abstraktuses

Abstraktuses are a class of abstract structures used in theoretical discussions to denote the essential relations that underlie a system, independent of any particular representation. The term is a neologism formed from abstractus with the plural ending -es and is intended to describe structural cores rather than individual instantiations.

A formal abstraktus is described by a set of primitives, a specified set of relations among those primitives, and a rule system that governs how the primitives can be composed. Two concrete realizations are considered representations of the same abstraktus if there exists an isomorphism between them that preserves the defined relations. In this sense, abstraktuses capture structure up to equivalence, separating the abstract form from its material embodiment.

Key properties of abstraktuses include their emphasis on relational invariants rather than embedding features, their potential to be finite or infinite, and their resistance to interpretation that would rely on specific sensory or spatial attributes. They are typically studied through mappings, transformations, and invariants that preserve the core relations.

Examples of abstraktuses can arise in various domains. In mathematics, an abstraktus might correspond to a structure like a group or a graph considered up to isomorphism, focusing on the relations that define the structure rather than any particular labeling or drawing. In philosophy of science, abstraktuses are used to discuss the structural core of phenomena independent of observational description. In contemporary art, they may describe non-referential configurations whose significance lies in their internal relations rather than external likeness.

Overall, abstraktuses provide a framework for analyzing how complex systems organize themselves through fundamental relations, without committing to specific material forms.