Mathematics, Mental Imagery, and Ontology: A New Interpretation of the Divided Line

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  • 1 University of Texas at Arlington


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.

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