The divided line analogy is brought up in The Republic, by Socrates while in conversation with Glaucon. It is described as a line divided into four sections. Socrates explains the four sections as representing four different affections, with the higher two representing the intelligible and the lower two representing the visible. As one progresses upwards towards the intelligible, one is also thought to be progressing in their knowledge of the ultimate form of all things.
In The Republic, Plato’s Socrates claims that the philosopher must understand the Idea of Justice to live a just life or to organize and govern a just state. This could be represented as someone who lives in the upper level of the divided line. It is not enough for the philosopher to understand the Forms, he must also understand the relation of Ideas to all four levels of the divided line parable to be able to truly know anything at all.
The parable of the cave is also brought up in The Republic as a comparative example of the effects of education, or lack thereof, on human nature. The parable of the cave compares the different levels of education to three forms of life among the subjects in the parable: imprisonment in the cave, departure from the cave, and the return to the cave. As such, Aristotle likens our perception of the world around us “to the habitation in prison, the firelight there to the sunlight here, the ascent and the view of the upper world is the rising of the soul into the world of the mind”.