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

International Journal of the Platonic Tradition 12 (2):111-131 (2018)
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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.

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10.1163/18725473-12341411

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Miriam Byrd
University of Texas at Arlington

Citations of this work

Dianoia & Plato’s Divided Line.Damien Storey - 2022 - Phronesis 67 (3):253-308.
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Ammonius and Philoponus on the Activity of Syllogizing.Luca Gili - 2021 - History of Philosophy & Logical Analysis 24 (1):140-160.

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References found in this work

Greek Mathematical Thought and the Origin of Algebra.Jacob Klein, Eva Brann & J. Winfree Smith - 1969 - British Journal for the Philosophy of Science 20 (4):374-375.
Plato's Republic. A philosophical Commentary.R. C. Cross & A. D. Woozley - 1964 - Les Etudes Philosophiques 19 (4):606-607.
The Cambridge Companion to Plato’s R Epublic.G. R. F. Ferrari (ed.) - 2007 - New York: Cambridge University Press.

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