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.

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)

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 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)

Attempts at solving what has been labeled as Eugene Wigner’s puzzle of applicability of mathematics are still far from arriving at an acceptable solution. The accounts developed to explain the “miracle” of applied mathematics vary in nature, foundation, and solution, from denying the existence of a genuine problem to designing structural theories based on mathematical formalism. Despite this variation, all investigations treated the problem in a unitary way with respect to the target, pointing to one or two ‘why’ or ‘how’ (...) questions to be answered. In this paper, I argue that two analyses, a semantic analysis ab initio and a metatheoretical analysis starting from the types of unreasonableness involved in this problem, will establish the interdisciplinary character of the problem and reveal many more targets, which may be addressed with different methodologies. In order to address objectively the philosophical problem of applicability of mathematics, a foundational revision of the problem is needed. (shrink)

Attempts at solving what has been labeled as Eugene Wigner’s puzzle of applicability of mathematics are still far from arriving at an acceptable solution. The accounts developed to explain the “miracle” of applied mathematics vary in nature, foundation, and solution, from denying the existence of a genuine problem to designing structural theories based on mathematical formalism. Despite this variation, all investigations treated the problem in a unitary way with respect to the target, pointing to one or two ‘why’ or ‘how’ (...) questions to be answered. In this paper, I argue that two analyses, a semantic analysis ab initio and a metatheoretical analysis starting from the types of unreasonableness involved in this problem, will establish the interdisciplinary character of the problem and reveal many more targets, which may be addressed with different methodologies. In order to address objectively the philosophical problem of applicability of mathematics, a foundational revision of the problem is needed. (shrink)

Attempts at solving what has been labeled as Eugene Wigner’s puzzle of applicability of mathematics are still far from arriving at an acceptable solution. The accounts developed to explain the “miracle” of applied mathematics vary in nature, foundation, and solution, from denying the existence of a genuine problem to designing structural theories based on mathematical formalism. Despite this variation, all investigations treated the problem in a unitary way with respect to the target, pointing to one or two ‘why’ or ‘how’ (...) questions to be answered. In this paper, I argue that two analyses, a semantic analysis ab initio and a metatheoretical analysis starting from the types of unreasonableness involved in this problem, will establish the interdisciplinary character of the problem and reveal many more targets, which may be addressed with different methodologies. In order to address objectively the philosophical problem of applicability of mathematics, a foundational revision of the problem is needed. (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)

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 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 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)

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)

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 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)

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)

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)

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 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 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)

Aceasta nu este o carte de matematică, ci una despre matematică, care se adresează elevului sau studentului, dar şi dascălului său, cu un scop cât se poate de practic, anume acela de a iniţia şi netezi calea către înţelegerea completă a matematicii predate în şcoală. Tradiţia predării matematicii într-o abordare preponderent procedural-formală a avut ca efect o viziune deformată a elevilor asupra matematicii, ca fiind ceva strict formal, instrumental şi calculatoriu. Pierzând contactul cu baza conceptuală a matematicii, elevii dezvoltă pe (...) parcurs o "anxietate matematică" şi renunţă la a mai căuta înţelegerea matematicii, care devine "duşmanul tradiţional" din şcoală. Această lucrare şi-a propus materializarea rezultatelor cercetărilor inter- şi trans-disciplinare având ca obiect înţelegerea matematicii, care au concluzionat că domeniile care au potenţialul de a contribui în acest fel la educaţia matematicii, unificând abordările procedurală şi conceptuală, sunt epistemologia şi filosofia matematicii şi ştiinţei, precum şi fundamentele şi istoria matematicii. Aceste rezultate susţin teza că teama de matematică poate fi înlăturată prin abordarea conceptuală, iar un elev cu o bună înţelegere conceptuală va fi un rezolvitor de probleme mai bun. Autorul a identificat acele zone şi concepte aparţinând acestor discipline, care pot fi adaptate şi prelucrate în vederea familiarizării elevului sau studentului cu acest tip de cunoştinţe, care să însoţească conţinutul tradiţional al matematicii şcolare. Lucrarea a fost astfel organizată încât să contureze cititorului o imagine unificatoare asupra complexităţii naturii matematicii, precum şi o perspectivă conceptuală necesară, în final, înţelegerii de tip holistic a matematicii şcolare. Autorul vorbeşte despre matematică, pentru a convinge că a înţelege matematica înseamnă mai întâi să o înţelegem ca întreg, dar şi ca parte a unui întreg. Natura matematicii, conceptele sale primare (cum ar fi numerele şi mulţimile), structurile, limbajul, metodele, rolurile şi aplicabilitatea matematicii, sunt prezentate în conţinutul lor esenţial, iar explicarea conceptelor non-matematice este făcută într-un limbaj accesibil, însoţită de multe exemple relevante. Cartea este o unitate didactică concepută să reprezinte punctul de plecare şi un ghid de orientare către dobândirea înţelegerii de tip holistic a matematicii (pentru elev sau student) şi (pentru dascăl) către o predare de tip epistemic-conceptual, în care înţelegerea conceptuală este la fel de importantă ca antrenarea abilităţilor procedural-aplicative. (shrink)

