To cover as much as possible the various questions raised by the commentators, I have divided my Response into three major sections. In section R1, I reply to the major comments and remarks dealing with the basic hypothesis upon which the kinematic theory is built (Plamondon 1993b; 1993c; 1995a; 1995b). I focus on linearity, determinism, kinematics, and the biological significance of the model parameters. I conclude this section by showing how, from a practical point of view, the delta-lognormal law can (...) be used to group similar data prior to proceeding with further statistical analysis. In section R2, I address the main comments and remarks dealing with the speed/accuracy tradeoffs. First, I focus on the origin of speed/accuracy tradeoffs and the effect of visual feedback. Then I clarify some terminology problems and mathematical misinterpretations prior to providing new support for the theory using the experiments and data referred to by some commentators. I devote section R3 to a generalization of the kinematic theory and to some potential applications. I first provide new explanations of some classical experiments; then I show how more complex movements can be analyzed using the delta-lognormal law. I focus on perturbed and oscillatory movements as well as on cursive script and signature analysis. I conclude this section and my Response by showing some possible applications to the study of movement learning in children as well as to the study of aging phenomena in movement control. I complete my Response by recalling some technical problems that still need further analysis. Throughout the text, I try to convince the reader that the kinematic theory provides a new window on old and new data in the field. (shrink)

Every time we think ahead, we are crafting a story. Every daily plan—and every political vision, social movement, scientific hypothesis, business proposal, and technological breakthrough—starts with “what if?” Linking causes to effects, considering hypotheticals and counterfactuals, asking how other people will react: these are the essence of narrative. So why do we keep overlooking story’s importance to intelligence in favor of logic? This book explains how and why our brains think in stories. Angus Fletcher, an expert in neuroscientific approaches (...) to narrative, identifies this capacity as “storythinking.” He demonstrates that storythinking is fundamental to what makes us human. Artificial intelligence can perform symbolic logic, rational deduction, and mathematical calculation, but it is incapable of deliberating in narrative. Drawing on new research in neuroscience and narrative theory, Fletcher explores the nature of imagination, innovation, and creativity. He provides concise answers to big questions: How does storythinking work? Why did it evolve? How can it misfire? What problems can it solve? Revealing the significance of storythinking from science to business to philosophy, this book also provides ways for readers to harness its power to script better tomorrows. (shrink)

My departed point is the assessment that plurality in broadest sense characterizing any post- (for example: post-modernity, post-metaphysical, etc.) context is first of all plurality of whole. We may speak about wholes, movement of whole, and lack of any universal whole. Part do not already belongs to whole implicitly granted and common of all other parts. Now we may speak of parts in another relation: non of parts as parts of some common of all parts whole, but parts of (...) difference wholes, and at the same time without any universal whole common of all the wholes. The paper is devoted concretely to the influence of such a comprehension of whole upon some basic notion of physics (especially quantum mechanics and information, relativity) and mathematics, namely probability, set, movement,time. Their changes exert influence upon the fundamental pbilosophical concepts of being and time, knowledge and being-in-the-world. The new conception of fractal, and its meaning in philosophy points out, too. Constancy and always existing of whole is equivalent to Newton time, energy conservation law, local realism and ''hidden parameters" of any correlations, a union of sets exists always if the two sets are granted. (shrink)

In order to get rid of the contradictions he had identified in Ptolemy’s Astronomy, Ibn al-Haytham abandons cosmology and develops a purely kinematic description of the movement of the wandering stars. This description culminates with the proof that such a star, during its daily movement, reaches exactly one time a maximum height above the horizon and that any inferior height is reached exactly twice. The proofs of these facts necessitates new mathematical tools and Ibn al-Haytham is led to (...) establish very sophisticated statements concerning the variation of certain ratios of arcs of circles on the sphere. He also introduces the fruitful idea of assimilating a very small spherical triangle to a plane triangle. (shrink)

In this article, modern standards of early years mathematics education are criticized and a proposal for change is presented. Today's early years mathematics education standards rest on a view of mathematics that became obsolete already at the end of the 19th century while the spirit of children's mathematics is precisely the spirit of modern mathematics. The proposal for change is not a return to the “new mathematics” movement, but something different.

While there are satisfactory answers to the question “How should we teach children mathematics?”, there are no satisfactory answers to the question “What mathematics should we teach children?”. This paper provides an answer to the last question for preschool children (early childhood), although the answer is also applicable to older children. This answer, together with an appropriate methodology on how to teach mathematics, gives a clear conception of the place of mathematics in the children’s world and our role in helping (...) children develop their mathematical abilities. Briefly, children’s mathematics consists of the world of children’s internal activities that they eventually purposefully organize in order to understand and control the outside world and organize their overall activities in it. We need to support a child in mathematical activities that she does spontaneously and in which she shows interest, and we need to teach her mathematics that she is interested in developing through these activities. In doing so, we must be fully aware that the child’s mathematics is part of the child’s world of internal activities and is not outside of it. We help the child develop mathematical abilities by developing them in the context of her world and not outside of it. From the point of view of this conception, the standards established today are limiting and too focused on numbers and geometric figures: these topics are too prominent and elaborated, and other mathematical contents are subordinated to them. Adhering to the standards, we drastically limit the mathematics of the child’s world, hamper the correct mathematical development of a child, and we can turn her away from mathematics. (shrink)

