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CCC comments on Double Crux — A Strategy for Resolving Disagreement - Less Wrong

61 Post author: Duncan_Sabien 29 November 2016 09:23PM

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Comment author: CCC 01 December 2016 02:36:39PM *  4 points [-]

"Aluminium is better than steel!" cries Alice.

"Steel is better than aluminium!" counters Bob. Both of them continue to stubbornly hold these opinions, even in the face of vehement denials from the other.

It is not at once clear how to resolve this issue. However, both Alice and Bob have recently read the above article, and attempt to apply it to their disagreement.

"Aluminium is better than steel because aluminium does not rust," says Alice. "The statement 'aluminium does not rust, but steel does' is an equivalent argument to 'aluminium is better than steel'".

"Steel is better than aluminium because steel is stronger than aluminium," counters Bob. "Steel can hold more weight than aluminium without bending, which makes it a superior metal."

"So the crux of our argument," concludes Alice, "is really that we are disagreeing on what it is that makes a metal better; I am placing more importance on rustproofing, while you are showing a preference for strength?"

Comment author: Lumifer 01 December 2016 03:22:04PM 4 points [-]

For this example you don't need any double cruxes. Alice and Bob should have just defined their terms, specifically the word "better" to which they attach different meanings.

Comment author: Duncan_Sabien 01 December 2016 06:47:27PM 4 points [-]

True, but they then could easily have gone on to do a meaningful double crux about why their chosen quality is the most important one to attend to.

Comment author: CCC 02 December 2016 07:55:22AM 2 points [-]

That is true. In a disagreement where the root of the disagreement is applying different meanings to the word 'better', properly defining that term would identify the true disagreement straight away. The double crux method, by seeking equivalent statements for each position, brings that disagreement in terminology to light almost immediately (where a word-by-word process of definitions might well get mired down in the definition of 'steel' and whether or not it includes small amounts of chromium - which might be interesting and informative on its own, but does nothing to resolve the disagreement).

This appears to suggest that double crux, applied properly, will work in every case where the true disagreement is a matter is inconsistent definition of terms (as above). I'd go further, and say that the double crux method will also work in cases where the disagreement is due to one of the debaters having made an error in a mathematical equation that he believes supports his argument. So, when you don't know the root cause of the argument, double crux is probably at least as fast a route to finding that cause as a careful definition of all terms, and probably faster.

Comment author: MrMind 01 December 2016 04:07:54PM *  0 points [-]

Let me rephrase: does the double crux method contains any improvement that is not already covered by tabooing terms? Or simply saying "why do you think this is the case?"

"Steel is better than aluminum because aluminum is worse than steel" is also equivalent, adheres to the letter of the prescription but does not move the discussion forward.

What I'm trying to prove wrong is that the logical prescriptions, given as explanation of what a crux is, do not really capture anything substantial.

Comment author: CCC 02 December 2016 08:00:03AM 0 points [-]

Let me rephrase: does the double crux method contains any improvement that is not already covered by tabooing terms? Or simply saying "why do you think this is the case?"

In this particular argument, no. (In fact, if both participants are willing to examine their own chain of reasoning and consider that they might be wrong, then asking "why do you think this is the case?" sounds like a perfect first step in the double crux method to me)

In cases where the disagreement is due to (say) Bob making a mathematical error, tabooing terms is unlikely to reveal the error, while double crux seems likely to do so. So, as a general disagreement-solving technique, it seems powerful as it can be applied to a wide variety of causes of disagreement, even without knowing what the cause of the disagreement actually is.

Comment author: Duncan_Sabien 01 December 2016 06:44:01PM *  0 points [-]

If I'm understanding correctly, I think you've made a mistake in your formal logic above—you equated "If B, then A" with "If A, then B" which is not at all the same.

The search for a double crux encourages each side to adopt the causal model of the other (or, in other words, to search through the other's causal models until they find one they can agree is true). I believe "If B, then A," which is meaningfully different from your belief "If ¬B then ¬A." If each of us comes around to saying, "Yeah, I buy your similar-but-different causal model, too," then we've converged in an often-significant way, and have almost always CLARIFIED the underlying belief structure.

Comment author: CCC 02 December 2016 07:56:32AM 0 points [-]

If I'm understanding correctly, I think you've made a mistake in your formal logic above—you equated "If B, then A" with "If A, then B" which is not at all the same.

No, he only inferred "If A, then B" from "If not B, then not A" which is a valid inference.

Comment author: Duncan_Sabien 02 December 2016 10:06:50PM *  0 points [-]

1) if B then A

2) if not B, then not A. Which implies if A then B.

... but then he went on to say "How can an equivalent argument have explanatory power?" which seemed, to me, to assume that "if B then A" and "if A then B" are equivalent (which they are not).

Comment author: CCC 05 December 2016 08:48:55AM 0 points [-]

I read that statement as implying that argument A is equivalent to argument B. (Not (1) and (2), which are statements about arguments A and B)

And, if A implies B and B implies A, then it seems to me that A and B have to be equivalent to each other.