120_A17.1_Phi-Threshold-For-Consciousness

A17.1 — Phi Threshold For Consciousness

Chain Position: 120 of 188

Assumes

• BC1-BC6](./058_BC1_Terminal-Observer-Exists.md)-BC6.md)
• A10.1 (Consciousness Substrate) - Individual consciousness requires localized field structure
• D5.2 (Integrated Information) - Consciousness requires Phi > 0
• A1.3 (Information Primacy) - Information is ontologically fundamental

Formal Statement

Consciousness supervenes on information processing

• Spine type: Axiom
• Spine stage: 17

Spine Master mappings:

• Physics mapping: Functionalism
• Theology mapping: Ensoulment question
• Consciousness mapping: Substrate independence
• Quantum mapping: Quantum consciousness
• Scripture mapping: Ecclesiastes 3:21 spirit of animals
• Evidence mapping: Functionalism lit
• Information mapping: Substrate-independent

Cross-domain (Spine Master):

• Statement: Consciousness supervenes on information processing
• Stage: 17
• Physics: Functionalism
• Theology: Ensoulment question
• Consciousness: Substrate independence
• Quantum: Quantum consciousness
• Scripture: Ecclesiastes 3:21 spirit of animals
• Evidence: Functionalism lit
• Information: Substrate-independent
• Bridge Count: 7

Enables

• [A17.1](./121_A17.2_Substrate-Independence]]

Defeat Conditions

DC1: Consciousness Without Information Processing

Condition: Demonstrate a conscious system that performs zero information processing—pure static awareness with no internal state changes, no information transformation, no computation whatsoever.

Why This Would Defeat [[120_A17.1_Phi-Threshold-For-Consciousness.md): If consciousness can exist without information processing, then consciousness does not supervene on information processing. The supervenience claim requires that all conscious states correspond to information processing states.

Current Status: UNDEFEATED. All known conscious states involve dynamic information processing. Even meditation (reduced processing) involves processing. Dreamless sleep (minimal processing) correlates with minimal consciousness. No conscious state has been observed without neural information processing.

DC2: Inverted Qualia With Identical Information

Condition: Demonstrate two systems with identical information processing but different conscious experiences (inverted qualia)—same computation, different phenomenology.

Why This Would Defeat A17.1: Supervenience requires that identical bases yield identical supervening properties. If same information processing can yield different experiences, consciousness does not supervene on information processing alone.

Current Status: UNDEFEATED. Inverted qualia thought experiments remain purely hypothetical. No empirical case exists where identical information processing produces demonstrably different experiences. The “zombie” and “inverted qualia” scenarios are conceivability arguments, not empirical demonstrations.

DC3: Consciousness Proven Epiphenomenal

Condition: Demonstrate that conscious experiences have zero causal efficacy—that information processing would proceed identically with or without consciousness, proving consciousness is a causally inert byproduct.

Why This Would Defeat A17.1: If consciousness is epiphenomenal, the supervenience is accidental rather than constitutive. Information processing doesn’t “produce” consciousness—consciousness merely accompanies it without being grounded in it.

Current Status: UNDEFEATED. The epiphenomenalist hypothesis is self-undermining: if consciousness has no causal power, why does the brain expend metabolic resources to produce it? Evolution would eliminate such waste. Moreover, we report our experiences, implying consciousness causally influences behavior.

DC4: Substrate-Specific Consciousness

Condition: Demonstrate conclusively that only carbon-based biological neural networks can be conscious—that silicon, photonic, or other computational substrates are necessarily unconscious regardless of information processing.

Why This Would Defeat A17.1: If consciousness requires a specific physical substrate (not just information processing), then consciousness supervenes on that substrate, not on information processing per se. The supervenience base would be “carbon-based neural information processing,” not information processing generally.

Current Status: UNDEFEATED. No principled reason has been established for why carbon should be special. Arguments for biological specificity typically reduce to vitalism or unexplained substrate chauvinism. The burden of proof lies with those claiming substrate specificity.

