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.

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)

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)

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)

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)

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)

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)

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)

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".

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)

In this paper, I will reread the history of molecular genetics from a psychoanalytical angle, analysing it as a case history. Building on the developmental theories of Freud and his followers, I will distinguish four stages, namely: (1) oedipal childhood, notably the epoch of model building (1943–1953); (2) the latency period, with a focus on the development of basic skills (1953–1989); (3) adolescence, exemplified by the Human Genome Project, with its fierce conflicts, great expectations and grandiose claims (1989–2003) and (4) (...) adulthood (2003–present) during which revolutionary research areas such as molecular biology and genomics have achieved a certain level of normalcy—have evolved into a normal science. I will indicate how a psychoanalytical assessment conducted in this manner may help us to interpret and address some of the key normative issues that have been raised with regard to molecular genetics over the years, such as ‘relevance’, ‘responsible innovation’ and ‘promise management’. (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)

Current work in language models (LMs) helps us speed up or even skip thinking by accelerating and automating cognitive work. But can LMs help us with critical thinking -- thinking in deeper, more reflective ways which challenge assumptions, clarify ideas, and engineer new concepts? We treat philosophy as a case study in critical thinking, and interview 21 professional philosophers about how they engage in critical thinking and on their experiences with LMs. We find that philosophers do not find LMs to (...) be useful because they lack a sense of selfhood (memory, beliefs, consistency) and initiative (curiosity, proactivity). We propose the selfhood-initiative model for critical thinking tools to characterize this gap. Using the model, we formulate three roles LMs could play as critical thinking tools: the Interlocutor, the Monitor, and the Respondent. We hope that our work inspires LM researchers to further develop LMs as critical thinking tools and philosophers and other 'critical thinkers' to imagine intellectually substantive uses of LMs. (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)

Limitless is a movie (released in 2011) as well as a novel (published in 2001) about a tormented author who (plagued by a writer’s block) becomes an early user of an experimental designer drug. The wonder drug makes him highly productive overnight and even allows him to make a fortune on the stock market. At the height of his career, however, the detrimental side-effects become increasingly noticeable. In this article, Limitless is analysed from two perspectives. First of all, building on (...) the views of the French novelist Emile Zola, the novel is seen as the report of a closely monitored experiment. Subsequently, building on the phenomenology of Ludwig Binswanger, I will show how the cognitive enhancement drug not only boosts the protagonist’s information processing capacities, but also modifies his experience of space and time, his sense of spatiality, his way of being-in-the-world. On the basis of these (complementary) analyses I will indicate how genres of the imagination (such as movies and novels) may play a significant role in assessing the societal implications of emerging technological developments such as neuro-enhancement, especially during the preparatory or anticipatory stage. (shrink)

In this paper I offer a reconstruction of the account of meaning and language the Cyrenaics appear to have defended on the basis of a famous passage of Sextus, as well as showing the philosophical parentage of that account.

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)

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)

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)

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 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)

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)

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 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)

Research in education indicates that the Philosophy for Children (P4C) curriculum is instrumental in achieving important educational objectives. And yet, it is precisely this instrumentalist conception of P4C that has been challenged by a second generation of P4C scholars. Among other things, these scholars argue that P4C must remain vigilant toward, and avoid subscribing to 1) developmentalism and 2) a reductive identification of thinking with rationality. On the contrary, they suggest that P4C must ensure that it gives voice to childhood, (...) allowing it to enter a genuine dialogue with adulthood. Scholars who defend a non-reductive and non-instrumentalist approach to P4C, highlight the significance of play in philosophy sessions with children. In this paper I examine the extent to which the philosophical inquiry that takes place in the context P4C can be understood as a playful activity. I submit that Fink’s account of play can help us reach a better understanding of what we mean by play, which in turn can help us examine the compatibility between the activities of P4C and play. In the first part of the paper, I examine some of the basic ideas of P4C and raise the question about the compatibility of philosophical inquiry and play. In the second part of the paper, I engage in a philosophical appreciation of play by drawing on the work of Eugen Fink. In the final part of the paper, I show how play – understood along Fink’s lines – is compatible with philosophical inquiry as practiced in school settings. (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)

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)

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)

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)

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)

Dr Stockmann, the principal character in Henrik Ibsen's A Public Enemy, is a classic example of a whistle-blower who, upon detecting and disclosing a serious case of environmental pollution, quickly finds himself transformed from a public benefactor into a political outcast by those in power. If we submit the play to a 'second reading', however, it becomes clear that the ethical intricacies of whistle-blowing are interwoven with epistemological issues. Basically, the play is about the complex task of communicating (...) scientific (notably microbiological) data to lay audiences. This becomes even more apparent when we realise that Stockmann was a contemporary of real 'microbe hunters' such as Pasteur and Koch. The play's basic message is that epoch-making scientists (such as Pasteur and Koch) not only produced convincing and reliable data from a scientific point of view, but also acquired the skills and insights needed to enter into a dialogue with their cultural and societal environment. (shrink)

Using William Shakespeare’s Hamlet and the play-within-the play, The Murder of Gonzago, as a case study, this essay argues that theatrical utterances constitute a special case of language usage not previously elucidated: the utterance of a statement with propositional content in theatre functions as an event. In short, the propositional content of a particular p (e.g. p1, p2, p3 …), whether or not it is true, is only understood—and understood to be true—if p1 is uttered in a particular (...) time, place, and situation (i.e. during a theatrical event); otherwise, the propositional content in those theatrical utterances can either be false or contingently true. (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)

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.

