17 research outputs found

    Collected Papers (on various scientific topics), Volume XIII

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    This thirteenth volume of Collected Papers is an eclectic tome of 88 papers in various fields of sciences, such as astronomy, biology, calculus, economics, education and administration, game theory, geometry, graph theory, information fusion, decision making, instantaneous physics, quantum physics, neutrosophic logic and set, non-Euclidean geometry, number theory, paradoxes, philosophy of science, scientific research methods, statistics, and others, structured in 17 chapters (Neutrosophic Theory and Applications; Neutrosophic Algebra; Fuzzy Soft Sets; Neutrosophic Sets; Hypersoft Sets; Neutrosophic Semigroups; Neutrosophic Graphs; Superhypergraphs; Plithogeny; Information Fusion; Statistics; Decision Making; Extenics; Instantaneous Physics; Paradoxism; Mathematica; Miscellanea), comprising 965 pages, published between 2005-2022 in different scientific journals, by the author alone or in collaboration with the following 110 co-authors (alphabetically ordered) from 26 countries: Abduallah Gamal, Sania Afzal, Firoz Ahmad, Muhammad Akram, Sheriful Alam, Ali Hamza, Ali H. M. Al-Obaidi, Madeleine Al-Tahan, Assia Bakali, Atiqe Ur Rahman, Sukanto Bhattacharya, Bilal Hadjadji, Robert N. Boyd, Willem K.M. Brauers, Umit Cali, Youcef Chibani, Victor Christianto, Chunxin Bo, Shyamal Dalapati, Mario Dalcín, Arup Kumar Das, Elham Davneshvar, Bijan Davvaz, Irfan Deli, Muhammet Deveci, Mamouni Dhar, R. Dhavaseelan, Balasubramanian Elavarasan, Sara Farooq, Haipeng Wang, Ugur Halden, Le Hoang Son, Hongnian Yu, Qays Hatem Imran, Mayas Ismail, Saeid Jafari, Jun Ye, Ilanthenral Kandasamy, W.B. Vasantha Kandasamy, Darjan Karabašević, Abdullah Kargın, Vasilios N. Katsikis, Nour Eldeen M. Khalifa, Madad Khan, M. Khoshnevisan, Tapan Kumar Roy, Pinaki Majumdar, Sreepurna Malakar, Masoud Ghods, Minghao Hu, Mingming Chen, Mohamed Abdel-Basset, Mohamed Talea, Mohammad Hamidi, Mohamed Loey, Mihnea Alexandru Moisescu, Muhammad Ihsan, Muhammad Saeed, Muhammad Shabir, Mumtaz Ali, Muzzamal Sitara, Nassim Abbas, Munazza Naz, Giorgio Nordo, Mani Parimala, Ion Pătrașcu, Gabrijela Popović, K. Porselvi, Surapati Pramanik, D. Preethi, Qiang Guo, Riad K. Al-Hamido, Zahra Rostami, Said Broumi, Saima Anis, Muzafer Saračević, Ganeshsree Selvachandran, Selvaraj Ganesan, Shammya Shananda Saha, Marayanagaraj Shanmugapriya, Songtao Shao, Sori Tjandrah Simbolon, Florentin Smarandache, Predrag S. Stanimirović, Dragiša Stanujkić, Raman Sundareswaran, Mehmet Șahin, Ovidiu-Ilie Șandru, Abdulkadir Șengür, Mohamed Talea, Ferhat Taș, Selçuk Topal, Alptekin Ulutaș, Ramalingam Udhayakumar, Yunita Umniyati, J. Vimala, Luige Vlădăreanu, Ştefan Vlăduţescu, Yaman Akbulut, Yanhui Guo, Yong Deng, You He, Young Bae Jun, Wangtao Yuan, Rong Xia, Xiaohong Zhang, Edmundas Kazimieras Zavadskas, Zayen Azzouz Omar, Xiaohong Zhang, Zhirou Ma.‬‬‬‬‬‬‬

    Mathematical Explanation and Ontology: An Analysis of Applied Mathematics and Mathematical Proofs

