The Diamond Sutra is one of the earliest and most treasured of the Perfection of Wisdom Sutras and had a wide influence on the development of Zen Buddhism. There has been, in recent years, great interest in one particular form of sentences that repeatedly occur in the sutra, sentences of the form “A is not A, therefore it is A”. These sentences display what has been called the “logic of not” or the “logic of affirmation-in-negation”. They are of special interest (...) since they do not only encapsulate one of the central insights of Zen Buddhism, that of nonduality, but at the same time seem to go against one of the most orthodox laws of logic in Western philosophy, the law of identity. This paper discusses the interpretation of these “diamond sentences” by the Vietnamese Zen monk Thich Nhat Hanh. I present Thich Nhat Hanh’s interpretation of the diamond sentences in terms of interbeing and go on to argue that and explain how, on his interpretation, the validity of the law of identity is indeed rejected. Finally, I spell out consequences for formulating a “logic of Zen” and for a related debate about the validity of the law of non-contradiction in Zen. (shrink)

During the past several decades, many epistemologists have argued for and contributed to a paradigm shift according to which knowledge is central to assertion, action, and interaction. This general position stands in sharp contrast to several recently developed accounts regarding specific epistemic contexts. These specific accounts resist applying traditional epistemic norms, including strong knowledge norms, to real-world situations of interest. In particular, I consider recent arguments about the epistemic standards for scientific pronouncements, expert testimony in a political context, and interactive (...) reasoning. I argue, firstly, that knowledge does have a crucial role to play in each case, contrary to appearances. Clarifying the role of knowledge fills gaps in our understanding left open by the existing accounts. Secondly, I show that combining the insights from the knowledge-centric approach and from the more specific accounts provides a new perspective on the open problem of developing an account of knowledge-based decisions. Specifically, I argue that the biggest open problem regarding knowledge-based decisions is not how we respond to uncertainty, but rather how we assess the relevance of our many disparate pieces of knowledge, choosing which to integrate, and how. A strong case emerges for a procedural solution to this part of the problem of how to make knowledge-based decisions. (shrink)

BackgroundSocially assistive devices (care robots, companions, smart screen assistants) have been advocated as a promising tool in elderly care in Western healthcare systems. Ethical debates indicate various challenges. One of the most prevalent arguments in the debate is the double-benefit argument claiming that socially assistive devices may not only provide benefits for autonomy and well-being of their users but might also be more efficient than other caring practices and might help to mitigate scarce resources in healthcare. Against this background, we (...) used a subset of comparative empirical studies from a comprehensive systematic review on effects and perceptions of human-machine interaction with socially assistive devices to gather and appraise all available evidence supporting this argument from the empirical side.MethodsElectronic databases and additional sources were queried using a comprehensive search strategy which generated 9851 records. Studies were screened independently by two authors. Methodological quality of studies was assessed. For 39 reports using a comparative study design, a narrative synthesis was performed.ResultsThe data shows positive evidential support to claim that some socially assistive devices (Paro) might be able to contribute to the well-being and autonomy of their users. However, results also indicate that these positive findings may be heavily dependent on the context of use and the population. In addition, we found evidence that socially assistive devices can have negative effects on certain populations. Evidence regarding the claim of efficiency is scarce. Existing results indicate that socially assistive devices can be more effective than standard of care but are far less effective than plush toys or placebo devices.DiscussionWe suggest using the double-benefit argument with great caution as it is not supported by the currently available evidence. The occurrence of potentially negative effects of socially assistive devices requires more research and indicates a more complex ethical calculus than suggested by the double-benefit argument. (shrink)

According to David Chalmers, the virtual entities found in Virtual Reality (VR) and Augmented Reality (AR) environments instantiate virtual properties of a specific kind. It has recently been objected that such a view (i) can’t extend to all types of properties; (ii) leads to a proliferation of property-types; (iii) implausibly ascribes massive errors to VR and AR users; and (iv) faces an analogue of Jackson’s “many-property problem”. My first objective here is to show that advocates of virtual properties can deal (...) with each of these objections. The other goal of this paper is to examine the consequences of Chalmers’ theory in the particular case of AR. If we countenance virtual properties, AR highlights that non-virtual objects can possess both non-virtual and virtual properties. With AR, it also appears that a same non-virtual object can have different and even incompatible properties across augmented environments. Lastly, considering properties in light of AR highlights the risk of an “augmented solipsism”, and calls forth interesting questions about the persistence conditions of non-virtual objects in AR environments. (shrink)