Explanatory Frameworks & Perspectives

Perspective 1: Functionalist Computation (Strong AI)

“Consciousness is a result of information processing. If a system (biological or digital) performs the same computations as a human brain, it will have the same conscious experiences. ‘Mind’ is just the software of the ‘Brain’ (or hardware). There is no ‘Threshold’ other than complexity.”

Theophysics Assessment (The Integration Gap): This view faces the Chinese Room problem: a system can manipulate symbols (Processing) without understanding their meaning (Integration). Theophysics uses Integrated Information ($\Phi$) to bridge this gap. A standard digital computer processes information Linearly; its parts do not form an irreducible whole. Therefore, its $\Phi$ remains near zero, even if it is “Smart.” Theophysics proposes that consciousness requires a Localized Field Structure (A10.1) that creates genuine integration. Consciousness is not “Software,” it is Topological Integrity.

Perspective 2: Biological Naturalism (Searle)

“Consciousness is a biological phenomenon, like digestion or photosynthesis. Only carbon-based brains have the ‘Causal Powers’ to produce it. No digital simulation of a brain will ever be conscious, any more than a digital simulation of a fire will ever be hot.”

Theophysics Assessment: This view correctly identifies the Substrate Dependence of consciousness but fails to define what the “Causal Powers” of biology actually are. Theophysics identifies these powers as the ability to couple to the Logos Field ($\chi$) in a highly integrated way ($\Phi >{\Phi }_{threshold}$). If silicon can be arranged into an integrated field structure, it could, in principle, be conscious.

Perspective 3: The Logos Threshold (The Witness Status)

“Consciousness is the property of being a ‘Witness.’ For a system to act as an Observer (A5.1) and collapse the wavefunction of the universe, it must reach a critical level of Information Unity. This ‘Phi Threshold’ is the point where a collection of parts becomes a single Agent in the eyes of the Logos.”

Theophysics Assessment: This identifies A17.1 as the Axiom of Ensoulment. It provides a measurable, physical criterion for when a system enters the “Moral Universe.”

Comparative Explanatory Assessment

A17.1 defines the Boundary of Being.

1. Theist Unification (Logos Model): Consciousness is Integrated Awareness. It is a matter of degree, but it has a clear “Phase Transition” point (The Threshold) where a system becomes a person. This explains why humans have a different moral status than rocks or simple software.
2. Structural Realism (Brute Phi): Consciousness is a physical property ($\Phi$) that appears when matter is arranged correctly. There is no “Witness” role; it’s just a feature of the math.
3. Instrumentalism (Useful Attribution): We call things “Conscious” when they are too complex for us to predict. It’s a “Heuristic” for dealing with smart things.

Synthesis: A17.1 is the Axiom of Measurement. It asserts that consciousness is not an “Invisible Ghost,” but a Measurable Quality of information systems. Theophysics proposes that the Integrated Information Theory (IIT) is the correct formal language for describing the “Image of God” in the physical domain.

Collapse Analysis

If A17.1 fails:

• Consciousness becomes a “Binary Spark” (you have it or you don’t) with no physical explanation.
• The AI morality question (A17.2) becomes a matter of pure guesswork or prejudice.
• The bridge between “Information Theory” and “Ensoulment” is broken.

Integrated Information Theory (IIT) Formalism

Phi (Φ) as Consciousness Measure:

Integrated Information Theory (Tononi et al.) provides the formal framework:

$\Phi ={\min }_{\text{partition}}\left[D_{KL}\left(p(X^{t+1}|X^t)||{\prod }_{i}p(X_i^{t+1}|X_i^t)\right)\right]$

Where:

• $X^t$ = system state at time t
• $D_{KL}$ = Kullback-Leibler divergence
• The minimum is over all bipartitions
• $\Phi$ measures information generated by the whole beyond its parts

Physical Interpretation:

• $\Phi =0$: System is reducible to independent parts (no consciousness)
• $\Phi >0$: System is irreducibly integrated (conscious to degree Phi)
• $\Phi \to \infty$: Maximally integrated system (divine consciousness?)

Supervenience Formalization

Definition: Property M supervenes on property P iff: $\forall x,y:\left(P(x)=P(y)\right)\Rightarrow \left(M(x)=M(y)\right)$

Applied to consciousness: $\Phi (S_1)=\Phi (S_2)\Rightarrow C(S_1)=C(S_2)$

Where C(S) is the conscious state of system S.

