• "In like manner, then, you are to say that the objects of knowledge not only receive from the presence of the Good their being known, but their very Being [ α / to einai] and essence [ousia / α] is derived to them from it, though the Good itself is not essence but still transcends essence [κα α / epekaina tes ousias] in dignity and power." This passage is the high point of Platonism.

Plato and the concept of "Idea" (Eidos)

• For Plato, Being, which always is and remains identical to itself, is identified with the idea. Plato’s major metaphysical thesis is the assertion that Being is idea (eidos).

• The concept of the idea has become so familiar that we forget its creation was quite a feat for its creator, Plato. The “abstract” use of the term idea, which even a six-year-old can understand now, did not exist before Plato.

• Form, the δ, (Eidos), designates what is common to several things and what persists in all things having the “same form.” The form, or shape, of an urn, of a dog, are common to all urns or dogs. There may never be two identical dogs, but all dogs have the same general form. One may say, as Plato does, that the “form” is what allows one to say that a dog is a dog and an urn is an urn. This will lead Plato to ascribe a “principial” status to the idea. The idea or “form” is what makes something what it is

• Plato discovers the "noetic space" - realm of pure ideas, always identical to themselves, i.e. beauty. What is the form of existence of this space? Does it not create a separation between the world of the sensible and the world of ideas? ("Chorismos")

• How do we recognize this noetic space? Anamnesis, reminiscence. life of the soul? Retroactive recognition, through the operation of the mind. This is very hard to do, we get easily stuck on the level of the senses.

• Thinking is also an "unburdening" from the corporal.

• Are ideas like a hypothesis? Presuppositions, what lies beneath our perceptions and only makes them possible?

• But how are we to understand the sensible world’s “imitation” of the intelligible?'

• The Separation of the Ideas: Plato describes the thought of an idea as “a movement that starts from the sensible–that is, what can be perceived by the senses–and draws out a common characteristic by which one can raise oneself to the “contemplation” of the idea.” (Grondin, 2012: 28)

• Plato conceives of the relation between the idea and the sensible as both a separation, insofar as knowledge involves abstracting ideas from their sensible manifestations, and a non-separation, insofar as ideas are in some sense present in their sensible manifestations.

• Reminiscence: As embodied beings, we do not apprehend the ideas in their pure state. Plato suggested that before our souls entered our bodies, they may have contemplated the ideas in their pure state; and we recall these ideas when we recognize their imperfect occurrences in the sensible world.

• “The ideas are rendered almost unrecognizable by their intermingling in the sensible, but reminiscence can put us on the road to thought.” (Grondin, 2012: 31)

Reality, Mathematics and Philosophy

“... mathematics, more than any other discipline, teaches us that true knowledge pertains to ideal shapes and sizes rather than sensible ones.  When a geometer discusses the properties of the triangle or the circle, he does not speak of the figures he can draw on the board… but only of the triangle or the circle as it can be apprehended by the mind… In the so-called real world, there are no really parallel lines, nor any triangles whose angles actually add up to 180 degrees.  In mathematics, one must posit “intelligible” entities; the likeness of which can only be achieved through thought.” (Grondin, 2012: 35)

The “Metaphysical” Separation of the Line: Republic VI

To hold the system together and integrate it into our experienced reality of flux, Plato needs some opposing principles. According to him, philosophical or dialectical knowledge necessarily leads to a “non-hypothetical” (anhypotheton) principle which “not only pertains exclusively to ideas and their interrelations, it also justifies the hypotheses themselves.” (Grondin, 2012: 38)  “... all the other ideas derive their Being and their essence from the idea of the Good.” (Ibid., 40)

The Sun Parable: “According to Plato, the sun allows sensible objects to be seen and our eyes to see them.  The cause of seeing thus resides neither in the eye nor in the visible things, but in a third term:  the sun’s light. … Now, the idea of the Good, says Plato, has a similar role in the intelligible world.  It is the intermediary between intelligence and the intelligible.  The principle of the idea of the Good would therefore be the cause (aitia) that makes the sight of what is intelligible possible… and bestows on our minds the ability to grasp them.” (Grondin, 2012: 39)

The Demiurg:  In his Timaeus, Plato suggests that the world may have been created by a demiurge, who provided order to the cosmos by “mixing two ideas:  the same and the different.” (Grondin, 2012: 42)

• The same is that which is forever and remains identical to itself (i.e., the Good and the ideas). 

• The difference is that which has a body and is subject to becoming. 

The principle of unity: According to Aristotle, Plato posited two important principles to reality:  the One (hen) and the indeterminate dyad (aoristos duas).

• The One (another name for the idea of the Good) was thought to be the unifying principle of reality.  

• The indeterminate dyad was thought to be the principle of multiplication and dispersion (i.e., matter), which receives its essential determination from an idea (i.e., a unifying principle).