Scientific journal presented by Bogdan Khmelnitsky Melitopol State Pedagogical University, Ukraine, Melitopol. Main points: 1. Actual Problems of Modern Philosophy 2. Researches in Philosophy connected with natural components, sociological aspects and self - identity development.

Urbaniana University Journal 73.3 (2020): 73-99. -/- A close reading of Hume’s Dialogues Concerning Natural Religion reveals that it is not what it appears. Rather than a work of natural theology, meant to show something about arguments concerning the existence and nature of God, the Dialogues turn out to embody a moral pedagogy exemplifying and attempting to instill a conception of piety and religion as virtues. This paper defends this interpretation by reviewing three alternative, but ultimately inadequate, (...) interpretations of the text, and then compares Hume’s moral pedagogy with that of Aquinas in the Summa Theologiae to highlight the ambition, and the limitation,of Hume’s attempt to characterize piety without metaphysics. (shrink)

Over the past few years we have seen an increasing number of legal proceedings related to inappropriately implemented technology. At the same time career paths have diverged from the foundation of statistics out to Data Scientist, Machine Learning and AI. All of these new branches being fundamentally branches of statistics and mathematics. This has meant that formal training has struggled to keep up with what is required in the plethora of new roles. Mathematics as a taught subject is still based (...) in decades old teaching specifications and has not been updated centrally as a curriculum to include new technologies, coding or ethics. This subject area is firmly split between ICT and Mathematics in secondary school, continuing on to be split between Computer Science and Mathematics at University. As we move forwards with technology we see these once seperate fields becoming increasingly intertwined. We propose that existing provision for concepts such as ethics and societal responsibility in analysis currently exist but have not been incorporated into the mainstream curriculum of School or University. This is partially due to the split between fields in an educational setting but also the speed with which education is able to keep up with Industry and its requirements. Principles and frameworks of socially responsible modelling beginning at school level means that ethics and real-life modelling are introduced much earlier than normal. Integrating these concepts with philosophical principles of society and politics ensures a suitable background for future modellers and users of technology to draw on. Modelling is currently undertaken in technical sciences at University but the Subject Benchmark Statements are not current (Subject Benchmark Statements describe the nature of study and the academic standards expected of graduates in specific subject areas. They show what graduates might reasonably be expected to know, do and understand at the end of their studies). Even in 2019 the UK did not yet have Benchmark Statements that discuss the learning to be done in Higher Education around AI and advanced Machine Learning. Where there is provision for AI and Data Science within degree courses ethics is not generally highlighted as a key concept. As such there can be a lack of focus on the teaching of modelling or ethics as specific skills. The skills required to use a basic statistical model, for example would not be sufficient to start from scratch and build an ethical model reflecting real-world scenarios with which to inform policy or organisational decision making. This is a skill in itself and includes such aspects as awareness of data quality, ethics, user implementation problems, context and an understanding of the environment that the model is being created in. As the field of analytics has progressed so quickly in the last decade modules such as those covering AI have simply been bolted on to Maths or Computing degrees rather than being fully detailed as key areas of study or driving new, more integrated courses of study. This paper posits that gaps at primary, secondary and tertiary educational levels need to be addressed. Implementing and integrating key concepts from school level is essential so that areas such as assumptions, caveats, quality assurance and answering the right questions with constructive challenge become a cultural fixture. This not only helps developers of technology but users of rapidly developing technology also. In addition, leadership and soft skills as part of this education will ensure that a cultural shift can take place and promote continuous improvement in analysis within organisations. The addition of key concepts throughout the educational system and the updating of potentially outdated curriculums is key to ensuring a functional society. A society where every citizen is a user of tech and those that develop it can be ethical and socially responsible in its development. (shrink)

Josiah Parsons Cooke established chemistry education at Harvard University, initiated an atomic weight research program, and broadly impacted American chemical education through his students, the introduction of laboratory instruction, textbooks, and influence on Harvard's admissions requirements. The devoutly Unitarian Cooke also articulated and defended a biogeochemical natural theology, which he defended by arguing for commonalities between the epistemologies of science and religion. Cooke's pre-Mendeleev classification scheme for the elements and atomic weight research were motivated by his interest in numerical (...) order in nature, which reflected his belief in a divine lawgiver. (shrink)

This paper addresses specific concerns that emerge as a consequence to the current educational reforms in the Philippines. These concerns are philosophical and pedagogical. The philosophical concern underscores the importance to situate philosophical thought within concrete historical conditions. In this way, philosophy does not only become a pure abstract enterprise, but an intellectual struggle at the service of historical novelties. I propose a philosophical paradigm that values collective practice at the service of truth. As new situations demand new interpretations and (...) contextualization, I shall also employ a philosophical discourse and practice not only contemporary to, but also one of the bests of our times: the philosophy of Alain Badiou. The pedagogical concern elucidates the political nature of education, which is what Critical Pedagogy argues essentially. This paradigm puts importance above all on the role critical knowledge and collective practice plays in the educational and socio-political arena. The critical pedagogy which I propose is not far from the emancipation politics also embedded in Badiouian Philosophy. Hence, there is a connection between the kind of philosophy I propose and the pedagogical paradigm I present as an alternative. From the philosophical and pedagogical arguments presented, I shall argue for the need to rescue education from the influence of neoliberalism. The resistance necessitates the movement of the collective through the agency of the teacher-militant. (shrink)

Natural Pedagogy refers to social learning based on ostensive communication between adults and infants which results in rapid and efficient transmission of cultural information. The theory predicts that children are able to recognize communicative intention when adults address them using ostensive signals. Furthermore, natural pedagogy predicts that infants ascribe the knowledge they have acquired to others according to what is called the “assumption of universality”. In other words, infants are able to ascribe informative contents to others (...) even when they are outside the bounds of the learning context. Although Csibra and Gergely have so far denied any type of relationship between natural pedagogy and mindreading capacities, I suggest that early mindreading capacities are components of the natural pedagogy system, as recent experimental findings on early Theory of Mind abilities appear to show. (shrink)

Pedagogy is a pillar of human culture and society. Telling each other information and showing each other how to do things comes naturally to us. A strong case has been made that declarative knowledge is the norm of assertion, which is our primary way of telling others information. This article presents an analogous case for the hypothesis that procedural knowledge is the norm of instructional demonstration, which is a primary way of showing others how to do things. Knowledge is (...) the norm of telling and showing. It is the prime pedagogical principle. (shrink)

