The line from Plato's parable is divided into 4 sections, named
- Animals, plants, artificial objects.
- Deduction from imitations.
Herefrom Aristotle later develops the method of reasoning by deduction from first axioms.
- Search for the beginnings. Herefrom Aristotle later develops the method to find first principles and axioms.
The first two sections are named the domain of the “visible (horaton)”, the latter two the domain of “the intelligible (noeton)”.
The method of deduction is characteristic for mathematics, while searching for the beginnings is characteristic for dialectics. Dialectic (to dialegesthai) is Plato’s name for his kind of philosophy, developing philosophical insights by discussion.
The results of vision and thinking in each of the 4 sections are classified as
- Likeness (eikasia)
- Trust (pistis)
- Thought (dianoia)
- Understanding (noesis)
(All translations from Perseus online dictionary)
Apparently Plato’s thinking does not make the technical distinction between ontology and epistemology as we do today. The dichotomy between the domain of the visible and the domain of the intelligible can be found as a characteristics in all of Plato’s philosophy.
Kant’s reasoning in his critical philosophy focus on epistemology. So Kant's constructivist epistemology has a different aim than Plato. Even when thing-in-itself is a technical term from Kant’s ontology, Kant claims that we cannot know anything about it. It is just a necessary hypothesis.
Kant’s term noumenon often equalizes with thing-in-itself. Hence it has a different meaning than Plato’s noeton.
Summing up: I would not press Plato’s concepts into a 1:1-relation with Kant’s concepts. Illuminative is Kant’s criticism of Plato (Kant, Immanuel: Critique of Pure Reason, B9)
The light dove cleaving in free flight the thin air, whose resistance it feels, might imagine that her movements would be far more free and rapid in airless space. Just in the same way did Plato, abandoning the world of sense because of the narrow limits it sets to the understanding, venture upon the wings of ideas beyond it, into the void space of pure intellect. He did not reflect that he made no real progress by all his efforts; for he met with no resistance which might serve him for a support, as it were, whereon to rest, and on which he might apply his powers, in order to let the intellect acquire momentum for its progress.