The shortest definition of a number by a first order formula with one free variable, where the notion of a formula defining a number extends a notion used by Boolos in a proof of the Incompleteness Theorem, is shown to be non computable. This is followed by an examination of the complexity of sets associated with this function.

The complexity of aII 4 set of natural numbers is encoded into a linear order to show that the finite condensation of a recursive linear order can beII 2–II 1. A priority argument establishes the same result, and is extended to a complete classification of finite condensations iterated finitely many times.

The properties of antisymmetry and linearity are easily seen to be sufficient for a recursively enumerable binary relation to be recursively isomorphic to a recursive relation. Removing either condition allows for the existence of a structure where no recursive isomorph exists, and natural examples of such structures are surveyed.

In this paper, we define correlation coefficient measure between any two rough neutrosophic sets. We also prove some of its basic properties.. We develop a new multiple attribute group decision making method based on the proposed correlation coefficient measure. An illustrative example of medical diagnosis is solved to demonstrate the applicability and effecriveness of the proposed method.

In this paper, the sine, cosine and cotangent similarity measures of interval rough neutrosophic sets is proposed. Some properties of the proposed measures are discussed. We have proposed multi attribute decision making approaches based on proposed similarity measures. To demonstrate the applicability, a numerical example is solved.

Maintenance of skeletal muscle mass and strength throughout life is crucial for heathy living and longevity. Several signaling pathways have been implicated in the regulation of skeletal muscle mass in adults. TGF‐β‐activated kinase 1 (TAK1) is a key protein, which coordinates the activation of multiple signaling pathways. Recently, it was discovered that TAK1 is essential for the maintenance of skeletal muscle mass and myofiber hypertrophy following mechanical overload. Forced activation of TAK1 in skeletal muscle causes hypertrophy and attenuates denervation‐induced muscle (...) atrophy. TAK1‐mediated signaling in skeletal muscle promotes protein synthesis, redox homeostasis, mitochondrial health, and integrity of neuromuscular junctions. In this article, we have reviewed the role and potential mechanisms through which TAK1 regulates skeletal muscle mass and growth. We have also proposed future areas of research that could be instrumental in exploring TAK1 as therapeutic target for improving muscle mass in various catabolic conditions and diseases. (shrink)

In this paper, we define projection and bidirectional projection measures between interval rough neutrosophic sets and prove their basic properties. Then two new multi attribute decision making strategies are proposed based on interval rough neutrosophic projection and bidirectional projection measures respectively. Then the proposed methods are applied for solving multi attribute decision making problems. Finally, a numerical example is solved to show the feasibility, applicability and effectiveness of the proposed strategies.

Romila Thapar, The Past as Present: Forging Contemporary Identities through History, 2014, New Delhi: Aleph Book Company, pp. 329, ₹ 595, ISBN: 978-93-83064-01-4.

Cross entropy measure is one of the best way to calculate the divergence of any variable from the priori one variable. We define a new cross entropy measure under interval neutrosophic set environment.

The notion of neutrosophic cubic set is originated from the hybridization of the concept of neutrosophic set and interval valued neutrosophic set. We define similarity measure for neutrosophic cubic sets and prove some of its basic properties. We present a new multi criteria group decision making method with linguistic variables in neutrosophic cubic set environment. Finally, we present a numerical example to demonstrate the usefulness and applicability of the proposed method.

In the Nyaya view a causal condition is a non-superfluous invariable antecedent of the effect. Does this mean that causality for the Nyaya is a necessary connection as some scholars suggest? No. Invariable antecedence means that a causal condition is not the negatum of any absolute absence in the locus of the effect immediately before the latter’s origin (a causal condition is not absent where the effect arises immediately before origin). Non-superfluity means fulfilling requirements of economy three main kinds of (...) which are economy in constitution (non-inclusion of anything redundant), economy in relation (something related directly is preferable to something related indirectly) and economy in cognitive order (being knowable in fewer steps). None of the above jointly or severally involve necessity. (shrink)