This paper shows how the classical finite probability theory (with equiprobable outcomes) can be reinterpreted and recast as the quantum probability calculus of a pedagogical or toy model of quantum mechanics over sets (QM/sets). There have been several previous attempts to develop a quantum-like model with the base field of ℂ replaced by ℤ₂. Since there are no inner products on vector spaces over finite fields, the problem is to define the Dirac brackets and the probability calculus. The previous attempts (...) all required the brackets to take values in ℤ₂. But the usual QM brackets <ψ|ϕ> give the "overlap" between states ψ and ϕ, so for subsets S,T⊆U, the natural definition is <S|T>=|S∩T| (taking values in the natural numbers). This allows QM/sets to be developed with a full probability calculus that turns out to be a non-commutative extension of classical Laplace-Boole finite probability theory. The pedagogical model is illustrated by giving simple treatments of the indeterminacy principle, the double-slit experiment, Bell's Theorem, and identical particles in QM/Sets. A more technical appendix explains the mathematics behind carrying some vector space structures between QM over ℂ and QM/Sets over ℤ₂. (shrink)

Nepal has a diverse ethnic population, some of whom have indigenous knowledge. Their sociocultural knowledge has largely influenced their daily environmental sustainability practices as they highly respect Mother Nature. However, these days, in the name of modernization, people have slowly embraced Western culture and values by adding a disastrous footprint on the earth. They started to ignore the uniqueness of their indigenous knowledge, which prioritizes sustainability. Hence, this paper focuses on viewing indigenous knowledge as ecopreneurship and developing ecopreneurship as an (...) innovative pedagogy for sustainable development. This paper applies action research to intervene in the current pedagogical practice to introduce ecopreneurship as an innovative pedagogy. The participants of this research are the teachers of grade eight of a private school from Lalitpur. This paper concludes that when students explore their indigenous knowledge, it creates an attachment to their indigenous know-how. They learn to value their ancestors’ knowledge for their contribution to ecology, sustainability, and self-dependence. Furthermore, ecopreneurship enables their learning to be authentic and meaningful through their active involvement in producing eco-friendly material, which they showcased at the fair and motivated them to think and act as ecopreneurs for sustainable development. (shrink)

This essay is part of a larger project in which I construct a new, historically-informed, social justice-centered philosophy of dance, centered on four central phenomenological constructs, or “Moves.” This essay in particular is about the fourth Move, “resilience.” More specifically, I explore how Judith Butler engages with the etymological aspects of this word, suggesting that resilience involves a productive form of madness and a healthy form of compulsion, respectively. I then conclude by showing how “resilience” can be used in the (...) analysis of various Wittgensteinian “families” of dance, which in turn could facilitate positive educational changes in philosophy, dance and society, with particular efficacy on the axis of gender. In brief, by teaching a conception of strength as vulnerability (instead of machismo’s view of strength as apathetic “toughness”), a pedagogy of dancing resilience provides additional support for feminists (including Anzaldúa, Haraway, Butler and Concepción) who advocate a cautious openness toward seemingly-unlikely resources and allies (including analytic methodologies, Machiavellian politics, and the discourses of the natural sciences). (shrink)

Despite raising awareness and promoting knowledge and skills-development for education about climate change, efforts by the education sector to promote the development of climate change science literacy in schools is challenged by the nature of climate science. We illuminated the nature of climate science by analysing literature on the nature of science that foregrounds discussions in climate science, and found that climate science involves mostly complex systems and problems; the scope of climate science is vast and interdisciplinary; most issues and (...) problems in climate science are geographic in nature; climate science is characterised by uncertainty and disagreement; and, it is highly politicised. Unless education policymakers and curriculum designers consider these factors when formulating pedagogical intervention frameworks for a more effective and efficient climate change education; nurturing climate change science literacy in schools will be ever more elusive. (shrink)

Critical thinking involves deliberate application of tests and standards to beliefs per se and to methods used to arrive at beliefs. Pedagogical license is authorization accorded to teachers permitting them to use otherwise illicit means in order to achieve pedagogical goals. Pedagogical license is thus analogous to poetic license or, more generally, to artistic license. Pedagogical license will be found to be pervasive in college teaching. This presentation suggests that critical thinking courses emphasize two topics: first, the nature and usefulness (...) of critical thinking; second, the nature and pervasiveness of pedagogical license. Awareness of pedagogical license alerts the student to the need for critical thinking. Indoctrination is done to students; education is done by students. (shrink)

Indian Philosophy has reached across the globe. It is popular for its practical way towards life. Study of Indian philosophy should be part of all streams of education. Film is effective tool of communication. It attracts all generations and makes strong impression in the mind. Film is always considered as an effective tool in Pedagogy. Philosophy deals with abstract concepts, their correlation and logical reasoning. It deals with the complex problem of reality. People have notion that philosophy is a (...) dry and theoretical subject. Students can understand complex philosophical ideas if they are demonstrated through films. There are films based on biographies of philosophers, life picture of great people, incidences in life of philosophers. But it can attract only limited number of audience. Some popular Hollywood films have amalgamation of science fiction, super natural elements, fantastic story guided by some philosophical principles. Such films attract audience from different strata. Viewer is totally captivated by extra ordinary super natural and fictional elements in the film. As a result, certain philosophical principles are taught to audience without their conscious effort. (Kantāsammita upadeśa) Teaching philosophy with the means of such films can be definitely effective tool in Pedagogy. Such practise will not only create liking for Indian Philosophy but will result in effective understanding of complex ideas. It can create awareness that Indian Philosophy is embraced across the globe, there are no boundaries for philosophical deliberations and there are certain common threads in different philosophical schools. Paper will take example of popular movie ‘Matrix’ to explain the principles of Advaita Vedānta. The Matrix is a 1999 science fiction film written and directed by The Wachowskis, starring Keanu Reeves, Laurence Fishburne, Carrie-Anne Moss, Hugo Weaving, and Joe Pantoliano. It states the journey of hero of the film ‘Neo’ who is aspiring for reality. He is struggling between illusory world and the real world which is presented through the means of science fiction. This paper will analyse Matrix from the perspective of Advaita Vedānta. Māyā projects the illusory world (vikṣepa) in place of Brahman (āvaraṇa). Film portrays digital world as illusory world. One sees this world as real due to limitations of body, mind and intellect. Neo goes to the real world and realises his true nature. True reality is beyond senses and sense objects (atindrīya). Concepts of Advaita Vedānta can be explained with this film. Such movies can be shown to students along with Vedanta discourses. Paper will explore ‘Film and Philosophy’ as an effective pedagogical model. (shrink)

What is the relation between small-scale collaborative plans and the execution of those plans within interactive contexts? I argue here that joint attention has a key role in explaining how shared plans and shared intentions are executed in interactive contexts. Within singular action, attention plays the functional role of enabling intentional action to be guided by a prior intention. Within interactive joint action, it is joint attention, I argue, that plays a similar functional role of enabling the agents to act (...) in a collaborative way such that their actions are rationally guided by a prior shared intention. This understanding of joint attention – as having a key functional role of enabling the rational guidance of joint intentional action by a prior shared intention – allows for an alternative understanding of the kind of minimal cooperation that infants can engage in. On this understanding, infants’ capacity to engage in joint actions is already an incipient capacity to engage in rational and intentional joint actions, albeit a capacity that is necessarily scaffolded by an adult rational co-partner. (shrink)

