plato and aristotle painting
Conversely, Aristotle’s hand is a visual representation of his belief that knowledge comes from experience. Empiricism, as it is known, theorizes that humans must have concrete evidence to support their ideas and is very much grounded in the physical world.
The School of Athens was the third painting Raphael completed after Disputa (representing theology) and Parnassus (representing literature). It’s positioned facing Disputa and symbolizes philosophy, setting up a contrast between religious and lay beliefs.
Plato, (born 428/427 bce, Athens, Greece—died 348/347, Athens) ancient Greek philosopher, student of Socrates (c. 470–399 bce), teacher of Aristotle (384–322 bce), and founder of the Academy, best known as the author of philosophical works of unparalleled influence.
Plato and Aristotle are discussing the respective merits of Idealism vs. Realism. Plato holds his book, Timaeus, one of the few works by Plato that had been recovered by the Renaissance, while explaining how the universe was created by the demiurge from perfect mathematical models, forms and the regular geometric solids. With his right hand Plato gestures upwards, indicating that the eternal forms, such as the ideals of Beauty, Goodness and Truth, are not in or of this world, but beyond, in a timeless realm of pure Ideas.
Nevertheless, the fresco has even recently been interpreted as an exhortation to philosophy and, in a deeper way, as a visual representation of the role of Love in elevating people toward upper knowledge, largely in consonance with contemporary theories of Marsilio Ficino and other neo-Platonic thinkers linked to Raphael. 
A number of drawings made by Raphael as studies for the School of Athens are extant.  A study for the Diogenes is in the Städel in Frankfurt  while a study for the group around Pythagoras, in the lower left of the painting, is preserved in the Albertina Museum in Vienna.  Several drawings, showing the two men talking while walking up the steps on the right and the Medusa on Athena’s shield,  [a] the statue of Athena (Minerva) and three other statues,  a study for the combat scene in the relief below Apollo  and “Euclid” teaching his pupils  are in the Ashmolean Museum of Art and Archaeology at Oxford University.
Part of a portait by Raphael assumed to represent Francesco Maria della Rovere (1490-1538)
The Greek painter Apelles (О‘ПЂОµО»О»О®П‚), shown as a self-portrait by Raphael who had been nicknamed by Vasari the “new Apelles. Raphael is directly gazing at us, as if he was questioning what we thought about his painting. Apelles was probably the most important Greek painter born about 370 BC in Colophon. He studied at Ephesus and spent 12 years at Sikyon. He worked for Alexander the Great and his father Philip. None of his works survived! Apelles used to show his pictures to the public listening to comments. A shoemaker once faulted the painter for a sandal with one loop too few, which Apelles corrected. The shoemaker, emboldened by this acceptance of his views, then criticized the subject’s leg. According to Pliny Apelles replied to this that the shoemaker should not judge beyond his sandals. He is also famous for saying: вЂњNot a day without a lineвЂќ, i.e. do something every day!
The heads of the Gods Apollo and Athena are aligned with Plato’s and Aristotle’s heads respectively. The point where the two diagonals intersect can be referred to as the divine center between the two philosophers.
Leonardo da Vinci’s portrait is also self evident in the School of Athens. His reincarnation as Plato is somewhat curious though, given that Leonardo left Florence, and its overt Platonism, for the more congenial Aristotelian circle of scholars, scientists and engineers at Milan. Perhaps it was Raphael’s duel admiration and preference for Plato, combined with his respect for his teacher (Leonardo) that led him to identify the two men.