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    The present work aims at providing an account of mathematical explanation in two different areas: scientific explanation and within mathematics. The research is addressed from two different perspectives: the one arising from an ontological concern about mathematical entities, and the other originating from a methodological choice: to study our chosen problems (mathematical explanation in science and in mathematics itself) in mathematical practice, that is to say, looking at the way mathematicians understand and perform their work in these diverse areas, including a case study for the context of intra-mathematical explanation. The central target is the analysis of the role that mathematical explanation plays in science and its relevance to the success or failure of scientific theories. The ontological question of whether the explanatory role of abstract objects, mathematical objects in particular, is enough to postulate their existence will be one of the issues to be addressed. Moreover, the possibility of a unified theory of explanation which can accommodate both external and internal mathematical explanation will also be considered. In order to go deeper into these issues, the research includes: (1) an analysis how the question of what is involved in internal mathematical explanation has been addressed in the literature, an analysis of the role of mathematical proof and the reasons why it makes sense to search for more explanatory proofs of already known results, and (2) an analysis of the relation between the use of mathematics in scientific explanation and the ontological commitment that arises from these explanatory tools in science. Part of the present work consists of an analysis of the explanatory role of mathematics through the study of cases reflecting this role. Case studies is one of the main sources of data in order to clarify the role mathematical entities play, among other methodological resources

    The art and architecture of mathematics education: a study in metaphors

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    This chapter presents the summary of a talk given at the Eighth European Summer University, held in Oslo in 2018. It attempts to show how art, literature, and history, can paint images of mathematics that are not only useful but relevant to learners as they can support their personal development as well as their appreciation of mathematics as a discipline. To achieve this goal, several metaphors about and of mathematics are explored

    Merging the Natural with the Artificial: The Nature of a Machine and the Collapse of Cybernetics

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    This thesis is concerned with the rise and fall of cybernetics, understood as an inquiry regarding the nature of a machine. The collapse of this scientific movement, usually explained by external factors such as lack of funding, will be addressed from a philosophical standpoint. Delving deeper into the theoretical core of cybernetics, one could find that the contributions of William Ross Ashby and John von Neumann shed light onto the particular ways in which cybernetics understood the nature and behavior of a machine. Ross Ashby offered an account of the nature of a machine and then extended the scope of “the mechanical”. This extension would encompass areas that will later be shown to be problematic for mechanization, such as learning and adaptation. The way in which a machine-ontology was applied would trigger effects seemingly contrary to cybernetics’ own distinctive features. Von Neumann, on the other hand, tinkered with a mechanical model of the brain, realizing grave limitations that prompted him to look for an alternative for cybernetics to work on. The proposal that came out of this resulted in a serious blow against the theoretical core of cybernetics. Why did cybernetics collapse? The contributions coming from both thinkers, in their own ways, spelled out the main tenets of the cybernetic proposal. But these very contributions led to cybernetics’ own demise. The whole story can be framed under the rubric of a serious inquiry into the metaphysical underpinnings of a machine. The rise and fall of cybernetics could thus help us better understand what a machine is from a philosophical standpoint. Although a historical component is present, my emphasis relies on a philosophical consideration of the cybernetic phenomenon. This metaphysical dissection will attempt to clarify how a machine-based ontology remained at the core of cybernetics. An emerging link will hopefully lead towards establishing a tri-partite correlation between cybernetics’ own evolution, its theoretical core, and its collapse. It will hopefully show how cybernetic inquiries into the nature of a machine might have proved fatal to the very enterprise at large, due to unsolvable theoretical tensions

