The Italian word disputa has unfortunately been translated into English as dispute, suggesting argument, contention, and quarrel. The more probable meaning of disputa here is discussion, deriving ultimately from the Latin disputare, “to reckon.”
The central "discussion" in the Disputa mirrors the interaction between Plato and Aristotle across the room in The School of Athens.
"In the painting, Raphael has created a scene spanning both heaven and earth. Above, Christ is surrounded by an aureole, flanked by the Blessed Virgin Mary and John the Baptist to his right and left (an arrangement known as the Deësis). Other various biblical figures such as Adam (far left, bared chest), Jacob (far right, red robe and sword) and Moses (right, with horns of light and holding tablets of the Ten Commandments) are to the sides. God the Father sits above them all in the golden light of heaven and adored by angels. Below Christ's feet is the Holy Spirit, to whose sides are books of the four Gospels held open by putti.
"Below, on an altar sits the monstrance. The altar is flanked by theologians who are depicted debating Transubstantiation. Christ's Body, Blood, Soul, and Divinity is the Holy Eucharist, which is discussed by representatives of the Church; among them are the original four Doctors of the Church (identified by their names inscribed into their halos), with Pope Gregory I and Jerome seated to the left of the altar and Augustine and Ambrose to the right, along with Pope Julius II, Pope Sixtus IV, Savonarola and Dante Alighieri. Pope Sixtus IV is the gold dressed pope in the bottom of the painting. Directly behind Sixtus is Dante, wearing red and sporting a laurel wreath (symbolizing his greatness as a poet). The bald figure reading a book and leaning over a railing in the left hand corner could be Raphael's mentor and Renaissance architect Bramante. The Disputation includes over 100 figures." -- Wikipedia
Click the image to visit a page with over fifty details images from the Disputation: