This book extends the concept of linguistic coordinate geometry using linguistic planes or semi-linguistic planes. In the case of coordinate planes, we are always guaranteed of the distance between any two points in that plane. However, in the case of linguistic and semi-linguistic planes, we can not always determine the linguistic distance between any two points. This is the first limitation of linguistic planes and semi-linguistic planes.

It is commonly assumed that the expression “an sich selbst” (“in itself”) in Kant combines with terms to form complex nouns such as “thing in itself” and “end in itself.” I argue that the basic use of “an sich selbst” in Kant’s German is as a sentence adverb, which has the role of modifying subject-predicate combinations, rather than either subject or predicate on their own. Expressions of the form “S is P an sich selbst” mean roughly that S is P (...) ‘in its own right’ or without some further ‘condition’. Accordingly, “an sich selbst” should not be treated as forming complex nouns. This analysis has significant consequences for the interpretation of “thing in itself” in particular, for it implies that the latter is not a complete nominal expression. Instead, one must treat ‘an sich selbst’ as expressing how some S is a ‘thing’, looking to the wider sentential context. I conclude with a brief account of the new significance granted to the concept of a ‘thing’ (Ding) according to the present interpretation. (shrink)

As automating technologies are increasingly integrated into workplaces, one concern is that many of the human workers who remain will be relegated to more dull and less positively impactful work. This paper considers two rival theories of meaningful work that might be used to evaluate particular implementations of automation. The first is achievementism, which says that work that culminates in achievements to workers’ credit is especially meaningful; the other is the practice view, which says that work that takes the form (...) of an open-ended practice is especially meaningful. Of the two, the practice view is the better tool for assessing the future of meaningful work, because achievementism is explanatorily inadequate in two ways. Moreover, the practice view can explain why the most meaningful forms of work cannot be automated. A procedure can only be automated as long as the steps are defined, whereas, in such work, which steps to take is indefinitely open to redefinition. This reveals the real threat to meaningful work to be a political-economic one. The relevant ethical questions there have to do with how much creative control workers retain in crafting their own jobs, when those jobs involve meaningful work in collaboration with machines; and how to liberate workers from jobs that do not involve meaningful work, which should be left to machines anyway. (shrink)

In this paper, I contest increasingly common "realist" interpretations of Hegel's theory of "the concept" (der Begriff), offering instead a "isomorphic" conception of the relation of concepts and the world. The isomorphism recommended, however, is metaphysically deflationary, for I show how Hegel's conception of conceptual form creates a conceptually internal standard for the adequacy of concepts. No "sideways-on" theory of the concept-world relationship is envisioned. This standard of conceptual adequacy is also "graduated" in that it allows for a lack of (...) fit between concept and world. The possibility for a "maximally isomorphic" fit between concept and world obtains through the teleological realization of concepts, which marks especially the "artificial" world of human culture (law, art, religion, etc.). Some of the most seemingly exaggerated claims Hegel makes about the concept, I contend, can be understood when we consider the significance Hegel ascribes to human making, which is provided for in his conceptual theory. But my framework provides an interpretive key for the way Hegel sees concepts imperfectly realized in the natural world as well. (shrink)

Nudging works through dispositions to decide with specific heuristics, and has three component parts. A nudge is a feature of an environment that enables such a disposition; a person is nudged when such a disposition is triggered; and a person performs a nudged action when such a disposition manifests in action. This analysis clarifies an autonomy-based worry about nudging as used in public policy or for private profit: that a person’s ability to reason well is undermined when she is nudged. (...) Reasoning well is a component of self-guidance, which is an aspect of autonomy and so something there is reason to promote, preserve, or respect. However, a person can reason well when she is nudged: Many of these heuristics are good rules to reason with, and she can be flexible with respect to them when she takes there to be a better way to reason. Along the way, this paper uncovers several design specifications for responsible nudging, and discusses open empirical questions. However, nudging’s being compatible with reasoning well crystallizes a distinct worry about manipulation: that nudge designers can rely on nudged people guiding themselves toward the designers’ own ends. Manipulation of this sort exploits one aspect of autonomy (namely, self-guidance) to undermine autonomy in other respects. (shrink)

