Plato’s theory of Forms is one of the most enduringly strange parts of his philosophy. It is also one of the main centers of gravity around which Plato’s work turns. In the centuries since Plato, philosophers have disagreed about the nuances of Plato’s theory. But most of them have agreed that his theory of forms is a way of thinking about the relationship between two things.
According to his theory, in an unrefined stature, there is the messy, untidy world that we access through our sense experience. And on the other hand, there is the world of ideas that we access through the intellect. In his writings, through Socratic dialogues, Plato argues that because the material world is changeable it is also unreliable. Yet, behind this unreliable world of appearances is a world of permanence and reliability. Plato calls this more real world, the world of ‘Forms’ or ‘Ideas’.
Take for example a perfect triangle, as it might be described by a mathematician. This would be a description of the Form or Idea of a Triangle. Plato says such Forms exist in an abstract state but are independent of minds in their own realm. Considering this idea of a perfect triangle, as we draw it, our attempts will of course fall short. Plato would say that peoples’ attempts to recreate the Form will end up being a pale facsimile of the perfect Idea, just as everything in this world is an imperfect representation of its perfect yet disguised Form.