In his Metrica, Hero provides four procedures for finding the area of a circular segment (with b the base of the segment and h its height): an Ancient method for when the segment is smaller than a semicircle, $$(b + h)/2 \, \cdot \, h$$ ( b + h ) / 2 · h ; a Revision, $$(b + h)/2 \, \cdot \, h + (b/2)^{2} /14$$ ( b + h ) / 2 · h + ( b / 2 (...) ) 2 / 14 ; a quasi-Archimedean method (said to be inspired by the quadrature of the parabola) for cases where b is more than triple h, $${\raise0.5ex\hbox{$\scriptstyle 4$} \kern-0.1em/\kern-0.15em \lower0.25ex\hbox{$\scriptstyle 3$}}(h \, \cdot \, b/2)$$ 4 / 3 ( h · b / 2 ) ; and a method of Subtraction using the Revised method, for when it is larger than a semicircle. He gives superficial arguments that the Ancient method presumes $$\pi = 3$$ π = 3 and the Revision, $$\pi = {\raise0.5ex\hbox{$\scriptstyle {22}$} \kern-0.1em/\kern-0.15em \lower0.25ex\hbox{$\scriptstyle 7$}}$$ π = 22 / 7. We are left with many questions. How ancient is the Ancient? Why did anyone think it worked? Why would anyone revise it in just this way? In addition, why did Hero think the Revised method did not work when $$b > 3\;h$$ b > 3 h? I show that a fifth century BCE Uruk tablet employs the Ancient method, but possibly with very strange consequences, and that a Ptolemaic Egyptian papyrus that checks this method by comparing the area of a circle calculated from the sum of a regular inscribed polygon and the areas of the segments on its sides as determined by the Ancient method with the area of the circle as calculated from its diameter correctly sees that the calculations do not quite gel in the case of a triangle but do in the case of a square. Both traditions probably could also calculate the area of a segment on an inscribed regular polygon by subtracting the area of the polygon from the area of the circle and dividing by the number of sides of the polygon. I then derive two theorems about pairs of segments, that the reviser of the Ancient method should have known, that explain each method, why they work when they do and do not when they do not, and which lead to a curious generalization of the Revised method. Hero’s comment is right, but not for the reasons he gives. I conclude with an exploration of Hero’s restrictions of the Revised method and Hero’s two alternative methods. (shrink)

Descendre acheter le journal? Réflexion : vous délibérez, construisez un projet, argumentez. Décision prise, la volonté vous met debout. Alors, dès le premier pas, l'acte vient à la rencontre de l'action-projet qui agrégeait dans votre tête réflexion, délibération, argumentation, décision, volonté. L'acte est une aventure. Toute la réalité imprévisible du monde se trouvait là, en réserve, dont les créations intellectuelles de l'action escamotaient la part d'inconnu. On décide une action, c'est l'acte qu'on rencontre. Mais alors, pourquoi les deux mots sont-ils (...) communément employés l'un pour l'autre, obligeant à penser l'acte dans une réduction à l'action " dans la tête "? Tel est le sujet de ce livre magistral de Gérard Mendel qui prend la suite de La psychanalyse revisitée (1988) et La société n'est pas une famille (1992). A partir d'une lecture critique de l'œuvre des grands philosophes, d'Aristote à Habermas, en passant par Saint Augustin, Descartes ou Nietzsche, Gérard Mendel montre comment la naissance philosophique de l'être il y a vingt-cinq siècles a chassé l'acte de la réflexion intellectuelle. En s'appuyant sur une étude approfondie de l' " intelligence pratique " nourrie de son expérience de terrain sur le champ social et sur la relecture des travaux fondamentaux de Winnicott, il propose une nouvelle approche théorique du sujet et de l'acte. Loin du fantasme occidental d'une domination absolue de l'esprit sur la nature et la société, s'affirme alors l'idée d'un acte, pouvoir individuel et collectif en quête d'un rapport plus harmonieux avec la réalité qui, parce qu'elle résiste continûment, reste toujours aussi blessante pour le narcissisme humain. Cette réflexion passionnante, d'une écriture toujours claire, intéressera tous ceux qui ne se satisfont pas de la césure entre théorie et pratique dans la compréhension de l'activité humaine : psychanalystes, psychologues et philosophes, bien sûr, mais aussi travailleurs sociaux et sociologues. (shrink)

It is commonly held that moral judgements are implicitly general — or universalizable — in that if anyone is morally obligated to perform or refrain from some action, everyone in relevantly similar circumstances is similarly obligated. I undertake here to show that David Hume fully subscribed to this thesis and that because of the way it is related to his conceptions of obligation and what he terms the practicality of morals he is pushed to insist that the moral sentiments of (...) human beings across space and time are much more uniform than he knew them to be. My discussion places Hume in the historical context of the controversy about 'the general foundation of morals' referred to near the beginning of the second Enquiry, and it is part of my thesis that Hume's moral philosophy can be understood only in terms of arguments and counter-arguments developed by other contributors to the controversy. (shrink)

