In this handbook, I put into practice my philosophical views on children's mathematics. The handbook contains brief instructions and examples of mathematical activities. In the INSTRUCTIONS section, instructions are given on how, and in part why that way, to help preschool children in their mathematical development. In the ACTIVITIES section, there are examples of activities through which the child develops her mathematical abilities.

Mindset plays a vital role in tackling the barriers to improving the preservice mathematics teachers’ (PMTs) conceptual understanding of problem-solving. As the COVID-19 pandemic has continued to pose a challenge, online learning has been adopted. This led this study to determining the PMTs’ mindset and level of conceptual understanding in problem-solving in an online learning environment utilising Google Classroom and the Khan Academy. A quantitative research design was employed specifically utilising a descriptive, comparative, and correlational design. Forty-five PMTs were chosen (...) through simple random sampling and willingly took part in this study. The data was gathered using validated and reliable questionnaires and problem-solving tests. The data gathered was analysed using descriptive statistics, analysis of variance, and simple linear regression. The results revealed that the college admission test, specifically numerical proficiency, influences a strong mindset and a higher level of conceptual understanding in problem-solving. Additionally, this study shows that mindset predicts the levels of conceptual understanding in problem-solving in an online environment where PMTs with a growth mindset have the potential to solve math problems. The use of Google Classroom and the Khan Academy to aid online instruction is useful in the preparation of PMTs as future mathematics teachers and problem-solvers. Further studies may be conducted to validate these reports and to address the limitations of this study. (shrink)

A work on the philosophy of mathematics (2017) -/- ‘Number’, such a simple idea, and yet it fascinated and absorbed the greatest proportion of human geniuses over centuries, not to mention the likes of Pythagoras, Euclid, Newton, Leibniz, Descartes and countless maths giants like Euler, Gauss and Hilbert, etc.. Einstein thought of pure maths as the poetry of logical ideas, the exactitude of which, although independent of experience, strangely seems to benefit the study of the objects of reality. And, interestingly (...) as well as surprisingly we are nowhere near any clear understandings of numbers despite discoveries of many productive usages of numbers. This is - rightly or wrongly - a humble attempt to approach the subject from an angle hitherto unthought-of. (shrink)

This paper gives a framework for understanding causal counterpossibles, counterfactuals imbued with causal content whose antecedents appeal to metaphysically impossible worlds. Such statements are generated by omissive causal claims that appeal to metaphysically impossible events, such as “If the mathematician had not failed to prove that 2+2=5, the math textbooks would not have remained intact.” After providing an account of impossible omissions, the paper argues for three claims: (i) impossible omissions play a causal role in the actual world, (...) (ii) causal counterpossibles have broad applications in philosophy, and (iii) the truth of causal counterpossibles provides evidence for the nonvacuity of counterpossibles more generally. (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)

Researchers interested in player’s experience would assumedly, across disciplines, agree that the goal behind enquiries into player’s experience is to understand the how games’ features end up affecting the player’s experience. Much of the contemporary interdisciplinary research into player’s experience leans toward the empirical-scientific, in the forms psychology, sociology and cognitive science, to name a few. In such approaches, for example demonstrating correlation between physiological symptoms and an in-game event may amount to ‘understanding’. However, the experience of computer game (...) class='Hi'>play is a viable topic also for computer game studies within the general tradition of humanities. In such context, the idea of ‘understanding an experience’ invites an approach focusing on the experienced significance of events and objects within computer game play. This focus, in turn, suggests turning to the principles associated with phenomenology, among which is the idea of describing things as they appear, or as they are given, in the experience, from the first-person perspective. From the first-person perspective the challenge lies not in the subjective experience’s inaccessibility but in the inherent personal richness of the experience’s content. Rather than trying to embrace the richness by engaging in direct introspection, it makes sense to focus the search on the conditions of the player’s experience. In this paper, I discuss the idea of “firstperson perspective” in the context of computer game studies. I propose that conditions for player’s experience could be sought from the materiality of the computer game artefact, rather than from the ‘processual’ or ‘ideal game’. I derive the notion of gameplay condition3 from the overlap of the player’s “lusory attitude” and the materiality of the single-player computer game artefact as it appears in the player’s experience. (shrink)

This study delved into the perceptions of Mathematics’ student teachers regarding the implementation of gamification in secondary schools at Nasugbu, Batangas. This research investigates the rising global trend of implementing gamification in education, particularly in Mathematics teaching, to address contemporary learner needs by examining student teachers' use of gamified activities, their design factors, encountered challenges, and perceived benefits. Purposive sampling was utilized in a multiple-case study approach to select ten (10) secondary school Mathematics’ student teachers engaged in practice teaching in (...) Nasugbu, Batangas. Qualitative findings revealed common gamified activities employed by student teachers, emphasizing the importance of student-centered design, alignment with learning objectives, student engagement, assessment, and adaptation to the classroom context. Challenges faced by student teachers in integrating gamification included technical limitations, sustaining engagement, time management, and addressing diverse learning styles. Despite these challenges, integrating gamification showed benefits such as increased engagement, improved learning outcomes, reduced math anxiety, and enhanced attitudes towards Mathematics. In conclusion, gamified activities play a significant role in enhancing student engagement and learning outcomes in Mathematics classrooms. The findings suggest student teachers to explore and integrate gamified activities into Mathematics lessons to create engaging environments supporting student success. (shrink)

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)

