F1: The Crux Finder

The argument you have had before

Imagine your sister calls to talk about her children's school, which is banning phones for the whole day. One of you is delighted and the other thinks it is a mistake. One says the children will finally pay attention; the other says they need a way to reach their parents. Twenty minutes later you are both repeating yourselves a little louder, and you hang up feeling that she simply will not listen. Whichever side you were on, she hung up feeling the same about you.

Now suppose a friend had asked each of you, separately, one question before the call: what would you need to learn to change your mind? The one against the ban might have said that if the school could reach parents quickly in an emergency, the ban would not matter much. The one in favor might have said that if the ban made no difference to how much the children learned, it would not be worth the fight. Neither of you was arguing about either of those things. You were both arguing about the conclusion, which is where this site's premise says an argument like this is least likely to get settled. And if you are honest, the urge to win the call was stronger than the urge to find out where the two of you actually split.

The move

The Crux Finder is a tool, which on this site means a mental operation you can run on a claim in real time. A crux, in ordinary English, is the decisive point of a problem: the thing everything else turns on.

The question your disagreement depends on is usually unstated, and tends to be one of two kinds. Sometimes it is a factual premise: a belief about how the world works that, if it turned out differently, would change your view. Sometimes it is a value weighting: how much you care about one good compared with another. Running the tool takes four steps.

1. Write down the conclusion you are disagreeing about in one plain sentence, and agree that it is not the thing you will argue about next.
2. Ask yourself what would need to be true for you to switch positions. Be specific: name the fact, or the weighting, that would do it.
3. Ask the other person the same question, and listen to the answer without rebutting it.
4. Compare the two answers and look for the shared question underneath them. Then decide together what kind of question it is: one that evidence could settle, or one where you simply weigh things differently.

A well-known modern version of this move is "double crux," developed at the Center for Applied Rationality (CFAR), a group that has run reasoning workshops, and written up by Duncan Sabien, then of its staff, in a post dated January 2017 on LessWrong, an online forum about reasoning where CFAR's circle publishes. A crux, in his definition, is a belief such that "If it turned out that B was not true, that would be sufficient to make you think A was false, too"; a double crux is one that two people hold in opposite directions. Finding it counts as progress before anyone settles it, he argues, because "arriving at B means you've already dissolved a significant chunk of your disagreement."

Sabien's first step is to pin terms down, and he steers toward observables: "try to talk about what would be observable in the world rather than how things feel or what's good or bad." This site gives more room to the possibility that the crux is a value, a distinction older than double crux. The philosopher Charles Stevenson in 1944 separated disagreement in belief from disagreement in attitude, which "springs more from divergent preferences than from divergent beliefs." (Stevenson is quoted from the Stanford Encyclopedia of Philosophy; his book was not read.) A factual crux is something you can look up together. A value crux need not mean that either of you is stupid or dishonest; you may simply weigh things differently, and can say so.

Why it works

The tool belongs to the family the site calls Discourse Practice, which treats disagreement as a skill that can be done well or badly. Most arguments are fought at the conclusion, while the real disagreement lives in an unstated premise or weighting, so reasons traded at the conclusion miss what each view rests on.

The site counts the Crux Finder among five tools it treats as most important across every subject, because it turns unwinnable arguments into answerable questions. That is the site's judgment, and the research behind it is thin. CFAR's own handbook, posted publicly in 2022, claims "some preliminary success" for the technique but says it "has yet to receive formal study," and CFAR teaches it, so it is an interested party. A LessWrong critic writing as "Thrasymachus" argued in 2017 that "'double cruxes' are rare in topics where reasonable people differ," because beliefs on contested questions usually rest on many considerations. He suggested that "'Look for key considerations' captures the key motivation for double crux better than 'double crux' itself." That is what this tool does when there is no single shared question. Each side names its own crux, the consideration it weighs most, and you at least learn which considerations you are really disagreeing about. The phone call above is like that: the two cruxes were different questions, not one.

