On the Stability Conditions of Invariance Ontology
A Structural Account of Ontological Commitment Under Representational Transformation
Abstract
This paper develops a formal account of ontological stability under conditions of representational transformation. We propose Invariance Ontology (IO) as an alternative to substance-based metaphysics, grounded in the claim that ontological commitment is determined not by primitive existence but by structural persistence across convergent modeling systems. We introduce a set of stability conditions under which invariant structures emerge as necessary features of successful predictive frameworks. We further argue that cross-agent convergence, rather than intrinsic metaphysical status, provides the criterion for ontological commitment. The resulting framework replaces substance ontology with a constraint-theoretic model of reality defined by invariance under transformation, predictive indispensability, and causal closure.
1. Introduction: The Problem of Ontological Stability
Traditional metaphysics assumes that ontology concerns what exists independently of representation. From Aristotle’s substance ontology to contemporary analytic frameworks, this assumption has remained largely intact.
However, modern developments in physics, cognitive science, and artificial intelligence suggest a different structure: what persists across theory change, model revision, and representational heterogeneity is not substance, but invariant structure under transformation.
This paper addresses the central question:
What conditions must hold for a structure to be ontologically stable across all successful representational systems?
We argue that ontological stability is not primitive but emerges from constraints imposed by predictive success and cross-model convergence.
2. Invariance Ontology: Core Thesis
We define Invariance Ontology (IO) as follows:
A structure S is ontologically committed if and only if it remains invariant under admissible transformations of all successful representational systems mapping a shared causal domain.
This replaces classical existential quantification (“there exists x”) with structural persistence conditions (“there exists invariant S under transformation T”).
Ontology is thus not a catalog of entities but a theory of cross-representational fixed points.
3. Stability Condition I: Predictive Constraint
Let M_A be a model constructed by agent A over causal domain D.
We define predictive success as:
Success(M_A, D) → M_A contains structures that minimize predictive error under transformation of D.
Proposition 1
Any successful model necessarily contains invariant substructures.
Proof Sketch:
If a model fails to identify invariant regularities in D, it cannot compress or generalize predictions across novel instances of D. Therefore, predictive success implies extraction of invariant structure.
4. Stability Condition II: Cross-Model Convergence
Let M_A and M_B be independent models of the same causal domain D.
Convergence Hypothesis
If both M_A and M_B achieve predictive success over D, then:
∃ S such that S ∈ M_A ∩ M_B under transformation-equivalence mapping.
However, this intersection is not set-theoretic but structural: it is defined over equivalence classes of representational transformations.
Proposition 2 (Convergence Condition)
Successful modeling systems must converge on invariant structures modulo representational encoding differences.
This replaces epistemic relativism with a constraint-based equivalence principle.
5. Stability Condition III: Representational Transformation Closure
We define a transformation space T over representations of D.
A structure S is stable if:
∀ t ∈ T, t(S) preserves predictive functionality within tolerance ε.
Thus, invariance is not exact identity preservation but functional closure under transformation space.
This yields a graded notion of ontological stability.
6. Stability Condition IV: Causal Efficacy Constraint
Not all invariant structures are ontologically committed. We therefore introduce a causal constraint:
S is real only if it is causally efficacious within D.
Formally:
Real(S) ⇔ Stable(S) ∧ Causal(S)
This excludes purely representational invariants (e.g., gauge redundancies) from ontological status.
7. The Dependency Reversal Thesis
Classical ontology assumes:
Substance → Identity → Persistence → Representation
We propose the inverse ordering:
Invariance → Persistence → Identity → Substance
Substance is thus not primitive but a limiting case of highly compressed invariant structure.
8. Ontological Selection Principle
We distinguish Invariance Ontology from Structural Realism:
- Structural Realism: reality is structure
- Invariance Ontology: reality is the subset of structures stable under representational transformation
This introduces a selection constraint absent from structural realism: not all structure is real, only structurally invariant fixed points across modeling systems.
9. Implications for Artificial and Human Cognition
Representational systems—biological or artificial—are constrained by the same invariance conditions.
Thus:
- AI systems
- human cognitive systems
- hypothetical alien intelligences
must converge on shared invariant structures if they are successful in modeling the same causal domain.
This yields a non-anthropocentric grounding for objectivity.
10. Conclusion: Ontology as Stability Theory
We conclude that ontology is not a theory of what exists in itself, but a theory of:
what remains stable under all admissible representational transformations of successful modeling systems.
This reframes metaphysics as a constraint-theoretic discipline:
- not concerned with substance
- but with invariance under transformation
- not with being as such
- but with structural survival across epistemic regimes
References (Indicative)
- Quine, W. V. O. “On What There Is.”
- Kripke, Saul. Naming and Necessity.
- Ladyman, James et al. Every Thing Must Go.
- Shannon, Claude. “A Mathematical Theory of Communication.”
- Kolmogorov, Andrey. “Three Approaches to Information Theory.”
- Friston, Karl. “The Free Energy Principle.”
- Lewis, David. On the Plurality of Worlds.
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