“Neutrosophics Knowledge” has been created for publications on advanced studies in neutrosophy, neutrosophic set, neutrosophic logic, neutrosophic probability, neutrosophic statistics that started in 1995 and their applications in any field, such as the neutrosophic structures developed in algebra, geometry, topology, etc. The submitted papers should be professional, in good English and Arabic, containing a brief review of a problem and obtained results. Neutrosophy is a new branch of philosophy that studies the origin, nature, and scope of neutralities, as well as (...) their interactions with different ideational spectra. (shrink)

Since the world is full of indeterminacy, the Neutrosophics found their place into contemporary research. We now introduce for the first time the notions of Neutrosophic Crisp Sets and Neutrosophic Topology on Crisp Sets. We develop the 2012 notion of Neutrosophic Topological Spaces and give many practical examples. Neutrosophic Science means development and applications of Neutrosophic Logic, Set, Measure, Integral, Probability etc., and their applications in any field. It is possible to define the neutrosophic measure and consequently the neutrosophic integral (...) and neutrosophic probability in many ways, because there are various types of indeterminacies, depending on the problem we need to solve. Indeterminacy is different from randomness. Indeterminacy can be caused by physical space, materials and type of construction, by items involved in the space, or by other factors. In 1965 [51], Zadeh generalized the concept of crisp set by introducing the concept of fuzzy set, corresponding to the situation in which there is no precisely defined set;there are increasing applications in various fields, including probability, artificial intelligence, control systems, biology and economics. Thus, developments in abstract mathematics using the idea of fuzzy sets possess sound footing. In accordance, fuzzy topological spaces were introduced by Chang [12] and Lowen [33]. After the development of fuzzy sets, much attention has been paid to the generalization of basic concepts of classical topology to fuzzy sets and accordingly developing a theory of fuzzy topology [1-58]. In 1983, the intuitionistic fuzzy set was introduced by K. Atanassov [55, 56, 57] as a generalization of the fuzzy set, beyond the degree of membership and the degree of non-membership of each element. In 1999 and 2002, Smarandache [71, 72, 73, 74] defined the notion of Neutrosophic Sets, which is a generalization of Zadeh’s fuzzy set and Atanassov's intuitionistic fuzzy set. Some neutrosophic concepts have been investigated by Salama et al. [61-70]. Forwarding the study of neutrosophic sets, this book consists of seven chapters, targeting to:  generalize the previous studies in [1-59], and[91-94] so to define the neutrosopic crisp set and neutrosophic set concepts;  discuss their main properties; A. A. Salama & Florentin Smarandache  introduce and study some concepts of neutrosophic crisp and neutrosophic topological spaces and deduce their properties;  deduce many types of functions and give the relationships between different neutrosophic topological spaces, which helps to build new properties of neutrosophic topological spaces;  stress once more the importance of Neutrosophic Ideal as a nontrivial extension of neutrosophic set and neutrosophic logic [71, 72, 73, 74];  propose applications on computer sciences by using neutrosophic sets. (shrink)

Takeuti and Titani have introduced and investigated a logic they called intuitionistic fuzzy logic. This logic is characterized as the first-order Gödel logic based on the truth value set [0,1]. The logic is known to be axiomatizable, but no deduction system amenable to proof-theoretic, and hence, computational treatment, has been known. Such a system is presented here, based on previous work on hypersequent calculi for propositional Gödel logics by Avron. It is shown that the system is sound and (...) complete, and allows cut-elimination. A question by Takano regarding the eliminability of the Takeuti-Titani density rule is answered affirmatively. (shrink)

Recently, research on uncertainty modeling is progressing rapidly and many essential and breakthrough stud ies have already been done. There are various ways such as fuzzy, intuitionistic and neutrosophic sets to handle these uncertainties. Although these concepts can handle incomplete information in various real-world issues, they cannot address all types of uncertainty such as indeterminate and inconsistent information. Also, plithogenic sets as a generalization of crisp, fuzzy, intuitionistic fuzzy, and neutrosophic sets, which is a set (...) whose elements are characterized by many attributes’ values. In this paper, our aim is to demonstrate and review the history of fuzzy, intuitionistic and neutrosophic sets. For this purpose, we divided the paper as: section 1. History of Fuzzy Sets, section 2. History of Intuitionistic Fuzzy Sets and section 3. History of Neutrosophic Theories and Applications, section 4. History of Plithogenic Sets. (shrink)

In this paper, we introduce the plithogenic set (as generalization of crisp, fuzzy, intuitionistic fuzzy, and neutrosophic sets), which is a set whose elements are characterized by many attributes (parameters)’ values. An attribute value v has a corresponding (fuzzy, intuitionistic fuzzy, or neutrosophic) degree of appurtenance d(x,v) of the element x, to the set P, with respect to some given criteria. In order to obtain a better accuracy for the plithogenic aggregation operators in the (...) plithogenic set, and for a more exact inclusion (partial order), a (fuzzy, intuitionistic fuzzy, or neutrosophic) contradiction (dissimilarity) degree is defined be-tween each attribute value and the dominant (most important) attribute value. The plithogenic intersection and union are linear combinations of the fuzzy operators tnorm and tconorm, while the plithogenic complement, inclusion (inequality), equality are influenced by the attribute values contradiction (dissimilarity) degrees. This article offers some examples and applications of these new concepts in our everyday life. (shrink)

Abstract: In this paper, we study a new notion of fuzzy subimplicative ideal of a BH-algebra, namely fuzzy subimplicative ideal with respect to an element in BH-algebra is introduced and some related properties are investigated.

Although Fuzzy logic and Fuzzy Mathematics is a widespread subject and there is a vast literature about it, yet the use of Fuzzy issues like Fuzzy sets and Fuzzy numbers was relatively rare in time concept. This could be seen in the Fuzzy time series. In addition, some attempts are done in fuzzing Turing Machines but seemingly there is no need to fuzzy time. Throughout this article, we try to change this picture and (...) show why it is helpful to consider the instants of time as Fuzzy numbers. In physics, though there are revolutionary ideas on the time concept like B theories in contrast to A theory also about central concepts like space, momentum… it is a long time that these concepts are changed, but time is considered classically in all well-known and established physics theories. Seemingly, we stick to the classical time concept in all fields of science and we have a vast inertia to change it. Our goal in this article is to provide some bases why it is rational and reasonable to change and modify this picture. Here, the central point is the modified version of “Unexpected Hanging” paradox as it is described in "Is classical Mathematics appropriate for theory of Computation".This modified version leads us to a contradiction and based on that it is presented there why some problems in Theory of Computation are not solved yet. To resolve the difficulties arising there, we have two choices. Either “choosing” a new type of Logic like “Para-consistent Logic” to tolerate contradiction or changing and improving the time concept and consequently to modify the “Turing Computational Model”. Throughout this paper, we select the second way for benefiting from saving some aspects of Classical Logic. In chapter 2, by applying quantum Mechanics and Schrodinger equation we compute the associated fuzzy number to time. (shrink)

In this paper, we introduce the concepts of Pythagorean fuzzy valued neutrosophic set (PFVNS) and Pythagorean fuzzy valued neutrosophic (PFVNV) constructed by considering Pythagorean fuzzy values (PFVs) instead of numbers for the degrees of the truth, the indeterminacy and the falsity, which is a new extension of intuitionistic fuzzy valued neutrosophic set (IFVNS). By means of PFVNSs, the degrees of the truth, the indeterminacy and the falsity can be given in Pythagorean fuzzy environment and (...) more sensitive evaluations are made by a decision maker in decision making problems compared to IFVNSs. In other words, such sets enable a decision maker to evaluate the degrees of the truth, the indeterminacy and the falsity as PFVs to model the uncertainty in the evaluations. (shrink)

