The current report presents results of the qualitative analysis of the usage of the key math terms in the content of the reviewed websites in the current sample, with emphasis on the necessary distinctions for the word and concept of ‘odds’. Patterns, motivations, conceptual and contextual aspects of the usage are discussed. The theoretical norms of adequacy of this usage in the context of gambling are briefly presented. -/- Technical report of the research project 'Reflection of the mathematical dimension of (...) gambling in iGaming online content - A qualitative analysis'. (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 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 considers a generalization of Peano arithmetic, Hilbert arithmetic as the basis of the world in a Pythagorean manner. Hilbert arithmetic unifies the foundations of mathematics (Peano arithmetic and set theory), foundations of physics (quantum mechanics and information), and philosophical transcendentalism (Husserl’s phenomenology) into a formal theory and mathematical structure literally following Husserl’s tracе of “philosophy as a rigorous science”. In the pathway to that objective, Hilbert arithmetic identifies by itself information related to finite sets and series and quantum (...) information referring to infinite one as both appearing in three “hypostases”: correspondingly, mathematical, physical and ontological, each of which is able to generate a relevant science and area of cognition. Scientific transcendentalism is a falsifiable counterpart of philosophical transcendentalism. The underlying concept of the totality can be interpreted accordingly also mathematically, as consistent completeness, and physically, as the universe defined not empirically or experimentally, but as that ultimate wholeness containing its externality into itself. (shrink)

Ктратката форма "Верблюд" (която условно меже да се нарече "разказ") от класика на българската литература Йордан Радичков е предмет на анализ. по-скоро философски. екзистенциален и металитературен. Какво е "верблюд" по Радичков? Нещо толкова неопределено, че може да бъде открито навсякъде ... подобно на една философска категория или философски дискурс, релевантен към всичко ...

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)

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)

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 current technical report presents the partial results of the quantitative analysis of the research project, after the review of 247 gambling websites. It is focused on and discusses the usage of the math terms specific to gambling in the reviewed sample. In particular, the fifth technical report discusses the usage of math terms associated with the game of slots, as found in the reviewed sample.

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.

With regard to existing concept of the moral education (ethics) in Slovakia, the questions of ethics and morals are only one of the partial sections. The dominant role is played by psychology based on Roberto Olivar’s concept with emphasis on pro–socialization and on Erickson’s concept of the psychosocial development. From the philosophy basis point of view, only Aristotle, even in reduced form and Spranger’s concept of the life forms are mentioned. Philosophy and ethics are only complements to more psychologically based (...) educational program which is resulting from the problematic division of a social and moral experience into egoistic and prosocial. Egoism is presented in a distorted form and is characterized as the cause of all moral evil. However, there are several different types of understanding of the term egoism in philosophy and ethics as for example psychological and ethical egoism, or self-interest. Ethical egoism or self-interest cannot be identified with selfishness. The main aim of moral education should not be only to form the desired children and youth moral orientation but on the other hand, to form morally self-confident individuals who are able to solve the moral problems, to help the others to solve them as well and to be able to bear moral responsibility for their own deeds. (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)

This second technical report shows some partial results for the variables of the proposed statistical analysis and a discussion about some changes in sampling. In what concerns the qualitative analysis of content, the report presents the general predominant tendencies that get contoured with the first two samples.

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 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.

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 text is a continuation of the article of the same name published in the previous issue of Philosophical Alternatives. The philosophical interpretations of the Kochen- Specker theorem (1967) are considered. Einstein's principle regarding the,consubstantiality of inertia and gravity" (1918) allows of a parallel between descriptions of a physical micro-entity in relation to the macro-apparatus on the one hand, and of physical macro-entities in relation to the astronomical mega-entities on the other. The Bohmian interpretation ( 1952) of quantum mechanics proposes (...) that all quantum systems be interpreted as dissipative ones and that the theorem be thus derstood. The conclusion is that the continual representation, by force or (gravitational) field between parts interacting by means of it, of a system is equivalent to their mutual entanglement if representation is discrete. Gravity (force field) and entanglement are two different, correspondingly continual and discrete, images of a single common essence. General relativity can be interpreted as a superluminal generalization of special relativity. The postulate exists of an alleged obligatory difference between a model and reality in science and philosophy. It can also be deduced by interpreting a corollary of the heorem. On the other hand, quantum mechanics, on the basis of this theorem and of V on Neumann's (1932), introduces the option that a model be entirely identified as the modeled reality and, therefore, that absolutely reality be recognized: this is a non-standard hypothesis in the epistemology of science. Thus, the true reality begins to be understood mathematically, i.e. in a Pythagorean manner, for its identification with its mathematical model. A few linked problems are highlighted: the role of the axiom of choice forcorrectly interpreting the theorem; whether the theorem can be considered an axiom; whether the theorem can be considered equivalent to the negation of the axiom. (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)

