Double Crux
A cooperative disagreement practice for finding the belief both sides would need to update before the surface disagreement can move.
Full Practice · Foundation · Revising Beliefs Under Evidence
Mechanism
Most disagreements stay stuck because people argue at the level of conclusions. One person says the product should ship now. Another says it should wait. One person says the policy will help. Another says it will backfire. The debate keeps returning to the same surface sentence, because neither side has found the belief underneath it that would actually make the conclusion move.
Double Crux is the practice of finding that underneath belief. A crux is a claim your conclusion depends on: if you stopped believing the crux, your conclusion would change. A double crux is a claim that both sides recognize as load-bearing for their disagreement. If we disagree about whether a feature should ship, and we discover that both of us would change our recommendation if the enterprise customers needed it by next Friday, then the deadline is not just a detail. It is the hinge. We can stop performing the whole argument and investigate the hinge.
That shift is the whole practice. The ordinary debate asks, "How do I make you accept my conclusion?" Double Crux asks, "What would make either of us change?" The first question turns the other person into an obstacle. The second turns the disagreement into a map of the beliefs underneath both positions.
Inside Revising Beliefs Under Evidence, Double Crux is the cooperative version of the Update Protocol's solitary question. The Update Protocol asks what evidence would change my mind. Double Crux asks what claim, if settled, would change both of our minds or at least explain why only one of us is movable. It makes update conditions visible between people. That visibility is why the method belongs in the Foundation even though it often happens in conversation: the object being trained is still the belief and its relationship to evidence.
Double Crux is not compromise. It does not ask both parties to meet in the middle, soften their claims, or agree for the sake of peace. Sometimes the crux reveals that one side is just wrong. Sometimes it reveals that both sides were using the same words for different claims. Sometimes it reveals that the disagreement is not about evidence at all but about values, interests, or trust. Those are not failures. They are better maps of the disagreement.
The method does require conditions that ordinary argument often lacks. Both parties need enough good faith to expose their belief structure instead of hiding it. They need enough humility to admit that they may be the one who should update. They need enough specificity to move from slogans to observable claims. Without those conditions, Double Crux can become a trap: one person reveals their update conditions while the other uses that information as ammunition. The method is powerful because it is cooperative. If the cooperation is absent, use the weaker version carefully: ask what the other person sees that you do not, expose your own cruxes first, and do not force vulnerability from someone who is not playing the same game.
Practice
The diagnostic question is: "What belief, if it changed, would actually move my conclusion?"
If you cannot answer that question, you do not yet know the structure of your own position. You may have a conclusion. You may have arguments. You may even be right. But you do not yet know where the position is attached to reality.
Operationalize the disagreement. Turn the surface claim into something specific enough to test. "Remote work is better" is too large. "For this team, over the next six months, two remote days per week will improve delivery quality without hurting junior onboarding" is a claim you can reason about. Operationalizing is not pedantry. It is how you stop arguing over a fog bank.
Find your own cruxes before arguing. Write down the claims that would move your view. If this evidence appeared, would I change my recommendation? If this prediction failed, would I lower confidence? If this value had to be weighted more heavily, would I choose differently? Do this before you anchor on the other person's map. Your own cruxes are easiest to lose once the debate becomes social.
Search for the shared hinge. Compare your cruxes with the other person's. Look for a claim close enough to both positions that settling it would change the disagreement. The best hinge is concrete enough to investigate and important enough to move the conclusion. Once you find it, the next move is no longer debate. It is evidence-seeking: run the test, consult the data, ask the person who knows, define what would count as an answer.
A useful sign that you are near a crux is the sentence, "If that were true, I would have to think differently." Another useful sign is resistance. When a proposed claim feels dangerous to look at, because a bad result would disturb the position you want to keep, you may have found the hinge. That is not a reason to retreat. It is the reason to look more carefully.
The common failure is false cruxing. You name a condition that sounds update-relevant but would not actually move you. "I would change my mind if there were strong evidence against this" is not a crux. It is a self-description with no content. "I would change my mind if the pilot cohort's completion rate falls below 40% after the onboarding redesign" is a crux. A person could check it later. A future you could not quietly move it around.
Another failure is crux inflation. You keep naming deeper and deeper beliefs until the disagreement has become a philosophy seminar and nobody can act. The method asks for the hinge that makes this disagreement move, not the metaphysical root of all disagreement between the parties. If the next decision is whether to ship the feature, the useful crux is the claim that changes the shipping decision.
In the Wild
A product team was split on whether to launch a freemium plan. The growth lead believed it would increase adoption. The finance lead believed it would flood support with low-value users and damage margins. For two weeks, they argued at the level of the conclusion: launch or wait. When they finally ran Double Crux, the hinge was not "freemium good or bad." It was a narrower claim: whether users who activated three core features in the first week converted to paid at a rate high enough to cover support cost. Both sides agreed that this claim would move them. The team ran a limited cohort test. The conversion rate cleared the threshold, but support cost was higher than expected. The launch went ahead with a narrower user segment and a support cap. The disagreement did not vanish. It became useful.
