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.
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.
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.
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.
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.