There is a problem about belief and knowledge in Plato's epistemology that has exercised serious students of Plato only to settle into a recent orthodoxy. Guthrie characterizes the problem and its current resolution this way: ‘In the Meno doxa appeared to be a dim apprehension of the same objects of which knowledge is a clear and complete understanding … in the Republic each is directed to different objects, knowledge to the Forms and doxa to the sensible world alone … at (...) least the opinion seems now to prevail that on the relationship between doxa and knowledge Meno and Republic are irreconcilable, and exhibit a complete change of mind on Plato's part.'. (shrink)

I offer a new interpretation of Aristotle's philosophy of geometry, which he presents in greatest detail in Metaphysics M 3. On my interpretation, Aristotle holds that the points, lines, planes, and solids of geometry belong to the sensible realm, but not in a straightforward way. Rather, by considering Aristotle's second attempt to solve Zeno's Runner Paradox in Book VIII of the Physics , I explain how such objects exist in the sensibles in a special way. I conclude by considering the (...) passages that lead Jonathan Lear to his fictionalist reading of Met . M3,1 and I argue that Aristotle is here describing useful heuristics for the teaching of geometry; he is not pronouncing on the meaning of mathematical talk. (shrink)

La autora aborda el problema de los entes matemáticos intermedios analizando MetafiSica l017a9-l4, por ser este pasaje, simultáneamente, fuente ycrítica de la teoría que Aristóteles atribuye a Platón. El objetivo es identificar cuatro puntos de orientación que ofrezcan una base para el diálogo entre las encontradas posiciones respecto del problema. Gracias a ellos, se pone de manifiesto que Aristóteles aborda la cuestión de la naturaleza inteligible de los entes matemáticos recortándola -con el bisturí del aparato conceptual de su propia ousiología- (...) de la perspectiva mucho más ampliade Platón. Al romper la continuidad entre matemática y dialéctica. Aristóteles"reduce" y demuele la imagen de la concepción matemática de Platón. (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)

There is a problem about belief and knowledge in Plato's epistemology that has exercised serious students of Plato only to settle into a recent orthodoxy. Guthrie characterizes the problem and its current resolution this way: ‘In the Meno doxa appeared to be a dim apprehension of the same objects of which knowledge is a clear and complete understanding … in the Republic each is directed to different objects, knowledge to the Forms and doxa to the sensible world alone … at (...) least the opinion seems now to prevail that on the relationship between doxa and knowledge Meno and Republic are irreconcilable, and exhibit a complete change of mind on Plato's part.'. (shrink)