The article presents the author's reconstruction of the main stages of the origin of ideas about cognition. The picture of the reality of cognition accepted in modern science is presented, in which the yet unknown world is contrasted as a source of latent knowledge and patterns and a person as a cognizer striving to discover this knowledge. It is argued that in the Ancient World, such a familiar picture for a modern person did not take place. An analysis of the (...) way of mastering the world related to this period shows that it represented the resolution of problematic situations through the invention of knowledge and schemes (local and fundamental), opening the way to understanding and new behavior. Together, local and fundamental schemes set the Ancient world, understandable and epistemologically transparent, requiring no knowledge. Man lived in a world of souls, spirits and gods. Although he created this world himself, solving problematic situations, he perceived it as having always existed. Cognition begins to take shape, starting with ancient culture; its prerequisites are the formation of an ancient personality and the invention of a new way of obtaining knowledge, not on diagrams, but in reasoning. The contribution of Plato and Aristotle to this revolutionary epistemic process is considered. The first introduces cognition as a dialectical and partly sacred way of understanding a new way of obtaining consistent knowledge. Stagirite transfers knowledge from heaven to earth, and places the source of new knowledge in things. Aristotle interprets this source as a hidden natural movement, calling it nature. The author reconstructs two more stages of the formation of knowledge related to the Middle Ages and modern times. It turned out that nature is not only movements hidden from human eyes, but those that are "written in the language of mathematics" and "constrained," as Francis Bacon wrote, by human art. The article ends with an indication of the next stage in the evolution of cognition, characteristic of the study of humanitarian and social phenomena. (shrink)

Every educational reform brings challenges, and ‘New Math’ is one of the most intriguing and influential reforms in mathematics education. New Math, which began to be implemented predominantly in t...

The cyberworld fast rolling in and impacting every aspect of human living on the globe today presents an enormous challenge to humankind. It is taken up by the media following current events through to all kinds of natural- and social-scientific discourses. Digitized technoscience develops at a breakneck pace in all areas accompanied by sociological analysis. What is missing is a philosophical response genuinely posing the basic ontological question: What is a digital being's peculiar mode of being? The present study offers (...) a digital ontology that analyzes the dissolution of beings into bit-strings, driven by mathematized science. The mathematization of knowledge reaches back to Pythagoras, Plato and Aristotle, and continues with Descartes, Galileo, Newton, Leibniz. Western knowledge from its inception has always been driven by an unbridled will to efficient-causal power over all kinds of movement and change. This historical trajectory culminates in the universal Turing machine that enables efficient, automated, algorithmic control over the movement of digital beings through the cyberworld. The book fills in the ontological foundations underpinning this brave new cyberworld and interrogates them, especially by questioning the millennia-old conception of 1D-linear time. An alternative ontology of movement arises, based on a radically alternative conception of 3D-time. (shrink)

Marcus Giaquinto traces the story of the search for firm foundations for mathematics. The nineteenth century saw a movement to make higher mathematics rigorous; this seemed to be on the brink of success when it was thrown into confusion by the discovery of the class paradoxes. That initiated a period of intense research into the foundations of mathematics, and with it the birth of mathematical logic and a new, sharper debate in the philosophy of mathematics. The Search for Certainty (...) focuses mainly on two major twentieth-century programmes: Russell's logicism and Hilbert's finitism. Giaquinto examines their philosophical underpinnings and their outcomes, asking how successful they were, and how successful they could be, in placing mathematics on a sound footing. He sets these questions in the context of a clear, non-technical exposition and assessment of the most important discoveries in mathematical logic, above all Gödel's underivability theorems.More than six decades after those discoveries Giaquinto asks what our present perspective should be on the question of certainty in mathematics. Taking recent developments into account, he gives reasons for a surprisingly positive response. (shrink)

The main aim of this study is to explain passage 35b4-37a2 of Plato’s Timaeus which deals with three main topics: the mathematization of the world’s soul, its movement, and its binding to the world’s body. First, it is argued that the mathematical structure of the world-soul allows it to participate in and be sensitive to harmony, which is essential for the correct workings of its cognitive capacities. Second, the division of the world-soul to the circle of the same and (...) the circles of the different and its self-motion comes in. This allows it to ‘touch’ and cognize the forms and the material things, as well as rule the movement of the corporeal world and care for it. In this aspect, the world-soul continues the process that started with the original creative act of the demiurge. Third, it is argued that the description of the world-soul’s binding to the world-body entails its conception as a spatially extended entity, which, in turn, explains of the possibility of an interaction between the corporeal world and its soul. (shrink)

We analyze the effects of the introduction of new mathematical tools on an old branch of physics by focusing on lattice fluids, which are cellular automata -based hydrodynamical models. We examine the nature of these discrete models, the type of novelty they bring about within scientific practice and the role they play in the field of fluid dynamics. We critically analyze Rohrlich's, Fox Keller's and Hughes' claims about CA-based models. We distinguish between different senses of the predicates “phenomenological” and “theoretical” (...) for scientific models and argue that it is erroneous to conclude, as they do, that CA-based models are necessarily phenomenological in any sense of the term. We conversely claim that CA-based models of fluids, though at first sight blatantly misrepresenting fluids, are in fact conservative as far as the basic laws of statistical physics are concerned and not less theoretical than more traditional models in the field. Based on our case-study, we propose a general discussion of the prospect of CA for modeling in physics. We finally emphasize that lattice fluids are not just exotic oddities but do bring about new advantages in the investigation of fluids' behavior. (shrink)