The concept of heterotopia challenges political theory, which has often focused on utopic thinking. Foucault describes a heterotopia as a heterogenous space that juxtaposes in a single real place several spaces, several sites that are in themselves incompatible. Streets, squares and parks form heterotopias when their utopic purity as public space is juxtaposed with the private spaces created by the cardboard boxes and other temporary shelters of homeless people. Since citizenship has traditionally been thought of as participation in a democratic (...) public sphere, how do heterotopias of homelessness challenge the ideas about citizenship? Based on narrative research with homeless people in Poland, I show how the homeless conceive of their marginality. Their participation or non-participation in democracy is not hidden but, on the contrary, very visible in public spaces where they are included as excluded. (shrink)

This paper presents an attempt to describe parents’ activities, in which context it is puzzling that – on the basis of a negative assessment of the current reality (current crises, including the privatization of what is public) – parents seem to be searching intensively for new solutions that would make better not only the school but also the world it is a part of. Their focus, in this, is on the local dimension of activities that refer to sustainability and emphasize (...) place. In this approach, place is a field of confrontation and constant becoming. Parental activities in one sustainable community school in Chicago is the point of departure to introduce a pedagogy of the vital place that pays specific attention to how the heritage of these places makes them (partially) resistant to capitalist capture, and somewhat ready to take on the challenges of the crisis in which we live on the planet today. The reflection presented in this article is guided by the assumption that, in these times, when the survival of humankind is at stake, we desperately need a more-than-human format of world. (shrink)

The author argues, Contra hume, That "the motives of human action are not related to the action in the way in which the causes of the sort of physical behaviour to which hume refers are related to that behaviour." the author contends this because he is opposed to the consequence of hume's theory that "moral appraisal presupposes 'necessity' or determinism." he concludes that we do have to explain morality in terms of human motives, But that a different sort of causality (...) is involved here than in the physical world. (staff). (shrink)

Following the practice of human beings everywhere historians distinguish the real or most significant cause of an occurrence or state of affairs from ‘less important considerations’, ‘precipitating circumstances’, or ‘mere conditions’. I shall term claims that some phenomenon is most basically to be attributed to some one of the factors causally necessary for its occurrence attributive causal explanations or causal attributions and discuss here the extent to which moral convictions are constitutive of them.

Name der Zeitschrift: Naharaim Jahrgang: 10 Heft: 1 Seiten: 57-77.

The first part of this paper examines conditions in accord with Einstein's criterion of regularity on the field solutions everywhere that would correspond to the existence of a black hole star, following from solutions of his (nonvacuum) field equations. ‘Black hole’ is defined here as a star whose matter is so condensed as to correspond to a complete family of spatially closed geodesics. The condition imposed is that the angular momentum of a test body in each of the closed geodesics (...) is a constant of the motion. The second part of the paper examines the implications in the problem of the condensed star of a generalized (factorized) version of the metrical field equations, discovered earlier by the author. It is found that in general relativity stars should naturally pulsate, and in its succeeding cycles the gravitational radius of the star is attenuated by a factor exp(−0.349T), where T is the pulsation period. Conditions are discussed for the possibility that the (relatively) regular emissions of radiation from a pulsar may be dynamically rooted in a (smaller) part of the pulsation cycle when the star is out of the black hole state (less dense → open geodesics)—when radiation would be emitted to the outside world—and the (greater) part of the cycle when it is in the black hole state (more dense → closed geodesics)—when radiation would not be emitted. (shrink)

Myth, Utopia, and Political ActionStarting from the premise that some form of "reality transcendence", i.e. the ability to imagine a different reality and reach out for the (un)thinkable, is necessary for political action, the aim of this paper is to analyse the concepts of myth and utopia elaborated by Georges Sorel and Karl Mannheim and to examine their possible contributions to a theory of political action and social change. By comparing the role the authors assign to rationality and irrationality in (...) human affairs, methodological and conceptual differences between Sorel's and Mannheim's approaches to the political are illustrated. It turns out that due to its immunity to critique Sorel's concept of the social myth is highly problematic. Mannheim's concept of utopia, on the other hand, culminates in a technocratic understanding of the political. Though both approaches emphasise the collective dimension of political action, they ultimately exhibit elitist understandings of the political. (shrink)