The second volume of “Advancing Uncertain Combinatorics through Graphization, Hyperization, and Uncertainization: Fuzzy, Neutrosophic, Soft, Rough, and Beyond” presents a deep exploration of the progress in uncertain combinatorics through innovative methodologies like graphization, hyperization, and uncertainization. This volume integrates foundational concepts from fuzzy, neutrosophic, soft, and rough set theory, among others, to further advance the field. Combinatorics and set theory, two central pillars of mathematics, focus on counting, arrangement, and the study of collections under defined rules. Combinatorics excels (...) in handling uncertainty, while set theory has evolved with concepts such as fuzzy and neutrosophic sets, which enable the modeling of complex real-world uncertainties by addressing truth, indeterminacy, and falsehood. These advancements, when combined with graph theory, give rise to novel forms of uncertain sets in "graphized" structures, including hypergraphs and superhypergraphs. Innovations such as Neutrosophic Oversets, Undersets, and Offsets, as well as the Nonstandard Real Set, build upon traditional graph concepts, pushing both theoretical and practical boundaries. The synthesis of combinatorics, set theory, and graph theory in this volume provides a robust framework for addressing the complexities and uncertainties inherent in both mathematical and real-world systems, paving the way for future research and application. In the first chapter, “A Review of the Hierarchy of Plithogenic, Neutrosophic, and Fuzzy Graphs: Survey and Applications”, the authors investigate the interrelationships among various graph classes, including Plithogenic graphs, and explore other related structures. Graph theory, a fundamental branch of mathematics, focuses on networks of nodes and edges, studying their paths, structures, and properties. A Fuzzy Graph extends this concept by assigning a membership degree between 0 and 1 to each edge and vertex, representing the level of uncertainty. The Turiyam Neutrosophic Graph is introduced as an extension of both Neutrosophic and Fuzzy Graphs, while Plithogenic graphs offer a potent method for managing uncertainty. The second chapter, “Review of Some Superhypergraph Classes: Directed, Bidirected, Soft, and Rough”, examines advanced graph structures such as directed superhypergraphs, bidirected hypergraphs, soft superhypergraphs, and rough superhypergraphs. Classical graph classes include undirected graphs, where edges lack orientation, and directed graphs, where edges have specific directions. Recent innovations, including bidirected graphs, have sparked ongoing research and significant advancements in the field. Soft Sets and their extension to Soft Graphs provide a flexible framework for managing uncertainty, while Rough Sets and Rough Graphs address uncertainty by using lower and upper approximations to handle imprecise data. Hypergraphs generalize traditional graphs by allowing edges, or hyperedges, to connect more than two vertices. Superhypergraphs further extend this by allowing both vertices and edges to represent subsets, facilitating the modeling of hierarchical and group-based relationships. The third chapter, “Survey of Intersection Graphs, Fuzzy Graphs, and Neutrosophic Graphs”, explores the intersection graph models within the realms of Fuzzy Graphs, Intuitionistic Fuzzy Graphs, Neutrosophic Graphs, Turiyam Neutrosophic Graphs, and Plithogenic Graphs. The chapter highlights their mathematical properties and interrelationships, reflecting the growing number of graph classes being developed in these areas. Intersection graphs, such as Unit Square Graphs, Circle Graphs, and Ray Intersection Graphs, are crucial for understanding complex graph structures in uncertain environments. The fourth chapter, “Fundamental Computational Problems and Algorithms for SuperHyperGraphs”, addresses optimization problems within the SuperHypergraph framework, such as the SuperHypergraph Partition Problem, Reachability, and Minimum Spanning SuperHypertree. The chapter also adapts classical problems like the Traveling Salesman Problem and the Chinese Postman Problem to the SuperHypergraph context, exploring how hypergraphs, which allow hyperedges to connect more than two vertices, can be used to solve complex hierarchical and relational problems. The fifth chapter, “A Short Note on the Basic Graph Construction Algorithm for Plithogenic Graphs”, delves into algorithms designed for Plithogenic Graphs and Intuitionistic Plithogenic Graphs, analyzing their complexity and validity. Plithogenic Graphs model multi-valued attributes by incorporating membership and contradiction functions, offering a nuanced representation of complex relationships. The sixth chapter, “Short Note of Bunch Graph in Fuzzy, Neutrosophic, and Plithogenic Graphs”, generalizes traditional graph theory by representing nodes as groups (bunches) rather than individual entities. This approach enables the modeling of both competition and collaboration within a network. The chapter explores various uncertain models of bunch graphs, including Fuzzy Graphs, Neutrosophic Graphs, Turiyam Neutrosophic Graphs, and Plithogenic Graphs. In the seventh chapter, “A Reconsideration of Advanced Concepts in Neutrosophic Graphs: Smart, Zero Divisor, Layered, Weak, Semi, and Chemical Graphs”, the authors extend several fuzzy graph classes to Neutrosophic graphs and analyze their properties. Neutrosophic Graphs, a generalization of fuzzy graphs, incorporate degrees of truth, indeterminacy, and falsity to model uncertainty more effectively. The eighth chapter, “Short Note of Even-Hole-Graph for Uncertain Graph”, focuses on Even-Hole-Free and Meyniel Graphs analyzed within the frameworks of Fuzzy, Neutrosophic, Turiyam Neutrosophic, and Plithogenic Graphs. The study investigates the structure of these graphs, with an emphasis on their implications for uncertainty modeling. The ninth chapter, “Survey of Planar and Outerplanar Graphs in Fuzzy and Neutrosophic Graphs”, explores planar and outerplanar graphs, as well as apex graphs, within the contexts of fuzzy, neutrosophic, Turiyam Neutrosophic, and plithogenic graphs. The chapter examines how these types of graphs are used to model uncertain parameters and relationships in mathematical and real-world systems. The tenth chapter, “General Plithogenic Soft Rough Graphs and Some Related Graph Classes”, introduces and explores new concepts such as Turiyam Neutrosophic Soft Graphs and General Plithogenic Soft Graphs. The chapter also examines models of uncertain graphs, including Fuzzy, Intuitionistic Fuzzy, Neutrosophic, and Plithogenic Graphs, all designed to handle uncertainty in diverse contexts. The eleventh chapter, “Survey of Trees, Forests, and Paths in Fuzzy and Neutrosophic Graphs”, provides a comprehensive study of Trees, Forests, and Paths within the framework of Fuzzy and Neutrosophic Graphs. This chapter focuses on classifying and analyzing graph structures like trees and paths in uncertain environments, contributing to the ongoing development of graph theory in the context of uncertainty. (shrink)

Kripke frames (and models) provide a suitable semantics for sub-classical logics; for example, intuitionistic logic (of Brouwer and Heyting) axiomatizes the reflexive and transitive Kripke frames (with persistent satisfaction relations), and the basic logic (of Visser) axiomatizes transitive Kripke frames (with persistent satisfaction relations). Here, we investigate whether Kripke frames/models could provide a semantics for fuzzy logics. For each axiom of the basic fuzzy logic, necessary and sufficient conditions are sought for Kripke frames/models which satisfy them. It (...) turns out that the only fuzzy logics (logics containing the basic fuzzy logic) which are sound and complete with respect to a class of Kripke frames/models are the extensions of the Gödel logic (or the super-intuitionistic logic of Dummett); indeed this logic is sound and strongly complete with respect to reflexive, transitive and connected (linear) Kripke frames (with persistent satisfaction relations). This provides a semantic characterization for the Gödel logic among (propositional) fuzzy logics. (shrink)

In this ninth book of scilogs collected from my nest of ideas, one may find new and old questions and solutions, – in email messages to research colleagues, or replies, and personal notes, some handwritten on the planes to, and from international conferences, about topics on Neutrosophy and its applications, such as: Neutrosophic Bipolar Set, Linguistic Neutrosophic Set, Neutrosophic Resonance Frequency, n-ary HyperAlgebra, n-ary NeutroHyperAlgebra, n-ary AntiHyperAlgebra, Plithogenic Crisp Graph, Plithogenic Fuzzy Graph, Plithogenic Intuitionistic Fuzzy Graph, Plithogenic (...) Neutrosophic Graph, Plithogenic Real Number Graph, Plithogenic Complex Number Graph, Plithogenic Neutrosophic Number Graph, and many more. -/- Exchanging ideas with: Tareq Al-Shami, Riad Khidr Al-hamido, Mohammad Akram, B. De Baets, Robert Neil Boyd, Said Broumi, Terman Frometa-Castillo, Yilmaz Ceven, D. Dubois, Harish Garg, L. Godo, Erik Gonzalez, Yanhui Guo, Mohammad Hamidi, E. Hüllermeier, W. B. Vasantha Kandasamy, Mary Jansi, Nivetha Martin, Mani Parimala, Akbar Rezaei, Bouzina Salah, Christy Vincent, Jun Ye.‬‬‬. (shrink)

