In the present article, we consider the question of the primary elements in Plato’s Timaeus, the components of the whole universe reduced, by an extraordinarily elegant construction, to two right triangles. But how does he reconcile such a model with the infinite diversity of the universe? A large part of this study is devoted to Cornford’s explanation in his commentary of the Timaeus and its shortcomings, in order to finally propose a revised one, which we think to be entirely consistent (...) with Plato’s text. This analysis is an essential step for the understanding of the connection between the sensible world and the mathematical principles that underlies Timaeus’ cosmological account. (shrink)

In this paper, we study the so-called ‘Mathematical part’ of Plato’s Theaetetus. Its subject concerns the incommensurability of certain magnitudes, in modern terms the question of the rationality or irrationality of the square roots of integers. As the most ancient text on the subject, and on Greek mathematics and mathematicians as well, its historical importance is enormous. Its interpretation presents a certain degree of difficulty because of the intertwined fields that play a role in it : philosophy, history and mathematics. (...) But conversely, correctly understood, it provides clues on both the question of the origins of the irrationals in Greek mathematics and some points concerning Plato’s thought. Taking into account the historical context and the philosophical background generally forgotten in mathematical analyses, we get a new interpretation of this text which, far from being a tribute to some mathematicians, is a radical criticism of their ways of thinking. And the mathematical lesson, far from being a tribute to some future mathematical achievements, ends on an aporia, in accordance with the whole dialogue. (shrink)

History is familiar with great scientific traditions which have been substantial, effective, cumulative and progressive.* At the level of great eras of civilization, extensive and not episodic phenomena, very ancient Chinese science, Greek science and Arab science are objects of investigation for historical erudition, but also for the scientific historian and the philosopher of sciences. Many of the elements of these systems were the source of “modern science”, as it is called, or are integral parts ol’ this system of knowledge (...) and practice which has been constructed over a little more than three centuries. Diachronically, the “scientific revolution” of the classical age in Europe does not signify a total break with what preceded it: Chinese astronomy, Arab algebra and the hospital organization of the Islamic world were used, even if the ideology of scientists when they wrote their own history, particularly from the 19th century onward, tends to make of modern science a purely European phenomenon. (shrink)

Existentialism and Sociology is the first work to systematically and critically analyze the existential ideas of Jean-Paul Sartre and to demonstrate their importance and connection to central sociological categories found in the theories of Weber, Durkheim, Freud, Mead, and others.

In chapter one I cover the basic concepts developed in Being and Nothingness, notable those of "temporality," "negation," "anguish" and "bad faith." In chapter two I move from the individual as the center of free action, to the individual in relation to the Other. In chapter three I attempt to unify the perspectives in the first two chapter and present a theory of action. In chapter four I introduce the reader to the Critique and establish its thematic links with Being (...) and Nothingness. In chapter five I analyze the ramifications of the concept of the practico-inert, which, for Sartre, is inseparable from human sociality. In chapter six I deal with the concept of organization, which refers to the contradictions within the social group as it moves into advanced stages of social integration. In chapter seven I cover the concepts of power and authority. Chapter eight deals with the idea of dialectical humanism and highlights essential concepts in the work by way of concluding it. --Introduction. (shrink)

If politics is about the state, can a stateless people be political? The field of Jewish political thought examines how Jewish individuals and communal organizations have behaved politically both within and beyond statehood. The study of Jewish political thought promises to expand received conceptions of what counts as "political.".

Extraits de la Source de vie de Salomon ibn-Gebirol.--Ibn-Gebirol, ses écrits et sa philosophie.--Des principaux philosophes arabes et de leurs doctrines.--Esquisse historique de la philosophie chez les Juìfs.--Appendice.--Texte hébreu des extraits de la Source de vie (2 p.l., 36 numb. l. at end).

