Plato clearly makes a distinction between two levels of being: the world of Forms with its perfect exemplars, and the world of sensible objects, with its ever-changing things. But beyond that basic division, in Republic Book 6, he identifies four levels of reality, and alongside of them, four levels of cognition for knowing them.[1]
At the lowest level are images, which Plato’s Socrates explains as shadows and reflections. Next above the images are visible objects, including animals, plants, and artifacts like tables and chairs. Above that level are mathematical objects such as triangles and squares and their properties such as odd and even. Above that are the real objects, the first principles (archai, singular archē) such as the Triangle Itself which are investigated through their mathematical representations. This highest level is the world of Forms, for which mathematical entities are hypotheses or stepping stones.
Plato considers the first two levels, those of images and of sensible objects, respectively, to belong to the realm of opinion. The second two levels, those of mathematicals and Forms, respectively, belong to the intelligible realm, where they are objects of knowledge, not opinion. Thus we end up with a hierarchy of entities: images, sensible objects, mathematicals, Forms.
To each level of reality there corresponds a way of knowing. The lowest level is grasped by imagination or imaging (eikasia); the second is grasped by trust (pistis); the third is grasped by calculation (dianoia); the fourth is grasped by comprehension (noēsis). The first two ways of grasping are types of opinion (doxa); the second two are types of knowledge (epistēmē).
So we arrive at a table of reality and cognition as follows:
| Level of Cognition | Objects of Cognition | ||
| Knowledge | Comprehension | Forms | Being |
| Knowledge | Calculation | Mathematicals | Being |
| Opinion | Trust | Sensible Objects | Becoming |
| Opinion | Imaging | Images | Becoming |
As Plato’s world is split into a lower world and a higher, the lower marked by temporal instability in the form of coming-to-be, the higher marked by timeless stability in the form of complete being, so the entities he recognizes fall into these two groups. But each is further subdivided, the world of becoming into images on the one hand, sensible objects on the other. Similarly, the world of being is subdivided into mathematical and logical objects on the one hand—triangles and squares, hypotheses and consequences—and into transcendent Forms on the other hand—Beauty Itself, Justice Itself, and so on. And there seems to be a descent from the top to bottom, such that in some sense the mathematical and logical entities are images of their prototypes, the Forms. “Now [mathematicians] make use of visible figures and discuss them, but they do not study them, but rather the objects they represent, reasoning concerning the Square Itself and the Diagonal Itself, not the ones they draw, in each case. The figures which they create and draw, of which there are shadows and reflections in water, they use likewise as images, seeking to make visible those things that you cannot behold otherwise than in thought.”[2] In other words, behind the world of mathematical calculations, there is a Form of Square or Triangle or Circle, or whatever figure one is working with, that the mathematician seeks to elucidate by drawing copies to represent it.
Similarly, if we are talking about human beings, there will be in the background a Form of Man. Perhaps at the level of logic and calculation there will be a set of all human beings, or perhaps a scientific description of members of the species. Below that, there will be human beings in the flesh, Socrates and Xanthippe and the like, which are images of the abstract class. And then there will be pictures and reflections of the physical human beings. At each level the copy is less ideal and more transient.
Similarly, at each level the cognition of the object will be more impermanent and unreliable. We will move from intellectual conception (two highest levels) to sense perception. At the level of sensible object, the particular object of perception, for instance Socrates, is concrete, but in constant flux and variation. At the level of the image of the sensible object, we have only, for instance, an ephemeral shadow of Socrates in two dimensions and totally dependent on a light source.
Plato’s theory of being, his ontology, and his theory of knowledge, epistemology, are vertically complex and top-down in their orientation. The best being and the best object of knowledge at are the Form at the top. We, living human beings, are near the bottom of the hierarchy, condemned to eke out a poor living as mortal creatures until we die, and only then being released to flourish with the possibility of direct contact with the transcendent Forms.
[1] Plato Republic 6, 509d-511e.
[2] Plato Republic 6, 510d-511a.