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


Authors
Miriam Byrd
University of Texas at Arlington
Abstract
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.
Keywords Plato   Republic   dianoia   hypothesis  mathematics
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DOI 10.1163/18725473-12341411
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References found in this work BETA

Beginning the 'Longer Way'.Mitchell Miller - 2007 - In G. R. F. Ferrari (ed.), The Cambridge Companion to Plato's Republic. Cambridge University Press. pp. 310--344.
Greek Mathematical Thought and the Origin of Algebra.Jacob Klein, Eva Brann & J. Winfree Smith - 1968 - British Journal for the Philosophy of Science 20 (4):374-375.
Plato's Republic, A Philosophical Commentary.R. C. Cross & A. D. Woozley - 1964 - Philosophical Review 75 (3):405-407.

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