Appeals to intersectionality serve to remind us that social categories like race and gender cannot be adequately understood independently from each other. But what, exactly, is the intersectional thesis a thesis about? Answers to this question are remarkably diverse. Intersectionality is variously understood as a claim about the nature of social kinds, oppression, or experience ; about the limits of antidiscrimination law or identity politics ; or about the importance of fuzzy sets, multifactor analysis, or causal modeling in social (...) science. (shrink)

Hilbert’s choice operators τ and ε, when added to intuitionistic logic, strengthen it. In the presence of certain extensionality axioms they produce classical logic, while in the presence of weaker decidability conditions for terms they produce various superintuitionistic intermediate logics. In this thesis, I argue that there are important philosophical lessons to be learned from these results. To make the case, I begin with a historical discussion situating the development of Hilbert’s operators in relation to his evolving program in (...) the foundations of mathematics and in relation to philosophical motivations leading to the development of intuitionistic logic. This sets the stage for a brief description of the relevant part of Dummett’s program to recast debates in metaphysics, and in particular disputes about realism and anti-realism, as closely intertwined with issues in philosophical logic, with the acceptance of classical logic for a domain reflecting a commitment to realism for that domain. Then I review extant results about what is provable and what is not when one adds epsilon to intuitionistic logic, largely due to Bell and DeVidi, and I give several new proofs of intermediate logics from intuitionistic logic+ε without identity. With all this in hand, I turn to a discussion of the philosophical significance of choice operators. Among the conclusions I defend are that these results provide a finer-grained basis for Dummett’s contention that commitment to classically valid but intuitionistically invalid principles reflect metaphysical commitments by showing those principles to be derivable from certain existence assumptions; that Dummett’s framework is improved by these results as they show that questions of realism and anti-realism are not an “all or nothing” matter, but that there are plausibly metaphysical stances between the poles of anti-realism and realism, because different sorts of ontological assumptions yield intermediate rather than classical logic; and that these intermediate positions between classical and intuitionistic logic link up in interesting ways with our intuitions about issues of objectivity and reality, and do so usefully by linking to questions around intriguing everyday concepts such as “is smart,” which I suggest involve a number of distinct dimensions which might themselves be objective, but because of their multivalent structure are themselves intermediate between being objective and not. Finally, I discuss the implications of these results for ongoing debates about the status of arbitrary and ideal objects in the foundations of logic, showing among other things that much of the discussion is flawed because it does not recognize the degree to which the claims being made depend on the presumption that one is working with a very strong logic. (shrink)

The ideal of the United Nations was first put forward by Immanuel Kant in his 1795 essay Perpetual Peace. Kant, in the tradition of Locke and Rousseau is a liberal who believes that relations between individuals can either be based upon law and consent or upon force and violence. One way that such the ideal of world peace could be achieved would be through the creation of a single world state, of which every human being was a citizen. (...) Such an ideal was advocated by a number of eighteenth century liberals. Kant, however, rejects this ideal and instead argues that the universal rule of law can be achieved through the establishment a federation of independent states. I examine the relevance of Kant’s arguments today, focusing on two questions: Firstly, as advocates of the rule of law, why advocate a federation of independent nations rather than a single world state. Secondly, is this ideal realizable? Is Kant right to think that republics are natural and are likely to live peacefully with one another? Kant’s arguments on this issue have been taken up again in recent decades by defenders of the theory of the “democratic peace”, the theory that democracies are more likely to live at peace with one another. (shrink)

‘Reasoning’ can be considered a general concept that, upon speaking, is the ‘enraonar’, a Catalan word that should not be mistaken with ‘explain’ nor with ‘discuss’ which imply more detail, and cover different situations. This article is presented as an essay on the ancient ideal of ‘enraonar’. To that end, it is explained in what sense ‘enraonar’ and reason are one of the most complex phenomena thought has to deal with. Here it is argued that these natural phenomena require (...) a systematic and ‘scientific’ study, and that withoutthis knowledge computer science cannot simulate people’s every-day ‘enraonar’. (shrink)

Today, soft computing is a field that is used a lot in solving real-world problems, such as problems in economics, finance, banking... With the aim to serve for solving the real problem, many new theories and/or tools which were proposed, improved to help soft computing used more efficiently. We can mention some theories as fuzzy sets theory (L. Zadeh, 1965), intuitionistic fuzzy set (K Atanasov, 1986), neutrosophic set (F. Smarandache 1999). In this paper, we introduce a new (...) notion of sup port-neutrosophic set (SNS), which is the combination a neutrosophic set with a fuzzy set. So, SNS set is a direct extension of fuzzy set and neutrosophic sets (F. Smarandache). Then, we define some operators on the support-neutrosophic sets, and investigate some properties of these operators. (shrink)

Smarandache (1995) defined the notion of neutrosophic sets, which is a generalization of Zadeh's fuzzy set and Atanassov's intuitionistic fuzzy set. In this paper, we first develop some similarity measures of neutrosophic sets. We will present a method to calculate the distance between neutrosophic sets (NS) on the basis of the Hausdorff distance. Then we will use this distance to generate a new similarity measure to calculate the degree of similarity between NS. Finally we will prove some (...) properties of the proposed similarity measures. (shrink)

In this paper, we generalize the soft set to the hypersoft set by transforming the function F into a multi-attribute function. Then we introduce the hybrids of Crisp, Fuzzy, Intuitionistic Fuzzy, Neutrosophic, and Plithogenic Hypersoft Set.

Neutrosophic theory has many applications in graph theory, bipolar single valued neutrosophic graphs (BSVNGs) is the generalization of fuzzy graphs and intuitionistic fuzzy graphs, SVNGs. In this paper we introduce some types of BSVNGs, such as subdivision BSVNGs, middle BSVNGs, total BSVNGs and bipolar single valued neutrosophic line graphs (BSVNLGs), also investigate the isomorphism, co weak isomorphism and weak isomorphism properties of subdivision BSVNGs, middle BSVNGs, total BSVNGs and BSVNLGs.

In this paper one introduces for the first time the IndetermSoft Set, as extension of the classical (determinate) Soft Set, that deals with indeterminate data, and similarly the HyperSoft Set extended to IndetermHyperSoft Set, where ‘Indeterm’ stands for ‘Indeterminate’ (uncertain, conflicting, not unique outcome). They are built on an IndetermSoft Algebra that is an algebra dealing with IndetermSoft Operators resulted from our real world. Afterwards, the corresponding Fuzzy / Intuitionistic Fuzzy / Neutrosophic / and other fuzzy-extension (...) IndetermSoft Set & IndetermHyperSoft Set are presented together with their applications. (shrink)

We use a neutrosophic set, instead of an intuitionistic fuzzy because the neutrosophic set is more general, and it allows for independent and partial independent components, while in an intuitionistic fuzzy set, all components are totally dependent. In this article, we present and demonstrate the concept of neutrosophic invariant subgroups. We delve into the exploration of this notion to establish and study the neutrosophic quotient group. Further, we give the concept of a neutrosophic normal subgroup as (...) a novel concept. (shrink)

In this book, we approach different topics related to neutrosophics, such as: Neutrosophic Set, Intuitionistic Fuzzy Set, Inconsistent Intuitionistic Fuzzy Set, Picture Fuzzy Set, Ternary Fuzzy Set, Pythagorean Fuzzy Set, Atanassov’s Intuitionistic Fuzzy Set of second type, Spherical Fuzzy Set, n-HyperSpherical Neutrosophic Set, q-Rung Orthopair Fuzzy Set, truth-membership, indeterminacy-membership, falsehood-nonmembership, Regret Theory, Grey System Theory, Three-Ways Decision, n-Ways Decision, Neutrosophy, Neutrosophication, Neutrosophic Probability, Refined Neutrosophy, Refined Neutrosophication, Nonstandard Analysis; (Theory, (...) NeutroTheory, AntiTheory), S-denying an Axiom, Multispace with Multistructure, and so on. (shrink)

In this paper, we first defined soft intervalvalued neutrosophic rough sets(SIVN- rough sets for short) which combines interval valued neutrosophic soft set and rough sets and studied some of its basic properties. This concept is an extension of soft interval valued intuitionistic fuzzy rough sets( SIVIF- rough sets). Finally an illustartive example is given to verfy the developped algorithm and to demonstrate its practicality and effectiveness.