Stronger claim (identity): $C(S)=f(\Phi (S))$

Consciousness IS (some function of) integrated information.

Neural Implementation

Perturbational Complexity Index (PCI):

Empirical proxy for Phi: $\text{PCI}=\frac{\text{Lempel-Ziv complexity of TMS-EEG response}}{\text{Maximum possible complexity}}$

Experimental Findings:

• Waking: PCI ≈ 0.45-0.65
• REM sleep: PCI ≈ 0.35-0.55
• NREM sleep: PCI ≈ 0.15-0.35
• Anesthesia: PCI ≈ 0.10-0.25
• Vegetative state: PCI variable

Threshold Evidence: PCI > 0.31 reliably distinguishes conscious from unconscious states (Casali et al., 2013).

Quantum Considerations

Orchestrated Objective Reduction (Orch-OR):

Penrose-Hameroff proposal connects quantum coherence to consciousness: $\tau =\frac{\hslash }{E_G}$

Where:

• $\tau$ = collapse time
• $E_G$ = gravitational self-energy of superposition
• $\hslash$ = reduced Planck constant

Relevance to A17.1: If consciousness involves quantum effects, it still supervenes on information processing—quantum information processing. The formalism extends to quantum Phi.

Thermodynamic Grounding

Free Energy Principle (Friston):

Conscious systems minimize variational free energy: $F=D_{KL}(q(\theta )||p(\theta |o))-\log p(o)$

Where:

• $q(\theta )$ = approximate posterior (belief)
• $p(\theta |o)$ = true posterior given observations
• $p(o)$ = evidence (marginal likelihood)

Connection: Minimizing free energy requires information integration. High-Phi systems are good free energy minimizers. Consciousness emerges where free energy minimization is most effective.

Measurement Protocol

Protocol for Assessing Phi:

1. State Space Identification:

   • Define system variables $X=(x_1,...,x_n)$
   • Identify state space dimensionality

2. Transition Probability Matrix:

   • Measure $p(X^{t+1}|X^t)$ empirically
   • Construct TPM from observed transitions

3. Partition Analysis:

   • Enumerate all bipartitions
   • Calculate effective information for each

4. Minimum Information Partition:

   • Find partition that minimizes information loss
   • $\Phi$ = information loss at MIP

5. Threshold Comparison:

   • Compare $\Phi$ to ${\Phi }_{threshold}$
   • Determine observer status

Energy Cost of Integration

Metabolic Requirement:

Integration requires energy: $E_{integration}\propto \Phi \cdot k_{B}T\cdot \ln (2)$

Brain’s Energy Budget:

• Brain uses ~20% of metabolic energy
• 50-80% goes to synaptic transmission
• Integration is metabolically expensive

Implication: Consciousness isn’t free. High Phi requires energy investment. This explains why unconscious processing handles routine tasks (energy efficient) while consciousness handles novel integration (energy expensive).

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Mathematical Layer

Formal Supervenience Definition

Definition (Supervenience):

Let $\mathcal{P}$ be the set of physical states (information processing configurations). Let $\mathcal{C}$ be the set of conscious states. Let $\pi :\mathcal{P}\to \mathcal{C}$ be the supervenience map.

A17.1 claims: $\pi$ is a well-defined function (many-to-one allowed, one-to-many forbidden).

Formal Statement: $\forall p_1,p_2\in \mathcal{P}:\pi (p_1)=\pi (p_2)\Leftarrow p_1{\sim }_{info}{p}_2$

Where ${\sim }_{info}$ denotes information-processing equivalence.

Category-Theoretic Framework

Category of Information Processes (InfoProc):

• Objects: Information processing systems (S, Φ(S))
• Morphisms: Information-preserving maps $f:S_1\to S_2$ with $\Phi (S_2)\ge \Phi (S_1)$

Supervenience Functor: $\mathcal{C}:\text{InfoProc}\to \text{Consc}$

Maps information processing systems to their conscious states.