Stephen Yablo’s notion of proportionality, despite controversies surrounding it, has played a significant role in philosophical discussions of mental causation and of high-level causation more generally. In particular, it is invoked in James Woodward’s interventionist account of high-level causation and explanation, and is implicit in a novel approach to constructing variables for causal modeling in the machine learning literature, known as causal feature learning (CFL). In this article, we articulate an account of proportionality inspired by both Yablo’s account of proportionality (...) and the CFL account of variable construction. The resulting account has at least three merits. First, it illuminates an important feature of the notion of proportionality, when it is adapted to a probabilistic and interventionist framework. The feature is that at the center of the notion of proportionality lies the concept of “determinate intervention effects.” Second, it makes manifest a virtue of (common types of) high-level causal/explanatory statements over low-level ones, when relevant intervention effects are determinate. Third, it overcomes a limitation of the CFL framework and thereby also addresses a challenge to interventionist accounts of high-level causation. (shrink)

Things and Their Place in Theories Our talk of external things, our very notion of things, is just a conceptual apparatus that helps us to foresee and ...

This book is a translation of W.V. Quine's Kant Lectures, given as a series at Stanford University in 1980. It provide a short and useful summary of Quine's philosophy. There are four lectures altogether: I. Prolegomena: Mind and its Place in Nature; II. Endolegomena: From Ostension to Quantification; III. Endolegomena loipa: The forked animal; and IV. Epilegomena: What's It all About? The Kant Lectures have been published to date only in Italian and German translation. The present book is filled out (...) with the translator's critical Introduction, "The esoteric Quine?" a bibliography based on Quine's sources, and an Index for the volume. (shrink)

European Journal of Philosophy, Volume 29, Issue 4, Page 1026-1038, December 2021.

ArgumentIn the United States, scientific knowledge is brought before the courts by way of testimony – the testimony of scientific experts. We argue that this expertise is best understoodfirstas related to the quality of the underlying scienceand thenin terms of who delivers it. Bloodstain pattern analysis (BPA), a contemporary forensic science, serves as the vaulting point for our exploration of objectivity as a metric for the quality of a science in judicial contexts. We argue that BPA fails to meet the (...) minimal standard set by Helen Longino’s social-procedural account of objectivity (1990, 2002). In light of some pressing issues for social-procedural accounts, we offer an infrastructural account of objectivity. This account offers what amounts to a friendly amendment to Longino’s account and adds to the ways in which we might analyze social-procedural objectivity. Finally, we address an issue that is pressing in the legal context: given that scientific knowledge is delivered by individuals, not communities, at least in U.S. courts, we (may) need a way to evaluate individual scientific and epistemic agents. We suggest a means for making this evaluation that is derived from our infrastructural account of objectivity. (shrink)

I offer a line of argument that aims at the conclusion that the notion of radically different and incommensurable systems of value is incoherent, which would mean that the presumption of some significant common ground of valuation is rationally required in value inquiry.

In this paper, a modified form of Collatz conjecture for neutrosophic numbers n ∈ (Z U I) is defined. We see for any n ∈ (Z U I) the related sequence using the formula (3a + 1) + (3b + 1)I converges to any one of the 55 elements mentioned in this paper. Using the akin formula of Collatz conjecture viz. (3a- 1) + (3b -1)I the neutrosophic numbers converges to any one of the 55 elements mentioned with appropriate modifications. (...) Thus, it is conjectured that every n ∈ (Z U I) has a finite sequence which converges to any one of the 55 elements. (shrink)

Some cognitive processes appear to have “phenomenal” properties that are directly revealed to the subject and not determined by physical properties. I suggest that the source of this appearance is the method by which our brain processes sensory information. The appearance is an illusion. Nonetheless, we are not mistaken when we judge that people sometimes fee lpain.

