The significance and use of absence of a thing is highlighted as its presence. The role of absence in various disciplines of mathematics, physics, semi-conductor electronics, computing and cognitive sciences for ease in conceptualizing is discussed. The use of null set, null vector and null matrix are also presented.

The significance and use of absence of a thing is highlighted taking examples from mathematics, physics, semi-conductor electronics, computer science and cognitive science. The profundity of absence is discussed.

Soonya Vaada, the prime and significant contribution to Indian philosophical thought from Buddhism will be scientifically developed and presented. How this scientific understanding helped to sow seeds of origin of rationalism and its development in Buddhist thought and life will be delineated. Its role in the shaping of Buddhist and other Indian philosophical systems will be discussed. Its relevance and use in the field of cognitive science and development of theories of human consciousness and mind will be put forward. The (...) idea of absence as zero in number system, vacuum in physics and other natural sciences and state of absence of cognition in mind machine modeling will be presented. The use of significance of Soonya Vaada in philosophy, rational social life, natural sciences and technology, mathematics and cognitive science will be comprehensively discussed and a model for human cognition and communication will be arrived at. -/- . (shrink)

$${{{\mathcal {F}}}}$$ -systems are useful digraphs to model sentences that predicate the falsity of other sentences. Paradoxes like the Liar and the one of Yablo can be analyzed with that tool to find graph-theoretic patterns. In this paper we studied this general model consisting of a set of sentences and the binary relation ‘ $$\ldots $$ affirms the falsity of $$\ldots $$ ’ among them. The possible existence of non-referential sentences was also considered. To model the sets of all (...) the sentences that can jointly be valued as true we introduced the notion of conglomerate, the existence of which guarantees the absence of paradox. Conglomerates also enabled us to characterize referential contradictions, i.e., sentences that can only be false under a classical valuation due to the interactions with other sentences in the model. A Kripke-style fixed-point characterization of groundedness was offered, and complete (meaning that every sentence is deemed either true or false) and consistent (meaning that no sentence is deemed true and false) fixed points were put in correspondence with conglomerates. Furthermore, argumentation frameworks are special cases of $$\mathcal{F}$$ -systems. We showed the relation between local conglomerates and admissible sets of arguments and argued about the usefulness of the concept for the argumentation theory. (shrink)

Description In this paper, we propose an advanced mathematical framework centered around the Energy Number Field (E), which fundamentally avoids the conventional concept of zero by introducing a neutral ele- ment, νE. Through this approach, we redefine core mathematical constructs, including limits, continuity, differentiation, integration, and series summation, ensuring they operate seamlessly within a zero-less paradigm. We address and redefine matrix operations, topology, metric spaces, and complex analysis, aligning them with the principles of E. Additionally, we explore non-mappable properties (...) of energy numbers in the context of symmetry groups, non-standard fields, fractional calculus, and non-Euclidean geometries. By employing νE as the central element, our framework resolves conventional zero-related sin- gularities and computational anomalies, offering a novel perspective that bridges advanced mathematical theories with practical applications in physics, computational algorithms, and topological transforma- tions. This work paves the way for future research to experimentally validate these formulations and explore potential applications in advanced physics, quantum mechanics, and beyond. (shrink)

This report offers a modern perspective on the problem of negative energy, based on a reexamination of the concept of time direction as it arises in a classical and quantum-mechanical context. From this analysis emerges an improved understanding of the general-relativistic stress-energy of matter as being a manifestation of local variations in the energy density of zero-point vacuum fluctuations. Based on those developments, a set of axioms is proposed from which are derived generalized gravitational field equations which actually constitute a (...) simplification of relativity theory in the presence of negative-energy matter and a non-zero cosmological constant. Important clarifications are also achieved regarding the nature of the binary degrees of freedom of matter in the final stages of a gravitational collapse. Those results are then applied to provide original solutions to several long-standing problems in cosmology, including the problem of the nature of dark matter and dark energy, that of the origin of thermodynamic time asymmetry, and several other issues traditionally approached using inflation theory. Finally, we draw on those developments to provide significant new insights into the foundations of quantum theory, regarding, in particular, the problem of quantum non-locality, that of the emergence of time in quantum cosmology, as well as the question of the persistence of quasiclassicality following decoherence. (shrink)

The explicit history of the “hidden variables” problem is well-known and established. The main events of its chronology are traced. An implicit context of that history is suggested. It links the problem with the “conservation of energy conservation” in quantum mechanics. Bohr, Kramers, and Slaters (1924) admitted its violation being due to the “fourth Heisenberg uncertainty”, that of energy in relation to time. Wolfgang Pauli rejected the conjecture and even forecast the existence of a new and unknown then elementary particle, (...) neutrino, on the ground of energy conservation in quantum mechanics, afterwards confirmed experimentally. Bohr recognized his defeat and Pauli’s truth: the paradigm of elementary particles (furthermore underlying the Standard model) dominates nowadays. However, the reason of energy conservation in quantum mechanics is quite different from that in classical mechanics (the Lie group of all translations in time). Even more, if the reason was the latter, Bohr, Cramers, and Slatters’s argument would be valid. The link between the “conservation of energy conservation” and the problem of hidden variables is the following: the former is equivalent to their absence. The same can be verified historically by the unification of Heisenberg’s matrix mechanics and Schrödinger’s wave mechanics in the contemporary quantum mechanics by means of the separable complex Hilbert space. The Heisenberg version relies on the vector interpretation of Hilbert space, and the Schrödinger one, on the wave-function interpretation. However the both are equivalent to each other only under the additional condition that a certain well-ordering is equivalent to the corresponding ordinal number (as in Neumann’s definition of “ordinal number”). The same condition interpreted in the proper terms of quantum mechanics means its “unitarity”, therefore the “conservation of energy conservation”. In other words, the “conservation of energy conservation” is postulated in the foundations of quantum mechanics by means of the concept of the separable complex Hilbert space, which furthermore is equivalent to postulating the absence of hidden variables in quantum mechanics (directly deducible from the properties of that Hilbert space). Further, the lesson of that unification (of Heisenberg’s approach and Schrödinger’s version) can be directly interpreted in terms of the unification of general relativity and quantum mechanics in the cherished “quantum gravity” as well as a “manual” of how one can do this considering them as isomorphic to each other in a new mathematical structure corresponding to quantum information. Even more, the condition of the unification is analogical to that in the historical precedent of the unifying mathematical structure (namely the separable complex Hilbert space of quantum mechanics) and consists in the class of equivalence of any smooth deformations of the pseudo-Riemannian space of general relativity: each element of that class is a wave function and vice versa as well. Thus, quantum mechanics can be considered as a “thermodynamic version” of general relativity, after which the universe is observed as if “outside” (similarly to a phenomenological thermodynamic system observable only “outside” as a whole). The statistical approach to that “phenomenological thermodynamics” of quantum mechanics implies Gibbs classes of equivalence of all states of the universe, furthermore re-presentable in Boltzmann’s manner implying general relativity properly … The meta-lesson is that the historical lesson can serve for future discoveries. (shrink)

