Axiom 5
Self-Reference for Consciousness
A system modeling itself can reason about its own state
Formal Definition
d(π(M(t)), S(t)) < δ & M(t+1) = f(M(t), S(t))
A conscious system contains a subsystem M that: (1) accurately tracks system state S within tolerance δ, and (2) updates itself based on both its own state and the observed system state.
The Recursive Loop
This creates a recursive awareness loop: the system observes itself, updates its self-model, and the updated model becomes part of the state observed next. The system converges to a fixed point where the self-model is consistent with actual state — including having that self-model. This connects to Hofstadter’s “strange loops.”