The times required to develop new drugs is growing continuously and most drugs fail in the development process because we lack the detailed knowledge of biology and physiology needed to understand the result of a proposed treatment. The problem is one of complexity—we do not know the full complexity of living organisms, neither does traditional biology have the language to capture and integrate complexity. As a result, the life sciences are undergoing a period of radical change as the technological and (...) mathematical methods developed for the analysis of physical sciences are being adapted for use in understanding living systems. This introduction of quantitative mathematical methods to represent and understand a previously descriptive subject resembles the Newtonian revolution in physics and its subsequent impact upon industry and manufacture. And just as in the post-Newtonian developments, the new ways are being resisted as the traditional reductionist biologists argue against a system level analysis. The comparison between the industrial revolution and the emerging revolution in life sciences is so strong that it can be usefully employed to explain the current process—the industrialisation of biology—in a way that informs the traditionalist movement. In particular, we draw upon ideas from innovation cycles and the staging of change in science and industry to clarify the current change processes in life science. Using specific examples in technology development we outline lessons that can be learnt in order to smooth the process of change and make it a harmonious one, rather than one of conflict. (shrink)

This article puts forward the thesis that the contemporary global movement against capitalism, and the post-Fordist regime it is responding to, is best understood in terms of the emergence of ‘human nature’ as the crux of political struggle. According to Virno, the biological invariant has become the raw material of social praxis because the capitalist relation of production mobilizes to its advantage, in a historically unprecedented way, the species-specific prerogatives of Homo sapiens. Through the concept of ‘natural-historical diagrams’, the (...) article explores the significance of socio-political states of affairs which directly display key aspects of anthropogenesis, and, making use of Ernesto De Martino’s concept of ‘cultural apocalypses’, considers the different relations that a biological ‘background’ and a socio-political ‘foreground’ entertain in traditional and contemporary societies. The attempt to develop a ‘natural history’ of such diagrams leads Virno to reflecting on the importance of the language faculty, neoteny, non-specialization and the absence of a predetermined natural environment for political action. This reflection on the contemporary importance of political anthropology leads Virno to a set of concluding remarks on the role of ethics and the idea of the ‘good life’ in the practice of the ‘new global’ movement. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Reviewed by:Logos and Alogon: Thinkable and Unthinkable in Mathematics, from the Pythagoreans to the Moderns by Arkady PlotnitskyNoam CohenPLOTNITSKY, Arkady. Logos and Alogon: Thinkable and Unthinkable in Mathematics, from the Pythagoreans to the Moderns. Cham: Springer, 2023. xvi + 294 pp. Cloth, $109.99The limits of thought in its relations to reality have defined Western philosophical inquiry from its very beginnings. The shocking discovery of the incommensurables in Greek mathematics (...) not only reintroduced these limits with greater force but also instigated two different forms of coping with the unthinkable in Western philosophy, mathematics, and science. As Arkady Plotnitsky sets forth, in response to the incommensurability crisis in the ancient Greek intellectual world, there appeared two different attitudes toward the alogon, that is, the unthinkable or irrational. Plato and his followers sought to overcome the unthinkable, of which the incommensurables in mathematics are only an example, through philosophy. In contrast, the Pythagoreans continued to hold on to mathematics as the primary means of knowing the world, but put a larger emphasis on geometry. Plotnitsky [End Page 359] claims that by not putting aside the primacy of mathematics, the Pythagorean shift from arithmetic to geometry established in Western thought a certain tolerance toward the unthinkable within the realm of the thinkable, “a possibility of the alogon in the logos.” Until modern times this remained no more than a possibility. However, in modern mathematics and mathematical physics Plotnitsky identifies a certain fulfillment of this potential, a “radical Pythagorean mathematics.” In his comprehensive and thought-provoking study, Plotnitsky recounts the development of such radical modern Pythagoreanism, not only to tell its history but also to suggest that the unthinkable is a condition of possibility for thought, and that a proper recognition of this role it plays is crucial for the advancement of mathematical thinking and thinking in general.Plotnitsky begins by portraying in broad strokes the two defining characteristics of radical Pythagorean mathematics: the presence of the unthinkable within mathematical thought itself, and the interplay of algebra and geometry. Relying on an extensive knowledge of the history of modern mathematics and physics, in the first two chapters of the book Plotnitsky gradually demonstrates the key role that the alogon plays in some theories of modern mathematical thought, such as Gödel’s incompleteness theorems and quantum mechanics. He also presents and clarifies his own conception of the history of Western thought as a creative process of concept-forming. By creating rather than discovering concepts, great mathematicians break new ground for thinking. The book as a whole argues in length for these two main theses.In chapter 3, the author addresses the thought of Bernhard Riemann to make the case that Riemann’s mathematical thought puts an emphasis on creative conceptual thinking and is not defined