"Darshanika Cintan ke Vividha Āyāma" (Diverse dimensions of philosophical thinking), is a compilation book of various research articles in which the discursive diversity of philosophy is reflected. On the one hand, it pursues the basic problems of philosophy, such as the relevance of philosophy, the nature and justification of metaphysics, the metaphysical analysis of the nature of value, etc., while on the other hand, it Is involved in the analysis and testing of the concept of life-world, globalization and multiculturalism, environmental (...) ethics and applied ethics etc. Proper analysis and evaluation of the most important problems of Indian epistemology, for example, the idea of syntax (Vākyārtha Vicāra), Prāmanyavāda , and the issue of evidential implication (Pramānatarabhāva), has been heuristically presented. Some lively topics of contemporary Indian philosophy like Logical conclusion of Manvendra Nath Roy's materialism, Kant's influence on contemporary Indian philosophy, Post-independence Indian philosophical thinking, and the future form of Indian philosophy are included. There is a unique combination of linguistic beauty and clarity, systematic presentation, critical attitude and philosophical insight in the writings of the author duo. This is undoubtedly a valuable work which deserves to be welcomed by teachers, scholars and students of philosophy. (shrink)

Analyzing a sample of 13,917 US firm–years from 1991 to 2006, we find that more innovative firms demonstrate high corporate social responsibility performance subsequent to a successful innovation. These high-CSR innovative firms enjoy significantly higher valuation post-innovation. These findings imply that firms with demonstrated potential growth opportunities, as evident from the number of registered patents and their citations, benefit by strategically investing more in CSR activities; that is, CSR investment entails ‘doing well by [strategically] doing good.’.

Logical pluralism is the view that there is more than one formal logic that correctly (or best, or legitimately) codifies the logical consequence relation in natural language. This essay provides a taxonomy of different variations on the logical pluralist theme based on a five-part structure, and then identifies an unoccupied position in this taxonomy: perspectival logical pluralism. Perspectival pluralism provides an attractive position from which to formulate a philosophy of logic from a feminist perspective (and from other, identity-based perspectives, such (...) as critical race theory). An example of how such an account might be developed is sketched. The essay concludes by defusing an obvious objection to the perspectival approach: the claim that the correct logic (or logics), in virtue of the formal nature of logic, should be independent of considerations regarding the identity of the reasoner. (shrink)

Can God create a stone too heavy for him to lift? Can time have a beginning? Which came first, the chicken or the egg? Riddles, paradoxes, conundrums--for millennia the human mind has found such knotty logical problems both perplexing and irresistible. Now Roy Sorensen offers the first narrative history of paradoxes, a fascinating and eye-opening account that extends from the ancient Greeks, through the Middle Ages, the Enlightenment, and into the twentieth century. When Augustine asked what God was doing before (...) He made the world, he was told: "Preparing hell for people who ask questions like that." A Brief History of the Paradox takes a close look at "questions like that" and the philosophers who have asked them, beginning with the folk riddles that inspired Anaximander to erect the first metaphysical system and ending with such thinkers as Lewis Carroll, Ludwig Wittgenstein, and W.V. Quine. Organized chronologically, the book is divided into twenty-four chapters, each of which pairs a philosopher with a major paradox, allowing for extended consideration and putting a human face on the strategies that have been taken toward these puzzles. Readers get to follow the minds of Zeno, Socrates, Aquinas, Ockham, Pascal, Kant, Hegel, and many other major philosophers deep inside the tangles of paradox, looking for, and sometimes finding, a way out. Filled with illuminating anecdotes and vividly written, A Brief History of the Paradox will appeal to anyone who finds trying to answer unanswerable questions a paradoxically pleasant endeavor. (shrink)

