In light of the observations and research design presented in the previous reports, the current technical report is focused on the relationship between the quality and specificity of the content of the gambling sites and the site’s SEO and marketing policy. This relationship is dependent upon the category of the gambling site and the difference in content quality, and the degree to which the mathematical dimension of gambling is reflected in this content is explained by this dependence.

The near-miss has been considered an important factor of reinforcement in gambling behavior, and previous research has focused more on its industry-related causes and effects and less on the gaming phenomenon itself. The near-miss has usually been associated with the games of slots and scratch cards, due to the special characteristics of these games, which include the possibility of pre-manipulation of award symbols in order to increase the frequency of these “engineered” near-misses. In this paper, we argue that starting from (...) an elementary mathematical description of the classical (by pure chance) near-miss, generalizable to any game, and focusing equally on the epistemology of its constitutive concepts and their mathematical description, we can identify more precisely the fallacious elements of the near-miss cognitive effects and the inadequate perception and representation of the observational-intentional “I was that close.” This approach further suggests a strategy of using non-standard mathematical knowledge of an epistemological type in problem-gambling prevention and cognitive therapies. (shrink)

The author proposes in this practical guide for both problem and non-problem gamblers a new pragmatic, conceptual approach of gambling mathematics. The primary aim of this guide is the adequate understanding of the essence and complexity of gambling through its mathematical dimension. The author starts from the premise that formal gambling mathematics, which is hardly even digestible for the non-math-inclined gamblers, is ineffective alone in correcting the specific cognitive distortions associated with gambling. By applying the latest research results in this (...) field, the author blends the gambling-mathematics concepts with the epistemology of applied mathematics and cognitive psychology for providing gamblers the knowledge required for rational and safe gambling. (shrink)

The current technical report of the research project investigating how the mathematical dimension of gambling is reflected in the communication and texts associated with the gambling industry raises the problem of the adequacy of sampling and proposes a new approach in this respect. The qualitative analysis of the reviewed websites is extended to a deeper analysis of language and also to the organization and structure of websites’ content. Although not stated as a goal of the initial project, the research will (...) also try to identify relationships between the specificity of content relative to the mathematical dimension of gambling, and the management and marketing of the website. An overview of the results of the statistical analysis of the current sample is also presented. (shrink)

The current study evaluates qualitatively how the mathematical dimension of gambling is reflected in the content of gambling websites. A number of gambling websites have been reviewed for their content in that respect. A statistical analysis recorded the presence of the mathematical dimension of gambling and its forms in the content of the participating websites, and a qualitative research study analyzed and assessed the quality of the content with respect to that dimension. The technical reports associated with this study describe (...) the methods used in the processes of review and content analysis, details of the processes, and the specific challenges and difficulties that they posed. (shrink)

Randomness, a core concept of gambling, is seen in problem gambling as responsible for the formation of the math-related cognitive distortions, especially the Gambler’s Fallacy. In problem-gambling research, the concept of randomness was traditionally referred to as having a mathematical nature and categorized and approached as such. Randomness is not a mathematical concept, and I argue that its weak mathematical dimension is not decisive at all for the randomness-related issues in gambling and problem gambling, including the correction of the misconceptions (...) and fallacies about probability and statistical concepts applied in gambling. I distinguish between mathematical and nonmathematical dimensions of randomness (the epistemic, the theoretical-methodological, the functional, and the ethical) falling within the general concept, and I argue that both the studies having as object the math-related cognitive distortions among gamblers and the educational programs aiming at correcting them should employ this distinction in their design and content. (shrink)

The resolving of the main problem of quantum mechanics about how a quantum leap and a smooth motion can be uniformly described resolves also the problem of how a distribution of reliable data and a sequence of deductive conclusions can be uniformly described by means of a relevant wave function “Ψdata”.

The attempts of theoretically solving the famous puzzle-dictum of physicist Eugene Wigner regarding the “unreasonable” effectiveness of mathematics as a problem of analytical philosophy, started at the end of the 19th century, are yet far from coming out with an acceptable theoretical solution. The theories developed for explaining the empirical “miracle” of applied mathematics vary in nature, foundation and solution, from denying the existence of a genuine problem to structural theories with an advanced level of mathematical formalism. Despite this variation, (...) methodologically fundamental questions like “Which is the adequate theoretical framework for solving Wigner’s conjecture?” and “Can the logico-mathematical formalism solve it and is it entitled to do it?” did not receive answers yet. The problem of the applicability of mathematics in the physical reality has been treated unitarily in some sense, with respect to the semantic-conceptual use of the constitutive terms, within both the structural and non-structural theories. This unity (of consistency) applied to both the referred objects and concepts per se and the aims of the investigations. For being able to make an objective study of the possible alternatives of the existent theories, a foundational approach of them is needed, including through semantic-conceptual distinctions which to weaken the unity of consistency. (shrink)

The author studies the role of Christianity in two forms of 9th century political ethics in the history of Great Moravia, represented by the Great Moravian rulers Rastislav and Svatopluk. Rastislav’s conception predominantly uses the pre-Erasmian model of political ethics based on the pursuit of welfare for the country and its inhabitants by achieving the clerical-political independence of Great Moravia from the Frankish kingdom and, moreover, by utilising Christianity for the advancement of culture, education, literature, law and legality, as well (...) as by spreading Christian ethics and morality in the form of the Christian code of ethics expressed in ethicallegal documents. Svatopluk’s political conception was a prototype of Machiavellian political ethics, according to which one is, in the interest of the country and its power and fame, allowed to be a lion and/or a fox. Svatopluk abused Christianity in the name of achieving his power-oriented goals. Great Moravia outlived Rastislav; it did not, however, outlive Svatopluk, as, shortly after his death, it broke up and ceased to exist. The author came to the conclusion that Rastislav’s conception was more viable, as its cultural heritage lives on in the form of works by Constantine and Methodius. (shrink)