Tractatus Politico-Philosophicus (Political-Philosophical Treatise) of W. Julian Korab-Karpowicz proposes a new idea-system. Ideas concerning different topics related to politics are introduced. The work aims to establish the principles of good governance and of a happy society, and to open up new directions for the future development of humankind. It is also in part a critique of the epistemology of early Wittgenstein as presented in his Tractatus Logico-Philosophicus. It argues that one can speak about politics and ethics with sense, and that (...) political philosophy is still a viable enterprise for us. This explanation is provided in response to the review of Tractatus Politico-Philosophicus by Katarzyna Heremska and a critical note of Pawel Kloczowski that were both published in Argument 6(1), 2016. (shrink)

A counteridentical is a counterfactual with an identity statement in the antecedent. While counteridenticals generally seem non-trivial, most semantic theories for counterfactuals, when combined with the necessity of identity and distinctness, attribute vacuous truth conditions to such counterfactuals. In light of this, one could try to save the orthodox theories either by appealing to pragmatics or by denying that the antecedents of alleged counteridenticals really contain identity claims. Or one could reject the orthodox theory of counterfactuals in favor of a (...) hyperintensional semantics that accommodates non-trivial counterpossibles. In this paper, I argue that none of these approaches can account for all the peculiar features of counteridenticals. Instead, I propose a modified version of Lewis’s counterpart theory, which rejects the necessity of identity, and show that it can explain all the peculiar features of counteridenticals in a satisfactory way. I conclude by defending the plausibility of contingent identity from objections. (shrink)

Ausgangspunkt ist die Frage, was Masse ist, wodurch sie insbesondere befähigt ist, Dauer zu konstituieren und deshalb - im Sinn des kinematischen Relativitätsprinzips - ebenso als bewegt wie als ruhend betrachtet werden kann. In einem Gedankenexperiment wird diese Frage, in Umkehrung der Perspektive, hier nicht von der Masse selbst, sondern von einer stehenden Lichtwelle her angegangen. In diesem Modell lassen sich masse-analoge Strukturen rekonstruieren, die in relativer Bewegung sein können. Die (empirisch bekannte) Unabhängigkeit der Lichtgeschwindigkeit vom Bezugssystem ist dabei nicht (...) vorausgesetzt. Doch kann gezeigt werden, dass die Lichtgeschwindigkeit Grenzgeschwindigkeit solcher relativer Bewegungen ist, dass dies für alle durch masse-analoge Strukturen konstituierte, relativ zueinander gleichförmig bewegten Bezugssysteme gilt und dass die Lichtgeschwindigkeit selbst in allen diesen Systemen gleich ist. Die Absolutheit der Lichtgeschwindigkeit und die Relativität der Massebewegungen erweisen sich so als zwar differente, aber intrinsisch zusammengehörende Momente des kinematischen Relativitätsprinzips: ein Beitrag zu einer Philosophie der Relativitätstheorie. - Die mathematischen Zusammenhänge werden im Anhang ausführlicher dargelegt. (shrink)

In this paper, we reconstruct Kant’s notion of the practically conditioned, introduced in the Dialectic of Pure Practical Reason, by drawing on Kant’s general account of the faculty of reason presented in the Transcendental Dialectic of the Critique of Pure Reason. We argue that practical reason’s activity of seeking the practically unconditioned for a given condition generates two different conceptions of the practically unconditioned and identify these as virtue and (the ideal of) happiness. We then account for how and why (...) reason proceeds to combine these two distinct ideas into the composite idea of the highest good. Last, we draw on our discussion to determine more precisely what Kant intends by the ‘supremacy’ of virtue within reason’s idea of the highest good. (shrink)