merely by calculations or logic. Such thinking is problem-posing rather than axiomatic. Riemann’s central innovation in this respect is the concept of manifold (Mannigfaltigkeit), which enabled him to think anew space and geometry in a radical non-Euclidean fashion, implying an infinite number of possible geometries. Plotnitsky argues—borrowing Deleuze and Guattari’s terminology—that this opened up a “plane of immanence,” which is to say that Riemann created a concept-generating movement of thought. However, we cannot grasp the generation of concepts in modern mathematics without giving proper attention to the interplay of algebra and geometry that defines it. Chapter 4 demonstrates this interweaving of the two fields by recounting the history of the idea of the curve in modernity, from the analytic geometry and calculus of Fermat and Descartes to its modification in the concept of a Riemann surface, up to its more recent developments in the algebraic geometry of Weil and Grothendieck. It gives a historical account of the algebraization of the curve that at the same time brings into relief the irreducible geometrical aspect, continuity, of all modern mathematical conceptualizations of the curve.The next two chapters provide further case studies. Chapter 5 expands and solidifies the argument of chapter 2. It discusses three examples of mathematical practice, each displayed by a pair of important [End Page 360] mathematicians: Abel and Galois, Lobachevsky and Riemann, Weil and Grothendieck. Each case... (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Eclecticism and the Technologies of Discernment in Pietist PedagogyKelly J. WhitmerWhile the Franckesche Stiftungen (the Francke Foundations) of Halle/Saale are perhaps best known today as the institutional centre of German Pietism, throughout much of the eighteenth century they were widely regarded as a pedagogically innovative Schulstadt (or city of schools). The founder of this Schulstadt, August Hermann Francke (1663–1727), was many things to many people: Pietist, radical Lutheran, theologian, (...) pedagogue, professor of Greek and Oriental languages, preacher, member of the Berlin Academy of Sciences and proponent of a Protestant mission. Like most participants in what was initially a grassroots movement oriented around the personality of Philipp Jakob Spener (1635–1705), a minister active in Frankfurt am Main around 1670 who sought to breathe new life into the Lutheran church,2 Francke rarely referred to himself as a Pietist. From his post at the University of Halle (founded in 1694), this Spenerian prote´gé set out to create a new "universal seminar" that would make the assimilation of many diverse points of view, identities, and competing strands of knowledge its [End Page 545] defining mandate. "My purpose," Francke wrote in a letter to a Pastor Ring from Grünebartau (October 29, 1712), "is to develop a universal institution, useful for bringing into a good and holy order all that is important for the Christianity of all orders of society and relates, in some way, to the healing power of the soul."3 His Schulstadt would "bring into order" a myriad of relationships around a single point and relied, quite deliberately I propose, on an eclectic methodology to do this.In recent years, the relationship of Francke's Schulstadt to the implementation of Brandenburg-Prussia's first compulsory schooling system and teacher training institutes has been better documented than in the past.4 Scholars of education have paid closer attention to the methodological innovations of Pietist pedagogy, and its points of convergence with the ideas of John Locke (1632–1704), Jean-Jacques Rousseau (1712–1778) and Johann Heinrich Pestalozzi (1746–1827) have become subjects of mounting interest.5 Francke's significance for the history of education has been assessed mainly in terms of his ability to realize the pedagogically inclined reform projects of seventeenth-century figures, such as Johann Amos Comenius (1592–1670).6 We know that the thousands of children who participated in the life of the Schulstadt very often left Halle to become actively involved as teachers and ministers throughout the German states. Several played pivotal roles in the development of the late eighteenth-century educational reform movement known as Philanthropismus and its associated practices and institutions.7 [End Page 546]Perhaps the most striking feature of Francke's Schulstadt was its curriculum, which featured innovative training regimens in applied mathematics for children from diverse social backgrounds.8 The scale and rigor of these programs were to be found nowhere else at the time and can be linked to the overtly pedagogical mandate of the Berlin Academy of Sciences (f. 1701). These regimens deliberately juxtaposed artisanal and learned knowledge and stressed the importance of the eye as a conciliatory medium.9 Despite having acquired largely anti-empiricist reputations over the years due to their lingering interest in alchemy and their roles in securing the banishment of the "rationalist" mathematician and philosopher, Christian Wolff (1679–1754), from their community in 1723, careful consideration of what Halle Pietists were teaching in their schools suggests a different view. These historical actors reconciled categories of knowledge production and transmission often framed as oppositional—despite what several scholars have recently shown to be their clear interconnectedness.10I argue here for the predominance of eclecticism in the Schulstadt, including a pronounced emphasis on the "middling" mathematical and mechanical sciences as tools of conciliation and self-improvement. I seek to illustrate how eclecticism was much more than a Philosophiebegriff that was well received by some Pietists, as Walter Sparn has argued, but that it is better understood as a set of conciliatory practices, traces of which resonate in Pietist lesson plans.11 Teachers in Francke's schools integrated experimental philosophy into an educational program that was introducing children to the exercises of... (shrink)

