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

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

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Comment author: Unnamed 05 December 2016 09:41:07PM 2 points [-]

(This is Dan from CFAR)

This is easier to think about in the context of specific examples, rather than as abstract logical propositions. You can generally tell when statement B is progress towards making the disagreement about A more concrete / more tractable / closer to the underlying source of disagreement.

I typically think of the arrows as causal implication between beliefs. For example, my belief that school uniforms reduce bullying causes me to believe that students should wear uniforms. With logical implication the contrapositive is equivalent to the original statement (as you say). With causal implication, trying to do the contrapositive would give us something like "If I believed that students should not wear uniforms, that would cause me to believe that uniforms don't reduce bullying" which is not the sort of move that I want to make in my reasoning.

Another way to look at this, while sticking to logical implication, is that we don't actually have B-->A. Instead we have (B & Q & R & S & T ... & Z) --> A. For example, I believe that students should wear uniforms because uniforms reduce bullying, and uniforms are not too expensive, and uniforms do not reduce learning, and uniforms do not cause Ebola, etc. If you take the contrapositive, you get ~A --> (~B or ~Q or ~R or ~S or ~T ... or ~Z). Or, in English, I have many cruxes for my belief that students should wear uniforms, and changing my mind about that belief could involve changing my mind about any one of those cruxes.