Kant’s formula of universal law (FUL) is standardly understood as a test of the moral permissibility of an agent’s maxim: maxims which pass the test are morally neutral, and so permissible, while those which do not are morally impermissible. In contrast, I argue that the FUL tests whether a maxim is the cause or determining ground of an action at all. According to Kant’s general account of causality, nothing can be a cause of some effect unless there is a law-like (...) relation between the putative cause and effect. Applied to the case of action, no maxim can be the cause of an agent’s action unless there is a law-like relation between maxims of that kind and actions of that kind. The special capacity to act according to maxims as law-like causes is what Kant calls a will; the basic constitutive principle of the will is a non-normative principle I call the categorical declarative. While the actions of a perfectly good will would be described by the categorical declarative alone, human action is determined not only by the causality of the will, but also by competing causes, namely those stemming from inclination. There is thus need for a causal test for putative maxims. The test contained in the FUL is meant to determine whether an action could be grounded solely on the agent’s maxim, or whether it requires a cause external to the will. This account permits one to build eventual distinctions concerning the morality of actions on prior and independent distinctions concerning their causality. (shrink)

ABSTRACTThe close connection often cited between Hegel and Wilfrid Sellars is not only said to lie in their common negative challenges to the ‘framework of givenness,’ but also in the positive less...

In the world of philosophy of science, the dominant theory of confirmation is Bayesian. In the wider philosophical world, the idea of inference to the best explanation exerts a considerable influence. Here we place the two worlds in collision, using Bayesian confirmation theory to argue that explanatoriness is evidentially irrelevant.

While the idea of philosophy as conceptual analysis has attracted many adherents and undergone a number of variations, in general it suffers from an authority problem with two dimensions. First, it is unclear why the analysis of a concept should have objective authority: why explicating what we mean should express how things are. Second, conceptual analysis seems to lack intersubjective authority: why philosophical analysis should apply to more than a parochial group of individuals. I argue that Hegel’s conception of social (...) ontology, focused on his concept of “ethical life” (Sittlichkeit), helps to explain how concepts (and their explication) have both objective and intersubjective authority in the social domain. Hegel claims that modern institutions are the product of self-conscious purposes, so that they are conceptually constituted. Concepts do not just represent these objects and so depend on a contingent relation to them. As many contemporary social ontologists agree, this means that our concepts of these institutions are uniquely epistemically “transparent.” They have objective authority. Concepts have intersubjective authority in the modern world as well, according to Hegel. However, I show that this feature of Hegel’s account does not rely on the solution to a philosophical problem. Rather, since the concepts of modern ethical life are “essentially contested,” their content depends on the practical and political agreement of modern subjects. This means that concepts can only have objective authority if some prior intersubjective agreement has been reached. The role of philosophy as conceptual analysis is thus importantly dependent on political developments. (shrink)

Clade selection is unpopular with philosophers who otherwise accept multilevel selection theory. Clades cannot reproduce, and reproduction is widely thought necessary for evolution by natural selection, especially of complex adaptations. Using microbial evolutionary processes as heuristics, I argue contrariwise, that (1) clade growth (proliferation of contained species) substitutes for clade reproduction in the evolution of complex adaptation, (2) clade-level properties favoring persistence – species richness, dispersal, divergence, and possibly intraclade cooperation – are not collapsible into species-level traits, (3) such properties (...) can be maintained by selection on clades, and (4) clade selection extends the explanatory power of the theory of evolution. (shrink)

Hegel often says that his "logic" is meant to replace metaphysics. Since Hegel's Science of Logic is so different from a standard logic, most commentators have not treated the portion of that work devoted to logical forms as relevant to this claim. This paper argues that Hegel's discussion of logical forms of judgment and syllogism is meant to be the foundation of his reformation of metaphysics. Implicit in Hegel's discussion of the logical forms is the view that the metaphysical concepts (...) discussed in Books I and II of the Science of Logic supervene on the role of subject and predicate terms in the logical forms discussed in Book III. Hegel thus has an explanation for the nature and significance of metaphysical concepts that resembles Kant's "metaphysical deduction," according to which the categories can be derived from the table of judgments. Though Hegel's metaphysics is often supposed to be influenced by Kant, prevailing interpretations do not show how Hegel's fine-grained treatment of logical forms is relevant to his critical view of metaphysics. The present interpretation provides a model for Hegel's explanation of metaphysical concepts, as well as a new picture of the structure of his Science of Logic that emphasizes the priority of its Doctrine of the Concept. (shrink)

This is an encyclopedia entry on consequentializing. It explains what consequentializing is, what makes it possible, why someone might be motivated to consequentialize, and how to consequentialize a non-consequentialist theory.