A school board debated banning phones during the school day. One side argued that phones damaged attention and classroom culture. The other argued that students needed access for safety and family coordination. The debate had the shape of a values conflict until one member asked what would change each side's mind. The shared hinge turned out to be emergency access: if students could reach parents and parents could reach the office quickly during emergencies, the pro-phone side would accept a ban during class hours; if the ban prevented timely contact, the anti-phone side would revise. The policy that emerged was not a compromise for its own sake. It answered the crux: phones locked away during instruction, office-mediated emergency channel guaranteed, exceptions documented.
Two co-founders disagreed about whether to hire a senior operator before the next funding round. One thought the hire was premature. The other thought the company was already fraying. The Double Crux revealed the hinge: whether the founders themselves were the bottleneck in decisions that should have been owned by team leads. They reviewed the last month of escalations. The answer was uncomfortable. Almost every consequential decision still routed through the founders, and the delay was costing the team speed. The skeptical founder updated. They made the hire. The method did not make the decision easy. It made the hidden dependency visible enough to decide.
The next time a disagreement repeats for the third time, stop rehearsing the conclusion. Ask what would move it. If both sides can name the hinge, you have something to investigate. If neither side can, the argument was never as evidence-responsive as it sounded.
Lineage
The Codex did not invent Double Crux. The Center for Applied Rationality developed and taught it as part of the applied rationality curriculum, and the rationalist community refined it through practice, writeups, and repeated public critique.
Duncan Sabien's 2017 LessWrong essay, "Double Crux: A Strategy for Mutual Understanding," is the main public entry point. Sabien describes the method as one of CFAR's newer concepts at the time, with the core idea settled but the execution still in flux. The essay names several people involved in experimentation and refinement, including Julia Galef, Kenzi Amodei, Andrew Critch, Eli Tyre, Anna Salamon, and Sabien himself. The point of the post is not to present a finished formula. It is to transmit the generators of the practice: truth-seeking, good faith, operationalization, crux-finding, and shared investigation.
The CFAR handbook carried Double Crux as a workshop technique alongside related rationality practices such as Trigger Action Plans, Inner Simulator, Focusing, and Internal Double Crux. The handbook version presents the basic algorithm: find a disagreement, operationalize it, seek cruxes, resonate with the proposed hinge, and repeat. That workshop context matters. Double Crux is hard to learn from a page because the hardest part is not the concept; it is the social and emotional discipline of exposing your own belief structure without turning the conversation into a contest.
Internal Double Crux developed as a sibling technique for resolving conflict inside one person: two internal positions, each holding part of the map, brought into a truth-seeking conversation rather than forced into compliance. It belongs to the same family but is not identical. The public Double Crux profile here focuses on disagreement between parties because the Workshop category is revising beliefs under evidence, and the two-party form makes the update conditions visible between people.
The deeper lineage reaches into older traditions of disciplined disagreement. Socratic questioning, Mill's defense of understanding the opposing view, Rapoport's rules for criticism, Dennett's practical version of those rules, and Steelmanning all share the same broad commitment: if you do not understand what would move the belief, you do not yet understand the belief. Double Crux contributes the hinge-finding procedure. That is its distinct place in the Toolkit.
Cross-references
Within the category. Steelmanning prepares one of the inputs Double Crux needs: the strongest version of the other person's view, not the version easiest to reject. The Update Protocol is the solitary version of the same discipline: it records the conditions under which your belief should move. Double Crux makes those conditions visible between parties and searches for overlap. Chesterton's Fence supplies a brake when the proposed update would remove an existing structure before its function is understood. Murphyjitsu supplies the future-facing version: stress-testing the plan before reality does it for you.
Within the Foundation. Scout Mindset is the orientation without which Double Crux becomes a tactic. Noticing catches the moment you stop searching for the hinge and start defending your conclusion. Identity Decoupling is often the difference between being able to name a crux and protecting it from view. Calibrating Confidence to Evidence is the static partner: once the crux is investigated, your confidence has to move proportionally rather than dramatically or not at all.
Across to the Bond. Double Crux often happens in relationship, and it requires trust. Its Bond-side relatives are Productive Conflict and Receiving Disagreement Well: the practices that let two people stay cooperative while the disagreement becomes sharper. The Foundation placement remains primary because the tool's distinctive mechanism is belief-revision architecture. It reveals what would change the map.
Limitation. Double Crux is strongest for disagreements where the parties can articulate beliefs, specify observable claims, and share enough truth-seeking to make exposure safe. It is weaker when the dispute is mainly about power, harm, trauma, or material interests. In those cases, searching for a hinge belief can become a way of avoiding the real issue. Sometimes the honest answer is not "we need a better crux." Sometimes it is "this is not a disagreement about evidence."