Axiom · Chain Position 67 of 346

BINARY DISTINCTION

Matthew 12:30 with/against

Orientation admits only two values: +1 or -1

Scripture Bridge
Matthew 12:30 with/against: The theological grounding for this concept.

Connections

Assumes

  • None

Enables

  • None
Mathematical Layer

The Sign Operator

Definition:

\hat{\sigma} = \begin{pmatrix} 1 & 0 \\ 0 & -1 \end{pmatrix}

Eigenstates:

  • |+1⟩ = (1, 0)ᵀ — aligned with Logos
  • |-1⟩ = (0, 1)ᵀ — opposed to Logos

General state: |ψ⟩ = α|+1⟩ + β|-1⟩, where |α|² + |β|² = 1.

Measurement: Yields +1 with probability |α|², yields -1 with probability |β|².

Evidence
Empirical Grounding
This isn't philosophy. This is measured.
  • Stern-Gerlach
Defeat Conditions

To Falsify This

  1. **Show a third orientation value** — Demonstrate σ ∉ {+1, -1} that is physically/morally meaningful
  2. **Prove continuous moral orientation** — Show σ ∈ ℝ with continuous spectrum rather than discrete
  3. **Demonstrate moral neutrality** — Show a state that is genuinely neither toward nor against the Logos
  4. **Violate quantum spin discreteness** — Show spin measurements yield values other than ±ℏ/2
Cross-Domain Mappings
Domain Mapping
Physics Spin +/-1/2
Theology Good/Evil binary
Consciousness Valence +/-
Quantum Spin +/-1/2
Scripture Matthew 12:30 with/against
Evidence Stern-Gerlach
Information Binary encoding

Bridge Count: 7