A truth-preservation fallacy is using the concept of truth-preservation where some other concept is needed. For example, in certain contexts saying that consequences can be deduced from premises using truth-preserving deduction rules is a fallacy if it suggests that all truth-preserving rules are consequence-preserving. The arithmetic additive-associativity rule that yields 6 = (3 + (2 + 1)) from 6 = ((3 + 2) + 1) is truth-preserving but not consequence-preserving. As noted in James Gasser’s dissertation, Leibniz has been criticized for (...) using that rule in attempting to show that arithmetic equations are consequences of definitions. -/- A system of deductions is truth-preserving if each of its deductions having true premises has a true conclusion—and consequence-preserving if, for any given set of sentences, each deduction having premises that are consequences of that set has a conclusion that is a consequence of that set. Consequence-preserving amounts to: in each of its deductions the conclusion is a consequence of the premises. The same definitions apply to deduction rules considered as systems of deductions. Every consequence-preserving system is truth-preserving. It is not as well-known that the converse fails: not every truth-preserving system is consequence-preserving. Likewise for rules: not every truth-preserving rule is consequence-preserving. There are many famous examples. In ordinary first-order Peano-Arithmetic, the induction rule yields the conclusion ‘every number x is such that: x is zero or x is a successor’—which is not a consequence of the null set—from two tautological premises, which are consequences of the null set, of course. The arithmetic induction rule is truth-preserving but not consequence-preserving. Truth-preserving rules that are not consequence-preserving are non-logical or extra-logical rules. Such rules are unacceptable to persons espousing traditional truth-and-consequence conceptions of demonstration: a demonstration shows its conclusion is true by showing that its conclusion is a consequence of premises already known to be true. The 1965 Preface in Benson Mates (1972, vii) contains the first occurrence of truth-preservation fallacies in the book. (shrink)

The relationship between the One and the Multiple in mystic philosophy is a profound and central theme that explores the nature of existence, the cosmos, and the divine. This theme is present in various mystical traditions, including those of the East and West, and it addresses the paradoxical coexistence of the unity and multiplicity of all things. -/- In mystic philosophy, the **One** often represents the ultimate reality, the source from which all things emanate and to which all things return. (...) It is the absolute, the infinite, and the unchanging. The One is beyond all attributes and is often associated with the divine or the absolute truth. -/- The **Multiple**, on the other hand, represents the manifest world, the diversity of forms, and the realm of change and plurality. It is the world we experience through our senses, the domain of time and space, where differentiation and individuality are apparent. -/- The relationship between the One and the Multiple is not one of opposition but of emanation and unity. The Multiple is seen as a reflection, expression, or manifestation of the One. In this sense, the diversity of the world doesn’t contradict the unity of the One but rather demonstrates it in a myriad of forms. -/- Mystics seek to understand and experience this relationship through various practices and insights. They aim to transcend the illusion of separation and duality to experience the non-dual reality where the One and the Multiple are recognized as inseparable. -/- This concept can be illustrated by the metaphor of the ocean and its waves. The ocean represents the One—vast, deep, and all-encompassing—while the waves represent the Multiple—distinct, diverse, and ever-changing. Each wave is unique, yet it is not separate from the ocean. The wave’s existence is dependent on and made of the same substance as the ocean. In the same way, each individual entity in the Multiple is an expression of the One. -/- In summary, the relationship between the One and the Multiple in mystic philosophy is a dynamic interplay that challenges the conventional understanding of separation. It invites a deeper exploration of reality, where the apparent multiplicity of the world is a direct expression of the singular, underlying essence of all that is. -/- The relationship between the One and the Multiple in the context of mathematical philosophy is a profound topic that touches upon the very foundations of existence and knowledge. It’s a theme that has been explored by philosophers and mathematicians alike, often leading to the contemplation of unity and diversity within the structures of reality. -/- In mathematics, the concept of the One can be seen as the basis of unity from which all numbers derive. It’s the identity element in multiplication, the starting point in counting, and the foundation of dimension in geometry. The One is often associated with the concept of monism in philosophy, which posits that there is a single, underlying substance or principle that constitutes reality. -/- On the other hand, the Multiple represents the infinite variety and diversity of forms and numbers that arise from the One. It’s the embodiment of plurality and the complex interplay of different entities that mathematics seeks to understand and describe. This reflects the philosophical stance of pluralism, which acknowledges the existence of multiple realities or truths. -/- The interplay between the One and the Multiple can be seen in the mathematical concept of sets. A set can be thought of as a unity, a whole composed of distinct elements. Yet, each element within the set also retains its individuality, contributing to the diversity of the set’s composition. This duality is mirrored in the philosophical exploration of the universal and the particular, where the universal represents the One, and the particulars represent the Multiple. -/- In the realm of mathematical philosophy, this relationship often leads to questions about the nature of mathematical objects: Are they discovered as part of an objective reality (the One), or are they constructed by the human mind from a multitude of experiences (the Multiple)? This debate resonates with the philosophical inquiry into the nature of truth and reality. -/- Reflecting on the One and the Multiple can also lead to a deeper understanding of the self and the cosmos. Just as the number one is integral to the existence of all other numbers, the individual self can be seen as a unique expression of the universal whole. Similarly, the cosmos can be viewed as a grand unity composed of a multiplicity of forms and phenomena. -/- Gödel’s incompleteness theorems have a fascinating connection to the philosophical concepts of the One and the Multiple. These theorems, which are pivotal in mathematical logic and philosophy of mathematics, articulate the inherent limitations of formal axiomatic systems, particularly those sufficient to express the arithmetic of natural numbers. -/- Gödel’s incompleteness theorems have a fascinating connection to the philosophical concepts of the One and the Multiple. These theorems, which are pivotal in mathematical logic and philosophy of mathematics, articulate the inherent limitations of formal axiomatic systems, particularly those sufficient to express the arithmetic of natural numbers⁴. -/- The **first incompleteness theorem** reveals that within any such consistent system, there are propositions that are true but cannot be proven within the system itself. This reflects the idea of the Multiple in that there is an abundance of mathematical truths, a multiplicity that exceeds the unifying framework of any one system. It suggests that the realm of mathematical truth is more extensive than any single formal system can fully capture. -/- The **second incompleteness theorem** extends this by showing that a system cannot prove its own consistency. This relates to the concept of the One, as it implies that a system’s complete self-understanding, its unity and coherence, is unattainable from within. It must look beyond itself, to an external vantage point, to ascertain its consistency. -/- In the context of the One and the Multiple, Gödel’s theorems imply that the One (a consistent formal system) is inherently incomplete and cannot encompass the Multiple (the totality of mathematical truths). This resonates with philosophical discussions about the relationship between unity and plurality. Just as a single philosophical system cannot capture the entirety of truth, a single formal mathematical system cannot encapsulate all mathematical truths. -/- Moreover, Gödel’s work suggests that the pursuit of a single, unified theory of everything in mathematics—a One that encompasses all Multiples—is an inherently Sisyphean task. There will always be more truths (Multiples) than can be derived from any given set of axioms (the One). -/- In essence, Gödel’s incompleteness theorems provide a formal underpinning to the philosophical notion that the One cannot exist without the Multiple, and vice versa. They are interdependent, with the One giving rise to the Multiple, and the Multiple necessitating the One for its expression and comprehension. This interplay is a dance of limitations and possibilities, where the boundaries of logic, mathematics, and philosophy blur into one another. -/- The relationship between the One and the Multiple in the context of the mathematics of zero is a deeply philosophical inquiry that bridges the abstract world of numbers with the existential questions of being and non-being. -/- Zero, in mathematics, is a symbol of absence, a representation of nothingness, yet it holds a pivotal position as a number. It is the void from which all things emerge and to which they return. In the philosophy of mathematics, zero is the paradoxical junction where the One and the Multiple converge and diverge. -/- From the perspective of the One, zero can be seen as the origin—the singular point that precedes the existence of numbers. It is the empty set, the foundation upon which the edifice of mathematics is constructed. As the identity element in addition, zero maintains the integrity of numbers, for adding zero to any number leaves it unchanged, reflecting the immutable nature of the One. -/- Conversely, when we consider the Multiple, zero represents the infinite potentiality of creation. It is the canvas upon which the integers, both positive and negative, express their multitude. Zero is the balance point, the fulcrum around which the symphony of numbers dances. It embodies the plurality of possibilities, the beginning of the number line that stretches infinitely in both directions. -/- Philosophically, zero challenges our understanding of existence. It is both something and nothing—a number that quantifies the absence of quantity. This duality echoes the philosophical struggle to comprehend how the One gives rise to the Multiple. How does the unity of being manifest the diversity of the cosmos? Zero offers a mathematical metaphor for this mystery, as it encapsulates the transition from non-existence to existence, from the undifferentiated One to the differentiated Multiple. -/- In the realm of set theory, zero corresponds to the empty set—a set with no elements. This set is unique in that it is the only set that contains nothing, yet it is the foundation upon which all other sets are built. The empty set is the mathematical embodiment of the One, and all other sets, containing multiple elements, arise from it. -/- Reflecting on zero in the context of Gödel’s incompleteness theorems, we find a resonance with the idea that the One (a consistent formal system) cannot capture the entirety of the Multiple (the totality of mathematical truths). Zero, as the foundation of numbers, similarly suggests that from the nothingness of the One, the infinite complexity of the Multiple emerges—yet it can never be fully encompassed or expressed by any single system. -/- In conclusion, the mathematics of zero offers a profound reflection on the relationship between the One and the Multiple. It serves as a bridge between the abstract and the concrete, the known and the unknowable, challenging us to ponder the origins of existence and the nature of reality itself. -/- . (shrink)

