Die Frage, ob die Gültigkeit alternativer begrifflicher Strukturen empirisch entscheidbar oder eine Sache der willkürlichen Festsetzung ist, wird, eingeschränkt auf den Fall der physikalischen Geometrie, diskutiert. Die erkenntnistheoretischen Komponenten der empirischen Bestimmung von metrischen und topologischen Eigenschaften des physikalischen Raumes werden in der neueren Wissenschaftstheorie verfolgt. In Anschluß an die Auseinandersetzung zwischen A. Grünbaum und H. Putnam wird eine Interpretation des semantischen Status des Kongruenzprädikates vorgeschlagen, die Schwierigkeiten im Verhältnis von Intension und Extension dieses Terms beseitigen soll. Bei der Konfrontation (...) von Folgerungen aus der Konventionalitätsthese mit der dynamischen Raumtheorie, wie sie im Anschluß an Clifford von J. A. Wheeler entwickelt wurde, treten Unvereinbarkeiten auf, die in der Gegensätzlichkeit von absoluter und relationaler Raumauffassung gründen. (shrink)

This paper takes a detailed look at the Republic’s Divided Line analogy and considers how we should respond to its most contentious implication: that pistis and dianoia have the same degree of ‘clarity’ (σαφήνεια). It argues that we must take this implication at face value and that doing so allows us to better understand both the analogy and the nature of dianoia.

Many have argued that Plato’s intermediates are not independent entities. Rather, they exemplify the incapacity of discursive thought to cognizing Forms. But just what does this incapacity consist in? Any successful answer will require going beyond the intermediates themselves to another aspect of Plato’s mathematical thought - his attribution of a quasi-numerical structure to Forms. For our purposes, the most penetrating account of eidetic numbers is Jacob Klein’s, who saw clearly that eidetic numbers are part of Plato’s inquiry into the (...) ontological basis for all counting: the existence of a plurality of formal elements, distinct yet combinable into internally articulate unities. However, Klein’s study of the Sophist reveals such articulate unities as imperfectly countable and therefore opaque to διάνοια. And only this opacity, I argue, successfully explains the relationship of intermediates to Forms. (shrink)

This paper presents a new interpretation of the objects of dianoia in Plato’s divided line, contending that they are mental images of the Forms hypothesized by the dianoetic reasoner. The paper is divided into two parts. A survey of the contemporary debate over the identity of the objects of dianoia yields three criteria a successful interpretation should meet. Then, it is argued that the mental images interpretation, in addition to proving consistent with key passages in the middle books of the (...) Republic, better meets those criteria than do any of the three main positions. (shrink)

La exposición y crítica de las doctrinas antiguas tiene un lugar importante en los escritos de Aristóteles. Sin embargo, ciertas dudas se han vuelto corrientes acerca de la confiabilidad de sus descripciones. Más aún, se ha sostenido que Aristóteles deforma la comprensión histórica a través de la introducción de conceptos y términos propios. En este libro se aborda el problema a través de un análisis de las críticas que Aristóteles dirige a la teoría platónica de las Ideas, que permite explicar (...) la constitución y desarrollo de importantes conceptos aristotélicos a partir de la confrontación dialéctica con las doctrinas de su maestro. En efecto, las dificultades genuinas que Aristóteles descubre en el platonismo constituyen el motor para gestar nuevos conceptos, que no son ajenos, sino que surgen como implicaciones del examen crítico. Así, la imposición de términos propios no debe interpretarse como distorsión, sino como el modo que Aristóteles adopta para exhibir su particular solución a los problemas que los filósofos anteriores dejaron sin solución. (shrink)

What is the function of logic in al-Kindī's corpus? What kind of relation does it have with mathematics? This article tackles these questions by examining al-Kindī's theory of categories as it was presented in his epistle On the Number of Aristotle's Books, from which we can learn about his special attitude towards Aristotle theory of categories and his interpretation, as well. Al-Kindī treats the Categories as a logical book, but in a manner different from that of the classical Aristotelian tradition. (...) He ascribes a special status to the categories Quantity and Quality, whereas the rest of the categories are thought to be no more than different combinations of these two categories with the category Substance. The discussion will pay special attention to the function of the categories of Quantity and Quality as mediators between logic and mathematics. (shrink)

In a 1985 article entitled “The Art of Glaukos,” Diskin Clay suggested that the enigmatic passage at the beginning of the geological myth in Phaedoreferred toRepublic10, where the soul is likened to the sea-creature Glaucus whose true nature, like the soul’s, is obscured by the distortions imposed by underwater life. Starting with a defense of Clay’s ingenious suggestion, my purpose is to compare Phaedoto Glaucus, with its true nature obscured by traditional assumptions about the order in which Plato composed his (...) dialogues, and thus how they should be read. At least part of the reason that Clay’s thesis has not been embraced is because it clashes with the dogma that Phaedocannot refer back to Republic; I want to challenge that dogma. Borrowing from Catherine Zuckert the notion that, since Phaedocomes at the end of Socrates’ story, it can usefully be read as the culmination of the Platonic dialogues, I will show how a “late” Phaedo—i.e., a reading of the dialogue that is open to the possibility that it refers to more than one dialogue generally considered to be later than it with respect to composition—recovers its true nature, presently encrusted with the oysters and seaweed of an outdated developmentalism that has obscured this culminating masterpiece of Plato’s dramatic and philosophical art. (shrink)