At the end of Book VI and the beginning of Book VII, Plato offers several striking analogies to explain the structure of reality, the knowledge of it, and how people can acquire that knowledge. Plato begins his discussion by having Socrates offer a critique of other theories.
“I think you have often heard,” he says, “that the Form of the good is the greatest object to grasp, since by it just acts and other undertakings become useful and beneficial.” For if your objective is wrong, you will misuse the means at your disposal for a bad end. “You know this, too, that pleasure seems to the many to be the good, while wisdom seems so to the more sophisticated thinkers. … And you know that those who hold the latter view are not able to determine what wisdom is, but they are finally compelled to say it is knowledge of the good.”[36] On the other hand, those who say pleasure is the good are forced to concede that there are bad pleasures. So both sides of the debate seem to be at a loss to understand what the good is.
Yet Plato holds that the good is “what every soul seeks and for the sake of which it does every act.”[37] Call this view Agathism. It is a view held by Plato and his master Socrates. Plato here rejects the theory known as Hedonism (from Greek hedonē “pleasure”), according to which pleasure is the good. He is also rejecting the theory known as Ethical Intellectualism (from Latin intellectus “understanding”) that virtue is knowledge of the good. Plato’s rejection of Hedonism is not surprising.[38] But his rejection of Intellectualism is a renunciation of the view of his master Socrates—in whose mouth he puts his criticism. Plato makes it appear that Socrates’ view is circular: What is the good? Knowledge of the good. But how then can we understand good if we define it in terms of itself?
Socrates’ view seems to be rather that virtue is knowledge, perhaps knowledge of the good. But he uses good to define ‘virtue,’ not ‘knowledge.’[39] So is Plato being unfair to Socrates? Plato can at least argue that Socrates leaves ‘good’ undefined, and hence the definitions he recognizes are incomplete and vulnerable to objections.
In any case, Plato here decisively abandons Socrates’ Intellectualism and goes on to reassert the Theory of Forms, stipulating that for every property there is a Form that specifies the “being” (ho estin) of it.[40] He goes on to point out that in the sensible world, the objects of sight require not only a power of sight in a perceiver, but a light source to illuminate them. The natural source of light in the world is the sun. And as the sun is necessary to enable sight, so the Form of the Good is necessary to allow us to grasp the other Forms. In this way, it is not only a Form itself, but a Form that makes other Forms intelligible. “Accordingly, that which imparts truth to the things known and which gives the power of knowing to the knower you must say is the Form of the Good.”[41]
While the full import of the Form of the Good is not evident, clearly Plato wants to put value at the center, or rather the pinnacle, of his Theory of Forms, and to guarantee the worth of every Form. The Forms are to be, not just general terms or concepts, but Ideals after which the sensible world must strive. To grasp any Form is, then, to grasp a piece of Goodness.
Plato’s Socrates goes on to offer another important analogy. Draw a vertical line, and divide it into unequal sections (with the longer section above); then divide each part again into unequal sections (still with the longer section above). You will have a Divided Line with four sections, from top to bottom, with each section smaller than the one above it. The lowest section represents images, shadows, and reflections; the one above that, physical objects; the two lower sections represent the sensible world. Above the sensible world is the intelligible world. The third section (counting from the bottom) represents mathematical objects such as triangles and squares; the fourth section, transcendent Forms.
To each level of reality (for that is what we are depicting with the Divided Line), there is a corresponding kind of cognition. Images and reflections are known by imagination; physical objects are known by belief; mathematical entities are known by calculation; Forms are known by insight. Further, each level of reality is a kind of image or copy of the one above it, while each level of cognition is a copy of the one above it. Thus, reality is arranged hierarchically, as is cognition. Thus (ignoring the differences of spacing between the lower and higher levels:
| Divided Line Level | Cognition | Reality |
| 1 | Insight (noēsis) | Forms |
| 2 | Calculation (dianoia) | Mathematical entities |
| 3 | Belief (pistis) | Physical objects |
| 4 | Imagination (eikasia) | Images and reflections |
[36] Plato Republic VI, 505a-b.
[37] Plato Republic VI, 505e.
[38] Plato Protagoras 354c. Some scholars see Plato or Socrates as accepting Hedonism, e.g. Irwin 1977: 114. I take Plato’s Socrates as accepting the position only provisionally to show that even Hedonism entails Intellectualism. Socrates explicitly rejects Hedonism in the Gorgias, 495d-e and following.
[39] See Plato Protagoras 360d, there defining courage; but Socrates holds that the virtues are ultimately all one (cf. ibid. 329d-330b, 333a-b.
[40] Plato Republic VI, 507b.
[41] Plato Republic VI, 508d-e.