The discussion of mathematical knowledge and its relation to the construction of an appropriate diagram in Aristotle's Metaphysics Θ 9. 1051 a21—33 is an important, if compressed, account of Aristotle's most mature thoughts on mathematical knowledge. The discussion of what sort of previous knowledge one must have for understanding a theorem recalls the discussion at An. Post. A 1. 71 a 17–21, where the epistemological point is similar and the examples the same. The first example, that the interior angles of (...) a triangle equal two right angles, appears no less than thirty times in the corpus . The example of the angle inscribed in a semicircle being a right angle also occurs at An. Post. B 11. 94a 27–34, but in a very different context from its two companions. Illustrations of both theorems provided clear stock examples for Aristotle. (shrink)

The topic of instrumentalism has engaged many scholars of contemporary educational thought. One can distinguish the positions of anti-instrumentalism from those that stress noninstrumental values of education, both conceived in the context of neoliberal/neoconservative and consumption-driven reality. In this text, Maria Mendel enters into this engagement from the perspective of the current political consumption of memory. While taking up the problem of the role public pedagogy plays in contemporary nation-states — especially in the current turn toward the past — (...) Mendel focuses on both educational and sociopolitical issues in the context of what she calls “retroactive instrumentalism.” When return to the past is the “principle of the contemporary,” she argues, instrumentalism does not necessarily result from intentional planning ex ante. If education is broadly understood as a practice of public space formation, it may be composed of experiences that do not have to be “traditionally” purposeful and oriented toward the future. They may gain their instrumental character ex post. To illustrate this possibility, Mendel analyzes snippets of Polish reality concerning the construction of “the good nation.” Many of the elements of public pedagogy in this case contain unifications that pertain directly to the instrumental character of the learning experiences employed by a society as it transforms into a nation. The instrumentalism of those elements is discovered post factum. In its ontological dimension, then, education may gain or solidify its instrumental character ex post. Based on the analysis proposed in this text, one could say that when instrumentality is retroactive, it becomes displaced intentionality — that is, it provides an instrumental story that disguises the intentions of the one writing the narrative. Mendel concludes by using the Aristotelian notion of phantasia, which regards “being without a matter,” to encourage productive thought about how to create public narratives that are free of instrumentalism. This grounds a version of public pedagogy that is oriented toward the animation of people's active imagining and thus becoming public. By epistemologically shifting learning into a public space, such public pedagogy serves to recultivate society and humanity as plurality, diversity, and coproduction of the public. (shrink)

The most general expression of electromagnetic theory is examined in the light of (1) Faraday's interpretation of the field as a potentiality for the force of charged matter to act upon a test body, and (2) Einstein's view of the field equations as an example of a covariant expression of special relativity. Faraday's original interpretation, in which all physical variables must be expressible as nonsingular fields, implies a particular generalization of the standard forms of the conservation equations and leads to (...) a removal of the problem of the infinite self-energy of point sources. A further generalization of the mathematical expression of electromagnetism occurs when it is asserted that the form of the laws must be compatible with the symmetry requirements of the irreducible representations of the Poincaré group. This yields a factorization of the vector field equations, giving a set of two uncoupled two-component spinor equations. It is shown that the latter lead to twice as many conservation equations for electromagnetism, compared with the vector formalism, thus making extra predictions that are not made in the latter formalism. It is shown that the extra conservation equations reveal themselves only when incorporating the requirements of Faraday's interpretation of the field solutions. (shrink)

This paper responds briefly to the criticism of Rodrigues and Rosa on my earlier analysis of the twin paradox. The main point that I have emphasized (and that the authors have not refuted, either logically or mathematically) is the error in directly identifying anabstract measure relative to a reference frame [and its transformations to all other possible reference frames in which the laws of nature are to be compared (such as temporal and spatial measures)], with aphysical extension and duration of (...) a material body. (shrink)

Based on several cases, this article develops a thought inspired by the Journal of Philosophy of Education’s special issue on the Educational Value of Monuments (55.3). The article is a reflection about the locations which make statues able to be transformed materially and semiotically, and which provoke discussion about what is to be learnt by understanding the monument as a fragment and semiophore. I argue that the monument—located in a specific place which makes its contextual meaning—represents fragments, in Latin fractures (...) or cracks, as an expression of the violence inflicted on an imaginary whole. Defining and accepting a monument as a fragment allows us to understand each change that may happen to it—including removal or relocation—as an incentive to learn about the meanings of new wholes and to consciously respond to them. On the one hand, this can effectively stop mimetic pressures to reproduce aggression towards monuments. On the other, it can create a ground for shaping an ethical attitude of co-responsibility for a common world that is not exclusively human. The strictly educational sense of the proposed redefinition of the monument would be to radicalize sensitivity to its inherent feature, which is its fragmentary nature, resulting in the fragility of the heritage it co-creates in the space of commonality. In the proposed understanding of the monument, apart from the emphasis on significant fragmentation, an important role is played by the decisive abandonment of the anthropocentric perspective. In the new perspective of the common world, the monument becomes an ephemeral heritage, and its most current educational value seems to lie there. (shrink)