Our starting point is the question ‘What is mass’, what in particular enables mass to constitute duration: so that mass can be regarded as moving as well as at rest (the kinematic principle of relativity). In a thought experiment, this question is attacked here not from the perspective of mass itself, but from that of a standing light wave. In this model, mass-analogous structures can be re- constructed that can be in relative motion to each other. The (empirically known) constancy (...) of the speed of light in every reference system is not as- sumed here. However, it can be shown that the speed of light is identical in all systems constituted by mass-analogous structures that move uniformly relative to each other and that the speed of light moreover is the limiting speed of mo- tions. This indepence of the motion of light from the system of reference, this character of absoluteness, and the relativity of mass motions thus prove to be contrary but inextricably linked moments of the kinematic principle of relativi- ty: an interesting perspective concerning a philosophy of relativity theory. - The mathematical relationships are explained in more detail in the appendix. (shrink)

In terms of validity in Kripke frames, a modal formula expresses a universal monadic second-order condition. Those modal formulae which are equivalent to first-order conditions are called elementary. Modal formulae which have a certain persistence property which implies their validity in all canonical frames of modal logics axiomatized with them, and therefore their completeness, are called canonical. This is a survey of a recent and ongoing study of the class of elementary and canonical modal formulae. We summarize main ideas and (...) results, and outline further research perspectives. (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)

This essay defends a reading of Hegel as a metametaphysical antirealist. Metametaphysical antirealism is a denial that metaphysics has as its subject matter answers to theoretical questions about the mind-independent world. Hence, on this view, metaphysical questions are not, in principle, knowledge transcendent. I hold that Hegel presents a version of metametaphysical antirealism in the Science of Logic because he pursues his project by suspending reference to all supposed objects of metaphysical theory as practiced before him. Hegel introduces reference in (...) his theory only by the self-reference of thought to itself in the Doctrine of the Concept. I motivate the relevance of Hegel’s approach to metaphysics by comparing it to Kit Fine’s (2017) concept of “naïve metaphysics.” I argue that Hegel’s theory results from a comprehensively naïve metaphysics. (shrink)

In accordance with Leo Strauss’s ingenious suggestion, the Athenian Stranger of Plato’s Laws is best understood as an alternative ‘Socrates’, fleeing from the hemlock to Crete. Situated between Crito and Phaedo, Laws effectively tests the reader’s loyalty to the real Socrates who obeys Athenian law and dies cheerfully in Athens. Having separated Plato from the Stranger, a nuanced defence of Karl Popper’s suspicions about Laws confronts the apologetic readings of both Strauss and Christopher Bobonich. As hinted by his preference for (...) wine, the antidote for hemlock, the Athenian Stranger repeatedly proves himself the opposite of Socrates, particularly with respect to piety. Once the Stranger is recognized as ‘an unreliable narrator’, this apparently ponderous product of Plato’s senility becomes the taut thriller of an innovative teacher at the peak of his powers. (shrink)

On what I take to be the standard account of supererogation, an act is supererogatory if and only if it is morally optional and there is more moral reason to perform it than to perform some permissible alternative. And, on this account, an agent has more moral reason to perform one act than to perform another if and only if she morally ought to prefer how things would be if she were to perform the one to how things would be (...) if she were to perform the other. I argue that this account has two serious problems. The first, which I call the latitude problem, is that it has counterintuitive implications in cases where the duty to be exceeded is one that allows for significant latitude in how to comply with it. The second, which I call the transitivity problem, is that it runs afoul of the plausible idea that the one-reason-morally-justifies-acting-against-another relation is transitive. What’s more, I argue that both problems can be overcome by an alternative account, which I call the maximalist account. (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.

The Swiss psychologist Jean Piaget contends that children below the age of 12 see no necessity for the logical law of non-contradiction. I argue this view is problematic. First of all, Piaget's dialogues with children which are considered supportive of this position are not clearly so. Secondly, Piaget underestimates the necessary nature of following the logical law of non-contradiction in everyday discourse. The mere possibility of saying something significant and informative at all presupposes that the law of non-contradiction is enforced.

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.

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)

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)

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)

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)

In De Anima 1.4, Aristotle asks whether the soul can be moved by its own affections. His conclusion—that to say the soul grows angry is like saying that it weaves and builds—has traditionally been read on the assumption that it is false to credit the soul with weaving and building; I argue that Aristotle’s analysis of psychological motions implies his belief that the soul does in fact weave and build.