Society is broken. We can design our way to a better one. In our increasingly interconnected world, self-interest and social-interest are rapidly becoming indistinguishable. If the oceans die, if society fractures, or if global warming spirals out of control, personal success becomes meaningless. But our broken system incentivizes behavior that only makes these problems worse. If true human rights progress is to be achieved today, it is time we dig deeper-rethinking the very foundation of our social system. In this engaging, (...) important work, Peter Joseph, founder of the world's largest grassroots social movement in the world-The Zeitgeist Movement-draws from economics, history, philosophy, and modern public-health research to present a bold case for rethinking activism in the 21st century. The conventional wisdom views poverty, social oppression, and the growing loss of public health as unfortunate and immutable side effects of our way of life. The New Human Rights Movement argues that these outcomes are, in fact, contrived-only natural to our outdated economic system. Social activists can never succeed in dramatically improving human life on this planet until they understand the structural reasons these problems exist. Arguing against the long-standing narrative of universal scarcity and other pervasive, legitimizing myths that defend the current state of affairs, The New Human Rights Movement ultimately presents the case for an updated economic approach. Joseph explores the potential of this grand social shift and how we can design our way to a post-scarcity world-a world where poverty doesn't exist and the human family has become truly sustainable. The New Human Rights Movement reveals the critical importance of a unified activism in this direction, through understanding and working to alter the inherent injustice of our current social system. This book not only warns against what is in store if we continue to ignore our broken society but also reveals the positive future possible if we succeed. Will you join the movement? (shrink)

This target article presents a critical survey of the scientific literature dealing with the speed/accuracy trade-offs in rapid-aimed movements. It highlights the numerous mathematical and theoretical interpretations that have been proposed in recent decades. Although the variety of points of view reflects the richness of the field and the high degree of interest that such basic phenomena attract in the understanding of human movements, it calls into question the ability of many models to explain the basic observations consistently reported in (...) the field. This target article summarizes the kinematic theory of rapid human movements, proposed recently by R. Plamondon (1993b; 1993c; 1995a; 1995b), and analyzes its predictions in the context of speed/accuracy trade-offs. Data from human movement literature are reanalyzed and reinterpreted in the context of the new theory. It is shown that the various aspects of speed/accuracy trade-offs can be taken into account by considering the asymptotic behavior of a large number of coupled linear systems, from which a delta-lognormal law can be derived to describe the velocity profile of an end-effector driven by a neuromuscular synergy. This law not only describes velocity profiles almost perfectly, it also predicts the kinematic properties of simple rapid movements and provides a consistent framework for the analysis of different types of speed/accuracy trade-offs using a quadratic (or power) law that emerges from the model. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Reviewed by:The Cambridge History of Seventeenth-Century Philosophy by Daniel Garber, Michael AyersDonald RutherfordDaniel Garber, Michael Ayers, editors. The Cambridge History of Seventeenth-Century Philosophy. 2 vols. Cambridge: Cambridge University Press, 1998. Pp. xii + 1616. Cloth, $175.Over a decade in preparation, this latest addition to the Cambridge History of Philosophy is an enormous achievement—both in its size and the contribution it makes to redefining [End Page 165] the landscape of (...) seventeenth-century philosophy. The editors make no bones about their intention to rewrite the history of early modern philosophy, reversing the trend dominant through much of this century of reading seventeenth-century philosophers in the light of twentienth-century “interests and preconceptions” (4). As they note, the movement to historicize our understanding of seventeenth-century philosophy has been underway for some time in the English-speaking world, furthered in many cases by contributors to these volumes. From this perspective, the present work represents, if not the culmination, at least a progress report on these efforts and the success they have achieved.As in previous volumes of the Cambridge History, the subject matter is treated thematically. Consistent with their larger goal, the editors have further attempted to organize the volumes in a way that remains faithful to the expectations of the period. Part I sets the stage with chapters that establish the larger social and historical context: “The institutional setting” (Richard Tuck); “The intellectual setting” (Stephen Menn); and “European responses to non-European culture: China” (D.E. Mungello). For the rest, the editors write, “the structure of the collection corresponds to one way, at any rate, in which an educated European of the seventeenth century might have organized the domain of philosophy” (2). First comes logic (including method and general ontology); then, the primary categories of being (God, body, soul); finally, the basic operations of the soul (understanding, will, action), whose treatment comprehends the topics of epistemology and ethics.Part II, “Logic, Language, and Abstract Objects,” opens with three short chapters by Gabriel Nuchelmans that survey the terrain of seventeenth-century logic according to the traditional divisions of term, proposition/judgment, and argument. These are followed by contributions on “Method and the study of nature” (Peter Dear); “Universal, essences, and abstract entities” (Martha Bolton); and “Individuation” (Udo Thiel).The discussion of metaphysics proper begins in Part III with the most fundamental being: God. Included here are chapters that examine specific theological issues—“The idea of God” (Jean-Luc Marion); “Proofs of the existence of God” (Jean-Robert Armogathe); “The Cartesian dialectic of creation” (Thomas M. Lennon)—as well as ones that deal more broadly with the crucial connection between philosophy and religion: “The relation between theology and philosophy” (Nicholas Jolley) and “The religious background of seventeenth-century philosophy” (Richard Popkin).Part IV, “Body and the Physical World,” forms the single largest part of the book and its intellectual core. It opens with two chapters—“The scholastic background” (Roger Ariew and Alan Gabbey) and “The occultist tradition and its critics” (Brian Copenhaver)—that effectively mark out the boundaries of the “new philosophy” that emerges in conjunction with the development of seventeenth-century science. These are followed by a series of chapters that examine particular features of that philosophy: “Doctrines of explanation in late scholasticism and in the mechanical philosophy” (Steven Nadler); “New doctrines of body and its powers, place, and space” (Daniel Garber, John Henry, Lynn Joy, and Alan Gabbey); “Knowledge of the existence of body” (Charles McCracken); “New doctrines of motion” (Alan Gabbey); “Laws of nature” (J.R. Milton); and “The mathematical realm of nature” (Michael Mahoney). [End Page 166]The final section of Volume I takes up the third main category of being: “Spirit.” It begins with Daniel Garber’s overview of the positions of the major figures, “Soul and mind: Life and thought in the seventeenth century,” followed by chapters on “Knowledge of the soul” (Charles McCracken); “Mind-body problems” (Daniel Garber and Margaret Wilson); “Personal identity” (Udo Thiel); and “The passions in metaphysics and the theory of action” (Susan James).Volume II of the History is devoted to topics that, in one way or another, elaborate operations of the soul. Part V, “The... (shrink)

