Double Crux Lecture by Preston Greene

Introduction to Double Crux

This lecture, titled "Double Crux", was delivered by guest lecturer Preston Greene on May 12, 2026. The session focuses on a specialized technique for rational disagreement and belief analysis.

Defining the Crux

A crux is defined as a specific reason for a belief such that, if that reason were determined to be false, you would change your mind regarding the belief in question. To identify a crux, an individual must engage in deep self-reflection regarding the underlying foundations of their convictions.

Essential Questions for Identifying a Crux

To evaluate the strength and validity of a belief, one should ask the following questions:

  • Why do I believe this?

  • What are some good reasons in favor of this?

  • What would cause me to change my belief?

Case Study: Effectiveness and Ethics of Spanking

The lecture provided a practical application of identifying cruxes using the topic of physical punishment in childrearing. The central belief examined was: "Spanking isn't that effective at making kids behave in the long run."

Several potential reasons (cruxes) for this belief were evaluated:

  • Ease of Alternatives: The statement "It's easy to find alternatives to spanking" was considered but ultimately rejected as a primary crux (marked with an X).

  • Mental Health Impact: The statement "Spanking is linked to higher anxiety and depression" was identified as a significant factor (marked with both an X and a V, suggesting internal debate or specific criteria for its use as a crux).

  • Mechanism of Discipline: The statement "Spanking teaches compliance through fear instead of reasoning" was identified as a valid crux (marked with a V).

Procedures for Identifying Personal Cruxes

The lecture outlined two specific procedures for uncovering the fundamental reasons behind a stance.

Procedure 1: Logical Stress Testing

This method involves a direct interrogation of the link between a reason (X) and a belief (A).

  1. Question: "Why do you believe A?"

  2. Response: "X."

  3. The Counter-Factual Test: "Ok, let's imagine X was false - would you no longer believe A?"

Procedure 2: The Collaborative Imaginary

This method utilizes empathy and the desire for social cohesion to identify necessary information.

  1. Imagine someone you love and care about disagrees with you on a specific topic.

  2. Imagine you want to be in agreement with this person.

  3. Question: "What information would you need?"

The Mechanics of "Double Crux"

The "Double Crux" occurs when two parties in a disagreement find a shared crux. The dialogue facilitates a move from a general disagreement to a specific empirical or logical investigation.

The Exchange Format:

  • Person 1: "I believe A and one of my cruxes is X."

  • Person 2: "I believe not-A and one of my cruxes is not-X."

  • Conclusion: "Cool, let's talk about X!"

This shifts the focus of the conversation to a single, pivotal point of disagreement (X) that would change the minds of both parties if resolved.

Binary Crux Prompts and Exercises

The following prompts were provided to practice identifying cruxes in situations with limited options. Participants were asked to choose one side for each binary scenario:

  1. Resource Allocation: You are given a total of 1×1091 \times 10^9 dollars to designate to either space exploration research or to human life extension research. A choice must be made within 5 seconds5\,\text{seconds}, or the money will disappear.

    • Option A: Human life extension

    • Option B: Space Exploration

  2. Nuclear Policy: Complete global nuclear disarmament would be good.

    • Choices: Good / Bad

  3. Legal Ethics: Prostitution should be legal/illegal.

    • Choices: Legal / Illegal

  4. Environmental Importance: Is it important to recycle?

    • Choices: It is important / It isn't important

  5. Educational Value: Is it worthwhile to get a PhD in philosophy?

    • Choices: Worthwhile / Not worthwhile

  6. Transparency vs. Privacy: Would the world be improved if people could see all of each others' thoughts? There would be no privacy, but also every person would have full context on the thoughts of every other person.

    • Choices: Improved / Made Worse

  7. Marketing: Advertising makes the world better.

    • Choices: Agree / Disagree

  8. Existentialism: Death makes life worth living.

    • Choices: Agree / Disagree

  9. Childrearing: Should parents use physical punishment in childrearing?

    • Choices: Yes / No

  10. Higher Education Reform: The world would be improved if universities stopped having in-person classes and published online video courses to a mass audience instead.

    • Choices: Online courses / In-Person Classes

  11. Political Stability: There is a probability (PP) of the United States collapsing (ceasing to be a political entity, falling into anarchy or totalitarianism, etc.) over the next 20 years20\,\text{years}.

    • Choices: P > 5\% / P≤5%P \le 5\%

  12. Risk/Benefit of Smoking: For some smokers, the benefits of smoking outweigh the risk of health problems.

    • Choices: Sometimes outweighs / Never outweighs

  13. Sexuality Shift: You have to press a button that makes all humans either bisexual or asexual.

    • Choices: Bisexual / Asexual