Recent scientific approaches to aesthetics include evolutionary theories about the origin of art behavior, psychological investigations into human aesthetic experience and preferences, and neurophysiological explorations of the mechanisms underlying art experience. Critics of these approaches argue that they are ultimately irrelevant to a philosophical aesthetics because they cannot help us understand the distinctive conceptual basis and normativity of our art experience. This criticism may seem plausible given the piecemeal nature of these scientific approaches, but a more comprehensive naturalistic framework can (...) help us understand the conceptual basis and normativity of art. In particular, the ecology of art, an understanding of how individuals interact within particular environments, can help us understand the engineered art niches in which we create and experience art. Each niche is associated with a particular deme, or set of individuals that interact within that niche, and a set of cognitive, epistemic, and pedagogical technologies that form the conceptual basis of a niche-dependent normativity. This is to be contrasted with the niche-independent normativity revealed by many of the scientific approaches. This framework, and the conflicting streams of normativity it reveals, allows us to better understand conflicts in normativity and the implausibility of unequivocal and universal normative principles. (shrink)

This article aims to conceptually delimit the term “epistemic subalternization”, from the approach offered by postcolonial theories. For this, it is oriented to examine the situation that occurs when the educational system does not contemplate the diverse epistemic-cultural knowledge belonging to the student body. In particular, it focuses on analyzing what happens with access to the right to education of the indigenous communities of Argenti-na, when the school naturalizes epistemic injustices. Finally, it is proposed to reflect on in-tercultural education as (...) a proposal of intrinsic relevance to think about cultural and epistemic co-construction. In the conclusion, it was considered that, from the approach of epistemic injustices, there is a form of subalternization that generally coexists with other factors (social, political, economic, cultural and territorial) that complicate the approach to the problem and installed as social determinants of education and the pedagogical situation of these communities. For this reason, it was proposed to think about the need to build intercultural, that is, decolonizing, pedagogies. Indeed, the centrality of the proposal lies in the relevance of local, geosituated narratives, typical of indigenous communities to performatively transform, from the foundations of common sense and in an intercultural key, pedagogical praxis. (shrink)

PARC is an "appended numeral" system of natural deduction that I learned as an undergraduate and have taught for many years. Despite its considerable pedagogical strengths, PARC appears to have never been published. The system features explicit "tracking" of premises and assumptions throughout a derivation, the collapsing of indirect proofs into conditional proofs, and a very simple set of quantificational rules without the long list of exceptions that bedevil students learning existential instantiation and universal generalization. The system can be (...) used with any Copi-style set of inference rules, so it is quite adaptable to many mainstream symbolic logic textbooks. Consequently, PARC may be especially attractive to logic teachers who find Jaskowski/Gentzen-style introduction/elimination rules to be far less "natural" than Copi-style rules. The PARC system is also keyboard-friendly in comparison to the widely adopted Jaskowski-style graphical subproof system of natural deduction, viz., Fitch diagrams and Copi "bent arrow" diagrams. (shrink)

The aim of this paper is to motivate the need for and then present the outline of an alternative explanation of what Dan Zahavi has dubbed “open intersubjectivity,” which captures the basic interpersonal character of perceptual experience as such. This is a notion whose roots lay in Husserl’s phenomenology. Accordingly, the paper begins by situating the notion of open intersubjectivity – as well as the broader idea of constituting intersubjectivity to which it belongs – within Husserl’s phenomenology as an approach (...) distinct from his more well-known account of empathy in the Fifth Cartesian Meditation. I then recapitulate and criticize Zahavi’s phenomenological explanation of open intersubjectivity, arguing that his account hinges on a flawed phenomenology of perceptual experience. In the wake of that criticism, I supply an alternative phenomenological framework for explaining open intersubjectivity, appealing to the methodological principles of Husserl’s genetic phenomenology and his theory of developmentally primitive affect. Those principles are put to work using the resources of recent studies of cognitive developmental and social cognition. From that literature, I discuss how infants learn about the world from others in secondary intersubjectivity through natural pedagogy. Lastly, the paper closes by showing how the discussion of infant development explains the phenomenon of open intersubjectivity and by highlighting the relatively moderate nature of this account compared to Zahavi’s. (shrink)

In the darkness of difficult times, in the degradation of human nature and in the slumber of consciences, we resolutely affirm with the accuracy of the hermeneutic lógos and the mild gentleness of the óneiro the centrality of the human person within the pedagogical discourse. In the knowledge and care of the dignity, richness and wholeness constitutive of the potential of intentional consciousness we recognize the specific object of educational theory and the safe path to the global empowerment of individual (...) and society. That is why we conceive of tea-ching as a paideia of virtues: that is to say, as a most excellent art to which the whole of existence is to be devoted. That is why our children and pupils are welcomed, loved and accustomed to freely exercise their will and judgment, guided by imagination, enthusiasm, history, great ideals, faith and example, so that their hearts and intelligence learn to recognize, cherish and grow the seeds of hope in a better future. (shrink)

We refer to the remarkable thought of Erwin Schrödinger expressed in his book “What is life?” regarding the connection between life and a decrease of entropy realized via feeding (eating). This thought is “transferred” into the field of human psychology, explaining hooligan behavior (e.g. the “days of violence”) as a natural human response to the improper (in its content or form) “informational feeding” that does not allow one to normally treat (‘’digest”) the received information, i.e. to make ones thoughts (...) simpler in their logical structure. Delivering information without pedagogical, psychological, and (when children are involved) neurological supervision or assistance is supposed to be the cause for the hooliganism that more and more often obtains a dangerous organized form. (shrink)

A report on the pioneering of a new pedagogy designed to challenge students to use and improve their memory, increase their awareness of logical fallacies and tacitly embedded contradiction(s) and sensitize them to the deeply symbolic nature of thought in all its expressions (math, logos, music, picture and motor skills), as created, by the author, from in situ research at a senior level (ESL) course in Storytelling at Hankuk University of Foreign Studies, South Korea’s premier university for foreign languages (...) and translation.in. (shrink)