Introduction -- Matter, form of cognition, form of sensibility, form of understanding, time and space -- Sensibility, imagination, understanding, pure a priori concepts of the understanding or categories, schemata, answering the question Quid Juris, answering the question Quid Facti, doubts about the latter -- Ideas of the understanding, ideas of reason, etc. -- Subject and predicate. the determinable and the determination -- Thing, possible, necessary, ground, consequence, etc. -- Identity, difference, opposition, reality, logical, and transcendental negation -- Magnitude, alteration, change, (...) etc. -- Truth, subjective, objective, logical, metaphysical -- On the I, materialism, idealism, dualism, etc. -- Short overview of the whole work -- My ontology -- On symbolic cognition and philosophical language. (shrink)

This paper is an updated translation of an article published in French in the Journal Lato Sensu (I, 2014, p. 70-80). We study here the so-called 'Mathematical part' of Plato's Theaetetus. Its subject concerns the incommensurability of certain magnitudes, in modern terms the question of the rationality or irrationality of the square roots of integers. As the most ancient text on the subject, and on Greek mathematics and mathematicians as well, its historical importance is enormous. The difficulty to understand it (...) lies in the close intertwining of different fields we found in it: philosophy, history and mathematics. But conversely, correctly understood, it gives some evidences both about the question of the origins of the irrationals in Greek mathematics and some points concerning Plato's thought. Taking into account the historical context and the philosophical background generally forgotten in mathematical analyses, we get a new interpretation of this text, which far from being a tribute to some mathematicians, is a radical criticism of their ways of thinking. And the mathematical lesson, far from being a tribute to some future mathematical achievements, is ending on an aporia, in accordance with the whole dialogue. Résumé. Cet article est une traduction anglaise révisée d'un article paru en français dans la revue Lato Sensu (I, 2014, p. 70-80). (shrink)

Pour rendre compte de la première démonstration d’existence d’une grandeur irrationnelle, les historiens des sciences et les commentateurs d’Aristote se réfèrent aux textes sur l’incommensurabilité de la diagonale qui se trouvent dans les Premiers Analytiques, les plus anciens sur la question. Les preuves usuelles proposées dérivent d’un même modèle qui se trouve à la fin du livre X des Éléments d’Euclide. Le problème est que ses conclusions, passant par la représentation des fractions comme rapport de deux entiers premiers entre eux, (...) i.e. la proposition VII.22 des Éléments, ne correspondent pas aux écrits aristotéli­ciens. Dans cet article, nous proposons une nouvelle démonstration, conforme aux textes des Analytiques, fondés sur des résultats très anciens de la théorie du pair et de l’impair. Ne passant pas par la proposition VII.22, ni par aucune autre propriété établie par l’absurde, cette irrationalité apparaît comme le premier résultat que l’on ne pouvait établir par une autre méthode. L’importance de ce résultat, révélant un nouveau domaine mathématique, celui des grandeurs irrationnelles, rend compte de la centralité que cette forme de raisonnement acquiert alors, d’abord en mathématique, puis dans tout type de discours rationnel. À partir des conséquences qui suivent de cette nouvelle démonstration, on peut interpréter très simplement la leçon sur les irrationnels du passage mathématique figurant dans le Théétète de Platon (147d-148b), ce que nous ferons dans un article à paraître dans un prochain numéro. (shrink)

Challenges to the exercise of the basic socio-economic rights of half the global population give rise to some of the most pressing issues today. This timely book focuses on world poverty, providing a systematic exposition of the evolving legal responsibility of the international community of states to cooperate in addressing the structural obstacles that contribute to this injustice. This book analyzes the approach, contribution, and current limitations of the international law of human rights to the manifestations of world poverty, inviting (...) the reader to rethink human rights, and, in particular, the framing of responsibilities that are essential to their contemporary protection. (shrink)

El trabajo desea mostrar la especial relación que se entabla entre el pensamiento de heidegger y la metafísica. En tal sentido se propone la tentativa de dotar de un nuevo fundamento a la metafísica a través de la analítica existenciaria emprendida en El Ser en el Tiempo. Siguiendo esta misma obra señala cómo un análisis original del tiempo aunado a la revisión crítica (de-construcción) de la Historia de la Metafísica -tarea te será asumida ulteriormente- concluyen 1 un "abandono" del pensamiento (...) fundacional y por tanto en una "renuncia" a la metafísica. Ella empero no ha de ser rechazada sino más bien plenamente asumida ·y sobrepasada- comprendiéndola dentro del pensamiento que medita la Historia del ser como auténtico nihilismo, es decir como la "época" necesaria en la que el Ser en proceso de su desocultación se dispensa tanto retirada. (shrink)