It is complex to interpret the exact meaning of this theory and that it is not systematically exposed in any Platonic dialogue. On the other hand, the doctrine is revised in a visible evolution throughout the work.
Aristotle who must have known quite well the doctrine of his master highlights:
“ Plato, in general, agrees with the theories of the Pythagorists, although he also has things of his own. Indeed, since his youth he had become familiar with Cratile and Heraclitus' opinion that all sensitive things are in permanent flow, so there is no possible science (episteme) of these objects and he himself maintained this doctrine later. On the other hand, he was a disciple of Socrates, who disunderstood Nature as a whole — devoted himself exclusively to moral problems, proposing the universal as the object of his inquiries and being the first to apply thought to give definitions. Therefore, Plato, heir to this doctrine and accustomed to the inquiry of the universal, thought that the definitions could not refer to sensitive beings because it is not possible to give a common definition of objects that change continuously-, but to another type of beings. He called these beings “ideas” and added that sensible things exist separate from Ideas, but from them they receive their name because all things by virtue of their participation in Ideas receive the same name as Ideas. As for participation. Plato did nothing but change the name, because the Pythagorists claimed that the entities are by imitation of numbers and Plato by participation, but neither those nor this one cared to inquire into what participation or imitation of ideas was.” Aristotle, Metaphysics .
Plato remains faithful to the fundamental orientation of Socratic research: to seek the definition of virtues. Thus, faced with the question “What is a value” while a sophist would claim that it cannot be universally defined, Plato and Socrates would consider that on the contrary, there should be something in common to all courageous acts that could be defined as “courage”. That “common thing” is what Plato calls “idea”.
In this first stage then, the Theory of Ideas has an ethical intentionality of clearly socratic inspiration because in order to be virtuous it is necessary to know what each virtue is. Once we have discovered what virtue is, we can use it as a stick to judge the moral value of actions. Virtue will no longer be relative or subjective but definitely objective and independent of any opinion.
“ - It seems to me that if there is something beautiful apart from what is beautiful in itself, it will not be beautiful for any other reason, but because it participates in that beauty. And by style I say everything. Do you admit this kind of cause
I admit, he answered.
So he continued (...) if someone claims that anything is beautiful, or because it has an attractive color or a form or anything else, but the presence or communication or presentation in it in any other way- of that which is beautiful in itself.
Plato, Fedon.
Ideas are essences: that is to say “that which is why a particular thing is what it is”.
Ideas exist separate from particular things: these are no longer a “common character”, nor are they concepts or mental representations. Ideas are conceived as entities that possess real and independent existence: each idea is a substance that “exists in itself” as a reality transcendent and not immanent to things.
Duplication of the world: There are two worlds, on the one hand the visible world, that of particular things; and on the other the intelligible world, which is not a place or physical space but a “sphere” of intelligible essences. By calling ideas “substances”, Plato seeks to subdue their objectivity or universal validity. The myth of the cave is the famous allegory that seeks to explain this conception of the world by contrasting the unreal world of shadows with that of sunlight. While the visible world is a fleeting world and in continuous change to the image described by Heraclitus, particular things practically lack reality because they do not contain in themselves their own essence. Instead, the intelligible world is the truly real world, because every idea (as it exists in itself) is a substance.
Unique, eternal and immutable ideas: Ideas possess the attributes of Being according to Parmenides. In contrast, things are multiple, temporal and mutable. Indeed, there would be only Eternal Beauty and always equal to itself. But ideas are not corporeal realities (platonic immaterialism) nor sensitive realities but only intelligible . This is only accessible through intelligence.
Participation: The relationship between ideas and things is called with diverse expressions. From the point of view of things it is said to be a relationship of participation or imitation . It can also be said that Ideas are the cause of things (not as far as they produce them but as they are their essences), what {Aristotle would call “formal cause”) or, model of them.