In this paper, we make distinctions between Classical Logic (where the propositions are 100% true, or 100 false) and the Neutrosophic Logic (where one deals with partially true, partially indeterminate and partially false propositions) in order to respond to K. Georgiev’s criticism [1]. We recall that if an axiom is true in a classical logic system, it is not necessarily that the axiom be valid in a modern (fuzzy, intuitionistic fuzzy, neutrosophic etc.) logic system.

Neutrosophic Over-/Under-/Off-Set and -Logic were defined for the first time by Smarandache in 1995 and published in 2007. They are totally different from other sets/logics/probabilities. He extended the neutrosophic set respectively to Neutrosophic Overset {when some neutrosophic component is > 1}, Neutrosophic Underset {when some neutrosophic component is < 0}, and to Neutrosophic Offset {when some neutrosophic components are off the interval [0, 1], i.e. some neutrosophic component > 1 and other neutrosophic component < 0}. This is no surprise with (...) respect to the classical fuzzy set/logic, intuitionistic fuzzy set/logic, or classical/imprecise probability, where the values are not allowed outside the interval [0, 1], since our real-world has numerous examples and applications of over-/under-/off-neutrosophic components. (shrink)

A Plithogenic Logical proposition P is a proposition that is characterized by many degrees of truth-values with respect to many corresponding attribute-values (or random variables) that characterize P. Each degree of truth-value may be classical, fuzzy, intuitionistic fuzzy, neutrosophic, or other fuzzy extension type logic. At the end, a cumulative truth of P is computed.

This fourteenth volume of Collected Papers is an eclectic tome of 87 papers in Neutrosophics and other fields, such as mathematics, fuzzy sets, intuitionistic fuzzy sets, picture fuzzy sets, information fusion, robotics, statistics, or extenics, comprising 936 pages, published between 2008-2022 in different scientific journals or currently in press, by the author alone or in collaboration with the following 99 co-authors (alphabetically ordered) from 26 countries: Ahmed B. Al-Nafee, Adesina Abdul Akeem Agboola, Akbar Rezaei, Shariful Alam, (...) Marina Alonso, Fran Andujar, Toshinori Asai, Assia Bakali, Azmat Hussain, Daniela Baran, Bijan Davvaz, Bilal Hadjadji, Carlos Díaz Bohorquez, Robert N. Boyd, M. Caldas, Cenap Özel, Pankaj Chauhan, Victor Christianto, Salvador Coll, Shyamal Dalapati, Irfan Deli, Balasubramanian Elavarasan, Fahad Alsharari, Yonfei Feng, Daniela Gîfu, Rafael Rojas Gualdrón, Haipeng Wang, Hemant Kumar Gianey, Noel Batista Hernández, Abdel-Nasser Hussein, Ibrahim M. Hezam, Ilanthenral Kandasamy, W.B. Vasantha Kandasamy, Muthusamy Karthika, Nour Eldeen M. Khalifa, Madad Khan, Kifayat Ullah, Valeri Kroumov, Tapan Kumar Roy, Deepesh Kunwar, Le Thi Nhung, Pedro López, Mai Mohamed, Manh Van Vu, Miguel A. Quiroz-Martínez, Marcel Migdalovici, Kritika Mishra, Mohamed Abdel-Basset, Mohamed Talea, Mohammad Hamidi, Mohammed Alshumrani, Mohamed Loey, Muhammad Akram, Muhammad Shabir, Mumtaz Ali, Nassim Abbas, Munazza Naz, Ngan Thi Roan, Nguyen Xuan Thao, Rishwanth Mani Parimala, Ion Pătrașcu, Surapati Pramanik, Quek Shio Gai, Qiang Guo, Rajab Ali Borzooei, Nimitha Rajesh, Jesús Estupiñan Ricardo, Juan Miguel Martínez Rubio, Saeed Mirvakili, Arsham Borumand Saeid, Saeid Jafari, Said Broumi, Ahmed A. Salama, Nirmala Sawan, Gheorghe Săvoiu, Ganeshsree Selvachandran, Seok-Zun Song, Shahzaib Ashraf, Jayant Singh, Rajesh Singh, Son Hoang Le, Tahir Mahmood, Kenta Takaya, Mirela Teodorescu, Ramalingam Udhayakumar, Maikel Y. Leyva Vázquez, V. Venkateswara Rao, Luige Vlădăreanu, Victor Vlădăreanu, Gabriela Vlădeanu, Michael Voskoglou, Yaser Saber, Yong Deng, You He, Youcef Chibani, Young Bae Jun, Wadei F. Al-Omeri, Hongbo Wang, Zayen Azzouz Omar. (shrink)

We present in this paper the neutrosophic randomized variables, which are a generalization of the classical random variables obtained from the application of the neutrosophic logic (a new nonclassical logic which was founded by the American philosopher and mathematical Florentin Smarandache, which he introduced as a generalization of fuzzy logic especially the intuitionistic fuzzy logic ) on classical random variables. The neutrosophic random variable is changed because of the randomization, the indeterminacy and the values it takes, which (...) represent the possible results and the possible indeterminacy. Then we classify the neutrosophic randomized variables into two types of discrete and continuous neutrosophic random variables and we define the expected value and variance of the neutrosophic random variable then offer some illustrative examples. -/- . (shrink)

The traditional soft set is a mapping from a parameter set to family of all crisp subsets of a universe. Molodtsov introduced the soft set as a generalized tool for modelling complex systems involving uncertain or not clearly defined objects. In this paper, the notion of neutrosophic soft set is reanalysed. The novel theory is a combination of neutrosophic set theory and soft set theory. The complement, “and”, “or”, intersection and union operations are defined on the neutrosophic soft sets. The (...) neutrosophic soft relations accompanied with their compositions are also defined. The basic properties of the neutrosophic soft sets, neutrosophic soft relations and neutrosophic soft compositions are also discussed. (shrink)

E. F. Carritt (1876-1964) was educated at and taught in Oxford University. He made substantial contributions both to aesthetics and to moral philosophy. The focus of this entry is his work in moral philosophy. His most notable works in this field are The Theory of Morals (1928) and Ethical and Political Thinking (1947). Carritt developed views in metaethics and in normative ethics. In meta-ethics he defends a cognitivist, non-naturalist moral realism and was among the first to respond to A. J. (...) Ayer’s emotivist challenge to this view. In normative ethics he advocates a deontological view in which there is a plurality of obligations and of non-instrumental goods. In the context of defending this view he raised some penetrating and novel criticisms of ideal utilitarianism. He held that it is not acceptable to revise our reflective common-sense moral attitudes in the face of philosophical moral theories, and that moral philosophy is only indirectly practical. (shrink)

The theory of plithogeny developed by Smarandache is described as a more generalized form of representing sets of different nature such as crisp, fuzzy, intuitionistic and neutrosophic. Plithogenic set comprises degree of appurtenance and contradiction degree with respect only to the dominant attribute. This paper introduces extended plithogenic sets comprising degrees of appurtenance and contradiction with respect to both dominant and recessive attributes. The extension of the 5-tuple Plithogenic sets to a 7- tuple plithogenic sets helps in developing (...) a more comprehensive kind of Plithogenic sociogram. The newly developed plithogenic sets and its implications in Plithogenic sociogram is validated by the decision making problem on food processing industries. The obtained results using extended plithogenic sets are more promising in comparison to the conventional plithogenic sets. The proposed kind of plithogenic sets will benefit the decision makers to make optimal decisions based on both optimistic and pessimistic approaches. (shrink)

