# Double Crux

> 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".

- Skill: `equistamp/double-crux` (Agent Skill)
- Install (CLI): `npx skillmds@latest add equistamp/double-crux`
- Raw SKILL.md: https://api.skillmd.com/api/skills/equistamp/double-crux/raw
- Safety review: pending
- Works with: Claude Code, Claude.ai, OpenAI Codex
- Category: Coding & Dev Tools
- Author: EquiStamp (https://skillmd.com/u/equistamp)
- Updated: 2026-09-22
- Page: https://skillmd.com/skills/equistamp/double-crux

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# 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