AgentSkillsCN

double-crux

CFAR 合理化技巧：通过探寻双方共同的核心信念分歧点（即“关键点”），化解分歧与争执。当用户希望：(1) 找到真正的争议焦点，从而化解分歧；(2) 通过梳理信念结构，为一场艰难的对话做好准备；(3) 在协作中践行求真精神；(4) 通过追问“如果改变某个信念，会让我有何不同？”来审视自己的固有观念；(5) 促进双方立场之间更具建设性的意见交锋。触发关键词：“双重关键点”“产生分歧”“什么能改变我的想法”“关键点”“化解分歧”“找到真正的问题”“信念审视”“CFAR”。

SKILL.md
--- frontmatter
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

  1. •Design Mode — Prepare for a disagreement by mapping belief structure and identifying likely cruxes
  2. •Practice Mode — Walk through Double Crux on a practice topic to build skill
  3. •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:

  1. •Identify your own cruxes
  2. •Predict the other person's likely cruxes
  3. •Find likely overlap
  4. •Prepare operationalized versions of key claims
  5. •Enter with genuine curiosity about their reasoning

Solo Belief Examination

  1. •Pick a belief you hold strongly
  2. •Steelman the opposing position
  3. •Identify what facts would need to differ for you to hold the opposing view
  4. •Research whether those facts are as you assume
  5. •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