Consequentialist theories that directly assess multiple focal points face an important objection: that one right option may conflict with another. Robert Adams raises an instance of this objection regarding the possibility that the right act conflicts with the right motives. Whereas only partial responses have previously been given, assuming particular views of the relation between motives and acts, an exhaustive treatment is in order. Either motives psychologically determine acts, or they do not – and I defend direct consequentialism on each (...) assumption. Crucially, if motives determine acts, this may be compatible with the ability to act otherwise, but there remains a defense for consequentialism even on these assumptions. What clears consequentialism of conflict is not necessarily that the apparently right act is unavailable, but rather that its outcome is suboptimal once we account for necessary motives. Even if the agent remains free to perform the act, the act costs too much. (shrink)

This paper weaves together a number of separate strands each relating to an aspect of Wittgenstein’s Philosophical Investigations. The first strand introduces his radical and incoherent idea of a private object. Wittgenstein in § 258 and related passages is not investigating a perfectly ordinary notion of first person privacy; but his critics have treated his question, whether a private language is possible, solely in terms of their quite separate question of how our ordinary sensation terms can be understood, in a (...) philosophical context, to acquire meaning. Yet it is no part of his intention to demonstrate logically that ordinary sensations are not intrinsically meaningful. This is a tempting yet misleading picture, the picture also expressed through the idea of Augustine’s child who is conceptually articulateprior to learning how to talk. This picture lies behind the born Crusoe, an idea at the centre of the dichotomy between language as essentially shared and essentially shareable, a dichotomy considered here to result from a misconception of two quite separate but related aspects of Wittgenstein’s treatment offollowing a rule. The notion of a misleading picture, in both its pre-theoretical and philosophical aspects, also plays a crucial role in a treatment of Saul Kripke’s well-known “Postscript: Wittgenstein and Other Minds.”. (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.

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

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)

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 ...

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)

Nanotechnology, as with many technologies before it, places a strain on existing legislation and poses a challenge to all administrative agencies tasked with regulating technology-based products. It is easy to see how statutory schemes become outdated, as our ability to understand and affect the world progresses. In this article, we address the regulatory problems that nanotechnology posses for the Food and Drug Administration’s (FDA) classification structure for ‘‘drugs’’ and ‘‘devices.’’ The last major modification to these terms was in 1976, with (...) the enactment of the Medical Device Amendments. There are serious practical differences for a classification as a drug or device in terms of time to market and research. Drugs are classified, primarily, as acting by ‘‘chemical action.’’ We lay out some legal, philosophic, and scientific tools that serve to provide a useful, as well as legally and scientifically faithful, distinction between drugs and devices for the purpose of regulatory classification. These issues we raise are worth the consideration of anyone who is interested in the regulation of nano-products or other novel technologies. (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)

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)

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)

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)

I argue that considerations pertaining to constitutive luck undermine historicism—the view that an agent’s history can determine whether or not she is morally responsible. The main way that historicists have motivated their view is by appealing to certain cases of manipulation. I argue, however, that since agents can be morally responsible for performing some actions from characters with respect to which they are entirely constitutively lucky, and since there is no relevant difference between these agents and agents who have been (...) manipulated into acting from a character bestowed upon them by their manipulators, we should give up historicism. After presenting this argument and defending it against some potential objections, I briefly criticize the standard structuralist alternative and propose a new structuralist position that is shaped by reflection on constitutive luck. (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)

In the Transcendental Aesthetic (TA), Kant is typically held to make negative assertations about “things in themselves,” namely that they are not spatial or temporal. These negative assertions stand behind the “neglected alternative” problem for Kant’s transcendental idealism. According to this problem, Kant may be entitled to assert that spatio-temporality is a subjective element of our cognition, but he cannot rule out that it may also be a feature of the objective world. In this paper, I show in a new (...) way how Kant’s view (focusing on his conclusions about space) is not subject to this objection, by showing that he does not make the denial about mind-independent reality that he is typically held to make. The argument develops consequences of a new reading of Kant’s expression “an sich selbst” (‘in itself’; ‘in themselves’). I argue that “an sich selbst” or “per se” has a special, judgment-level role, so that this expression does not form new noun-terms adjectivally. It follows that the conceptual unit of Kant’s “Conclusions” in the TA is simply “things” (Dinge), since “things in themselves” is not a nominal expression; Kant adopts the Wolffian ontological use of “thing” as the basic kind-term for any existent. The arguments that things per se are not in space are arguments that space cannot be a necessary property or relations of things as a kind. I show that this does not involve the positive claim about mind-independent reality that inspires the neglected alternative objection. (shrink)