Lucrarea tratează unul dintre “misterele” filosofiei analitice şi ale raţionalităţii însăşi, anume aplicabilitatea matematicii în ştiinţe şi în investigarea matematică a realităţii înconjurătoare, a cărei filosofie este dezvoltată în jurul sintagmei – de acum paradigmatice – ‘eficacitatea iraţională a matematicii’, aparţinând fizicianului Eugene Wigner, problemă filosofică etichetată în literatură drept “puzzle-ul lui Wigner”. Odată intraţi în profunzimea acestei probleme, investigaţia nu trebuie limitată la căutarea unor răspunsuri explicative la întrebări precum “Ce este de fapt aplicabilitatea matematicii?”, “Cum explicăm prezenţa în (...) natură a conceptelor matematice simple şi complexe?” sau “Cum explicăm rata de succes uriaşă a aplicaţiilor matematice, care presupun modele aproximativ false ale unei realităţi idealizate?”, ci extinsă în plan metateoretic către căutarea unei justificări teoretice a utilizării metodei matematice în practica ştiinţifică, independent de succesul acestei metode. Aceste întrebări şi probleme sunt abordate în detaliu în lucrarea de faţă. Lucrarea, care va continua cu un al doilea titlu, dedicat modelelor teoretice ale aplicabilităţii şi alternativelor structurale ale acestora, se adresează în special – dar nu exclusiv – matematicienilor, fizicienilor, filosofilor ştiinţei, filosofilor limbajului şi epistemologilor, dar şi studenţilor acestor discipline. (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)

Over the past two decades, gamblers have begun taking mathematics into account more seriously than ever before. While probability theory is the only rigorous theory modeling the uncertainty, even though in idealized conditions, numerical probabilities are viewed not only as mere mathematical information, but also as a decision-making criterion, especially in gambling. This book presents the mathematics underlying the major games of chance and provides a precise account of the odds associated with all gaming events. It begins by explaining in (...) simple terms the meaning of the concept of probability for the layman and goes on to become an enlightening journey through the mathematics of chance, randomness and risk. It then continues with the basics of discrete probability, combinatorics and counting arguments for those interested in the supporting mathematics. These mathematic sections may be skipped by readers who do not have a minimal background in mathematics; these readers can skip directly to the Guide to Numerical Results to pick the odds and recommendations they need for the desired gaming situation. Doing so is possible due to the organization of that chapter, in which the results are listed at the end of each section, mostly in the form of tables. The chapter titled The Mathematics of Games of Chance presents these games not only as a good application field for probability theory, but also in terms of human actions where probability-based strategies can be tried to achieve favorable results. Through suggestive examples, the reader can see what are the experiments, events and probability fields in games of chance and how probability calculus works there. The main portion of this work is a collection of probability results for each type of game. Each game s section is packed with formulas and tables. Each section also contains a description of the game, a classification of the gaming events and the applicable probability calculations. The primary goal of this work is to allow the reader to quickly find the odds for a specific gaming situation, in order to improve his or her betting/gaming decisions. Every type of gaming event is tabulated in a logical, consistent and comprehensive manner. The complete methodology and complete or partial calculations are shown to teach players how to calculate probability for any situation, for every stage of the game for any game. Here, readers can find the real odds, returned by precise mathematical formulas and not by partial simulations that most software uses. Collections of odds are presented, as well as strategic recommendations based on those odds, where necessary, for each type of gaming situation. The book contains much new and original material that has not been published previously and provides great coverage of probabilities for the following games of chance: Dice, Slots, Roulette, Baccarat, Blackjack, Texas Hold em Poker, Lottery and Sport Bets. Most of games of chance are predisposed to probability-based decisions. This is why the approach is not an exclusively statistical one, but analytical: every gaming event is taken as an individual applied probability problem to solve. A special chapter defines the probability-based strategy and mathematically shows why such strategy is theoretically optimal.". (shrink)