The purpose of this paper is to show that the mathematics of quantum mechanics is the mathematics of set partitions linearized to vector spaces, particularly in Hilbert spaces. That is, the math of QM is the Hilbert space version of the math to describe objective indefiniteness that at the set level is the math of partitions. The key analytical concepts are definiteness versus indefiniteness, distinctions versus indistinctions, and distinguishability versus indistinguishability. The key machinery to go from indefinite (...) to more definite states is the partition join operation at the set level that prefigures at the quantum level projective measurement as well as the formation of maximally-definite state descriptions by Dirac’s Complete Sets of Commuting Operators. This development is measured quantitatively by logical entropy at the set level and by quantum logical entropy at the quantum level. This follow-the-math approach supports the Literal Interpretation of QM—as advocated by Abner Shimony among others which sees a reality of objective indefiniteness that is quite different from the common sense and classical view of reality as being “definite all the way down”. (shrink)

In his paper ‘Words on Play’, Bernard Suits famously defines play as an autotelic activity. Some philosophers like Stephen E. Schmid argue against Suits’s position by pointing out that the concept of autotelicity in Suits’s work is too unclear to serve as a defining feature for play. Due to that fact, Schmid dismisses autotelicity in favor of a definition of play in terms of the player’s engagement in an activity for intrinsic reasons. The purpose of this (...) paper is to defend Suits’s claim by clarifying the concept of autotelicity in the context of play and by arguing against some typical misconceptions about autotelicity in Schmid’s work and in the work of others. First, I define autotelic activities as activities that are engaged in for their own sake. Then, I argue that the engagement in an activity for its own sake is neither in conflict with the activity’s potential internal instrumental structure nor with the existence of certain intrinsic rea-sons (such as pleasure). (shrink)

Identity labels like “woman”, “Black,” “mother,” and “evangelical” are pervasive in both political and personal life, and in both formal and informal classification and communication. They are also widely thought to undermine agency by essentializing groups, flattening individual distinctiveness, and enforcing discrimination. While we take these worries to be well-founded, we argue that they result from a particular practice of using labels to rigidly label others. We identify an alternative practice of playful self-labelling, and argue that it can function as (...) a tool for combating oppression by expressing and enhancing individual and collective agency. (shrink)

This paper addresses the concept of play concerning human formation, especially as manifested in the philosophies of Gadamer and Schiller. Gadamer depicted understanding as an organic motion that unfolds through seeing differences and characterized play as a flexible back-and-forth movement or interplay between possibilities and transformations. Schiller structured play as the playful impulse similarly as an interactive moving force that connects the two seemingly oppositional impulses of reason and sensation and lets the two affect the other dialogically. (...) Both Gadamer and Schiller suggest that play, as in essence an inter-play, orients us into seeing more possibilities of making a refreshing sense of our intellectual and perceptual abilities and thereby transfiguring our living being into richer and fuller meaningfulness. (shrink)

In the paper “Math Anxiety,” Aden Evens explores the manner by means of which concepts are implicated in the problematic Idea according to the philosophy of Gilles Deleuze. The example that Evens draws from Difference and Repetition in order to demonstrate this relation is a mathematics problem, the elements of which are the differentials of the differential calculus. What I would like to offer in the present paper is an historical account of the mathematical problematic that Deleuze deploys in (...) his philosophy, and an introduction to the role that this problematic plays in the develop- ment of his philosophy of difference. One of the points of departure that I will take from the Evens paper is the theme of “power series.”2 This will involve a detailed elaboration of the mechanism by means of which power series operate in the differential calculus deployed by Deleuze in Difference and Repetition. Deleuze actually constructs an alternative history of mathematics that establishes an historical conti- nuity between the differential point of view of the infinitesimal calculus and modern theories of the differential calculus. It is in relation to the differential point of view of the infinitesimal calculus that Deleuze determines a differential logic which he deploys, in the form of a logic of different/ciation, in the development of his proj- ect of constructing a philosophy of difference. (shrink)

Much has been written about the free energy principle (FEP), and much misunderstood. The principle has traditionally been put forth as a theory of brain function or biological self-organisation. Critiques of the framework have focused on its lack of empirical support and a failure to generate concrete, falsifiable predictions. I take both positive and negative evaluations of the FEP thus far to have been largely in error, and appeal to a robust literature on scientific modelling to rectify the situation. A (...) prominent account of scientific modelling distinguishes between model structure and model construal. I propose that the FEP be reserved to designate a model structure, to which philosophers and scientists add various construals, leading to a plethora of models based on the formal structure of the FEP. An entailment of this position is that demands placed on the FEP that it be falsifiable or that it conform to some degree of biological realism rest on a category error. To this end, I deliver first an account of the phenomenon of model transfer and the breakdown between model structure and model construal. In the second section, I offer an overview of the formal elements of the framework, tracing their history of model transfer and illustrating how the formalism comes apart from any interpretation thereof. Next, I evaluate existing comprehensive critical assessments of the FEP, and hypothesise as to potential sources of existing confusions in the literature. In the final section, I distinguish between what I hold to be the FEP—taken to be a modelling language or modelling framework—and what I term “FEP models.”. (shrink)

The idea that concepts play a significant role in some perceptions is widespread but everybody seems to differ as to where to draw the line. Some researchers say that the difference between direct and indirect, concept driven acts of perception manifests itself whenever we perceive abstract or general properties. Others point at second order properties or causal properties. I call this inability to precisely differentiate between acts of direct and indirect perception “The Division Problem”. Furthermore there is always a (...) question as to how widespread indirect perceptions are. Can we attribute them to prelingual cognitive systems? I call this second problem “The Distribution Problem”. -/- The main aim of the paper is providing a solution to both problems by proposing a naturalistic explication of the notion of “concept”. -/- I propose to identify the role concepts were supposed to play in perception with a mechanism of “soft detection”. Unlike hard detectors which react to a specific target in virtue of their constitution and placement in the system, soft detectors are understood as dynamic categorization devices enabling the cognitive system to selectively react to an undetectable property via flexible exploitation of data from hard detectors. -/- I conclude by showing how the notion of soft detection retains some of the aspects traditionally attributed to concepts and how does it differ from similar accounts known from contemporary literature. (shrink)