Rice is the most important crop species on earth, providing staple food for 70% of the world's human population. Over the past four decades, successes in classical breeding, fertilization, pest control, irrigation and expansion of arable land have massively increased global rice production, enabling crop scientists and farmers to stave off anticipated famines. If current projections for human population growth are correct, however, present rice yields will be insufficient within a few years. Rice yields will have to increase by an (...) estimated 60% in the next 30 years, or global food security will be in danger. The classical methods of previous green revolutions alone will probably not be able to meet this challenge, without being coupled to recombinant DNA technology. Here, we focus on the promise of these modern technologies in the area of nitrogen acquisition in rice, recognizing that nitrogen deficiency compromises the realization of rice yield potential in the field more than any other single factor. We summarize rice‐specific advances in four key areas of research: (1) nitrogen fixation, (2) primary nitrogen acquisition, (3) manipulations of internal nitrogen metabolism, and (4) interactions between nitrogen and photosynthesis. We develop a model for future plant breeding possibilities, pointing out the importance of coming to terms with the complex interactions among the physiological components under manipulation, in the context of ensuring proper targeting of intellectual and financial resources in this crucial area of research. BioEssays 26:683–692, 2004. © 2004 Wiley Periodicals, Inc. (shrink)

This book examines the intricate dynamics of when individuals adhere to laws, taking into account the context in which laws attempt to shape human behavior. While existing literature touches upon various reasons why people comply with laws, the book focuses on a critical question which has been missing from the discussion: when do people obey laws? By treating law as a form of social communication, it develops an integrated framework to answer this question. It explores how social, psychological, and institutional (...) conditions shape compliance decisions of individuals. What does a law signify? When does the compulsion to obey arise? When do individuals comply out of a fear for legal sanctions or social repercussions? Why do some laws have high symbolic values and others fail despite harsh punishments? The book unveils the contextual intricacies that underlie obedience to law. It challenges conventional wisdom and offers a fresh perspective on the power and limitations of law in shaping human behavior. For scholars and academics seeking a deeper understanding of legal compliance and role of law in shaping behaviors, this book will be an indispensable resource. (shrink)

The Vedanta of conciousness : transcendence, enlightenment and everyday life -- The alienated self and the Kabbala of transformation -- The Zen of creativity and the critique of the discursive intellect -- The Tao of love and unconditionality in commitment -- The yoga of action and effortless efficiency -- The nous of perception and the re-enchantment of the tree of life -- The gnosis of freedom and the Fana of fulfilment.

Using labelled formulae, a cut-free sequent calculus for intuitionistic propositional logic is presented, together with an easy cut-admissibility proof; both extend to cover, in a uniform fashion, all intermediate logics characterised by frames satisfying conditions expressible by one or more geometric implications. Each of these logics is embedded by the Gödel–McKinsey–Tarski translation into an extension of S4. Faithfulness of the embedding is proved in a simple and general way by constructive proof-theoretic methods, without appeal to semantics other than in the (...) explanation of the rules. (shrink)

In A. Kumar, & M. Banerjee [(2012). Definable and rough sets in covering-based approximation spaces. In T. Li. (eds.), Rough sets and knowledge technology (pp. 488–495). Springer-Verlag], A. Kumar, & M. Banerjee [(2015). Algebras of definable and rough sets in quasi order-based approximation spaces. Fundamenta Informaticae, 141(1), 37–55], authors proposed a pair of lower and upper approximation operators based on granules generated by quasiorders. This work is an extension of algebraic results presented therein. A characterisation has been presented (...) for those quasiorder-generated covering-based approximation spaces whose corresponding collections of definable and rough sets form Stone algebras. The notion of rough lattice was proposed in A. Kumar, & M. Banerjee [(2015). Algebras of definable and rough sets in quasi order-based approximation spaces. Fundamenta Informaticae, 141(1), 37–55], A. Kumar [(2020). A Study of Algebras and Logics of Rough Sets Based on Classical and Generalized Approximation Spaces. In Transactions on Rough Sets XXII, LNCS (Vol. 12485, pp. 123–251). Springer]. Some special rough lattices are introduced in this work, viz. rough Stone algebra, ∼1-complemented and ∼2-complemented rough lattices. Representations of these algebras in terms of rough sets are obtained. Moreover, logics for these algebras are shown to be sound and complete with respect to rough set semantics. (shrink)

