In paintings and sculptures, you can find people pointing up with their index finger.
What does an artist or sculptor mean by this?
By Raphael, The School of Athens (Public Domain) (source).
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In your example, Raphael's fresco The School of Athens, the gesture is made by Plato, the ancient Greek philosopher.
He is pointing upwards because his philosophical inquiries (as outlined in his Theory of Forms) have led him to conclude that the true nature of things is of a higher order than reality as we perceive it.
His pupil Aristotle, standing next to him, has his hand hovering in front of him, indicating - possibly arguing - that he has come to conclude that there is no reality separate from the one we can perceive.
An additional function of these gestures is that these two figures, the most prominent in this particular fresco, indicate the major axes of the space: the vertical indication leads the gaze of the spectator upwards, even outside of the fresco into a suggested, virtual realm (the painted skies above the painted architecture - which is especially poignant for Plato's idealism), whereas Aristotle points towards the spectator, into the very room they are standing.
Through these gestures, the audience is pulled into the artworks, made part of it, and at the same time invited to look around in the chamber where this fresco is made, the Stanze di Raffaello.
Often, however, in European visual art, the finger pointing upwards suggest the existence or presence of God.
This becomes obvious once you see how many depictions of Jesus, saints, angels, or other figures in Christian religious visual art make this gesture.
|St. John the Baptist, by Leonardo da Vinci.
John is pointing upward as the true salvation does not come from the act of baptism alone but from God.
|The Angel of Death, by Émile Jean-Horace Vernet.
The soul of a young woman is being taken out of bed. She is pointing upwards, suggesting she will ascend to heaven.