The main idea consists in researching the existence of certain characteristics of nature similar to human reasonability and purposeful actions, originating and rigorously inferable from the postulates of quantum mechanics as well as from those of special and general relativity. The pathway of the “free-will theorems” proved by Conway and Kochen in 2006 and 2009 is followed and pioneered further. Those natural reasonability and teleology are identified as a special subject called “God” and studyable by “quantum theology”, a scientific counterpart (...) of classical theology as far as the latter endeavors to justify rationally God (without quotation marks) postulated by religion, but meaning in the present study, first of all, Christianity. The suggested “quantum theology” is situated in the historical opposition and conflict of science and religion in Modernity and its reflection in Heidegger’s conception of “ontotheology”. The conception of “ontomathematics” introduced in previous papers to unite and unify physics, mathematics, and philosophy is reinterpreted in the present context to be conservatively generalized in a way to include “quantum theology”. Two conceptions, “locality” and “nonlocality”, originating initially from physics and especially, from theory of entanglement and quantum information, are also generalized ontomathematically, and thus in relation to the newly introduced “quantum theology”. The “quantum theology” subject of “God” is juxtaposed with God of religion and billions of believers all over the world. Husserl’s conception of “philosophy as a rigorous science” is considered to be generalized now to theology as quantum theology, particularly by the phenomenon (in the sense of his “phenomenology”) of “God”, or by an “epoché” to whether God exists or not. The research of the phenomenon of “God” is extended to the conception of the “totality” being inherent for philosophy, especially for classical German philosophy preceding Husserl’s phenomenology. Those sequences for philosophy implied by the introduction of quantum theology are investigated further, on the pathway of ontomathematics, also in relation to what “God” should mean for today’s physics and mathematics. The option and research field of “experimental quantum theology” is discussed as a direct corollary from quantum theology though being sacrilegious as for classical theology. The concluding section reflects in a more loose way on the relation of “God” for quantum theology to God for religion and billions of believers all over the world. (shrink)

The paper is the final, fifth part of a series of studies introducing the new conceptions of “Hilbert mathematics” and “ontomathematics”. The specific subject of the present investigation is the proper philosophical sense of both, including philosophy of mathematics and philosophy of physics not less than the traditional “first philosophy” (as far as ontomathematics is a conservative generalization of ontology as well as of Heidegger’s “fundamental ontology” though in a sense) and history of philosophy (deepening Heidegger’s destruction of it from (...) the pre-Socratics to the Pythagoreans). Husserl’s phenomenology and Heidegger’s derivative “fundamental ontology” as well as his later doctrine after the “turn” are the starting point of the research as established and well known approaches relative to the newly introduced conception of ontomathematics, even more so that Husserl himself started criticizing his “Philosophy of arithmetic” as too naturalistic and psychological turning to “Logical investigations” and the foundations of phenomenology. Heidegger’s “Aletheia” is also interpreted ontomathematically: as a relation of locality and nonlocality, respectively as a motion from nonlocality to locality if both are physically considered. Aristotle’s ontological revision of Plato’s doctrine is “destructed” further from the pre-Socratics' “Logos” or Heideger’s “Language” (after the “turn”) to the Pythagoreans “Numbers” or “Arithmetics” as an inherent and fundamental philosophical doctrine. Then, a leap to contemporary physics elucidates the essence of ontomathematics overcoming the Cartesian abyss inherited from Plato’s opposition of “ideas” versus “things”, and now unifying physics and mathematics, particularly allowing for the “creation from nothing” instead of the quasi-scientific myth of the “Big Bang”. Furthermore, ontomathematics needs another interpretation of arithmetic, propositional logic and set theory in the foundations of mathematics, where the latter two ones are both identified with Boolean algebra, and the former is considered to be a “half of Boolean algebra” in the exact meaning to be equated to it after doubling by a dual anti-isometric counterpart of Peano arithmetic. That unified algebraic realization of the foundations of mathematics is related to Hilbert mathematics in both “narrow and wide senses” where the latter is isomorphic to the qubit Hilbert space, thus underlying all the physical world by the newly introduced substance of quantum information being physically dimensionless and generalizing classical information measured in bits. The substance of information, whether classical or quantum, visualizes the way of the unification of physics and mathematics by merging their foundations in Hilbert arithmetic and Hilbert mathematics: thus how ontomathetics is a “first philosophy”. The relation of ontomathematics to the Socratic “human problematics”, furthermore being fundamental for Western philosophy in Modernity, is discussed. Ontomathematics implies its “substitution” by abstract information (or by “subjectless choice” relevant to it), thus “obliterating the human outline on the ocean beach sand” (by Michel Foucault’s metaphor). A reflection back from the viewpoint of mathematic to Western philosophy as the philosophy of locality ends the study. (shrink)

The paper is a partly provocative essay edited as a humanitarian study in philosophy of science and social philosophy, reflecting on the practical, “anti-metaphysical” turn taken place since the 20th century and continuing until now. The article advocates that it is about time it to be overcome because it is the main obstacle for the further development of exact and natural sciences including mathematics therefore restoring the unity of philosophy and sciences in the dawn of modern science when the great (...) scientists were philosophers as a necessary condition for their revolutionary achievements, and the physicists were simultaneously mathematicians not less than philosophers and even theologians as Descartes, Newton, Leibnitz were just as their predecessors, Copernicus or Galileo Galilei. The revolution in science accomplished by them needed philosophy since any scientific revolution, then necessarily growing into social, needs philosophy; and if ones wish to prevent social revolutions originating from fundamental scientific discoveries, in turn relying on the close link of sciences and philosophy, they are to cut the link at issue, and just that happened in the 20th centuries therefore implicitly heralding a “brave new world” of eternal normal science without revolutions whether scientific or social. Fukuyama’s “end of history” requires an “end of scientific history” as it is an obligatory premise, and separating sciences from philosophy is sufficient for that, though proclaimed quite otherwise: as overcoming metaphysics preventing sciences and substituting them by quasi-sciences. Particularly, that “anti-metaphysical turn” has established for science to obey society absolutely and thoroughly, obviously a condition contradicting the scientific and social revolutions in Modernity featured by the domination of science over society by the mediation of philosophy able to translate all epochal scientific discoveries as social corollaries. A special attention is paid to quantum mechanics, being the frontier of physics in the 20th century, where that anti-metaphysical turn is discernibly concentrated and may be notated by the famous slogan “Shut up and calculate!” regardless of its authorship. Just the revolutionary discoveries in physics, for example those of “dark mass” and “dark energy” or entanglement force now its rejection therefore restoring the unity of philosophy, mathematics and physics, made ever possible the establishment of modern science by its emancipation from religion, and thus and ind final analysis, from society. (shrink)