The debates of the 1980s and 1990s on methodological individualism versus methodological holism have not been adequately resolved. Within analytical Marxism, G.A. Cohen, John Roemer, Jon Elster and others have come down in favour of methodological individualism as part of the effort to make analytical Marxism more 'scientific' and 'rigorous' than earlier versions of Marxism. In doing so they have presented methodological individualism as a necessary ingredient in ridding Marxism of obscurantism. This view is here challenged from a pragmatist philosophical (...) perspective. It is argued that, from such a perspective, the debates between the individualists and holists should have been dissolved rather than resolved in favour of the individualists. It is suggested that such dissolution would even strengthen analytical Marxism by redirecting analytical energies towards real social and political problems in the contemporary world and away from endless methodological debate. (shrink)

This book provides the latest research and developments to determine the disengagement detection of students or learners through online learning system. It explores how detecting and analyzing students' disengagement in online learning using various tools, techniques and systems will help to automatically detect disengagement learners and offer the opportunity to make online learning more efficient.

Paradoxes are arguments that lead from apparently true premises, via apparently uncontroversial reasoning, to a false or even contradictory conclusion. Paradoxes threaten our basic understanding of central concepts such as space, time, motion, infinity, truth, knowledge, and belief. In this volume Roy T Cook provides a sophisticated, yet accessible and entertaining, introduction to the study of paradoxes, one that includes a detailed examination of a wide variety of paradoxes. The book is organized around four important types of paradox: the semantic (...) paradoxes involving truth, the set-theoretic paradoxes involving arbitrary collections of objects, the Soritical paradoxes involving vague concepts, and the epistemic paradoxes involving knowledge and belief. In each of these cases, Cook frames the discussion in terms of four different approaches one might take towards solving such paradoxes. Each chapter concludes with a number of exercises that illustrate the philosophical arguments and logical concepts involved in the paradoxes. _Paradoxes_ is the ideal introduction to the topic and will be a valuable resource for scholars and students in a wide variety of disciplines who wish to understand the important role that paradoxes have played, and continue to play, in contemporary philosophy. (shrink)

This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it. This work was reproduced from the original artifact, and remains as true to the original work as possible. Therefore, you will see the original copyright references, library stamps (as most of these works have been housed in our most important libraries around the world), and other notations in the work. This work is in the public domain (...) in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work. As a reproduction of a historical artifact, this work may contain missing or blurred pages, poor pictures, errant marks, etc. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant. (shrink)

An entertaining history of the idea of nothing - including absences, omissions, and shadows - from the Ancient Greeks through the 20th century How can nothing cause something? The absence of something might seem to indicate a null or a void, an emptiness as ineffectual as a shadow. In fact, 'nothing' is one of the most powerful ideas the human mind has ever conceived. This short and entertaining book by Roy Sorensen is a lively tour of the history and philosophy (...) of nothing, explaining how various thinkers throughout history have conceived and grappled with the mysterious power of absence -- and how these ideas about shadows, gaps, and holes have in turned played a very positive role in the development of some of humankind's most important ideas. Filled with Sorensen's characteristically entertaining mix of anecdotes, puzzles, curiosities, and philosophical speculation, the book is ordered chronologically, starting with the Taoists, the Buddhists, and the ancient Greeks, moving forward to the middle ages and the early modern period, then up to the existentialists and present day philosophy. The result is a diverting tour through the history of human thought as seen from a novel and unusual perspective. (shrink)

The highly contagious 2019 novel coronavirus disease (COVID-19) outbreak has not only impacted health systems, economies, and governments, it has also rapidly grown into a global health crisis, which is now threatening the lives of millions of people globally. While, on one hand, medical institutions are critically attempting to find a cure, on the other hand, governments have introduced striking measures and policies to curtail the rapid spread of the disease. Although COVID-19 has achieved pandemic status and is predominantly viewed (...) as a biomedical issue, it is argued that it should also be treated as a psychological crisis. This paper also reviews the literature to examine and comment on the detrimental effects of isolation, which has been enforced as one of the primary preventative measures to manage the spread of COVID-19. This paper further outlines key recommendations that should be addressed across different levels to buffer against the known adverse effects of isolation, which is especially relevant for the current COVID-19 situation, where a large proportion of the global population is isolated, confined, and/or quarantined. (shrink)