There are no contemporary documents explaining the meaning of the figures, their postures, or the symbolism Raphael used.

There were no universally understood artistic depictions for many of the philosophers Raphael painted; he had to paint them strictly from his imagination.

The School of Athens is a difficult painting to interpret because all of the ancient genuises that are displayed in the painting either had one self-portrait or Raphael painted them to what he believed they looked like. You also have to remeber that any type of sketch or portrait of any of the subjects in the painting could have been lost during the period of the Renaissance.