Book Review Mathematics of casino carnival games by Mark Bollman, New York: CRC Press 2021, 318 pp., GBP 48.99 (hardback), ISBN 9780367348656.

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)

In his article, the author considers possible forms of relationship between Kant’s ethics and consequentialism. In this context, he analyses David Cummiskey’s views which are expressed in his book, Kantian Consequentialism (1996). He demonstrates the possibility of justifying the consequentialism on the basis of Kant’s ethics and its values. Likewise, several other authors (such as Scott Forschler, Philipp Stratton-Lake, Michael Ridge) are of the opinion of the possible compatibility of Kant’s ethics and consequentialism. On the other hand, however, Christine M. (...) Korsgaard is an example of a strict rejection of the similarity between Kant and the consequentialist ethics. The author based on the ethics of social consequences as a form of non-utilitarian consequentialism claims (like Cummiskey), that there are similarities between Kant’s ethics and consequentialism. Unlike Cummiskey, however, he sees similarity in the Kant’s formula of humanity and the understanding of humanity in ethics of social consequences, especially in the form of additional moral value. (shrink)

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)

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 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)

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)

The paper addresses the problem, which quantum mechanics resolves in fact. Its viewpoint suggests that the crucial link of time and its course is omitted in understanding the problem. The common interpretation underlain by the history of quantum mechanics sees discreteness only on the Plank scale, which is transformed into continuity and even smoothness on the macroscopic scale. That approach is fraught with a series of seeming paradoxes. It suggests that the present mathematical formalism of quantum mechanics is only partly (...) relevant to its problem, which is ostensibly known. The paper accepts just the opposite: The mathematical solution is absolute relevant and serves as an axiomatic base, from which the real and yet hidden problem is deduced. Wave-particle duality, Hilbert space, both probabilistic and many-worlds interpretations of quantum mechanics, quantum information, and the Schrödinger equation are included in that base. The Schrödinger equation is understood as a generalization of the law of energy conservation to past, present, and future moments of time. The deduced real problem of quantum mechanics is: “What is the universal law describing the course of time in any physical change therefore including any mechanical motion?”. (shrink)

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

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)

We can read about the morality of that time in works by authors who describe or criticize the conduct and activity of the members of those classes taking the lead in the morality of that time. Thus, we can find a lot of information about ancient Greece and its morality in Plato’s presentation of Socrates, Peter Abelard presenting the Middle Ages, Erasmus of Rotterdam, Niccolo Machiavelli, Baldesar Castiglione, but even also Slovak authors such as Martin Rakovský and Juraj Koppay presenting (...) very interesting contemporary facts about the Renaissance. (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)

“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)

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)