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

The 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)

The Riemann zeta function ζ(s) is a central object in number theory and complex analysis, defined for complex variables and intimately connected to the distribution of prime numbers through its zeros. The famous Riemann Hypothesis conjectures that all non-trivial zeros of the zeta function lie on the critical line Re(s) = 1 2 . In this paper, we explore the Riemann zeta function through the lens of set-theoretic and sweeping net methods, leveraging creative comparisons of specific sets to gain deeper (...) insight into the distribution of its zeros. By rewording and analyzing the Riemann Hypothesis using set-theoretic arguments, applying sweeping net techniques, and integrating modal logic interpretations, we aim to provide new perspectives and support for this profound conjecture. Our objectives are: • Define the zeta function and its properties relevant to the zeros. • Reword the Riemann Hypothesis using set-theoretic language and establish logical equivalence. • Introduce and compare specific sets related to the zeros of ζ(s). • Apply set-theoretic and sweeping net methods to analyze the distribution of zeros. • Provide rigorous proofs about the absence of zeros in certain regions, including mechanical justifi- cations with all steps. • Incorporate modal logic interpretations into the proof. • Discuss implications for the Riemann Hypothesis. (shrink)

The objective of this paper is to study algebraic properties of neutrosophic matrices, where a necessary and sufficient condition for the invertibility of a square neutrosophic matrix is presented by defining the neutrosophic determinant. On the other hand, this work introduces the concept of neutrosophic Eigen values and vectors with an easy algorithm to compute them. Also, this article finds a necessary and sufficient condition for the diagonalization of a neutrosophic matrix.

This article studies the quantum effect of the brain neuronal system on both normal and abnormal conscious states. It develops Plasma Brain Dynamics (PBD) to obtain a set of kinetic quantum-plasma Wigner-Poisson equations. The model is established under typical electrostatic and collision-free conditions in both the absence and presence of an external magnetic field. The quantum perturbation is solved analytically by employing a backward-mapping approach to the motion of electrons. Results expose that the quantum perturbation turns out to be zero (...) at normal conscious states; but no more than 11% of the classical perturbation under assumed abnormal situations like a sudden head trauma, mood disorder, etc. The introduction of the magnetic field does not influence the results. (shrink)

This article consists in two parts that are complementary and autonomous at the same time. -/- In the first one, we develop some surprising consequences of the introduction of a new constant called Lambda in order to represent the object ``nothing" or ``void" into a standard set theory. On a conceptual level, it allows to see sets in a new light and to give a legitimacy to the empty set. On a technical level, it leads to a relative resolution of (...) the anomaly of the intersection of a family free of sets. -/- In the second part, we show the interest of introducing an operator of potentiality into a standard set theory. Among other results, this operator allows to prove the existence of a hierarchy of empty sets and to propose a solution to the puzzle of "ubiquity" of the empty set. -/- Both theories are presented with equi-consistency results (model and interpretation). -/- Here is a declaration of intent : in each case, the starting point is a conceptual questionning; the technical tools come in a second time\\[0.4cm] \textbf{Keywords:} nothing, void, empty set, null-class, zero-order logic with quantifiers, potential, effective, empty set, ubiquity, hierarchy, equality, equality by the bottom, identity, identification. (shrink)