This is a partly provocative essay edited as a humanitarian study in philosophy of science and social philosophy. The starting point is Isaac Asimov’s famous sci-fi novella “Profession” (1957) to be “back” extrapolated to today’s relation between Thomas Kuhn’s “normal science” and “scientific revolutions” (1962). The latter should be accomplished by Asimov’s main personage George Platen’s ilk (called “feeble minded” in the novella) versus the “burned minded” professionals able only to “normal science”. Francis Fukuyama’s “end of history” in post-Hegelian manner (...) is now interpreted to an analogically supposed “end of scientific history” without “scientific revolutions” any more. The relevant dystopia of the prolonged or even “eternal” period of normal science is justified to the contemporary institution of science due to mechanisms such as “peer-review”, “impact-factor rating”, the projects’ competition for funding, etc. Positive feedbacks forcing all scientists needing careers to be more and more orthodox are demonstrated therefore establishing for that dystopia to be the real state of contemporary science. Two counterfactual case studies based correspondingly on Feyerabend’s “Against method” (1975) if Galilei should make his discoveries today and Sokal’s hoax (1996) if he suggested a scientific masterpiece to be really rejected by journals are discussed. Still one case study considering the abundance of Kelvin’s “clouds” on the horizon of today’s physics (dark matter, dark energy, entanglement, quantum gravitation, phenomena refuting the Big Bang, etc.) serves to verify the aforementioned conjecture that science has already entered that dystopia of eternal normal science. The conception of “ontomathematics” implying “creation ex nihilo” being scandalous for the dominating paradigm is sketched as an eventual revolutionary way out. An imaginary and utopic “happy end” reinterpreting the analogical “happy end” of Asimov’s “Profession” finishes the essay “instead of conclusion” relying on the Internet and AI in an increasingly “fluid” and anti-hierarchical society. (shrink)

Research on epistemic circularity has focused more on the problem of whether circular arguments are able to justify their conclusions rather than on the nature of circularity itself, and has kept a sharp delimitation from other types of circularities (logical, linguistic, and of definition). In this paper, I aim to move the focus toward the general concept of circularity, which I relate to the concept of ‘epistemic worry’. Through a brief overview on the known types of circularities, I show that (...) circularity has multiple natures (not only that associated with its type), and the linguistic aspect is essential in qualifying a construct as circular, which in turn raises the problem of genuineness of a circularity. Within an extensional approach, I suggest generalizing the meaning of the key epistemological terms referred to in the classical definition of epistemic circularity to also cover additional associated concepts specific to other theoretical disciplines beyond epistemology. The proposed concepts and ideas are reflected in a structural unificatory account of circularity in terms of epistemic determination, which raises a challenge to the relational accounts of determination in regard to the transitivity of the determination relation. (shrink)

The paper discusses this year’s Nobel Prize in physics for experiments of entanglement “establishing the violation of Bell inequalities and pioneering quantum information science” in a much wider, including philosophical context legitimizing by the authority of the Nobel Prize a new scientific area out of “classical” quantum mechanics relevant to Pauli’s “particle” paradigm of energy conservation and thus to the Standard model obeying it. One justifies the eventual future theory of quantum gravitation as belonging to the newly established quantum information (...) science. Entanglement, involving non-Hermitian operators for its rigorous description, non-unitarity as well as nonlocal and superluminal physical signals “spookily” (by Einstein’s flowery epithet) synchronizing and transferring some nonzero action at a distance, can be considered to be quantum gravity so that its local counterpart to be Einstein’s gravitation according to general relativity therefore pioneering an alternative pathway to quantum gravitation different from the “secondary quantization” of the Standard model. So, the experiments of entanglement once they have been awarded by the Nobel Prize launch particularly the relevant theory of quantum gravitation grounded on “quantum information science” thus granted to be nonclassical quantum mechanics in the shared framework of the generalized quantum mechanics obeying rather quantum-information conservation than only energy conservation. The concept of “dark phase” of the universe naturally linked to the very well confirmed “dark matter” and “dark energy” and opposed to its “light phase” inherent to classical quantum mechanics and the Standard model obeys quantum-information conservation, after which reversible causality or the mutual transformation of energy and information are valid. The mythical Big Bang after which energy conservation holds universally is to be replaced by an omnipresent and omnitemporal medium of decoherence of the dark and nonlocal phase into the light and local phase. The former is only an integral image of the latter and borrowed in fact rather from religion than from science. Physical, methodological and proper philosophical conclusions follow from that paradigm shift heralded by this year’s Nobel Prize in physics. For example, the scientific theory of thinking should originate from the dark phase of the universe, as well: probably only approximately modeled by neural networks physically belonging to the light phase thoroughly. A few crucial philosophical sequences follow from the break of Pauli’s paradigm: (1) the establishment of the “dark” phase of the universe as opposed to its “light” phase, only to which the Cartesian dichotomy of “body” and “mind” is valid; (2) quantum information conservation as relevant to the dark phase, furthermore generalizing energy conservation as to its light phase, productively allowing for physical entities to appear “ex nihilo”, i.e., from the dark phase, in which energy and time are yet inseparable from each other; (3) reversible causality as inherent to the dark phase; (4) the interpretation of gravitation only mathematically: as an interpretation of the incompleteness of finiteness to infinity, for example, following the Gödel dichotomy (“either contradiction or incompleteness”) about the relation of arithmetic to set theory; (5) the restriction of the concept of hierarchy only to the light phase; (6) the commensurability of both physical extremes of a quantum and the universe as a whole in the dark phase obeying quantum information conservation and akin to Nicholas of Cusa’s philosophical and theological worldview. (shrink)

The article addresses the necessity of increasing the role of mathematics in the psychological intervention in problem gambling, including cognitive therapies. It also calls for interdisciplinary research with the direct contribution of mathematics. The current contributions and limitations of the role of mathematics are analysed with an eye toward the professional profiles of the researchers. An enhanced collaboration between these two disciplines is suggested and predicted.