    The Contemporary Encyclopedic Novel

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    This dissertation will define the contemporary American encyclopedic novel and the significant role that irony plays in shaping meaning. The dissertation constructs a model of the encyclopedic novel based upon the history of the encyclopedia – from Denis Diderot\u27s Enlightenment influenced Encyclopédie – and Northrop Frye\u27s conception of the encyclopedic form. It claims (1) that the contemporary encyclopedic novel continues in the cycle of modal progression toward mythic integration that Frye proposes in Anatomy of Criticism; and (2) that the encyclopedic novel utilizes different forms of irony to challenge authoritative discourse and elevate marginal discourse. The first chapter defines the encyclopedic novel by examining the history of the encyclopedia and existing criticism on the encyclopedic text in literature. It draws on theorists such as Denis Diderot and Richard Yeo to define an “encyclopedic project” that adopts a dialogic rhetorical style and seeks to democratize access to information. This chapter also defines the encyclopedic novel as a generic form that combines other forms into a unified whole and utilizes irony as a tool for integration. The second and third chapters form a thematic pairing that shows the self-reflexive progression of the encyclopedic novel from individualistic to humanistic focus. The second chapter argues that Thomas Pynchon\u27s Gravity\u27s Rainbow is an “anarchistic encyclopedic novel” that promotes associational thinking – in the form of paranoia, open forms, and horizontal transmission of knowledge. Gravity\u27s Rainbow adopts a disintegrative irony to empower the oppressed individual against industry-state collusion in the post-WWII era. The third chapter argues that David Foster Wallace\u27s Infinite Jest seeks to reinvent irony as an integrative force and redirect Pynchon\u27s individualistic anarchism toward an inclusive humanism. The fourth chapter demonstrates a break from both of the preceding chapter and argues that Leon Forrest\u27s Divine Days adopts a syndetic model of composition that further works to incorporate forms and integrate irony. Using Northrop Frye\u27s “interpenetration,” I argue that Divine Days integrates competing traditions and discourses by demonstrating their mutual-necessity. In the concluding chapter, I examine “meta-encyclopedic” by Jorge Luis Borges and Roberto Bolaño as an extension of the dissertation

    Peircean Interpretation of Postmodern Architecture

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    The influence of philosophy on architectural theory contributes to the formulation of architectural theory in the history of architecture. This relationship created the oscillation of architectural theory between rationalism and romanticism reflecting the woven tendency of philosophy such as enlightenment and counter- enlightenment movement. This dissertation research focuses on architectural language theory which maintains a tight relationship with the philosophy of language. Postmodern architecture during the period of the 1970s through 1980s is examined to determine meanings of architecture, and the language theory of architecture. It followed the philosophy of language originated from Ferdinand de Saussure who influenced theorists, and explicitly sign theorists influenced by Charles Sanders Peirce. This theoretical underpinning of language theory is questionable because of an inappropriate application of the sign theory of Charles Sanders Peirce in terms of principal interpretation of language structure, dyadic and triadic type of language. This research re-interprets the meaning of architecture during postmodern period along with Peirce's semeiotic theory, and American Pragmatism that Peirce originally invented. The collection of evidence from architectural history and the influence from philosophy provides a conceptual sketch that the oscillation of theoretical tendency is the source of architectural creation. This creative process is analyzable based on Peirce's sign theory and his logic. The research applies current Peircean scholars' development including 'Peircean Algebraic Logic' by Robert W. Burch to develop a conceptual model to frame Peircean interpretation. The multiple-case study (four architects with eight architectures) demonstrates the effectiveness of the conceptual model to facilitate a Peircean interpretation of postmodern scenographic architecture and contextual postmodern architecture. The results of this interpretation draws the limitation of some type of scenographic architecture that uses a proxy referential method, while Pragmatism provides the contents to Postmodernism's needs that is parallel to architectural theory