A case study of quantum mechanics is investigated in the framework of the philosophical opposition “mathematical model – reality”. All classical science obeys the postulate about the fundamental difference of model and reality, and thus distinguishing epistemology from ontology fundamentally. The theorems about the absence of hidden variables in quantum mechanics imply for it to be “complete” (versus Einstein’s opinion). That consistent completeness (unlike arithmetic to set theory in the foundations of mathematics in Gödel’s opinion) can be interpreted furthermore as (...) the coincidence of model and reality. The paper discusses the option and fact of that coincidence it its base: the fundamental postulate formulated by Niels Bohr about what quantum mechanics studies (unlike all classical science). Quantum mechanics involves and develops further both identification and disjunctive distinction of the global space of the apparatus and the local space of the investigated quantum entity as complementary to each other. This results into the analogical complementarity of model and reality in quantum mechanics. The apparatus turns out to be both absolutely “transparent” and identically coinciding simultaneously with the reflected quantum reality. Thus, the coincidence of model and reality is postulated as necessary condition for cognition in quantum mechanics by Bohr’s postulate and further, embodied in its formalism of the separable complex Hilbert space, in turn, implying the theorems of the absence of hidden variables (or the equivalent to them “conservation of energy conservation” in quantum mechanics). What the apparatus and measured entity exchange cannot be energy (for the different exponents of energy), but quantum information (as a certain, unambiguously determined wave function) therefore a generalized law of conservation, from which the conservation of energy conservation is a corollary. Particularly, the local and global space (rigorously justified in the Standard model) share the complementarity isomorphic to that of model and reality in the foundation of quantum mechanics. On that background, one can think of the troubles of “quantum gravity” as fundamental, direct corollaries from the postulates of quantum mechanics. Gravity can be defined only as a relation or by a pair of non-orthogonal separable complex Hilbert space attachable whether to two “parts” or to a whole and its parts. On the contrary, all the three fundamental interactions in the Standard model are “flat” and only “properties”: they need only a single separable complex Hilbert space to be defined. (shrink)

The emergent properties are properties referring to a system as a whole, but they do not make sense to its elements or parts being small enough. Furthermore certain emergent properties are reducible to those of elements or relevant parts often. The paper means the special case where the description of the system by means of its emergent properties is much simpler than that of its relevant elements or parts. The concept is investigated by a case study based on statistic thermodynamics, (...) general relativity, and quantum mechanics. (shrink)

The paper discusses the philosophical conclusions, which the interrelation between quantum mechanics and general relativity implies by quantum measure. Quantum measure is three-dimensional, both universal as the Borel measure and complete as the Lebesgue one. Its unit is a quantum bit (qubit) and can be considered as a generalization of the unit of classical information, a bit. It allows quantum mechanics to be interpreted in terms of quantum information, and all physical processes to be seen as informational in a generalized (...) sense. This implies a fundamental connection between the physical and material, on the one hand, and the mathematical and ideal, on the other hand. Quantum measure unifies them by a common and joint informational unit. Furthermore the approach clears up philosophically how quantum mechanics and general relativity can be understood correspondingly as the holistic and temporal aspect of one and the same, the state of a quantum system, e.g. that of the universe as a whole. The key link between them is the notion of the Bekenstein bound as well as that of quantum temperature. General relativity can be interpreted as a special particular case of quantum gravity. All principles underlain by Einstein (1918) reduce the latter to the former. Consequently their generalization and therefore violation addresses directly a theory of quantum gravity. Quantum measure reinterprets newly the “Bing Bang” theories about the beginning of the universe. It measures jointly any quantum leap and smooth motion complementary to each other and thus, the jump-like initiation of anything and the corresponding continuous process of its appearance. Quantum measure unifies the “Big Bang” and the whole visible expansion of the universe as two complementary “halves” of one and the same, the set of all states of the universe as a whole. It is a scientific viewpoint to the “creation from nothing”. (shrink)

The problem of indeterminism in quantum mechanics usually being considered as a generalization determinism of classical mechanics and physics for the case of discrete (quantum) changes is interpreted as an only mathematical problem referring to the relation of a set of independent choices to a well-ordered series therefore regulated by the equivalence of the axiom of choice and the well-ordering “theorem”. The former corresponds to quantum indeterminism, and the latter, to classical determinism. No other premises (besides the above only mathematical (...) equivalence) are necessary to explain how the probabilistic causation of quantum mechanics refers to the unambiguous determinism of classical physics. The same equivalence underlies the mathematical formalism of quantum mechanics. It merged the well-ordered components of the vectors of Heisenberg’s matrix mechanics and the non-ordered members of the wave functions of Schrödinger’s undulatory mechanics. The mathematical condition of that merging is just the equivalence of the axiom of choice and the well-ordering theorem implying in turn Max Born’s probabilistic interpretation of quantum mechanics. Particularly, energy conservation is justified differently than classical physics. It is due to the equivalence at issue rather than to the principle of least action. One may involve two forms of energy conservation corresponding whether to the smooth changes of classical physics or to the discrete changes of quantum mechanics. Further both kinds of changes can be equated to each other under the unified energy conservation as well as the conditions for the violation of energy conservation to be investigated therefore directing to a certain generalization of energy conservation. (shrink)