Games of chance are developed in their physical consumer-ready form on the basis of mathematical models, which stand as the premises of their existence and represent their physical processes. There is a prevalence of statistical and probabilistic models in the interest of all parties involved in the study of gambling – researchers, game producers and operators, and players – while functional models are of interest more to math-inclined players than problem-gambling researchers. In this paper I present a structural analysis of (...) the knowledge attached to mathematical models of games of chance and the act of modeling, arguing that such knowledge holds potential in the prevention and cognitive treatment of excessive gambling, and I propose further research in this direction. (shrink)

The paper examines the relationship between the biological and the social in morals. Its conclusion is that the biological is one among other sources of moarls. The social developed as another, much more dynamic source. An important role is played by free will or the moral freedom, especially on the individual morals level. It is the consequences, and especially social consequences, that in the author's viewpoint to the actual state of social and individual morals.

Gravitation is interpreted to be an “ontomathematical” force or interaction rather than an only physical one. That approach restores Newton’s original design of universal gravitation in the framework of “The Mathematical Principles of Natural Philosophy”, which allows for Einstein’s special and general relativity to be also reinterpreted ontomathematically. The entanglement theory of quantum gravitation is inherently involved also ontomathematically by virtue of the consideration of the qubit Hilbert space after entanglement as the Fourier counterpart of pseudo-Riemannian space. Gravitation can be (...) also interpreted as purely mathematical or logical “force” or “interaction” as a corollary from its ontomathematical (rather than physical) realization. The ontomathematical approach to gravitation is implicit in general relativity equating it to operators in pseudo-Riemannian space obeying the Einstein field equation and also well-known by the “geometrization of physics”. Quantum mechanics shares the same by the separable complex Hilbert space and defining “physical quantity” by the Hermitian operators on it. One can interpret special Minkowski space involved by special relativity and the qubit Hilbert space of quantum information as Fourier counterparts immediately noticing that general relativity means gravitation as the Fourier counterpart of non-Hermitian operators implying non-unitarity and the violation of energy conservation and thus destroying Pauli’s particle paradigm. Since the Standard model obeys it, this explains the impossibility of “quantum gravitation” in any framework conservatively generalizing the Standard model so that it would include gravitation along with electromagnetic, weak, and strong interactions. Einstein’s geometrization of gravitation can be continued into a purely mathematical theory of it following Euclid’s realization for geometry to be exhaustively built in a deductive and axiomatic way as well as Riemann’s parametrization of all the class of Euclidean and non-Euclidean geometries by “space curvature”, then being generalized to Minkowski space as the operators on pseudo-Riemannian space as the Einstein field equation means gravitation. The transition from mathematical gravitation to logical one can rely on the historical lesson of the pair of Lobachevski’s and Riemann’s approaches now “reversely”, i.e., from the latter to the former. Logical gravitation is linkable to Hegel’s dialectical logic and ontological dialectics abandoning their interpretations as a new zero logic substituting classical propionyl logic. The approach of ontomathematics generalizing that of ontology, traceable even to Aristotle’s reformation of Plato’s doctrine, needs Hegel’s doctrine to be formalized as a first-order logic naturally containing Boolean algebra, isomorphic to both classical propositional logic and set theory being the class of all first-order logics, as a sub-logic along with Peano arithmetic as another sub-logic. The first-order logic at issue is called Hilbert arithmetic and elaborated in detail in other papers. It allows for both self-foundation of mathematics to be internally proved as complete and furthermore, quantum mechanics reinterpreted as quantum information to be included by the qubit Hilbert space interpretable in turn as a dual and physical counterpart of Hilbert arithmetic in a narrow sense, that is, both counterparts constitute Hilbert arithmetic in a wide sense, being mathematical and physical simultaneously and thus overcoming the Cartesian dualism of “body” gapped from “mind” by an abyss. Then, the proper philosophical interpretation of gravitation to be the fundamental ontomathematical force or interaction overcomes the ridiculous belief of the Big Bang wrongly alleged to be a scientific theory. Ontomathematical gravitation suggests an omnipresent and omnitemporal medium of “God’s” creation “ex nihilo” following only the natural necessity of quantum-information conservation particularly and locally manifested as energy conservation. (shrink)

Slot machines gained a high popularity despite a specific element that could limit their appeal: non-transparency with respect to mathematical parameters. The PAR sheets, exposing the parameters of the design of slot machines and probabilities associated with the winning combinations are kept secret by game producers, and the lack of data regarding the configuration of a machine prevents people from computing probabilities and other mathematical indicators. In this article, I argue that there is no rational justification for this secrecy by (...) giving two reasons, one psychological and the other mathematical. For the latter, I show that mathematics provides us with some statistical methods of retrieving the missing data, which are essential for the numerical probability computations in slots. The slots case raises the problem of the exposure of the parametric configuration and mathematical facts of any game of chance as an ethical obligation. (shrink)