A central task of schooling is to cultivate reasonableness in students. In this chapter we show how the teaching of reasonableness can be practiced successfully in secondary schools, using materials from the Western Australian curriculum. The discussion proceeds in four stages. We first defend the claim that the teaching of reasonable is a key aim of schooling. Here we offer an account of reasonableness, which we take to be both a skill and a disposition. Students learn reasonableness through the practice (...) of specific skills such as open and curious questioning, clarifying, and categorizing, and evaluating the merits of each contribution toward the problem or question under consideration. Reasonableness comes about as a joint commitment between the individual and the group to be honest in their views, to take care of those views, and for everyone to recognize that each member is a partial bearer of truth. Secondly, we discuss the pedagogies that cultivate reasonableness. The Philosophical Community of Inquiry is a natural pedagogy for this purpose. This can be supplemented with the thinking tools approach of Cam’s Twenty Thinking Tools or Harvard Project Zero’s Thinking Routines. In addition, we introduce our own two skill-building exercises, the Reasoning Game and the Argument Game. Thirdly, we show how this approach can be applied not just in Philosophy classes, but in the Humanities and Social Sciences. We argue that our approach brings these subjects to life, it develops understanding and reasonableness, and it bumps up student engagement. Fourthly, we discuss the assessment of reasonableness. In this type of learning environment, the way students perform in the philosophical community of inquiry is the focus of assessment. The desirable qualities of being reasonable become the assessment criteria for an on-balanced judgment about the student. (shrink)

As the Philippines continues to grapple with the effects of the COVID-19 pandemic, new modalities of instruction are being devised by the administration of Rodrigo Duterte, through the Department of Education (DepEd). Among these are what the DepEd provided as self-learning modules (SLMs) combined with “alternative learning delivery modalities” which include radio-based instruction (DepEd 2020). The SLMs and radiobased instruction are the most common modalities of learning, being the most accessible especially for the poor students of the country. This paper (...) will examine the pedagogical and political dimensions of a radio-based instruction. Coming from the tradition of philosophy of technology that emphasizes the political nature of technology, I will argue how the logic of radio broadcasting predetermines a specific pedagogy and form of communication. I will further argue how this predetermined form of communication carries the danger of being an effective support for authoritarianism. (shrink)

Newtonian impact on Rousseau’s Thinking Summary The most prominent works of Rousseau are written in the field of political philosophy. However, the success of his model of social contract, Rousseau acknowledges, depends on pedagogics. The best way to proceed with it is to return to the natural sources. Rousseau literally brings Emile “back to nature”, and goes to play in and study their natural environment. Playfully directing the kid, he makes experiments devoted to the gradual development of the (...) kid’s body and mind, finding out and emphasizing his own personal abilities. When approaching adulthood, Rousseau switches to more spiritual teaching. in the Profession of Faith of Savoyard Vicar, Rousseau distinguishes as his main predecessor “the illustrious Clarke” who, as we all know, was a friend of Newton, and mainly spread his outlook in metaphysics. interest in ancients and criticism towards their contemporaries, emphasis on the free will within a fragile system hoping for divine support also relates Rousseau and Newton. This opens up a new way in the interpretation of Rousseau through the lens of Newton, an attempt, hopefully, promising us the discovery of a whole new spectrum of colors in Rousseau’s thinking. (shrink)

This paper concerns the role of examples (paradeigmata) as propaedeutic to philosophical inquiry, in light of the methodological digression of Plato’s Statesman. Consistent with scholarship on Aristotle’s view of example, scholars of Plato’s work have privileged the logic of example over their rhetorical appeal to the soul of the learner. Following a small but significant trend in recent rhetorical scholarship that emphasizes the affective nature of examples, this essay assesses the psychagogic potential of paradeigmata, following the discussion of example in (...) Plato’s Statesman. I argue that, by creating an expectation for finding similarities, the use of examples in philosophical pedagogy cultivates in the soul of the learner a desire to discern the intelligible principles the ground experiential knowledge. Thus, examples not only serve as practice at the dialectician’s method of abstraction, but also cultivate a dialectical ethos, characterized by the desire to know the logoi of all things. (shrink)

Schools, colleges, and universities have become homogenizing systems that are almost exclusively focused on imposing a pre-ordered curricula through exams and grades or tight research lines. In the process, they are killing passion, creativity, and individuals’ potential and skills. Ultimately, schools and academia make up a system that serves a collective machinery but suffocates individual growth. This state of affairs is not a necessary evil. Learning, discovering and teaching can be a natural, spontaneous and luminous expressions of a free (...) and progressive growth if they are allowed to be practiced in an appropriate environment. This is a ‘manifesto’ for a Free-Progress-Education (FPE) paradigm according to which the best way of learning, acquiring knowledge, and doing research comes through a process of free self-directed learning, and a progress of self-unfoldment and self-discovery, that must be guided from within. In schools, colleges, universities and beyond. A FPE learning centre would be expected to foster curiosity, intuition, self-directed-learning in diversity, and, especially, wholesome respect for the practice of complete and responsible freedom of individual expression.FPE goes beyond the standard paradigm of unschooling or the pedagogical approach of democratic schools since it includes self-directed-education that can also work in high schools, colleges, universities, and research centres. It iAfter a brief introductory presentation, a personal preamble of the author describes his experiences with institutionalized learning from childhood to the doctoral dissertation and in a high school as a teacher. Then, the roots of the stagnant state of education will be investigated which is still based on an industrial and mechanistic mindset, and is perceived with increasing dissatisfaction. While analysing the detrimental effects that a managerial and industrial mentality has had on the education and intellectual growth of several generations, we will take as an example the deficiencies of the so-called big science, i.e. of the modern, large-scale scientific initiatives. Surveying past and present learning approaches such as the interesting renaissance of homeschooling and welcoming new trends such as unschooling or democratic education, the second part of this book looks beyond these paradigms searching for a wider spirit of education. It is emphasized that no reform is possible inside the current school and university paradigm, because it is in its essence an authoritarian system that won't allow itself to be dismantled from within. The last part of this book focuses upon a brief set of alternative proposals, which aim at overcoming the centuries-old shortcomings of the present educational system, by favouring intrinsic over extrinsic motivation. Preliminary practical ideas are put forward on what a free-progress learning community might look like, and what the first steps for its realization might be. It is explained there why it is only through a change from the ground up that the certificate-oriented educational system can transform itself into a project-oriented, self-organized, competence-portfolio based one, with no exams, grades, degrees, or other administrative trammels. At the same time, it must be made clear that the ultimate aim of doing away with the present system of assessment criteria would be to install a much deeper and articulated paradigm shift than some superficial reform and even beyond the actually undeveloped democratic education concept which still falls short beyond high-school level. What is visualized is an evolutionary pedagogical perspective, compared to the conventional one, and presented as the necessary condition for a 'Copernican approach' to education. Only after that perspective has been realized can new competences, curiosity, intuition, and real forms of creative learning return to flourish in schools and academia. (shrink)