This paper presents for the first time the IndetermSoft Set, as an extension of the classical (determinate) Soft Set, which operates on indeterminate data, and similarly the HyperSoft Set extended to the IndetermHyperSoft Set, where 'Indeterm' means 'Indeterminate' (uncertain, conflicting, non-unique result). They are built on an IndetermSoft Algebra which is an algebra dealing with IndetermSoft Operators resulting from our real world. Subsequently, the IndetermSoft and IndetermHyperSoft Sets and their Fuzzy/Fuzzy Intuitionistic/Neutrosophic and other fuzzy extensions and (...) their applications are presented. (shrink)

Neutrosophy has been introduced some years ago by Florentin Smarandache as a new branch of philosophy dealing with “the origin, nature and scope of neutralities, as well as their interactions with different ideational spectra”. A variety of new theories have been developed on the basic principles of neutrosophy: among them is neutrosophic logics, a family of many-valued systems that can be regarded as a generalization of fuzzy logics. In this paper we present a critical introduction to neutrosophic logics, focusing (...) on the problem of defining suitable neutrosophic propositional connectives and discussing the relationship between neutrosophic logics and other well-known frameworks for reasoning with uncertainty and vagueness, such as (intuitionistic and interval-valued) fuzzy systems and Belnap’s logic. (shrink)

Fericirea este un concept fuzzy. Ea poate fi definită în termeni de a trăi o viață bună sau de a înflori, mai degrabă decât de a experimenta o emoție. Fericirea în acest sens a fost folosită pentru a traduce eudaimonia greacă și este încă folosită în etica virtuții. A existat o tranziție în timp, de la accent pe fericirea virtuții la virtutea fericirii. În psihologie, fericirea este o stare mentală sau emoțională a bunăstării, care poate fi definită, printre altele, (...) de emoții pozitive sau plăcute, variind de la mulțumire până la bucuria intensă. În Vedele hinduse, ānanda semnifică fericirea veșnică, cea care însoțește sfârșitul ciclului de renaștere. Pentru grecii antici, ataraxia este o stare lucidă de echilibru robust, caracterizată de elibertatea continuă de teama primejdiei și îngrijorare. Filosofii consideră că fericirea poate fi înțeleasă ca fiind scopul moral al vieții sau ca aspect al hazardului, explicând fericirea fie ca o stare de spirit, fie ca o viață înfloritoare pentru persoana căreia i se aplică. „Conceptul de fericire este un concept atât de vag încât, în ciuda dorinței fiecărui om de a fi fericit, nimeni nu poate spune niciodată în termeni preciși și coerent ce vrea și dorește cu adevărat. Motivul este că elementele care fac parte din conceptul de fericire sunt în totalitate empirice, adică trebuie împrumutate din experiență, și că în același timp, pentru ideea fericirii, un întreg absolut, este necesar un maxim de bunăstare în starea actuală și cea viitoare. Ori, este imposibil ca o persoană finită să fie atât de perspicace și, în același timp, atât de puternică încât să se presupună că poate crea un concept cert despre ceea ce își dorește cu adevărat. Bogăție? ... Cunoaștere? ... Viață lungă? .. Sănătate? Prin urmare, nu există, în acest sens, un imperativ care să ne impună în sensul strict al cuvântului ce să facem pentru a fi fericiți, deoarece fericirea este un ideal nu al rațiunii, ci al imaginației." (Emmanuel Kant, Critica facultății de judecată) -/- CUPRINS: -/- Fericirea - Definiție - Legătura cu sănătatea fizică - Filozofie - Religie - - Religiile orientale - - - Budism - - - Hinduism - - - Confucianismul - - Religiile abrahamice - - - Iudaismul - - - Catolicismul roman - - - Islam - Psihologie - - Ierarhia nevoilor a lui Maslow - - Teoria autodeterminării - - Psihologie pozitivă - - Măsurarea fericirii - Viziunea economică și politică Ānanda - Diferite sensuri de fericire în filosofia hindusă - - Swami Vivekananda - - Sri Aurobindo - - Advaita vedanta - - Dvaita vedanta - - Vishishtadvaita vedanta - - Sri Ramana Maharshi - Modalități de realizare a ānandei Ataraxia - Epicureismul - Pironism - Stoicism Indici ai fericirii: Fericirea Națională Brută - Definirea FNB - Implementarea FNB în Bhutan - Răspândirea FNB în afara Bhutan - Critica Filosofia fericirii - Grecia antică - - Platon - - Aristotel - - Cinism - - Cirenaicism - - Pironism - - Epicureism - - Stoicism - Roma antică - - Școala lui Sextius - - Augustin de Hippo - - Boețiu - Evul Mediu - - Avicenna - - Al-Ghazali - - Maimonide - - Thomas de Aquino - Perioada modernă timpurie - - Michel de Montaigne - - Jeremy Bentham - - Arthur Schopenhauer - Perioada contemporană - - Władysław Tatarkiewicz - - Herbert Marcuse - - Viktor Frankl - - Robert Nozick - Scientismul - Studiul fericirii - - Sonja Lyubomirsky Teoria (etica) virtuții - Concepte cheie - Istoria virtuții - - „Turnura aretaică” contemporană Consecințialism - Filosofii - - Consecințialismul de stat - - Utilitarism - - Egoismul etic - - Altruismul etic - - Consecințialismul regulilor - - Consecințialismul pe două niveluri - - Consecințialismul motivațional - - Consecințialism negativ - - Etica teleologică - - Actele și omisiunile, și "doctrina actelor și omisiunilor" Referințe Despre autor - Nicolae Sfetcu - - De același autor - - Contact Editura - MultiMedia Publishing . (shrink)

Commonplace syntactic constructions in natural language seem to generate ontological commitments to a dazzling array of metaphysical categories - aggregations, sets, ordered n-tuples, possible worlds, intensional entities, ideal objects, species, intensive and extensive quantities, stuffs, situations, states, courses of events, nonexistent objects, intentional and discourse objects, general objects, plural objects, variable objects, arbitrary objects, vague kinds and concepts, fuzzy sets, and so forth. But just because a syntactic construction in some natural language appears to invoke a new category (...) of entity, are we theoreticians epistemically justified in holding that there are such entities? This would hardly seem sufficient. To be epistemically justified, the ontology to which we theoreticians are committed must pass strict standards: the entities must be of the sort required by our best comprehensive theory of the world. The thesis of this paper is that fine-grained type-free intensional entities are like this. If the thesis is right, these entities have a special objective status perhaps not possessed by some of the other ontological categories associated with special syntactic constructions in natural language. In fact, it is plausible to hold that fine-grained type-free intensional entities provide the proper minimal framework for constructing logical and linguistic theories. In this paper my strategy will be to survey the competing conceptions of fine-grained type-free intensionality and to present arguments in support of one of them. Following this narrowing down process, I will go on to the indicated epistemological considerations. (shrink)

The move from respecting science to scientism, i.e., the idealization of science and scientific method, is simple: We go from acknowledging the sciences as fruitful human activities to oversimplifying the ways they work, and accepting a fuzzy belief that Science and Scientific Method, will give us a direct pathway to the true making of the world, all included. The idealization of science is partly the reason why we feel we need to impose the so-called scientific terminologies and methodologies to (...) all aspects of our lives, education too. Under this rationale, educational policies today prioritize science, not only in curriculum design, but also as a method for educational practice. One might expect that, under the scientistic rationale, science education would thrive. Contrariwise, I will argue that scientism disallows science education to give an accurate image of the sciences. More importantly, I suggest that scientism prevents one of science education’s most crucial goals: help students think. Many of my arguments will borrow the findings and insights of science education research. In the last part of this paper, I will turn to some of the most influential science education research proposals and comment on their limits. If I am right, and science education today does not satisfy our most important reasons for teaching science, perhaps we should change not just our teaching strategies, but also our scientistic rationale. But that may be a difficult task. (shrink)