Now that she is old enough to be taken to boring, so-called “cultural” events by her aging, academic relatives, we have just taken Anya to see a performance of Julius Caesar. When it’s over, we discuss the acting, the poetry, the famous lines. At some point, Anya asks: “I wonder if it happened like that?” Anya has not radically misunderstood what we just watched; she did not, for example, rush down and yell at Caesar that he’d better read that scroll. (...) Her question is not uncommon as a response to a history play, from audience members both young and old. It is perfectly intelligible; I would like to give her an answer. Before I sketch some possible answers, it is worth saying something more about Anya’s. (shrink)

The debate over whether ‘fair-play’ can serve as a justification for legal punishment has recently resumed with an exchange between Richard Dagger and Antony Duff. According to the fair-play theorist, criminals deserve punishment for breaking the law because in so doing the criminal upsets a fair distribution of benefits and burdens, and punishment rectifies this unfairness. Critics frequently level two charges against this idea. The first is that it often gives the wrong explanation of what makes crime deserving (...) of punishment, since the wrongfulness of murder is not primarily about unfairness. The second is that it implies that all crimes deserve the same degree of punishment, because all crimes create the same degree of unfairness. These objections are viewed as revealing fatal flaws in the theory. Although Dagger attempts to meet these objections by drawing on political theory, Duff responds that this still draws upon the wrong kind of resources for meeting these objections. This paper argues that these two objections rest on a crucial mistake that has been overlooked by both the defenders and critics of fair-play. This mistake results from failing to distinguish between what justifies punishment as a response to crime (which requires a common element to all crime) and what justifies attaching particular penalties to crimes (which requires making distinctions in the severity of crime). The arguments presented will give reasons to consider fair-play as a viable justification for legal punishment. (shrink)

This article proposes a brief argument for why mathematics is transcendental in so far as the concept of infinity emerges from it; this ultimately relies on the understanding that math gives a metaphysical justification for non-existence or "0".

Games, play and gamification, used in organized public library programs, are ways in which libraries can attract a larger audience, especially those who are not yet interested in reading. In this way, contact with the library would enable them to find out about other resources that these cultural institutions offer, thus encouraging them to become regular patrons of non-game services. This paper aims to find out whether these new ways have been used in activities carried out with the public (...) in the Bucharest Metropolitan Library. Research on games, play and gamification in public libraries is very limited in Romania and it could benefit researchers and librarians alike. A content analysis was done on the posts made on Facebook in 2023 by the Bucharest Metropolitan Library. The findings of the study showed that games, play and gamification were used mostly in thematic activities combined with reading, learning and creative workshops. Collaboration with institutions, associations and other organizations has increased the quality of the services offered. The research is valuable in that it presents activities in which librarians have used games, play and gamification, thus offering ideas for all Romanian librarians who could implement these tools on a larger scale in our public libraries. (shrink)

While trying to preserve the autonomy of their playful activity consisting in a game of ‘questioning and answering’, the Gymnosophists defy Alexander the Great and, more importantly, go against their own chances of survival (since giving a wrong answer to the king’s question amounts to losing their life). Thankfully, we do not need to face such dilemmas when philosophising with children. Nevertheless, the Gymnosophists’ example helps construct a notion of philosophy for/with children as an autonomous playful activity that albeit (implicitly) (...) purposive it is, however, without (explicit) purpose (something akin to Kant’s aesthetic judgement). Alluding to an Aristotelian sense of ‘telos’ in its connection with Platonic ‘paideia’ I understand philosophy for/with children as an activity that we carry out for its own sake. This does not mean that we are to abolish elements such as antagonism, competition, excellence, etc.―there is no question: the competitive element is there. But what does it mean? We could fix its meaning according to a purpose (we compete to excel or persuade and win) or we might entertain the idea of keeping its meaning rather vague or undetermined, implicit. (shrink)

What is the value of intellectual playfulness? Traditional characterizations of the ideal thinker often leave out playfulness; the ideal inquirer is supposed to be sober, careful, and conscientiousness. But elsewhere we find another ideal: the laughing sage, the playful thinker. These are models of intellectual playfulness. Intellectual playfulness, I suggest, is the disposition to try out alternate belief systems for fun – to try on radically different perspectives for the sheer pleasure of it. But what would the cog-nitive value be (...) of such playfulness? I suggest that intellectual playfulness function as, at the very least, a kind of intellectual insurance policy against epistemic traps. An epistemic trap is a belief system that re-directs good-faith inquiry to bad results. Am epistemic trap manipulates background beliefs to fend off contrary evidence. For example, a conspiracy theory might include a set of beliefs about how the mainstream media has been taken over by some vicious cabal. Normal epistemic attempts will be captured by a well-wrought epistemic trap, because normal attempts at inquiry are guided by these background beliefs -- which set what counts as a plausible path to explore, and what is implausible or beyond the pale. And a clever epistemic trap will manipulate those background beliefs for ill effect. Intellectual playfulness, on the other hand, isn’t motivated by an epistemic interest in the truth, but in the sheer pleasure of intellectual exploration. Since intellectual playfulness isn’t oriented towards the truth, it won’t be constrained by an agent’s background beliefs – it won’t, for example, prefer to investigate apparently more plausible pathways. Intellectual playfulness offers an opportunity to escape from epistemic traps. But intellectual playfulness has its own limitations. It will only drive us to explore belief systems when that exploration is fun. What we need is an array of differently-motivated exploratory tendencies – empathy, curiosity, playfulness – each of which will each cover for the others’ limitations. (shrink)

