under the influence of Hilary Putnam’s collapse of the fact/value dichotomy, a resurging approach that challenges the movements of American pragmatism and discourse ethics, I tease out in the first section of my paper the demand for the warranted assertibility hypothesis in Putnam’s sense that may be possible, relying on moral realism to get rid of ‘rampant Platonism’. Tracing back to ‘communicative action’ or the Habermasian way that puts forward the reciprocal understanding of discourse instigates the idea of life-world (...) as composed of ‘culturally transmitted and linguistically organized stock of interpretative patterns’, this section looks for whether Habermas’ psychoanalysis of prolonged discussion can accord with Putnam’s thick ethical terms or not. The last section of the paper pitfalls Putnam’s stance to accepting Habermas’ ‘discourse ethics’ that centers around the context of entangling ‘rational thoughts’ to ‘communication’, but he introduces the idea of fallibilism in a rational query that also attacks the Habermasian metaphysical idea of the validity of ethical statements that goes towards the truth. My next attempt is to see whether Putnam’s objective dictum towards morality that resonates the collapse of fact/value dichotomy from a universalistic stand can successfully evade Rorty’s naive realism (structured by linguistic representation) and Habermas’ ‘sociologism about values’ (a kind of minimalist ethics depending on solidarity) respectively. This sort of claim insists on a universalizable pattern of culture-relative value. I consider that the idea of a fact/value dichotomy engages with the inextricable entanglement between the normative and descriptive content, besides the epistemic values having exclusively intertwined with the structure of factual discourse that intends towards collapsing the fact/value dichotomy, a subjective universalizability predilection. (shrink)

Cancer is fast becoming an alarming cause of human death. However, it has been reported that if the disease is detected at an early stage, diagnosed, treated appropriately, the patient has better chances of survival long life. Machine learning technique with feature-selection contributes greatly to the detecting of cancer, because an efficient feature-selection method can remove redundant features. In this paper, a Fuzzy Preference-Based Rough Set (FPRS) blended with Support Vector Machine (SVM) has been applied in order to predict cancer (...) biomarkers for biological and gene expression datasets. Biomarkers are determined by deploying three models of FPRS, namely, Fuzzy Upward Consistency (FUC), Fuzzy Downward Consistency (FLC), and Fuzzy Global Consistency (FGC). The efficiency of the three models with SVM on five datasets is exhibited, and the biomarkers that have been identified from FUC models have been reported. (shrink)

Electronegativity is an important physico-chemical concept to study the chemical structure and reactivity. Although, the conundrum related to measurement of electronegativity still persists. In view of this fact, a simple yet rigorous scale of electronegativity, invoking an inverse relationship with atomic nucleophilicity index, has been proposed for 103 elements of the periodic table. The computed data follows periodicity distinctly satisfying all the sine qua non of a standard scale of electronegativity. Further, electronegativity values display a sound similarity with the standard (...) electronegativity scales validating the suitability of the proposed model. Molecular electronegativities of some polyatomic molecules have also been calculated using the proposed scale of electronegativity.Graphic. (shrink)

This book carries forward the discourse on the mind’s engagement with the world. It reviews the semantic and metaphysical debates around internalism and externalism, the location of content, and the indeterminacy of meaning in language. The volume analyses the writings of Jackson, Chomsky, Putnam, Quine, Bilgrami and others, to reconcile opposing theories of language and the mind. It ventures into Cartesian ontology and Fregean semantics to understand how mental content becomes world-oriented in our linguistic communication. Further, the author explores the (...) liaison between the mind and the world from the phenomenological perspective, particularly, Husserl’s linguistic turn and Heidegger’s intersubjective entreaty for Dasein. The book conceives thought as a biological and socio-linguistic product which engages with the mind-world question through the conceptual and causal apparatuses of language. A major intervention in the field of philosophy of language, this book will be useful for scholars and researchers interested in philosophy, phenomenology, epistemology, and metaphysics . (shrink)

This paper attempts to revisit how ‘acquaintance’ could bring about belief and how belief becomes knowledge in our language system due to the credential undertaking of truth, justification, evidence, and causal or conceptual preservation. My quest in this paper is to interrogate belief and the cessation of belief (I call this the ‘death of belief’) from the perspective of the doxastic approach of externalism and internalism in the philosophy of language and philosophy of mind. I will attempt to make sense (...) of the nominal appeal (an approach that conserves the process of continuing belief through evidence and conceptualization) to both of these ideas in a sophisticated manner. The linguistic form of using words seems allied to the context sensitivity of the speakers involved in social practices. A tripartite structure pivots the model of linguistic belief, where minds are causally entrenched in a world that stimulates conceptual or internal states, representing how objectivity works. The entanglements of concepts with pictures hinge on conceptual prerequisites to impact the world. (shrink)