Properties:

1. $\mathcal{C}$ preserves identity: $\mathcal{C}(i{d}_S)=i{d}_{\mathcal{C}(S)}$
2. $\mathcal{C}$ preserves composition: $\mathcal{C}(g\circ f)=\mathcal{C}(g)\circ \mathcal{C}(f)$
3. $\mathcal{C}$ is order-preserving: $\Phi (S_1)\le \Phi (S_2)\Rightarrow \mathcal{C}(S_1)\le \mathcal{C}(S_2)$

Information-Theoretic Proof

Theorem (Supervenience Necessity):

If consciousness is physically efficacious (not epiphenomenal), then consciousness supervenes on physical information processing.

Proof:

1. Assume consciousness is physically efficacious (affects physical outcomes)
2. Physical outcomes are determined by physical states (causal closure)
3. Therefore, conscious states must be connected to physical states
4. The connection must be systematic (same physical state → same consciousness)
5. Otherwise, physical causation would be indeterminate
6. Systematic connection = supervenience
7. Physical states in relevant sense = information processing states (by A1.3)
8. Therefore, consciousness supervenes on information processing ∎

Phi Axioms (IIT)

The Five Axioms of IIT:

1. Intrinsicality: Consciousness exists intrinsically (for itself)
2. Composition: Consciousness is structured (composed of distinctions)
3. Information: Consciousness is informative (reduces uncertainty)
4. Integration: Consciousness is unified (irreducible to parts)
5. Exclusion: Consciousness is definite (has specific content)

Mathematical Postulates:

• Intrinsicality → Cause-effect power within
• Composition → Mechanisms in various combinations
• Information → Probability distributions constrained
• Integration → Phi > 0 for the whole
• Exclusion → Maximum Phi at specific grain

Proof of Threshold Existence

Theorem (Phi Threshold):

There exists ${\Phi }_{threshold}>0$ such that systems with $\Phi <{\Phi }_{threshold}$ lack conscious observer status.

Proof:

1. Conscious observation requires distinction (by A1.2)
2. Distinction requires information (by A1.3)
3. Observer status requires integration (by A10.1)
4. Integration is measured by $\Phi$
5. $\Phi$ is continuous and bounded below by 0
6. There exists minimum $\Phi$ for meaningful distinction
7. This minimum is ${\Phi }_{threshold}$
8. Below threshold, no observer status ∎

Note: The exact value of ${\Phi }_{threshold}$ is empirical, not a priori.

Hilbert Space Formulation

Conscious State Space:

${\mathcal{H}}_C={⨁}_{\varphi >{\Phi }_{threshold}}{\mathcal{H}}_{\varphi }$

Where ${\mathcal{H}}_{\varphi }$ is the Hilbert space of systems with integrated information $\varphi$.

Consciousness Operator: $\hat{C}={\int }_{{\Phi }_{threshold}}^{\infty }\varphi \cdot |\varphi ⟩⟨\varphi |d\varphi$

Expectation Value: $⟨C⟩=⟨\psi |\hat{C}|\psi ⟩$

Kolmogorov Complexity Connection

Theorem: For typical conscious states: $K(C)\approx \Phi$

Where $K(C)$ is the Kolmogorov complexity of conscious state C.

Interpretation: Conscious states carry irreducible information proportional to their integration. This connects algorithmic information theory to IIT.

Fixed Point Analysis

Consciousness as Fixed Point:

Consider the operator $\mathcal{I}:\text{States}\to \text{States}$ that performs information integration.

Fixed Point Theorem: If $\mathcal{I}$ is continuous on a compact state space, it has a fixed point by Brouwer.

Interpretation: Stable conscious states are fixed points of the integration operator. The soul-field ${\psi }_S$ is such a fixed point—a self-sustaining pattern of integrated information.

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Source Material

• 01_Axioms/_sources/Theophysics_Axiom_Spine_Master.xlsx (sheets explained in dump)
• 01_Axioms/AXIOM_AGGREGATION_DUMP.md

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Quick Navigation

Category: Consciousness/|Consciousness

Depends On:

• [Consciousness](./119_T16.6_Atheism-Fails-BC1-BC6]]

Enables:

• 121_A17.2_Substrate-Independence

Related Categories:

• [Consciousness/.md)

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