I discuss the aesthetic power of painful art. I focus on artworks that occasion pain by “hitting too close to home,” i.e., by presenting narratives meant to be “about us.” I consider various reasons why such works may have aesthetic value for us, but I argue that the main reason has to do with the power of such works to transgress conversational boundaries. The discussion is meant as a contribution to the debate on the paradox of tragedy.

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)

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)

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)

A common response to claims of bias, harassment, or discrimination is to say that these claims are made in bad faith. Claimants are supposedly not motivated by a credible or even sincere belief that unfair or unequal treatment has occurred, but simply seek to illicitly gain public sympathy or private reward. Characterizing discrimination claims as systematically made in bad faith enables them to be screened and dismissed prior to engaging with them on their merits. This retort preserves the dominant group’s (...) self-image as unprejudiced and innocent without having to risk critical analysis of the claim’s substance. (shrink)

This article contrasts the sense in which those whom Bernard Williams called ‘political realists’ and John Rawls are committed to the idea that political philosophy has to be distinctively political. Distinguishing the realist critique of political moralism from debates over ideal and non-ideal theory, it is argued that Rawls is more realist than many realists realise, and that realists can learn more about how to make a distinctively political vision of how our life together should be organised from his theorising, (...) although it also points to a worrying tendency among Rawlsians to reach for inappropriately moralised arguments. G. A. Cohen's advocacy of socialism and the second season of HBO's The Wire are used as examples to illustrate these points. (shrink)

The category of works of fiction is a very broad and heterogeneous one. I do have a general thesis in mind about such works, namely, that they themselves are fictional, in much the same way as are the fictional events or entities that they are about. But a defense of such a broad thesis would provide an intractably complex topic for an introductory essay, so I shall here confine myself to a presentation of a similar thesis for narrative theatrical works (...) or plays, performances of which are naturally regarded as involving, or evoking, a “fictional world” whose fictional characters and events are what the work in question is about. Another reason for initially focusing on such narrative plays is because performances of them provide a rich source of epistemic issues about evidence for artistic authenticity or correctness of artworks, which will turn out to be of integral importance to my fictionalist account of plays. (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)

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)

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 study is a phenomenological inquiry into several relatively unexplored phenomena, including certain key methodological issues. It seeks to elicit and explicate the grounds of free-fantasy variation, which Husserl insists contains his “fundamental methodological insight” since it articulates “the fundamental form of all particular transcendental methods…” In the course of pursuing the full sense of this method and its grounds, the essay also uncovers the origins and eventual presence of “self” and explores the multiple connections among self, mental life, embodiment (...) and the surrounding world. To that end, it is necessary to take seriously Husserl’s otherwise odd declaration that “‘feigning’ [‘Fiktion’] makes up the vital element of phenomenology as of every other eidetic science…”, and thus that every philosopher must “fertilize” his or her “fantasy” through works of art and history as well as other areas and practices of human life. The essay offers an in-depth probing of several striking but largely unexplored phenomena: exemplifying and possibilizing, and concludes with an exploration of one of the most pervasive themes in phenomenological inquiry: intersubjectivity. (shrink)

The purpose of this essay is to point out the diversity in post-Proppian plot analysis—and, more specifically, to argue that within it one can discern two fundamentally different conceptions of narrative structure. These are not merely different theoretical grids superimposed upon the same phenomena, but represent, in fact, two objectively different types of narrative structure. These two types will be referred to as dramatic structure and instrumental structure, and they may be succinctly characterized by the antonyms 'play' and 'work' (...) respectively. It will be argued that there is a basis in Propp for both conceptions of narrative structure and that Bremond and Greimas, in their efforts to 'generalize' Propp, have each only isolated one of two tendencies coexisting in his analytic approach. Our point of departure will be Propp's concept of the basic unit of plot structure, which he terms the function. This is a complex term. Two senses are distinguished, biological and mathematical-logical. (shrink)

Is there a right or wrong way to play a game? Many think not. Some have argued that, when we insist that players obey the rules of a game, we give too much weight to the author’s intent. Others have argued that such obedience to the rules violates the true purpose of games, which is fostering free and creative play. Both of these responses, I argue, misunderstand the nature of games and their rules. The rules do not tell (...) us how to interpret a game; they merely tell us what the game is. And the point of the rules is not always to foster free and creative play. The point can be, instead, to communicate a sculpted form of activity. And in games, as with any form of communication, we need some shared norms to ground communicative stability. Games have what has been called a “prescriptive ontology.” A game is something more than simply a piece of material. It is some material as approached in a certain specified way. These prescriptions help to fix a common object of attention. Games share this prescriptive ontology with more traditional kinds of works. Novels are more than just a set of words on a page; they are those words read in a certain order. Games are more than just some software or cardboard bits; they are those bits interacted with according to certain rules. Part of a game’s essential nature is the prescriptions for how we are to play it. What’s more, we investigate the prescriptive ontology of games, we will uncover at least distinct prescriptive categories of games. Party games prescribe that we encounter the game once; heavy strategy games prescribe we encounter the game many times; and community evolution games prescribe that we encounter the game while embedded in an ongoing community of play. (shrink)