The paper discusses Hilbert mathematics, a kind of Pythagorean mathematics, to which the physical world is a particular case. The parameter of the “distance between finiteness and infinity” is crucial. Any nonzero finite value of it features the particular case in the frameworks of Hilbert mathematics where the physical world appears “ex nihilo” by virtue of an only mathematical necessity or quantum information conservation physically. One does not need the mythical Big Bang which serves to concentrate all the violations of (...) energy conservation in a “safe”, maximally remote point in the alleged “beginning of the universe”. On the contrary, an omnipresent and omnitemporal medium obeying quantum information conservation rather than energy conservation permanently generates action and thus the physical world. The utilization of that creation “ex nihilo” is accessible to humankind, at least theoretically, as long as one observes the physical laws, which admit it in their new and wider generalization. One can oppose Hilbert mathematics to Gödel mathematics, which can be identified as all the standard mathematics until now featureable by the Gödel dichotomy of arithmetic to set theory: and then, “dialectic”, “intuitionistic”, and “Gödelian” mathematics within the former, according to a negative, positive, or zero value of the distance between finiteness and infinity. A mapping of Hilbert mathematics into pseudo-Riemannian space corresponds, therefore allowing for gravitation to be interpreted purely mathematically and ontologically in a Pythagorean sense. Information and quantum information can be involved in the foundations of mathematics and linked to the axiom of choice or alternatively, to the field of all rational numbers, from which the pair of both dual and anti-isometric Peano arithmetics featuring Hilbert arithmetic are immediately inferable. Noether’s theorems (1918) imply quantum information conservation as the maximally possible generalization of the pair of the conservation of a physical quantity and the corresponding Lie group of its conjugate. Hilbert mathematics can be interpreted from their viewpoint also after an algebraic generalization of them. Following the ideas of Noether’s theorem (1918), locality and nonlocality can be realized both physically and mathematically. The “light phase of the universe” can be linked to the gap of mathematics and physics in the Cartesian organization of cognition in Modernity and then opposed to its “dark phase”, in which physics and mathematics are merged. All physical quantities can be deduced from only mathematical premises by the mediation of the most fundamental physical constants such as the speed of light in a vacuum, the Planck and gravitational constants once they have been interpreted by the relation of locality and nonlocality. (shrink)

The paper continues the consideration of Hilbert mathematics to mathematics itself as an additional “dimension” allowing for the most difficult and fundamental problems to be attacked in a new general and universal way shareable between all of them. That dimension consists in the parameter of the “distance between finiteness and infinity”, particularly able to interpret standard mathematics as a particular case, the basis of which are arithmetic, set theory and propositional logic: that is as a special “flat” case of Hilbert (...) mathematics. The following four essential problems are considered for the idea to be elucidated: Fermat’s last theorem proved by Andrew Wiles; Poincaré’s conjecture proved by Grigori Perelman and the only resolved from the seven Millennium problems offered by the Clay Mathematics Institute (CMI); the four-color theorem proved “machine-likely” by enumerating all cases and the crucial software assistance; the Yang-Mills existence and mass gap problem also suggested by CMI and yet unresolved. They are intentionally chosen to belong to quite different mathematical areas (number theory, topology, mathematical physics) just to demonstrate the power of the approach able to unite and even unify them from the viewpoint of Hilbert mathematics. Also, specific ideas relevant to each of them are considered. Fermat’s last theorem is shown as a Gödel insoluble statement by means of Yablo’s paradox. Thus, Wiles’s proof as a corollary from the modularity theorem and thus needing both arithmetic and set theory involves necessarily an inverse Grothendieck universe. On the contrary, its proof in “Fermat arithmetic” introduced by “epoché to infinity” (following the pattern of Husserl’s original “epoché to reality”) can be suggested by Hilbert arithmetic relevant to Hilbert mathematics, the mediation of which can be removed in the final analysis as a “Wittgenstein ladder”. Poincaré’s conjecture can be reinterpreted physically by Minkowski space and thus reduced to the “nonstandard homeomorphism” of a bit of information mathematically. Perelman’s proof can be accordingly reinterpreted. However, it is valid in Gödel (or Gödelian) mathematics, but not in Hilbert mathematics in general, where the question of whether it holds remains open. The four-color theorem can be also deduced from the nonstandard homeomorphism at issue, but the available proof by enumerating a finite set of all possible cases is more general and relevant to Hilbert mathematics as well, therefore being an indirect argument in favor of the validity of Poincaré’s conjecture in Hilbert mathematics. The Yang-Mills existence and mass gap problem furthermore suggests the most general viewpoint to the relation of Hilbert and Gödel mathematics justifying the qubit Hilbert space as the dual counterpart of Hilbert arithmetic in a narrow sense, in turn being inferable from Hilbert arithmetic in a wide sense. The conjecture that many if not almost all great problems in contemporary mathematics rely on (or at least relate to) the Gödel incompleteness is suggested. It implies that Hilbert mathematics is the natural medium for their discussion or eventual solutions. (shrink)

The paper develops the theory of right action in ethics of social consequences as a form of non-utilitarian consequentialism.

The previous Part I of the paper discusses the option of the Gödel incompleteness statement (1931: whether “Satz VI” or “Satz X”) to be an axiom due to the pair of the axiom of induction in arithmetic and the axiom of infinity in set theory after interpreting them as logical negations to each other. The present Part II considers the previous Gödel’s paper (1930) (and more precisely, the negation of “Satz VII”, or “the completeness theorem”) as a necessary condition for (...) granting the Gödel incompleteness statement to be a theorem just as the statement itself, to be an axiom. Then, the “completeness paper” can be interpreted as relevant to Hilbert mathematics, according to which mathematics and reality as well as arithmetic and set theory are rather entangled or complementary rather than mathematics to obey reality able only to create models of the latter. According to that, both papers (1930; 1931) can be seen as advocating Russell’s logicism or the intensional propositional logic versus both extensional arithmetic and set theory. Reconstructing history of philosophy, Aristotle’s logic and doctrine can be opposed to those of Plato or the pre-Socratic schools as establishing ontology or intensionality versus extensionality. Husserl’s phenomenology can be analogically realized including and particularly as philosophy of mathematics. One can identify propositional logic and set theory by virtue of Gödel’s completeness theorem (1930: “Satz VII”) and even both and arithmetic in the sense of the “compactness theorem” (1930: “Satz X”) therefore opposing the latter to the “incompleteness paper” (1931). An approach identifying homomorphically propositional logic and set theory as the same structure of Boolean algebra, and arithmetic as the “half” of it in a rigorous construction involving information and its unit of a bit. Propositional logic and set theory are correspondingly identified as the shared zero-order logic of the class of all first-order logics and the class at issue correspondingly. Then, quantum mechanics does not need any quantum logics, but only the relation of propositional logic, set theory, arithmetic, and information: rather a change of the attitude into more mathematical, philosophical, and speculative than physical, empirical and experimental. Hilbert’s epsilon calculus can be situated in the same framework of the relation of propositional logic and the class of all mathematical theories. The horizon of Part III investigating Hilbert mathematics (i.e. according to the Pythagorean viewpoint about the world as mathematical) versus Gödel mathematics (i.e. the usual understanding of mathematics as all mathematical models of the world external to it) is outlined. (shrink)

