Resumen

GUTIERREZ, Raúl. On the Soul, the Diánoia and the Mathematical Entities in the Republic. Prax. filos. [online]. 2019, n.48, pp.11-33. ISSN 0120-4688.  https://doi.org/10.25100/pfilosofica.v0i48.7308.

Having in mind the images of the sun, line and cave as an outline and its coincidence with the structure of the Republic as a whole, the author discusses the nature of dianoia and its objects. He pretends to show that the analysis of the structure of the soul at Republic IV proceeds according to dianoia, that is, in the same way as the hypothetical-deductive method used in mathematics. Thus he proposes that this investigation assumes the law of non-contradiction as hypothesis and as a principle. He concludes, therefore, that the mathematical entities are not the only objects of dianoia and, that as the so called “parts” of the soul, are of a purely conceptual nature. Furthermore, he characterizes the relation between the objects of dianoia and pistis as a dialectic of original and image. This is well represented by the consciously intended equality and inequality of the middle sections of the line. Last but not least, this also valid for the relation between the civic and personal virtues, as much as for the two different kinds of mathematical entities corresponding to the levels of corresponding mathematical disciplines distinguished by Plato.

Palabras clave : Soul; Dianoia; Hypothetical-deductive Method; Mathematical Entities.

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