Math literacy is miniscule compared to the near universal language literacy of mother tongues. Our search for the root cause of this undesirable human condition led us to: Grammar (or the abstract essence) of a language. Language learning begins with grammar, unless the language happens to be mathematics, which is unique in not even considering including the grammar (abstract general/theory) of mathematics in the mathematical pedagogy. Here we make a case for introducing the abstract essence of mathematics--Conceptual Mathematics--in high (...) school math curriculum. Recognizing that the singular purpose of education is to nurture the universal yearning for understanding, we show how a nurturing pedagogy naturally resolves the "learning crisis", with the solution manifesting as human development. Furthermore, the nurturing pedagogy that we advocate invariably results in the culture of research excellence. (shrink)

This paper takes a fresh look at Johannes Clauberg’s Logica vetus et nova, in order to try to clarify its nature and character. Differently from prior readings of Clauberg that analyze his philosophy from the point of view of the construction of ‘ontology’, the approach of the present paper sees in Clauberg’s philosophy a late-Humanist work, accentuating his pedagogic and hermeneutical interests. Indeed, in Clauberg’s philosophy, hermeneutics and pedagogy are intrinsically bound together. This, the paper suggests, is supported not (...) only by the concrete subject-matters of his logic, but also by the examination of Clauberg’s milieu and of his sources. Analysis, in this framework, has a strictly hermeneutical usage. (shrink)

Beginning with an examination of the deep history of making things and thinking about making things made-up in our minds, I argue that the resultant declarative understanding of the procedural knowledge of abstracting theories and building models—the essence(s) of the practice of science—embodied in Conceptual Mathematics is worth learning beginning with high school, along with grammar and calculus. One of the many profound scientific insights introduced—in a manner accessible to total beginners—in Lawvere and Schanuel's Conceptual Mathematics textbook is: the way (...) we ought to think about things varies with the nature of things. In light of the universal yearning for understanding, it may be pedagogically unethical not to teach the eminently learnable Conceptual Mathematics. Summing it all, we need to champion the cause of taking Conceptual Mathematics to classrooms. (shrink)

In this paper we prove the completeness of three logical systems I LI, IL2 and IL3. IL1 deals solely with identities {a = b), and its deductions are the direct deductions constructed with the three traditional rules: (T) from a = b and b = c infer a = c, (S) from a = b infer b = a and (A) infer a = a(from anything). IL2 deals solely with identities and inidentities {a ± b) and its deductions include both (...) the direct and the indirect deductions constructed with the three traditional rules. IL3 is a hybrid of IL1 and IL2: its deductions are all direct as in IL1 but it deals with identities and inidentities as in IL2. IL1 and IL2 have a high degree of naturalness. Although the hybrid system IL3 was constructed as an artifact useful in the mathematical study of IL1 and IL2, it nevertheless has some intrinsically interesting aspects. The main motivation for describing and studying such simple systems is pedagogical. In teaching beginning logic one would like to present a system of logic which has the following properties. First, it exemplifies the main ideas of logic: implication, deduction, non-implication, counterargument(or countermodel), logical truth, self-contradiction, consistency,satisfiability, etc. Second, it exemplifies the usual general metaprinciples of logic: contraposition and transitivity of implication, cut laws, completeness,soundness, etc. Third, it is simple enough to be thoroughly grasped by beginners. Fourth, it is obvious enough so that its rules do not appear to be arbitrary or purely conventional. Fifth, it does not invite confusions which must be unlearned later. Sixth, it involves a minimum of presuppositions which are no longer accepted in mainstream contemporary logic. (shrink)

Conceptions about the nature of scientific models held by science students frequently involve distorted views, with a tendency to consider them as mere copies of reality. Besides encompassing an untenable view about the nature of science itself, this misconstruction can effectively be a pedagogical impediment to learning. Objectives: We evaluate whether Mario Bunge’s epistemology might contribute to tackling issues related to the nature of models in science education contexts. De-sign: After identifying Bunge’s main model categories, we employ them to examine (...) aspects of the historical development of atomic models and contrast the resulting framework with issues about model conceptions in science education, as pointed out in the literature. Setting and participants: Due to this research’s theoretical nature, this study did not include human participants other than authors from the literature and the theoretical framework. Data collection and analysis: We per-formed a constant comparative analysis to identify patterns of meanings shared between the historical case and the theoretical framework. Results: Features of models pointed out by Bunge were identified in the development of atomic models and could provide consistent and explanatory viewpoints about key issues related to model conceptions in science education. Conclusions: Bunge’s framework might help to clarify aspects of the nature of models relevant to science education contexts. -/- . (shrink)

This paper argues that Rousseau’s lawgiver is best thought of as a fictional teacher of peoples. It is fictional as it reflects an idea that is entertained despite its contradictory nature, and it is contradictory in the sense that it describes ‘an undertaking beyond human strength and, to execute it, an authority that amounts to nothing’ (II.7; 192). Rousseau conceives of the social contract as a necessary device for enabling the transferal of individual power to the body politic, for subsuming (...) individual wills under the general will, and for aligning the good of the individual with the common good. For the social contract to be valid, however, it needs to be preceded by a desire to belong to a moral community that can induce people to join willingly, and that will grant legitimacy to the laws established. If the social contract is the machinery that makes the body politic function, the lawgiver is ‘the mechanic who invents the machine’ (II.7; 191). In this paper we will look closer at the pedagogical functions of Rousseau’s mythical lawgiver by first examining the relationship between the social contract, the general will and the lawgiver. Then, we aim to flesh out a pedagogical understanding of the figure of the lawgiver by way of the two educational dimensions of accommodation and transformation. Finally, we will argue for the importance of understanding Rousseau’s lawgiver as a fictional device allowing for the fundamental and enduring educational task of balancing between the preservation and renewal of society. (shrink)

Externalist theories hold that a comprehensive understanding of mental disorder cannot be achieved unless we attend to factors that lie outside of the head: neural explanations alone will not fully capture the complex dependencies that exist between an individual’s psychiatric condition and her social, cultural, and material environment. Here, we firstly offer a taxonomy of ways in which the externalist viewpoint can be understood, and unpack its commitments concerning the nature and physical realization of mental disorder. Secondly, we apply a (...) strongly externalist approach to the case of Autistic Spectrum Disorder, and argue that this condition can be illuminated by appeal to the hypothesis of extended cognition. We conclude by briefly considering the significance this strongly externalist approach may have for psychiatric practice and pedagogy. (shrink)