Problemele filosofie sensibile pe care le pune aplicabilitatea matematicii în ştiinţe şi viaţa de zi cu zi au conturat, pe un fond interdisciplinar, o nouă “ramură” a filosofiei ştiinţei, anume filosofia aplicabilităţii matematicii. Aplicarea cu succes a matematicii de-a lungul istoriei ştiinţei necesită reprezentare, încadrare, explicaţie, dar şi o justificare de ordin metateoretic a aplicabilităţii. Între rolurile matematicii în practica ştiinţifică, rolul constitutiv teoriilor ştiinţifice este cel a cărui analiză poate contribui esenţial la această justificare. În lucrarea de faţă, am (...) analizat acest rol constitutiv prin prisma relaţiilor sale cu celelalte roluri importante ale matematicii (descriptiv-semantic-reprezentaţional, inferenţial-explicativ-predictiv), încercând să surprind motivaţia primară a acestui rol relativ la ideea de structură matematică şi epistemică, componente esenţiale ale ştiinţei structurale matematizate. (shrink)

Continuing his series of books on the mathematics of gambling, the author shows how a simple-rule game such as roulette is suited to a complex mathematical model whose applications generate improved betting systems that take into account a player's personal playing criteria. The book is both practical and theoretical, but is mainly devoted to the application of theory. About two-thirds of the content is lists of categories and sub-categories of improved betting systems, along with all the parameters that might stand (...) as the main objective criteria in a personal strategy - odds, profits and losses. The work contains new and original material not published before. The mathematical chapter describes complex bets, the profit function, the equivalence between bets and all their properties. All theoretical results are accompanied by suggestive concrete examples and can be followed by anyone with a minimal mathematical background because they involve only basic algebraic skills and set theory basics. The reader may also choose to skip the math and go directly to the sections containing applications, where he or she can pick desired numerical results from tables. The book offers no new so-called winning strategies, although it discusses them from a mathematical point of view. It does, however, offer improved betting systems and helps to organize a player's choices in roulette betting, according to mathematical facts and personal strategies. It is a must-have roulette handbook to be studied before placing your bets on the turn of either a European or American roulette wheel. (shrink)

A complete probability guide of Hold'em Poker, this guide covers all possible gaming situations. The author focuses on the practical side of the presentation and use of the probabilities involved in Hold'em, while taking into account the subjective side of the probability-based criteria of each player's strategy.

This eighth book of the author on gambling math presents in accessible terms the cold mathematics behind the sparkling slot machines, either physical or virtual. It contains all the mathematical facts grounding the configuration, functionality, outcome, and profits of the slot games. Therefore, it is not a so-called how-to-win book, but a complete, rigorous mathematical guide for the slot player and also for game producers, being unique in this respect. As it is primarily addressed to the slot player, its goal (...) is to present practical applications of the mathematical models of slot games, in order to provide numerical results that a player can use as criteria for gaming decisions or just as information for any slot game and any predicted winning event. These results are focused on probability and expected value, these being the most important parameters for decisional criteria in slots. The book is packed with plenty of figures, tables, and formulas. The content is organized so that readers can skip the theoretical parts and go picking the practical results (numerical, in tables of values where possible, or ready-to-compute formulas) for the desired situation. The practical results are gathered in the last chapter, titled "Practical Applications and Numerical Results," the largest part of the book, for the most popular categories of slot machines, namely with 3, 5, 9, and 16 reels. Any other category of slot games is covered in the theoretical part of the book, where the general formulas apply not only to existing slot games, but also to possible future slot games of any design and configuration. The author does not just throw the slot mathematics to the audience and run away, but offers an ultimate practical contribution with the chapter "How to estimate the number of stops and the symbol distribution on a reel", a surprise for both players and producers, where one can see that mathematics provides players with some statistical methods as well as methods based on physical measurements for retrieving these missing data. Having these data along with the mathematical results of this book, anyone can generate the PAR sheet of any slot machine. In the last decade, mathematics has been taken more and more seriously into account in gaming, as being the essence that governs the games of chance and the only rigorous tool providing information on optimal play, where possible. For the popular game of slots, mathematics already fulfilled its duty by providing all the data that it can provide and that cannot be found on the display of the slot machines - it is all here in this book. (shrink)

