Figure 62 Right triangle (α^2 + β^2 = γ^2 ).
Geometric figures are not available to the senses, but we do apprehend with the senses physical objects
that approximate to geometric figures, like the triangular pediments of a temple or a hoplite’s circular
shield. This distinction, between a world of permanently unchanging entities about which we can have
certain knowledge and the unstable, imperfect world of the senses which arouses unending debate,
suggested to Plato the existence of a realm in which everything that we are familiar with from the world
of the senses has a permanently unchanging correlate. To refer to these correlates Plato used the Greek
word idea, meaning “shape, form, appearance,” and this theory is often referred to as Plato’s “Theory of
Forms.” While Plato’s thinking about geometric figures may have inspired him to construct this theory, the
Forms do not consist only of geometric shapes. Rather, there is an eternal, unchanging Form of everything,
from sandals to triremes to sealing wax. More importantly, there are Forms of justice, courage, and self-
restraint. We cannot perceive the Forms with our senses, just as we cannot perceive the hypotenuse of a
right triangle. If the Forms can be apprehended at all, it is only through reason (the Greek for which is
logos), just as it is by reason alone that we know what we know about right triangles. Reason, then, must
have affinities with the realm of the Forms, rather than with the world of the senses. That is, reason must
be everlasting, like the Forms themselves. But we humans are not everlasting, and yet we are endowed to
a limited extent with reason. There must be, therefore, some part of us that is everlasting, in which reason
can reside. That part, for Plato, is the soul, which according to the teaching of Pythagoras has an existence
separate from and more enduring than that of the body.
The philosophy of Plato, it should be stressed, is never laid out in explicit terms, as it has been above, but
must be reconstructed on the basis of the discussion in his dialogues, which rarely comes to conclusions
that the interlocutors can agree upon. But that is part of the point of the dialogue form, which is an
inheritance from the conversational method of Socrates and from Socrates’ profession of his own
ignorance. Philosophy is a process which, because of the inherent fallibility of human nature, cannot attain
the certain knowledge that it seeks to attain. To read the dialogues of Plato is to accept an invitation to
think and to question. That invitation has been repeatedly accepted, and Plato is generally regarded as one