ICT for development projects often focus on integrating social factors in information systems design. A well-designed ICT4D solution must be tailored to the needs of the people who will use them and subsequently, requires an extensive understanding of the context and constraints in people’s lives. With an objective to explore how context-specific issues influence the conveyance of appropriate agricultural information to women, this paper uses PROTIC, a 5-year collaborative project between Monash University and Oxfam, as a case. PROTIC was implemented (...) in three climate vulnerable ecological zones of Bangladesh with an aim to overcome the agricultural information gap for rural women. Based on a study in mixed research method and triangulation, this paper brings evidence on the significance of considering context-specific attributes in designing effective and sustainable information services for marginalized women farmers in developing countries. The paper upfolds some significant recommendations which is expected to contribute to the domain of context-specific information system design in resolving socio-economic problems to pave the way of sustainable development. (shrink)

The present book discusses all aspects of paraconsistent logic, including the latest findings, and its various systems. It includes papers by leading international researchers, which address the subject in many different ways: development of abstract paraconsistent systems and new theorems about them; studies of the connections between these systems and other non-classical logics, such as non-monotonic, many-valued, relevant, paracomplete and fuzzy logics; philosophical interpretations of these constructions; and applications to other sciences, in particular quantum physics and mathematics. Reasoning with contradictions (...) is the challenge of paraconsistent logic. The book will be of interest to graduate students and researchers working in mathematical logic, computer science, philosophical logic, linguistics and physics. (shrink)

This thematic volume entitled Human Minds and Cultures deciphers different aspects of human minds and cultures that differ in their methodological patterns. It exhibits humanity as a universal, underlying cultural multiplicity coping with diverse prospects of normative morality, semiotics, and socio-linguistic human affairs. Two major concerns that the thematic volume anticipates here are as follows.

Recent literature shows that ethics of care can be used as a theoretical basis to add a new, important dimension to social issues. Th.

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)

This chapter critiques the notion of identity, a philosophical reaction in the Quinean sense that vindicates another significant hypothesis, which is called the “No entity without identity” theorem. Here, the identification of an entity relies upon its identity. The first segment of this chapter revisits the following question: How do we encounter the concept of a subjective “mind”? Could we “infer” or “experience” the concept of “mind” in our daily lives? Every entity has some characteristics that prompt comparison with similar (...) entities. Although I think that other minds have a subjective periphery and that other minds have an objective periphery lurking behind this (privileged access), we can construe the relationship in a subjective way (individual mind). In the second section of the chapter, I address a different point by considering why the idea of “other minds” causes philosophical dilemmas. Can “other minds” exist as a substance in one’s own mind? The category of human knowledge encompasses the reality of minds and other minds. The other minds remain an accompanying part of the individual mind since the expression, belief, and mental content of the individual mind merge in the linguistic expression in a split manner that we may ascribe as privileged access (subjective incorrigible knowledge) and corrigible knowledge. But I think that the relation between minds and other minds sounds especially idiosyncratic in its own identity. Despite becoming diverse, the individual mind can still be intimate by blending and attunement between the subjective and objective dichotomy. (shrink)

The nominal ground that entwines human beings and animal behaviours is unwilling to admit moral valuing as a non-human act. Just to nail it down explicitly, two clauses ramify the moral conscience of human beings as follows: a) Can non-humans be moral beings?, b) Unconscious animal behaviours go beyond any moral judgments. My approach aims to rebuff these anthropomorphic clauses by justifying animals’ moral beings and animals’ moral behaviours from a meta-ethical stance. A meta-ethical outlook may enable an analysis of (...) ethical and normative views through the limit of moral motives and reasoning. Animals’ sense of moral motives and their apparatus of getting involved in moral acts cannot be compared with human actions. In human moral engagement, we abide by moral paradigmatic theories and their diversified attitudes that could have conceptual and linguistic use in our societal discourses. However, animals’ intentional apparatus may have the propensity to choose an act following the moral consequences (care, utility, responsibility, etc.) in their life-forms. (shrink)

In this review article we discuss some of the applications of noncommutative geometry in physics that are of recent interest, such as noncommutative many-body systems, noncommutative extension of Special Theory of Relativity kinematics, twisted gauge theories and noncommutative gravity.

In this paper, we study two companions of a logic, viz., the left variable inclusion companion and the restricted rules companion, their nature and interrelations, especially in connection with paraconsistency. A sufficient condition for the two companions to coincide has also been proved. Two new logical systems—intuitionistic paraconsistent weak Kleene logic (IPWK) and paraconsistent pre-rough logic (PPRL)—are presented here as examples of logics of left variable inclusion. IPWK is the left variable inclusion companion of intuitionistic propositional logic and is also (...) the restricted rules companion of it. PPRL, on the other hand, is the left variable inclusion companion of pre-rough logic but differs from the restricted rules companion of it. We have discussed algebraic semantics for these logics in terms of Płonka sums. This amounts to introducing a contaminating truth value, intended to denote a state of indeterminacy. (shrink)