This work is a complete mathematical guide to lottery games, covering all of the problems related to probability, combinatorics, and all parameters describing the lottery matrices, as well as the various playing systems. The mathematics sections describe the mathematical model of the lottery, which is in fact the essence of the lotto game. The applications of this model provide players with all the mathematical data regarding the parameters attached to the gaming events and personal playing systems. By applying these data, (...) one can find all the winning probabilities for the play with one line, and how these probabilities change with playing the various types of systems containing several lines, depending on their structure. Also, each playing system has a formula attached that provides the number of possible multiple prizes in various circumstances. Other mathematical parameters of the playing systems and the correlations between them are also presented. The generality of the mathematical model and of the obtained formulas allows their application for any existent lottery and any playing system. Each formula is followed by numerical results covering the most frequent lottery matrices worldwide and by multiple examples predominantly belonging to the 6/49 lottery. The listing of the numerical results in dozens of well-organized tables, along with instructions and examples of using them, makes possible the direct usage of this guide by players without a mathematical background. The author also discusses from a mathematical point of view the strategies of choosing involved in the lotto game. The book does not offer so-called winning strategies, but helps players to better organize their own playing systems and to confront their own convictions with the incontestable reality offered by the direct applications of the mathematical model of the lotto game. As a must-have handbook for any lottery player, this book offers essential information about the game itself and can provide the basis for gaming decisions of any kind. (shrink)

This book presents not only the mathematical concept of probability, but also its philosophical aspects, the relativity of probability and its applications and even the psychology of probability. All explanations are made in a comprehensible manner and are supported with suggestive examples from nature and daily life, and even with challenging math paradoxes.

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)

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

Book Review Luck, logic, and white lies: the mathematics of games, second edition by Jörg Bewersdorff, New York, Taylor & Francis, CRC Press, 2021, 568 pp., GBP 42.99 (paperback), ISBN 9780367548414, Number of chapters 51.

In archaic societies myths were believed to tell true stories - stories about the ultimate origin of reality. For us, on the contrary, the term 'myth' denotes a false belief. Between the archaic notion of myth and ours stands Plato's. This volume is a collection of ten studies by eminent scholars that focus on the ways in which some of Plato's most famous myths are interwoven with his philosophy. The myths discussed include the eschatological myths of the Gorgias, the Phaedo, (...) the Republic and Laws 10, the central myths of the Phaedrus and the Statesman, and the so-called myth of the Noble Lie from the Republic. The mythical character of the Timaeus cosmology is also amply discussed. The volume also contains seventeen rare Renaissance illustrations of Platonic myths. The contributors argue that in Plato myth and philosophy are tightly bound together, despite Plato's occasional claim that they are opposed modes of discourse. (shrink)

At the beginning of Book 9 of the Politeia (571cd), Platon suggests that all people bear in themselves unlawful desires like the desire to have sex with their own mother or with any other human, god, or beast, the desire to murder anyone, or the desire to eat anything. Modern scholars take it for granted that by the desire to eat anything, Platon means cannibalism. This view is based on the fact that Platon discusses unlawful desires in connection with the (...) tyrannical man and that the tyrant is, elsewhere in the Politeia, twice connected with anthropophagy (at 8.565d–566a and 10.619c). This paper challenges this communis opinio and argues that we have no reason to assume that at Politeia 9.571d Platon claims that every one of us has the hidden desire to consume human flesh. Also, the alleged cannibalism of the Platonic tyrant is questioned. A close reading of the passages 8.565d–566a and 10.619c reveals that in the depiction of the tyrant Platon makes use of mythological motifs and literary topoi but never literally claims that the tyrant has cannibalistic desires. (shrink)

We present a variant of ATL with incomplete information which includes the distributed knowledge operators corresponding to synchronous action and perfect recall. The cooperation modalities assume the use the distributed knowledge of coalitions and accordingly refer to perfect recall incomplete information strategies. We propose a model-checking algorithm for the logic. It is based on techniques for games with imperfect information and partially observable objectives, and involves deciding emptiness for automata on infinite trees. We also propose an axiomatic system and prove (...) its completeness for a rather expressive subset. As for the constructs left outside this completely axiomatised subset, we present axioms by which they can be defined in the subset on the class of models in which every state has finitely many successors and give a complete axiomatisation for a “flat” subset of the logic with these constructs included. (shrink)

Dragomir was not interested in writing philosophy, although his archive amounts to almost 100 notebooks, containing fragments, notes, essays and studies. This essay addresses Dragomir’s disregard for written philosophy and argues that his main message will lose its force in his posthumously published archive. His message, as it emerges from the way he lived his life, is, I argue, this: if we are to restore the lost harmony of our lives, philosophy, as essential as it may be, isn’t everything.

