Descartes' philosophy contains an intriguing notion of the infinite, a concept labeled by the philosopher as indefinite. Even though Descartes clearly defined this term on several occasions in the correspondence with his contemporaries, as well as in his Principles of Philosophy, numerous problems about its meaning have arisen over the years. Most commentators reject the view that the indefinite could mean a real thing and, instead, identify it with an Aristotelian potential infinite. In the first part of this article, I (...) show why there is no numerical infinity in Cartesian mathematics, as such a concept would be inconsistent with the main fundamental attribute of numbers: to be comparable with each other. In the second part, I analyze the indefinite in the context of Descartes' mathematical physics. It is my contention that, even with no trace of infinite in his mathematics, Descartes does refer to an actual indefinite because of its application to the material world within the system of his physics. This fact underlines a discrepancy between his mathematics and physics of the infinite, but does not lead a difficulty in his mathematical physics. Thus, in Descartes' physics, the indefinite refers to an actual dimension of the world rather than to an Aristotelian mathematical potential infinity. In fact, Descartes establishes the reality and limitlessness of the extension of the cosmos and, by extension, the actual nature of his indefinite world. This indefinite has a physical dimension, even if it is not measurable. La filosofía de Descartes contiene una noción intrigante de lo infinito, un concepto nombrado por el filósofo como indefinido. Aunque en varias ocasiones Descartes definió claramente este término en su correspondencia con sus contemporáneos y en sus Principios de filosofía, han surgido muchos problemas acerca de su significado a lo largo de los años. La mayoría de comentaristas rechaza la idea de que indefinido podría significar una cosa real y, en cambio, la identifica con un infinito potencial aristotélico. En la primera parte de este artículo muestro por qué no hay infinito numérico en las matemáticas cartesianas, en la medida en que tal concepto sería inconsistente con el principal atributo fundamental de los números: ser comparables entre sí. En la segunda parte analizo lo indefinido en el contexto de la física matemática de Descartes. Mi argumento es que, aunque no hay rastro de infinito en sus matemáticas, Descartes se refiere a un indefinido real a causa de sus aplicaciones al mundo material dentro del sistema de su física. Este hecho subraya una discrepancia entre sus matemáticas y su física de lo infinito, pero no implica ninguna dificultad en su física matemática. Así pues, en la física de Descartes, lo indefinido se refiere a una dimensión real del mundo más que a una infinitud potencial matemática aristotélica. De hecho, Descartes establece la realidad e infinitud de la extensión del cosmos y, por extensión, la naturaleza real de su mundo indefinido. Esta indefinición tiene una dimensión física aunque no sea medible. (shrink)

Motivated by the alarming recurrence of wars, Lanza del Vasto became Gandhi’s disciple. From a social interpretation of biblical texts he derived a characterization of non-violence as the conversion from not only personal negative drives, but also from the influences of negative social institutions and the entire civilization. His intellectual categories comprise an ethical conception of four essentially different models of development. This pluralism subsists inasmuch as the representatives of each model do not search the destruction or the suppression of (...) the adversaries, but reconciliation through non-violent means. (shrink)

George Gemistos Plethon’s work in all its dimensions has attracted many scholars across the ages. One of those scholars was Alexandre Joseph Hidulphe Vincent, a French mathematician and erudite, who in the first and the only critical edition of Plethon’s Book of Laws by C. Alexandre in the nineteenth century, added three notes on his calendar, metrics and music, as he could reconstruct them from the ancient text. Vincent’s calculations were dictated by the main scientific thought of his time, which (...) was Positivism, and through this he thus contributed to the elucidation of some practical aspects of Plethon’s metaphysics. The results of meticulous calculations of the Plethonian calendar, metrics and musical modes show that the scientific spirit, which started appearing in the last days of Byzantium and during the Renaissance, was not only a revival of Antiquity, but an innovative attempt at explaining and being in accordance with the social demands and the physical reality of the time, both being understood as an extension of the metaphysical order. Vincent’s positivistic approach allows considering the impact of Plethon’s system in a postmodern perspective. (shrink)