In this essay I propose that what design principles in systems biology and systems neuroscience do is to present abstract characterizations of mechanisms, and thereby facilitate mechanistic explanation. To show this, one design principle in systems neuroscience, i.e., the multilayer perceptron, is examined. However, Braillard (2010) contends that design principles provide a sort of non-mechanistic explanation due to two related reasons: they are very general and describe non-causal dependence relationships. In response to this, I argue that, on the one hand, (...) all mechanisms are more or less general (or abstract), and on the other, many (if not all) design principles are causal systems. (shrink)

Smarandache in 2019 has generalized the algebraic structures to NeutroAlgebraic structures and AntiAlgebraic structures. In this paper, authors, for the first time, define the NeutroAlgebra of neutrosophic triplets group under usual+ and x, built using {Zn, x}, n a composite number, 5 < n < oo, which are not partial algebras. As idempotents in Zn alone are neutrals that contribute to neutrosophic triplets groups, we analyze them and build NeutroAlgebra of idempotents under usual + and x, which are not partial (...) algebras. We prove in this paper the existence theorem for NeutroAlgebra of neutrosophic triplet groups. This proves the neutrals assocaited with neutrosophic triplet groups in { Zn, X} under product is a NeutroAlgebra of triplets. We also prove the non-existence theorem of NeutroAlgebra for neutrosophic triplets in case of Zn when n = 2p, 3p and 4p (for some primes p). Several open problems are proposed. Further, the NeutroAlgebras of extended neutrosophic triplet groups have been obtained. (shrink)

This study investigates all available literature related to critical thinking in business education in a survey of publications in the field produced from 1990-2019. It conducts a thematic analysis of 787 articles found in Web of Science and Google Scholar, including a specific focus on 55 highly-cited articles. The aim is to investigate the importance of critical thinking in business education, how it is conceptualised in business education research, the business contexts in which critical thinking is situated, and the key (...) and more marginal themes related to critical thinking outlined in the business and business education literature. The paper outlines six key areas and topics associated with those areas. It suggests future directions for further scholarly work in the area of critical thinking in business education. (shrink)

First put forth in June 2005, the altered nuclear transfer-oocyte assisted reprogramming (ANT-OAR) proposal has been promoted as an ethically-acceptable alternative to the embryo-destructive methods now used to obtain embryonic stem cells. According to its proponents, the goal of ANT-OAR is to use the cloning process to create a pluripotent stem cell. This would be achieved through overexpression of the transcription factor Nanog (or a hypothetical substitute) both in the enucleated egg cell and in the somatic cell prior to transfer (...) of its nucleus. Although the ethical acceptability of ANT-OAR has been publicly debated, its scientific feasibility has not. This paper aims to help rectify this situation. It argues that ANT-OAR, as currently conceived, cannot realistically work. It presents evidence from the scientific literature showing that Nanog cannot single-handedly establish pluripotency in cells, but rather works together with a network of other transcription factors to maintain pluripotency. It argues that ANT-OAR is based on a flawed understanding of stem cell biology, and emphasizes that, in this debate about embryonic stem cells, scientists must strive to accurately and realistically assess the feasibility of the embryo research strategies they propose. (shrink)

The current study is a pilot trial to examine the effects of a nonelective, classroom-based, teacher-implemented, mindfulness meditation intervention on standard clinical measures of mental health and affect in middle school children. A total of 101 healthy sixth-grade students (55 boys, 46 girls) were randomized to either an Asian history course with daily mindfulness meditation practice (intervention group) or an African history course with a matched experiential activity (active control group). Self-reported measures included the Youth Self Report (YSR), a modified (...) Spielberger State-Trait Anxiety Inventory, and the Cognitive and Affective Mindfulness Measure –Revised. Both groups decreased significantly on clinical syndrome subscales and affect but did not differ in the extent of their improvements. Meditators were significantly less likely to develop suicidal ideation or thoughts of self-harm than controls. These results suggest that mindfulness training may yield both unique and non-specific benefits that are shared by other novel activities. (shrink)