The closest research this site has found tests a related move: asking people to explain how a policy they have views on would actually work. A 2013 study (described here as later papers describe it) reported that this made positions less extreme. Jarret Crawford and John Ruscio failed three times to repeat it, concluding in 2021 that explaining "is unlikely to increase their political moderation, at least under these conditions." They did find that listing reasons for your view made people slightly more extreme, in line with what they call "well-established findings that providing justifications for prior beliefs strengthens those beliefs," though the 2013 study had found no such effect. In 2022 Steven Sloman, an author of the original study, and Marc-Lluis Vives found the explanation effect again, in a sample that was 64 per cent Democrats, but "only for consequentialist issues, not those based on protected values": where views rested on what a policy would do, not on a value people would not trade. The drop in extremity was 0.15 of a point, with positions rated on a seven-point agree–disagree scale, and in their study listing reasons changed nothing. None of this tests the Crux Finder directly. It is consistent with the tool's split between factual cruxes and value cruxes: in that study, explanation moved views based on consequences and did not move views based on protected values.

Using it well

The legitimate use is each side asking what would need to be true for them to switch positions, then comparing notes to find the shared question underneath the fight.

On 30 October 2006 a British government review led by the economist Nicholas Stern called for deep, immediate cuts in emissions. William Nordhaus of Yale, who favored cuts that "increasingly tighten or ramp up over time," argued that Stern's recommendations "depend decisively on the assumption of a near-zero social discount rate," a parameter "that measures the importance of the welfare of future generations relative to the present." He treated that partly as a matter of values ("alternative ethical perspectives are possible") and partly as a matter of fact: Stern's conclusions would not survive "the substitution of discounting assumptions that are consistent with today's market place." He also put his own answer on the table. Rerunning his own model with Stern's discount rate, he reported, "dramatically changes the trajectory of climate-change policy": the model's carbon price for 2005 rose from about $17 to $159 a ton of carbon. That is a person naming his own crux: here is the assumption that, if changed, changes my answer.

Stern did not simply accept that framing. At a Yale symposium in February 2007, answering Nordhaus and other panelists, he called it "A common misconception" that "the Stern Review uses this or that discount rate," and wrote that "to use market interest rates to derive ethical values is misplaced." He named a factual crux as well: the damage estimates were "just as sensitive to small but plausible changes to the climate damage sensitivity parameter than they are to discounting assumptions," meaning how much harm a given amount of warming does. And he wrote that "There are, and should be, genuine differences of opinion on ethics." The argument did not end, but it was now being fought over named assumptions, one ethical and others factual, rather than over the conclusion.

Sometimes the honest answer is that the crux is a commitment, and the tool's job is to get that said. At the end of a debate on 4 February 2014 at the Creation Museum in Kentucky, the moderator asked Ken Ham, the president of the organization Answers in Genesis and the man behind the museum, "What, if anything, would ever change your mind?" Ham answered directly: "the Bible is the Word of God. I admit that that's where I start from," and "no one's ever going to convince me that the Word of God is not true," though the models he builds on the Bible "are always subject to change." Then he asked the question back. The science educator Bill Nye answered with a list: "We would just need one piece of evidence," ending "You can bring on any of those things and you would change me immediately." Neither man moved, but the audience could see exactly where they split: one view rested on evidence, the other on a starting commitment its holder named openly. Nye went on, "Mr. Ham what can you prove?" A reader on Nye's side may hear that as fair pressing, and a reader on Ham's as scoring off an honest answer; that line is what the next section is about. (The transcript is a third-party one, not checked against the video.)

The hard part is choosing the right shared question. The economist Julian Simon and the biologist Paul Ehrlich, who came to stand in American argument for resource optimism and environmental pessimism respectively, bet on whether five metals would cost more after ten years. Simon dated his public offer to 1980, and the agreed terms, as quoted by a 2021 study whose authors side with Simon, priced the metals from 29 September 1980. When the bet was settled in 1990, Simon later wrote, "They sent me a check for $576.07." The clean test did not settle the argument. Simon agreed that "a single bet proves little," while holding, in the epilogue to The Ultimate Resource 2, that scarcities "are best measured by prices, of course." Ehrlich and the climate scientist Stephen Schneider, as Simon quoted them, wrote that "'indirect trends' such as those [they list] are more relevant to human welfare than direct ones such as the prices of metals." Simon wanted "Measures of actual welfare, rather than intermediate conditions," and wrote that "There apparently is agreement among us that the condition of humanity is the ultimate interest." The disagreement had moved to what should be measured, and no second bet was made. Every word here about Ehrlich's side comes through Simon, a party to the dispute; Ehrlich's own account could not be found in an open copy.