A principle, according to which any scientific theory can be mathematized, is investigated. That theory is presupposed to be a consistent text, which can be exhaustedly represented by a certain mathematical structure constructively. In thus used, the term “theory” includes all hypotheses as yet unconfirmed as already rejected. The investigation of the sketch of a possible proof of the principle demonstrates that it should be accepted rather a metamathematical axiom about the relation of mathematics and reality. Its investigation needs philosophical (...) means. Husserl’s phenomenology is what is used, and then the conception of “bracketing reality” is modelled to generalize Peano arithmetic in its relation to set theory in the foundation of mathematics. The obtained model is equivalent to the generalization of Peano arithmetic by means of replacing the axiom of induction with that of transfinite induction. A comparison to Mach’s doctrine is used to be revealed the fundamental and philosophical reductionism of Husserl’s phenomenology leading to a kind of Pythagoreanism in the final analysis. Accepting or rejecting the principle, two kinds of mathematics appear differing from each other by its relation to reality. Accepting the principle, mathematics has to include reality within itself in a kind of Pythagoreanism. These two kinds are called in paper correspondingly Hilbert mathematics and Gödel mathematics. The sketch of the proof of the principle demonstrates that the generalization of Peano arithmetic as above can be interpreted as a model of Hilbert mathematics into Gödel mathematics therefore showing that the former is not less consistent than the latter, and the principle is an independent axiom. An information interpretation of Hilbert mathematics is involved. It is a kind of ontology of information. Thus the problem which of the two mathematics is more relevant to our being is discussed. An information interpretation of the Schrödinger equation is involved to illustrate the above problem. (shrink)

Quantum invariance designates the relation of any quantum coherent state to the corresponding statistical ensemble of measured results. The adequate generalization of ‘measurement’ is discussed to involve the discrepancy, due to the fundamental Planck constant, between any quantum coherent state and its statistical representation as a statistical ensemble after measurement. A set-theory corollary is the curious invariance to the axiom of choice: Any coherent state excludes any well-ordering and thus excludes also the axiom of choice. It should be equated to (...) a well-ordered set after measurement and thus requires the axiom of choice. Quantum invariance underlies quantum information and reveals it as the relation of an unordered quantum “much” (i.e. a coherent state) and a well-ordered “many” of the measured results (i.e. a statistical ensemble). It opens up to a new horizon, in which all physical processes and phenomena can be interpreted as quantum computations realizing relevant operations and algorithms on quantum information. All phenomena of entanglement can be described in terms of the so defined quantum information. Quantum invariance elucidates the link between general relativity and quantum mechanics and thus, the problem of quantum gravity. (shrink)

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)

"Това, което прави от една история историческото, никога не може да произлиза само от източниците: изисква се теория на възможната история, така че да може източниците да бъдат въобще накарани да говорят" (Райнхарт Козелек). "Следователно ние се нуждаем от теория: една теория на възможната история. Такава теория е имплицитна вьв всички работи по историография: вьпросьт е само да се направи експлицитна." (Райнхарт Козелек).

Сред времевите модуси "Сега" заема особено място между винаги добре нареденото минало и напълно неопределено и неподредено бъдеще. Така същността на настоящия момент може да се определи като избор и така нуждаещ се от свободна воля, способен да превръща неподреденото в подредено: едно свойство постулирано в теорията на множствата като аксиома за избора, а нейната еквивалентност с т. нар. теорема за добрата наредба може да бъде доказана елементарно. Физическата същност на "Сега" може да се представи и като прехода от кохерентно (...) състояние на една квантова система преди измерване в добре наредената последователност от измерими стойности на същата квантова система. (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)

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 article is devoted to quantum information (including its subdomains, namely: quantum communication, quantum computer, quantum cryptography), and its philosophical meaning. Paradox EPR, Bell’s inequality, phenomena of teleportation are discussed of a philosophical point of view. Quantum mechanical nonlocal correlations are interpreted as topological inseparabilities. Information is considered both as a fundamental physical quantity and as a philosophical category.