BioéthiqueOnline was launched in March 2012 as a non-peer reviewed journal with the aim of providing a platform to facilitate and encourage the development of a bilingual bioethics community in Canada and internationally. In light of discussions amongst the Editorial Committee over the past few months regarding the growth of the journal, we have decided to move to a peer-reviewed process for articles submitted to the journal.

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.

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 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.

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)

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)

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)

I argue that any account attempting to do away with resultant or circumstantial moral luck is inconsistent with a natural response to the problem of constitutive moral luck. It is plausible to think that we sometimes contribute to the formation of our characters in such a way as to mitigate our constitutive moral luck at later times. But, as I argue here, whether or not we succeed in bringing about changes to our characters is itself a matter of resultant and (...) circumstantial moral luck. I conclude with a dilemma, both horns of which require accepting some form of moral luck. (shrink)

For many years there has been a debate about the role of the parietal lobe in the generation of behavior. Does it generate movement plans (intention) or choose objects in the environment for further processing? To answer this, we focus on the lateral intraparietal area (LIP), an area that has been shown to play independent roles in target selection for saccades and the generation of visual attention. Based on results from a variety of tasks, we propose that LIP acts as (...) a priority map in which objects are represented by activity proportional to their behavioral priority. We present evidence to show that the priority map combines bottom-up inputs like a rapid visual response with an array of top-down signals like a saccade plan. The spatial location representing the peak of the map is used by the oculomotor system to target saccades and by the visual system to guide visual attention. (shrink)

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)

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.

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)

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 paper explores the relation of the theory of time and the theory of truth in Deleuze’s philosophy. According to Deleuze, a mutation in our conception of time occurred with Kant. In antiquity, time had been subordinated to movement, it was the measure or the “number of movement” (Aristotle). In Kant, this relation is inverted: time is no longer subordinated to movement but assumes an independence and autonomy of its own for the first time. In Deleuze’s phrasing, time becomes the (...) pure and empty form of everything that moves and changes — not an eternal form (as in Plato), but precisely the form of what is not eternal. In turn, the theory of time is inextricably linked to the concept of truth, since to say that a proposition is true means that it is true “in all times and in all places.” Truth, in other words, is timeless, eternal, non-temporal. When the form of the true is confronted with the form of time, the concept of truth is necessarily put into crisis, and Deleuze’s argument is that time allows the power of the false to assume an autonomy of its own. The analysis will attempt to show how the liberation of time from movement (the pure and empty form of time) leads to a liberation of the false from the true (the power of the false). (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)

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)

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)

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)

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...

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.

Some compatibilists are internalists. On their view, whether an agent is morally responsible for an action depends only on her psychological structure at that time. Other compatibilists are externalists. On their view, an agent’s history can make a difference as to whether or not she is morally responsible. In response to worries about manipulation, some internalists have claimed that compatibilism requires internalism. Recently, Alfred Mele has argued that this internalist response is untenable. The aim of this paper is to vindicate (...) the claim that compatibilism requires internalism, showing where Mele’s argument goes wrong along the way. (shrink)

Computational neuroscience attributes coloured areas and other perceptual qualia to calculations that are realizable in multiple cellular forms. This faces serious issues in explaining how the various qualia arise and how they bind to form overall perceptions. Qualia may instead be neuroelectrical. Growing evidence indicates that perceptions correlate with neuroelectrical activity spotted by locally activated EEGs, the different qualia correlate with the different electrochemistries of unique detector cells, a unified neural-electromagnetic field binds this activity to form overall perceptions, and this (...) field interacts with sensory circuits to help attentively guide perception. The coloured areas in images may thus be seated in the electrochemistry of unique cells, while constancy mechanisms and other multiply realizable computations just help refine these images behind the scenes. This theory is ultimately testable. (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)

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.