Socrates explains to his listeners that philosophers have a love of knowledge. This is called philosophical temperament. He also defines a philosopher as someone who loves wisdom and the truth. When he defines the parts of a polis: the Guardians, who are rulers or auxiliary, and the craftsmen, he assigns wisdom to be the dominant force behind the rulers. Since philosophers are the lovers of knowledge, who better than them to be the rulers of the polis? There are three basic types of men, and each finds pleasure in seeking wisdom, success, or gain/satisfaction. The seeker of wisdom is the philosopher. Socrates explains that since the philosopher has lived all three lives where as the other

two men have never lived the philosophic life, the philosopher is the better person to judge which life is better. When he judges that the philosophic life is best, Socrates takes it as fact. In order for the philosophic man to rule the polis, he needs special education to learn about abstract ideas and the highest forms of knowledge.

Another abstract idea that philosophers understand is the concept of the Forms. Being able to understand this means having the ability to define a word without making reference to other objects. So, in order to define Beauty, I cannot say, "Beauty is a butterfly," because that is describing a beautiful "thing", not Beauty itself. If you can see the One instead of the Many (Beauty instead of a beautiful butterfly), according to Socrates, you have wisdom and will be high up on the ladder of the Divided Line. So, in order for philosophers to have knowledge in the Forms, they need to think abstractly, especially with numbers. Not only will they be able to understand the properties of abstract objects such as circles, but because a philosopher understands the Form of Circularity, he understands what a circle is. So, a philosopher definitely differs from a mathematician. And in order to express and explain these observations to others, a philosopher needs to learn Dialectic. Once a philosopher has mastered this, he has learned how to argue logically. This begins with a question about something and proceeds with a long, drawn out discussion, to hopefully end with a definition or answer to the question originally

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