It is shown that the infinite-valued first-order Gödel logic G° based on the set of truth values {1/k: k ε w {0}} U {0} is not r.e. The logic G° is the same as that obtained from the Kripke semantics for first-order intuitionistic logic with constant domains and where the order structure of the model is linear. From this, the unaxiomatizability of Kröger's temporal logic of programs (even of the fragment without the nexttime operator O) and of the authors' (...) temporal logic of linear discrete time with gaps follows. (shrink)

For Putnam in "Representation and Reality", there cannot be any intentional science, thus dooming cognitive science. His argument is that intentional concepts are functional, and that functionalism cannot explain anything because "everything has every functional organization", providing a proof. Analyzing his proof, we find that Putnam is assuming an ideal interpreting subject who can compute effortlessly and who is not intentional. But the subject doing science is a human being, and we are not that way. Therefore, in order to (...) save cognitive science, we propose to replace the ideal subject with a real and intentional human subject, and we propose to model intentionality by using a problem theory which is an intuitionist set theory where the resolving subject is a computing device. We are intentional because we are living beings, where life is the intention of not to die, so we are embodied intentions designed by evolution. We are real and then we have to compute our resolutions to the survival problem, and fortuitously we are computationally Turing complete, so our language is complete and then full and self referable. In summary, evolutionary subjectivism modeled as problem solving by computing should save cognitive science. Or, in other words, we are proposing to update Kant with Darwin and Turing. (shrink)

TWENTIETH-CENTURY ETHICS. AFTER NIETZSCHE -/- Preface This book tells the story of twentieth-century ethics or, in more detail, it reconstructs the history of a discussion on the foundations of ethics which had a start with Nietzsche and Sidgwick, the leading proponents of late-nineteenth-century moral scepticism. During the first half of the century, the prevailing trends tended to exclude the possibility of normative ethics. On the Continent, the trend was to transform ethics into a philosophy of existence whose self-appointed task was (...) that of describing the human condition as consisting of choices, as unavoidable as arbitrary, without any attempt at providing criteria for making such choices. In the Anglo-Saxon countries, the heir of ethics was a philosophy of morality, that is, an analysis of the language of morality that intended to clarify valuations without trying to justify them. 1958 was the year of the normative turn that led to the Rehabilitation of practical philosophy, a turn followed by decades of controversies between distinct kinds of normative ethics: utilitarian, Kantian, virtue ethics. While the controversy was raging, a quiet revolution took place, that of applied ethics which surprisingly dissolved the controversy's very subject matter by providing methods for making convergence possible on intermediate principles even when no agreement was available about first principles. The normative turn and the revolution of applied ethics have led us, at the turn of the century, to a goal that was quite far from the starting point. Instead of scepticism and relativism that was the fashion at the beginning of the century, at the beginning of the third millennium impartial and universal moral arguments seem to hold the spot being supported, if not by a final rational foundation, at least by reasonableness, the most precious legacy of the Enlightenment. -/- ● TABLE OF CONTENTS -/- ● I Anglo-Saxon philosophy: naturalism 1. Dewey beyond evolutionism and utilitarianism 2. Dewey and anti-essentialist moral epistemology 3. Dewey and naturalist moral ontology 4. Dewey and normative ethics of conduct and function 5. Perry and semantic naturalism -/- ● II Anglo-Saxon philosophy: ideal utilitarianism and neo-intuitionism 1. Moore's critique of utilitarian empiricism 2. Moore on the naturalistic fallacy 3. Moore on the nature of intrinsic value 4. Moore on ideal utilitarianism 5. Prichard on the priority of the right over the good 6. Ross's coherentist moral epistemology 7. Ross's moral ontology: realism, pluralism, and non-naturalism 8. Ross's normative ethics of prima facie duties -/- The chapter reconstructs the background of ideas, concerns and intentions out of which Moore's early essays, the preliminary version, and then the final version of Principia Ethica originated. It stresses the role of religious concerns, as well as that of the Idealist legacy. It argues that PE is more a patchwork of somewhat diverging contributions than a unitary work, not to say the paradigm of a new school in Ethics. -/- ●III Anglo-Saxon philosophy: non-cognitivism 1. The Scandinavian School, the Vienna circle and proto-emotivism 2. Wittgenstein and the ineffability of ethics 3. Russell's and Ayer's radical emotivism 4. Stevenson and moderate emotivism 5. Stevenson and the pragmatics of moral language 6. Stevenson and the methods for solving ethical disagreement 7. Hare and prescriptivism The chapter reconstructs first the discussion after Moore. The naturalistic-fallacy argument was widely accepted but twisted to prove instead that the intuitive character of the definition of 'good', its non-cognitive meaning, in a first phase identified with 'emotive' meaning. Alfred Julius Ayer is indicated as a typical proponent of such non-cognitivist meta-ethics. More detailed discussion is dedicated to Bertrand Russell's ethics, a more nuanced and sophisticated doctrine, arguing that non-cognitivism does not condemn morality to arbitrariness and that the project of rational normative ethics is still possible, heading finally to the justification of a kind of non-hedonist utilitarianism. Stevenson's theory, another moderate version of emotivism is discussed at some length, showing how the author comes close to the discovery of the role of a pragmatic dimension of language as a basis for ethical argument. A section reconstructs the discussion from the Forties about Hume's law, mentioning Karl Popper's argument and Richard Hare's early non-cognitivist but non-emotivist doctrine named prescriptivism. -/- ●IV Anglo-Saxon philosophy: critics of non-cognitivism 1. Neo-naturalism and its objections to the naturalistic fallacy argument 2. Objections to Hume's law 3. Clarence Lewis and the pragmatic contradiction 4. Toulmin and the good reasons approach 5. Baier and moral reasons 5. Baier, social moralities and the absolute morality 6. Baier and the moral point of view 7. Baier and the contents of absolute ethics -/- ● V Continental philosophy: the philosophy of values 1. Max Weber and the polytheism of values 2. Phenomenology against psychologism and rationalism 3. Reinach and the theory of social acts 4. Scheler and the material ethics of values 5. Hartmann and the ontology of values 6. Plessner, Gehlen and the Philosophische Anthropologie -/- The chapter illustrates first the idea of phenomenology and the Husserl's project of a phenomenological ethic as illustrated in his 1908-1914 lectures. The key idea is dismissing psychology and trying to ground a new science of the apriori of action, within which a more restricted field of inquiry will be the science of right actions. Then the chapter illustrates the criticism of modern moral philosophy conducted in the 1920 lectures, where the main target is naturalism, understood in the Kantian meaning of primacy of common sense. The third point illustrate is Adolph Reinach's theory of social acts as a key the grounding of norms, a view that sketches the ideas 'discovered' later by Clarence I. Lewis, John Searle, Karl-Otto Apel and Jürgen Habermas. A final section discusses Nicolai Hartman, who always refused to define himself a phenomenologist and yet developed a more articulated and detailed theory of 'values' – with surprising affinities with George E. Moore - than philosophers such as Max Scheler, who claimed to be Husserl's legitimate heirs. -/- ● VI Continental philosophy: the critics of the philosophy of values 1. Freud, the Superego and Civilization 2. Heidegger on original ethos against ethics 3. Sartre and de Beauvoir on authenticity and ambiguity 4. Adorno and Horkheimer on emancipation and immoralism -/- ●VII Post-liberal theologians and religious thinkers 1. Barth on the autonomy of faith from ethics 2. Developments of Reformed moral theology after Barth 3. Bonhoeffer on the concrete divine command and ethics of penultimate realities 4. Developments of Reformed and Catholic moral theology after world war II 5. Baeck and the transformation of liberal Judaism 6. Rosenzweig against liberal Judaism 7. Buber and religion as the vital lymph of morality 8. Heschel and Judaism as a science of actions -/- The chapter examines the main protagonists of Christian theology and Jewish religious thinking in the twentieth century. It stresses how the main dilemmas of contemporary philosophical ethics lie at the root of the various path of inquiry taken by these thinkers. -/- ● VIII Normative ethics: neo-Utilitarianism 1. The discussion on act and rule utilitarianism 2. Hare on two-tiered preference utilitarianism 3. Harsanyi, Gauthier and rational choice ethics 4. Parfit, utilitarianism and the idea of a person 5. Brandt and indirect conscience utilitarianism -/- The chapter addresses the issue of the complex process of self-transformation Utilitarianism underwent after Sidgwick's and Moore's fatal criticism and the unexpected Phoenix-like process of rebirth of a doctrine refuted. Two examples give the reader a glimpse at this uproarious process. The first is Roy Harrod Wittgensteinian transformation of utilitarianism in pure normative ethics depurated from hedonism as well as from whatsoever theory of the good. This transformation results in preference utilitarianism combined with a 'Kantian' version of rule utilitarianism. The second is Richard Hare's two-level preference utilitarianism, where act utilitarianism plays the function of the eventual rational justification of moral judgments and rule-utilitarianism that of an action-guiding practical device. -/- ● IX Normative ethics: neo-Aristotelianism and virtue ethics 1. Hannah Arendt, action and judgement 2. Hans-Georg Gadamer and phronesis 3. Alasdair MacIntyre on practices, virtues, and traditions 5. Stuart Hampshire on deliberation 6. Bernard Williams and moral complexity 7. Feminist ethics -/- Sect 1 reconstructs the post-war rediscovery of ethics by many German thinkers and its culmination in the Sixties in the movement named 'Rehabilitation of practical philosophy' is described. Heidegger's most brilliant disciples were the promoters of this Rehabilitation. Hans-Georg Gadamer is a paradigmatic example. His reading of Aristotle's lesson I reconstructed, starting with Heidegger's lesson but then subtly subverting its outcome thanks to the recovery of the significant role of the notion of phronesis. Sect 3 discusses the three theses defended by Anscombe in 'Modern Moral Philosophy'. It argues that: a) her answer to the question "why should I be moral?" requires a solution of the problem of theodicy, and ignores any attempts to save the moral point of view without recourse to divine retribution; b) her notion of divine law is an odd one more neo-Augustinian than Biblical or Scholastic; c) her image of Kantian ethics and intuitionism is the impoverished image manufactured by consequentialist opponents for polemical purposes and that she seems strangely accept it; d) the difficulty of identifying the "relevant descriptions" of acts is not an argument in favour of an ethics of virtue and against consequentialism or Kantian ethics, and indeed the role of judgment in the latter is a response to the difficulties raised by the case of judgment concerning future action. The chapter gives a short look at further developments in the neo-naturalist current trough a reconstruction of Philippa Foot's and Peter Geach's critiques to the naturalist-fallacy argument and Alasdair MacIntyre's grand reconstruction of the origins and allegedly inevitable failure of the Enlightenment project of an autonomous ethic. -/- ● X Normative ethics: Kantian and rights-based ethics 1. Dialogical constructivism 2. Apel, Habermas and discourse ethics 3. Gewirth and rights-based ethics 4. Nagel on agent-relative reasons 5. Donagan and persons as ends in themselves Parallel to the neo-Aristotelian trend, there was in the Rehabilitation of practical philosophy a Kantian current. This current started with the discovery of the pragmatic dimension of language carried out by Charles Peirce and the Oxford linguistic philosophy. On this basis, Karl-Otto Apel singled out as the decisive proponent of the linguistic and Kantian turn in German-speaking ethics, worked out the performative-contradiction argument while claiming that this was able to provide a new rational and universal basis for normative ethics. The chapter offers an examination of his argument in some detail, followed by a more cursory reconstruction of Jürgen Habermas's elaboration on Apel's theory. -/- ● XI The applied ethics renaissance 1. Elisabeth Anscombe on the atom bomb 2. From medical ethics to bioethics 3. Rawls and public ethics 3. Nozick, Dworkin and further developments of public ethics 5. Sen and the revival of economic ethics -/- The chapter presents the revolution of applied ethics while stressing its methodological novelty, exemplified primarily by Beauchamp and Childress principles approach and then by Jonsen and Toulmin's new casuistry. The chapter argues that Rawls's distinction between a "political" and a "metaphysical" approach to the theory of justice, one central part of ethical theory, is a formulation of the same basic idea at the root of both the principles approach and the new casuistry, both discussed in the following chapter. The idea is that it is possible to reach an agreement concerning positive moral judgments even though the discussion is still open – and in Rawls' view never will be close – on the essential criteria for judgment. -/- ● XII Fin-de-siècle metaethics 1. Deontic logics 2. Anti-realism 3. External realism 4. Internal realism 5. Kantian constructivism -/- The chapter illustrates the fresh start of meta-ethical discussion in the Eighties and Nineties and the resulting new alignments: metaphysical naturalism, internal realism, anti-realism, and constructivism. (shrink)