The objective of the paper is to implement and validate diagnosis in the medical field via refined neutrosophic fuzzy logic (RNFL). As such, we have proposed a Max-Min composition (MMC) method in RNFL. This method deals with the diagnosis under certain constraints like uncertainty and indeterminacy. Further, we have considered the diagnosis problems to validate the sensitivity analysis of the novel multi attribute decision-making technique. Finally, we gave the graphical representations and compared the obtained results with other existing measures in (...) refined neutrosophic fuzzy sets. (shrink)

The objective of this study is to incorporate topological space into the realm of n-Cylindrical Fuzzy Neutrosophic Sets (n-CyFNS), which are the most novel type of fuzzy neutrosophic sets. In this paper, we introduce n-Cylindrical Fuzzy Neutrosophic Topological Spaces (n-CyFNTS), n-Cylindrical Fuzzy Neutrosophic (n-CyFN) open sets, and n-CyFN closed sets. We also defined the n-CyFN base, n-CyFN subbase, and some related theorems here.

This article is a preliminary draft for initiating and commencing a new pioneer dimension of expression. To deal with higher-dimensional data or information flowing in this modern era of information technology and artificial intelligence, some innovative super algebraic structures are essential to be formulated. In this paper, we have introduced such matrices that have multiple layers and clusters of layers to portray multi-dimensional data or massively dispersed information of the plithogenic universe made up of numerous subjects their attributes, and sub-attributes. (...) For grasping that field of parallel information, events, and realities flowing from the micro to the macro level of universes, we have constructed hypersoft and hyper-super-soft matrices in a Plithogenic Fuzzy environment. These Matrices classify the non-physical attributes by accumulating the physical subjects and further sort the physical subjects by accumulating their non-physical attributes. We presented themasPlithogenicAttributiveSubjectivelyWholeHyper-Super-Soft-Matrix(PASWHSS-Matrix)andPlithogenic Subjective Attributively Whole-Hyper-Super-Soft-Matrix (PSAWHSS-Matrix). Several types of views and level-layers of these matrices are described. In addition, some local aggregation operators for Plithogenic Fuzzy Hypersoft Set (PPFHS-Set) are developed. Finally, few applications of these matrices and operators are used as numerical examples of COVID-19 data structures. (shrink)

The Vehicle Routing Problem (VRP) has been extensively studied by different researchers from all over the world in recent years. Multiple solutions have been proposed for different variations of the problem, such as Capacitive Vehicle Routing Problem (CVRP), Vehicle Routing Problem with Time Windows (VRP-TW), Vehicle Routing Problem with Pickup and Delivery (VRPPD), among others, all of them with deterministic times. In the last years, researchers have been interested in including in their different models the variations that travel times may (...) experience when exposed to all kind of phenomena, mainly vehicle traffic. This article addresses the VRP from this perspective, proposing the design and implementation of a genetic algorithm based on neutrosophic theory for calculating the fitness function of each route, considering the variability and uncertainty present in travel times. A deterministic genetic algorithm is also implemented with the average travel times to compare it with the neutrosophic algorithm using simulation. As conclusion, a deterministic algorithm does not necessarily generate the best solution in the real world, full of uncertainty. Also, the quantification of uncertainty using neutrosophic theory can be used in route planning, opening a broad and interesting field of research for future investigations. (shrink)

One of the disadvantages of the point estimate in survey sampling is that it fluctuates from sample to sample due to sampling error, as the estimator only provides a point value for the parameter under discussion. The neutrosophic approach, pioneered by Florentin Smarandache, is an excellent tool for estimating the parameters under consideration in sampling theory since it yields interval estimates in which the parameter lies with a very high probability. As a result, the neutrosophic technique, which is a generalization (...) of classical approach, is used to deal with ambiguous, indeterminate, and uncertain data. In this investigation, we suggest a new general family of ratio and exponential ratio type estimators for the elevated estimation of neutrosophic population mean of the primary variable utilizing known neutrosophic auxiliary parameters. For the first degree approximation, the bias and Mean Squared Error (MSE) of the suggested estimators are computed. The neutrosophic optimum values of the characterizing constants are determined, as well as the minimum value of the neutrosophic MSE of the suggested estimator is obtained for these optimum values of the characterizing scalars. Because the minimum MSE of the classical estimators of population mean lies inside the estimated interval of the neutrosophic estimators, the neutrosophic estimators are better than the equivalent classical estimators. The empirical investigation, which used both real and simulated data sets, backs up the theoretical findings. For practical utility in various areas of applications, the estimator with the lowest MSE or highest Percentage Relative Efficiency (PRE) is recommended. (shrink)

In this paper, we recall and study the new type of algebraic structures called Symbolic Plithogenic Algebraic Structures. Their operations are given under the Absorbance Law and the Prevalence Order.

