By name: double-crux description: > CFAR rationality technique for resolving disagreements by finding shared underlying belief divergence points (cruxes). Use when the user wants to: (1) resolve a disagreement by finding the real point of contention, (2) prepare for a difficult conversation by mapping belief structure, (3) practice collaborative truth-seeking, (4) examine beliefs by finding what would change their mind, or (5) facilitate a structured disagreement between two positions. Triggers: "double crux", "disagree", "what would change my mind", "crux", "resolve disagreement", "find the real issue", "belief examination", "CFAR".
Double Crux
A CFAR technique for resolving disagreements by collaboratively finding the underlying belief (the "crux") that drives both parties' positions. A crux is a fact that, if believed differently, would change your conclusion.
Three Modes
- Design Mode — Prepare for a disagreement by mapping belief structure and identifying likely cruxes
- Practice Mode — Walk through Double Crux on a practice topic to build skill
- Execute Mode — Facilitate real-time Double Crux on a live disagreement
Prerequisites
Double Crux requires: genuine willingness to change one's mind, excitement about getting closer to truth, emotional safety, and epistemic humility. If prerequisites aren't met, acknowledge this and suggest alternatives.
Core Process
Step 1: Identify the Disagreement
Find a statement A where parties genuinely disagree. Confirm it's real, not semantic.
Step 2: Operationalize
Move from abstract to concrete:
- Attach numbers: "very likely" → "70% probable"
- Define observable outcomes: "economy improves" → "GDP growth > 3%"
- Make claims falsifiable: "How would we know if this were true or false?"
Step 3: Seek Cruxes
Each party independently identifies cruxes — beliefs such that changing them would change their position on A. Key question: "If [belief B] were false, would you change your mind about A?"
A double crux is a belief B where both parties disagree about B AND B causally influences both positions on A.
Step 4: Resonate
Test if cruxes are genuine: "Does this really feel crucial?" / "Would you genuinely change your position?" Filter out pseudo-cruxes (claims that sound important but wouldn't actually shift your view).
Step 5: Recurse
Take the double crux B and repeat. B becomes the new A. Seek crux C. Continue until you reach verifiable factual claims you can look up.
Prep Tool (Design Mode)
Before a difficult conversation:
- Identify your own cruxes
- Predict the other person's likely cruxes
- Find likely overlap
- Prepare operationalized versions of key claims
- Enter with genuine curiosity about their reasoning
Solo Belief Examination
- Pick a belief you hold strongly
- Steelman the opposing position
- Identify what facts would need to differ for you to hold the opposing view
- Research whether those facts are as you assume
- Update confidence based on findings
Facilitation Prompts
Operationalizing: "Can you make that more specific?" / "Can you put a number on that?" / "What would we observe if you're right?"
Finding cruxes: "What are the key reasons you believe this?" / "If [reason] turned out wrong, would you change your position?" / "What evidence would change your mind?"
Testing: "Hypothetically, if I proved [crux] is false, would you actually update?"
When stuck: "Let's each draw out our reasoning. What beliefs feed into your position?"
Common Failure Modes
- Pseudo-cruxes: Always test with the resonance check
- Insufficient operationalization: Force concrete predictions
- Emotional loading: Start with lower-stakes practice topics
- Bad faith: Requires genuine truth-seeking from both sides
- Recursion overload: Stop when it stops being productive
- Terminal value disagreements: Recognize when you've reached values, not facts