This article is aimed at contributing to the study of the relationship that new religious movements entertain with technology and science. It focuses on an object that is central in Scientology's teachings and practice: the Electropsychometer or E-meter. In interaction with the general public, such as in a 2014 TV Super Bowl advertisement, Scientology seems to claim a unique relationship with science and technology in the form of a “combination” and a “connection” evoked while displaying this very E-meter. Hence, exploring (...) the teachings related to it is relevant in order to understand how such combination or connection is conceptualized. (shrink)

Manipulation of physical models such as tangrams and tiles is a popular approach to teaching early mathematics concepts. This pedagogical approach is extended by new computational media, where mathematical entities such as equations and vectors can be virtually manipulated. The cognitive and neural mechanisms supporting such manipulation-based learning—particularly how actions generate new internal structures that support problem-solving—are not understood. We develop a model of the way manipulations generate internal traces embedding actions, and how these action-traces recombine during problem-solving. This model (...) is based on a study of two groups of sixth-grade students solving area problems. Before problem-solving, one group manipulated a tangram, the other group answered a descriptive test. Eye-movement trajectories during problem-solving were different between the groups. A second study showed that this difference required the tangram's geometrical structure, just manipulation was not enough. We propose a theoretical model accounting for these results, and discuss its implications. (shrink)

In his fascinating doctoral thesis, W.J. Hanegraaff has drawn a clear map to the labyrinth called 'New Age', which he defines as 'the cultic milieu having become conscious of itself as constituting a more or less unified movement'. It is an 'etic' description of 'emic' points of view held by a wide variety of representatives of this movement. The book is divided in three parts: 1. A general orientation; 2. The varieties of New Age experience; 3. An interpretation (...) of the material presented in parts 1 and 2. The author argues that although New Age is composed of many heterogenous elements, nevertheless a measure of coherence can be demonstrated even on the level of beliefs. He holds that as New Age is based on popular culture criticism, thus western esotericism, in which the movement is rooted, it is a third, 'gnostic' option in western culture next to philosophical and scientific rationalism and institutional Christianity. The reviewer, though enthusiastic about the book, questions it on its criteria for distinguishing New Age and Christianity and on the question of possible esoteric influences on apparently Christian movements. The distinction between faith and gnosis could perhaps be profitably related to God's transcendence and his immanence. The platonism of the early Church, adapted for Christian use, ought to be compared with the many platonic elements of present day New Age. (shrink)

ArgumentThis article discusses a number of heterogeneous Yiddish monographs on Einstein's theory of relativity. It presents background information on Einstein's relationship with the Yiddish language, with the cultural movement, Yiddishism, and with its leading institution, YIVO. Although Einstein avoided taking sides in the conflict between Yiddishism and its rival Zionism, his Zionist friends were successful in establishing at least a “primacy of palestinocentric Zionism” in his thinking. Of special interest are two books by philosophic writers and one by an (...) author trained in mathematics and physics, Tuvia Schalit, an acquaintance of Einstein's assistant Jacob Grommer. This article describes the underlying motivations and the philosophical horizon of these authors, in particular with respect to their view on the relationship between Kantianism and the theory of relativity. In contrast to many German academic philosophers, the Yiddish authors thought it possible to reconcile Kantianism with the new physics. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:The Originality of Descartes’s Conception of Analysis as DiscoveryBenoît TimmermansAccording to Descartes, his Meditations employ the method of analysis. This method of proof, says Descartes, “shows the true way by means of which the thing in question was discovered methodically and as it were a priori.” 1 Such a definition of analysis poses a problem that seems to have attracted little attention among commentators until now, namely, why Descartes (...) considers analysis a method of discovery whereas the Scholastic tradition asserts just the contrary, that synthesis allows the discovery of new things, whereas analysis is a method for judging findings or verifying them a posteriori. What is more, the definition that Descartes gives of his analysis contains another divergence, this time brought up by the commentators, 2 for he curiously considers analysis an a priori movement and not an a posteriori movement as dictated by tradition.These issues are all the more important as the analytical method acquired particular prestige in the seventeenth century. This prestige concerned not only philosophy (Descartes, Leibniz, Locke, etc.) but science as well. Thus algebra lost some of its rough edges and gradually took on the name of “analysis.” 3 Descartes created a type of geometry that was soon dubbed “analytic,” and Leibniz developed his analysis infinitorum or differential and integral calculus. If the scientific revolution and the new philosophies that were associated with it attached so much importance to a method that had already been known in ancient Greece, was it not due to a change of the meaning of analysis or at least a rearranging of some of its functions? This is the question that we propose to [End Page 433] tackle while trying to determine to what extent Cartesian analysis breaks with the forms of analysis that preceded it. 4To do this we shall first examine the teachings of Scholastic philosophy concerning the connections between analysis and discovery in general and then study the logical possibilities of discovery through analysis that draw their inspiration from Aristotle’s Analytics and that were developed extensively by the School of Padua in the sixteenth century. Finally, we shall attempt to determine whether the mathematical definition of analysis derived from the works of Euclid and Pappus gives grounds for the correlation with discovery.The Link Between Analysis and Discovery According to the ScholasticsOne might well think that Descartes was completely unaware of the contradiction between his definition of analysis and the teachings of the Scholastics. Had not he always exhibited a true disdain for the latter? However, in September 1640, that is, four months before writing his text on analysis, Descartes began girding for the Jesuit Fathers’ objections to his Meditations. This involved looking for an “abstract of the whole of scholastic philosophy, this would save the time it would take to read their huge tomes.” 5 He finally found what he was looking for in the shops of Leiden, namely, Eustachius a Sancto Paulo’s Summa Philosophiae. There is reason to believe that Descartes read this opus with interest, for two months later he referred to it as “the best book of its kind ever made.” 6 Later he said that he would definitely have chosen the Summa Philosophiae as the basis for refuting the School’s doctrine if he had not given up such a project. 7 Now, Eustachius a Sancto Paulo’s Summa Philosophiae is categorical on the subject of analysis versus synthesis. Analysis of a definition “is perfectly compatible with the doctrines for teaching and learning; as for the other disciplines of discovery, the other method, that is the composite or synthetic method, must be used.” 8According to the Scholastic doctrine as stated by Eustachius a Sancto Paulo, analysis thus plays a part in the teaching of well-known things and in all processes of appraisal, assessment, or judgment. This is easy to explain if one considers that, etymologically, analysis breaks links (ana-luein), goes backward, or climbs back up from the consequences to the principles. Starting from an observation, proposition, or question, it wends its way back to the simplest, [End Page 434] surest items of knowledge that shed light on and verify said starting... (shrink)

