Allegory

1. If you understand this first distinction, the much more difficult division of the intelligible world will make more sense. Think over this carefully: the visible world, that is, the world you see, has two kinds of visible objects in it. The first kind are shadows and reflections, that is, objects you see but aren't really there but derive from the second type of visible objects, that is, those that you see and are really there. The relation of the visible world to the intelligible world is identical to the relation of the world of reflections to the world of visible things that are real.

2. The lower region of the intelligible world corresponds to the upper region in the same way the lower region of the visible world corresponds to the upper region. Think of it this way: the lower region deals only with objects of thought (that are, in part, derived from visible objects), which is why it is part of the intelligible world. There have to be certain first principles (such as the existence of numbers or other mathematical postulates) that are just simply taken without question: these are hypotheses. These first principles, however, derive from other first principles; the higher region of the intelligible world encompasses these first principles. So you can see that the lower region derives from the higher region in that the thinking in the lower region derives from the first principles that make up the higher region, just as the mirror reflects a solid object. When one begins to think about first principles (such as, how can you prove that numbers exist at all?) and derives more first principles from them until you reach the one master, first principle upon which all thought is based, you are operating in this higher sphere of intellection. Plato's line is also a hierarchy: the things at the top (first principles) have more truth and more existence; the things at the bottom (the reflections) have almost no truth and barely exist at all.

Commentary for Plato's "Allegory of the Cave" by S. Marc CohenÐ'©2K2

1. Plato realizes that the general run of humankind can think, and speak, etc., without (so far as they acknowledge) any awareness of his realm of Forms.

2. The allegory of the cave is supposed to explain this.

3. In the allegory, Plato likens people untutored in the Theory of Forms to prisoners chained in a cave, unable to turn their heads. All they can see is the wall of the cave. Behind them burns a fire. Between the fire and the prisoners there is a parapet, along which puppeteers can walk. The puppeteers, who are behind the prisoners, hold up puppets that cast shadows on the wall of the cave. The prisoners are unable to see these puppets, the real objects, that pass behind them. What the prisoners see and hear are shadows and echoes cast by objects that they do not see. Here is an illustration of Plato's Cave:

4. Such prisoners would mistake appearance for reality. They would think the things they see on the wall (the shadows) were real; they would know nothing of the real causes of the shadows.

5. So when the prisoners talk, what are they talking about? If an object (a book, let us say) is carried past behind them, and it casts a shadow on the wall, and a prisoner says "I see a book," what is he talking about?

He thinks he is talking about a book, but he is really talking about