A principle, according to which any scientific theory can be mathematized, is investigated. Social science, liberal arts, history, and philosophy are meant first of all. That kind of theory is presupposed to be a consistent text, which can be exhaustedly represented by a certain mathematical structure constructively. In thus used, the term “theory” includes all hypotheses as yet unconfirmed as already rejected. The investigation of the sketch of a possible proof of the principle demonstrates that it should be accepted rather (...) a metamathematical axiom about the relation of mathematics and reality. The main statement is formulated as follows: Any scientific theory admits isomorphism to some mathematical structure in a way constructive. Its investigation needs philosophical means. Husserl’s phenomenology is what is used, and then the conception of “bracketing reality” is modelled to generalize Peano arithmetic in its relation to set theory in the foundation of mathematics. The obtained model is equivalent to the generalization of Peano arithmetic by means of replacing the axiom of induction with that of transfinite induction. The sketch of the proof is organized in five steps: a generalization of epoché; involving transfinite induction in the transition between Peano arithmetic and set theory; discussing the finiteness of Peano arithmetic; applying transfinite induction to Peano arithmetic; discussing an arithmetical model of reality. Accepting or rejecting the principle, two kinds of mathematics appear differing from each other by its relation to reality. Accepting the principle, mathematics has to include reality within itself in a kind of Pythagoreanism. These two kinds are called in paper correspondingly Hilbert mathematics and Gödel mathematics. The sketch of the proof of the principle demonstrates that the generalization of Peano arithmetic as above can be interpreted as a model of Hilbert mathematics into Gödel mathematics therefore showing that the former is not less consistent than the latter, and the principle is an independent axiom. The present paper follows a pathway grounded on Husserl’s phenomenology and “bracketing reality” to achieve the generalized arithmetic necessary for the principle to be founded in alternative ontology, in which there is no reality external to mathematics: reality is included within mathematics. That latter mathematics is able to self-found itself and can be called Hilbert mathematics in honour of Hilbert’s program for self-founding mathematics on the base of arithmetic. The principle of universal mathematizability is consistent to Hilbert mathematics, but not to Gödel mathematics. Consequently, its validity or rejection would resolve the problem which mathematics refers to our being; and vice versa: the choice between them for different reasons would confirm or refuse the principle as to the being. An information interpretation of Hilbert mathematics is involved. It is a kind of ontology of information. The Schrödinger equation in quantum mechanics is involved to illustrate that ontology. Thus the problem which of the two mathematics is more relevant to our being is discussed again in a new way A few directions for future work can be: a rigorous formal proof of the principle as an independent axiom; the further development of information ontology consistent to both kinds of mathematics, but much more natural for Hilbert mathematics; the development of the information interpretation of quantum mechanics as a mathematical one for information ontology and thus Hilbert mathematics; the description of consciousness in terms of information ontology. (shrink)

The authors of the contribution closely follow the published results of their sociological research regarding views of Slovak teachers at primary and secondary schools in the area of relationships with students, parents, colleagues and superiors (Gluchman, & Gluchmanová, 2016). The present contribution analyses views of students at the second level of primary school and at secondary schools by means of evaluating their relationship to teachers, as well as relationships between parents and teachers while students’ views regarding the presence of violence (...) and bullying at school are also addressed. The research results indicate that almost a third of students do not perceive their teachers as ethical models of behaviour and actions; moreover, they have also witnessed instances of corrupt behaviour on the part of teachers. On the other hand, almost two thirds of students appreciate that teachers, when addressing problems at school, proceed in accordance with ethical principles and norms. Unlike teachers, students do not believe serious problems are present when it comes to the behaviour of parents toward teachers. They, however, believe the behaviour of students towards teachers is a more problematic area. (shrink)