This chapter presents an overview of the life, work, and philosophical contributions of Śāntarakṣita (c. 725–788), who is known for his synthesis of Nāgārjuna’s Madhyamaka with elements of the Dignāga-Dharmakīrti tradition of logic and epistemology. His two most important independent treatises, the Compendium of True Principles (Tattvasaṃgraha) and the Ornament of the Middle Way (Madhyamakālaṃkāra), are characterized by an emphasis on the indispensable role of rational analysis on the Buddhist path as well as serious and systematic engagement with competing Buddhist (...) and non-Buddhist schools of thought. Śāntarakṣita employs a pedagogical-rhetorical device of provisionally adopting what he deems to be successively more rational views to reject less rational ones. Using this approach, in the Ornament of the Middle Way, he recommends a gradual path to arrive at an understanding of the Madhyamaka ultimate truth by incorporating Yogācāra idealist ontology into his presentation of conventional truth. In this same text, he presents an influential iteration of the neither-one-nor-many argument for the Madhyamaka ultimate truth, the emptiness of intrinsic nature—i.e., the universal negation of ontologically independent being—leaving a lasting and significant impact on both Indian and Tibetan Madhyamaka Buddhist philosophy. (shrink)

Kant begins his Lectures on Pedagogy by stating, “[t]he human being is the only creature that must be educated” (Kant, 2007, 9:441), and he argues that it is through education that we can transform our initial “animal nature into human nature” (ibid. 2007, 9:441). Kant understands education as involving an ordered process of care, discipline, instruction and formation through enculturating, civilizing and moralizing (Formosa 2011). Further, Kant envisages that we should pursue as a species the “moral perfection” that is (...) the “final destiny of the human race” through education (Collins, 1997, 27:470; see Dean, 2014). However, to engage in this pursuit Kant believes that, through education and social change, we have to regulate our “animal nature” and counter the moral corruption of our species, which he calls the “radical innate evil in human nature (not any the less brought upon us by ourselves)” (Kant, 1998, 6:32). If humanity is to pursue its final destiny of moral perfection, then education will need to respond responsibly to the propensity to evil that is deeply rooted in us as finite and imperfect rational beings living in imperfect and at times even in morally corrupted social conditions. This paper outlines some of the relevant issues. (shrink)

Yoga is a unique form of expert movement that promotes an increasingly subtle interpenetration of thought and movement. The mindful nature of its practice, even at expert levels, challenges the idea that thought and mind are inevitably disruptive to absorbed coping. Building on parallel phenomenological and ethnographic studies of skilful performance and embodied apprenticeship, we argue for the importance in yoga of mental access to embodied movement during skill execution by way of a case study of instruction and practice in (...) two related traditions, Iyengar and Anusara. Sharing a pose repertoire, they are based on distinctive philosophical systems with different teaching styles and metaphoric structures. To address relations between pedagogy and practice in embodied expertise, and to investigate the reciprocal influences of embodiment and thought, we explore in detail the linguistically mediated learning context where practitioners work with yoga teachers. Here, the mind/body problem comes to practical life. We demonstrate the effects of words on bodies, as knowledge is literally incorporated. We show why interpersonal influence on our movement capacities is sometimes needed to enhance expertise. We theorize and identify ?signature patterns of tension? among practitioners. These patterns have four sources: ghost gestures, innate differences in bodily form, functional fusing, and signature patterns of affective experience, modulation and expression. These patterns of tension produce ?silent zones?, cognitively impenetrable actions, functional fusing of a skilful, compensatory form, and signature patterns of pain and damage. We show how instruction can disrupt these silent zones, enhancing mental and physical flexibility. (shrink)

How can we improve business ethics education for the twenty first century? This study evaluates the effectiveness of a visual case exercise in the form of a 3D immersive game given to undergraduate students at two UK Universities as part of a mandatory business ethics module. We propose that due to evolving learning styles, the immersive nature of interactive games lends itself as a vehicle to make the learning of ethics more ‘concrete’ and ‘personal’ and therefore more engaging. To achieve (...) this, we designed and built an immersive 3D simulation game in the style of a visual case. The effectiveness of the game was evaluated using a mixed methods approach measuring recognised and adapted constructs from the technology acceptance model. Results demonstrate that students found the game beneficial to their learning of ethics with the development of knowledge and skills applicable to the real world and that they engaged with the process due to game elements. Findings demonstrate the potential for the development of simulated games to teach ethics at all levels and modes of delivery and the contribution of this type of visual case model as a pedagogic method. (shrink)

There is a long standing controversy in education as to whether education ought to be teacher- or student- centered. Interestingly, this controversy parallels the parent- vs. child-centered theoretical swings with regard to good parenting. One obvious difference between the two poles is the mode of communication. “Authoritarian” teaching and parenting strategies focus on the need of those who have much to learn to “do as they are told,” i.e. the authority talks, the child listens. “Non-authoritarian” strategies are anchored in the (...) assumption that youngsters ought to be encouraged to develop their natural interests and talents and hence that it is important to allow the children to do the talking and that adults listen. Both strategies seemed flawed due to the absence of the inherent wisdom of its opposing view. This chasm can be overcome. The Community of Inquiry, a pedagogical method used in Philosophy for Children, demands a method of communication which is able to bridge this gap. A Community of Inquiry is neither teacher-centered and controlled nor student-centered and controlled, but centered on and controlled by the demands of truth. Truth is absolutely essential to this method; it is only because of progress toward truth that participants are ultimately convinced of the fruitfulness of the process. Truth, however, is a hard taskmaster; it places severe restrictions on participants and puts exacting demands on the facilitator. These inherent restrictions and demands are too often underplayed, overlooked and sometimes seemingly overtly denied by those who, quite correctly emphasize that ultimately this method depends on maintenance and enhancement of student autonomy. This underrating of the role of the facilitator has led to a severe undervaluing of this otherwise brilliant pedagogical method, but worse, it has left novice teacher/facilitators ill prepared to utilize this method successfully. (shrink)

One very common style of teaching philosophy involves remaining publicly neutral regarding the views being debated—a technique commonly styled ‘teaching the debate.’ This paper seeks to survey evidence from the literature in social psychology that suggests teaching the debate naturally lends itself to student skepticism toward the philosophical views presented. In contrast, research suggests that presenting one’s own views alongside teaching the debate in question—or ‘engaging the debate’—can effectively avoid eliciting skeptical attitudes among students without sacrificing desirable pedagogical outcomes. Thus, (...) there are good reasons to engage philosophical debates as an educator, not merely teach them. (shrink)

In the APA Newsletter on Feminism and Philosophy, Lauren Freeman (2014) advocates that faculty turn their classrooms into “safe spaces” as a method for increasing the diversity of philosophy majors. The creation of safe spaces is meant to make women and minority students “feel sufficiently comfortable” and thereby increase the likelihood that they pursue philosophy as a major or career. Although I agree with Freeman’s goal, I argue that philosophers, and faculty in general, should reject the call for turning classrooms (...) into “safe spaces.” I begin by distinguishing extra-curricular safe spaces from the classroom as a safe space. I then argue that although faculty should not object to extra-curricular safe spaces, they should reject curricular ones. I argue that the classroom as a safe space is currently an impractical and inappropriate goal given the nature of academic philosophy, and that encouraging students to think of classrooms as safe/unsafe does not facilitate learning. Nonetheless, I agree with Freeman that faculty should take steps to ensure that students from all backgrounds have the tools they need to be successful in the classroom. I further argue that faculty calls for safe spaces creates confusion concerning the educative environment one should expect to find at the majority of America universities. (shrink)

