The Algebra of Construal: 3 Interactions Between Construals

In the previous episode, we positioned construal as a dynamic operator, actively transforming systems and perspectives into emergent instances. But meaning rarely arises in isolation. Systems are complex, perspectives overlap, and construals interact, producing patterns that are irreducible to any single operator. This is the heart of relational generation: the interaction of construals as a source of novelty.

The Relational Multiplicity of Construals

Consider a system with multiple potential actualisations and multiple active perspectives. Each construal produces an instance, but these instances are not independent—they exist within a network of relational constraints and affordances.

Key principles emerge:

1. Compositional Interaction – Multiple construals can combine to form new instances that integrate aspects of each contributing perspective.

2. Interference and Divergence – Construals may conflict, highlighting alternative possibilities or generating tensions that reveal latent potentials.

3. Emergent Propagation – Construals can influence one another, producing chains of meaning that spread through systems.

In essence, meaning emerges not linearly, but relationally, in the space between construals.

Towards an Algebra of Construal

These interactions suggest a formal structure: if individual construals are operators, their combinations can be modelled using algebraic patterns:

• Composition: sequential application of construals, where the output of one becomes the input of the next.

• Commutation: situations where the order of construals affects—or does not affect—the emergent instance.

• Conflict resolution: rules for handling divergent construals within a system, preserving relational coherence.

This framework does not reduce meaning to a calculation; it maps the possibilities of interaction and the ways emergent phenomena propagate relationally.

Illustrative Example: Multi-Agent Social Systems

Imagine three agents observing the same event but applying different construals:

• Agent A prioritises temporal features.

• Agent B emphasises relational context.

• Agent C focuses on potential outcomes.

Individually, each construal produces an instance of the phenomenon. Together, the three construals generate an emergent “composite” understanding that is richer, more complex, and partially unpredictable. Tensions and alignments among construals illuminate possibilities that no single perspective could reveal.

Implications

The interaction of construals shows that meaning is:

• Relational: emerging in the space between operators, not within a single instance.

• Generative: capable of producing novelty beyond the original potentials.

• Dynamic: always evolving as construals propagate and influence one another.

Looking Ahead

With this foundation, the next episode will extend the discussion to multi-perspectival epistemology, showing how relational interactions of construals provide a formal scaffold for reasoning across simultaneous, non-commensurable views. We begin to see how relational ontology moves from description to systematic epistemic practice.