    Emergent Design

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    Explorations in Systems Phenomenology in Relation to Ontology, Hermeneutics and the Meta-dialectics of Design SYNOPSIS A Phenomenological Analysis of Emergent Design is performed based on the foundations of General Schemas Theory. The concept of Sign Engineering is explored in terms of Hermeneutics, Dialectics, and Ontology in order to define Emergent Systems and Metasystems Engineering based on the concept of Meta-dialectics. ABSTRACT Phenomenology, Ontology, Hermeneutics, and Dialectics will dominate our inquiry into the nature of the Emergent Design of the System and its inverse dual, the Meta-system. This is an speculative dissertation that attempts to produce a philosophical, mathematical, and theoretical view of the nature of Systems Engineering Design. Emergent System Design, i.e., the design of yet unheard of and/or hitherto non-existent Systems and Metasystems is the focus. This study is a frontal assault on the hard problem of explaining how Engineering produces new things, rather than a repetition or reordering of concepts that already exist. In this work the philosophies of E. Husserl, A. Gurwitsch, M. Heidegger, J. Derrida, G. Deleuze, A. Badiou, G. Hegel, I. Kant and other Continental Philosophers are brought to bear on different aspects of how new technological systems come into existence through the midwifery of Systems Engineering. Sign Engineering is singled out as the most important aspect of Systems Engineering. We will build on the work of Pieter Wisse and extend his theory of Sign Engineering to define Meta-dialectics in the form of Quadralectics and then Pentalectics. Along the way the various ontological levels of Being are explored in conjunction with the discovery that the Quadralectic is related to the possibility of design primarily at the Third Meta-level of Being, called Hyper Being. Design Process is dependent upon the emergent possibilities that appear in Hyper Being. Hyper Being, termed by Heidegger as Being (Being crossed-out) and termed by Derrida as Differance, also appears as the widest space within the Design Field at the third meta-level of Being and therefore provides the most leverage that is needed to produce emergent effects. Hyper Being is where possibilities appear within our worldview. Possibility is necessary for emergent events to occur. Hyper Being possibilities are extended by Wild Being propensities to allow the embodiment of new things. We discuss how this philosophical background relates to meta-methods such as the Gurevich Abstract State Machine and the Wisse Metapattern methods, as well as real-time architectural design methods as described in the Integral Software Engineering Methodology. One aim of this research is to find the foundation for extending the ISEM methodology to become a general purpose Systems Design Methodology. Our purpose is also to bring these philosophical considerations into the practical realm by examining P. Bourdieu’s ideas on the relationship between theoretical and practical reason and M. de Certeau’s ideas on practice. The relationship between design and implementation is seen in terms of the Set/Mass conceptual opposition. General Schemas Theory is used as a way of critiquing the dependence of Set based mathematics as a basis for Design. The dissertation delineates a new foundation for Systems Engineering as Emergent Engineering based on General Schemas Theory, and provides an advanced theory of Design based on the understanding of the meta-levels of Being, particularly focusing upon the relationship between Hyper Being and Wild Being in the context of Pure and Process Being

    Hilbert's Metamathematical Problems and Their Solutions

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    This dissertation examines several of the problems that Hilbert discovered in the foundations of mathematics, from a metalogical perspective. The problems manifest themselves in four different aspects of Hilbert’s views: (i) Hilbert’s axiomatic approach to the foundations of mathematics; (ii) His response to criticisms of set theory; (iii) His response to intuitionist criticisms of classical mathematics; (iv) Hilbert’s contribution to the specification of the role of logical inference in mathematical reasoning. This dissertation argues that Hilbert’s axiomatic approach was guided primarily by model theoretical concerns. Accordingly, the ultimate aim of his consistency program was to prove the model-theoretical consistency of mathematical theories. It turns out that for the purpose of carrying out such consistency proofs, a suitable modification of the ordinary first-order logic is needed. To effect this modification, independence-friendly logic is needed as the appropriate conceptual framework. It is then shown how the model theoretical consistency of arithmetic can be proved by using IF logic as its basic logic. Hilbert’s other problems, manifesting themselves as aspects (ii), (iii), and (iv)—most notably the problem of the status of the axiom of choice, the problem of the role of the law of excluded middle, and the problem of giving an elementary account of quantification—can likewise be approached by using the resources of IF logic. It is shown that by means of IF logic one can carry out Hilbertian solutions to all these problems. The two major results concerning aspects (ii), (iii) and (iv) are the following: (a) The axiom of choice is a logical principle; (b) The law of excluded middle divides metamathematical methods into elementary and non-elementary ones. It is argued that these results show that IF logic helps to vindicate Hilbert’s nominalist philosophy of mathematics. On the basis of an elementary approach to logic, which enriches the expressive resources of ordinary first-order logic, this dissertation shows how the different problems that Hilbert discovered in the foundations of mathematics can be solved
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