Attempts to provide a coherent understanding of three analogies that appear at the center of Plato's Republic: The Sun and the Good, The Divided Line, and the Allegory of the Cave. The main innovation is to treat The Divided Line as an image‐object metaphor illustrating the nature of mathematical reasoning. On this reading, the middle two portions of the four‐part Divided Line both contain diagrams. In the lower middle portion, the diagram is treated as a physical object that can have reflected images. In the upper middle portion, the diagram is treated as a physical object, which is itself...

Attempts to provide a coherent understanding of three analogies that appear at the center of Plato's Republic: The Sun and the Good, The Divided Line, and the Allegory of the Cave. The main innovation is to treat The Divided Line as an image‐object metaphor illustrating the nature of mathematical reasoning. On this reading, the middle two portions of the four‐part Divided Line both contain diagrams. In the lower middle portion, the diagram is treated as a physical object that can have reflected images. In the upper middle portion, the diagram is treated as a physical object, which is itself an image of a form.