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Can you take the contrapositive of a causal statement? For example, if it said that A caused B, and we don't have B, is it logically corrected to say then we don't have A? Or does causation not work like that?
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Not sure what you mean by causal but I think this will help you (from JW's vid):
Sufficient satisfied: rule triggers, necessary must be satisfied
Sufficient failed: rule irrelevant, necessary is free to satisfy or fail
Necessary failed: rule triggers, sufficient must fail
necessary satisfied: rule irrelevant, sufficient could be true or false
Second what iolaw-12 says. Real world example: Smoking causes cancer, but not in everybody. Just because someone does not have cancer, that does not imply that they are not a smoker.
If A ALWAYS causes B then yes you can take the contrapositive: if you don't have B you also don't have A. But if A simply CAN cause B but doesn't always, then there is no contrapositive to be taken.