In this essay, we aim to provide an overview of the political and philosophical issues pertaining to asexuality. The first section, “What Is Asexuality?,” offers an account of asexuality. The second section, “Asexuality as a Unique Sexual Orientation,” argues that asexuality should be understood as a unique sexual orientation. The third section, “Asexuality and Oppression,” discusses the various forms of oppression facing asexual persons today. The fourth section, “The Goods of Asexuality,” articulates some goods that asexuality brings to human lives, (...) and we do this with an eye toward conceiving of asexuality as something other than a mere deficit. (shrink)

Blame is multifarious. It can be passionate or dispassionate. It can be expressed or kept private. We blame both the living and the dead. And we blame ourselves as well as others. What’s more, we blame ourselves, not only for our moral failings, but also for our non-moral failings: for our aesthetic bad taste, gustatory self-indulgence, or poor athletic performance. And we blame ourselves both for things over which we exerted agential control (e.g., our voluntary acts) and for things over (...) which we lacked such control (e.g., our desires, beliefs, and intentions). I argue that, despite this manifest diversity in our blaming practices, it’s possible to provide comprehensive account of blame. Indeed, I propose a set of necessary and sufficient conditions that aims to specify blame’s extension in terms of its constitution as opposed to its function. And I argue that this proposal has a number of advantages beyond accounting for blame in all its disparate forms. For one, it can account for the fact that one’s having had control over whether one was to φ is a necessary condition for one’s being fittingly blamed for having φ-ed. For another, it can account for why, unlike fitting shame, fitting blame is always deserved, which in turn explains why there is something morally problematic about ridding oneself of one’s fitting self-blame (e.g., one’s fitting guilt). (shrink)

The images of human suffering from New Orleans in the aftermath of Hurricane Katrina remain seared in our nation's collective memory. More than 8 years on, the city and its African-American population still have not recovered fully. This reality highlights an important truth: the disturbances that accompany climate change will first and foremost affect minority communities, many of whom are economically disadvantaged. This paper: (1) describes how Hurricane Katrina, an example of the type of natural disaster that will become more (...) prevalent with intensifying climate change, has impacted the black community of New Orleans; (2) explores the notion that African Americans, in the midst of racial oppression, have developed a unique and powerful brand of environmental thought that has much to contribute to mainstream environmentalism; and (3) argues that the voice of the black community, which has a vested interest in climate outcomes, is critically needed in today's climate debate. (shrink)

As individuals we often face complex issues about which we must weigh evidence and come to conclusions. Corporations also have to make decisions on the basis of strong and compelling arguments. Legal practitioners, compelled by arguments for or against a proposition and underpinned by the weight of evidence, are often required to make judgments that affect the lives of others. Medical doctors face similar decisions. Governments make purchasing decisions—for example, for expensive military equipment—or decisions in the areas of public or (...) foreign policy. These issues involve many arguments on all sides of difficult debates. These issues involve understanding the arguments of others and being able to make objections and provide rebuttals to objections. Students in universities deal with arguments all the time. A major purpose of a university education—regardless of subject matter—is to teach students how to read, understand, and respond to complex arguments. The ability to do this makes for highly employable, adaptable, and reflectively critical individuals. We often call the skill of marshaling arguments and assessing them “critical thinking.” All universities claim to instill the skill of critical thinking in their graduates and routinely note this in their advertising and promotional documents. This short paper outlines one way this skill can be taught. (shrink)

A counterpossible is a counterfactual with an impossible antecedent. Counterpossibles present a puzzle for standard theories of counterfactuals, which predict that all counterpossibles are semantically vacuous. Moreover, counterpossibles play an important role in many debates within metaphysics and epistemology, including debates over grounding, causation, modality, mathematics, science, and even God. In this article, we will explore various positions on counterpossibles as well as their potential philosophical consequences.