The main theory at the core of this monograph is that the person is an entity ontologically new, since she is able to perform an act of self-transcendence, which is meant as her critical distancing from her own “self”, understood as subject of social recognition (Anerkennung), in order to open to the encounter with the world (Weltoffenheit). This allows us to consider a person in a new way, different both from confessional interpretations that see her only as a center of (...) the spirit and from reductivistic views. Schelling examines the act of self-transcendence through the concept of ecstasy, whereas Scheler associates it with the phenomenological reduction. The act of self-transcendence, that Schelling sees as originated by the “hunger of being”, is at the roots of the formation process of a person (Bildung): the person takes her shape by exiting from her own self-referential dimension and encountering otherness. If considered from this viewpoint, Plato’s “epimeleia heautou” exceeds an intimistic perspective: the “care” is no more a solipsistic self-care, but rather becomes the care through which the person transcends her own self to open to the relationships with otherness. It turns, therefore, into a care for world-openness (care for Weltoffenheit). The transformation of the individual and of society so becomes the double-faced aspect of the same process. The development of this set of problems occurs through a dialogue with Schelling’s and Scheler’s positions, but it is also supported by a historical-philosophical investigation, that for instance provides evidence of the influences of Schelling’s Berlin period on Scheler’s last theories and on the philosophical anthropology of the 20th century. Schelling was the first to conceive the concept of “eccentricity” in an anthropological sense, since until then the term had been confined to Kepler’s astronomy. Consequently, the planets’ elliptic (eccentric) movement heightens to an emblematic metaphor of human nature and freedom. The monograph also examines a possible convergence between Plato’s epimeleia heautou and Scheler’s phenomenological reduction. The book ends with a chapter on the topic of Vorbild. The exemplary testimony, that is Vorbild, becomes witnessing evidence immune from any pedagogical-moralistic intent: in fact, if it should relapse into the rhetoric of the “wish to give a good example”, it would immediately conform to the opposite logic of the model. A model is universal in so far as it makes everyone more like the others, nullifying the diversity, whereas exemplariness is universal in so far as it makes everyone more unique and motivates each one to follow her own characteristic path of existential trans-formation. Exemplarity doesn’t convey any contents, but rather encourages a kind of solidaristic involvement. Yet there are also negative exemplarities (Gegenbild) that place obstacles in the formation and block the existence of the personal center. (shrink)

In the Fragment on Evil, Hume announces that he “shall not employ any rhetoric in a philosophical argument, where reason alone ought to be hearkened to.” To employ the rhetorical strategy, in the context of the Fragment, just is to “enumerate all the evils, incident to human life, and display them, with eloquence, in their proper colours.” However, in Part 11 of the Dialogues Concerning Natural Religion, Hume employs precisely this rhetorical strategy. I discuss three interpretations that might account (...) for Hume’s decision to employ the strategy in the Dialogues but not the Fragment. The heart of this discussion concerns the relationship between reason and rhetoric. The Dialogues can be understood as part of the education of Pamphilus. Consequently, the three interpretations align with three ways of understanding the roles that reason and rhetoric play in Hume’s views on pedagogy and education (or more specifically, Philo’s attitude towards the education of Pamphilus). (shrink)

Berkeley's doctrines about mind, the language of nature, substance, minima sensibilia, notions, abstract ideas, inference, and freedom appropriate principles developed by the 16th-century logician Peter Ramus and his 17th-century followers (e.g., Alexander Richardson, William Ames, John Milton). Even though Berkeley expresses himself in Cartesian or Lockean terms, he relies on a Ramist way of thinking that is not a form of mere rhetoric or pedagogy but a logic and ontology grounded in Stoicism. This article summarizes the central features of (...) Ramism, indicates how Berkeley adapts Ramist concepts and strategies, and chronicles Ramism's pervasiveness in Berkeley's education, especially at Trinity College Dublin. (shrink)

Creationists who object to evolution in the science curriculum of public schools often cite Jonathan Well’s book Icons of Evolution in their support (Wells 2000). In the third chapter of his book Wells claims that neither paleontological nor molecular evidence supports the thesis that the history of life is an evolutionary process of descent from preexisting ancestors. We argue that Wells inappropriately relies upon ambiguities inherent in the term ‘Darwinian’ and the phrase ‘Darwin’s theory’. Furthermore, he does not accurately distinguish (...) between the overwhelming evidence that supports the thesis of common descent and controversies that pertain to causal mechanisms such as natural selection. We also argue that Wells’ attempts to undermine the evidence in support of common descent are flawed and his characterization of the relevant data is misleading. In particular, his assessment of the ‘Cambrian explosion’ does not do justice to the fossil record. Nor do his selective references to debate about molecular and paleontological phylogenies constitute a case against common descent. We conclude that the fossil and molecular evidence is more than sufficient to warrant science educators to present common descent as a well-established scientific fact. We also argue that diagrams depicting the ‘tree of life’ can be pedagogically useful as simplified representations of the history of life. (shrink)

This dissertation concerns Kierkegaard’s theory of indirect communication. A central aspect of this theory is what I call the “indispensability thesis”: there are some projects only indirect communication can accomplish. The purpose of the dissertation is to disclose and assess the rationale behind the indispensability thesis. -/- A pair of questions guides the project. First, to what does ‘indirect communication’ refer? Two acceptable responses exist: (1) Kierkegaard’s version of Socrates’ midwifery method and (2) Kierkegaard’s use of artful literary devices. Second, (...) for what end does Kierkegaard use indirect communication? There are two acceptable responses here as well: (1) helping others become religious and (2) making others aware of the nature of existence. -/- These responses are interrelated. First, Kierkegaard’s notion of religion places restrictions on the means he can use to get readers to become religious. These restrictions ultimately entail that the only viable form of religious pedagogy is the midwifery method. Second, Kierkegaard engages in the midwifery method in part by making readers aware of the nature of existence (especially religious existence). But given the problems plaguing his readers, he thinks a straightforward approach to this project will likely fail. An approach that used artful literary devices such as deception and humor would be more successful. Third, Kierkegaard believes that there is one aspect of religious existence (viz. subjectivity) that people can come to know only first-hand. As such, he cannot directly impart knowledge of subjectivity to his readers. He argues that this means he must use the midwifery method. And he thinks the most productive way to do so is to provide readers with the kind of fictional narratives found in his early pseudonymous writings. Thus artful rhetorical devices play a role here as well. -/- All of Kierkegaard’s arguments for the indispensability thesis turn on debatable assumptions. But the arguments concerning artful rhetorical devices have the additional defect of being merely probabilistic in nature. They lack the strength to support the indispensability thesis even if we grant the relevant background assumptions. Therefore, to the degree that the indispensability thesis has merit, it lies with the arguments concerning the midwifery method. (shrink)