We attribute three major insights to Hegel: first, an understanding of the real numbers as the paradigmatic kind of number ; second, a recognition that a quantitative relation has three elements, which is embedded in his conception of measure; and third, a recognition of the phenomenon of divergence of measures such as in second-order or continuous phase transitions in which correlation length diverges. For ease of exposition, we will refer to these three insights as the R First Theory, Tripartite Relations, (...) and Divergence of Measures. Given the constraints of space, we emphasize the first and the third in this paper. (shrink)

Understandings of play are frequently tied to a sense of instinctual gratification—a something that must be completed, that all humans, young or old, should or need to partake in. Indeed, for many, play is characterised as a unique activity that stands apart from the ordinary and every day. While such assessments prefigure a clear demarcation between the fun of play and the more laborious, boring aspects of profane life, what this distinction alludes to is a greater sense (...) of the creativity that underlies play. Drawing from a Lacanian perspective, the following chapter will determine that an essential aspect of play and sport is the creativity it provides, namely, by considering how the act of creativity is intricately tied to the very lack that constitutes the Lacanian subject. To do so, the concept of sublimation is used to consider how the codified rules and regulations that sport both asserts and requires renders apparent the importance of the limit. Rather than conceiving of this limit as a barrier to creativity, what is revealed in sublimation is how this limit proves constitutive of our very creativity. That is, the ability to sublimate—to creatively perform unique displays of physical or artistic expression— lies in the mundanity and utter importance of the playful and sporting activity and, more importantly, the inherent restrictions and constraints these activities impose. It is in accordance with the limit that one’s creativity can expose an emancipatory potential in the context of play and sport. (shrink)

In ethical reflections on new technologies, a specific type of argument often pops up, which criticizes scientists for “playing God” with these new technological possibilities. The first part of this article is an examination of how these arguments have been interpreted in the literature. Subsequently, this article aims to reinterpret these arguments as symbolic arguments: they are grounded not so much in a set of ontological or empirical claims, but concern symbolic classificatory schemes that ground our value judgments in the (...) first place. Invoking symbolic arguments thus refers to how certain new technologies risk undermining our fundamental symbolic distinctions by which we organize and evaluate our interactions with the world and in society. Such symbolic distinctions, moreover, tend to be resilient against logical argumentation, mainly because they themselves form the basis on which we argue in the cultural and ethical sphere in the first place. Therefore, effective strategies to evaluate and counter these arguments require another approach, showing that these technologies either do not challenge these classifications or, if they do, how they can be accompanied by the proper actions to integrate these technologies into our society. (shrink)

The central concern of this paper is to explore the efforts of Schiller's post-Kantian idealism and Marcuse's critical theory to develop a new conception of free human experience. That conception is built on the notion of play. Play is said to combine the human capacities for physical pleasure and reason, capacities which the modern world has dualized. Analysis of their respective accounts of play reveals its ambivalent form in the work of both philosophers. Play supports the (...) ideal of ‘freedom from necessity’, understood as a release from all external constraint. But it also appears to serve as a model for ‘freedom as a higher necessity’. In the case of Schiller, the ambivalence encompasses idle play and an obligation to make ourselves worthy of freedom. For Marcuse, play represents a kind of libidinal idleness while also underpinning a non-alienated conception of labour. (shrink)

This article argues that the Indian philosopher-mystic Sri Aurobindo espoused a sophisticated form of cosmopsychism that has great contemporary relevance. After first discussing Aurobindo’s prescient reflections on the “central problem of consciousness” and his arguments against materialist reductionism, I explain how he developed a panentheistic philosophy of “realistic Adwaita” on the basis of his own spiritual experiences and his intensive study of the Vedāntic scriptures. He derived from this realistic Advaita philosophy a highly original doctrine of evolutionary cosmopsychism, according to (...) which the Divine Saccidānanda is “involved” in everything in the universe and gradually manifests itself at each stage of the evolutionary process from matter to life to mind, and ultimately, to Supermind—the final stage that is yet to come, upon the attainment of which we will attain knowledge of our true divine nature as Saccidānanda. I then reconstruct Aurobindo’s novel solution to the individuation problem, according to which the Divine Saccidānanda individuates into various distinct consciousnesses by playfully limiting itself through a process of “exclusive concentration.” Finally, I highlight the continued relevance of Aurobindo’s evolutionary cosmopsychism by bringing him into conversation with Itay Shani, a contemporary proponent of cosmopsychism. (shrink)

This paper examines Plato’s conception of shame and the role intoxication plays in cultivating it in the Laws. Ultimately, this paper argues that there are two accounts of shame in the Laws. There is a public sense of shame that is more closely tied to the rational faculties and a private sense of shame that is more closely tied to the non-rational faculties. Understanding this division between public and private shame not only informs our understanding of Plato’s moral psychology, but (...) his political and ethical theory as well. (shrink)

