In The Republic, Plato suggests the image of the Divided Line in book 6. The Line represents the Whole in two dimensions. The vertical axis of the Line shows the relationship between the intelligible and the visible world, and the soul stands in relation to its objects along the horizontal axis. These are the four stages that are represented by the Line. The top section represents intelligible realm and the soul's "insight," or noesis, in relation to these intelligible beings. The lower section of the Line represents both the visible things in the realm of becoming and the soul's state of "opinion" in relation to these things. The Line represents the Whole in that the intelligible and the visible domains are depicted as parts of one and the same line, and the Line also represents the close connection between the states of the soul and the character of its objects because the line is equally a likeness of both.
The Line thus represents the journey taken over the whole of the Republic, and the continuity or integrity of the Whole depends on the imaging relationships binding together its elements along both axes. The Line elucidates and exemplifies eikasia, or imagination, meaning the power to make and recognize images enabling a philosophic education by allowing us to move vertically on the Line toward the originals. This relates to the allegory of the Cave, which refers to the horizontal phenomenon of psychic imitation or mimesis by which the soul takes on the character of its objects.
Plato's conception of the existence of Forms as the ideals of the imperfect objects and ideas of this world derived in part from the ongoing discussion in Greek philosophy over change versus permanence. The allegory also relates to issues of epistemology as to what we can know and how we can know it. The cave becomes the touchstone, the example that serves to demonstrate the relationship between the idea and the reality, between percepti...