Research on interdisciplinarity has been concentrated on the methodological and educational aspects of this complex phenomenon and less on its theoretical nature. Within a theoretical framework specific to the philosophy of science, I propose a structural scheme of how interdisciplinary processes go, focusing on the concepts of availability of the methods, concept linking, and theoretical modeling. In this model, the challenges interdisciplinarity is claimed to pose to its practitioners are of the same nature as the challenges scientists encounter within the (...) evolution of their own disciplines. (shrink)

The paper is concentrated on the special changes of the conception of causality from quantum mechanics to quantum information meaning as a background the revolution implemented by the former to classical physics and science after Max Born’s probabilistic reinterpretation of wave function. Those changes can be enumerated so: (1) quantum information describes the general case of the relation of two wave functions, and particularly, the causal amendment of a single one; (2) it keeps the physical description to be causal by (...) the conservation of quantum information and in accordance with Born’s interpretation; (3) it introduces inverse causality, “backwards in time”, observable “forwards in time” as the fundamentally random probability density distribution of all possible measurements of any physical quantity in quantum mechanics; (4) it involves a kind of “bidirectional causality” unifying (4.1) the classical determinism of cause and effect, (4.2) the probabilistic causality of quantum mechanics, and (4.3) the reversibility of any coherent state; (5) it identifies determinism with the function successor in Peano arithmetic, and its proper generalized causality with the information function successor in Hilbert arithmetic. (shrink)

The paper questions the scientific rather than ideological problem of an eventual biological successor of the mankind. The concept of superhumans is usually linked to Nietzsche or to Heidegger’s criticism or even to the ideology of Nazism. However, the superhuman can be also viewed as that biological species who will originate from humans eventually in the course of evolution.While the society is reached a natural limitation of globalism, technics depends on the amount of utilized energy, and the mind is restricted (...) by its carrier, i.e. by the brain, it is language which seems to be the frontier of any future development of humans or superhumans. Language is a symbolization of the world and thus doubling in an ideal or virtual world fruitful for creativity and the modeling of the former. Consequently, the gap between the material and the ideal world is both produced by and productive for language. (shrink)

Хайдегер има цикъл статии, посветени на немския поет Хьолдерлин и обсъждащи отношението на философия и поезия. Една често срещана "дума" в тях е 'природа'. Нейни рзлични конотации в произведения на философа за поета са предмет на изследване.

Peano arithmetic cannot serve as the ground of mathematics for it is inconsistent to infinity, and infinity is necessary for its foundation. Though Peano arithmetic cannot be complemented by any axiom of infinity, there exists at least one (logical) axiomatics consistent to infinity. That is nothing else than a new reading at issue and comparative interpretation of Gödel’s papers (1930; 1931) meant here. Peano arithmetic admits anyway generalizations consistent to infinity and thus to some addable axiom(s) of infinity. The most (...) utilized example of those generalizations is the complex Hilbert space. Any generalization of Peano arithmetic consistent to infinity, e.g. the complex Hilbert space, can serve as a foundation for mathematics to found itself and by itself. (shrink)

În acest volum, autorul prezintă în mod critic modelele teoretice dezvoltate pentru a reprezenta aplicarea şi aplicabilitatea matematicii în ştiinţe şi universul fizic, oferind soluţii constructive care răspund obiecţiilor fundamentale ridicate la aceste modele. Atenţia principală este acordată modelelor structurale, deoarece noţiunea de structură matematică intervine esenţial atât în caracterizarea matematicii pure, cât şi aplicate, iar procesele mentale implică la rândul lor reprezentări de tip structural. Propunerile făcute, atât ca alternative structurale, cât şi prin noile cadre conceptuale şi metodologiile implicite, (...) vor fi analizate inclusiv în vederea posibilităţii unei unificări teoretice, către un model unic al aplicării şi aplicabilităţii matematicii, care să ofere justificarea metateoretică a utilizării matematicii ca metodă ştiinţifică de prim rang şi să contribuie cu aport explicativ la rezolvarea “misterelor” filosofice care înconjoară aplicabilitatea matematicii. -/- Lucrarea completează primul volum, dedicat puzzle-ului lui Wigner privind ‘eficacitatea iraţională a matematicii’ şi soluţiilor oferite la acesta, adresându-se în special – dar nu exclusiv – matematicienilor, fizicienilor, filosofilor ştiinţei, filosofilor limbajului şi epistemologilor, dar şi studenţilor acestor discipline. (shrink)

This is not a mathematics book, but a book about mathematics, which addresses both student and teacher, with a goal as practical as possible, namely to initiate and smooth the way toward the student’s full understanding of the mathematics taught in school. The customary procedural-formal approach to teaching mathematics has resulted in students’ distorted vision of mathematics as a merely formal, instrumental, and computational discipline. Without the conceptual base of mathematics, students develop over time a “mathematical anxiety” and abandon any (...) effort to understand mathematics, which becomes their “traditional enemy” in school. This work materializes the results of the inter- and trans-disciplinary research aimed toward the understanding of mathematics, which concluded that the fields with the potential to contribute to mathematics education in this respect, by unifying the procedural and conceptual approaches, are epistemology and philosophy of mathematics and science, as well as fundamentals and history of mathematics. These results argue that students’ fear of mathematics can be annulled through a conceptual approach, and a student with a good conceptual understanding will be a better problem solver. The author has identified those zones and concepts from the above disciplines that can be adapted and processed for familiarizing the student with this type of knowledge, which should accompany the traditional content of school mathematics. The work was organized so as to create for the reader a unificatory image of the complex nature of mathematics, as well as a conceptual perspective ultimately necessary to the holistic understanding of school mathematics. The author talks about mathematics to convince readers that to understand mathematics means first to understand it as a whole, but also as part of a whole. The nature of mathematics, its primary concepts (like numbers and sets), its structures, language, methods, roles, and applicability, are all presented in their essential content, and the explanation of non-mathematical concepts is done in an accessible language and with many relevant examples. (shrink)

Подходът на Хайдегер за синтез на философия и поезия е артикулиран преди всичко чрез цикъла работи на Хайдегер за Хьолдерлин. Привлечени са също някои иъ изследванията му за предсократиците, както и за езика като онтология.

