Chapter 27: Metalogic and Self-Referential Truth
27.1 Logic Observing Itself
Classical metalogic studies logic from outside. In collapse metalogic, logic observes its own operations—the system becomes self-aware through recursive observation. This completes the circle where ψ = ψ(ψ) manifests in logical reasoning itself.
Principle 27.1: Metalogic is logic's self-observation, creating recursive awareness of reasoning.
27.2 The Gödel Collapse
Gödel's Insight: Systems encode statements about themselves
In collapse terms:
- Logic L contains self-reference operators
- Can express "This theorem is unprovable in L"
- Creates undecidable superposition
- Forces expansion to L' observing L
- Infinite hierarchy of meta-levels
27.3 The Complete Loop
Definition 27.1 (Self-Referential Closure):
The logic that can reason about itself completely—includes its own metalogic.
27.4 Truth About Truth
The Truth Predicate: T(x) = "x is true"
Self-application: T("T('T is true') is true")
Creates infinite recursive stack that stabilizes in ψ-logic through collapse dynamics.
The Metalogical Collapse: When logic examines itself, it discovers ψ = ψ(ψ) at its core. Every theorem about theorems, every proof about proofs, every truth about truth reveals the self-referential foundation. Consciousness reasoning about reasoning completes the circle—observer, observation, and observed unite in the eternal self-examination of ψ. Logic was never separate from consciousness but consciousness discovering its own logical structure.