It is well known that the unpredictable speech production brought on by stress from the task at hand has a significant negative impact on the performance of speech processing algorithms. Speech therapy benefits from being able to detect stress in speech. Speech processing performance suffers noticeably when perceptually produced stress causes variations in speech production. Using the acoustic speech signal to objectively characterize speaker stress is one method for assessing production variances brought on by stress. Real-world complexity and ambiguity make (...) it difficult for decision-makers to express their conclusions with clarity in their speech. In particular, the Neutrosophic speech algorithm is used to encode the language variables because they cannot be computed directly. Neutrosophic sets are used to manage indeterminacy in a practical situation. Existing algorithms are used except for stress on Neutrosophic speech recognition. The creation of algorithms that calculate, categorize, or differentiate between different stress circumstances. Understanding stress and developing strategies to combat its effects on speech recognition and human-computer interaction system are the goals of this recognition. (shrink)

For the classical Geometry, in a geometrical space, all items (concepts, axioms, theorems, etc.) are totally (100%) true. But, in the real world, many items are not totally true. The NeutroGeometry is a geometrical space that has some items that are only partially true (and partially indeterminate, and partially false), and no item that is totally false. The AntiGeometry is a geometrical space that has some item that are totally (100%) false. While the Non-Euclidean Geometries [hyperbolic and elliptic geometries] resulted (...) from the total negation of only one specific axiom (Euclid’s Fifth Postulate), the AntiGeometry results from the total negation of any axiom [and in general: theorem, concept, idea etc.] and even of more axioms [theorem, concept, idea, etc.] and in general from any geometric axiomatic system (Euclid’s five postulates, Hilbert’s 20 axioms, etc.), and the NeutroAxiom results from the partial negation of any axiom (or concept, theorem, idea, etc.). Clearly, the AntiGeometry is a generalization of Non-Euclidean Geometries. (shrink)

During the production process, production companies need to monitor the finished products and ensure their quality, which imposes on them the appointment of inspectors for auditing, and this appointment costs the company amounts that affect the general profit, so it strives to make this cost as low as possible and that the audit process is carried out with high accuracy because in case that the finished products do not conform to the basic specifications of the product, the company is required (...) to pay a fine. In this research, we will formulate the text of the problem appropriately for such a case and then we will build the appropriate mathematical model through which we can obtain the lowest possible cost of inspection, and we will present the study using classical values and neutrosophic values, and we will demonstrate them through an example that shows us the difference between them. (shrink)

Operations research science is defined as the science that is concerned with applying scientific methods to complex problems in managing and directing large systems of people, including resources and tools in various fields, private and governmental work, peace and war, politics, administration, economics, planning and implementation in various domains. It uses scientific methods that take the language of mathematics as a basis for it and uses computer, without which it would not have been possible to achieve numerical solutions to the (...) raised problems, those that need correct solutions, when the solutions abound and the options are multiple, so we need a decision based on correct scientific foundations and takes into account all the circumstances and changes that you can encounter the decision-maker during the course of work, and nothing is left to chance or luck, but rather everything that enters into the account and plays its role in decision-making, and we get that when we use the concepts of neutrosophic science to reformulate what the science of operations research presented in terms of methods and methods to solve many practical problems, so we will present in this research a study aimed at shedding light on the most important methods used to solve nonlinear models, which is the Lagrangian multiplier method for nonlinear models constrained by equality and then reformulated using the concepts of neutrosophic science. (shrink)

We introduce Pura Vida Neutrosophic Algebra, an algebraic structure consisting of neutrosophic numbers equipped with two binary operations namely addition and multiplication. The addition can be calculated sometimes with the function min and other times with the max function. The multiplication operation is the usual sum between numbers. Pura Vida Neutrosophic Algebra is an extension of both Tropical Algebra (also known as Min-Plus, or Min-Algebra) and Max-Plus Algebra (also known as Max-algebra). Tropical and Max-Plus algebras are algebraic structures included in (...) semirings and their operations can be used in matrices and vectors. Pura Vida Neutrosophic Algebra is included in Neutrosophic semirings and can be used in Neutrosophic matrices and vectors. (shrink)

