The Expansion of Meaning Space: How Semiotic Systems Generate New Subpotentials

Language is often imagined as a fixed repository of meanings or, at the other extreme, as entirely invented in the moment of utterance. Relational ontology offers a third, disciplined path: language is structured potential, and texts are perspectival actualisations.

Every utterance, discourse, or text actualises one trajectory within a system of potential. And as semiotic systems evolve — through register, genre, and semantic differentiation — they generate new subpotentials of meaning, much like formal systems generate new derivable theorems.

---

1. Semiotic Systems as Structured Potential

A semiotic system $L$ consists of:

• Vocabulary and grammatical resources V

• Patterned combinatorial rules R

• Historical and cultural constraints C

This system does not “contain” meanings in a pre-existing sense. It specifies the field of possible meanings available for construal.

When an utterance $U$ occurs:

• System: the relational potential defined by $V$, $R$, and C

• Cut: the perspectival selection and construal that shapes one actual meaning

• Instance: the text as realised, situated meaning

The cut is not temporal generation. It is a shift in perspective: the actualisation of one path through relational potential.

---

2. Register and Subpotential Differentiation

Registers are not static categories. They represent subpotentials within the semiotic system:

• A register highlights certain combinatorial patterns and suppresses others.

• Semantic drift is the reconfiguration of potential, enabling new actualisations.

Just as adding axioms in mathematics creates new subpotentials, shifts in register expand the space of possible meanings while preserving the structural discipline of the system.

---

3. The Cut in Semiotics

Consider an utterance in context:

• The meaning is actualised perspectivally, influenced by situational constraints, speaker choices, and interpretive norms.

• The system itself does not change at the moment of utterance; only one path through potential is realised.

• Multiple readings are possible, each a different cut on the same structured potential.

This clarifies that actualisation is relational and perspectival, not a subjective invention nor a mechanical unfolding of stored meaning.

---

4. Constraints and Possibility

Structured potential imposes constraints:

• Not all sequences of words are meaningful.

• Not all interpretations are viable in context.

• Variation occurs within the relational architecture, not arbitrarily.

Constraint is not limitation; it is the form through which new subpotentials can be differentiated — new registers, new semantic trajectories.

---

5. Semiotics as Evidence of Relational Potential

Semiotic systems demonstrate that:

• Possibility is structured and real.

• Actualisation occurs via cuts that are perspectival, not temporal.

• Differentiation of subpotentials generates novelty without invoking process metaphysics.

This mirrors mathematics: the architecture is the same, but the content is symbolic, social, and context-sensitive.

---

6. Bridge to Social Formation

Once structured potential in semiotic systems is clarified:

• It becomes natural to see social institutions as similar fields of potential.

• Rules, roles, and norms are subpotentials actualised through action.

• Social change parallels semiotic differentiation: novelty emerges via relational articulation, not linear temporal causation.

With the semiotic domain mapped, we can now move to social formation, showing how institutions generate subpotentials of action while preserving the discipline of potential, cuts, and actualisation.