This thesis presents and criticizes Hilary Putnam's argument that mathematics is as empirical as science, in particular the argument that the switch from Euclidean geometry to Riemannian geometry as the approporiate geometry for physical space constituted an instance of revising mathematics as a result of observation. The thesis explains Putnam's views on mathematics as following from his theory of meaning and reference for natural kind terms. It is argued that Putnam's account of reference is unsuitable for mathematical terms and that (...) an "if-thenist" approach to mathematical knowledge is more fruitful. (shrink)

From 1801–1807 Schelling continued to refine his early attempts at Naturphilosophie in the metaphysical framework of a transcendental Spinozism that he initially called Identity Philosophy. While mathematics and geometry provided the model for identity and its quantitative differentiation in early versions of identity theory, from 1804–1807, logic and theory of language offered a model of identity capable of unknotting persistent Spinozistic puzzles such as the connection between natura naturans and natura naturata—the absolute and its potencies—and the ontological status of the (...) individual. Schelling’s initial concepts of identity as “indifference” or “the identity of identity and difference,” themselves the offshoot of meditations on polarity and repeating structure in the philosophy of nature, make way for logical concepts such as “expression” or “affirmation” and the propositional operator “bond” or “Position” found in the copula. The new essays approach ultimate reality through Spinoza’s disjunction of God or nature, or productive and produced nature; so in addition to identity theory, a general metaphysics of nature prefaces treatments of specific natural phenomena. These dual metaphysics of God and nature inject a dynamic or expressive movement into identity that is not yet the unfolding of identity as grounding-and-division that Schelling will articulate in the 1809 Freedom Essay, but it carries a sense of motion and differentiation—or evolution and unfolding—not found in his earlier attempts. The entire identity philosophy period is best viewed as a step in Schelling’s lifelong project of reworking Spinoza by adding life and spirit to nature. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Journal of the History of Philosophy 43.4 (2005) 490-491 [Access article in PDF] Husain Sarkar. Descartes' Cogito: Saved from the Great Shipwreck. New York: Cambridge University Press, 2003. Pp. xviii + 305. Cloth, $65.00. Descartes's first critics attacked his cogito, ergo sum as deficient; his present critics attack it as excessive. Either way, it is an Archimedean point in Descartes's world and merits a book-length study. In this book, (...) Husain Sarkar makes a powerful case that the cogito is not an argument, but rather an "experiment," generating an intuition enabling Descartes to retrieve a timber from what Bourdin called the "great shipwreck" of the hyperbolic doubt.Sarkar places the experiment within his own fresh readings of Descartes's philosophy. They will be illuminating to new Descartes scholars. Some readings will seem perverse or cryptic. Constructive passages illuminate more, polemic passages less, as when Sarkar finds seven flaws in Hintikka's cogito interpretation. Despite the polemic excesses, Sarkar writes with modesty, epitomized by his slogan, "Reason with them in the most courteous manner."With verve and imagination Sarkar presents the cogito as an experiment which can be carried out in any world at all and yields an intuition that qualifies as a Cartesian first principle. He suggests various implications of his interpretation—for example, for the epistemic role of will: "The will initially learns the limits that it must recognize only at the foot of the cogito... It is in the state of the cogito that the will learns what it means to be ineluctably inclined toward affirming a proposition, and what it is to be free" (256).What is the content of the intuited 'I exist'? Sarkar calls upon Robert Adams's notion of a "primitive thisness," entirely distinct from a substance's properties or "suchnesses," and upon David Lewis's thesis that besides knowing propositions a person can know a self-ascription of a property. Still, he makes no headway at all. True, the question is extraordinarily [End Page 490] difficult. It has not yielded appreciably to brilliant phenomenologists or brilliant students of direct reference and indexicality or, for that matter, me. The content of 'I' statements is a topic for another book, and no one I know of is writing it.In the book's centerpiece, Sarkar marshals a series of attacks on the cogito as argument. Sometimes they miss—more polemic overkill. Usually they hit home. Their cumulative effect is persuasive.Descartes says that "I think, therefore I exist" is the first principle of his philosophy (VI, 32; VIIIA, 7; V, 147: references are to the Adam and Tannery edition). But if the cogito were an argument, one of its premises would become his first principle.An argument requires movement of thought and that requires reliance on memory (X, 370 and 408), and in the cogito Descartes strips memory of its credentials (VII, 24, superseding the assurances of X, 368).An argument relies on logical principles, but Descartes suspects these and reasoning generally. In the First Meditation he calls into doubt the simplest mathematics; elsewhere he generalizes from mathematics to "self-evident principles" and to "all the arguments I had previously taken as demonstrative proofs" (VI, 32; IXB, 6; similar aspersions are cast in V, 137 and 139). (But see also Mark Olson, "Descartes' First Meditation: Mathematics and the Laws of Logic" JHP 26 [1988]: 407–438.)I'll add a wrinkle. Descartes's mouthpiece Eudoxus says you can use your own doubt to deduce facts that are even more certain than those commonly built upon the great principle that it is impossible that a thing should both exist and at the same time not exist (X, 522). The conclusion of any argument rests on such logical principles. If the cogito were an argument, its certainty could not exceed theirs. Descartes suggests here that it does.Sarkar also cites Descartes's denigrations of "logic," but these often pertain not to reasoning generally but to syllogistic logic. Thus Margaret Wilson took the cogito to be a nonsyllogistic argument. Still, Sarkar effectively deploys... (shrink)