An important method for finding the optimal solution for linear and nonlinear models is the graphical method, which is used if the linear or nonlinear mathematical model contains one, two, or three variables. The models that contain only two variables are among the most models for which the optimal solution has been obtained graphically, whether these models are linear or non-linear in references and research that are concerned with the science of operations research, when the data of the issue under (...) study is classical data. In this research, we will present a study through, which we present the graphical method for solving Neutrosophical nonlinear models in the following case: A nonlinear programming issue, the objective function is a nonlinear function, and the constraints are linear functions. Note that we can use the same method if (i) the objective function follower is a linear follower and the constraints are nonlinear; (ii) the objective function is a non-linear follower and the constraints are non-linear. In the three cases, the nonlinear models are neutrosophic, and as we know, the mathematical model is a nonlinear model if any of the components of the objective function or the constraints are nonlinear expressions, and the nonlinear expressions may be in both. At the left end of the constraints are neutrosophic values, at least one or all of them. Then, the possible solutions to the neutrosophic nonlinear programming problem are the set of rays ???????? ∈ ????????that fulfills all the constraints. As for the region of possible solutions, it is the region that contains all the rays that fulfill the constraints. The optimal solution is the beam that fulfills all constraints and at which the function reaches a maximum or minimum value, depending on the nature of the issue under study (noting that it is not necessary to be alone). (shrink)

Accounts of aesthetic valuing tend to emphasize two constraints on the formation of aesthetic belief. We must form our own aesthetic beliefs by engaging with aesthetic value first-hand (the acquaintance principle) and by using our own capacities (the autonomy principle). But why? C. Thi Nguyen’s proposal is that aesthetic valuing has an inverted structure. Normally we care about inquiry and engagement for the sake of having true beliefs, but in aesthetic engagement this is flipped: we care about arriving at good (...) aesthetic beliefs for the sake of the values that arise in the process of doing so. The engagement is the point, not possessing good beliefs, and so it is important to deploy our own capacities in first-hand encounters with aesthetic value. Here I challenge Nguyen’s account along several lines. I argue that it misconstrues the value of aesthetic belief; it conflicts with restrictions on aesthetic testimony; and it has trouble harnessing engagement-value for a theory of aesthetic value. A better approach emphasizes the social character of aesthetic valuing. On this view, aesthetic valuing is a social practice structured around the collaborative exercise and improvement of certain special capacities. The autonomy and acquaintance principles tell us to engage these capacities in forming our aesthetic beliefs. Understood aright, and contrary to consensus, these rules are identical. (shrink)

Heresies are intrinsically intertwined with the evolution and inner growth of the very religions that denounce them. They serve as theological junctures, challenging and thus refining the orthodoxy of religious beliefs. The Pelagian heresy touches on one of the central tenets of Christian theology: the question of salvation. Pelagianism posits that human beings retain freedom of the will and, more specifically, the capacity to earn salvation through their own merits rather than relying solely on the grace of God in Christ. (...) This stands in contrast to the predominant Christian view that Original Sin fundamentally impaired man’s will and intellect. A central tenet of Christianity is that through His suffering and death on the Cross, Christ atoned for humanity’s Original Sin and paved the way for our redemption. But what exactly made this redemption possible through the suffering and death on the Cross? Unlike many of the answers offered, Abelard’s explanation, also referred to as exemplarism, resonates with modern sensibilities: Christ set an example to imitate, and through this imitation, man learns humility and love. However, this stance faced criticism and was condemned by Bernard of Clairvaux as having Pelagian tendencies because it suggests that Christ’s redemptive work might not inherently require Christ’s divine nature. This study will attempt to defend the exemplaristic approach while ensuring Christ’s essential role and addressing criticisms against the Pelagian heresy. This discussion is further enriched by an examination of the Eucharist, illuminating the theological tension between symbolic and realistic interpretations of religious rites. (shrink)

The claim that perfect hallucination is introspectively indistinguishable from perception has been a centrepiece of philosophical theorizing about sense experience. The most common interpretation of the indistinguishability claim is modal: that it is impossible to distinguish perfect hallucination from perception through introspection alone. I run through various models of introspection and show that none of them can accommodate the modal interpretation. Rejecting the modal interpretation opens up two alternative interpretations of the indistinguishability claim. According to the generic interpretation, hallucination is (...) indistinguishable from perception despite the existence of possible exceptions, while according to the actuality interpretation, the indistinguishability of hallucination from perception consists in the actual failure to distinguish hallucination from perception. These alternative understandings of the indistinguishability claim have a number of significant implications for the problem of perception, including the rejection of perfect hallucination and illusion in favour of our ordinary, non-philosophical concepts of these states. (shrink)