This papers responds to a recent argument by Sophie Gibert concerning the wrong of wrongful manipulation. I argue that the more serious explanatory question is whether manipulation is wrong by default, not whether, when manipulation is wrong, this wrong is ‘basic’. The former better elucidates the significance of Gibert’s arguments. I then respond to her argument, construed as the argument that manipulation is not wrong by default. First, the putative counterexamples she presents are drawn from areas of work and (...) class='Hi'>play – legal advocacy, negotiation, and gameplay – where the moral status of manipulative tactics is very much in dispute; thus, her reported intuitions are not persuasive. Second, even if we grant that manipulation in these contexts is morally permissible, we can explain how it remains wrong by default by appealing to competitive conventions that realize common epistemic, aesthetic, and hedonistic goods. I also show why Gibert’s reply to this conventionalist maneuver fails. (shrink)

For praising Jehovah (Yahowah is Yeshua Ben Joseph) do I publish these mathematical gesturing forms by His graciousness. The Book of Eternity proposes a new, mathematical balancing language in which the logic stems from infinity instead of zero. The designation of the balance comes from the location at which different meanings of infinity linguistically balance with each other and provides a way for people to continue extrapolating forms and functions that logically would follow. This balancing at oneness is analogous to (...) the resurrection of Jesus as the phenomenological velocity can come into being or be canceled out and have no effect. So, when Jesus died, that was the canceling out, and when Jesus (Yeshua Ben Joseph Jehovah) was raised, that was the coming into being. As the Resurrection, He is intimately tied to the creation as the savior. This can be expressed mathematically. As oneness, this balancing is infinite and meets symbolically with the differentiated meanings of oneness. The oneness is both the canceling (of the square roots within the height function), and the intersection of meanings (of infinity through the word of Jehovah (Yahowah)). This book elucidates the kinds of dimensionality with which man interacts normally: distance, angle, number, mass. (shrink)

Recent philosophy of science has seen a number of attempts to understand scientific models by looking to theories of fiction. In previous work, I have offered an account of models that draws on Kendall Walton’s ‘make-believe’ theory of art. According to this account, models function as ‘props’ in games of make-believe, like children’s dolls or toy trucks. In this paper, I assess the make-believe view through an empirical study of molecular models. I suggest that the view gains support when we (...) look at the way that these models are used and the attitude that users take towards them. Users’ interaction with molecular models suggests that they do imagine the models to be molecules, in much the same way that children imagine a doll to be a baby. Furthermore, I argue, users of molecular models imagine themselves viewing and manipulating molecules, just as children playing with a doll might imagine themselves looking at a baby or feeding it. Recognising this ‘participation’ in modelling, I suggest, points towards a new account of how models are used to learn about the world, and helps us to understand the value that scientists sometimes place on three-dimensional, physical models over other forms of representation. (shrink)

This paper sought to investigate the fundamental differences in mathematics education through a comparison of curriculum of 2 countries—Singapore and Canada (as represented by Ontario)—in order to discover what the Ontario education system may learn from Singapore in terms of mathematics education. Mathematics curriculum were collected for Grades 1 to 8 for Ontario, and the equivalent in Singapore. The 2 curriculums were textually analyzed based on both the original and the revised Bloom’s taxonomy to expose their foci. The difference in (...) focus was then compared and discussed to find the best ways to improve the Ontario mathematics curriculum. With one of the best education systems in North America, the Ontario mathematics curriculum would only need to refocus its attention towards a more balanced approach, with greater focus on understanding through practices. Ontario would benefit greatly from a deeper research into the Singaporean math curriculum. (shrink)

The ecological approach to object pretend play, developed from the ecological perspective, suggests an action- and affordance based perspective to account for pretend object play. Theoretical, as well as empirical reasons, support the view that children in pretense incorporate objects into their play in a resourceful and functionally appropriate way based on the perception of affordances. Therefore, in pretense children are not distorting reality but rather, they are perceiving and acting upon action possibilities. In this paper, we (...) argue for the viability of an ecological theoretical framework to pretend object play which has been traditionally understood as a representational and metarepresentational ability. We discuss the origins and basic assumptions of the ecological approach to pretense. We layout details by presenting a qualitative analysis of a pretend play episode and discuss the results of an experimental study inspired by the ecological assumptions. We discuss pretend object play in the context of ecological work on tool use. We address the relationship between the enactive and the ecological approaches to pretend play, pointing out similarities as well as differences. We conclude that ecological and enactive approaches have shown that it is possible to challenge accepted interpretations and seek explanatory frameworks that could move the field in new directions. (shrink)

According to cognitive psychologists, moral decision-making is a dual-process phenomenon involving two types of cognitive processes: explicit reasoning and implicit intuition. Moral development involves training and integrating both types of cognitive processes through a mix of instruction, practice, and reflection. Serious games are an ideal platform for this kind of moral training, as they provide safe spaces for exploring difficult moral problems and practicing the skills necessary to resolve them. In this article, we present Morality Play, a model for (...) the design of serious games for ethical expertise development based on the Integrative Ethical Education framework from moral psychology and the Lens of the Toy model for serious game design. (shrink)

In this paper I investigate the relationship between the serious and the playful elements in Socrates’ character as these unfold within the context of Xenophon’s Symposium. For the Greeks, the concept of value is attached to the meaning of seriousness, and this accounts for the natural preference for the serious over the playful. Despite the potential rivalry of the playful and philosophy, Socrates mixes the playful with the serious in such a way as to conceal their boundary. This mixing serves (...) the purpose of education, by both attracting us to Socrates and placing us at a distance from the intended meaning of his words. (shrink)

Sabine Hossenfelder’s recent book “Lost in Math” has attracted numerous responses, including by notable physicists such as Frank Wilczek. In this article we focus on Wilczek’s remark on that book, in particular on the perils of postempirical science. We also discuss shortly multiverse hypothesis from philosophical perspective. In last section, we offer a resolution from the perspective of Neutrosophic Logic on this problem of classical tension between mathematics and experience approach to physics, which seems to cause the stagnation of (...) modern physics. (shrink)