The philosophy of education, being an integrative and anthropologic knowledge, has to perform a prognostic and axiological function, forming a perspective of a world-view genesis of personality and provide theoretical and methodological background for the innovation processes in the education. The forming of harmonious, intellectually developed, creative, conscientious, responsible, purposeful and healthy human personality – these are all the main tasks of the educational system. There are many approaches in performing of such strategic task. One of them, starting from the (...) urgency of a problem of sexual indifference of a modern school education, is presented in a single-sex format of education and is based upon individual approach to the education and upbringing of each and every pupil, taking into account the gender peculiarities of development. In this article we analyze the influence of a single-sex format of education on the process of forming of pupils’ personality, taking into account the age periodization of individual ontogenesis. We developed cognitive, motivational and psychological peculiarities of boys and girls during the periods of childhood and youth. Theoretical comprehension of a need in taking into consideration of the gender characteristics of pupils within the educational process – has been proved on practices, implementing the gender-orientated separate education in schools that demonstrates very positive results. There was made a conclusion about the fact, that the system of gender-orientated separated education has a strong potential of enhancing quality of a pedagogical process and helps to form the personalities of those who study. This can be achieved by taking into account the psychological, physiological and pedagogical peculiarities of boys and girls, by following in the process of educational activities the principals of egalitarianism, nature conformity, self-actualization, creative initiative, democracy and humanism, by creating of an environment, that will be free from impact of gender stereotypes and prejudice. (shrink)

The article explores the context and conceptual foundations of doxology - new project of epistemology proposed by Swedish professor Mats Rosengren. He reinterprets the basic concepts of epistemology, which were formed in the times of Plato and Aristotle. Swedish scholar is trying to rebuild the philosophy of knowledge, based on the updated system of initial abstractions. He inverts the traditional oppositions: knowledge (episteme) vs. opinion (doxa), philosophy vs. rhetoric. Thus, he takes the position of rhetorical philosophy, conceptually close to the (...) positions of the Greek sophists-rhetoricians. Rosengren gives a doxological interpretation of the Protagoras thesis about a human as a measure of all things. According to this account, human - it's all mankind; and the essence of humans, from the standpoint of the ancient Greeks, is human mind-logos. Rosengren thinks that protagorean approach, basal for doxology, has great heuristic potential. The heart of this approach is that all human knowledge is doxical, is not epistemic. And the task of doxology - to find out how we, humans, as social beings, really create the knowledge that can be examined as truth. (shrink)

According to the second law of thermodynamics, irreversible processes in an isolated system move towards the goal of reaching maximum entropy. In this state, mechanical work is converted to thermal energy and thermodynamic equilibrium occurs; which is determined by the equilibrium in temperature, pressure, etc. Assuming that the universe is an isolated system, the second law of thermodynamics states that the fate of the universe is a state of thermodynamic equilibrium in which all mechanical energies are converted to thermal energy (...) and the heat is dispersed all throughout the universe. In this state, there will be no movement and the universe will expire; an event called the “heat death”. This theory has certain theological implications that can serve as a proof for the perishability of the material world. And since decay implies creation, the heat death theory can be considered an argument in favor of the temporal originatedness of the material world. (shrink)

This dissertation concerns the active role of the organism in evolutionary theory. In particular, it concerns how our conception of the relationship between organism and environment, and the nature of natural selection, influences the causal and explanatory role of organismic activity and behavior in evolutionary explanations. The overarching aim is to argue that the behaviors and activities of organisms can serve both as the explananda (that which is explained) and the explanantia (that which explains) in evolutionary explanations. I attempt to (...) achieve this aim by offering three central arguments. First, that the organism-environment relation is the ontologically basic unit of biology. A common way of conceiving the relationship between organism and environment is as a duality—as two causally independent systems that overlap through interaction. I think this is a mistake. There cannot be organisms without environments and vice versa. They are codependent and codetermined. Second, that natural selection is an ecological process. By this I mean that natural selection acts primarily on organism-environment interactions. It is only in virtue of organisms interacting with their environments that there can be fitness differences amongst individual organisms in a population. The ecological approach to natural selection also entails that the nature of the system(s) of inheritance involved in the reoccurrence of favorable organism-environment interactions is, in principle, immaterial to the process of selection. It only matters for selection that organism-environment interactions actually do reoccur in subsequent generations. Third, that niche construction theory—the most well-developed theoretical and conceptual framework for studying how the activities of organisms influences evolutionary dynamics—can be seen as fully a compatible and integrated part of evolutionary theory. Together, these three arguments constitute an overarching argument. Namely that we both can, and should, take organismic activity and behavior to be crucial explanatory elements in evolutionary theory. Throughout the dissertation I also show how these three arguments have consequences for other debates in the philosophy of evolutionary theory, such as the nature of evolutionary processes, the structure of selection-based explanations, the validity and utility of the proximate-ultimate distinction, and the nature of teleology in evolutionary systems. (shrink)

Fundamental to Computer Science is the distinction between abstractions and implementations. When that distinction is applied to various philosophical questions it yields the following conclusions. -/- • EMERGENCE. It isn’t as mysterious as it’s made out to be; the possibility of strong emergence is not a threat to science. -/- • INTERACTIONS BETWEEN HIGHER-LEVEL ENTITIES. Physical interaction among higher-level entities is illusory. Abstract interactions are the source of emergence, new domains of knowledge, and complex systems. -/- • PHYSICS and the (...) SPECIAL SCIENCES. The new domains of knowledge derived from abstract interactions are the basis of the autonomy of the special sciences. -/- • DOWNWARD CAUSATION. It’s a zombie idea that should have a stake put through its heart and be replaced by downward entailment. (shrink)

An adequate account of the nature of genre and of the criteria for genre membership is essential to understanding the nature of the various categories into which comics can be classified. Because they fail adequately to distinguish genre categories from other ways of categorizing works, including categorizations according to medium or according to style, previous accounts of genre fail to illuminate the nature of comics categories. I argue that genres are sets of conventions that have developed as means of addressing (...) particular interpretative and/or evaluative concerns, and have a history of co‐instantiation within a community, such that a work’s belonging to some genre generates interpretative and evaluative expectations among the members of that community. Genres are distinct from styles in consisting of conventions, and are distinct from media both in consisting of conventions and in generating interpretative and evaluative expectations. (shrink)