The depth-bounded approach seeks to provide realistic models of reasoners. Recognizing that most useful logics are idealizations in that they are either undecidable or likely to be intractable, the approach accounts for how they can be approximated in practice by resource-bounded agents. The approach has been applied to Classical Propositional Logic (CPL), yielding a hierarchy of tractable depth-bounded approximations to that logic, which in turn has been based on a KE/KI system. -/- This Thesis shows that the approach can be (...) naturally extended to useful nonclassical logics such as First-Degree Entailment (FDE), the Logic of Paradox (LP), Strong Kleene Logic (K3 ) and Intuitionistic Propositional Logic (IPL). To do this, we introduce a KE/KI-style system for each of those logics such that: is formulated via signed formulae, consist of linear operational rules and branching structural rule(s), can be used as a direct-proof and a refutation method, and is interesting independently of the approach in that it has an exponential speed-up on its tableau system counterpart. The latter given that we introduce a new class of examples which we prove to be hard for all tableau systems sharing the V/& rules with the classical one, but easy for their analogous KE-style systems. Then we focus on showing that each of our KE/KI-style systems naturally yields a hierarchy of tractable depth-bounded approximations to the respective logic, in terms of the maximum number of allowed nested applications of the branching rule(s). The rule(s) express(es) a generalized rule of bivalence, is (are) essentially cut rule(s) and govern(s) the manipulation of virtual information, which is information that an agent does not hold but she temporarily assumes as if she held it. Intuitively, the more virtual information needs to be invoked via the branching rule(s), the harder the inference is for the agent. So, the nested application the branching rule(s) provides a sensible measure of inferential depth. We also show that each hierarchy approximating FDE, LP, and K3 , admits of a 5-valued non-deterministic semantics; whereas, paving the way for a semantical characterization of the hierarchy approximating IPL, we provide a 3-valued non-deterministic semantics for the full logic that fixes the meaning of the connectives without appealing to “structural” conditions. -/- Moreover, we show a super-polynomial lower bound for the strongest possible version of clausal tableaux on the well-known class of “truly fat” expressions (which are easy for KE), settling a problem left open in the literature. Further, we investigate a hierarchy of tractable depth-bounded approximations to CPL based only on KE. Finally, we propose a refinement of the p-simulation relation which is adequate to establish positive results about the superiority of a system over another with respect to proof-search. (shrink)