SEMANTIC ARITHMETIC: A PREFACE John Corcoran Abstract Number theory, or pure arithmetic, concerns the natural numbers themselves, not the notation used, and in particular not the numerals. String theory, or pure syntax, concems the numerals as strings of «uninterpreted» characters without regard to the numbe~s they may be used to denote. Number theory is purely arithmetic; string theory is purely syntactical... in so far as the universe of discourse alone is considered. Semantic arithmetic is a broad subject which begins (...) when numerals are mentioned (not just used) and mentioned as names of numbers (not just as syntactic objects). Semantic arithmetic leads to many fascinating and surprising algorithms and decision procedures; it reveals in a vivid way the experiential import of mathematical propositions and the predictive power of mathematical knowledge; it provides an interesting perspective for philosophical, historical, and pedagogical studies of the growth of scientific knowledge and of the role metalinguistic discourse in scientific thought. (shrink)

Supporters of the philosophy for children movement often claim that philosophy is the ideal subject to teach children if we seek to improve their critical thinking. Claiming that only philosophy encompasses the whole of the critical thinking enterprise, and that it alone teaches meta-cognition, these proponents argue for its inclusion in both elementary and secondary school curricula. Yet, if we accept a mainstream description of critical thinking as an activity demanding both aptitude and disposition, the discipline of philosophy, independent of (...) any particular pedagogy, does not offer the unique ability to improve either aspect of the critical thinker. Indeed, matched with the "wrong" pedagogy, the teaching of philosophy does nothing to encourage the disposition to think critically.The pedagogy of Community of Inquiry, however, does encourage such a disposition, even independent of its use in teaching philosophy. As a public model of the process of critical thinking, this pedagogy acts as the "training wheels" of the critical thinker, allowing the individual to both observe and participate in the process. The expectation of the educator is that exposure to the model will, in time, result in its internalization. While philosophy itself may not improve either critical aptitude or disposition, the nature of the discipline does uniquely enable efficient, productive, and extended practice of Community of Inquiry in an educational context. And it is this indirect link between philosophy and critical thinking, a link mediated by the pedagogy of Community of Inquiry, that should be cited by proponents of philosophy for children. (shrink)

This interview, conducted over the span of several months, tracks the respective journeys of Constantin V. Boundas and Daniel W. Smith with the philosophy of Gilles Deleuze. Rather than “becoming Deleuzian,” which is neither desirable nor possible, these exchanges reflect an array of encounters with Deleuze. These include the initial discoveries of Deleuze’s writings by Boundas and Smith, in-person meetings between Boundas and Deleuze, and the wide-ranging and influential philosophical work on Deleuze’s concepts produced by both Boundas and Smith. At (...) stake in this discussion are key contributions by Deleuze to continental philosophy, including the distinction between the virtual and the actual and the very nature of a “concept.” Also at stake is the formative or pedagogical impact of a philosopher, like Deleuze, on those who find and fully engage with his texts, concepts, and project. Cette interview, menée sur plusieurs mois, suit les parcours respectifs de Constantin V. Boundas et Daniel W. Smith avec la philosophie de Gilles Deleuze. Au lieu de « devenir Deleuzien, » ce qui n’est ni souhaitable ni possible, ces échanges reflètent un éventail de rencontres avec Deleuze. Il s’agit notamment des premières découvertes des écrits de Deleuze par Boundas et Smith, des rencontres en personne entre Boundas et Deleuze, et du travail philosophique vaste et in????luent sur les concepts de Deleuze produit par Boundas et Smith. L’enjeu ici étant les contributions clés de Deleuze à la philosophie continentale, y compris la distinction entre le virtuel et l’actuel, et la nature même d’un « concept. » Mais il y a aussi l’impact formateur ou pédagogique d’un philosophe, comme Deleuze, sur ceux qui trouvent et s’engagent pleinement dans ses textes, ses concepts et ses projets. (shrink)

In this article I develop an elementary system of axioms for Euclidean geometry. On one hand, the system is based on the symmetry principles which express our a priori ignorant approach to space: all places are the same to us, all directions are the same to us and all units of length we use to create geometric figures are the same to us. On the other hand, through the process of algebraic simplification, this system of axioms directly provides the Weyl’s (...) system of axioms for Euclidean geometry. The system of axioms, together with its a priori interpretation, offers new views to philosophy and pedagogy of mathematics: it supports the thesis that Euclidean geometry is a priori, it supports the thesis that in modern mathematics the Weyl’s system of axioms is dominant to the Euclid’s system because it reflects the a priori underlying symmetries, it gives a new and promising approach to learn geometry which, through the Weyl’s system of axioms, leads from the essential geometric symmetry principles of the mathematical nature directly to modern mathematics. (shrink)

The Guggenheim’s spring retrospective of the seminal Swedish painter, Hilma Af Klint, has, naturally, evoked a multitude of art critics and visual culture scholars who laud her radical abstraction which, at the beginning of the 20th century, preceded Kandinsky, Malevich, Mondrian. Yet, where much attention has been given to the symbology and motifs riddling Klint’s work – bold, private, untethered and nonrepresentational as they are – there has been a modicum of nuanced thought on how, exactly, esotericism and theology fomented (...) Klint’s pedagogical projects. Jillian Steinhauer, for instance, has underscored Klint’s naturalistic watercolors; featuring flowers and lifelike drawings of women; Summer Landscape (1888) suggests Klint’s technical aptitude for rendering light. Jadranka Ryle, in a clever article titled “Reinventing the Yggdrasil,” invokes Klint’s motif of the Yggdrasil, or the holy tree of Norse mythology, as a political axle for Nordic romanticism. Ryle makes the claim that by redirecting the Yggdrasil towards androgynous abstraction, Klint’s engagement with Norse mythology subverts the nationalist and patriarchal romanticism that previously characterized the nineteenth century’s use of the Yggdrasil. Others have adroitly uncovered biographical fragments from Klint’s life, detailing how she and four friends formed De Fem (“the Five”), an exclusively female coven that met weekly, praying, meditating, and holding seances to commune with spiritual guides. Rather than poise the Swedish maverick within the cannon of abstraction qua a political praxis, feminist subject-being, or historiography – projects that have been exhaustively overwrought, to the point of rendering Klint’s work both mute and reductively technical– I would like to take this time to closely examine simply one of Klint’s paintings and foreground it as an axiomatic modernist injunction between metaphysics and epistemology. (shrink)