The quantum information introduced by quantum mechanics is equivalent to a certain generalization of classical information: from finite to infinite series or collections. The quantity of information is the quantity of choices measured in the units of elementary choice. The “qubit”, can be interpreted as that generalization of “bit”, which is a choice among a continuum of alternatives. The axiom of choice is necessary for quantum information. The coherent state is transformed into a well-ordered series of results in time after (...) measurement. The quantity of quantum information is the transfinite ordinal number corresponding to the infinity series in question. The transfinite ordinal numbers can be defined as ambiguously corresponding “transfinite natural numbers” generalizing the natural numbers of Peano arithmetic to “Hilbert arithmetic” allowing for the unification of the foundations of mathematics and quantum mechanics. (shrink)

G. E. Moore’s critical analysis of right action in utilitarian ethics and his consequentialist concept of right action is a starting point for a theory of moral/right action in ethics of social consequences. The terms right and wrong have different meanings in these theories. The author explores different aspects of right and wrong actions in ethics of social consequences and compares them with Moore’s ideas. He positively evaluates Moore’s contributions to the development his theory of moral/right action.

“Negative probability” in practice. Quantum Communication: Very small phase space regions turn out to be thermodynamically analogical to those of superconductors. Macro-bodies or signals might exist in coherent or entangled state. Such physical objects having unusual properties could be the basis of quantum communication channels or even normal physical ones … Questions and a few answers about negative probability: Why does it appear in quantum mechanics? It appears in phase-space formulated quantum mechanics; next, in quantum correlations … and for wave-particle (...) dualism. Its meaning:- mathematically: a ratio of two measures (of sets), which are not collinear; physically: the ratio of the measurements of two physical quantities, which are not simultaneously measurable. The main innovation is in the mapping between phase and Hilbert space, since both are sums. Phase space is a sum of cells, and Hilbert space is a sum of qubits. The mapping is reduced to the mapping of a cell into a qubit and vice versa. Negative probability helps quantum mechanics to be represented quasi-statistically by quasi-probabilistic distributions. Pure states of negative probability cannot exist, but they, where the conditions for their expression exists, decrease the sum probability of the integrally positive regions of the distributions. They reflect the immediate interaction (interference) of probabilities common in quantum mechanics. (shrink)

The aim of this article is to explore the ontological difference within Parmenides’s poem “Peri physeōs,” with a specific focus on line B 2.3, which reads: “exists, and it is not possible not to exist” (estin te kai hōs ouk esti mē einai). By interpreting “ouk esti” as a negative judgment and “mē einai” as a negative predication, I argue that this line already conceals the essence of the ontological difference, insofar as being is not an entity, and entities are (...) not-being. This interpretation draws on Plato’s notion of negation and difference as discussed in "The Sophist," as well as on Kantian infinite judgment. The distinction between these two negations enables the development of the concept of a meontological difference between“non-being” and “non-entities,” which lies at the core of the ontological difference between being and entities, and also illuminates Heidegger’s pairing of Ereignis and Enteignis. Additionally, I argue that Heidegger’s interpretation of Heraclitus in light of truth as alethēia relies on a similar double-negativity. Finally, I show the illuminating potential of examining the ontological difference in Parmenides by analyzing Heidegger’s 1949 preface to the third edition of the treatise “On the Essence of Ground” (1929). (shrink)

Many researchers determine the question “Why anything rather than nothing?” as the most ancient and fundamental philosophical problem. Furthermore, it is very close to the idea of Creation shared by religion, science, and philosophy, e.g. as the “Big Bang”, the doctrine of “first cause” or “causa sui”, the Creation in six days in the Bible, etc. Thus, the solution of quantum mechanics, being scientific in fact, can be interpreted also philosophically, and even religiously. However, only the philosophical interpretation is the (...) topic of the text. The essence of the answer of quantum mechanics is: 1. The creation is necessary in a rigorous mathematical sense. Thus, it does not need any choice, free will, subject, God, etc. to appear. The world exists in virtue of mathematical necessity, e.g. as any mathematical truth such as 2+2=4. 2. The being is less than nothing rather than more than nothing. So, the creation is not an increase of nothing, but the decrease of nothing: it is a deficiency in relation of nothing. Time and its “arrow” are the way of that diminishing or incompleteness to nothing. (shrink)

In his Education of a Christian Prince Erasmus applies ancient and Christian virtues to the functions of a Christian prince. Slovak humanist writer Ján Milo- chovský , who new Erasmus’s work, expanded in his Ornamentum Magistratus Politici the scope of the ethical and moral functions of a prince, focusing on three fundamental virtues: piety, justice and tolerance.The paper offers an analysis of Erasmus’s political ethics and examines the impact of the latter on the Slovak humanism of the second half of (...) the 17th century, especially in the writings of Ján Milochovský. (shrink)

In this article, I examine Heraclitus’s 50th fragment with regard to the pronominal negation, ouk emou. In the first part of the paper, I argue that the dictum «one is all» is not something uttered by the logos, but rather is a response given by the human being according to the silent voice of the logos. Secondly, I proceed to analyze the deictic character of the negation ouk emou, aligning my interpretation with Agamben’s exposition of pronouns in Language and Death. (...) Thus, I argue that in Heraclitus’s case, the pronoun testifies to the event, or the happening, of language. This happening is demonstrated in a showing manner, rather than a communicative one. This reading enforces the argument that logos itself does not say anything, let alone that one is all, supporting Heidegger’s interpretation of language as consonance of silence (Geläut der Stille). (shrink)