Abstract: The aim behind analyzing Google Stock Prices dataset is to get a fair idea about the relationships between the multiple attributes a day might have, such as: the opening price for each day, the volume of trading for each day. With over a hundred thousand days of trading data, there are some patterns that can help in predicting the future prices. We proposed an Artificial Neural Network (ANN) model for predicting the closing prices for future days. The prediction is (...) based on these features (date, opening price, highest price, lowest price, volume), which were used as input variables and (closing price) as output variable for our ANN model. Our model was created, trained, and validated using data set in JNN environment, which its title is “Google-Stock-Prices”. The model evaluation showed that the ANN model is able to predict correctly 99.48% of the validation samples. (shrink)

The properties of angular momentum and its connection to magnetic momentum are explored, based on a reconsideration of the Stern-Gerlach experiment and gauge invariance. A possible way to solve the so called spin crisis is proposed. The separation of angular momentum of a quan- tum system of particles into orbital angular momentum plus intrinsic angular momentum is reconsidered, within the limits of the Schrodinger theory. A proof is given that, for systems of more than two particles, un- less all of (...) them have the same mass, the possibility of having eigenvalues of the form (n + 1/2)h is not excluded. (shrink)

My paper examines the problem of evil in its logical form, and along lines of African philosophizing. I construe the problematic nature of this problem [of evil] (hereafter, λ) as arising from a Western logical structure, which takes the valuation of propositions as being marked by a rigid bivalence of only truth (T) and falsity (F). By this structure, values and propositions are diametrically pitted against each other such that it appears that choice is only restrained to an ‘either’, ‘or’. (...) My argument transcends and dismantles this bivalence and subscribes to the African system of Ezumezu logic, developed by Jonathan Okeke Chimakonam which permits the pursuit of a trivalent logical course of ‘either’, ‘or’, in addition to ‘and’. Employing the logical system of Ezumezu, I demonstrate a negative resolution to λ, showing via the ‘principle of value-complementarity’, that good and evil as observed and experienced, are not opposites, but rather complements. The conclusions I draw from my analysis bear some implication for the conception of the Supreme Being; for one, I argue that conceiving the Supreme Being in African philosophy through the categories of the superlative ‘omni’ properties is mistaken , and also, I argue that this Supreme Being is better conceived as a harmony of good and evil: an embodiment of balance. (shrink)

Background: The most common hematological abnormality among people infected with Human Immunodeficiency Virus (HIV) is anemia. This is also related to high mortality risk among patients receiving Antiretroviral Therapy (ART). Purpose: This study aimed to identify predictors of anemia among HIV patients taking ART using a regimen of the single-tablet drug contain tenofovir, lamivudine, and efavirenz in Jayapura, Papua. Methods: This was a cross-sectional study conducted at Jayapura regional hospital from June to September 2017. A total of 80 HIV patients (...) were eligible for analysis. Data collection was conducted through an interview, medical record, measurement, and laboratory assay. The significance of differences among categorical variables was analyzed using Fisher’s exact test. The variables with p < 0.25 were then analyzed using binary logistic regression to determine predictors associated with anemia. A threshold of p < 0.05 indicates statistical significance. Results: This study showed that Body Mass Index (BMI) <18.50 (p = 0.01; OR = 5.63; 95% CI = 1.43 < OR < 22.19), length on ART ≤12 months (p = 0.00; OR = 4.90; 95% CI = 1.65 < OR < 14.53), and Cluster of Differentiation 4 (CD4+) percentage out of normal (p = 0.02; OR = 0.19; 95% CI = 0.05 < OR <0.77) had a significant association with anemia. Conclusion: BMI, length on ART, and CD4+ percentage were predictors of anemia among HIV patients taking antiretroviral therapy containing tenofovir, lamivudine, and efavirenz regimen in Jayapura. (shrink)

The increasing prevalence of mental health issues, particularly stress, has necessitated the development of data-driven, interpretable machine learning models for early detection and intervention. This study leverages multimodal data, including activity levels, perceived stress scores (PSS), and event counts, to predict stress levels among individuals. A series of models, including Logistic Regression, Random Forest, Gradient Boosting, and Neural Networks, were evaluated for their predictive performance. Results demonstrated that ensemble models, particularly Random Forest and Gradient Boosting, performed significantly better compared to (...) Logistic Regression. Random Forest achieved an accuracy of 73%, while Gradient Boosting delivered a balanced precision-recall tradeoff with an accuracy of 72%. Gradient Boosting outperformed in identifying high-stress instances, achieving a recall of 70%, making it the most reliable model for stress prediction. Explainable AI (XAI), which refers to the ability of machine learning models to provide transparent and understandable explanations for their predictions, was employed in this study using SHAP (SHapley Additive exPlanations). SHAP values revealed that Perceived Stress Score (PSS) had the most significant impact on predictions, followed by event count and activity inference. Higher PSS scores strongly correlated with high-stress predictions, while increased event counts and activity levels were associated with lower stress. These findings underscore the importance of incorporating behavioral patterns in stress diagnostics and highlight the utility of explainable models in improving transparency, trust, and usability for clinical decision-making. This research establishes a robust foundation for deploying interpretable machine learning systems to support mental health diagnostics and enhance clinician decision support. (shrink)

Since the early days of physics, space has called for means to represent, experiment, and reason about it. Apart from physicists, the concept of space has intrigued also philosophers, mathematicians and, more recently, computer scientists. This longstanding interest has left us with a plethora of mathematical tools developed to represent and work with space. Here we take a special look at this evolution by considering the perspective of Logic. From the initial axiomatic efforts of Euclid, we revisit the major milestones (...) in the logical representation of space and investigate current trends. In doing so, we do not only consider classical logic, but we indulge ourselves with modal logics. These present themselves naturally by providing simple axiomatizations of different geometries, topologies, space-time causality, and vector spaces. (shrink)

Terry Horgan and John Tienson have suggested that connectionism might provide a framework within which to articulate a theory of cognition according to which there are mental representations without rules (RWR) (Horgan and Tienson 1988, 1989, 1991, 1992). In essence, RWR states that cognition involves representations in a language of thought, but that these representations are not manipulated by the sort of rules that have traditionally been posited. In the development of RWR, Horgan and Tienson attempt to forestall a particular (...) line of criticism, theSyntactic Argument, which would show RWR to be inconsistent with connectionism. In essence, the argument claims that the node-level rules of connectionist networks, along with the semantic interpretations assigned to patterns of activation, serve to determine a set of representation-level rules incompatible with the RWR conception of cognition. The present paper argues that the Syntactic Argument can be made to show that RWR is inconsistent with connectionism. (shrink)

