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The requirement that B is crucial for A is equivalent to "If A then B", not "if B then A".
For example:
A = self-driving cars would be safer
B = the chances that a bug would cause all self-driving cars to crash spectacularly on the same day are small.
If A is true, then B must be true, because if B is false, A is clearly false. But B does not imply A: even if B is true (there could be zero chance of such a bug), A could still be false (self-driving cars might be bad at avoiding crashes due to, say, object recognition being too slow to react in time). So B being crucial for A means that A implies B.
There's confusion here between logical implication and reason for belief.
Duncan, I believe, was expressing belief causality -- not logical implication -- when he wrote "If B, then A." This was confusing because "if, then" is the traditional language for logical implication.
With logical implication, it might make sense to translate "A because B" as "B implies A". However, with belief causality, "I believe A because I believe B" is very different from "B implies A".
For example:
A: Uniforms are good.
B: Uniforms reduce bullying.
C: Uniforms cause death.
Let's assume that you believe A because you believe B, and also that you would absolutely not believe A if it turned out that C were true. (That is,... (read more)