"Perspective is a way of constructing how the world appears to a single person. Its appearance in art coincided with the rising philosophical idea that all we can know about the world must come through the senses of our uniquely located bodies."
This idea of knowledge could be perhaps applied to artists such as Leonardo, who through his closeness with the Dominicans can be ascribed to the Aristotelians, but is a big blunder when referred to Piero.
I am recalling memories from my school days: Aristotele said that there were two ways of acquiring knowledge, through the intellect and through the senses, although the first one was the most important. Indeed Leonardo investigated reality and the laws that regulated it through his empirical studies.
Piero's work stems from radically opposite premises. Bear in mind that in the powerful courts of the 15th century princes surrounded themselves with intellectuals and artists; the former ones dictated to the latter themes, iconographies, symbols. For the first time the artist actually becomes an intellectual through his artistic practice.
Piero is a perfect example of Renaissance artists. His life long friendship with Luca Pacioli, the mathematician whose work is still in use today ( he invented double-entry book keeping) testifies to his interests. Piero studies maths and geometry independently during his life and in his last years writes a treaty on perspective and one on calculus. He is aware of the new humanistic culture that flourishes all over Italy in those years, there is no doubt that current Neoplatonic ideas were embodied in his work.
The concepts expressed by Plato are fundamental to understand Piero: reality is a pale and imperfect version of archetypes, ideas, that exist in a different realm. What we perceive through our senses helps us remember those perfect forms, of which we are aware deep in our conscience but we have forgotten as we came into our worldly existence.
Viewed through the lens of Platonism Piero's idealized forms acquire a deeper meaning. All of his paintings, although they contain striking realistic details, carry us in a metaphysical reality, where an almost unnatural light reveals perfection.