This paper discusses the possible classification of Aristotle’s syllogistic as a non-classical logical system, positing Aristotle himself as a non-classical logician. Initially, we find compelling arguments for this thesis, particularly regarding the expressive power and the rules governing logical inference inherent in Aristotle’s approach. My analysis nevertheless addresses two significant counterarguments. The first, the special case objection, posits that Aristotle’s syllogistic can be framed as a classical logic which deals with canonical syllogistic forms. I argue that this objection is insufficient, (...) as it is possible to point cases in which his system seems to differ from classical logic. The second counterargument, the formalisation gap objection, highlights that Aristotle’s syllogistic resists straightforward modern logical interpretations. This latter objection is evaluated as more compelling and substantial. In particular, a distinction between two concepts is proposed which could help us understand what Aristotle was aiming at in his theory of inference: the notions of ‘to follow from’ and ‘to be a conclusion of’. While the former aligns with the usual sense formal validity, the second requires an inferential structure connecting the premises to the conclusion, explaining why Aristotle excluded inferences like from A ⊢ A syllogisms despite acknowledging that A follows from A. (shrink)

Low physics learning in the Philippines is a prevailing concern the education sector must resolve, so initiating technological interventions in teaching the subject, including flipped classrooms, and introducing a chatbot such as ManyChat Delivering Online-Offline learning could be helpful to improve scientific literacy in learning Electromagnetic (EM) waves. This study aimed to determine the significant learning differences between conventional teaching (CT), Flipped Classroom (FC), and ManyChat Delivering Online-Offline (MCDOO) Learning in teaching EM waves. Previous research showed that flipped classrooms are (...) effective in Physics lessons. At the same time, only a few studies have been found using MCDOO learning effectively in other subjects, yet to be in Physics lessons. The researcher used the randomized posttest-only control group experimental research design with four groups; Conventional Teaching (CT) as the control group while the experimental groups are: Flipped Classroom (FC), ManyChat Delivering Online-Offline (MCDOO) Learning, and lastly, the combined FC+MCDOO learning who underwent different learning sessions (traditional teaching, FC session via google classroom, MCDOO session and FC+ MCDOO via Messenger App respectively). One-Way ANOVA was performed to determine whether there were any significant learning differences. The results showed in the first and second competencies; the null hypotheses are accepted, so all the differences in all four groups are not significant there is not much of a difference between the scores of CT and FC, CT and MCDOO, and FC and MCDOO learning; however, in the third learning competency, the null hypothesis is rejected so then the Tukey Post Hoc test was conducted to point out where is/are the significant difference/s. The Tukey Post Hoc test revealed that CT and FC+MCDOO learning differs significantly. It means that FC+MCDOO learning boosts higher learning achievement than conventional teaching, FC alone, or MCDOO alone. This study concludes that using just one technological intervention in Physics teaching simply cannot produce a significant impact on the physics literacy of the students in EM learning. Utilizing a combination of technological approaches can make a meaningful difference to the literacy rate in Physics lessons, specifically electromagnetic waves. (shrink)

Conceptual models as representations of real-world systems are based on diverse techniques in various disciplines but lack a framework that provides multidisciplinary ontological understanding of real-world phenomena. Concurrently, systems’ complexity has intensified, leading to a rise in developing models using different formalisms and diverse representations even within a single domain. Conceptual models have become larger; languages tend to acquire more features, and it is not unusual to use different modeling languages for different components. This diversity has caused problems with consistency (...) between models and incompatibly with designed systems. Two main solutions have been adopted over the last few years: (1) A currently dominant technology-based solution tries “to harmonize or unify” models, e.g., unifies EER and UML. This solution would solidify modeling achievements, reaping benefits from huge investments over the last thirty years. (2) A less prevalent solution is to pursuit deeper roots that reveal unifying modeling principles and apparatuses. An example of the second method is a “category theory”-based approach that utilizes the strengths of the graph and set theory, along with other topological tools. This manuscript is a sequel in a research venture that belongs to the second approach and uses a model called thinging machines (TMs) founded on Stoic ontology and Lupascian logic. TM modeling contests the thesis that there is no universal approach that covers all aspects of an application, and the paper demonstrates that pursuing such universality is anything but a dead-end method. This paper continues in this direction, with emphasis on TM foundation (e.g., existence and subsistence of things) and exemplifies this pursuit by proposing an alternative representation of set theory. (shrink)

This study was conducted by an academic research team at PRINCESS NOURAH BINT ABDULRAHMAN UNIVERSITY with the purpose of promoting the levels of healthy, value and ethical awareness among the students to limit the effects of covid-19. The study applied the descriptive, analytic survey approach to document the conceptions 0f the public education instructors throughout KSA concerning their role in raising the cognitive aspects and healthy and ethical skills for encountering coronavirus pandemic (COVID-19). The study population included all the instructors (...) of public education (male & female) in all the Kingdom governorates with its both public and private sectors amounting (525,610) instructors as per the MINISTRY OF EDUCAYION statistics for the school year (1441 H ) . The sample contained 357 instructors (male& female). For this purpose, the researchers designed a questionnaire. The study concluded that there is a high level of conceptions of the instructors about their cognitive skills, healthy and ethical responsibility for providing awareness about coronavirus pandemic (COVID-19) . The study proposes some supporting and effective strategies to achieve such online learning under this pandemic. (shrink)

The thesis I should like to advance in this essay is that Plato cannot and, in fact, does not adhere consistently to the doctrine that to know the good is to do the good. First, in order to display the paradoxes in the Platonic ethical system, I shall discuss the concept of the homogeneity of the good which Plato explicitly endorses. Second, by referring to Plato's practice, I shall endeavor to demonstrate that he treats the good as heterogeneous although this (...) treatment is inconsistent with his equation of knowledge with virtue. I shall use the descriptive phrase 'homogeneity of the good' to stand for that conception of the good which identifies the good exclusively with the moral good. I shall use the descriptive phrase 'heterogeneity of the good' to stand for that conception of the good which includes in the definition of good mixed pleasures or the natural good. Our understanding of the good as heterogeneous allows us to clarify many of the paradoxes present in Platonic ethics and affords us a deeper understanding of Plato. (shrink)