On the question of whether gambling behavior can be changed as result of teaching gamblers the mathematics of gambling, past studies have yielded contradictory results, and a clear conclusion has not yet been drawn. In this paper, I bring some criticisms to the empirical studies that tended to answer no to this hypothesis, regarding the sampling and laboratory testing, and I argue that an optimal mathematical scholastic intervention with the objective of preventing problem gambling is possible, by providing the principles (...) that would optimize the structure and content of the teaching module. Given the ethical aspects of the exposure of mathematical facts behind games of chance, and starting from the slots case – where the parametric design is missing, we have to draw a line between ethical and optional information with respect to the mathematical content provided by a scholastic intervention. Arguing for the role of mathematics in problem-gambling prevention and treatment, interdisciplinary research directions are drawn toward implementing an optimal mathematical module in cognitive therapies. (shrink)

The paper focuses on the differences between utilitarianism and non-utilitarian consequentialism.

The writings of Martin Rakovský can be seen as a reflection of the problems, including political ones, of his time. His aim was also to offer an idea of a perfect ruler, who would bring peoples the peace and calm down the stormy events of the 16th century. The personal virtues of such a ruler should have been the guarantee of the welfare of all citizens. Given Rakovský’s religious attitude he can be regarded as a re- formation humanist standing between (...) Machiavelli and Luther. (shrink)

Contemporary philosophical accounts of the applicability of mathematics in physical sciences and the empirical world are based on formalized relations between the mathematical structures and the physical systems they are supposed to represent within the models. Such relations were constructed both to ensure an adequate representation and to allow a justification of the validity of the mathematical models as means of scientific inference. This article puts in evidence the various circularities (logical, epistemic, and of definition) that are present in these (...) formal constructions and discusses them as an argument for the alternative semantic and propositional-structure accounts of the applicability of mathematics. (shrink)

The UNESCO Chair in Bioethics has been established at the University of Presov (Slovakia) in 2010.

The predisposition of the Indispensability Argument to objections, rephrasing and versions associated with the various views in philosophy of mathematics grants it a special status of a “blueprint” type rather than a debatable theme in the philosophy of science. From this point of view, it follows that the Argument has more an epistemic character than ontological.

The paper considers the symmetries of a bit of information corresponding to one, two or three qubits of quantum information and identifiable as the three basic symmetries of the Standard model, U(1), SU(2), and SU(3) accordingly. They refer to “empty qubits” (or the free variable of quantum information), i.e. those in which no point is chosen (recorded). The choice of a certain point violates those symmetries. It can be represented furthermore as the choice of a privileged reference frame (e.g. that (...) of the Big Bang), which can be described exhaustively by means of 16 numbers (4 for position, 4 for velocity, and 8 for acceleration) independently of time, but in space-time continuum, and still one, 17th number is necessary for the mass of rest of the observer in it. The same 17 numbers describing exhaustively a privileged reference frame thus granted to be “zero”, respectively a certain violation of all the three symmetries of the Standard model or the “record” in a qubit in general, can be represented as 17 elementary wave functions (or classes of wave functions) after the bijection of natural and transfinite natural (ordinal) numbers in Hilbert arithmetic and further identified as those corresponding to the 17 elementary of particles of the Standard model. Two generalizations of the relevant concepts of general relativity are introduced: (1) “discrete reference frame” to the class of all arbitrarily accelerated reference frame constituting a smooth manifold; (2) a still more general principle of relativity to the general principle of relativity, and meaning the conservation of quantum information as to all discrete reference frames as to the smooth manifold of all reference frames of general relativity. Then, the bijective transition from an accelerated reference frame to the 17 elementary wave functions of the Standard model can be interpreted by the still more general principle of relativity as the equivalent redescription of a privileged reference frame: smooth into a discrete one. The conservation of quantum information related to the generalization of the concept of reference frame can be interpreted as restoring the concept of the ether, an absolutely immovable medium and reference frame in Newtonian mechanics, to which the relative motion can be interpreted as an absolute one, or logically: the relations, as properties. The new ether is to consist of qubits (or quantum information). One can track the conceptual pathway of the “ether” from Newtonian mechanics via special relativity, via general relativity, via quantum mechanics to the theory of quantum information (or “quantum mechanics and information”). The identification of entanglement and gravity can be considered also as a ‘byproduct” implied by the transition from the smooth “ether of special and general relativity’ to the “flat” ether of quantum mechanics and information. The qubit ether is out of the “temporal screen” in general and is depicted on it as both matter and energy, both dark and visible. (shrink)

The classical (set-theoretic) concept of structure has become essential for every contemporary account of a scientific theory, but also for the metatheoretical accounts dealing with the adequacy of such theories and their methods. In the latter category of accounts, and in particular, the structural metamodels designed for the applicability of mathematics have struggled over the last decade to justify the use of mathematical models in sciences beyond their 'indispensability' in terms of either method or concepts/entities. In this paper, I argue (...) that these metamodels employ structures of different natures and epistemologies, and this diversity does pose a serious problem to the intended justification. (shrink)

The history of phenomenology is usually portrayed within its methodological scope and the same goes for its turning points, such as the hermeneutical approach developed by Martin Heidegger. I argue, however, that Gustav Shpet’s hermeneutical phenomenology has an ontological bearing and its methodological acceptance is subsidiary. I extract textual pieces of evidence from his critical appraisal of Husserl’s Ideen I, i.e. Appearance and Sense (1914), as well as from his phenomenological essay, The Consciousness and its Owner (1916), in order to (...) show that at the basis of hermeneutics as a method lies a hermeneutical being on its own. I support this claim by comparing in a topological-contemplative way—that is a methodological procedure found in Viorel Cernica’s work on history of Romanian philosophy—the ideas of Gustav Shpet and those of Martin Heidegger that converge on this point. I show that both of them conceived human subjectivity as being both unique and historical, a notion that denounces Husserl’s transcendental turn. However, I claim that this differentiation doesn’t imply a dissent from phenomenology, but rather its recasting into a different philosophical ethos. (shrink)