Example still being found. a dated present-day political instance from the left and one from the right in which each side says what would change its mind. The cases above are expert or religious-versus-scientific disputes, not party-political ones. Leads not yet read: Kahneman and Klein's 2009 adversarial collaboration ("A Failure to Disagree").

When it becomes a weapon

The weaponized form is demanding that the other side name their crux while treating your own position as needing no such examination.

It persuades because the question sounds open-minded. Asked in one direction only, "What would it take to change your mind?" becomes an interrogation: the other person names a condition, and the questioner treats it as a confession (something like "so one study would be enough to make you drop the whole thing?") while never putting their own view on the table.

The essay's author anticipated this. Sabien warned that "people can 'smell it' if you're just playing at good faith to get them to expose themselves," and suggested "meditating on times in your past when you were embarrassingly wrong." His advice elsewhere in the essay matches this page's test: "Expose your own belief structure, show how your own beliefs might be falsified."

Some signs help tell the two forms apart:

• In the legitimate form, both people answer the question. In the weaponized form, one person only asks it.
• In the legitimate form, the asker offers their own crux first, or at least alongside. In the weaponized form, the asker's crux never appears.
• In the legitimate form, the other person's answer is treated as information about where the disagreement lives. In the weaponized form, it is treated as an admission.
• In the legitimate form, the asker could move if their own condition were met. In the weaponized form, nothing the other side could show would change anything.

Example still being found. a real, quoted, dated instance, one from the left and one from the right, of someone demanding that opponents say what would change their minds while declining to say what would change their own, ideally after being asked back. Tried: searches of debate and congressional-hearing exchanges; none found where the asker's wider record could be checked.

Run it on your own side first

For this tool the instruction is close to the whole tool, because the first step is naming your own crux.

• Pick a position you hold firmly on a contested issue. Can you name one specific fact that, if it turned out differently, would make you switch? If you cannot, is your position really resting on facts, or on a value weighting you have been presenting as a fact?
• Think of the last argument you lost patience with. Did you ever ask what the other person would need to learn to change their mind? Did you ever say what you would need?
• When you last asked someone "what would change your mind?", were you ready to answer the same question yourself?

If you find that no fact would move you, that is not automatically a failure. It may mean your crux is a value or a commitment, and the honest thing is to say so, as Ham did, rather than keep arguing as though it were a matter of evidence.

Grammars it works against

A grammar, on this site, is a recurring pattern of argument that turns up across many subjects. The Crux Finder is a first-line tool against two grammars and a supporting tool against a third.

• G2: Liberty versus Safety. A real trade-off between freedom and protection from harm gets argued as though only one value existed. Asking each side what would change its mind tends to show that both value freedom and safety and differ on how much risk justifies how much restriction, which is an answerable question, or at least an honest one.
• G12: Fixed Pie or Growing Pie. A situation that is partly zero-sum and partly positive-sum gets argued as though it were only one or the other. The Crux Finder separates the parts: which component of the conflict is actually fixed, which can grow, and which of those questions each side's position really depends on.
• G3: Sacred Values versus Trade-offs. A value declared beyond price ends the weighing out loud but not in practice. As a supporting tool, the Crux Finder shows whether a disagreement is about facts or about a value one side will not weigh, in both directions: it asks those who invoke the sacred what is quietly being traded off, and it asks those who dismiss sacredness whether "nothing would change my mind" might be a real and defensible answer.

Related tools

• C1: The Falsifier Question asks what would change your mind, written down in advance; the Crux Finder asks the same question of both sides at once and compares the answers.
• C2: The Steelman Protocol builds the strongest version of the other side's view, which is often where its real crux becomes visible.
• B3: The Trade-off Surfacing asks what is being given up, and for what; it is the Crux Finder's partner when the crux turns out to be a value weighting rather than a fact.
• A4: The Mirror Check asks whether you held a claim to the same standard as its opposite, which is the direct guard against the Crux Finder's weaponized form.

Where the site uses it

In use: the site's article on the 2026 backlash against AI data centers uses this tool: Do Data Centers Raise Your Electric Bill?