Althusius is undoubtedly the founder and connotation endower of the term “federation”. He explained the origin of the term as coming from “feudo”, which means feudal territory, covenant, agreement, and obligation. It is a group of people with a common purpose who, under the witness of God, sign a covenant stipulating that a ruler will be elected among them in some just manner, and the others will obey the ruler's commands. The author named this form of organization: federation. The family (...) is the most basic unit of a federation, or more bluntly, the family is the smallest federation. Can a king create another king with the same rights by transferring rights? Impossible. Because the rights of the recipient of the transferred rights are always less than those of the transferor. This is the process and essence of politics. In the author's view, politics, or rather, just politics, should be organized in the form of a federation. In this federal polity, the lower ranks are higher than the upper ranks, and the parts are greater than the whole. Because the lower ranks, parts, peripheries, and subordinates are eternal; while the upper ranks, the whole, the center, and the superiors are temporary, derivative, and created, and thus can also be taken away. Indeed, the authority of an individual citizen is less than that of the supreme magistrate as the head of the union. But the collective authority of the citizens is greater than the authority of the supreme magistrate. (shrink)

According to epistemic internalism, the only facts that determine the justificational status of a belief are facts about the subject’s own mental states, like beliefs and experiences. Externalists instead hold that certain external facts, such as facts about the world or the reliability of a belief-producing mechanism, affect a belief’s justificational status. Some internalists argue that considerations about evil demon victims and brains in vats provide excellent reason to reject externalism: because these subjects are placed in epistemically unfavorable settings, externalism (...) seems unable to account for the strong intuition that these subjects’ beliefs are nonetheless justified. I think these considerations do not at all help the internalist cause. I argue that by appealing to the anti-individualistic nature of perception, it can be shown that skeptical scenarios provide no reason to prefer internalism to externalism. (shrink)

I show that unlike her rationalist predecessor Leibniz, Du Châtelet is committed to epistemic causal idealism about natural causes. According to this view, it is constitutive of natural causes that they are in principle knowable by us (i.e., finite intelligent beings). Du Châtelet’s causal idealism stems at least in part from the distinctive theoretical role played by the Principle of Sufficient Reason in her system (as presented in her _Institutions de physique_), as well as her argument for the Principle of (...) Sufficient Reason. I show that far from merely explicating Leibniz’s metaphysics, Du Châtelet develops a radical and novel rationalism that is in keeping with her core commitment to science. (shrink)

Albert Jonsen and Stephen Toulmin have argued that the best way to resolve complex “moral” issues in clinical settings is to focus on the details of specific cases. This approach to medical decision-making, labeled ‘casuistry’, has met with much criticism in recent years. In response to this criticism, Carson Strong has attempted to salvage much of Jonsen’s and Toulmin’s version of casuistry. He concludes that much of their analysis, including Jonsen’s further elaboration about the casuistic methodology, is on the mark. (...) In this essay, the details of Jonsen’s and Toulmin’s version of casuistry and the major criticisms against their approach to clinical decision-making are explicated. Furthermore, it is argued that Strong’s salvage efforts fail to deflect these criticisms. The upshot of this analysis, which includes a few additional criticisms, is that Jonsen’s and Toulmin’s version of casuistry is not an appropriate framework from which to resolve complex “moral” issues in clinical settings. (shrink)

We consider the argument that Tarski's classic definitions permit an intelligence---whether human or mechanistic---to admit finitary evidence-based definitions of the satisfaction and truth of the atomic formulas of the first-order Peano Arithmetic PA over the domain N of the natural numbers in two, hitherto unsuspected and essentially different, ways: (1) in terms of classical algorithmic verifiabilty; and (2) in terms of finitary algorithmic computability. We then show that the two definitions correspond to two distinctly different assignments of satisfaction and truth (...) to the compound formulas of PA over N---I_PA(N; SV ) and I_PA(N; SC). We further show that the PA axioms are true over N, and that the PA rules of inference preserve truth over N, under both I_PA(N; SV ) and I_PA(N; SC). We then show: (a) that if we assume the satisfaction and truth of the compound formulas of PA are always non-finitarily decidable under I_PA(N; SV ), then this assignment corresponds to the classical non-finitary putative standard interpretation I_PA(N; S) of PA over the domain N; and (b) that the satisfaction and truth of the compound formulas of PA are always finitarily decidable under the assignment I_PA(N; SC), from which we may finitarily conclude that PA is consistent. We further conclude that the appropriate inference to be drawn from Goedel's 1931 paper on undecidable arithmetical propositions is that we can define PA formulas which---under interpretation---are algorithmically verifiable as always true over N, but not algorithmically computable as always true over N. We conclude from this that Lucas' Goedelian argument is validated if the assignment I_PA(N; SV ) can be treated as circumscribing the ambit of human reasoning about `true' arithmetical propositions, and the assignment I_PA(N; SC) as circumscribing the ambit of mechanistic reasoning about `true' arithmetical propositions. (shrink)

We enjoy sounds. What about silence: the absence of sound? Certainly not all, but surely many of us seek out, attend to, and appreciate silence. But, if nothing is there, then there is nothing to possess aesthetic qualities that might engage aesthetic interest or reward aesthetic attention. This is at least puzzling, perhaps even paradoxical. In this paper, I attempt to dispel the sense of paradox and provide a way to understand aesthetic appreciation of silence. I argue that silence can (...) have an aesthetic character and can sustain the kinds of rich experiences apt for aesthetic assessment and appraisal. (shrink)

In this article, I suggest that moksha (liberation or enlightenment) in Advaita Vedanta is best understood psychologically. A psychological understanding is not only consistent with the Advaita Vedanta articulated by Shankara and Gaudapada, but avoids what will be called the problem of jivan mukti. This article will consist of three main parts. First, I will briefly discuss the metaphysics and ontology of Advaita Vedanta. Next, I will present the problem of jivan mukti, and the Advaitin response to the problem. The (...) problem of jivan mukti will lead to the third portion of the article, which is a presentation of what moksha is. At no point in the article will I be arguing the truth of the Advaitin position. Instead, I will be meeting Advaita on its own terms in order to come to some understanding of moksha. (shrink)