Focusing on the 'today'/'yesterday' case, I argue that Perry is wrong in accounting for and explaining indexical belief states in terms of Kaplanian characters and in taking these states to be internal (narrow) mental states inside the subject's mind. It is shown that this view is at odds with Perry's own reliance on remembering a past day as a necessary condition for retaining a belief about it. As a better tool for explaining appropriate indexical beliefs, I offer an alternative which (...) is neo-Fregean in that it takes senses or modes of presentation as playing only a cognitive, not a semantic role. It, however, takes remembering a past day as necessary for retaining a belief about it, rather than keeping track of time as urged by Evans. I also consider unfeasible Evans's further requirement which he takes over from Frege: that in order to retain a belief about a certain past day we need to think of it now under the same mode of presentation as we did on that very day. (shrink)

Scott Kretchmar recently put forth a new definition of what it is to play a game. Unfortunately, it must be rejected. In this paper, I show that this new definition is far too broad by discussing an activity that is not an instance of playing a game but is wrongfully ruled as one on this new definition.

“Playing the Academic Game” is the culmination of two years of weekly posts on the BrynStorming blog by Bryn Williams-Jones, professor of bioethics in the School of Public Health at the Université de Montréal. -/- As an ethicist long interested by questions of justice, an important motivator for this project has been Williams-Jones’ need to respond to the injustices encountered in academia. Many students and researchers fail in their studies or career progression not because they don’t have the intellectual abilities (...) or drive, but simply because they don’t know what’s expected of them or how to best present themselves in a competitive environment. That is, they don’t know “the rules of the game,” and this isn’t fair, because the rules are rarely made explicit. -/- In this book, which is organized into 5 major sections – The Academic Career Path, Professional Identity, University Life, Productivity and Creativity, and Multiple Responsibilities and Mental Health – Williams-Jones shares 30 years of experience in academia to make explicit the often-implicit norms and rules of academic life, so that all who wish to can fairly play the academic game. (shrink)

This study focused on creating an Audio-Visual Strategic Intervention Material (SIM) to help Grade 7 students improve their skills in performing fundamental operations on integers in Mathematics. The research used an Educational Design Research approach and selected participants through purposive sampling. Data collection involved a checklist and rating scale, and analysis was carried out using frequency and mean. The findings revealed that mastering fundamental operations on integers had consistently been the most challenging skill for Grade 7 students during the first (...) quarter over the past three academic years. The SIM underwent a thorough validation process done by expert validators, including Mathematics teachers and content specialists, who assessed its content, instructional design, and technical quality. The experts provided a mean rating of 3.63, indicating that the material was of very high quality. The high validation scores affirmed that the Audio-Visual SIM met high standards in terms of content accuracy, instructional effectiveness, and technical presentation. The study highlights the potential of audio-visual materials as an effective tool for addressing learning gaps in Mathematics, providing educators with a valuable resource to improve students' foundational skills in integer operations. The findings also guided the planning of extension activities, and recommendations for further refinement and broader use of the SIM were provided. To continue assisting students in overcoming these challenges, the Institution, through its extension program, may offer workshops, seminars, and training sessions on the creation and use of Audio-Visual SIMs. (shrink)

Recent work has explored the extent to which intercollegiate athletics even belong at the university or meet the university’s mission. Just as play seems evident in athletics, it is also present in music, art, and theater. While these programs are popular targets when discussing possible cuts, few question their legitimacy at the university. In this article I argue that the justification for retaining the extracurricular status of intercollegiate sports should be based on their being especially playful. Indeed, on the (...) basis of this argument, I suggest that universities offer even greater and wider access to sport through club and intramural sports. However, while athletics might appear to be more playful, I hold that there is substantially more play present in university music, art, and theater programs than there is in intercollegiate sports. (shrink)

It is trivially true that comedians make jokes and thus are not serious; they are “just playing.” But watching Louis CK, especially his performances in Chewed Up, Shameless, and Hilarious, it is evident that he has more in mind than simply getting his audience to frivolously guffaw. I will make the case that this is so given the content of some of his humor which centers on areas of socio-political-ethical tensions that can be uncomfortable when addressed in a direct, “bona-fide” (...) communicative mode. I will concentrate upon his playful, yet serious, account of issues surrounding race and privilege which, though not obvious center-pieces, can be found in almost all of his performances. These are complex areas that are not obvious fodder for humor, and it is clear that his comedic repertoire is broad enough that he is not including these issues for lack of funnier bits. I will argue that through his humor, he at once brings to consciousness hidden biases, challenges them in a subversive manner on behalf of those harmed by cultural stereotypes, e.g., and opens up an otherwise adversarial audience to the possibility that they harbor such unwanted stereotypes—a necessary element in consciousness-raising. My account will require a brief distinction between seriousness and playfulness, a defense of the claim that we are drawn to humor even when it is used to question our cherished presuppositions, and an interpretation of thought experiments that parallels Louis CK’s comedic mechanisms in his stand-up performances and episodes from Louie. In some cases he is explicit that he is just “making shit up” (Oh My God), or, as he cautions in the setup to a story in Shameless, “it doesn’t matter cus’ I’m gonna lie to you.” But that does not take away from my point that he is serious with his humor about social reality in the same way that philosophers have traditionally “made shit up” with thought experiments for serious purposes. Louis CK employs a similar device with his humor, and in many ways is more effective than philosophers in making the implicit explicit for his (much larger) audiences who then spread his word. (shrink)

