Visible things are symbols of a reality that can be thought but not seen. Plato illustrates this kind of mental activity by referring to the mathematician. Although scientists may look at a particular object, a triangle or a brain, they go beyond this particular triangle or brain and think about the Triangle or the Brain. Science require that we "let go" our senses and rely instead upon our intellects. Thinking therefore, represents the power of the mind to abstract from a visible object that property which is the same in all objects in that class even though each such actual object will have other variable properties.
Thinking is characterized not only by its treatment of visible objects as symbols, but also by reasoning from hypotheses. By a hypothesis Plate meant a truth which is taken as self-evident but which depends upon some higher truth: "You know," says Plate, "how students of subjects like geometry and arithmetic begin by postulating odd and even numbers, or the various figures and the three kinds of angle... These data they take as known, and having adopted them as assumptions, they do not feel called upon to give any account of them to themselves or to anyone else but treat them as self-evident."
For Plato, then, an hypothesis did not mean what it meas to us, namely, a temporary truth. He meant by it a firm truth but one that is related to a larger context. The special sciences and mathematics treat their subjects as if they were independent truths. All Plato want to say here is that if we could view all things as they really are, we should discover that all things are related or connected.