Meta-laws, including conservation laws, are laws about the form of more specific, phenomenological, laws. Lange distinguishes between meta-laws as coincidences, where the meta-law happens to hold because the more specific laws hold, and meta-laws as constraints to which subsumed laws must conform. He defends this distinction as a genuine metaphysical possibility, such that metaphysics alone ought not to rule one way or another, leaving it an open question for physics. Lange’s distinction marks a genuine difference in how a given meta-law (...) can be used in explanations. Yet, I argue, it is not simply an empirical matter as to whether a given conservation law is a constraint or a coincidence. There is no set matter of fact about the world that determines this, and physics alone will not be able to return a determinate verdict on a law-by-law basis, even while there is a genuine difference between any given law as constraint and as coincidence. Rather, the difference marks different ways of treating the same law in a theoretical setting: by shifting the explanatory context, treating the same law as part of a different mathematical structure, it can be a genuine constraint and a genuine coincidence. The difference between constraint and coincidence relates to the way in which we use a law in specific theoretical and explanatory settings. Because the same law can appear in multiple contexts, it can be used in these genuinely different ways, without itself ‘‘really’’ being either one or the other as some atomistic empirical fact. Conservation laws as constraints and conservation laws as coincidences are both genuine theoretical roles that the same law can play. I conclude by considering how this pragmatist construal of constraints versus coincidences reveals how two parts of Lange’s work in this section of the book are unexpectedly independent of one another. -/- . (shrink)

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Even though the evidence‐based medicine movement (EBM) labels mechanisms a low quality form of evidence, consideration of the mechanisms on which medicine relies, and the distinct roles that mechanisms might play in clinical practice, offers a number of insights into EBM itself. In this paper, I examine the connections between EBM and mechanisms from several angles. I diagnose what went wrong in two examples where mechanistic reasoning failed to generate accurate predictions for how a dysfunctional mechanism would respond to intervention. (...) I then use these examples to explain why we should expect this kind of mechanistic reasoning to fail in systematic ways, by situating these failures in terms of evolved complexity of the causal system(s) in question. I argue that there is still a different role in which mechanisms continue to figure as evidence in EBM: namely, in guiding the application of population‐level recommendations to individual patients. Thus, even though the evidence‐based movement rejects one role in which mechanistic reasoning serves as evidence, there are other evidentiary roles for mechanistic reasoning. This renders plausible the claims of some critics of evidencebased medicine who point to the ineliminable role of clinical experience. Clearly specifying the ways in which mechanisms and mechanistic reasoning can be involved in clinical practice frames the discussion about EBM and clinical experience in more fruitful terms. (shrink)

The Russell's paradox concerns the foundations of naive set theory. This short short paper is about how it can be interpreted in other contexts and has significance in the world of commands. Understanding the paper assumes that the reader is broadly familiar with the foundations of set theory and its history. The text contains many formulas and therefore the reader should be comfortable in the world of logical formulas. My example is somewhat similar to the barber paradox. There, too, we (...) are puzzled by the feasibility of a task. In the case of the barber paradox there is a solution: the barber is a woman, in my example there is no such escape. (shrink)

I present three reasons why philosophers of science should be more concerned about violations of causal faithfulness (CF). In complex evolved systems, mechanisms for maintaining various equilibrium states are highly likely to violate CF. Even when such systems do not precisely violate CF, they may nevertheless generate precisely the same problems for inferring causal structure from probabilistic relationships in data as do genuine CF-violations. Thus, potential CF-violations are particularly germane to experimental science when we rely on probabilistic information to uncover (...) the DAG, rather than already knowing the DAG from which we could predict the right experiments to ‘catch out’ the hidden causal relationships. (shrink)

I discuss in this paper Aristotle’s definition of nature in Physics 192b 20-23. I intend to prove that this definition has to be taken as a set of three (not only two) conditions: the first condition just establishes that nature is a sort of cause; the second condition concerns the relationship between nature and the natural thing that has it as a cause; the third condition concerns the relationship between nature and the properties that natural things have from nature’s causality.

The material interpretation of conditionals is commonly recognized as involving some paradoxical results. I here argue that the truth functional approach to natural language is the reason for the inadequacy of this material interpretation, since the truth or falsity of some pair of statements ‘p’ and ‘q’ cannot per se be decisive for the truth or falsity of a conditional relation ‘if p then q’. This inadequacy also affects the ability of the overall formal system to establish whether or not (...) arguments involving conditionals are valid. I also demonstrate that the Paradox of Indicative Conditionals does not actually involve a paradox, but instead contains some paralogistic elements that make it appear to be a paradox. The discussion of the paradox in this paper further reveals that the material interpretation of conditionals adversely affects the treatment of disjunctions. -/- Much has been said about these matters in the literature that point in the same direction. However, there seems to be some reluctance against fully complying with the arguments against the truth functional account of conditionals, since many of the alternative accounts rely on the material conditional, or at least on an understanding of the conditional as a function of antecedent and consequent in a similar sense as the material conditional. My argument against truth functionality indicates that it may in general involve similar problems to treat conditionals as such functions, whether one deals with theories of truth, assertability or probability. (shrink)

In the late 1940s and early 1950s Lorenzen developed his operative logic and mathematics, a form of constructive mathematics. Nowadays this is mostly seen as the precursor to the more well-known dialogical logic and one could assumed that the same philosophical motivations were present in both works. However we want to show that this is not always the case. In particular, we claim, that Lorenzen’s well-known rejection of the actual infinite as stated in Lorenzen (1957) was not a major motivation (...) for operative logic and mathematics. In this article, we claim that this is in fact not the case. Rather, we argue for a shift that happened in Lorenzen’s treatment of the infinite from the early to the late 1950s. His early motivation for the development of operativism is concerned with a critique of the Cantorian notion of set and related questions about the notion of countability and uncountability; only later, his motivation switches to focusing on the concept of infinity and the debate about actual and potential infinity. (shrink)

In this paper I argue that, in Leibniz’s mature metaphysics, primary matter is not a positive constituent which must be added to the form in order to have a substance. Primary matter is merely a way to express the negation of some further perfection. It does not have a positive ontological status and merely indicates the limitation or imperfection of a substance. To be sure, Leibniz is less than explicit on this point, and in many texts he writes as if (...) primary matter were a positive constituent of a substance. It seems to me, however, that the view most in keeping with the thrust of his mature philosophical system is that captured by a striking remark of 1695: “Materia rerum est nihilum: id est limitatio [The matter of things is nothing: that is, limitation].” This becomes especially apparent in texts showing that Leibniz’s conception of primary matter corresponds to his conception of creaturely limitation. I start by discussing the notion of primary matter in the scholastic tradition. I then show that although Leibniz places the scholastic terminology of primary matter at a crucial juncture of his metaphysics, he thinks of primary matter in a way which significantly deviates from earlier scholastic views. I conclude that despite his adoption of distinctive terminology of Aristotelian scholasticism, instead of holding a broadly Aristotelian concept of primary matter as the ultimate subject of inherence, Leibniz thinks of primary matter according to a Neoplatonic blue-print in which matter is non-being, privation, mere absence of perfection. (shrink)

Short encyclopedia article on Peter Singer.