In this dissertation I achieve the following: (1) I present motivating criteria for a general comprehensive theory of scientific explanation. I review historical approaches to modeling explanation in light of these criteria. (2) I present New Mechanist Explanation ("NME") as the leading candidate for a contemporary, complete theory of scientific explanation. (3) I present constraints on the applicability of New Mechanism in modeling biology, chemistry, and physics. I argue for the unsuitability of NME as a candidate for a general theory (...) of explanation due to its significant omissions of explanatory content and subsequent incompleteness. (4) I present arguments for the indispensable explanatory power of mathematics in science, noting that much of NME's failures are owed to its poor integration of mathematical explanation as applied to science. (5) I propose a Rational-Relational theory of explanation(“RRE”). I present RRE in detail and demonstrate it as a true working general theory of explanation which best meets the motivating criteria presented in (1). I disambiguate RRE from structural explanation ("SE"). I show that historical models of explanation, including the deductive nomological (DNE) model, statistical relevance ("SRE") model, structural model (SE) and unification model ("UE") may be successfully treated as sub-classes of explanation within the scope of RRE. I provide a rubric for selecting amongst sub-theories of explanation under RRE in the purpose of highlighting particular features of relational explanations. (6) In conclusion, I argue that philosophers of science should move forward using RRE as a general model of scientific explanation as a working alternative to the incomplete model of NME. (shrink)

When the phrase “playing God” is used in debates concerning the use of new technologies, such as cloning or genetic engineering, it is usually interpreted as a warning not to interfere with God’s creation or nature. I think that this interpretation of “playing God” arguments as a call to non-interference with nature is too narrow. In this paper, I propose an alternative interpretation of “playing God” arguments. Taking an argumentation theory approach, I provide an argumentation scheme and accompanying critical questions (...) that capture the moral concerns expressed by “playing God” arguments. If I am right, then “playing God” arguments should be understood, not as a warning to leave God’s creation or nature alone, but rather as an invitation to think carefully about all the ways in which the use of new technologies could go seriously wrong. (shrink)

This is a reply to commentators in the Journal of the Philosophy of Sport's special issue symposium on GAMES: AGENCY AS ART. I respond to criticisms concerning the value of achievement play and striving play, the transparency and opacity of play, the artistic status of games, and many more.

Citation:Christodoulou, Marina. “Technopolis as the Technologised Kingdom of God. Fun as Technology, Technology as Religion in the 21st Century. God sive Fun.” Cahiers d'études germaniques N° 74, 2018. La religion au XXIe siècle - Perpectives et enjeux de la discussion autour d'une société post-séculière. Études reunites par Sébastian Hüsch et Max Marcuzzi, 119-132. -/- -------- -/- Neil Postman starts his book Technopoly: The Surrender of Culture to Technology (1993)1 with a quote from Paul Goodman’s New Reformation: “Whether or not it (...) draws on new scientific research, technology is a branch of moral philosophy, not of science.” (Postman 1993: motto; Goodman 2010: 40). I would extend Postman’s Technopoly to Technopolis, to give it more of a presence in time and space. Hence, I will use the term Technopoly when I am referring to Postman; the term Technopolis is my own. -/- In his book From Faith to Fun: The Secularisation of Humour, Russel Heddendorf argues that humour is a technology (Heddendorf 2009: 32-34), as it is understood and theorized by Neil Postman in Technopoly. Russel Heddendorf also argues that “Technopoly” is a term correlated with Wittgenstein’s use of the term “worldview” (Weltanschauung) (Heddendorf 2009: 11). -/- I would like to draw on these thoughts to propose that Technopoly (or Technopolis) could be the secularized Kingdom of God, namely that Technology is the Religion of the 21st century, and that Fun is a paradigm of such a Technology / Technique. God is yet another technique or Technology of and in Technopoly. -/- The godless individual in the 21st century, I will argue, is as much a believer as the faithful in the Sacred Religion (term used in opposition to Secular or rather Technological or Technologized Religion, which is Fun). He believes in Fun (as a post-modern form of pleasure), as much as the believer believes, or more accurately, believed in God. In the 21st century, the faithful in Sacred Religion believes in a fun God, as opposed to the serious God of the past. Fun is turning into the Technologized Religion for all; for the faithful in Godly / Sacred Religion, as well for as the unfaithful. Fun (pleasure, humour) is the definitive qualia of 21st century pleasure. The mechanics of Fun make it absolutely functional for controlling people; as Aldous Huxley wrote in Brave New World, people “are controlled by inflicting pleasure” (cited in Heddendorf 2009: 158). Now, indulging in pleasure is having Fun. In the 21st century, nobody is unfaithful, nobody disputes God, because God has been manufactured into Fun. We are living in the most religious century of all. -/- The commodity of God, now inextricably blended into work and leisure ethics and culture, is as unavoidable as survival. You don’t work, you don’t survive, you don’t exist. You work, you are entitled to leisure, or free time – the time (“busy-time”) when you are busy is work. The free time of leisure (“fun-time”) is a time for fun (pleasure). The time dedicated to Fun is culturally (capitalistically) pre-defined; no moment is actually free, each moment that is sold as free is to be bought with Work Time tokens –which is money. Believe is Enjoy. Happiness, achieved through pleasure, and pleasure through Fun, and Life as Play, is the recipe for Teleology in the 21st century. -/- The Technological God (Fun), as the Sacred God before him, is sovereignty’s technique or a social “mode of release”: demonstrations, marches, petitions, freedom of speech, citizen and human rights vindications, are “modes of release”, so that the next day, feeling relieved and released that you are working for a better life and a better world, you can wake up cheerfully to walk to your workplace, feeling it will change because of your marching, or your petition, or your speech, or the mass you attended, or the prayer you said yesterday. Thus life continues unchanging, through postponing hope; the tension of the tragedy is always released (lysis) in catharsis: refreshment for the next day of work. Art, especially cinema, (namely, simulated life) follows the same cathartic principles as real life. Thus, you can keep coping, and hoping in the meantime is of much help. Religion, Art, Science, Therapy, and Technology are all technologies used to market life, sell it or lend it, and humans are buying it back. Fun is free to produce, and expensive to buy. (shrink)