The article starts off with some meditations on the question of the much-debated “non-translatibility of German philosophy”, which, in the particular case of Martin Heidegger, proves to be even more acute. Nevertheless, the conclusion of these thoughts is that, on the contrary, a translation of a philosophical text is meant finally not only to mediate between two languages, but also to be for itself a necessary step in a more profound understanding of an original text. Following this logic, the article (...) presents in details the decisions taken by the Romanian translators in rendering the concept most difficult to translate from Being and Time: Bewandtnis. (shrink)

Annotation Based on the research he undertook in rare book collections housed in Scotland, the United States, Finland, Iceland, Holland, Germany and Austria, the author presents a systematic history of cannabalism as reflected in the mirror of philosophy.

The article starts off with some meditations on the question of the much-debated “non-translatibility of German philosophy”, which, in the particular case of Martin Heidegger, proves to be even more acute. Nevertheless, the conclusion of these thoughts is that, on the contrary, a translation of a philosophical text is meant finally not only to mediate between two languages, but also to be for itself a necessary step in a more profound understanding of an original text. Following this logic, the article (...) presents in details the decisions taken by the Romanian translators in rendering the concept most difficult to translate from Being and Time: Bewandtnis. (shrink)

Après des études de droit et de philosophie à l'Université de Bucarest, Alexandru Dragomir part à Fribourg-en-Brisgau comme doctorant de Martin Heidegger. Il y reste deux ans; en 1943 il est rappelé en Roumanie et envoyé au front. Après la guerre, sous le nouveau régime, il ne peut pas poursuivre une carrière universitaire. Il meurt en 2002 à Bucarest sans avoir rien publié. Ce n'est qu'après sa mort que ses cahiers sont découverts et publiés. L'œuvre de Dragomir comprend cinq volumes, (...) parus à Bucarest, aux Éditions Humanitas. Deux sont parus en traduction française chez Vrin : Banalités métaphysiques et Cahiers du temps. Cet article présente sa personnalité et son œuvre, notamment les Cahiers du temps, qui renferment la recherche de toute sa vie. Dragomir y développe sa propre théorie sur la nature du temps, tout en faisant des commentaires des textes classiques de la philosophie qui portent sur ce sujet. Des traductions en allemand et en anglais des Cahiers du temps paraîtront bientôt. Between 1933 and 1939 Alexandru Dragomir studied philosophy and law at the University of Bucharest. In 1941 he was awarded a Humboldt Fellowship, which allowed him to enroll as a doctoral student at the University of Freiburg im Breisgau, Germany, under the supervision of Martin Heidegger. In 1943 he was drafted into the Romanian armed forces and left Freiburg without a degree. In Romania, under the communist regime, he could not pursue an academic career. He died in 2002 without publishing anything. His work has been published posthumously in five volumes by Humanitas Press. Two of the volumes have been published in French translation by Jean Vrin Press : Banalités métaphysiques [Metaphysical Banalities] and Cahiers du temps [Notebooks on Time]. This article offers an overview of Dragomir's personality and work, with an emphasis on his Notebooks on Time — his lifelong research on the nature of time. In these notebooks he develops his own views on time and comments on the classical philosophical texts that deal with the subject. (shrink)

Dragomir was not interested in writing philosophy, although his archive amounts to almost 100 notebooks, containing fragments, notes, essays and studies. This essay addresses Dragomir’s disregard for written philosophy and argues that his main message will lose its force in his posthumously published archive. His message, as it emerges from the way he lived his life, is, I argue, this: if we are to restore the lost harmony of our lives, philosophy, as essential as it may be, isn’t everything.

For Martin Heidegger the "fall" of philosophy into metaphysics begins with Plato. Thus, the relationship between the two philosophers is crucial to an understanding of Heidegger--and, perhaps, even to the whole plausibility of postmodern critiques of metaphysics. It is also, as the essays in this volume attest, highly complex, and possibly founded on a questionable understanding of Plato. As editors Catalin Partenie and Tom Rockmore remark, a simple way to describe Heidegger's reading of Plato might be to say that (...) what began as an attempt to appropriate Plato (and through him a large portion of Western philosophy) finally ended in an estrangement from both Plato and Western philosophy. The authors of this volume consider Heidegger's thought in relation to Plato before and after the " Kehre " or turn. In doing so, they take up various central issues in Heidegger's Being and Time (1927) and thereafter, and the questions of hermeneutics, truth, and language. The result is a subtle and multifaceted reinterpretation of Heidegger's position in the tradition of philosophy, and of Plato's role in determining that position. (shrink)