The divided line of Plato

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Plato's Forms, also known as The Divided Line
  Thought Objects  
Knowledge Reason
Higher Forms Intelligible World
(Science, Mathematics)
Forms of Science and Mathematics
Opinion Belief
Things, Objects Visible World
Shadows, Images, Reflections

Conjecture (Imagining)

This knowledge is the lowest degree of truth; it is all mere reflections or dreams, and only shadows of the real object itself. Plato is thus saying that a still-life painting of an apple points less to the truth of the apple than the apple itself.

Belief (Perception)

This knowledge is higher and helps explain (or make more intelligible) the Conjecture level; this level is the physical apple itself. However, this level is still very limited in that its knowledge of the physical apple cannot grasp the botanist's knowledge of an apple. The botanist's knowledge, what defines an apple, is in the above levels, past the "divided line" between knowledge and opinion.

Understanding (Science, Mathematics)

This level puts us into knowledge instead of belief or opinion; at this level the apple is understood by the botanist's definition of it. Here, all is abstract and universal and unchanging; below, all is concrete and in flux. The limitation, however, is that science and mathematics depend on particulars and physical (the level below, Belief) representations.

Reason (Dialectic)

Finally, we reach pure reason itself. At this level all of the Forms developed in the Understanding level are brought together into unity and into a single Form, the Idea of the Good. Through dialectic reasoning, one can analyze all forms and see their relation to one another.

To complete the example of the apple:

  • Conjecture: a mirror image, a painting, or a reflection off the water
  • Belief: seeing and feeling
  • Understanding: the definition or concept
  • Reason: the form of the apple is brought together with all other forms and melded into the supreme and complete Idea of the Good

(Source: From Socrates to Sartre: the Philosophic Quest, by T.Z. Lavine)