Meta-Genealogical Reflection: 3 Abstraction and Structure — Forms, Categories, and Systems

Following the relational orientations of early thought, the classical period introduces a new layer: abstraction as a medium of construal. Here, the relational field is not abandoned, but formalised and systematised. Possibility becomes intelligible through principles, patterns, and categories that structure what can emerge and how it can be understood.

Plato exemplifies this approach. The realm of Forms renders the flux of sensible experience intelligible, not by negating relation, but by articulating patterns of participation. Individual phenomena instantiate possibilities defined by structural relations to ideal patterns. In this sense, abstraction itself becomes a relational cut: it delineates potentialities, distinguishing what coheres with the Forms from what falls outside.

Aristotle extends this logic into systematic categorisation. Substances, causes, and functions create a taxonomy of potential, where the actualisation of each entity is intelligible only within its network of relations — teleological, material, and formal. The Aristotelian schema foregrounds hierarchical relationality, demonstrating that even in seemingly static systems, possibility is shaped by embedded contextual dependencies.

Key construal strategies emerge:

1. Relational abstraction — categories, forms, and systems capture the relational conditions under which potential manifests.

2. Structural intelligibility — the field of possibility is organised to reveal coherent patterns across instances.

3. Constraint and enablement — formal structures simultaneously limit and expand what can be realised within the system.

Modulatory voices highlight alternative readings. Pythagorean mathematics treats number as both generative and relational, illustrating that abstraction can itself enact potential. Similarly, Stoic cosmology frames possibility in terms of harmonically constrained relational order, emphasising the co-emergence of structure and potential.

In sum, classical abstraction demonstrates that relational ontologies can be formalised without being flattened into mere substance. Possibility is codified, structured, and systematised, yet remains fundamentally relational: each entity, category, and system exists within a network of interdependencies that define the horizon of what can be.