From the earliest times, American ethics, the rules for the moral \& intellectual life of the West, used to be founded upon the two principles of self-reliance and good neighborliness. Here we consider the underlying functions of neural brain circuits, organic structures that have evolved adaptively by Darwinian rules subject to selection pressure. In the left brain resides our self-reliant private Ego, making plans, launching initiatives. Your public Ego dwells in the right brain, looking around, meeting with your friendly neighbor. (...) A main component is our bilateral interior cosmos, providing us with all the detailed information about our environment as well as the universe at large. (shrink)

In recent years, academics and educators have begun to use software mapping tools for a number of education-related purposes. Typically, the tools are used to help impart critical and analytical skills to students, to enable students to see relationships between concepts, and also as a method of assessment. The common feature of all these tools is the use of diagrammatic relationships of various kinds in preference to written or verbal descriptions. Pictures and structured diagrams are thought to be more comprehensible (...) than just words, and a clearer way to illustrate understanding of complex topics. Variants of these tools are available under different names: “concept mapping”, “mind mapping” and “argument mapping”. Sometimes these terms are used synonymously. However, as this paper will demonstrate, there are clear differences in each of these mapping tools. This paper offers an outline of the various types of tool available and their advantages and disadvantages. It argues that the choice of mapping tool largely depends on the purpose or aim for which the tool is used and that the tools may well be converging to offer educators as yet unrealised and potentially complementary functions. (shrink)

In this book authors for the first time introduce the notion of super interval matrices using special intervals. The advantage of using super interval matrices is that one can build only one vector space using m × n interval matrices, but in case of super interval matrices we can have several such spaces depending on the partition on the interval matrix.

In this book authors for the first time introduce the notion of supermatrices of refined labels. Authors prove super row matrix of refined labels form a group under addition. However super row matrix of refined labels do not form a group under product; it only forms a semigroup under multiplication. In this book super column matrix of refined labels and m × n matrix of refined labels are introduced and studied.

In this book, for the first time, authors try to introduce the concept of linguistic variables as a continuum of linguistic terms/elements/words in par or similar to a real continuum. For instance, we have the linguistic variable, say the heights of people, then we place the heights in the linguistic continuum [shortest, tallest] unlike the real continuum (–∞, ∞) where both –∞ or +∞ is only a non-included symbols of the real continuum, but in case of the linguistic continuum we (...) generally include the ends or to be more mathematical say it is a closed interval, where shortest denotes the shortest height of a person, maybe the born infant who is very short from usual and the tallest will denote the tallest one usually very tall; however this linguistic continuum [shortest, tallest] in the real continuum will be the closed interval say [1 foot, 8 feet] or [1, 8] the measurement in terms of feet. So, the real interval is a subinterval with which we have associated the real continuum in terms of qualifying unit feet and inches in this case. (shrink)

In this book, the authors systematically define the new notion of linguistic graphs associated with a linguistic set of a linguistic variable. We can also define the notion of directed linguistic graphs and linguistic-weighted graphs. Chapter two discusses all types of linguistic graphs, linguistic dyads, linguistic triads, linguistic wheels, complete linguistic graphs, linguistic connected graphs, disconnected linguistic graphs, linguistic components of the graphs and so on. Further, we define the notion of linguistic subgraphs of a linguistic graph. However, like usual (...) graphs, we will not be able to arbitrarily connect any two linguistic words of a linguistic set associated with a linguistic variable. They can be related or adjacent depending on the linguistic variable associated with the linguistic set. This is an exceptional feature of a linguistic graph. (shrink)

