Socrates is still attempting to elucidate his point; Glaucon asks that Socrates continue the analogy. But Socrates introduces a new illustration, The Analogy of the Divided Line. Socrates is still making the distinction between knowledge and belief, the difference between the Forms and ordinary objects. (We should also recall here that Socrates says that objects of belief are like reflections of objects of knowledge.) At this juncture of the dialogue, Socrates argues that there exist two degrees of knowledge and two of belief.
Socrates tells us now that there exist four levels of what we may call intellect (intellectual functioning, cognition) and four levels of objects that the intellect perceives. (See the illustration of the Levels of Intellect.)
- The lowest level of intellect (cognition, thinking process) is called imagining. Thinking at this level seems to be the mental activity pursued by people whose state of mind might be called, in comparison to higher states of mind, unclear, or vague. (This state of mind may be manifested in the unreleased people in the Allegory of the Cave, which Socrates discusses later in the dialogue. These people in the Cave perceive only images of images.)
- The next higher level of intellect is called belief, or common-sense belief. Mental activity at this level seems to be the thought processes of people who perceive tangible things, real objects, things of material substance. These people, like the young Guardians, hold moral beliefs, but they have no knowledge of the things in which they believe; they have been taught to believe. A higher education is intended for the Guardians as they mature (in order for them to escape from the Cave). The Guardians are to be educated in mathematics and then in moral philosophy.
- The next higher level of intellect is called thinking. Formal training in this level of mental activity involves studying the mathematical sciences. Guardians at this level of mental activity are taught the use of visible diagrams and physical models meant to symbolize the workings of pure thought. Next, the Guardians are taught to reason from assumptions (premises) to conclusions (deductive thought).
- The highest level of intellect is called Dialectic, which for Plato means a conversation (question and response) that seeks to determine, without the aid of diagrams or physical models, a conclusion about some Form, for example, the conversation about Justice in the present dialogue. This level of mental activity does not move from an assumed premise to a conclusion (deductive thinking); rather, the premise itself is analyzed through Dialectic (as in the present dialogue) to try to determine the nature of a given Form. Knowledge of the Form might then be construed as a premise, from which we can deduce conclusions proving out the whole of mathematics and moral philosophy. This level of intellect is also called intelligence or knowledge (the condition of the prisoner who is released from the Cave in the Allegory of the Cave).
It is important at this juncture in our conversation that we do not confuse Plato's theories on Dialectic with the ideas of later thinkers, such as Friedrich Hegel (1770-1831) and Karl Marx (1818-1883), who read Plato and, in their times, advanced their respective theories of systematic philosophy in terms that differ from Plato's.