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)

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)

This essay constitutes an attempt to probe the very idea of a saying/showing distinction of the kind that Wittgenstein advances in the Tractatus—to say what such a distinction consists in, to say what philosophical work it has to do, and to say how we might be justified in drawing such a distinction. Towards the end of the essay the discussion is related to Wittgenstein’s later work. It is argued that we can profitably see this work in such a way that (...) a saying/showing distinction arises there too. In particular, in the final sub-section of the essay, it is suggested that we can see in Wittgenstein’s later work an inducement to say what we are shown. (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)

This papers responds to a recent argument by Sophie Gibert concerning the wrong of wrongful manipulation. I argue that the more serious explanatory question is whether manipulation is wrong by default, not whether, when manipulation is wrong, this wrong is ‘basic’. The former better elucidates the significance of Gibert’s arguments. I then respond to her argument, construed as the argument that manipulation is not wrong by default. First, the putative counterexamples she presents are drawn from areas of work and play (...) – legal advocacy, negotiation, and gameplay – where the moral status of manipulative tactics is very much in dispute; thus, her reported intuitions are not persuasive. Second, even if we grant that manipulation in these contexts is morally permissible, we can explain how it remains wrong by default by appealing to competitive conventions that realize common epistemic, aesthetic, and hedonistic goods. I also show why Gibert’s reply to this conventionalist maneuver fails. (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)

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)

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 paper, we attempt to show that if Plantinga’s free will defence succeeds, his O Felix Culpa theodicy fails. For if every creaturely essence suffers from transworld depravity, then given that Jesus has a creaturely essence (as we attempt to show), it follows that Incarnation and Atonement worlds cannot be actualized by God, in which case we have anything but a felix culpa.

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)

(Expected) adverse effects of the ‘ICT Revolution’ on work and opportunities for individuals to use and develop their capacities give a new impetus to the debate on the societal implications of technology and raise questions regarding the ‘responsibility’ of research and innovation (RRI) and the possibility of achieving ‘inclusive and sustainable society’. However, missing in this debate is an examination of a possible conflict between the quest for ‘inclusive and sustainable society’ and conventional economic principles guiding capital allocation (including the (...) funding of research and innovation). We propose that such conflict can be resolved by re-examining the nature and purpose of capital, and by recognising mainstream economics’ utilitarian foundations as an unduly restrictive subset of a wider Aristotelian understanding of choice. (shrink)

I begin with a distinction between narrow and broad defenses to the logical problem of evil. The former is simply an attempt to show that God and evil are not logically incompat-ible whereas the latter attempts the same, but only by appealing to beliefs one takes to be true in the actual world. I then argue that while recent accounts of original sin may be consistent with a broad defense, they are also logically incoherent. After considering potential replies, I conclude (...) by proposing an account of original sin that is both logically coherent and consistent with a broad defense. (shrink)

The purpose of this article is to show a structural relationship in Dutch between sentences with the main verb "duren" (last) and specifying complements such as een week (a week) or "drie kwartier" (three quarters of an hour) on the one hand, and sentences with Duration Measuring Adverbials such as "gedurende een week" (for a week), "gedurende die week" (lit: for that week) on the other.

In a previous issue of this journal Michael Veber argued that God could not answer certain prayers because doing so would be immoral. In this article I attempt to demonstrate that Veber’s argument is simply the logical problem of evil applied to a possible world. Because of this, his argument is susceptible to a Plantinga-style defense.

In this essay I suggest that we view design principles in systems biology as minimal models, for a design principle usually exhibits universal behaviors that are common to a whole range of heterogeneous (living and nonliving) systems with different underlying mechanisms. A well-known design principle in systems biology, integral feedback control, is discussed, showing that it satisfies all the conditions for a model to be a minimal model. This approach has significant philosophical implications: it not only accounts for how design (...) principles explain, but also helps clarify one dispute over design principles, e.g., whether design principles provide mechanistic explanations or a distinct kind of explanations called design explanations. (shrink)

Amazon Book Review Series of “Better Economics for the Earth: A Lesson from Quantum and Information Theories”.

I argue that a common interpretation of DA 3.4, which sees Aristotle as there rejecting Anaxagoras’s account of mind, is mistaken. Instead, I claim that, in providing his solution to the main puzzles of this chapter, Aristotle takes special care to preserve the essential features that he thinks Anaxagoras ascribes to mind, namely, its ability to know all things, its being unmixed, and its inability to be affected by mixed objects.

This paper considers a problem that arises for free will defenses when considering the nature of God's own will. If God is perfectly good and performs praiseworthy actions, but is unable to do evil, then why must humans have the ability to do evil in order to perform such actions? This problem has been addressed by Theodore Guleserian, but at the expense of denying God's essential goodness. I examine and critique his argument and provide a solution to the initial problem (...) that does not require abandoning God's essential goodness. (shrink)

Recently, John Maier has developed a unified account of various agentive modalities. According to him, however, adopting the account provides an alternative framework for thinking about free will and moral responsibility, one that reveals an unacceptable instability in semicompatibilism. In this paper, I argue that Maier is mistaken about the implications of his account and sketch a semicompatibilist proposal that can, without countenancing any instability, accept Maier’s unified account of the agentive modalities.

In this paper we respond to three objections raised by Joshua Harris to our article, “Against a Postmodern Pentecostal Epistemology,” in which we express misgivings about the conjunction of Pentecostalism with James K. A. Smith’s postmodern, story-based epistemolo- gy. According to Harris, our critique: 1) problematically assumes a correspondence theory of truth, 2) invalidly concludes that “Derrida’s Axiom” conflicts with “Peter’s Axiom,” and 3) fails to consider an alternative account of the universality of Christian truth claims. We argue that Harris’s (...) objections either demonstrate a deficient interpretation of the relevant biblical pas- sages or are not directed at us at all. (shrink)

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)

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)

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

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 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)

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.

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.

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)