The next two sections of the line are of the intellectual. The third is lower forms, and the final is higher forms. Plato uses the line to differentiate between what he views as different kinds of objects and ways we can obtain knowledge. Each line gets smaller the higher it goes, and the smaller the line becomes the closer to absolute truth it becomes.
To briefly summarize the story of the cave, Plato envisaged people held prisoner within a cave who only saw the shadows of objects carried by a fire. One person briefly escaped from the cave, saw the sun, and returns to tell the other prisoners what was seen. The prisoners respond by threatening the person that briefly escaped if he continued to tell them about the sun. Plato is saying that people are like the prisoners, in that all people see are illusions, shadows of objects passing by a fire. They are seeing the material world, which he believed to be a copy of the higher forms. The person who escaped was able to see the sun, which represented the highest level of truth in this world: "But, whether true or false, my opinion is that in the world of knowledge the idea of good appears last of all, and is seen only with an effort; and, when seen, is also inferred to be the universal author of all things beautiful and right, parent of light and of the lord of light in this visible world, and the immediate source of reason and truth in the intellectual; and that this is the power upon which he who would act rationally, either in public or private life must have his eye fixed" (Plato). The escaped person's eyes took a while to adjust before they were actually able to see the sun; the person was able to see things at night better first, then reflections in water and such, and then finally objects themselves. This was supposed to represent a gradual increase in the realness of the objects until the sun was able to be seen. When the person went back to the cave and told the other prisoners what he saw, they rejected it. This represents how Plato felt that most people are so used to seeing what they see everyday that they can't comprehend the idea that there is something of a higher truth out there. They've never seen it, and if they've never seen it, then it couldn't possibly exist. Plato was alluding to the fact that he thought that it was dangerous for him and other philosophers to tell other people of the truth since most people weren't willing to hear anything of the sort.
What Plato didn't realize was that he was in an even larger cave himself. He felt that there was absolute truth, and even though people might not be able to reach it, it still existed in the universe in some shape or form. He thought that because there are things called trees, we can only know that that is a tree because on some higher plane of existence there exists the perfect tree, its original and true form, and that is how people are able to recognize that trees when one is viewed. He felt that true knowledge could only be perceived a priori, and that the physical world was merely a reflection of this true world. A deconstructionist way to argue against this kind of thinking be to would say that there is no such thing as absolute truth, that thinking and language can not be separated, because without language, there is no canvas upon which to paint one's words. This viewpoint would claim that language isn't trying to reflect