“Husserl’s conception of formal ontology is intimately involved with his conceptions both of logic and of what comprises possible objects of theoretical inquiry. He inherited an Aristotelian metaphysical perspective from the school of Franz Brentano; his conception of logic was informed by an ontology that included both universals and particulars of ontologically dependent and independent types. The elucidation of his conception of logic as formal ontology therefore requires a consideration of his ontology of universal essences and his eidetic method. He distinguishes various types of universal essences (eide) in terms of the relations of generalization and formalization.
Husserl assumes that each thing is an instance of some eidos or essence, and that essences may not only have, but be instances (e.g., he holds that every essence is an instance of the universals “object in general” and “essence’). Besides the relation of instance to essence, he held that there is a second relation (of generalization) defined on essences. In Ideen zu einer reinen Phänomenologie und phänomenologischen Philosophie I (1913), the essence “red” is a specification (but not an instance) of the more general essence, “color.” Specification and generalization are inverses: for any two essences x and y, x is a generalization of y just in case y is a specification of x.
But the genus “essence” is not a generalization of the essence “red” or the essence “triangle.” These are instances (not specifications) of the genus “essence.” A (rough) guide for understanding this distinction: the instancing relation is to the generalization relation as the membership relation is to the subset relation; similar and easily confused but different. Husserl provides a part-whole characterization of the difference between the relations of instance to essence and specification to generalization (which he treats under the topics “formalization” and “generalization,” respectively). If y is a generalization of x, then y is a part of x (at least in some “comprehensive” use of the term “part” that Husserl is willing to accept). But if y is a part of x (even in the comprehensive use of the term “part”), then y is not a formalization of x.
From this it follows that no formalization is a generalization and vice versa. The relation of specification to generalization enables the definition of some important types of essences. Any essence x is a genus iff there is some different essence y such that x is a generalization of y. Similarly, any essence x is a species iff there is some different essence y such that y is a generalization of x. Any essence x is a highest genus iff it is a genus and not a species, and a lowest species iff it is a species and not a genus. Every essence either is a lowest (infima) species or is specifiable to an infima species, and is either a highest genus, or is generalizable to a highest genus.
Husserl distinguishes between the extension and the empirical extension of an essence. For any essence x, there exists an extension of instances of x. Any y is the extension of an essence x iff y is the class of all possible instances of x. Any y is the empirical extension of an essence x iff y is the class of all actual (i.e., real) instances of x. If both the empirical extension and the extension of a given essence are non-empty, then the former is a proper subclass of the latter.
But Husserl distinguishes further types of extensions relevant to his conception of formal ontology. For any essence x, there exists an eidetic extension of x. The eidetic extension of any essence x is the class of lowest species that are specifications of x. Husserl then distinguishes between two types of eidetic extensions of universals: “material” and “mathematical.” Any eidetic extension is mathematical just in case it is a subset of the eidetic extension of the essence “object in general” (etwas überhaupt); otherwise, it is a material eidetic extension.
A second set of distinctions regarding eide are developed by Husserl in terms of his notions of ontological dependence and independence. He calls things that require nothing else (other than the essences they instance) in order to exist ontologically independent (example: the nose of Socrates), and things that require something else (besides the essences they instance) in order to exist ontologically dependent (example: the pugness of the nose of Socrates). He refers to dependent individuals as moments of the things they require in order to exist.”
From: Gilbert T. Null, Formal and Material Ontology, in: Lester Embree et alii (eds.), Encyclopedia of Phenomenology, Dordrecht: Kluwer, 1997, pp. 238-239.