We have now established that relevance is constitutive, phenomena appear as this, and meaning is structured independently of value. The final question remains:
Why is incompleteness a necessary condition for ontology, rather than a defect or gap?
This post articulates why incompleteness is essential — not accidental — and how it grounds the intelligibility of phenomena and the operation of symbolic systems.
1. Incompleteness is the shadow of relevance
Every instantiation generates salience, and every salience necessarily excludes alternatives. Irrelevance is not the absence of being but the unactualised potential within the system of possibilities.
If ontology attempted completeness — capturing every possibility simultaneously — no distinctions could emerge. Every phenomenon would coincide with every other; salience would vanish.
Incompleteness is therefore the structural condition of intelligibility.
2. Gödelian resonance
There is an instructive parallel with Gödel’s incompleteness theorem:
In any sufficiently expressive formal system, there are truths that the system cannot prove from within itself.
In a relevance-structured ontology, not all possibilities can appear simultaneously; not all distinctions can be instantiated within one phenomenon.
Incompleteness is not a failure; it is a necessary precondition for the existence of meaningful construals.
3. Phenomena and structural limitation
Every phenomenon manifests a subset of the possible. This subset is determined by relevance, articulated by instantiation, and constrained by the structural impossibility of total representation.
Nothing appears as everything; everything that appears is necessarily partial. This is not deficiency but the ontological requirement for intelligibility.
4. Symbolic systems depend on incompleteness
Second-order systems of meaning, including symbolic and semiotic structures, rely on first-order incompleteness:
Symbols acquire significance because alternatives remain uninstantiated.
Communication depends on the differentiation between instantiated meaning and potential meaning.
Shared intelligibility emerges because not all possibilities are present in every phenomenon.
If the world were total, symbolic articulation would collapse into sameness; meaning would be indistinguishable from existence itself.
5. Implications for ontology
Incompleteness is a requirement, not a defect.
Relevance structures appearance; incompleteness ensures that this structuring can occur.
Phenomena emerge as first-order meaning precisely because the field is not fully actualised.
This insight completes the post-totality trajectory: totality is incoherent, relevance is unavoidable, and intelligibility is grounded in structural limitation.
No comments:
Post a Comment