The notion of linguistic geometry is defined in this book. It is pertinent to keep in the record that linguistic geometry differs from classical geometry. Many basic or fundamental concepts and notions of classical geometry are not true or extendable in the case of linguistic geometry. Hence, for simple illustration, facts like two distinct points in classical geometry always define a line passing through them; this is generally not true in linguistic geometry. Suppose we have two linguistic points as tall (...) and light we cannot connect them, or technically, there is no line between them. However, let's take, for instance, two linguistic points, tall and very short, associated with the linguistic variable height of a person. We have a directed line joining from the linguistic point very short to the linguistic point tall. In this case, it is important to note that the direction is essential when the linguistic variable is a person's height. The other way line, from tall to very short, has no meaning. So in linguistic geometry, in general, we may not have a linguistic line; granted, we have a line, but we may not have it in both directions; the line may be directed. The linguistic distance is very far. So, the linguistic line directed or otherwise exists if and only if they are comparable. Hence the very concept of extending the line infinitely does not exist. Likewise, we cannot say as in classical geometry; three noncollinear points determine the plane in linguistic geometry. Further, we do not have the notion of the linguistic area of well-defined figures like a triangle, quadrilateral or any polygon as in the case of classical geometry. The best part of linguistic geometry is that we can define the new notion of linguistic social information geometric networks analogous to social information networks. This will be a boon to non-mathematics researchers in socio-sciences in other fields where natural languages can replace mathematics. (shrink)

In this book, the authors introduce the linguistic set associated with a linguistic variable and the structure of matrices, which they define as linguistic matrices. The authors build linguistic matrices only for those linguistic variables which yield a linguistic continuum or an ordered linguistic set. This book is organised into three chapters. The first chapter is introductory, in which we introduce all the basic concepts of linguistic variables and the associated linguistic set to make this book self-contained. Chapter two introduces (...) linguistic matrices and develops basic properties associated with them, like types of matrices, transpose of matrices and diagonal matrices. Most of the properties enjoyed by real or complex matrices are satisfied by these linguistic matrices. Chapter three deals with operations on the linguistic matrices. (shrink)

Algebraic structures on linguistic sets associated with a linguistic variable are introduced. The linguistics with single closed binary operations are only semigroups and monoids. We describe the new notion of linguistic semirings, linguistic semifields, linguistic semivector spaces and linguistic semilinear algebras defined over linguistic semifields. We also define algebraic structures on linguistic subsets of a linguistic set associated with a linguistic variable. We define the notion of linguistic subset semigroups, linguistic subset monoids and their respective substructures. We also define as (...) in case of deals in classical semigroups, linguistic ideals in linguistic semigroups and linguistic monoids. This concept of linguistic ideals is extended to the case of linguistic subset semigroups and linguistic subset monoids. We also define linguistic substructures. (shrink)

The new notions of super column FRM model, super row FRM model and mixed super FRM model are introduced in this book. These three models are introduced specially to analyze the biased role of the print media on 27 percent reservation for the Other Backward Classes (OBCs) in educational institutions run by the Indian Central Government.

The systematic study of supermatrices and super linear algebra has been carried out in 2008. These new algebraic structures find their applications in fuzzy models, Leontief economic models and data-storage in computers.

The concept of supermatrix for social scientists was first introduced by Paul Horst. The main purpose of his book was to introduce this concept to social scientists, students, teachers and research workers who lacked mathematical training. This book introduces the concept of fuzzy super matrices and operations on them. The author has provided only those operations on fuzzy supermatrices that are essential for developing super fuzzy multi expert models. This book will be highly useful to social scientists who wish to (...) work with multi expert models. (shrink)

In this book, the authors introduce the notion of Super linear algebra and super vector spaces using the definition of super matrices defined by Horst (1963). Many theorems on super linear algebra and its properties are proved. Some theorems are left as exercises for the reader. These new class of super linear algebras which can be thought of as a set of linear algebras, following a stipulated condition, will find applications in several fields using computers. The authors feel that such (...) a paradigm shift is essential in this computerized world. (shrink)

The new classes of super special codes are constructed in this book using the specially constructed super special vector spaces. These codes mainly use the super matrices. These codes can be realized as a special type of concatenated codes.