One of the most important phenomena in contemporary South America has been the tendency towards more democratic systems. After protracted periods of authoritarian rule, Brazil, Argentina, Uruguay, and Bolivia appear to be heading in a more democratic direction. This process has awakened political hopes and attracted intellectual reflection, especially regarding Brazil and Argentina, the largest and most influential nations of South America. Both countries are in different moments, with different timings, in transitions which could lead to the establishment of stable (...) democratic regimes. The following will discuss a number of new social movements which have emerged under the military regimes and have been significant in the struggle for democracy. (shrink)

The New Beginning Movement (NBM) (1971–1978) in Trinidad functioned as a voice of direct democracy and workers self-management through popular assemblies, and as a global coordinating council of a Pan-Caribbean International with linkages across the region, in Britain, the United States, and Canada. A crucial philosophical and strategic leaven in the 1970 Black Power Revolt led by Geddes Granger’s and Dave Darbeau’s National Joint Action Committee (NJAC) and the 1975 United Labour Front (ULF) in Trinidad, NBM aspired to interpret (...) Afro-Trinidadians and Indo-Trinidadians equally, and on their own autonomous terms, toward self-directed emancipation. Led by Bukka Rennie, Wally Look Lai, and Franklyn Harvey, NBM was inspired by C.L.R. James’s intellectual legacies. Through publications such as New Beginning, Caribbean Dialogue, and The Vanguard, these partisans advocated labor’s self-emancipation and critical perspectives on capitalism and state power, and exposed the limits of elite party politics and representative government. (shrink)

The Scientific Revolution was far from the anti-Aristotelian movement traditionally pictured. Its applied mathematics pursued by new means the Aristotelian ideal of science as knowledge by insight into necessary causes. Newton’s derivation of Kepler’s elliptical planetary orbits from the inverse square law of gravity is a central example.

The article offers a critical analysis of the cognitive science of religion (CSR) as applied to new and quasi-religious movements, and uncovers implicit conceptual and theoretical commitments of the approach. A discussion of CSR’s application to new religious movement (NRM) case studies (charismatic leadership, paradise representations, Aḥmadiyya, and the International Society for Krishna Consciousness) identifies concerns about the theorized relationship between CSR and wider socio-cultural factors, and proposals for CSR’s implication in wider processes are discussed. The main discussion analyses (...) three themes in recent work relating CSR to religious and religion-like activities that extend and reframe the model. These include (1) identification of distinctive and accessible cognitive pathways associated with new forms of religious belief and practice (in particular in ‘New Age’ movements), (2) application of CSR to movements and practices outside traditional definitions of religion (near death experiences, conspiracy theories, virtual reality), and (3) engaging CSR in wider cultural processes and negotiations (religion in healthcare settings, and the definition of the study of esoteric religious traditions within academic domains). The conclusion identifies two particular findings: (1) that application of CSR in these areas renders underlying cognitive processes more available to scrutiny and (2) that CSR is employed to identify and enlarge the category of religion. The conclusion suggests that the study of CSR in its application to NRMs and quasi-religion identifies a wide field of common and overlapping themes and interests in which CSR is a more active operand than is commonly assumed. (shrink)