“… Hartmann regards ontology to be concerned with: (1) the two aspects (“moments”) of being: Dasein and Sosein, or that and what; (2) the two spheres of being: real and ideal; and (3) the modalities of being: actuality, possibility, and necessity.
One of the errors of phenomenology — including both Husserl’s and Scheler’s — is that when it regards itself as investigation into essences, as distinguished from existence (as a consequence of eidetic reduction), it forgets that essences also have their Dasein (existence) and their Sosein, that Dasein is not as such real existence. There is also, as with essences and mathematical idealities such as numbers, and values, ideal Dasein. Husserl does sometimes insist that essences are a kind of objects sui generis, so it may be just right to interpret eidetic reduction not as abstracting from existence, but as abstracting from real existence. But, then there is the curious consequence that essences have both real and ideal existence (when they are taken in their purity). Hartmann seems to have wavered on this question. In his early work Grundzüge einer Metaphysik der Erkenntnis, he denied existence and individuality to ideal entities, but still ascribed to them Ansichsein, intrinsic being. In Die Grundlegung der Ontologie, he ascribed existence to them, but that only means he was taking “existence” and “Ansichsein” as being the same.
So, for Hartmann, the Dasein-Sosein distinction is not quite the same as real-ideal distinction. In addition, Hartmann insisted that some Soseins are “neutral” as against both real and ideal existence: “roundness” belongs to a real spherical ball as well as a geometrical circle.
If concerns (1) and (2) do not coincide, it is also a mistake to collapse (2) with (3). The latter mistake is committed by those who hold that reality is the domain of all that is actual, while essences are pure possibilities. A corollary of this view is that truths about reality (i.e., about what is actual) are contingent, whereas truths about essences (i.e., about pure possibilities) are necessary. This is a widely held view, and one of Hartmann’s important theses is that this view is based on an inadequate analysis of modal concepts.
Hence the importance of modal concepts in Hartmann’s thinking. It is only the modal concepts as pertaining to a sphere of being, which explicate the precise mode of being of that sphere. In other words, Hartmann held that while in an important sense we cannot say much about what “real existence” (or “ideal existence”) consists in, the best we can do in this regard is to look at how the concepts of “possibility” “actuality,” and “necessity” (and their opposites) behave with regard to the domain of reality (or, with regard to the domain of ideality). So we shall turn to his modal theory, but before I do that, perhaps a quick sketch of what he counts as belonging to the two domains would be in order.
The real world is a stratified structure, on Hartmann’s view, with nonliving matter at the base, living organisms founded on it, mental reality founded on organic life, and spirit or Geist (including society and all social formations) at the apex. Each of these strata has its own categorial structure, and the entire domain of reality also has certain common structures.
The domain of idealities consists of: mathematical entities (such as numbers), essences, and values. None of the idealities is spatiotemporally individuated. An ideality maybe instantiated or be an ingredient in many real individuals, without surrendering its own identity.
Besides these two primary spheres of being, Hartmann also recognized two intermediate (or hybrid) spheres: those of logic and cognition. With this brief sketch, let us look at his modal theory worked out in Möglichkeit and Wirklichkeit.”
From: Jitendra Nath Mohanty – Phenomenology. Between essentialism and transcendental philosophy – Chapter 3: Nicolai Hartmann’s phenomenological ontology – Evanston, Northwestern University Press, 1997 pp. 26-27.