Over 40 years ago I read a small grey book with metaphysics in the title which began with the words “Metaphysics is dead. Wittgenstein has killed it.” I am one of many who agree but sadly the rest of the world has not gotten the message. Shoemaker’s work is nonsense on stilts but is unusual only in that it never deviates into sense from the first paragraph to the last. At least with Dennett, Carruthers, Churchland etc. one gets a breath (...) of fresh air when they discuss cognitive science (imagining they are still doing philosophy). As W showed so beautifully, the confusions that lead to metaphysics are universal and nearly inescapable aspects of our psychology. They occur not only in all thinking on behavior but throughout science as well. It’s easy to find examples in Hawking, Weinberg, Penrose, Green, who of course have no idea they have left science and entered metaphysics, that the statement they just made is not a matter of fact at all but a matter of conceptual (linguistic) confusion. “Law, event, space, time, force, matter, proof, connection, cause, follows, physical”, etc., all have clear uses in certain technical contexts, but these blend insensibly into quite different uses that have little in common but the spelling. Since it is pointless to waste time deconstructing Shoemaker line by line, showing the same errors over and over, I will describe some facts about how our psychology (language) works and with this outline and the references I give it is quite straightforward to give a meaningful description of the world in place of the metaphysical fantasies. If I were to debate Shoemaker we would never get beyond the title. Horwich gives one of the most beautiful summaries of where an understanding of Wittgenstein leaves us that I have ever seen. “There must be no attempt to explain our linguistic/conceptual activity (PI 126) as in Frege’s reduction of arithmetic to logic; no attempt to give it epistemological foundations (PI 124) as in meaning based accounts of a priori knowledge; no attempt to characterize idealized forms of it (PI 130) as in sense logics; no attempt to reform it (PI 124, 132) as in Mackie’s error theory or Dummett’s intuitionism; no attempt to streamline it (PI 133) as in Quine’s account of existence; no attempt to make it more consistent (PI 132) as in Tarski’s response to the liar paradoxes; and no attempt to make it more complete (PI 133) as in the settling of questions of personal identity for bizarre hypothetical ‘teleportation’ scenarios.” Those wishing a comprehensive up to date framework for human behavior from the modern two systems view may consult my book ‘The Logical Structure of Philosophy, Psychology, Mind and Language in Ludwig Wittgenstein and John Searle’ 2nd ed (2019). Those interested in more of my writings may see ‘Talking Monkeys--Philosophy, Psychology, Science, Religion and Politics on a Doomed Planet--Articles and Reviews 2006-2019 3rd ed (2019) and Suicidal Utopian Delusions in the 21st Century 4th ed (2019). (shrink)

I argue that, given evidence of the factors that tend to distort our intuitions, ethical intuitionists should disown a wide range of common moral intuitions, and that they should typically give preference to abstract, formal intuitions over more substantive ethical intuitions. In place of the common sense morality with which intuitionism has traditionally allied, the suggested approach may lead to a highly revisionary normative ethics.

According to moral intuitionism, at least some moral seeming states are justification-conferring. The primary defense of this view currently comes from advocates of the standard account, who take the justification-conferring power of a moral seeming to be determined by its phenomenological credentials alone. However, the standard account is vulnerable to a problem. In brief, the standard account implies that moral knowledge is seriously undermined by those commonplace moral disagreements in which both agents have equally good phenomenological credentials supporting their disputed (...) moral beliefs. However, it is implausible to think that commonplace disagreement seriously undermines moral knowledge, and thus it is implausible to think that the standard account of moral intuitionism is true. (shrink)

Intuitionistic logic provides an elegant solution to the Sorites Paradox. Its acceptance has been hampered by two factors. First, the lack of an accepted semantics for languages containing vague terms has led even philosophers sympathetic to intuitionism to complain that no explanation has been given of why intuitionistic logic is the correct logic for such languages. Second, switching from classical to intuitionistic logic, while it may help with the Sorites, does not appear to offer any advantages when (...) dealing with the so-called paradoxes of higher-order vagueness. We offer a proposal that makes strides on both issues. We argue that the intuitionist’s characteristic rejection of any third alethic value alongside true and false is best elaborated by taking the normal modal system S4M to be the sentential logic of the operator ‘it is clearly the case that’. S4M opens the way to an account of higher-order vagueness which avoids the paradoxes that have been thought to infect the notion. S4M is one of the modal counterparts of the intuitionistic sentential calculus and we use this fact to explain why IPC is the correct sentential logic to use when reasoning with vague statements. We also show that our key results go through in an intuitionistic version of S4M. Finally, we deploy our analysis to reply to Timothy Williamson’s objections to intuitionistic treatments of vagueness. (shrink)

Although Fuzzy logic and Fuzzy Mathematics is a widespread subject and there is a vast literature about it, yet the use of Fuzzy issues like Fuzzy sets and Fuzzy numbers was relatively rare in time concept. This could be seen in the Fuzzy time series. In addition, some attempts are done in fuzzing Turing Machines but seemingly there is no need to fuzzy time. Throughout this article, we try to change this picture and (...) show why it is helpful to consider the instants of time as Fuzzy numbers. In physics, though there are revolutionary ideas on the time concept like B theories in contrast to A theory also about central concepts like space, momentum… it is a long time that these concepts are changed, but time is considered classically in all well-known and established physics theories. Seemingly, we stick to the classical time concept in all fields of science and we have a vast inertia to change it. Our goal in this article is to provide some bases why it is rational and reasonable to change and modify this picture. Here, the central point is the modified version of “Unexpected Hanging” paradox as it is described in "Is classical Mathematics appropriate for theory of Computation".This modified version leads us to a contradiction and based on that it is presented there why some problems in Theory of Computation are not solved yet. To resolve the difficulties arising there, we have two choices. Either “choosing” a new type of Logic like “Para-consistent Logic” to tolerate contradiction or changing and improving the time concept and consequently to modify the “Turing Computational Model”. Throughout this paper, we select the second way for benefiting from saving some aspects of Classical Logic. In chapter 2, by applying quantum Mechanics and Schrodinger equation we compute the associated fuzzy number to time. These, provides a new interpretation of Quantum Mechanics.More exactly what we see here is "Particle-Fuzzy time" interpretation of quantum Mechanics, in contrast to some other interpretations of Quantum Mechanics like " Wave-Particle" interpretation. At the end, we propound a question about the possible solution of a paradox in Physics, the contradiction between General Relativity and Quantum Mechanics. (shrink)

Shared conceptualization, in the sense we take it here, is as recent a notion as the Semantic Web, but its relevance for a large variety of fields requires efficient methods of extraction and representation for both quantitative and qualitative data. This notion is particularly relevant for the investigation into, and construction of, semantic structures such as knowledge bases and taxonomies, but given the required large, often inaccurate, corpora available for search we can get only approximations. We see fuzzy description (...) logic as an adequate medium for the representation of human semantic knowledge and propose a means to couple it with fuzzy semantic networks via the propositional Łukasiewicz fuzzy logic such that these suffice for decidability for queries over a semantic-knowledge base such as “to what degree of sharedness does it entail the instantiation C(a) for some concept C” or “what are the roles R that connect the individuals a and b to degree of sharedness ε.” . (shrink)

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)

The dissertation has two parts, each dealing with a problem, namely: 1) What is the most adequate account of fuzziness -the so-called phenomenon of vagueness?, and 2) what is the most plausible solution to the sorites, or heap paradox? I will try to show that fuzzy properties are those which are gradual, amenable to be possessed in a greater or smaller extent. Acknowledgement of degrees in the instantiation of a property allows for a gradual transition from one opposite to (...) the other, each intermediate stage constituting an overlap in certain proportion of both contraries. Hence, degrees in the possession of a property give rise to simple contradictions. The reason why I have chosen those two questions is that they provide the main philosophical motivation for a particular brand of an infinite valued and paraconsistent logic. I will claim that Classical logic (CL) is not adequate to handle fuzzy situations, and, being deficient, is in need of being expanded to make room for degrees of truth and weak contradictions. One can hardly deny the importance of the debate, since what is ultimately at stake is what the limits of truth, rationality, intelligibility and possibility are. The main disciplines within which the research moves are the philosophy of language, philosophy of logic, and ontology. (shrink)

It is proposed to analyze fuzzy concepts and relations between them in the frame of triplet concept modeling. Fuzzy concepts are introduced by means of the so-called fuzzification of dichotomous concepts. The cognitive and psychological aspects of concept possession are separated and studied.

Here algebraic Routley-Meyer semantics is addressed for two fuzzy versions of the logic of relevant implication R. To this end, two versions R t and R T of R and their fuzzy extensions FRt and FRT , respectively, are first discussed together with their algebraic semantics. Next algebraic Routley-Meyer semantics for these two fuzzy extensions is introduced. Finally, it is verified that these logics are sound and complete over the semantics.