A central debate in philosophy and neuroscience pertains to whether PFC activity plays an essential role in the neural basis of consciousness. Neuroimaging and electrophysiology studies have revealed that the contents of conscious perceptual experience can be successfully decoded from PFC activity, but these findings might be confounded by post- perceptual cognitive processes, such as thinking, reasoning, and decision-making, that are not necessary for con- sciousness. To clarify the involvement of the PFC in consciousness, we present a synthesis of research (...) that has used intracranial electrical stimulation (iES) for the causal modulation of neural activity in the human PFC. This research provides compelling evidence that iES of only certain prefrontal regions (i.e., orbitofrontal cortex and anterior cingu- late cortex) reliably perturbs conscious experience. Conversely, stimulation of anterolateral prefrontal sites, often con- sidered crucial in higher-order and global workspace theories of consciousness, seldom elicits any reportable alterations in consciousness. Furthermore, the wide variety of iES-elicited effects in the PFC (e.g., emotions, thoughts, and olfactory and visual hallucinations) exhibits no clear relation to the immediate environment. Therefore, there is no evidence for the kinds of alterations in ongoing perceptual experience that would be predicted by higher-order or global workspace theories. Nevertheless, effects in the orbitofrontal and anterior cingulate cortices suggest a specific role for these PFC subregions in supporting emotional aspects of conscious experience. Overall, this evidence presents a challenge for higher-order and global workspace theories, which commonly point to the PFC as the basis for con- scious perception based on correlative and possibly confounded information. (shrink)

I respond to a hypothetical critique of sport, drawing on primarily post-modernist sources, that would view the high performance athlete in particular as a product of the application of technical disciplines of power and that opposes sport and play as fundamentally antithetical. Through extensive discussion of possible definitions of play, and of performance, I argue that although much of the critique is valid it confuses a method of sport for the whole of it. Play is indeed a (...) noncompellable spontaneity, but one that involves the improvisational transformation of the technical skills of a sport within the context of a dynamic situation. Technique is a condition of heightened play; it does not produce it. This also means that the best play is not undisciplined. Play and sport can exist apart, but both are better combined. (shrink)

In the sense-certainty chapter of the Phenomenology of Spirit, we find one of Hegel’s famous puns, which utilizes homophonic affinities and differences between the verb beiherspielen and the noun Beispiel. I argue that the effect of this pun is that the word Beispiel acquires, beyond its usual meaning of ‘example’ or ‘instance’, the meaning of a play of something inessential, a play in passing. After reviewing all available translations into English, I suggest that, in order to preserve this (...) wordplay, one can translate Beispiel as ‘by-play’. Furthermore, I analyse other occurrences of the word beiherspielen in the Phenomenology and elsewhere in Hegel’s texts. Next, I focus on the crucial importance of this pun for Derrida’s interpretation and critique of Hegel’s dialectic. Only for a certain loose translation of beiherspielen does Derrida’s reasoning appear plausible. I conclude with a discussion of the ideal of terminological uniformity in translating Hegel’s texts. In preserving the wordplay by translating Beispiel as ‘by-play’, one is forced to sacrifice the uniformity of translation. (shrink)

Elementary preservice teachers (EPTs) substantially impact the quality of mathematics education, and their subject preference and problem-solving performance are essential indicators of their readiness to teach. The study described EPTs’ subject preference and problem-solving performance. Through a sequential explanatory research design, the quantitative inquiry involved 125 random samples, while the qualitative inquiry was participated by 30 non-random samples. Data were obtained by using an online survey and conferencing. Quantitative data were analyzed through descriptive statistics and analysis of variance, whereas qualitative (...) data were themed accordingly. The EPTs displayed unsatisfactory problem-solving performance and preferred to handle subjects other than math. Besides, the analysis found no significant performance differences with the EPTs’ subject preferences. Further, the EPTs who preferred to teach mathematics expressed their confidence in mathematics. Meanwhile, the EPTs who preferred other subjects displayed math avoidance. The study revealed an alarming result indicating that the EPTs are unprepared for teaching. As agents in cultivating the nation’s mathematics education status, these EPTs must be equipped with fundamental content knowledge. It is suggested that educational decision-makers take measures to address the issues identified concerning EPTs’ readiness to teach mathematics successfully. (shrink)

Art is universal across cultures. Yet, it is biologically expensive because of the energy expended and reduced vigilance. Why do humans make and contemplate it? This paper advances a thesis about the psychological origins of perceptual art. First, it delineates the aspects of art that need explaining: not just why it is attractive, but why fine execution and form—which have to do with how the attraction is achieved—matter over and above attractiveness. Second, it states certain constraints: we need to explain (...) pleasure in contemplation, not value extracted from the object by activities other than contemplation. The theory is that aesthetic pleasure is a motivation for learning skills. Two forms of pleasure are postulated. The first accompanies the spontaneous activity necessary for learning a more or less universal basic level of skill. The second accompanies highly skilled activity. This second kind of pleasure is specific to art as such. (shrink)