“A line is cut into two unequal parts, and each of them is divided again in the same proportion. The two main divisions correspond to the intelligible world and to the visible world. One section in the visible division consists of images, that is,
shadows and reflections, and is accessed through imagination. The other, higher section in the visible division consists of sensible particulars and is accessed through belief. One section in the intelligible division consists of Forms and is accessed through thought, but via sensible particulars and hypotheses, as when geometers use a picture of a triangle to help reason about triangularity, or make appeal to axioms to prove theorems. The other, higher section in the intelligible division also consists of Forms but is accessed by understanding, a purely abstract science which requires neither sensible particulars nor hypotheses, but only an unhypothetical first principle, namely, the Form of the Good. The purpose of education is to move the philosopher through the various sections of the line until he reaches the Form of the Good.”
I was most confused about the significance of the line so that is where I dedicated most of my research and understanding. The quote from the hyperlinked website above helped me understand that the line is not only meant to bridge the gap between the sun and the cave, but it creates a sort of process in which somebody is meant to go through until they reach the good. Most people are unable to reach the good without first experiencing imagination and opinion, however, I’m still confused as to why that is. To me, it seems that Forms and abstract sciences are not dependent on imagination and opinion. However, perhaps that is the point, people must experience imagination and opinion and observe the effects of the two before Forms and abstract sciences. Maybe this is so that people can see that Forms and abstract sciences allow us to lead a better and “good” life.
The source above focuses on just the line, it breaks the line up similarly to the first source (into four sections), however, it shows that the different parts of the line are placed in a sort of hierarchy. This makes more sense to me since the four sections aren’t very dependent on one another. In addition, if the four parts of the line aren’t meant to be dependent on each other but are simply ranked, then it makes sense that the line bridges together the sun and cave. The lower-ranked parts are more towards the cave and the higher-ranked parts are more toward the sun. There is still a journey involved here in a way because people likely start at the cave but as they acquire new skills, closer to the side of the sun, they get closer to the “good”.