G1.4 — Coherent
[d9z6b84c-x92e-9z87-ybb0-3a7d6z4c8e92] | P1 | Axiom | Coherent
Mathematical truth is coherent; it possesses perfect internal consistency and no contradictions.
Ring 2 — Canonical Grounding
Ring 3 — Framework Connections
1. Formal Statement
The realm of truth is a unified whole. No two true mathematical or logical statements can contradict one another. This perfect integrity is the defining characteristic of the ordering principle of the cosmos.
2. Type Classification
🔴 Constraint — It forbids the existence of “logical noise” at the foundational level. It ensures the universe is a cosmos (order) and not a chaos.
3. Justification
The Law of Non-Contradiction is the physical proof of this axiom. If 2+2=4 and 2+2=5 were both true, information would have no meaning, and reality would dissolve into undifferentiated static.
4. Connection to Theology
The coherence of math points to the integrity of God. “God is not a God of disorder” (1 Corinthians 14:33). The Logos is the perfect, unified Word.
5. The Logic Chain
- Immaterial (G1.3)
- Coherent (G1.4) (this axiom)
- Truth that is coherent requires a source that is coherent.
- Source Coherent (G3.4)
Canonical Hub: CANONICAL_INDEX